**ICD Electrograms in Patients with Brugada Syndrome**

**ICD Electrograms in Patients with Brugada Syndrome**

DOI: 10.5772/intechopen.70145

Cismaru Gabriel, Serban Schiau, Gabriel Gusetu, Lucian Muresan, Mihai Puiu, Radu Rosu, Dana Pop and Dumitru Zdrenghea Gusetu, Lucian Muresan, Mihai Puiu, Radu Rosu, Dana Pop and Dumitru Zdrenghea Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Cismaru Gabriel, Serban Schiau, Gabriel

http://dx.doi.org/10.5772/intechopen.70145

#### **Abstract**

In patients with Brugada syndrome, implantable cardioverter‐defibrillator (ICD) is the only demonstrated treatment that prevents sudden cardiac death. The progress in ICD technology improved the diagnosis and efficacy of implantable devices in the management and treatment of ventricular tachycardia (VT) and ventricular fibrillation (VF). Recording of electrical events just before and after a delivered or aborted ICD therapy permits a more accurate characterization of the rhythm but also provides information on the electrical events preceding the arrhythmia. This chapter aims to gain insight into the mechanism of initiation and termination of spontaneous VF by analyzing intracardiac electrograms (IEGM) in Brugada patients implanted with ICDs. It has two parts: **(1) update on ICD electrograms in Brugada syndrome patients**, where we review the medical literature on ICD electrograms and their use for detecting electrical manifestations of Brugada syndrome, and **(2) examples of ICD electrograms,** from our own database of patients affected by Brugada syndrome.

**Keywords:** Brugada syndrome, ICD, defibrillation, ventricular fibrillation, premature ventricular contractions, electrophysiological study

#### **1. Introduction**

Brugada syndrome is a clinical syndrome associated with ventricular tachycardia (VT) and ventricular fibrillation (VF), in patients who have no structural heart disease. ECG is the most useful tool for the diagnosis and shows right bundle branch block with ST elevation in right precordial leads. Due to the high recurrence rate of ventricular fibrillation, an implantable cardioverter‐defibrillator (ICD) is the accepted mode of treatment and it improves the long‐ term prognosis.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Clinical studies suggest that spontaneous episodes of VF are induced by PVCs originating at the level of right ventricular outflow tract (RVOT). Abnormal electrophysiological features are present in this zone, with fragmented, low amplitude, late potentials. Programed ventricular stimulation at the level of RVOT increases the chance of VF induction compared to RV apex.

The progress in ICD technology improved the diagnosis and treatment efficacy of implantable devices in the management of VT and VF in Brugada syndrome. Recording of electrical events before and after a delivered or aborted ICD therapy permits not only a more accurate characterization of the rhythm but also provides information on the electrical events preceding the arrhythmia.

## **2. Mode of onset of ventricular fibrillation in Brugada syndrome**

In Brugada syndrome, VF episodes can be preceded by PVCs or start suddenly without a preceding premature ventricular contractions (PVC). This classification assumes distinct electrophysiological mechanism for the two types of VF. Although very few PVCs are observed on Holter monitoring, in Brugada syndrome PVCs tend to occur more frequently before the initiation of VF, as well as ST segment elevation in precordial leads [1]. The mechanism that explains the association of the two phenomena is the marked shortening of the action potential in the RVOT which gives the ST elevation, and phase 2 reentry responsible for PVC firing from the same area with short action potential, which initiates VF [2, 3]. Kofune et al. were able to identify the substrate of the Brugada syndrome by high‐resolution electroanatomical mapping. In patients with Brugada syndrome, they found that only the right ventricle is affected, the left being spared, and only a small area within the RVOT is responsible for the syndrome. At this level, they found low‐voltage potential with fractionated electrograms. The conduction abnormality from the RVOT gives the final phenotypic expression of right precordial ST segment elevation [4]. Previous studies of Antzelevitch et al. demonstrated that at cellular level the action potential dome propagates from the normal epicardial sites to the epicardial site without dome leading to phase 2 reentry. As the reentry fails to propagate to the endocardium, it leads to closely coupled ventricular premature beats [5]. Specific triggers can lead to heterogeneous repolarization: fever or after exercise when the body temperature rises, and specific medication like: ajmaline, flecainide, and propafenone.

In the study of Kakishita et al., frequent PVCs before the onset of VF were recorded in 67% of the patients. The morphology of preceding PVC electrogram (far‐field and near‐field) was identical to the PVC that initiated VF. Additionally, different VF episodes seen in the same patient were initiated by the same PVC morphology. The rest of 33% of patients had episodes of VF without preceding PVCs.

A long‐short sequence is very unlikely to initiate VF in Brugada syndrome and pause‐dependent VF is very rare [6].

## **3. Coupling interval of the VF initiating PVC**

Clinical studies suggest that spontaneous episodes of VF are induced by PVCs originating at the level of right ventricular outflow tract (RVOT). Abnormal electrophysiological features are present in this zone, with fragmented, low amplitude, late potentials. Programed ventricular stimulation at the level of RVOT increases the chance of VF induction compared to

The progress in ICD technology improved the diagnosis and treatment efficacy of implantable devices in the management of VT and VF in Brugada syndrome. Recording of electrical events before and after a delivered or aborted ICD therapy permits not only a more accurate characterization of the rhythm but also provides information on the electrical events preced-

In Brugada syndrome, VF episodes can be preceded by PVCs or start suddenly without a preceding premature ventricular contractions (PVC). This classification assumes distinct electrophysiological mechanism for the two types of VF. Although very few PVCs are observed on Holter monitoring, in Brugada syndrome PVCs tend to occur more frequently before the initiation of VF, as well as ST segment elevation in precordial leads [1]. The mechanism that explains the association of the two phenomena is the marked shortening of the action potential in the RVOT which gives the ST elevation, and phase 2 reentry responsible for PVC firing from the same area with short action potential, which initiates VF [2, 3]. Kofune et al. were able to identify the substrate of the Brugada syndrome by high‐resolution electroanatomical mapping. In patients with Brugada syndrome, they found that only the right ventricle is affected, the left being spared, and only a small area within the RVOT is responsible for the syndrome. At this level, they found low‐voltage potential with fractionated electrograms. The conduction abnormality from the RVOT gives the final phenotypic expression of right precordial ST segment elevation [4]. Previous studies of Antzelevitch et al. demonstrated that at cellular level the action potential dome propagates from the normal epicardial sites to the epicardial site without dome leading to phase 2 reentry. As the reentry fails to propagate to the endocardium, it leads to closely coupled ventricular premature beats [5]. Specific triggers can lead to heterogeneous repolarization: fever or after exercise when the body temperature rises, and specific medication like: ajmaline, flecainide, and

In the study of Kakishita et al., frequent PVCs before the onset of VF were recorded in 67% of the patients. The morphology of preceding PVC electrogram (far‐field and near‐field) was identical to the PVC that initiated VF. Additionally, different VF episodes seen in the same patient were initiated by the same PVC morphology. The rest of 33% of patients had episodes

A long‐short sequence is very unlikely to initiate VF in Brugada syndrome and pause‐depen-

**2. Mode of onset of ventricular fibrillation in Brugada syndrome**

RV apex.

ing the arrhythmia.

108 Interpreting Cardiac Electrograms - From Skin to Endocardium

propafenone.

of VF without preceding PVCs.

dent VF is very rare [6].

It is well known that PVCs occurring near the peak of the T‐wave (ventricular vulnerable period) may lead to ventricular fibrillation. However, in Brugada syndrome, the onset of PVCs inducing VF are close to the end of the T‐wave. Kakishita et al. found a coupling interval of 388 ms for the PVC initiating VF in patients with Brugada syndrome. Kasanuki et al found a value of > 300 ms coupling interval for the PVC inducing VF. Spontaneous VF is provoked by a single, long >300 ms coupled PVC. Induced VF can be provoked by multiple extrastimuli with shorter coupling interval < 200 ms for VF induced during electrophysiological study [7].

## **4. Ventricular fibrillation interval (VF interval)**

For long time, physicians thought that the amplitude of VF waves ("fine" or "coarse") is suggestive of defibrillation success, but Murakawa et al. demonstrated on dogs [8] that shorter ventricular fibrillation intervals are associated with higher energies for internal defibrillation. VF interval is a parameter that can be measured using the ICD electrograms. Kerber et al. [9] reported that slower polymorphic VT with cycle length >200 ms needs less energy for defibrillation than VF with cycle length of less than 200 ms. Cismaru et al. studied VF cycle length in patients with Brugada syndrome, induced VF during electrophysiology study, and showed that a longer cycle length that progressively increases is a sign of self‐terminating VF [10] (**Figures 1** and **2**).

**Figure 1.** Patient with Brugada syndrome and polymorphic VT induction during electrophysiology study. VT stops spontaneously without any defibrillation.

**Figure 2.** Patient with Brugada syndrome and ventricular fibrillation induction during electrophysiology study. Please note the short VF interval. VF stops after external defibrillation.

Hiratsuka et al. demonstrated that symptomatic patients with Brugada syndrome have significant shorter VF cycle length than asymptomatic patients. The difference is probably given by a different electrophysiological substrate between the two groups [11].

## **5. Unsuccessful internal defibrillation in Brugada syndrome**

Patients with Brugada syndrome have higher rates of unsuccessful internal defibrillation after the implantation of ICD. The study of Watanabe et al. [12] examined the incidence of VF not responding to internal defibrillation and found an incidence of 18%. One explanation could be the origin of the electrical abnormality at the level of RVOT [13] with defibrillation shock delivered between the right ventricular apex and left subclavicular can. Alternative explanation is the short effective refractory period and short ventricular fibrillation interval (FVI) in patients with Brugada syndrome.

## **6. Intracardiac electrograms (IEGM) compared to morphological changes of an ECG during provocative tests**

Probst et al. [14] compared the surface ECG with the intracardiac electrograms (IEGM) from internal defibrillator during an ajmaline test in patients with Brugada syndrome. The ECG morphology changed after ajmaline injection with ST elevation and negative T‐waves. The IEGM showed different morphological changes: ST deviation changes with negative T‐wave changes. The changes are in contrast with morphological changes from patients without Brugada syndrome where IEGM correlates to ST segment deviation on ECG. In countries where ajmaline is not available, procainamide can be used for the provocative test.

In the case report of Moore and Kaye, a change of the intracardiac electrogram after an internal defibrillation was compatible with a type 1 Brugada pattern and disappeared 1 min after the electrical shock [15, 16].

## **7. T‐wave alternans in patients with Brugada syndrome**

Hiratsuka et al. demonstrated that symptomatic patients with Brugada syndrome have significant shorter VF cycle length than asymptomatic patients. The difference is probably given

**Figure 2.** Patient with Brugada syndrome and ventricular fibrillation induction during electrophysiology study. Please

Patients with Brugada syndrome have higher rates of unsuccessful internal defibrillation after the implantation of ICD. The study of Watanabe et al. [12] examined the incidence of VF not responding to internal defibrillation and found an incidence of 18%. One explanation could be the origin of the electrical abnormality at the level of RVOT [13] with defibrillation shock delivered between the right ventricular apex and left subclavicular can. Alternative explanation is the short effective refractory period and short ventricular fibrillation interval (FVI) in

Probst et al. [14] compared the surface ECG with the intracardiac electrograms (IEGM) from internal defibrillator during an ajmaline test in patients with Brugada syndrome. The ECG morphology changed after ajmaline injection with ST elevation and negative T‐waves. The IEGM showed different morphological changes: ST deviation changes with negative T‐wave

by a different electrophysiological substrate between the two groups [11].

note the short VF interval. VF stops after external defibrillation.

110 Interpreting Cardiac Electrograms - From Skin to Endocardium

**5. Unsuccessful internal defibrillation in Brugada syndrome**

**6. Intracardiac electrograms (IEGM) compared to morphological** 

**changes of an ECG during provocative tests**

patients with Brugada syndrome.

T‐wave alternans is the ECG manifestation of action potential repolarization alternans. Beat‐to‐ beat alternation of ventricular action potential in both duration and amplitude reflects the risk of ventricular tachycardia and ventricular fibrillation [16]. T wave alternance (TWA) from ICD electrograms are concordant with TWA from the surface ECG because they measure the same alternans phenomenon [17] (**Figure 3**).

Tada et al. described a patient with Brugada syndrome that presented TWA after administration of a sodium channel blocker (cibenzoline) [18]. Ohkubo et al. also described TWA in a patient with Brugada syndrome after class 1 antiarrhythmic drug (pilsicainide). TWA persisted for 15 min and was followed by microvolt TWA [19].

Tada and colleagues [20] investigated the association between ventricular tachycardia and fibrillation with TWA induced by intravenous pilsicainide (sodium channel blocker). Pilsicainide provoked visible TWA in 17 of 77 Brugada patients. Those with TWA experienced a significantly higher incidence of spontaneous VF (52.9 vs. 8.3%) than those without TWA.

**Figure 3.** Method for determination of TWA: the amplitude for each T‐wave is calculated as the maximum minus the minimum value (horizontal red lines). The difference between the amplitude of the first beat and second beat of each pair is calculated using the formula: TWA = [(*Ta−Tb)<sup>1</sup> +(Ta−Tb)<sup>2</sup> +…(Ta−Tb*)x ]/*x*.

## **8. Use of stored ICD electrograms for catheter ablation of ventricular fibrillation in Brugada syndrome**

Stored electrograms can be used for catheter ablation of ventricular fibrillation. Both far‐field EGM and near‐field EGM are used [21]. First, the EGM that initiates ventricular fibrillation should be captured. This is used as a template for subsequent pacemapping (**Figure 4**). Information regarding the morphology and timing of the EGM are used to search for the best correlation during pacemap. Both spontaneous QRS complex morphology and far‐field ICD morphology are used for comparison with the paced morphology. Timing between far‐field and near‐field ICD electrograms is also used for the template when comparing with the paced beat.

Pacemapping is attempted at the level of RVOT with real‐time recording from the ICD electrogram. Both morphology and timing are used to delineate the zone with the best match and that zone will be a target for ablation. The study of Almendral et al. [22] showed spatial resolution of 2 cm2 for best match with electrogram morphology and timing. The same resolution was confirmed by Lowery et al. in patients with different types of ventricular fibrillation [21].

Substrate epicardial mapping is initiated in sinus rhythm to identify dense scar <0.5 V and border zone between 0.5–1.5 V. Abnormal electrograms consist in low amplitude–wide duration of >80 ms, with multiple or delayed components outside the end of the surface ECG QRS. The same RVOT zone is remapped after IV flecainide to determine increase in abnormal electrogram area after infusion. Catheter ablation targets the complete elimination of the substrate inside the low‐voltage areas [23].

**Figure 4.** Example of pacemapping of a trigger arising from the RVOT in a patient with Brugada syndrome. Panel A corresponds to the recorded spontaneous PVC inducing VF (A). Panels B and C show near‐ and far‐field electrograms with a bad correlation between the spontaneous RVOT (B) and paced electrogram (C).

## **9. Examples of ICD electrograms**

**8. Use of stored ICD electrograms for catheter ablation of ventricular** 

Stored electrograms can be used for catheter ablation of ventricular fibrillation. Both far‐field EGM and near‐field EGM are used [21]. First, the EGM that initiates ventricular fibrillation should be captured. This is used as a template for subsequent pacemapping (**Figure 4**). Information regarding the morphology and timing of the EGM are used to search for the best correlation during pacemap. Both spontaneous QRS complex morphology and far‐field ICD morphology are used for comparison with the paced morphology. Timing between far‐field and near‐field ICD electrograms is also used for the template when comparing with the paced beat. Pacemapping is attempted at the level of RVOT with real‐time recording from the ICD electrogram. Both morphology and timing are used to delineate the zone with the best match and that zone will be a target for ablation. The study of Almendral et al. [22] showed spatial reso-

was confirmed by Lowery et al. in patients with different types of ventricular fibrillation [21]. Substrate epicardial mapping is initiated in sinus rhythm to identify dense scar <0.5 V and border zone between 0.5–1.5 V. Abnormal electrograms consist in low amplitude–wide duration of >80 ms, with multiple or delayed components outside the end of the surface ECG QRS. The same RVOT zone is remapped after IV flecainide to determine increase in abnormal electrogram area after infusion. Catheter ablation targets the complete elimination of the sub-

**Figure 4.** Example of pacemapping of a trigger arising from the RVOT in a patient with Brugada syndrome. Panel A corresponds to the recorded spontaneous PVC inducing VF (A). Panels B and C show near‐ and far‐field electrograms

with a bad correlation between the spontaneous RVOT (B) and paced electrogram (C).

for best match with electrogram morphology and timing. The same resolution

**fibrillation in Brugada syndrome**

112 Interpreting Cardiac Electrograms - From Skin to Endocardium

strate inside the low‐voltage areas [23].

lution of 2 cm2

We present electrograms from our cardiology department in patients with Brugada syndrome:


**Figure 5.** The same coupling interval 330 ms and the same PVC morphology at the initiation of nonsustained VT in a patient with Brugada syndrome. (A) without PVCs; (B) PVC inducing NSVT; (C) same PVC inducing NSVT; (D) same PVC inducing NSVT.

**Figure 6.** The same coupling interval 322 ms and same morphology at the initiation of nonsustained VT in a patient with Brugada syndrome. (A) PVCs with ventricular trigeminism; (B) same PVC inducing NSVT; (C) same PVC inducing (D) self‐terminating VF.

**Figure 7.** Self‐terminating ventricular tachycardia. Please note the long cycle length. Upper electrogram is the far‐field ventricular IEGM; in the middle of the strip atrial IEGM; at bottom near‐field ventricular IEGM.

**Figure 8.** Self‐terminating (or nonsustained) ventricular tachycardia. Please note the long cycle length.

**Figure 9.** Ventricular fibrillation terminated with an external shock. Please note the short VF interval.

## **10. Conclusion**

Analysis of intracardiac electrograms during episodes of ventricular arrhythmias is effective for clarifying the mechanism of the episode. Many spontaneous episodes of VF are preceded by frequent PVCs. The coupling interval usually is long and reaches the end of the T‐wave. Ventricular fibrillation interval is short and may be responsible for failure of internal defibrillation. Longer VF interval values predict spontaneous termination of VF. A catheter ablation technique was described for catheter ablation of PVCs initiating VF in Brugada syndrome and uses the stored IEGMs as template for pacemapping.

## **Author details**

Cismaru Gabriel\*, Serban Schiau, Gabriel Gusetu, Lucian Muresan, Mihai Puiu, Radu Rosu, Dana Pop and Dumitru Zdrenghea

\*Address all correspondence to: gabi\_cismaru@yahoo.com

Cardiology‐Rehabilitation, Internal Medicine Department, Iuliu Hatieganu University of Medicine and Pharmacy, Cluj‐Napoca, Romania

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**Figure 8.** Self‐terminating (or nonsustained) ventricular tachycardia. Please note the long cycle length.

**Figure 7.** Self‐terminating ventricular tachycardia. Please note the long cycle length. Upper electrogram is the far‐field

ventricular IEGM; in the middle of the strip atrial IEGM; at bottom near‐field ventricular IEGM.

114 Interpreting Cardiac Electrograms - From Skin to Endocardium

**Figure 9.** Ventricular fibrillation terminated with an external shock. Please note the short VF interval.


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**Provisional chapter**

## **A Review of ICD Anti-Tachycardia Therapy Programming with Generic Programming for Primary and Secondary Prevention Programming with Generic Programming for Primary and Secondary Prevention**

**A Review of ICD Anti-Tachycardia Therapy** 

DOI: 10.5772/intechopen.69999

Fariha Sadiq Ali and Usama Boles Fariha Sadiq Ali and Usama Boles Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69999

#### **Abstract**

Intracardiac defibrillator plays a pivotal role in preventing sudden cardiac death; however, inappropriate shock delivery remains an important source of morbidity and mortality. Advancements in device technology along with various shock reduction strategies play a key role in reducing inappropriate and unnecessary shocks. Anti-tachycardia pacing (ATP) is the first-line therapy prior to shock delivery. Several trials have validated the efficacy of ATP for both slow and fast ventricular tachycardia without significant increase in occurrence of arrhythmia-related syncope. In addition, trials also support that therapy for non-sustained tachycardia can be prevented by higher programmed zones and prolonged intervals to detect without higher risk of syncope. With this perspective, authors employ a customized programming for both primary and secondary prevention to reduce inappropriate therapies or unnecessary therapies, in particular, progression to shock but allow for spontaneous termination at slower ventricular tachycardia rates. The programming was instituted at the time of device implantation or at follow up.

**Keywords:** intracardiac defibrillator, anti-tachycardia pacing, inappropriate therapies, shock, customized programming, ICD programming, ICD therapies, reducing ICD therapies, ICD templates

## **1. Introduction**

Implantable cardioverter-defibrillator (ICD) remains the main therapeutic option in reducing sudden cardiac death (SCD). Several randomized trials and registries have shown that ICD extends survival in patients with severe left ventricular function and mild-to-moderate heart failure [1–4]. The shocks delivered whether appropriate, inappropriate or unnecessary

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

remain an important source of mortality and morbidity from proarrhythmic potential, heart failure, painful delivery of shock causing significant anxiety, depression and post-traumatic stress disorder [5–11].

Inappropriate ICD shocks are those delivered for a condition other than true ventricular arrhythmias, which most commonly include supraventricular arrhythmias with rapid rates, mechanical failure of ICD lead/system like lead conductor fracture resulting in noise detection and non-mechanical issues such as T-wave over sensing resulting in double-counting [3]. Unnecessary or potentially avoidable shocks are those where the ventricular tachycardia (VT) was to terminate spontaneously or could have been interrupted by appropriately timed pacing stimuli.

**Table 1** lists the major clinical trials and registries reporting the incidence of inappropriate shocks. We review some of the trials here.

The anti-arrhythmics versus implantable defibrillators (AVID) was a multi-centre trial which patients were randomized to receive ICD or anti-arrhythmic drug therapy; 492 patients were randomized to receive an ICD over a follow-up period of 22 ± 12 months. Inappropriate shocks in this cohort were due to supraventricular tachycardia in 18% and 3% were due to ICD malfunction or inappropriate sensing [12].

The Pain FREE Rx II trial was a prospective randomized control trial consisting of 634 patients with a mean follow up of 11 ± 3 months. All patients received ICDs and were randomized to anti-tachycardia pacing versus shock only programming [13]. There were 4230 spontaneous episodes retrieved from all implanted ICDs, 1837 had complete electrogram data and were included in the analysis. Of these, 491 episodes (27%) were determined to be inappropriately detected supraventricular tachycardia (SVT), and 4 (0.2%) were non-physiological artifact. Sweeny et al. performed a subgroup analysis of the PainFree trial and showed that the proportion of true ventricular detections that resulted in shocks was similar between primary and secondary prevention groups (40% versus 32%, respectively) [14]. The proportion of inappropriate ventricular detections due to SVT that resulted in shocks was also similar between primary and secondary prevention groups (44% versus 42%, respectively).

MIRACLE ICD was a prospective, randomized double-blind trial of 978 patients with a mean 10-month follow-up [15]. This trial evaluated the safety and efficacy of cardiac resynchronization combined defibrillator therapy (CRT-D) versus ICD only therapy in both primary and secondary prevention patients. The reported incidence of inappropriate shocks was 30% in primary prevention patients and 14% in secondary prevention patients.

In the Multicenter Automatic Defibrillator Implantation Trial II (MADIT-II), inappropriate shocks constituted 31.2% (184/590) of the total shock episodes [16]. The most common triggers were atrial fibrillation (44%) and supraventricular tachycardia (36%) with improper discrimination by the ICD device, followed by abnormal sensing (20%). The majority of inappropriate ICD therapy episodes were delivered for rhythms below or equal to 200 bpm; the mean ventricular rate triggering inappropriate shock for atrial fibrillation (AF) or SVT was 174 ± 22 bpm. Patients with inappropriate ICD shocks showed a significantly higher mortality during the follow-up (HR = 2.29, 95% CI: 1.11–4.71, *p* = 0.02) than patients with


remain an important source of mortality and morbidity from proarrhythmic potential, heart failure, painful delivery of shock causing significant anxiety, depression and post-traumatic

Inappropriate ICD shocks are those delivered for a condition other than true ventricular arrhythmias, which most commonly include supraventricular arrhythmias with rapid rates, mechanical failure of ICD lead/system like lead conductor fracture resulting in noise detection and non-mechanical issues such as T-wave over sensing resulting in double-counting [3]. Unnecessary or potentially avoidable shocks are those where the ventricular tachycardia (VT) was to terminate spontaneously or could have been interrupted by appropriately timed

**Table 1** lists the major clinical trials and registries reporting the incidence of inappropriate

The anti-arrhythmics versus implantable defibrillators (AVID) was a multi-centre trial which patients were randomized to receive ICD or anti-arrhythmic drug therapy; 492 patients were randomized to receive an ICD over a follow-up period of 22 ± 12 months. Inappropriate shocks in this cohort were due to supraventricular tachycardia in 18% and 3% were due to

The Pain FREE Rx II trial was a prospective randomized control trial consisting of 634 patients with a mean follow up of 11 ± 3 months. All patients received ICDs and were randomized to anti-tachycardia pacing versus shock only programming [13]. There were 4230 spontaneous episodes retrieved from all implanted ICDs, 1837 had complete electrogram data and were included in the analysis. Of these, 491 episodes (27%) were determined to be inappropriately detected supraventricular tachycardia (SVT), and 4 (0.2%) were non-physiological artifact. Sweeny et al. performed a subgroup analysis of the PainFree trial and showed that the proportion of true ventricular detections that resulted in shocks was similar between primary and secondary prevention groups (40% versus 32%, respectively) [14]. The proportion of inappropriate ventricular detections due to SVT that resulted in shocks was also similar

between primary and secondary prevention groups (44% versus 42%, respectively).

primary prevention patients and 14% in secondary prevention patients.

MIRACLE ICD was a prospective, randomized double-blind trial of 978 patients with a mean 10-month follow-up [15]. This trial evaluated the safety and efficacy of cardiac resynchronization combined defibrillator therapy (CRT-D) versus ICD only therapy in both primary and secondary prevention patients. The reported incidence of inappropriate shocks was 30% in

In the Multicenter Automatic Defibrillator Implantation Trial II (MADIT-II), inappropriate shocks constituted 31.2% (184/590) of the total shock episodes [16]. The most common triggers were atrial fibrillation (44%) and supraventricular tachycardia (36%) with improper discrimination by the ICD device, followed by abnormal sensing (20%). The majority of inappropriate ICD therapy episodes were delivered for rhythms below or equal to 200 bpm; the mean ventricular rate triggering inappropriate shock for atrial fibrillation (AF) or SVT was 174 ± 22 bpm. Patients with inappropriate ICD shocks showed a significantly higher mortality during the follow-up (HR = 2.29, 95% CI: 1.11–4.71, *p* = 0.02) than patients with

stress disorder [5–11].

pacing stimuli.

shocks. We review some of the trials here.

120 Interpreting Cardiac Electrograms - From Skin to Endocardium

ICD malfunction or inappropriate sensing [12].


appropriate ICD shocks (HR = 3.36, 95% CI: 2.04–5.55, *p* < 0.01). This demonstrated that all shocks, although demonstrated to save lives, also have a detrimental effect and lead to heart failure deterioration and eventual mortality.

Similar data could be extrapolated from the sudden cardiac death in heart failure trial (SCD-HeFT) [17]. In this trial, 2521 patients with primary prevention indication and with mild-tomoderate heart failure were randomized in equal proportions to receive placebo, amiodarone or a single-chamber ICD programmed to shock-only mode. Follow-up was for an average of 46 months. In 811 patients assigned to the ICD arm, the rate of inappropriate shocks was 17% as compared to 22.4% appropriate shocks during a 46-month follow-up. Patients with an inappropriate ICD therapy had a twofold increase in the risk of all-cause mortality (HR = 1.98, 95% CI: 1.29–3.05, *p* = 0.002).

The results from the randomized trials were confirmed in larger registries. The ALTura Impact on the Treatment of Abdominal Aortic Aneurysms Using a Novel D-stent EVAR Design (ALTITUDE) registry involved 39,396 ICD patients and 29,904 patients implanted CRTDs. Patients were implanted for both primary and secondary indications [18]. The 1-year incidence of inappropriate shocks was 8% and 6% and at 5 years increased to 16% and 17% for ICD and CRT-D patients, respectively. The two most common reasons for shock were atrial flutter/atrial fibrillation and sinus tachycardia or supraventricular arrhythmia. Inappropriate shock was due to noise, artifact or over sensing in 3% of the episodes.

The Leiden group published a large scale study in 1544 ICD patients and reported an 18% incidence of inappropriate ICD therapy over 41 months of follow-up. This study also confirmed the increased risk of death for both inappropriate and appropriate ICD therapy (HR1.60 for both, *p* = 0.01 for inappropriate; *p* < 0.01 for appropriate ICD therapy) [19].

## **2. Possible mechanism of increased risk of death with ICD shocks**

It may be hypothesized that there is a direct mechanical or hemodynamic effect of the inappropriate ICD therapies themselves or that some of the inappropriate ICD therapies lead to fatal pro-arrhythmia due to an increase in sympathetic discharge, which in turn leads to raterelated changes in ventricular refractoriness and worsened myocardial ischemia [20].

It is likely that it is not the inappropriate shock *per se* that is detrimental, but the sequelae that hastens the adverse clinical outcome.

It has been suggested that high shock fields are associated with changes in electrophysiological properties of the heart and can be the primary source of activation wave fronts that may give rise to idioventricular rhythms after the shock and perhaps may even perpetuate ventricular fibrillation [21]. The cellular injury from intra-cardiac shock delivery whether it be appropriate or not is reflected in a rise in cardiac troponin I [22]. Though the result may be a rescue from acute ventricular arrhythmia, studies have shown a relationship with increased mortality and morbidity from progression to heart failure as a consequence of the myocardial stunning [5–11].

Minimizing the need for shock delivery overall will, therefore, ultimately prevent the downstream complications.

## **3. Shock reducing strategies**

appropriate ICD shocks (HR = 3.36, 95% CI: 2.04–5.55, *p* < 0.01). This demonstrated that all shocks, although demonstrated to save lives, also have a detrimental effect and lead to heart

Similar data could be extrapolated from the sudden cardiac death in heart failure trial (SCD-HeFT) [17]. In this trial, 2521 patients with primary prevention indication and with mild-tomoderate heart failure were randomized in equal proportions to receive placebo, amiodarone or a single-chamber ICD programmed to shock-only mode. Follow-up was for an average of 46 months. In 811 patients assigned to the ICD arm, the rate of inappropriate shocks was 17% as compared to 22.4% appropriate shocks during a 46-month follow-up. Patients with an inappropriate ICD therapy had a twofold increase in the risk of all-cause mortality (HR = 1.98,

The results from the randomized trials were confirmed in larger registries. The ALTura Impact on the Treatment of Abdominal Aortic Aneurysms Using a Novel D-stent EVAR Design (ALTITUDE) registry involved 39,396 ICD patients and 29,904 patients implanted CRTDs. Patients were implanted for both primary and secondary indications [18]. The 1-year incidence of inappropriate shocks was 8% and 6% and at 5 years increased to 16% and 17% for ICD and CRT-D patients, respectively. The two most common reasons for shock were atrial flutter/atrial fibrillation and sinus tachycardia or supraventricular arrhythmia. Inappropriate

The Leiden group published a large scale study in 1544 ICD patients and reported an 18% incidence of inappropriate ICD therapy over 41 months of follow-up. This study also confirmed the increased risk of death for both inappropriate and appropriate ICD therapy (HR1.60 for

It may be hypothesized that there is a direct mechanical or hemodynamic effect of the inappropriate ICD therapies themselves or that some of the inappropriate ICD therapies lead to fatal pro-arrhythmia due to an increase in sympathetic discharge, which in turn leads to rate-

It is likely that it is not the inappropriate shock *per se* that is detrimental, but the sequelae that

It has been suggested that high shock fields are associated with changes in electrophysiological properties of the heart and can be the primary source of activation wave fronts that may give rise to idioventricular rhythms after the shock and perhaps may even perpetuate ventricular fibrillation [21]. The cellular injury from intra-cardiac shock delivery whether it be appropriate or not is reflected in a rise in cardiac troponin I [22]. Though the result may be a rescue from acute ventricular arrhythmia, studies have shown a relationship with increased mortality and morbidity from progression to heart failure as a consequence of the myocardial

shock was due to noise, artifact or over sensing in 3% of the episodes.

both, *p* = 0.01 for inappropriate; *p* < 0.01 for appropriate ICD therapy) [19].

**2. Possible mechanism of increased risk of death with ICD shocks**

related changes in ventricular refractoriness and worsened myocardial ischemia [20].

failure deterioration and eventual mortality.

122 Interpreting Cardiac Electrograms - From Skin to Endocardium

95% CI: 1.29–3.05, *p* = 0.002).

hastens the adverse clinical outcome.

stunning [5–11].

There have been several technological advancements to improve ICD therapy delivery and to avoid inappropriate and unnecessary ICD therapies. The shock reduction programming strategies may be divided into the following categories:


## **4. Clinical evidence and the rationale to support ATP therapy**

Monomorphic VT can be interrupted when an appropriately timed pacing stimulus is delivered into the excitable gap of a re-entrant circuit where a collision with the orthodromic wave front results in termination of the tachycardia.

An alternative explanation is that the paced stimuli result in myocardial depolarization during the relative refractory period. This pre-excites the preceding wave front, thereby altering myocardial excitability and extinguishing the propagation re-entrant VT [23].

The duration of the excitable gap and the conduction time from the pacing stimulus site to the re-entrant circuit are the main factors influencing penetration of the excitable gap and termination of the arrhythmia [24].

Ventricular conduction time is influenced by anatomic and functional barriers as well as the influence of the sympathetic nervous system [25]. The efficacy of the ATP is improved with adequate beta blockade and is not adversely influenced by other anti-arrhythmic drugs as is the case with defibrillation thresholds [26].

## **5. Customized programming**

Several trials have validated the efficacy of ATP in terminating slower cycle length of VT.

The Pain FREE Rx II trial was the first trial that extended the use of ATP for fast VT (FVT) with heart rates of 188–250 beats/min. This study also used longer intervals to detect VT as compared to the previous conventional programming (**Figure 1**) [13, 27]. The result was that 73% of FVT episodes were successfully terminated by the ATP.

It also showed that FVT made up 76% of all ventricular arrhythmias that would have conventionally been treated by shock alone according to conventional ICD programming.

Acceleration of FVT occurred in patients programmed to receive ATP as well as those in the shock only group: 4/273 monomorphic VT episodes (2%) in the ATP arm versus 2/145 (1%) in the shock arm. There were also three episodes of syncope during treatment for FVT (ATP, *n* = 2; shock, *n* = 1). This study, therefore, established the safety and efficacy of ATP for both slow and FVT as first-line therapy in ICDs with a non-significant occurrence or difference in arrhythmia-related syncope in either therapy arm.

The next stage in the evolution of device therapy programming was to defer treatment (VT detection) till absolutely necessary. In this regard, the Primary Prevention Parameters Evaluation (PREPARE) trial (**Figure 2**) [28] evaluated a prolonged detection interval duration of 30/40 ventricular beats and an increased tachycardia detection interval (TDI) of 182 beats/ min. Supraventricular detection discrimination algorithms and ATP were also optimized in this programming strategy. Arrhythmic syncope was only 1.6% in the test programming strategy. All-cause mortality in the PREPARE study group was also relatively low (Kaplan-Meier estimated 12-month mortality of 4.9%). Thus, the overall safety behind the rationale of this programming was acceptable.

**Figure 1.** Programming strategy of experimental and control arm in Pain FREE Rx II trial.

A Review of ICD Anti-Tachycardia Therapy Programming with Generic Programming... http://dx.doi.org/10.5772/intechopen.69999 125

compared to the previous conventional programming (**Figure 1**) [13, 27]. The result was that

It also showed that FVT made up 76% of all ventricular arrhythmias that would have conven-

Acceleration of FVT occurred in patients programmed to receive ATP as well as those in the shock only group: 4/273 monomorphic VT episodes (2%) in the ATP arm versus 2/145 (1%) in the shock arm. There were also three episodes of syncope during treatment for FVT (ATP, *n* = 2; shock, *n* = 1). This study, therefore, established the safety and efficacy of ATP for both slow and FVT as first-line therapy in ICDs with a non-significant occurrence or difference in

The next stage in the evolution of device therapy programming was to defer treatment (VT detection) till absolutely necessary. In this regard, the Primary Prevention Parameters Evaluation (PREPARE) trial (**Figure 2**) [28] evaluated a prolonged detection interval duration of 30/40 ventricular beats and an increased tachycardia detection interval (TDI) of 182 beats/ min. Supraventricular detection discrimination algorithms and ATP were also optimized in this programming strategy. Arrhythmic syncope was only 1.6% in the test programming strategy. All-cause mortality in the PREPARE study group was also relatively low (Kaplan-Meier estimated 12-month mortality of 4.9%). Thus, the overall safety behind the rationale of

tionally been treated by shock alone according to conventional ICD programming.

73% of FVT episodes were successfully terminated by the ATP.

**Figure 1.** Programming strategy of experimental and control arm in Pain FREE Rx II trial.

arrhythmia-related syncope in either therapy arm.

124 Interpreting Cardiac Electrograms - From Skin to Endocardium

this programming was acceptable.

**Figure 2.** Programming strategy of experimental arm in PREPARE trial with controls from EMPIRIC and MIRACLE ICD patients.

The multicenter automatic defibrillator implantation trial–reduce inappropriate therapy (MADIT-RIT) trial compared three arms: (a) conventional ICD detection of VT with a (b) prolonged detection interval and (c) a higher tachycardia detection interval (**Figure 3**) [29].

The results validated the safety of both the active test arms. There was a 79% reduction in the incidence of therapy in the high-rate group than in the conventional therapy group and delayed therapy (longer detection interval programming) was associated with a 76% reduction in overall therapy delivery. Mortality was reduced by 55% in the high-rate group (*p* = 0.01) and by 44% in the delayed-therapy group (*p* = 0.06). Despite withholding therapies till absolutely needed, there was a mortality improvement in these active programming options.

The incidence of syncope was similar between the groups and was not clinically significant: high rate strategy and delayed therapy versus conventional arm (*p* = 0.39, *p* = 0.80).

Both delayed therapy and higher rate programming were shown to be safe and efficacious.

**Figure 3.** Programming strategy of MADIT-RIT patients.

The ADVANCE III (Avoid Delivering Therapies for Nonsustained Arrhythmias in ICD Patients III) [30] reinforced the findings from the MADIT-RIT trial and included both primary and secondary prevention patients, with or without atrial fibrillation, in whom single-, dualand triple-chamber ICD were implanted [30]. Thus, this randomized control trial applied an extended detection interval strategy to a heterogeneous cohort of ICD recipients and more likely to resemble a real world setting (**Figure 4**).

This delayed arrhythmia detection strategy resulted in a reduction in the combined end point of all ICD therapies (ATPs and shocks) with 346 delivered therapies (42 therapies per 100 person-years) in test group (extended-detection interval) versus 557 in the control group (standard-detection interval) (67 therapies per 100 person-years); *p* < 0.001.

The incidence of arrhythmic syncope was low in both groups and did not differ significantly with rates of 3.1 versus 1.9 per 100 patient-years (*p* = 0.220 in the extended detection and standard detection groups, respectively). The syncopal episodes were not associated with any additional adverse outcomes. The mortality rates were 5.5 versus 6.3 per 100 patient-years (*p* = 0.50) in extended detection and standard detection, respectively. Both were low and comparable to what was reported in the MADIT-RIT trial.

Similarly the PROVIDE (Programming Implantable Cardioverter Defibrillators in Patients with Primary Prevention Indication to Prolong Time to First Shock) trial was a programming strategy with combination of higher detection rates, prolonged detection intervals, optimized SVT discriminators and empiric ATP therapy compared to conventional parameters in patients receiving ICDs for primary prevention (**Figure 5**) [31]. The primary end point was time to first shock delivery. The median time to first shock was significantly longer at 13.1 months in experimental group versus 7.8 months in the control group. In addition, the 2-year shock rate was 12.4% in the experimental group compared to 19.4% in the control group. An overall reduction in both appropriate and inappropriate shock and ATP was observed. The decrease in ICD therapies was associated with a 30% relative reduction in all-cause mortality.

The incidence of arrhythmic syncope was not significantly different between the two groups with overall incidence of 1.7% over 2 years of follow-up.

With this perspective, we can summarize the overall current trends in ICD programming:

**1.** Higher zone thresholds

The ADVANCE III (Avoid Delivering Therapies for Nonsustained Arrhythmias in ICD Patients III) [30] reinforced the findings from the MADIT-RIT trial and included both primary and secondary prevention patients, with or without atrial fibrillation, in whom single-, dualand triple-chamber ICD were implanted [30]. Thus, this randomized control trial applied an extended detection interval strategy to a heterogeneous cohort of ICD recipients and more

This delayed arrhythmia detection strategy resulted in a reduction in the combined end point of all ICD therapies (ATPs and shocks) with 346 delivered therapies (42 therapies per 100 person-years) in test group (extended-detection interval) versus 557 in the control group

The incidence of arrhythmic syncope was low in both groups and did not differ significantly with rates of 3.1 versus 1.9 per 100 patient-years (*p* = 0.220 in the extended detection and standard detection groups, respectively). The syncopal episodes were not associated with any additional adverse outcomes. The mortality rates were 5.5 versus 6.3 per 100 patient-years (*p* = 0.50) in extended detection and standard detection, respectively. Both were low and com-

Similarly the PROVIDE (Programming Implantable Cardioverter Defibrillators in Patients with Primary Prevention Indication to Prolong Time to First Shock) trial was a programming strategy with combination of higher detection rates, prolonged detection intervals, optimized SVT discriminators and empiric ATP therapy compared to conventional parameters in patients receiving ICDs for primary prevention (**Figure 5**) [31]. The primary end point was time to first shock delivery. The median time to first shock was significantly longer at 13.1 months in experimental group versus 7.8 months in the control group. In addition, the 2-year shock rate was 12.4% in the experimental group compared to 19.4% in the control group. An overall reduction in both appropriate and inappropriate shock and ATP was observed. The decrease in ICD therapies was associated with a 30% relative reduction in all-cause mortality. The incidence of arrhythmic syncope was not significantly different between the two groups

(standard-detection interval) (67 therapies per 100 person-years); *p* < 0.001.

likely to resemble a real world setting (**Figure 4**).

**Figure 3.** Programming strategy of MADIT-RIT patients.

126 Interpreting Cardiac Electrograms - From Skin to Endocardium

parable to what was reported in the MADIT-RIT trial.

with overall incidence of 1.7% over 2 years of follow-up.


The aim of these strategies is to reduce inappropriate therapies (ITS) particularly progression to shock and not to over treat ventricular arrhythmias but to allow for spontaneous termination at ventricular rates that are safe to do so.

**Figure 4.** Programming strategy in ADVANCE III trial.

**Figure 5.** Programming strategy of experimental arm in PROVIDE trial with control population from the PROVE trial.

There has been no data to suggest that implanting dual chamber ICDs is more advantageous in ventricular arrhythmia over single chamber devices in any of the studies we have mentioned. However, there are some practical reasons where one may choose to implant an atrial lead as well to enhance discrimination algorithms [32].


• In patients with hypertrophic cardiomyopathy as they are prone to atrial arrhythmias but may also require pacing.

With this in mind, we employ the following customized ICD programming (**Tables 2** and **3**) for both primary and secondary prevention of SCD in our patients.


Time out: OFF (Boston Scientific); ATP smart mode: OFF (Medtronic); progressive therapy: ON (Medtronic >2 active zone); ATP optimization: ON (Biotronik); upper rate ATP cut off 260 beats/min (St. Jude); readaptive: ON (St. Jude); Ramp OFF unless specified.

NID: Numbers of interval to detect.

There has been no data to suggest that implanting dual chamber ICDs is more advantageous in ventricular arrhythmia over single chamber devices in any of the studies we have mentioned. However, there are some practical reasons where one may choose to implant an atrial lead as

**Figure 5.** Programming strategy of experimental arm in PROVIDE trial with control population from the PROVE trial.

• In patients who require pacing for bradycardia, AV sequential pacing would be preferable. • In patients with bradycardia-induced or pause-dependent ventricular tachyarrhythmia

• In patients with documented history of paroxysmal atrial arrhythmias (atrial EGMS will

(such as patients with long QT syndrome and torsades de pointes).

help distinguish the chamber of onset of the tachycardia).

well to enhance discrimination algorithms [32].

128 Interpreting Cardiac Electrograms - From Skin to Endocardium

**Table 2.** Suggested customized ICD programming strategy proposed by the authors for primary prevention.


Time out: OFF (Boston Scientific); ATP smart mode: OFF (Medtronic); progressive therapy: ON (Medtronic >2 active zone); ATP optimization: ON (Biotronik); upper rate ATP cut off 260 beats/min (St. Jude); readaptive: ON (St. Jude); Ramp OFF unless specified.

**Table 3.** Suggested customized ICD programming strategy proposed by the authors for secondary prevention.

The programming is instituted at the time of device implantation and refined (if needed) at follow-up in the device clinic.

The programming covers all manufacturers' ICDs that we commonly implant. The custom sets are preloaded onto our programmers, thus minimizing the need for tedious reprogramming and only need to be refined if the case warrants this.

In doing so, the work flow both in the implant suite and at the follow-up device visit is facilitated and the programming can be delegated to our allied professional nurses and cardiac technicians.

## **6. Conclusion**

With the complexity and sophistication of ICD algorithms, the programming of these cardiac devices has become a discipline and challenge in its own right. We have found that it has been difficult to maintain predictability and consistency in the programming of ICDs in our centre, hence a need arose to develop a programming template. This was derived from current trends in programming and is mentioned here in an extensive review of the literature. There is an obvious limitation in which each of the studies has been manufacturer specific. We have tried to identify the principles on which the programming was based and then developed a generic template. This was however still done with due consultation with the manufacturers to ensure applicability and safety with the specific algorithms. There have also been very few studies that deal with programming of secondary prevention of ICDs. We have strived to maintain a compromise between all manufacturers to reach a consensus on programming for primary prevention of ICDs.

## **Author details**

Fariha Sadiq Ali<sup>1</sup> \* and Usama Boles2


## **References**

The programming is instituted at the time of device implantation and refined (if needed) at

**Table 3.** Suggested customized ICD programming strategy proposed by the authors for secondary prevention.

Time out: OFF (Boston Scientific); ATP smart mode: OFF (Medtronic); progressive therapy: ON (Medtronic >2 active zone); ATP optimization: ON (Biotronik); upper rate ATP cut off 260 beats/min (St. Jude); readaptive: ON (St. Jude);

**Medtronic St. Jude medical Biotronik Boston Scientific Sorin**

NID 30 30 12/16 2.5 s initial

ATP during charge

NID 30 30 28 (RD-14) 10 s initial

NID 28 30 30 (RD-16) 30 s initial

ATP: Burst 1 + Burst 2

200 250 250 220 200–240

Shock × 6 Shock × 6 Shock × 6 Shock × 6 Shock × 6

Shock × 5 Shocks × 4 Shocks × 5 Shocks × 5 Shocks × 5

ATP: Burst 1 + Burst 2

Shocks ×4 Shocks ×3 Shocks ×4 Shocks ×4 Shocks ×4

150/VT-30 150/VT-30

Medtronic St. Jude Biotronik Boston Sorin

250 200 200 200 200

Therapy ATP: Burst 1 ATP: Burst 1 ATP: 1 Burst ATP: Burst 1 ATP: Burst 1

VT1 rate in bpm 171/VT-20 171/VT-20 171/VT-20 170/VT-20 170/VT-20

NID 32 12 cycles Therapy None None

Burst 1 8/88/3 8/88/3 8/85/3 8/88/3 8/85/3 Burst 2 8/84/3 8/84/3 8/85/3 8/84/3 8/85/3 Ramp 8/91 8/91 8/90 8/91 8/90

duration

duration

duration

ATP: Burst 1 + Burst 2

ATP: 1 Burst ATP: Burst 1

6 cycles

6 cycles

12 cycles

ATP: Burst 1 + Burst 2

The programming covers all manufacturers' ICDs that we commonly implant. The custom sets are preloaded onto our programmers, thus minimizing the need for tedious reprogram-

follow-up in the device clinic.

Ramp OFF unless specified.

VF (VF + FVT) rate in bpm

VT2 (FVT via VF) rate in bpm

Monitor rate in

ATP programming

bpm

Therapy ATP during

Therapy ATP: Burst 1 +

Burst 2

charge

130 Interpreting Cardiac Electrograms - From Skin to Endocardium

ming and only need to be refined if the case warrants this.


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[13] Wathen MS, DeGroot PJ, Sweeney MO, Stark AJ, Otterness MF, Adkisson WO, et al. Pain FREE Rx II Investigators. Prospective randomized multicenter trial of empirical anti tachycardia pacing versus shocks for spontaneous rapid ventricular tachycardia in patients with implantable cardioverter-defibrillators: Pacing fast ventricular tachycardia reduces shock therapies (Pain FREE Rx II) trial results. Circulation. 2004;**110**(17):2591-2596

[14] Sweeney MO, Wathen MS, Volosin K, Abdalla I, DeGroot PJ, Otterness MF, Stark AJ. Appropriate and inappropriate ventricular therapies, quality of life, and mortality among primary and secondary prevention implantable cardioverter defibrillator patients: Results from the pacing fast VT reduces shock therapies (Pain FREE Rx II) trial.

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**Provisional chapter**

## **Complexity of Atrial Fibrillation Electrograms Through Nonlinear Signal Analysis: In Silico Approach Nonlinear Signal Analysis: In Silico Approach**

**Complexity of Atrial Fibrillation Electrograms Through** 

DOI: 10.5772/intechopen.69475

Catalina Tobón, Andrés Orozco‐Duque, Juan P. Ugarte, Miguel Becerra and Javier Saiz Ugarte, Miguel Becerra and Javier Saiz Additional information is available at the end of the chapter

Catalina Tobón, Andrés Orozco-Duque, Juan P.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69475

#### **Abstract**

Identification of atrial fibrillation (AF) mechanisms could improve the rate of ablation success. However, the incomplete understanding of those mechanisms makes difficult the decision of targeting sites for ablation. This work is focused on the importance of EGM analysis for detecting and modulating rotors to guide ablation procedures and improve its outcomes. Virtual atrial models are used to show how nonlinear measures can be used to generate electroanatomical maps to detect critical sites in AF. A description of the atrial cell mathematical models, and the procedure of coupling them within two‐dimensional and three‐dimensional virtual atrial models in order to simulate arrhythmogenic mecha‐ nisms, is given. Mathematical modeling of unipolar and bipolar electrogramas (EGM) is introduced. It follows a discussion of EGM signal processing. Nonlinear descriptors, such as approximate entropy and multifractal analysis, are used to study the dynamical behavior of EGM signals, which are not well described by a linear law. Our results evince that nonlinear analysis of EGM can provide information about the dynamics of rotors and other mechanisms of AF. Furthermore, these fibrillatory patterns can be simulated using virtual models. The combination of features using machine learning tools can be used for identifying arrhythmogenic sources of AF.

**Keywords:** atrial fibrillation, arrhythmogenic sources, electrogram model, computer simulation, nonlinear features, electroanatomical mapping

## **1. Introduction**

The most common sustained cardiac arrhythmias in humans are associated with the atria. Atrial arrhythmias, mainly atrial fibrillation (AF), frequently provoke incapacitating symp‐ toms and severe complications such as stroke and heart failure [1]. Overall, 20–25% of all

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

strokes are caused by AF [2]. The presence of AF is related to a significant increase in morbid‐ ity and mortality [3]. Electrocardiogram‐based surveys suggest that 1% of the total population is affected by AF [4].

There are a large number of clinical conditions that are associated with an increased incidence of AF. This contributes to a progressive process of atrial remodeling characterized by a set of changes in atrial properties that contributes in sustaining of the arrhythmia. These changes include alterations in the electrical cellular activity, calcium handling and in the atrial struc‐ ture such as cellular hypertrophy and fibrosis. They have been described in some animal models [5–8] and in humans [9–11]. These alterations may favor the occurrence of triggers that initiate the AF and the formation of a substrate that promotes its perpetuation. Changes in electrical activity cause a significant shortening of the action potential duration (APD) and a decrease in refractoriness [8–10], which may support the initiation and maintenance of mul‐ tiple re‐entrant waves, as suggested by experimental studies [5, 9].

It is well known that AF can be caused by different mechanisms, including single‐circuit re‐ entry, multiple‐circuit re‐entry, rapid local ectopic activity and rotors [12–15]. It is very impor‐ tant to know the mechanisms underlying AF, since these have implications in the treatment of the disease. An important percentage of patients suffers of paroxysmal AF, which is initiated by focal triggers that are localized at preferential sites, mainly in the pulmonary veins (PV) [13]. Electrical isolation of pulmonary veins can prevent recurrence of AF in 70–80% of these lone AF patients. The rationale for this is the crucial observation, reported in [13], that AF was mostly triggered by ectopic beats arising from the muscle sleeves of the pulmonary veins. They demonstrated that atrial rapid paces or ectopic activity originated in the proximities or in the interior of the pulmonary veins could act like triggers, and, in some cases, they would be responsible for the maintenance of paroxysmal AF episodes [16, 17]. A unifying theory suggests that rapid focal activity is responsible for generating atrial, which is necessary to maintain a substrate for the generation of multiple re‐entrant waves [18, 19]. While parox‐ ysmal AF is maintained predominantly by ectopic focal activity or local re‐entrant circuits located in one or more pulmonary veins, as the arrhythmia evolves into more persistent forms promoted by atrial remodeling, the mechanisms that maintain AF move toward the atria and are increasingly based on re‐entry substrates [11, 20–22]. Based on clinical [23–25] and experi‐ mental [14, 26] results, certain types of AF can be attributed to a stable high‐frequency rotor or a small number of rotor waves in left atrium, which maintain the arrhythmia, whose periodic activation can be converted into a chaotic pattern when the wavefronts propagate across the atrial wall. This phenomenon, known as the *mother rotor hypothesis*, is the most recently pro‐ posed mechanism of AF [27], which suggests that AF is triggered by a series of ectopic beats, whose wave fronts give rise to a rotor. The rotor is a stable re‐entry around a functionally unexcitable core [15] that works as a maintenance mechanism with some spatial temporal stability, activating the local tissue at high frequency, generating wave fronts that fragment and propagate as multiple daughter wavelets. Stable rotors are at diverse locations, mostly in the left atrium, including sites outside the pulmonary veins, as well as the posterior, inferior, and roof regions. Several studies have observed rotors in in vitro and animal models [14, 28, 29], and its presence in humans has been reported [27, 30, 31].

All localized sources of AF as re‐entry circuits, ectopic foci, or rotors, cause fibrillatory conduc‐ tion remote from the source, which is difficult to distinguish from propagation that maintains the AF by multiple wavelets, and any of these phenomena may generate rotors registered by intracardiac recordings [32, 24]. Studies carried out by [33, 34] have shown evidence that human AF can be sustained by localized rotors; however, the existence of stable rotors maintaining AF remains a focus of discussion. Hence, the importance of the implementation of virtual models and computational tools in the studies of AF sources and its relation with the signals recorded from surface. In the same way, the rotors have been shown in computer models of AF [35–38].

strokes are caused by AF [2]. The presence of AF is related to a significant increase in morbid‐ ity and mortality [3]. Electrocardiogram‐based surveys suggest that 1% of the total population

There are a large number of clinical conditions that are associated with an increased incidence of AF. This contributes to a progressive process of atrial remodeling characterized by a set of changes in atrial properties that contributes in sustaining of the arrhythmia. These changes include alterations in the electrical cellular activity, calcium handling and in the atrial struc‐ ture such as cellular hypertrophy and fibrosis. They have been described in some animal models [5–8] and in humans [9–11]. These alterations may favor the occurrence of triggers that initiate the AF and the formation of a substrate that promotes its perpetuation. Changes in electrical activity cause a significant shortening of the action potential duration (APD) and a decrease in refractoriness [8–10], which may support the initiation and maintenance of mul‐

It is well known that AF can be caused by different mechanisms, including single‐circuit re‐ entry, multiple‐circuit re‐entry, rapid local ectopic activity and rotors [12–15]. It is very impor‐ tant to know the mechanisms underlying AF, since these have implications in the treatment of the disease. An important percentage of patients suffers of paroxysmal AF, which is initiated by focal triggers that are localized at preferential sites, mainly in the pulmonary veins (PV) [13]. Electrical isolation of pulmonary veins can prevent recurrence of AF in 70–80% of these lone AF patients. The rationale for this is the crucial observation, reported in [13], that AF was mostly triggered by ectopic beats arising from the muscle sleeves of the pulmonary veins. They demonstrated that atrial rapid paces or ectopic activity originated in the proximities or in the interior of the pulmonary veins could act like triggers, and, in some cases, they would be responsible for the maintenance of paroxysmal AF episodes [16, 17]. A unifying theory suggests that rapid focal activity is responsible for generating atrial, which is necessary to maintain a substrate for the generation of multiple re‐entrant waves [18, 19]. While parox‐ ysmal AF is maintained predominantly by ectopic focal activity or local re‐entrant circuits located in one or more pulmonary veins, as the arrhythmia evolves into more persistent forms promoted by atrial remodeling, the mechanisms that maintain AF move toward the atria and are increasingly based on re‐entry substrates [11, 20–22]. Based on clinical [23–25] and experi‐ mental [14, 26] results, certain types of AF can be attributed to a stable high‐frequency rotor or a small number of rotor waves in left atrium, which maintain the arrhythmia, whose periodic activation can be converted into a chaotic pattern when the wavefronts propagate across the atrial wall. This phenomenon, known as the *mother rotor hypothesis*, is the most recently pro‐ posed mechanism of AF [27], which suggests that AF is triggered by a series of ectopic beats, whose wave fronts give rise to a rotor. The rotor is a stable re‐entry around a functionally unexcitable core [15] that works as a maintenance mechanism with some spatial temporal stability, activating the local tissue at high frequency, generating wave fronts that fragment and propagate as multiple daughter wavelets. Stable rotors are at diverse locations, mostly in the left atrium, including sites outside the pulmonary veins, as well as the posterior, inferior, and roof regions. Several studies have observed rotors in in vitro and animal models [14, 28,

tiple re‐entrant waves, as suggested by experimental studies [5, 9].

29], and its presence in humans has been reported [27, 30, 31].

is affected by AF [4].

138 Interpreting Cardiac Electrograms - From Skin to Endocardium

Ablation has emerged as an important treatment strategy for AF [39]. Pulmonary veins iso‐ lation reaches single procedure success rates of 60–80% for paroxysmal AF treatment [40]. However, for the chronic case, this strategy does not achieve satisfactory outcomes [41]; con‐ sequently, complex ablation lines are added to the procedure [45]. Catheter ablation guided by electroanatomic mapping has revolutionized the treatment of permanent AF. Identification of AF mechanisms could improve the rate of ablation success. However, the incomplete under‐ standing of those mechanisms makes difficult the decision of targeting sites for ablation. To overcome this limitation, two‐dimensional and realistic three‐dimensional human atria com‐ puter models have been developed to investigate the relationship between the characteristics of EGM and the propagation pattern associated with them [42–45].

It is thought that the different mechanisms lead to changes in the characteristics of spatiotem‐ poral organization of AF [44, 45]. EGM‐guided ablation procedures have been proposed as an alternative strategy, which involves mapping and ablating focal sources or complex fraction‐ ated atrial electrograms (CFAE) [46]. Recent studies have shown that a large number of sites representing AF substrates are characterized by a high degree of disorganization in EGM signals [29], and therefore, signal processing methods are being designed in order to quantify their degree of fractionation [47, 48]. The relationship between the rotor tip and CFAE has been published in recent studies [36, 45, 47, 49, 50]; however, automatic rotor mapping meth‐ ods have not been fully developed.

Different mapping techniques are being used to identify target sites for ablation, and some of them are activation waves, voltage, dominant frequency [23, 51–55] and CFAE maps [39, 46, 56]. Nevertheless, there are several limitations with these techniques, and one of the most important is that they depend considerably on the electrophysiologist expertise [57].

The term CFAE was introduced by Nademanee [46] as a pathophysiological concept; however, its definition is unclear and broad and includes inherent subjectivity [58]. CFAE are formally defined as follows: (1) atrial EGM that have fractionated electrograms composed of two deflec‐ tions or more, and/or perturbation of the baseline with continuous deflection of a prolonged activation complex over a 10 s recording period; (2) atrial EGM with a very short cycle length (<120 ms) over a 10 s recording period. CFAE definition does not distinguish between different morphologies; consequently, fractionated EGM according with CFAE definition are not neces‐ sarily related to arrhythmogenic substrates. Moreover, several studies have shown conflicting results with Nademanee [56, 59]. This may lead the electrophysiologist to confuse the fractionated EGM that are functional in nature [60] with fractionated EGM corresponding to arrhythmogenic sources, leading to incorrect target sites for ablation. This also makes clinical results difficult to compare. Inconsistent results have been found in different studies using the CFAE concept. Although the concept of CFAE has made a great contribution to the study of AF, it may fail to describe the wide range of fractionation that occurs in the EGM signals in specific cases. Thus, the electrogram‐guided approach by mapping and targeting areas of CFAE is a technique that is still debated [61], and further studies are needed to strengthen the treatment techniques.

To date, indexes computation from EGM is carried out mostly based on the detection of local activation waves and time intervals. However, the concept of EGM fractionation, such as CFAE, defined using time criteria, is not enough to describe the complexity of EGM during AF. Morphological irregularity and temporal variability of the signal must be included. To overcome the limitations of CFAE definition, designation of different degree of fractionation has been proposed based on the perturbation of baseline and the presence of continuous deflection [36]. Some studies have presented evidence linking the vortex of the rotor with a high degree of fractionation in the EGM [36, 47]. However, the patterns of EGM signals associated with the rotors are still unknown, and the development of tools for characteriz‐ ing fractionated EGM signals is still a current topic. In addition, there is not a standard for description of fractionation degrees, and there are different descriptions in the literature. In order to quantify the behavior of different morphologies of EGM signals and the fraction‐ ation degrees, recent studies have helped to understand the concept of EGM fractionation as a nonlinear phenomenon [47, 48, 62]. Mathematical descriptors of the nonlinear dynamical behavior have been used to study cardiac signals and are based on the description of the state of the system and its evolution. If a linear law does not describe the evolution of the system, the dynamics is nonlinear. Thus, indexes and features calculated using nonlinear dynamics theory become an alternative for enhancing assessment of EGM complexity.

#### **2. Simulated atrial fibrillation dynamics**

The mathematical modeling of atrial electrophysiology has become a useful method for study‐ ing the underlying mechanisms responsible for AF. Different models of human atrial elec‐ trophysiology have been published with various formulations of ionic currents and calcium handling, therefore, with different electrophysiological properties [63–67]. In our studies, the transmembrane potential was based on the Courtemanche‐Ramirez‐Nattel and Kneller [63, 68] model of human atrial cell kinetics in the presence of 0.005 μM of acetylcholine (ACh). Based on the experimental data [9, 10, 69], the cell model was modified in order to reproduce electrophysiological conditions of permanent AF: the maximum conductance of delayed rec‐ tifier potassium current (*I* Kur) and transient potassium current (*I*to) was decreased by 50%, the maximum conductance of potassium time independent current (*I* K1) was increased by 100%, and the maximum conductance of L‐type calcium current (*I* CaL) was decreased by 70% (see **Table 1**). Thus, the action potential duration at 90% of the repolarization (APD90) was reduced by 70% (**Figure 1A**), which is in accordance with experimental studies developed by Workman et al. [9] and Bosch et al. [10] in isolated myocytes from patients with permanent AF, using the whole cell patch clamp technique.

The development of multi‐dimensional models has allowed representing fibers, pieces of tissue and atrial cavities. These models have served to approach, among other aspects, the biophysics of the action potential propagation under physiological and pathological conditions.

sources, leading to incorrect target sites for ablation. This also makes clinical results difficult to compare. Inconsistent results have been found in different studies using the CFAE concept. Although the concept of CFAE has made a great contribution to the study of AF, it may fail to describe the wide range of fractionation that occurs in the EGM signals in specific cases. Thus, the electrogram‐guided approach by mapping and targeting areas of CFAE is a technique that is still

To date, indexes computation from EGM is carried out mostly based on the detection of local activation waves and time intervals. However, the concept of EGM fractionation, such as CFAE, defined using time criteria, is not enough to describe the complexity of EGM during AF. Morphological irregularity and temporal variability of the signal must be included. To overcome the limitations of CFAE definition, designation of different degree of fractionation has been proposed based on the perturbation of baseline and the presence of continuous deflection [36]. Some studies have presented evidence linking the vortex of the rotor with a high degree of fractionation in the EGM [36, 47]. However, the patterns of EGM signals associated with the rotors are still unknown, and the development of tools for characteriz‐ ing fractionated EGM signals is still a current topic. In addition, there is not a standard for description of fractionation degrees, and there are different descriptions in the literature. In order to quantify the behavior of different morphologies of EGM signals and the fraction‐ ation degrees, recent studies have helped to understand the concept of EGM fractionation as a nonlinear phenomenon [47, 48, 62]. Mathematical descriptors of the nonlinear dynamical behavior have been used to study cardiac signals and are based on the description of the state of the system and its evolution. If a linear law does not describe the evolution of the system, the dynamics is nonlinear. Thus, indexes and features calculated using nonlinear dynamics

debated [61], and further studies are needed to strengthen the treatment techniques.

theory become an alternative for enhancing assessment of EGM complexity.

the maximum conductance of potassium time independent current (*I*

100%, and the maximum conductance of L‐type calcium current (*I*

The mathematical modeling of atrial electrophysiology has become a useful method for study‐ ing the underlying mechanisms responsible for AF. Different models of human atrial elec‐ trophysiology have been published with various formulations of ionic currents and calcium handling, therefore, with different electrophysiological properties [63–67]. In our studies, the transmembrane potential was based on the Courtemanche‐Ramirez‐Nattel and Kneller [63, 68] model of human atrial cell kinetics in the presence of 0.005 μM of acetylcholine (ACh). Based on the experimental data [9, 10, 69], the cell model was modified in order to reproduce electrophysiological conditions of permanent AF: the maximum conductance of delayed rec‐

(see **Table 1**). Thus, the action potential duration at 90% of the repolarization (APD90) was reduced by 70% (**Figure 1A**), which is in accordance with experimental studies developed by Workman et al. [9] and Bosch et al. [10] in isolated myocytes from patients with permanent

Kur) and transient potassium current (*I*to) was decreased by 50%,

K1) was increased by

CaL) was decreased by 70%

**2. Simulated atrial fibrillation dynamics**

140 Interpreting Cardiac Electrograms - From Skin to Endocardium

AF, using the whole cell patch clamp technique.

tifier potassium current (*I*

Different studies have developed and implemented two‐dimensional (2D) models of atrial tis‐ sue to study the action potential propagation dynamics under physiological and pathological conditions [36, 37, 68, 70].

We have developed a two‐dimensional model of human atrial tissue. The tissue surface was discretized into a 150 × 150 hexahedral mesh (22,500 elements and 45,602 nodes). Spatial reso‐ lution was 0.4 mm. The electrical propagation of the atrial action potential was modeled using the monodomain reaction–diffusion equation:

$$\frac{1}{S\_v} \nabla \cdot \left( D \nabla V\_m \right) \quad = \ C\_m \frac{\partial V\_m}{\partial t} + I\_{low} - I\_{stm} \tag{1}$$

where *S*<sup>v</sup> corresponds to the surface‐to‐volume ratio, *D* is the conductivity tensor, *C*m is the specific membrane capacitance (50 pF), *I* ion is the total ionic current that crosses the membrane cells, *V*m is the membrane potential, and *I* stim is the stimulus current. The electrophysiological model was integrated into the two‐dimensional virtual model. The equation was solved using the EMOS software, which is a parallel code that implements the finite element method and operator splitting [42, 71] for solving the monodomain model of electrical propagation and allows to calculate EGM as postprocess. The time step was fixed to 0.001 ms.

The tissue was considered isotropic. A conductivity of 0.3 S/cm was assigned to obtain a real‐ istic conduction velocity of 60 cm/s.

Rotor was generated by S1–S2 cross‐field stimulation protocol. Stimuli pulses were rectan‐ gular with 2 ms of duration and 6 mA of amplitude. The S1 was a train of five plane stimuli applied at the left boundary of the model at a basic cycle length of 1000 ms. The S2 stimulus was rectangular (3 × 2 cm) and was applied 40 ms after the last S1 in the inferior left corner of the model (**Figure 1B**).

A 4s stable clockwise spiral wave (rotor) was observed in the two‐dimensional model after applying the protocol (**Figure 1C**). The APD shortening due to the atrial remodeling allowed the rotor stability over time. Wijffels et al. [8] in goats demonstrated that maintenance of AF by pacing in the normal goat heart resulted in the development of sustained AF within 1–3 weeks. This observation of tachycardia‐induced electrical remodeling creating a back‐ ground for persistent AF led to the concept that "Atrial Fibrillation Begets Atrial Fibrillation." The longer duration and stability of the AF episodes was explained by a shortening of the wavelength of the atrial impulse. The simulated rotor pattern agrees with the "rotor hypothesis" proposed by Jalife [15]. The contour map was implemented to show the core of the rotor (circular point in **Figure 1D**).

Virtual models of cardiac structures are needed in the study of atrial arrhythmias that are critically dependent on the spatial organization of cardiac structures and fibers. Some atrial


**Table 1.** Conductance (*g*) changes of currents for permanent AF.

**Figure 1.** (A) Action potential under physiological and permanent AF conditions. (B) S1–S2 cross‐field protocol. The plane S1 and rectangular S2 stimulus are shown. (C) Stable rotor under permanent AF conditions. (D) Contour map, the circular point indicates the rotor tip location.

arrhythmias, such as AF, need complete structures to perpetuate them. The validity and enor‐ mous potential of multi‐scale heart models in improving diagnosis, prevention and therapy of cardiac pathologies are supported by different scientific results. These virtual models have opened new horizons in the study of the complex mechanisms underlying atrial arrhythmias and their treatment, either pharmacological or surgical. The earliest complex atrial models incorporated parts of the anatomical architecture of the atria [72, 73]. During the last few years, a significant number of new models of the animal and human atrial anatomy have been published [44, 74–88]. Some of these models included the atrial fiber architecture observed in histological sections. Studies developed by Seemann et al. [75] and Aslanidi et al. [79] included only the main bundles fiber orientation in their human atrial model. An image‐ based anatomical model of the sheep atrial has been published [80] including realistic fiber orientation. The model reproduces the whole atria with highly detailed myofiber architecture. The three‐dimensional models also allow relating the arrhythmic behaviors as focal activity, rotors and multiple wavelet reentries, with their manifestation in the electrograms [44, 81].

A realistic three‐dimensional model of human atria including the main anatomical struc‐ tures (**Figure 2A**), electrophysiological heterogeneity, anisotropy (conduction velocity in the direction of myocardial fibers is usually several times larger than that vertical to them), and fiber orientation (**Figure 2B**) was developed in an earlier work [42]. It includes 52,906 hexa‐ hedral elements (polyhedrons with six faces, eight corners or nodes, topologically equivalent to cubes). The mathematical atrial cell model coupled within three‐dimensional (3D) virtual atria model was used to simulate AF dynamics. AF episodes were generated by the S1–S2 stimulation protocol as follows [36]: a train of five stimuli with a basic cycle length of 1000 ms was applied in the sinus node area for a period of 5 s to simulate the atrial sinus rhythm (S1). Based on the study developed by Haissaguerre et al. [13], a burst pacing of 6 ectopic beats to high frequency (S2) at cycle length (CL) of 130 ms was delivered into the right superior pul‐ monary vein after the last S1.

During AF activity initiated by the ectopic activity, it was observed the generation of two rotors of stable activity during 5 s of simulation. One was located in the posterior wall of the left atrium, near the left pulmonary vein (#2 in **Figure 2D**), and the other was located in the superior vena cava (#1 in **Figure 2D**). The rotors were generated spontaneously, which is in agreement with the rotor hypothesis [27]. Additionally, a block line located over the inferior right pulmonary vein has been observed (#3 in **Figure 2D**).

arrhythmias, such as AF, need complete structures to perpetuate them. The validity and enor‐ mous potential of multi‐scale heart models in improving diagnosis, prevention and therapy of cardiac pathologies are supported by different scientific results. These virtual models have opened new horizons in the study of the complex mechanisms underlying atrial arrhythmias and their treatment, either pharmacological or surgical. The earliest complex atrial models incorporated parts of the anatomical architecture of the atria [72, 73]. During the last few years, a significant number of new models of the animal and human atrial anatomy have been published [44, 74–88]. Some of these models included the atrial fiber architecture observed in histological sections. Studies developed by Seemann et al. [75] and Aslanidi et al. [79] included only the main bundles fiber orientation in their human atrial model. An image‐ based anatomical model of the sheep atrial has been published [80] including realistic fiber orientation. The model reproduces the whole atria with highly detailed myofiber architecture.

**Figure 1.** (A) Action potential under physiological and permanent AF conditions. (B) S1–S2 cross‐field protocol. The plane S1 and rectangular S2 stimulus are shown. (C) Stable rotor under permanent AF conditions. (D) Contour map, the

circular point indicates the rotor tip location.

**Conductance Permanent AF** *gI*KL Increased by 100%

*gI*Kuv Decreased by 50% *gI*to Decreased by 50% *gI*CaL Decreased by 70%

*gI*KACh –

142 Interpreting Cardiac Electrograms - From Skin to Endocardium

**Table 1.** Conductance (*g*) changes of currents for permanent AF.

**Figure 2.** (A) Frontal view of the three‐dimensional model of human atria. (B) Fiber orientation. (C) AP for different atrial areas (CT: crista terminalis, PM: pectinate muscles, APG: appendages, AVR: atrioventricular rings, and AWM: atrial working myocardium) under physiological conditions. (D) Activation isochronal maps. Stable rotors located in the posterior wall of the left atrium (#2) and A in the superior vena cava (#1) are showed. A block line can be seen at the right inferior pulmonary vein (#3).

## **3. Simulated atrial electrograms**

Several studies [21, 60, 82–84] have investigated the effects of factors such as slow conduction, anisotropy, conduction blocks, re‐entries, and wave collisions, on the morphology of unipolar and bipolar EGM. However, it is still not entirely clear to what extent these factors contribute to temporal and spatial variations in EGM morphology as observed during AF.

Calculating atrial EGM from the virtual models allows the study of EGM morphology and their relationship with arrhythmogenic sources.

Unipolar EGM are modeled as the register of the extracellular potential measured by a posi‐ tive polarity electrode whose reference (zero potential) is located at infinity. The distance from the electrode to the surface quantifies the influence area of the electrode, so the closer it is to the tissue, the greater the field uptake. The extracellular potential (*Ф*<sup>e</sup> ) was computed using the large volume conductor approximation [85, 86]:

$$
\begin{array}{ccccc}
\dots & & \dots & & \dots & & \\
\\
& \phi\_{\epsilon}(r) & = & -\text{K} \|\| \nabla^{\top} V\_{w}(r') \cdot \nabla \left[\frac{1}{r' - r}\right] dv & & & \dots
\end{array}
\tag{2}
$$

where *K* is a constant that includes the ratio of intracellular and extracellular conductivities (*σi* /4*π σ<sup>e</sup>* ), ∇′*V*m is the spatial gradient of transmembrane potential *V*m, *r* is the distance from the source point (*x, y, z*) to the measuring point (*x*′*, y*′*, z*′) and *dv* is the differential volume.

Zlochiver et al. [45] investigated the regularity of EGM in the presence of stable rotors, in a two‐dimensional atrial model. Jacquemet et al. [87] in a computer model representing a monolayer of atrial cells concluded that microscale obstacles cause significant changes to EGM waveforms. Using two‐dimensional computer models and cell cultures, Navoret et al. [88] detected CFAE using the criteria of cycle length, number of deflections, and amplitude. They established a relationship between the detected CFAE and the presence of rotors and shock waves, but they failed to differentiate them. Ashihara et al. [89], using a two‐dimen‐ sional myocardial sheet of size 4.5 × 4.5 cm, studied the role of fibroblasts in CFAE during AF. Yun et al. [90] reported that CFAE in a homogeneous two‐dimensional AF model were weakly correlated with wave break, phase singularity, and local dominant frequency.

We simulated that in the two‐dimensional atrial model, a total of 22,500 virtual electrodes (150 × 150, one for each element of the model), spaced by 0.4 mm at a distance of 0.2 mm above the atrial surface, unipolar EGM were calculated with temporal resolution of 1 ms.

The 98.9% of EGM, located away from the rotor tip, present simple morphology (**Figure 3A**). The remaining 1.1% of EGM, located at the rotor tip, exhibits potentials composed by two or more deflections (**Figure 3B**).

The mechanism by which fractionation of unipolar EGM occurs in our simulations can be explained as follows: the rotor is a singularity point or phase singularity, when the rotor is stable it pivots around a circular trajectory forming the core of the spiral wave, afterwards the pivot point is affected by the wavefronts from the rotor tip. When the wavefront passes near to the pivot point in each rotation cycle, several electrotonic potentials (nonpropagated local potential) are observed; consequently, irregularity and fractionation arise [36]. Our results are consistent with other studies, in which unipolar EGM symmetry was affected by the wave‐ front curvature (convex, concave or amorphous) [44] and fractionated unipolar EGM were observed at pivot points (functionally unexcitable core around which the rotor turns) [82]. Umapathy et al. [50] reported that CFAE were located in the region of a rotor tip and sites where wave breaks, using a murine HL‐1 atrial monolayer model.

**3. Simulated atrial electrograms**

144 Interpreting Cardiac Electrograms - From Skin to Endocardium

their relationship with arrhythmogenic sources.

*φ<sup>e</sup>*

more deflections (**Figure 3B**).

(*σi* /4*π σ<sup>e</sup>*

using the large volume conductor approximation [85, 86]:

Several studies [21, 60, 82–84] have investigated the effects of factors such as slow conduction, anisotropy, conduction blocks, re‐entries, and wave collisions, on the morphology of unipolar and bipolar EGM. However, it is still not entirely clear to what extent these factors contribute

Calculating atrial EGM from the virtual models allows the study of EGM morphology and

Unipolar EGM are modeled as the register of the extracellular potential measured by a posi‐ tive polarity electrode whose reference (zero potential) is located at infinity. The distance from the electrode to the surface quantifies the influence area of the electrode, so the closer

*Vm*(*r*′

where *K* is a constant that includes the ratio of intracellular and extracellular conductivities

Zlochiver et al. [45] investigated the regularity of EGM in the presence of stable rotors, in a two‐dimensional atrial model. Jacquemet et al. [87] in a computer model representing a monolayer of atrial cells concluded that microscale obstacles cause significant changes to EGM waveforms. Using two‐dimensional computer models and cell cultures, Navoret et al. [88] detected CFAE using the criteria of cycle length, number of deflections, and amplitude. They established a relationship between the detected CFAE and the presence of rotors and shock waves, but they failed to differentiate them. Ashihara et al. [89], using a two‐dimen‐ sional myocardial sheet of size 4.5 × 4.5 cm, studied the role of fibroblasts in CFAE during AF. Yun et al. [90] reported that CFAE in a homogeneous two‐dimensional AF model were weakly

We simulated that in the two‐dimensional atrial model, a total of 22,500 virtual electrodes (150 × 150, one for each element of the model), spaced by 0.4 mm at a distance of 0.2 mm above

The 98.9% of EGM, located away from the rotor tip, present simple morphology (**Figure 3A**). The remaining 1.1% of EGM, located at the rotor tip, exhibits potentials composed by two or

The mechanism by which fractionation of unipolar EGM occurs in our simulations can be explained as follows: the rotor is a singularity point or phase singularity, when the rotor is stable it pivots around a circular trajectory forming the core of the spiral wave, afterwards the pivot point is affected by the wavefronts from the rotor tip. When the wavefront passes near to the pivot point in each rotation cycle, several electrotonic potentials (nonpropagated local

source point (*x, y, z*) to the measuring point (*x*′*, y*′*, z*′) and *dv* is the differential volume.

), ∇′*V*m is the spatial gradient of transmembrane potential *V*m, *r* is the distance from the

) ⋅ ∇′ [ \_1 ) was computed

*<sup>r</sup>*′ <sup>−</sup> *<sup>r</sup>*]*dv* (2)

to temporal and spatial variations in EGM morphology as observed during AF.

it is to the tissue, the greater the field uptake. The extracellular potential (*Ф*<sup>e</sup>

(*r*) = −*K*ʃʃʃ ∇′

correlated with wave break, phase singularity, and local dominant frequency.

the atrial surface, unipolar EGM were calculated with temporal resolution of 1 ms.

Most of the in silico studies using three‐dimensional atrial models have characterized the simulated arrhythmias by observing the re‐entrant patterns. Few authors [44] have also calcu‐ lated EGM in a circular region on the free wall of the right atrium, using the 16 unipolar vir‐ tual electrodes on a simplified three‐dimensional model of human atria. They suggested that analysis of the amplitude and symmetry of unipolar atrial electrograms can provide informa‐ tion about the electrophysiological substrate maintaining AF. Hwang et al. [81] calculated bipolar EGM in a personalized three‐dimensional left atrial model in order to applied virtual ablation at CFAE points.

We calculated 42,835 EGM in the whole atrial surface of the three‐dimensional atrial model, over a 4‐s window and recorded at 1 kHz. Bipolar EGM were calculated by subtracting two 1 mm‐spaced adjacent unipolar EGM.

Fractionated atrial EGM were shown to be located in rotor tip areas, when the tip of the rotor turned on this point, displaying low voltage and irregular morphology with potentials com‐ posed by two or more deflections (**Figure 4A** and **B**). The wavefront of the rotor surrounds the pivot point, without depolarizing it completely, which results in multiple low amplitude deflections in the EGM.

The EGM corresponding to the block line present fractionation; however, the activation pat‐ terns are visible, and their amplitudes are similar to nonfractionated EGM (**Figure 4C**). The EGM from sites with a plain wavefront are regular with potentials composed by one deflec‐ tion (**Figure 4D**).

We identified the area in the posterior wall of the left atrium where the rotor spins (shaded circle in **Figure 5A**). EGM signals obtained from this area were used. From the selected region of the model, a conversion was made from the three‐dimensional coordinate system to the two‐dimensional coordinate system (*x, z*), taking advantage of the very low dispersion in *y*. EGM were converted to bipolar EGM, and this task was accomplished by creating a virtual mesh with 1 mm spacing, and performing a match with the two‐dimensional model surface. In this way, the difference between two adjacent signals in the mesh was calculated, obtaining a bipolar signal. In the same way, the results show that the rotor vortex area is associated with

**Figure 3.** (A) Regular EGM calculated in '\*' from **Figure 1C**. (B) Fractionated EGM calculated in the rotor tip.

signals presenting high degree of fractionation (**Figure 5B**). For the contrary, the EGM from sites with a plain wavefront are regular with potentials composed by one deflection, similarly to the unipolar EGM morphology (**Figure 5C**).

### **4. Estimation of nonlinear features for electroanatomical mapping**

EGM‐guided ablation has been proposed as a strategy to find critical sites of AF as target sites for ablation. Multiple clinical trials have shown that ablation of fractionated electrograms adds no benefit to conventional AF ablation with pulmonary vein isolation [91, 92]. This is likely because sites of electrogram fractionation, according with CFAE definition, not always correlate with sites of arrhythmic drivers and can also represent sites of wavefront collision or slow conduction, among others. Although CFAE may be relevant to detect areas that maintain AF, further charac‐ teristics apart from fractionation should be important to identify the atrial sites that maintain AF.

To overcome the limitation of CFAE, nonlinear analysis of EGM signals has been proposed by several authors to analyze the signals using further characteristics apart from time intervals or number of deflection [93, 94]. Nonlinear features are studied using the raw EGM signals, and it is not necessary to detect local activation waves. This is an important property, because in fragmented signals detection of activation waves is not always feasible. Nonlinear features

**Figure 4.** EGM calculated in the three‐dimensional atrial model, under simulated AF episode. Fractionated EGM corresponding to the rotor in the posterior wall of the left atrium (A) and in the vena cava (B). (C) EGM corresponding to a functional block line. (D) Regular EGM corresponding to plain wavefront.

**Figure 5.** (A) The area in the posterior wall in the model to obtain bipolar EGM. Samples of two bipolar EGM are shown, a fractionated signal from the rotor tip (B) and a regular activation pattern from nonrotor area (C).

as entropy estimation and fractal analysis are compute over each single EGM, and its value is related to the complexity of the signal.

Nonlinear mathematical tools can be used to quantify the irregularity of a signal. During the last years, measures have been developed to estimate the complexity of biomedical signals. Main goal of these advancements is to provide new theories about the dynamics of biological systems. Such is the case of Kolmogorov‐Sinai entropy, Lempel‐Ziv complexity, and correlation dimension, among others [95]. However, most of the complexity indexes require long time series to obtain reliable and convergent measures. Pincus [96] proposed the statistic approximate entropy (*ApEn*), which solves the issue of short time series, and it is aimed to measure the complexity degree and the presence of similarity patterns. Further developments have followed the *ApEn*, taking this as a starting point, such as the sample entropy [97], the fuzzy entropy [98] or hierarchical entropy [99]. Some authors have reported the use of nonlinear features to evaluate their suitable for locat‐ ing critical sites in AF. For instances, Ganesas et al. [47] reported that sites near to the rotor tip present high values of Shannon Entropy (*ShEn*) in EGM signals recorded from cell cultures and simulated episodes of fibrillatory conduction in two‐dimensional models of atrial tissue.

#### **4.1. Approximate and Shannon entropy definitions**

In general words, entropy has been conceived as a measure of the degree of disorganization or irregularity of a process. The most organized the process is, the lower the entropy related to it.

The statistic *ApEn*(*m*, *<sup>r</sup>*, *<sup>N</sup>*) depends on the length *N* of the time series *x*(*n*) (where *n* is), the posi‐ tive integer m (where *m* ≤ *N*) and the positive real number *r*. Defining:

$$\mathfrak{O}^{m}(r) = \frac{\sum\_{i=1}^{N-m} \log \mathbb{C}\_{i}^{m}(r)}{N - (m - 1)} = \frac{\sum\_{i=1}^{N-m} \log \mathbb{C}\_{i}^{m}(r)}{N - (m - 1)} \tag{3}$$

we have that *ApEn*(*m*, *r*, *N* ) = *Φ<sup>m</sup>*(*r* ) −*Φ<sup>m</sup>*+1 (*r* ) .

signals presenting high degree of fractionation (**Figure 5B**). For the contrary, the EGM from sites with a plain wavefront are regular with potentials composed by one deflection, similarly

EGM‐guided ablation has been proposed as a strategy to find critical sites of AF as target sites for ablation. Multiple clinical trials have shown that ablation of fractionated electrograms adds no benefit to conventional AF ablation with pulmonary vein isolation [91, 92]. This is likely because sites of electrogram fractionation, according with CFAE definition, not always correlate with sites of arrhythmic drivers and can also represent sites of wavefront collision or slow conduction, among others. Although CFAE may be relevant to detect areas that maintain AF, further charac‐ teristics apart from fractionation should be important to identify the atrial sites that maintain AF. To overcome the limitation of CFAE, nonlinear analysis of EGM signals has been proposed by several authors to analyze the signals using further characteristics apart from time intervals or number of deflection [93, 94]. Nonlinear features are studied using the raw EGM signals, and it is not necessary to detect local activation waves. This is an important property, because in fragmented signals detection of activation waves is not always feasible. Nonlinear features

**Figure 5.** (A) The area in the posterior wall in the model to obtain bipolar EGM. Samples of two bipolar EGM are shown,

**Figure 4.** EGM calculated in the three‐dimensional atrial model, under simulated AF episode. Fractionated EGM corresponding to the rotor in the posterior wall of the left atrium (A) and in the vena cava (B). (C) EGM corresponding

a fractionated signal from the rotor tip (B) and a regular activation pattern from nonrotor area (C).

to a functional block line. (D) Regular EGM corresponding to plain wavefront.

**4. Estimation of nonlinear features for electroanatomical mapping**

to the unipolar EGM morphology (**Figure 5C**).

146 Interpreting Cardiac Electrograms - From Skin to Endocardium

The variable *Ci <sup>m</sup>*(*r* ) counts the number of segments of length *m* that are within the boundaries defined by *r*. Thus, *ApEn(m, r, N)* measures the logarithmic frequency of the tool measures the logarithmic frequency that those segments of length *m* that are close remain close after increasing the length of the segments by one. In such a way, the statistic *ApEn* provides a measure of irregularity of the signal, implying strong regularity when *ApEn* value is small, and irregularity when *ApEn* value is large [96].

In previous work, we have reported the use of *ApEn* to evaluate the location of rotors and block lines in a three‐dimensional model of human atrial [100]; and the use of multifractal analysis as a tool to discriminate between four levels of fractionation according with a modi‐ fied Well's approach [101]. In this work, we tested several nonlinear features using EGM sig‐ nals recorded from a two‐dimensional model of atrial tissue and a three‐dimensional model of human atrial. Additional, we test the used of combination of nonlinear features using clus‐ tering method to study the distribution of different EGM patterns over the atrial surface.

Another index that estimates the entropy value from an *N*‐point signal *x*(*n*) is Shannon entropy (*ShE*) defined as:

$$ShEn = -\sum\_{i=1}^{N} p\_i \log\_2(p\_i)$$

where *p*<sup>i</sup> is the probability of assuming the corresponding *x(i)* value. Both, *ApEn* and *ShEn,* consider that a high value of repeated patterns implies order. Thus, they make their respective estimations of a signal irregularity by counting repetitive patterns, where the *ApEn* has a more elaborate method of defining and counting these patterns.

#### **4.2. Nonlinear features to complexity estimation for building maps: two‐dimensional model case**

Nonlinear features such as *ShEn* and *ApEn* have been used and tested for locating stables rotors in simulated episodes of fibrillatory conduction. We have tested *ShEn* maps and *ApEn* maps using the EGM signals from the two‐dimensional model. Results of this approach are shown in **Figure 6A** and **E**. These maps are constructed with high resolution using all the signals available in the model: 22,500 with spatial resolution of 0.4 mm. However, in the real case, the resolution of the electrodes can be lower, so in Ref. [102] was carried out a study about the EGM maps analysis reducing their resolution. **Figure 6** shows the maps of two‐ dimensional model of AF reconstructed from the entire model with a 75% of reduction of the electrodes number (resolution: 37 × 38) and characterized using the features *ShEn* and *ApEn* of the EGM signals, respectively. A reconstruction of the entire model was developed using the interpolation techniques: Inverse distance weighted ‐IDW [103] (**Figure 6B** and **F**), IDW with Mean Filter–MF [104] (**Figure 6C** and **G**), and backpropagation artificial neural network—BPANN (**Figure 6D** and **H**). The best result is obtained with BPANN algorithm. Backpropagation artificial neural network (BPANN) is a type of artificial neural network that assumes the function of a common and complex nervous system, and BPANN is widely used in machine learning for clinical research [105, 106]. BPANN is trained using Levenberg‐ Marquardt backpropagation algorithm [107]. This technique was applied for predicting the

**Figure 6.** (A) Two‐dimensional ShEn map. ShEn map reconstructed 75% using IDW‐MF (B) and BPANN (C). (D) Log entropy map. (E) Two‐dimensional ApEn map. ApEn map reconstructed 75% using IDW‐MF (F) and BPANN (G). (H) Log entropy map.

values of unknown points in order to increase the resolution of the two‐dimensional Map. BPANN has a structure (layers and neurons—[2 5 4 3 2 1]), which was defined applying a heuristic adjustment based on the minimum error for the mean map. The performance was assessed using the root mean squared error (RMSE).

## **5. Approximate entropy for rotor detection: three‐dimensional model case**

Motivated by the features of the *ApEn*, as a signal analyzing tool, and its important presence in several studies of complex biological systems [108–113]; our group has performed a study that relates AF mechanisms, such as rotors, with high degree of irregularity of EGM by means of the *ApEn*. In the following sections, *ApEn* theoretical definition and its interpretation are presented. Moreover, *ApEn* electroanatomical maps obtained from the virtual models are pre‐ sented, as well as the feasibility of characterize fibrillatory mechanisms in space and time. It follows a detailed analysis of our results and their implications.

#### **5.1. Approximate entropy for locating critical sites in AF**

*ShEn* = −∑

148 Interpreting Cardiac Electrograms - From Skin to Endocardium

elaborate method of defining and counting these patterns.

where *p*<sup>i</sup>

**model case**

Log entropy map.

*i*=1 *N*

consider that a high value of repeated patterns implies order. Thus, they make their respective estimations of a signal irregularity by counting repetitive patterns, where the *ApEn* has a more

Nonlinear features such as *ShEn* and *ApEn* have been used and tested for locating stables rotors in simulated episodes of fibrillatory conduction. We have tested *ShEn* maps and *ApEn* maps using the EGM signals from the two‐dimensional model. Results of this approach are shown in **Figure 6A** and **E**. These maps are constructed with high resolution using all the signals available in the model: 22,500 with spatial resolution of 0.4 mm. However, in the real case, the resolution of the electrodes can be lower, so in Ref. [102] was carried out a study about the EGM maps analysis reducing their resolution. **Figure 6** shows the maps of two‐ dimensional model of AF reconstructed from the entire model with a 75% of reduction of the electrodes number (resolution: 37 × 38) and characterized using the features *ShEn* and *ApEn* of the EGM signals, respectively. A reconstruction of the entire model was developed using the interpolation techniques: Inverse distance weighted ‐IDW [103] (**Figure 6B** and **F**), IDW with Mean Filter–MF [104] (**Figure 6C** and **G**), and backpropagation artificial neural network—BPANN (**Figure 6D** and **H**). The best result is obtained with BPANN algorithm. Backpropagation artificial neural network (BPANN) is a type of artificial neural network that assumes the function of a common and complex nervous system, and BPANN is widely used in machine learning for clinical research [105, 106]. BPANN is trained using Levenberg‐ Marquardt backpropagation algorithm [107]. This technique was applied for predicting the

**Figure 6.** (A) Two‐dimensional ShEn map. ShEn map reconstructed 75% using IDW‐MF (B) and BPANN (C). (D) Log entropy map. (E) Two‐dimensional ApEn map. ApEn map reconstructed 75% using IDW‐MF (F) and BPANN (G). (H)

**4.2. Nonlinear features to complexity estimation for building maps: two‐dimensional** 

*pi* log2 (*pi* )

is the probability of assuming the corresponding *x(i)* value. Both, *ApEn* and *ShEn,*

As stated earlier, our group has performed numerical experiments to assess the regularity of atrial EGM signals by means of the *ApEn*. Our research is based on three hypotheses: (1) Fractionation of EGM increases the *ApEn* values. (2) High *ApEn* values can be related to the tip of a rotor. (3) Information about spatial and temporal dynamics of a rotor could be obtained using moving window *ApEn*.

In order to calculate the *ApEn* values from the virtual unipolar EGM, we define the parameters *m = 2* and *r = 0.1* according to the interval of values suggested by Pincus [96], and *N = 1000*. **Figure 1** shows three EGM of 1000 points each, corresponding to minimum, intermediate and maximum *ApEn* values. The *ApEn* corresponds with the morphological complexity of the EGM: High values of *ApEn* mean irregularity or fragmentation of the EGM, and vice versa. In **Figure 7**, the EGM of the bottom present fragmentation of activation waves and baseline irregularity. Intermediate values of *ApEn* represent transitions between nonfragmented and fragmented EGM, in which differences between the patterns of activation waves can be seen, as can be seen in the EGM of the middle.

**Figure 8** (middle) shows the electroanatomical map of *ApEn(2, 0.1, 1000)* for the first second of the episode. The areas of R1 and R2, right inferior pulmonary vein and coronary sinus, have high *ApEn* values (red). The *ApEn* values (green) increase in the appendix, in pulmonary veins, and on the posterior and inferior wall of the left atrium. Rotors are established at the R1 and R2 zones. The high *ApEn* regions in **Figure 8** are not specifically related to rotor activity. Some authors suggest that the standard *ApEn* parameters are not suitable for signals of fast dynamics, and that to solve these cases, the *r* and *m* parameters must be chosen from a larger set than the one proposed by Pincus [108, 114]. Following this idea, we designed an optimization process for the *ApEn* parameters obtaining the configuration *ApEn(3, 0.38, 1000).* **Figure 8** (right) shows the corresponding *ApEn* in which the rotors R1 and R2 are highlighted by high *ApEn* values. Moreover, intermediate values of *ApEn* (green) are related to perturbations in conduction such as blockades, at the right inferior pulmonary vein, and shockwaves, at the zone below the coro‐ nary sinus. For additional details of this procedure and the results please refer to Ref. [115].

**Figure 7.** Three degrees of EGM irregularity and the corresponding ApEn value.

The fibrillatory activity presented in **Figure 8** includes stable rotors that were characterized by the *ApEn* maps. We move now to the case in which the tip of the rotor meanders. To gain in temporal resolution, the parameter *N* was reduced to 500 points, and a nonoverlapping moving window was applied to each EGM of the model to obtain a time‐dependent *ApEn* value (**Figure 9**). We applied Pincus parameters *ApEn(2,0.1,500)* and optimized parameters *ApEn(2,0.3,500)*. The analysis is performed over window of observation located at the left atrial posterior wall, in which a meandering rotor is generated. **Figure 10** shows three consec‐ utive frames of the episode (firs two columns) and the *ApEn* electroanatomical maps for Pincus (third column) and optimized (fourth column) parameters. For both parameter configuration, the high *ApEn* region changes as the tip of the rotor meanders through the observation window. The bottom row shows no rotor within the window that induces a reduction of *ApEn* for opti‐ mized parameters, while for Pincus parameters, high *ApEn* values remain.

Under the assumptions of our computational model, we provide evidence that the hypotheses stated above: we are able to quantify fragmentation of EGM using the *ApEn* as a measure of regularity and to relate it with the tip of a stable and meandering rotors. Moreover, through an optimized version of *ApEn* parameters setup, other conduction anomalies can be identi‐ fied. There are several works, with similar approach but with different tools of measurement of irregularity [54, 26, 88, 116, 50]. The tools used for the fragmentation analysis are mostly based on the calculation of the length of the cycle and the amplitude of the EGM, in correspon‐ dence with the definition of Nademanee [46]. Although the concept of CFAE established by Nademanee has been an important contribution to the study of AF, it may not describe the wide range of EGM fragmentations that occur in different cases. Therefore, we propose to extend the concept of fragmentation as a nonstatic and nonlinear phenomenon. The *ApEn* has already been applied in other studies for EGM analysis in AF [117], and in ventricular fibrillation [118] Complexity of Atrial Fibrillation Electrograms Through Nonlinear Signal Analysis: In Silico... http://dx.doi.org/10.5772/intechopen.69475 151

**Figure 8.** ApEn electroanatomical maps for AF episode. The notations R1 and R2 correspond to the tip of rotors at the left atrial posterior wall and superior cava vein.

**Figure 9.** Nonoverlapping moving window procedure to obtain ApEn values varying in time.

The fibrillatory activity presented in **Figure 8** includes stable rotors that were characterized by the *ApEn* maps. We move now to the case in which the tip of the rotor meanders. To gain in temporal resolution, the parameter *N* was reduced to 500 points, and a nonoverlapping moving window was applied to each EGM of the model to obtain a time‐dependent *ApEn* value (**Figure 9**). We applied Pincus parameters *ApEn(2,0.1,500)* and optimized parameters *ApEn(2,0.3,500)*. The analysis is performed over window of observation located at the left atrial posterior wall, in which a meandering rotor is generated. **Figure 10** shows three consec‐ utive frames of the episode (firs two columns) and the *ApEn* electroanatomical maps for Pincus (third column) and optimized (fourth column) parameters. For both parameter configuration, the high *ApEn* region changes as the tip of the rotor meanders through the observation window. The bottom row shows no rotor within the window that induces a reduction of *ApEn* for opti‐

Under the assumptions of our computational model, we provide evidence that the hypotheses stated above: we are able to quantify fragmentation of EGM using the *ApEn* as a measure of regularity and to relate it with the tip of a stable and meandering rotors. Moreover, through an optimized version of *ApEn* parameters setup, other conduction anomalies can be identi‐ fied. There are several works, with similar approach but with different tools of measurement of irregularity [54, 26, 88, 116, 50]. The tools used for the fragmentation analysis are mostly based on the calculation of the length of the cycle and the amplitude of the EGM, in correspon‐ dence with the definition of Nademanee [46]. Although the concept of CFAE established by Nademanee has been an important contribution to the study of AF, it may not describe the wide range of EGM fragmentations that occur in different cases. Therefore, we propose to extend the concept of fragmentation as a nonstatic and nonlinear phenomenon. The *ApEn* has already been applied in other studies for EGM analysis in AF [117], and in ventricular fibrillation [118]

mized parameters, while for Pincus parameters, high *ApEn* values remain.

**Figure 7.** Three degrees of EGM irregularity and the corresponding ApEn value.

150 Interpreting Cardiac Electrograms - From Skin to Endocardium

obtaining a single *ApEn* value for each EGM signal. We applied the Dynamic *ApEn* using a mobile window of 500 and 1000 points. An EGM of 4 s can provide up to 8 *ApEn* values, aimed to gain temporal resolution, and information about the behavior of EGM fragmentation.

The fragmented EGM were characterized by means of the *ApEn*, using the standard param‐ eters suggested by Pincus and the parameters chosen from the proposed optimization method [115]. Both proposals reveal the relationship between CFAE and high values of *ApEn*, which is supported by Novak et al. [94]. Furthermore, EGM fragments with high *ApEn* values have been shown to be related to arrhythmogenic substrates, such as the rotor tip, blocking lines and the case of the coronary sinus area influenced by abrupt fiber direction, wave collision and passage from a narrow conducting zone to a wide but perpendicular zone. The rela‐ tionship between CFAE and arrhythmogenic substrates has been reported in recent studies [61, 82, 87, 50, 49, 119–121]. However, how to differentiate the fragmented EGM according to the substrate that generates it? It has been observed that the *ApEn* maps, calculated from the standard parameters (*ApEn* (2, 0.1, 500) and *ApEn* (2, 0.1, 1000)), present fragmentation with high *ApEn* levels for the rotors R1 and R2, for the blockade at right inferior pulmonary vein and the coronary sinus region; however, they do not present significant numerical differences. This has also been observed by Navoret et al. [88], who establish a relationship between detected

**Figure 10.** Three consecutive frames of propagation (first and second columns) of a meandering rotor and the Pincus parameters ApEn map (third column) and optimized parameters ApEn map (fourth column).

CFAE and the presence of wave and rotor shock, but they cannot differentiate them, using two‐dimensional computational models and cell cultures. They also report the development of an algorithm, which extracts five characteristics for the characterization of fragmented EGM. The algorithm is tested in two real databases: the first has EGM labeled as fragmented and nonfragmented. The algorithm shows good results in the classification. The second has EGM labeled as active fragmentation, whose ablation restored sinus rhythm, and fragmentation whose ablation did not restore sinus rhythm. The algorithm did not discriminate between both classifications [48]. However, the *ApEn* maps, calculated using the optimized parameters opti‐ mized (*ApEn*(3, 0.3, 500) and *ApEn*(3, 0.38, 1000)), assign values by ranges to areas of interest, the R1 and R2 rotors being the highest *ApEn*, followed by the intermediate values of *ApEn* in the zone of the blockade and the coronary sinus, and the smaller values of *ApEn* to the fibrilla‐ tory EGM of regular morphology. These results suggest that: the *ApEn* can solve the problem described by Navoret et al. [88]. On the other hand, if it is verified that the ablation guided by the *ApEn* maps restores the sinus rhythm, it solves the problem reported in Ref. [28]. Future work should focus on evaluating, in computational and experimental models, ablation guided by maps of dynamic *ApEn*.

Some authors have pointed out the disadvantages of *ApEn*: it is not a stable measure when the number of points N varies, and it has an inherent deviation from the real value, due to the inclusion of self‐comparison of segments [122, 123]. It has even been proposed a new statisti‐ cal, the sample entropy (*SampEn*), as an enhancement of the *ApEn* [97]. However, it has been shown that both have a same behavior for time series of fast dynamics [110, 114, 124]. In our research, the possible instability that can present the *ApEn* due to the variation of points does not influence the results: specific families of *ApEn* have been defined, starting from the elec‐ tion of the r y m parameters, using time series of 500 and 1000 points. Although it has been observed that the range of *ApEn* values varies for each case, the information provided by the *ApEn* is embedded in the continuous scale that it results, given the degrees of irregularity that the fibrillatory EGM may present. This feature is important, since it offers adaptability to the wide range of EGM morphologies that may present different cases. In addition, it is not necessary to define intervals of fixed *ApEn* values for CFAE identification. It is only necessary to define that the *ApEn* scale, during an AF episode, is proportional to the presence of frag‐ mentation, where the higher values of *ApEn* suggest the presence of rotors.

#### **5.2. Multifractal analysis of EGM signals**

CFAE and the presence of wave and rotor shock, but they cannot differentiate them, using two‐dimensional computational models and cell cultures. They also report the development of an algorithm, which extracts five characteristics for the characterization of fragmented EGM. The algorithm is tested in two real databases: the first has EGM labeled as fragmented and nonfragmented. The algorithm shows good results in the classification. The second has EGM labeled as active fragmentation, whose ablation restored sinus rhythm, and fragmentation whose ablation did not restore sinus rhythm. The algorithm did not discriminate between both classifications [48]. However, the *ApEn* maps, calculated using the optimized parameters opti‐ mized (*ApEn*(3, 0.3, 500) and *ApEn*(3, 0.38, 1000)), assign values by ranges to areas of interest, the R1 and R2 rotors being the highest *ApEn*, followed by the intermediate values of *ApEn* in the zone of the blockade and the coronary sinus, and the smaller values of *ApEn* to the fibrilla‐ tory EGM of regular morphology. These results suggest that: the *ApEn* can solve the problem described by Navoret et al. [88]. On the other hand, if it is verified that the ablation guided by the *ApEn* maps restores the sinus rhythm, it solves the problem reported in Ref. [28]. Future work should focus on evaluating, in computational and experimental models, ablation guided

**Figure 10.** Three consecutive frames of propagation (first and second columns) of a meandering rotor and the Pincus

parameters ApEn map (third column) and optimized parameters ApEn map (fourth column).

152 Interpreting Cardiac Electrograms - From Skin to Endocardium

Some authors have pointed out the disadvantages of *ApEn*: it is not a stable measure when the number of points N varies, and it has an inherent deviation from the real value, due to the inclusion of self‐comparison of segments [122, 123]. It has even been proposed a new statisti‐ cal, the sample entropy (*SampEn*), as an enhancement of the *ApEn* [97]. However, it has been shown that both have a same behavior for time series of fast dynamics [110, 114, 124]. In our research, the possible instability that can present the *ApEn* due to the variation of points does not influence the results: specific families of *ApEn* have been defined, starting from the elec‐ tion of the r y m parameters, using time series of 500 and 1000 points. Although it has been

by maps of dynamic *ApEn*.

Fluctuations in EGM signals are nonperiodic and exhibit nonlinear behavior. Fractal models could be used to describe this behavior through the identification of self‐similarity and scale invariance in the statistical properties of the signals. Fractal signals present self‐similarities and scale invariance properties that can be described by a single quantity, for example, the Hausdorff dimension or the Hurst exponent, and it is represented using a power law relation‐ ship. Fractal properties of physiological signals are not homogeneous, which means that local scaling properties change with time, and there is necessary to use different local Hurts expo‐ nent to describe the evolution of the system. Therefore, multifractal analysis could capture these changes in the global singularity distributions [101]. Then, the power law for multifractal behavior is written as follows:

$$N\_a \sim e^{-\wp(a)}\tag{4}$$

where *N<sup>α</sup>* corresponds to the number of balls with a singular exponent equal to some value of *<sup>α</sup>*, necessary to cover a specific set, ϵ is the diameter of the balls that covered the set, and *f*(*α*) corresponds to the Hausdorff dimension. Note that in fractal analysis, the exponent is a scalar, while here the exponent is a function that contain different local Hurts exponent.

To compute the singular spectrum *f*(*α*), we used a method called multifractal detrended fluc‐ tuation analysis proposed and described in Ref. [125]. Using *f*(*α*), we calculate the h‐fluctua‐ tion index as is described by Orozco‐Duque et al. [101].

#### **5.3. Location of simulated rotors using multifractal analysis**

Multifractal analysis can be used to calculate features such as h‐fluctuation index and to build electroanatomical maps to located sites fractal or multifractal activity. This measure is related to the complexity of the EGM signals recorded over the atrial surface. In this case, we work with signals recorded from a simulated episode of AF in the three‐dimensional model described above. **Figure 11A** shows a color map built with the values obtained by the mul‐ tifractal analysis according with Orozco‐Duque et al. [126]. Here, red dots are locating in regions where the rotor tip is presented in the model, and in the neighborhood of the rotor tip where the tip is meandering.

On the other hand, h‐fluctuation index was calculated in EGM signals recorded from the two‐dimensional simulated episode of fibrillatory conduction. For the sake of comparison, *ApEn* map was computed using the two‐dimensional model and the optimized parameters. These features were calculated for each EGM individually, and values were represented in a color map. **Figure 11B** shows the *ApEn* map and **Figure 5** represented the MF map. *ApEn* map exhibits the behavior of the rotor tip and illustrates the dynamics in the vicinity of the pivot point. In the central point of the rotor, there is a blue point representing some organized signals; however, in the neighborhood of the tip, there are reds dots that represent signals with high fragmented activity. A start‐shaped pattern can be identified, which represents the movement of the singularity point.

In **Figure 11C**, multifractal map exhibits an interesting behavior because it captures the dynamic of the whole rotor in the atrial tissue, not only the neighborhood of the tip. One can note that the direction of the rotation is illustrated and can be interpreted using this map.

**Figure 11.** (A) Three‐dimensional electroanatomical map using multifractal analysis. (B) Two‐dimensional electro‐ anatomical map using ApEn. (C) Two‐dimensional electroanatomical map using multifractal analysis.

## **6. Combination of features in the same EA map**

EGM signals exhibit different morphologies that have not been enough studied. An inad‐ equate characterization of EGM morphologies has limited the success of EGM‐guide ablation strategies. Looking for a better description of different EGM patterns, some authors have pro‐ posed the combination of features to detect critical sites in AF. This approach has the advan‐ tage of use different information from the signals and detects patterns that could be associated with wave collisions, conduction block, or pivot points.

Ravelli et al. [127] used a logical digital map to combined two indexes, one based on the detec‐ tion of activation rate, the cycle length; and another based on the analysis of similarities between activation waves, the similarity (S). Logical operator map can discriminate two morphologies: rapidly organized and rapidly fragmented. According with Kalifa et al. rapidly organized, EGM could be associated with localized source of AF, while rapidly fragmented could be asso‐ ciated with the neighborhood of a pivot point [52]. One limitation of the approach proposed by Ravelli et al. is that the computation of cycle length and S requires the segmentation of EGM signals and the detection of local activation waves (LAW). This process is not always feasible especially with high‐disorganized patterns.

These features were calculated for each EGM individually, and values were represented in a color map. **Figure 11B** shows the *ApEn* map and **Figure 5** represented the MF map. *ApEn* map exhibits the behavior of the rotor tip and illustrates the dynamics in the vicinity of the pivot point. In the central point of the rotor, there is a blue point representing some organized signals; however, in the neighborhood of the tip, there are reds dots that represent signals with high fragmented activity. A start‐shaped pattern can be identified, which represents the

In **Figure 11C**, multifractal map exhibits an interesting behavior because it captures the dynamic of the whole rotor in the atrial tissue, not only the neighborhood of the tip. One can note that the direction of the rotation is illustrated and can be interpreted using this map.

EGM signals exhibit different morphologies that have not been enough studied. An inad‐ equate characterization of EGM morphologies has limited the success of EGM‐guide ablation strategies. Looking for a better description of different EGM patterns, some authors have pro‐ posed the combination of features to detect critical sites in AF. This approach has the advan‐ tage of use different information from the signals and detects patterns that could be associated

**Figure 11.** (A) Three‐dimensional electroanatomical map using multifractal analysis. (B) Two‐dimensional electro‐

anatomical map using ApEn. (C) Two‐dimensional electroanatomical map using multifractal analysis.

Ravelli et al. [127] used a logical digital map to combined two indexes, one based on the detec‐ tion of activation rate, the cycle length; and another based on the analysis of similarities between

movement of the singularity point.

154 Interpreting Cardiac Electrograms - From Skin to Endocardium

**6. Combination of features in the same EA map**

with wave collisions, conduction block, or pivot points.

Schilling et al. proposed an approach based on a classifier called Fuzzy decision tree to com‐ bine features and classify the EGM signals among four classes [128]. Classes are assigned according to a modified Well's criteria, where class 0 corresponds to organized and nonfrag‐ mented signal, class 1 is assigned to signals with fragmented waves but periodic activity, class 2 corresponds to signals with fragmented waves with periodic and nonperiodic activity, and class 3 is assigned to signals with high frequency and continuous activity. A limitation for using supervised learning is that the classifier depends on the classes selected by the group who collected the training database. This could be critical and bias the results because there is not a complete understanding about EGM morphologies.

Unsupervised learning has been proposed to combine features and creates maps to show the distribution of EGM cluster according with conduction patterns. We have tested some cluster‐ ing methods based on machine learning such as K‐means and Self‐Organized Maps (SOM) in previous work. To locate rotors over simulation in two‐dimensional models, the best perfor‐ mance was obtained using the combination of Shannon Entropy and the mean value of the EGM signal as an input of K‐means algorithm with three clusters or the SOM algorithm with four clusters. **Figure 12B** and **C** shows the result of K‐means and SOM applied to signals from the two‐dimensional model. The classifiers performance was calculated using the distance between the rotor tip location and the mean of the points grouped by the nearest cluster. These results evince the capability of the combination of simple features using unsupervised algorithms for rotor tip location.

The issues related to the clustering approach are the selection of clusters number and the clas‐ sification of clusters to identify the set of EGM related to a specific pattern. To overcome these limitations, Orozco‐Duque et al. [129] have proposed a semisupervised clustering approach to combine features. Semisupervised clustering (SC) is not limited to previously defined classes. The method selected was spectral clustering with an automatic detection of cluster number. In a previous work, it was tested the performance of SC to discriminated between four classes according with the scheme proposed by Schilling et al. [130]. We tested SC and its feasibility to located pivot points in simulated episodes of AF. We used unipolar signals acquired in an AF simulation using the three‐dimensional model of human atrial. **Figure 12A** shows a map built from the results of SC evaluation. Four clusters were detected; the cluster that represents regular signals is displayed in blue, and the cluster with the highest disorganized pattern is displayed in red. This cluster is located in the areas where the two rotors meander. The distri‐ bution of yellow and green clusters gives us an idea about cluster rotation.

**Figure 12.** (A) Electroanatomical map using semisupervised clustering applied to signals from three‐dimensional model. (B) Two‐dimensional electroanatomical map using K‐means. (C) Electroanatomical map using SOM.

## **7. Concluding remarks**

Phase maps are, currently, the accepted tools for rotor characterization [131], by tracking the tip through the phase singularity. Although it is widely applied in computational studies [132, 133] and in vitro experimentation, such as optical mapping [134, 135], clinical applica‐ tion presents technical limitations: high spatial resolution and EGM require a preprocessing stage in which information of activation can be lost [136]. Here, we have presented how nonlinear features and clustering approaches provide information about the rotor dynamics during AF virtual episodes. Translated to a clinical context, these measures can be extracted from real EGM without needing special signal conditioning. However, our simulations provide high spatial resolution that places the same limitation as phase maps. In a recent report [137], we tested the influence of the spatial resolution over the *ApEn* electroanatomical maps in detecting rotors, using a two‐dimensional atrial fibrillation model. Our results indicate that the *ApEn* maps can identify the rotor tip with spatial resolutions close to those available in commercial mapping catheters. We also showed that a minor dependence of the *ApEn* maps on the virtual electrode array position, which implies that there is a transition of irregularity starting at the rotor tip and spreading to its surroundings. These findings encourage considering nonlinear features for EGM analysis. Although experimental valida‐ tion is needed, further in silico studies are needed to enhance and characterize the behavior of these tools.

Nonlinear features such as *ApEn* and indexes calculated from multifractal analysis allow the construction of maps to display the distribution of EGM morphologies and to study the dynamic of fibrillatory conduction in the atrial surface. Additionally, application of clustering tools allows us to incorporate the information from different features within the same system for study the distribution of EGM clusters in the atrial surface. The use of unsupervised learning approach has the vantage that does not depend on a training specific dataset, which is an impor‐ tant feature considering the gaps in the knowledge about EGM morphologies. In AF simulated models, rotors were located by the proposed methodology; however, further observations and clinical studies are needed to associate marked sites with arrhythmogenic substrates in humans.

## **Author details**

Catalina Tobón<sup>1</sup> , Andrés Orozco‐Duque2 , Juan P. Ugarte<sup>3</sup> , Miguel Becerra<sup>4</sup> \* and Javier Saiz5


## **References**

**7. Concluding remarks**

156 Interpreting Cardiac Electrograms - From Skin to Endocardium

of these tools.

Phase maps are, currently, the accepted tools for rotor characterization [131], by tracking the tip through the phase singularity. Although it is widely applied in computational studies [132, 133] and in vitro experimentation, such as optical mapping [134, 135], clinical applica‐ tion presents technical limitations: high spatial resolution and EGM require a preprocessing stage in which information of activation can be lost [136]. Here, we have presented how nonlinear features and clustering approaches provide information about the rotor dynamics during AF virtual episodes. Translated to a clinical context, these measures can be extracted from real EGM without needing special signal conditioning. However, our simulations provide high spatial resolution that places the same limitation as phase maps. In a recent report [137], we tested the influence of the spatial resolution over the *ApEn* electroanatomical maps in detecting rotors, using a two‐dimensional atrial fibrillation model. Our results indicate that the *ApEn* maps can identify the rotor tip with spatial resolutions close to those available in commercial mapping catheters. We also showed that a minor dependence of the *ApEn* maps on the virtual electrode array position, which implies that there is a transition of irregularity starting at the rotor tip and spreading to its surroundings. These findings encourage considering nonlinear features for EGM analysis. Although experimental valida‐ tion is needed, further in silico studies are needed to enhance and characterize the behavior

**Figure 12.** (A) Electroanatomical map using semisupervised clustering applied to signals from three‐dimensional model.

(B) Two‐dimensional electroanatomical map using K‐means. (C) Electroanatomical map using SOM.

Nonlinear features such as *ApEn* and indexes calculated from multifractal analysis allow the construction of maps to display the distribution of EGM morphologies and to study the


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#### **Loss of Complexity of the Cardiac Bioelectrical Signal as an Expression of Patient Outcomes** Loss of Complexity of the Cardiac Bioelectrical Signal as an Expression of Patient Outcomes

DOI: 10.5772/intechopen.70144

Pedro Eduardo Alvarado Rubio, Ricardo Mansilla Corona, Lizette Segura Vimbela, Alejandro González Mora, Roberto Brugada Molina, Cesar Augusto González López and Laura Yavarik Alvarado Avila Pedro Eduardo Alvarado Rubio, Ricardo Mansilla Corona, Lizette Segura Vimbela, Alejandro González Mora, Roberto Brugada Molina, Cesar Augusto González López and

Additional information is available at the end of the chapter Laura Yavarik Alvarado Avila

http://dx.doi.org/10.5772/intechopen.70144 Additional information is available at the end of the chapter

#### Abstract

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The loss of complexity of the cardiac bioelectrical signal, measured with tools of nonlinear dynamics (NLD), is studied in patients with very different pathologies. Two types of scenarios are studied: (a) patients who enter the critical care unit and recover from their condition; (b) severe patients whose condition worsen and finally die. It is shown that as the severity of the patients increases, the complexity of their cardiac bioelectric signal decreases. On the other hand, if patients, despite being severe, manage to recover, the cardiac bioelectric signal recovers its complexity.

Keywords: bioelectrical signal, nonlinear dynamics, complexity, variability, critical illness

## 1. Introduction

The application of tools of the theory of the dynamical systems to the study of physiological phenomena has a long inheritance. This starts from the original works of van der Pol and his collaborator [1, 2], passes through important contributions [3, 4], and reaches the comprehensive work by Glass and Mackey [5]. The application of these types of systems to describe the temporal evolution of the physiological phenomena has been established as a tool frequently used by researchers in this area of knowledge and is already a common place in the literature.

The initial works in the analysis of the dynamics of the cardiac rhythm showed a nonlinear dynamic (NLD) behavior. Period-doubling bifurcations, in which the period of a regular oscillation doubles, were predicted theoretically and observed experimentally in the heart cells of

distribution, and eproduction in any medium, provided the original work is properly cited.

embryonic chickens [6]. The tools with a new mathematical approach made it possible to apply the nonlinear dynamics to basic physiological concepts, proving for the first time evidence of nonlinear behavior in the electrocardiogram (ECG) [7]. Period multiplying evidence in arterial blood pressure traces of a dog that had been injected with noradrenaline was reported in 1984 [8]. Since the original reports on ischemic heart disease and arrhythmia [9, 10], the analysis of spontaneous variations of beat-to-beat intervals (BBIs) has become an important clinical tool [11–13].

For a long time, the construction of models was based on first principles, being this the main tool for the understanding of complex physiological phenomena in theoretical models of nerve and the membrane [14, 15], among which the functioning of the heart occupies a main place. On the other hand, some studies tried to obtain information about cardiac diseases from the time series that the measuring instruments offered, although very often they were noisy and limited data [16]. Procedures have been developed for the study of ventricular fibrillation using the data of implantable defibrillators [13, 17]. It is well known that these data are often noisy and only represent the sequence of R-R intervals and is typically morphologically different from surface electrocardiogram recordings. Many signal-processing algorithms have been designed to eliminate noise from a system; however, noise (i.e., stochastic processes) is a critical component of many biological and physiological systems [18]. Given the difficulties mentioned earlier, some authors tried to use measures of complexity and entropies, as well as other techniques of the theory of nonlinear phenomena [19, 20].

The initial clinical observation of heart rate variability (HRV), observing changes in the pattern of the R-R interval, which preceded changes in the heart rate in fetal distress, was reported in 1963 [21]. Later, the first approaches of the heart rate variability analysis based on nonlinear fractal dynamics were performed in 1987 [4]. It was suggested that self-similar (fractal) scaling may underlie the 1/f-like spectra [22] seen in multiple systems (e.g., interbeat interval variability, daily neutrophil fluctuations). They proposed that this fractal scale invariance may provide a mechanism for the "constrained randomness" underlying physiological variability and adaptability. In 1988, it was reported that patients prone to high risk of sudden cardiac death showed evidence of nonlinear heart rate (HR) dynamics, including abrupt spectral changes and sustained low-frequency (LF) oscillations. After this report, it has been suggested that a loss of complex physiological variability could occur under certain pathological conditions such as reduced HR dynamics before sudden death and aging [23, 24].

Methods of NLD and fractal analysis have opened up new ways for the analysis of HRV. Although time and frequency domain methods enable the quantification of HRV on different time scales, nonlinear methods provide additional information regarding the dynamics and structure of beat-to-beat time series in various physiological and pathophysiological conditions [25]. The apparent loss of multiscale complexity in life-threatening conditions suggests a clinical importance of this multiscale complexity measure. Studies on heart rate multiscale entropy at 3 h predict hospital mortality in patients with major trauma [26]. Joint symbolic dynamics, compression entropy, fractal dimension, and approximate entropy revealed significantly reduced complexity of heart rate time series and loss of efferent vagal activity in acute schizophrenia [27, 28].

The healthy human heart rate is mainly determined by three major inputs: the sinoatrial node; and the parasympathetic and sympathetic branches of the autonomous nervous system and several autocrine, paracrine, and endocrine substances effects on it [29]. The sinoatrial node or

pacemaker is responsible for the initiation of each heart beat; in the absence of other external stimuli, it is able to maintain an essentially constant interbeat interval. Experiments in which parasympathetic and sympathetic inputs are blocked reveal that the interbeat intervals are very regular and average 0.6 s. The parasympathetic fibers conduct impulses that increase the interbeat intervals. Suppression of sympathetic stimuli, while under parasympathetic regulation, can result in the increase of the interbeat interval to as much as 1.5 s. The activity of the parasympathetic system changes with external stimuli and with internal cycles. The sympathetic fibers conduct impulses that decrease the interbeat intervals. Abolition of parasympathetic influences when the sympathetic system remains active can decrease the interbeat intervals to less than 0.3 s. There are several centers of sympathetic activity which are highly sensitive to environmental influences [30, 31]. All the patients that are analyzed in this work have as a common factor a suffering of systemic repercussion that influences the dynamics of the sympathetic-parasympathetic balance and, therefore, of the heart rate. As will be seen subsequently, whatever the underlying condition, as it worsens, decreases the complexity of the cardiac bioelectrical signal, while its improvement is accompanied by an increase in the complexity of the cardiac signal. Hence, the measures of complexity of the heart electrical signals allow assessing the severity of the patient's condition, and as we will see later (Figure 3) they can be used as early warnings of severity episodes. This is why we focus on the observation of the complexity of the cardiac bioelectric signal.

The increasing availability of physiological data has allowed the study of long-time series with other techniques also coming from the theory of dynamical systems. The observations received from some organ of our body, as we have said before, very often are tainted of noise or are collected in an incomplete way. The signals of electrical activity of the heart are a good example of this. They are measured on the surface of the patient, in a finite number of places. The electrical signal from the heart must pass through several layers of tissues with different electrical conductivities before being measured by traditional devices. What we measure is actually a distorted observable of the authentic electric signal coming from the surface of the heart. Then the following question arises; how much information of the original phenomenon could be recovered from this distorted signal? Other relevant questions are how many magnitudes are necessary for a complete description of the phenomenon? In other words, what is the dimension of the attractor of the dynamical system that describes the evolution of the heart? Is there a difference between a healthy person and a sick person in the number of variables necessary to characterize their behavior? Or put in another way, is there a difference in the dimension of the attractor of the dynamical systems that describe the behavior of a healthy person and a sick person?

The Takens Embedding Theorem [32] answers these questions under certain assumptions about the recorded time series. In the following lines, we describe the theoretical framework, the fundamental results, and the techniques of valuation of the different magnitudes.

## 2. Mathematical theoretical framework

embryonic chickens [6]. The tools with a new mathematical approach made it possible to apply the nonlinear dynamics to basic physiological concepts, proving for the first time evidence of nonlinear behavior in the electrocardiogram (ECG) [7]. Period multiplying evidence in arterial blood pressure traces of a dog that had been injected with noradrenaline was reported in 1984 [8]. Since the original reports on ischemic heart disease and arrhythmia [9, 10], the analysis of spontaneous variations of beat-to-beat intervals (BBIs) has become an important clinical tool [11–13].

For a long time, the construction of models was based on first principles, being this the main tool for the understanding of complex physiological phenomena in theoretical models of nerve and the membrane [14, 15], among which the functioning of the heart occupies a main place. On the other hand, some studies tried to obtain information about cardiac diseases from the time series that the measuring instruments offered, although very often they were noisy and limited data [16]. Procedures have been developed for the study of ventricular fibrillation using the data of implantable defibrillators [13, 17]. It is well known that these data are often noisy and only represent the sequence of R-R intervals and is typically morphologically different from surface electrocardiogram recordings. Many signal-processing algorithms have been designed to eliminate noise from a system; however, noise (i.e., stochastic processes) is a critical component of many biological and physiological systems [18]. Given the difficulties mentioned earlier, some authors tried to use measures of complexity and entropies, as well as

The initial clinical observation of heart rate variability (HRV), observing changes in the pattern of the R-R interval, which preceded changes in the heart rate in fetal distress, was reported in 1963 [21]. Later, the first approaches of the heart rate variability analysis based on nonlinear fractal dynamics were performed in 1987 [4]. It was suggested that self-similar (fractal) scaling may underlie the 1/f-like spectra [22] seen in multiple systems (e.g., interbeat interval variability, daily neutrophil fluctuations). They proposed that this fractal scale invariance may provide a mechanism for the "constrained randomness" underlying physiological variability and adaptability. In 1988, it was reported that patients prone to high risk of sudden cardiac death showed evidence of nonlinear heart rate (HR) dynamics, including abrupt spectral changes and sustained low-frequency (LF) oscillations. After this report, it has been suggested that a loss of complex physiological variability could occur under certain pathological conditions

Methods of NLD and fractal analysis have opened up new ways for the analysis of HRV. Although time and frequency domain methods enable the quantification of HRV on different time scales, nonlinear methods provide additional information regarding the dynamics and structure of beat-to-beat time series in various physiological and pathophysiological conditions [25]. The apparent loss of multiscale complexity in life-threatening conditions suggests a clinical importance of this multiscale complexity measure. Studies on heart rate multiscale entropy at 3 h predict hospital mortality in patients with major trauma [26]. Joint symbolic dynamics, compression entropy, fractal dimension, and approximate entropy revealed significantly reduced complexity

of heart rate time series and loss of efferent vagal activity in acute schizophrenia [27, 28].

The healthy human heart rate is mainly determined by three major inputs: the sinoatrial node; and the parasympathetic and sympathetic branches of the autonomous nervous system and several autocrine, paracrine, and endocrine substances effects on it [29]. The sinoatrial node or

other techniques of the theory of nonlinear phenomena [19, 20].

170 Interpreting Cardiac Electrograms - From Skin to Endocardium

such as reduced HR dynamics before sudden death and aging [23, 24].

The most frequent problems in the study of the physiological signals of electrical type are that very often we have incomplete and deformed information of them. This is a very common problem in many branches of scientific knowledge. As far as the electrical activity of the cardiac muscle is concerned, a methodology has been developed, whose theoretical basis is found in the theory of dynamical systems. This result is known as the Takens' Embedding Theorem. This result allows us, under certain hypotheses, to answer the following questions: Is it possible to reconstruct the bioelectric dynamics of a cardiac phenomenon from incomplete information? How many variables are necessary to fully characterize this phenomenon?

Let us assume that n measurements would be necessary to fully characterize the phenomenon under study. We do not know them directly. Rather, we have a macroscopic observable g that is constructed from them:

$$\mathbf{g}(t) = \theta(\mathbf{x}\_1(t), \dots, \mathbf{x}\_n(t)) \tag{1}$$

Here, we assume that x1ðtÞ, …, xnðtÞ are the measurements necessary to characterize the system, measured at time t. The function θ is one that transforms the variables that characterize the system in the macroscopic observable to which we have access.

Almost all medical devices discreetly take samples with a certain frequency. Therefore, what in the practice we have is a time series {g1,…, gT}, where gi ¼ gðtiÞ, where very often it is assumed (as do we) that the times of measurement ti are equally spaced in time.

The Takens Embedding Theorem basically says that under the assumption that function g is "well behaved," that is, which can be measured continuously without very sudden jumps then, there are τ∈ R<sup>þ</sup> and N ∈ N such that the set of vectors:

$$A\_d = \left\{ (\mathbf{g}\_{i\prime}\mathbf{g}\_{i+\tau\prime}\dots\mathbf{g}\_{i+(N-1)\tau}), i \in \mathcal{N} \right\} \tag{2}$$

is for any practical purpose similar in its properties to the simultaneous behavior of the variables x1ðtÞ, …, xnðtÞ. Unfortunately, the theorem does not say how τ and N should be calculated. So a wide heuristic has been developed to estimate these parameters [33]. In this task, two concepts play an important role: the mutual information function and the correlation integral.

The mutual information function can be defined as follows:

$$M(\tau) = \sum\_{t=1}^{T-\tau} P(\mathbf{g}\_{t'} \mathbf{g}\_{t+\tau}) \ln \left[ \frac{P(\mathbf{g}\_{t'} \mathbf{g}\_{t+\tau})}{P(\mathbf{g}\_t)P(\mathbf{g}\_{t+\tau})} \right] \tag{3}$$

This concept is closely related to the concept of Boltzmann entropy and the Shannon information [34]. It is a measure of nonlinear correlation among the values of the series {gi }.

The values of the mutual information function can be calculated from the {g1, …, gT} series using appropriate software. The correct value for τ is the first local minimum of the mutual information function [15, 35]. It is well known that the mutual information function is more sensitive to correlations of data than other correlation measures [36].

The second important step is the calculation of the so-called embedding dimension N. For this, it is necessary to use a concept called integral correlation: consider now the collection of vector of the set Ad:

Loss of Complexity of the Cardiac Bioelectrical Signal as an Expression of Patient Outcomes http://dx.doi.org/10.5772/intechopen.70144 173

$$X\_i = \left(\mathbf{g}\_{i'}\mathbf{g}\_{i+\mathbf{r}'} \dots \mathbf{g}\_{i+(N-1)\tau}\right) \tag{4}$$

the correlation integral CmðεÞ is defined as

cardiac muscle is concerned, a methodology has been developed, whose theoretical basis is found in the theory of dynamical systems. This result is known as the Takens' Embedding Theorem. This result allows us, under certain hypotheses, to answer the following questions: Is it possible to reconstruct the bioelectric dynamics of a cardiac phenomenon from incomplete information? How many variables are necessary to fully characterize this phenomenon?

Let us assume that n measurements would be necessary to fully characterize the phenomenon under study. We do not know them directly. Rather, we have a macroscopic observable g that is

Here, we assume that x1ðtÞ, …, xnðtÞ are the measurements necessary to characterize the system, measured at time t. The function θ is one that transforms the variables that characterize

Almost all medical devices discreetly take samples with a certain frequency. Therefore, what in the practice we have is a time series {g1,…, gT}, where gi ¼ gðtiÞ, where very often it is assumed

The Takens Embedding Theorem basically says that under the assumption that function g is "well behaved," that is, which can be measured continuously without very sudden jumps

is for any practical purpose similar in its properties to the simultaneous behavior of the variables x1ðtÞ, …, xnðtÞ. Unfortunately, the theorem does not say how τ and N should be calculated. So a wide heuristic has been developed to estimate these parameters [33]. In this task, two concepts play an important role: the mutual information function and the correlation integral.

, gtþ<sup>τ</sup>Þln

This concept is closely related to the concept of Boltzmann entropy and the Shannon informa-

The values of the mutual information function can be calculated from the {g1, …, gT} series using appropriate software. The correct value for τ is the first local minimum of the mutual information function [15, 35]. It is well known that the mutual information function is more

The second important step is the calculation of the so-called embedding dimension N. For this, it is necessary to use a concept called integral correlation: consider now the collection of vector

Pðgt

Pðgt

, gtþ<sup>τ</sup><sup>Þ</sup>

<sup>Þ</sup>Pðgtþ<sup>τ</sup><sup>Þ</sup> � �

, giþ<sup>τ</sup>, …, giþðN�1Þ<sup>τ</sup>Þ, i<sup>∈</sup> <sup>N</sup> n o

the system in the macroscopic observable to which we have access.

(as do we) that the times of measurement ti are equally spaced in time.

Ad ¼ ðgi

then, there are τ∈ R<sup>þ</sup> and N ∈ N such that the set of vectors:

The mutual information function can be defined as follows:

<sup>M</sup>ðτÞ ¼ <sup>X</sup> T�τ

sensitive to correlations of data than other correlation measures [36].

t¼1 Pðgt

tion [34]. It is a measure of nonlinear correlation among the values of the series {gi

gðtÞ ¼ θðx1ðtÞ, …, xnðtÞÞ (1)

(2)

(3)

}.

constructed from them:

172 Interpreting Cardiac Electrograms - From Skin to Endocardium

of the set Ad:

$$\mathcal{C}\_{m}(\varepsilon) = \binom{m}{2}^{-1} \sum\_{1 \le i,j \le m} H(\|X\_i - X\_j\| < \varepsilon) \tag{5}$$

where H is the Heaviside function. From this concept, we can define the correlation dimension as

$$d\_{\varepsilon} = \lim\_{\varepsilon \to 0} \lim\_{m \to +\infty} \frac{\ln \mathbb{C}\_m(\varepsilon)}{\ln \varepsilon} \tag{6}$$

Now, the criteria for selecting the correct embedding dimension N are as follows: choose increasing embedding dimension and in each case, calculate the correlation integral. When no changes are observed in the behavior of the correlation integral with respect to increasing the embedding dimension, then a suitable dimension immersion [15, 33] will be found.

One of the advantages of this method is its robustness with respect to the noise of the signal under study. The numerical data obtained through a recording apparatus, in our case a Holter, are the basis of all the further calculations in this chapter. Despite the fine structures of the cardiac dynamics, a critical component of many biological and physiological systems [19], could be lost in conventional Holters [3], the attractor of the system is reconstructed with adequate embedding and correlation dimensions.

The entire process can be seen in Figure 1.

Figure 1. A representation of the entire embedding process. The phenomenon under study has an attractor which only has incomplete information through an observable. From this observable, the immersion process is executed, creating a reconstruction of the attractor.

## 3. Method

#### 3.1. Description of the patients under study

We have studied the biological electrical signal of electrocardiogram assuming that its evolution is governed by a dynamic system. A three-channel, 1-h Holter (Scott Care Corporation. Chroma: Model RZ153C) Monitor was used to monitor 30 patients to obtain data files which consist of 900,000 rows and three columns of comma separated values from 1 h of registration. Holter monitoring was performed on each patient every 24 h for a period of 1 h from admission until discharge. All admission Holter records were performed with the sedated patients, with amines and ventilatory mechanical support in the supine position. The Holter records of the surviving patients also are performed in supine position, without mechanical ventilation or cardiovascular support with amines. The diagnosis of patients was performed from the clinical point of view and confirmed by imaging studies such as computed tomography (CT) of the site topologically involved, such as computed axial tomography of the skull, chest, or abdomen. Some of the patients were surgically operated on one or more occasions. We studied 30 critically ill patients (18 females, 12 male age 54.815.3 years old) of various pathologies, qualified with APACHE II scale 29.26 3.16 on admission to intensive care.



The vital signs on the admission of these patients were as follows: Heart rate, 91.6 17.51; respiratory rate, 21.6 6.43; mean arterial pressure, 71.4 20.8; and temperature of 37.6 1.3.

3. Method

3.1. Description of the patients under study

174 Interpreting Cardiac Electrograms - From Skin to Endocardium

We have studied the biological electrical signal of electrocardiogram assuming that its evolution is governed by a dynamic system. A three-channel, 1-h Holter (Scott Care Corporation. Chroma: Model RZ153C) Monitor was used to monitor 30 patients to obtain data files which consist of 900,000 rows and three columns of comma separated values from 1 h of registration. Holter monitoring was performed on each patient every 24 h for a period of 1 h from admission until discharge. All admission Holter records were performed with the sedated patients, with amines and ventilatory mechanical support in the supine position. The Holter records of the surviving patients also are performed in supine position, without mechanical ventilation or cardiovascular support with amines. The diagnosis of patients was performed from the clinical point of view and confirmed by imaging studies such as computed tomography (CT) of the site topologically involved, such as computed axial tomography of the skull, chest, or abdomen. Some of the patients were surgically operated on one or more occasions. We studied 30 critically ill patients (18 females, 12 male age 54.815.3 years old) of various pathologies,

qualified with APACHE II scale 29.26 3.16 on admission to intensive care.

Seventy percent of the patients were admitted with cardiovascular support based on noradrenaline infusion and sedated with ventilatory mechanical support. The nonlinear time series [33] were obtained upon admission to intensive care in the morning every day, until their discharge for improvement or death. The numerical data obtained from the comma-separated values by means of the Holter are the data subject to analysis of each patient. The description of patients is shown in Table 1.



Table 1. Estimated mortality in critical patients according with APACHE II score.

The images show a CT scan where two images of patient No. 22 are shown of the posterior fossa of a 62-year-old man with hypertension treated with captopril 25 mg every 12 h. IMAGE "A" shows a hypodense zone of the left cerebellar hemisphere, suggesting an ischemic type lesion. IMAGE "B" shows decompressive craniotomy. The patient on day 10 of intensive care was without mechanical ventilation and interacting with the staff of the unit. As mentioned previously in the text, measures of the complexity of their cardiac signal were lower at the time of entry to the intensive care unit, which was recovered. Later, he was discharge from the critical medicine unit.

IMAGE "C" displayed is a cut of the cranial computed tomography of a 56-year-old woman with right occipital arteriovenous malformation. The patient during her stay in intensive care was complicated by acute myocardial infarction, cardiogenic shock, dying 12 days after her admission.

## 4. Results

Let us consider a moving window as shown in Figure 2.

For each moving windows, the correct value of τ and the embedding dimension N are calculated. Note that the last task means calculating the correlation integral for different dimensions of immersion, as shown in Figure 2.

Loss of Complexity of the Cardiac Bioelectrical Signal as an Expression of Patient Outcomes http://dx.doi.org/10.5772/intechopen.70144 177

Figure 2. Correlation integrals for different embedding dimensions.

The images show a CT scan where two images of patient No. 22 are shown of the posterior fossa of a 62-year-old man with hypertension treated with captopril 25 mg every 12 h. IMAGE "A" shows a hypodense zone of the left cerebellar hemisphere, suggesting an ischemic type lesion. IMAGE "B" shows decompressive craniotomy. The patient on day 10 of intensive care was without mechanical ventilation and interacting with the staff of the unit. As mentioned previously in the text, measures of the complexity of their cardiac signal were lower at the time of entry to the intensive care unit, which was recovered. Later, he was discharge from the

Yes/1 35/85% Died

N Age Sex Diagnosis Surgery N APACHE II/% Survived/died

26 60 F Hemorrhage Fisher III. Flegmásia Cerulea Dolens No 35/85% Died 27 42 F Hemorrhage Subarachnoid Fisher IV Yes/1 30/75% Died 28 62 F Fisher IV Brain Hemorrhage No 29/55% Died 29 71 F Cerebral Stroke No 30/75% Died

54.815.3 29.23.16

Table 1. Estimated mortality in critical patients according with APACHE II score.

30 69 F Traumatic Brain Injury—Intraparenchymal Hemorrhage

176 Interpreting Cardiac Electrograms - From Skin to Endocardium

IMAGE "C" displayed is a cut of the cranial computed tomography of a 56-year-old woman with right occipital arteriovenous malformation. The patient during her stay in intensive care was complicated by acute myocardial infarction, cardiogenic shock, dying 12 days after her admission.

For each moving windows, the correct value of τ and the embedding dimension N are calculated. Note that the last task means calculating the correlation integral for different dimensions

critical medicine unit.

4. Results

Let us consider a moving window as shown in Figure 2.

of immersion, as shown in Figure 2.

Once the appropriate dimension of embedding for each mobile window was calculated, we calculated the corresponding correlation dimension. In total, between sick and healthy people we amount 96,508 mobile windows of 5000 points each. We decided to choose the length of the mobile window equal to 5000 because we have observed that for that distance the average value of the mutual information function is practically zero, which indicates that over the time series, values separated by 5000 units of time or more have any correlation.

With these data, we calculate the probability density functions of the corresponding windows for healthy and sick behaviors. The results appear in Figure 3.

Figure 3. Probability density functions of correlation dimensions for windows sick (clearer) behavior an healthy (darker) behavior.

Note that there is a clear separation between the dimensions of correlation for sick and healthy behaviors. Finally, we note that small-dimensional correlation magnitudes are related to less complex behaviors than those with high correlation dimensions. It is important to note that in our database are records of people who were healthy and became in serious condition, as well as people who were sick and recovered later.

## 5. Discussion

The neural regulation of cardiac bioelectric signal has been explored in the frequency domain, showing the complexity of the sympathovagal balance which is tonically and phasically modulated by the interaction of at least three major factors: (a) central neural integration, (b) peripheral inhibitory reflex mechanisms (with negative-feedback characteristics), and (c) peripheral excitatory reflex mechanisms (with positive-feedback characteristics) [29]. Parasympathetic efferent nerve fibers come through the parasympathetic ganglia positioned in the periaortic and epicardial fat pad. Efferent sympathetic innervation arrives from superior, middle, and inferior cervical and the upper four or five thoracic ganglia. Medullary nuclei and reticular formation give both excitatory and inhibitory preganglionic efferent fibers as well as accept afferent fibers. Afferent pathways from baroreceptors and the so-called cardiopulmonary receptors to the brain stem are closing the loop assuring a feedback mechanism. These baroreceptors are located in the wall of aortic arch and great arteries arising from it, and in the carotid sinus. The hypothalamus is considered the most important supramedullary compound that integrates autonomic, somatic, mental, and emotional information via its extensive associations [29].

The applications of entropy on human physiological signals were developed earlier for analyzing the heart rate and beat-to-beat blood pressure. Heart rate is influenced by numerous factors including the liquid metabolism, hormonal and temperature variations, physical activity, circadian rhythms, and autonomic nervous system. As a result, heart rate variations are extremely complex in healthy individuals [37].

The entropy of heart rate was linked to neurological system since the modulation of heart beat was associated with the two components of autonomic nervous system: sympathetic and parasympathetic nerves [38]. Rhythmical oscillations of both heart rate and blood pressure have been indicated to reflect the sympathetic and parasympathetic modulation [39, 40].

The evaluation of the autonomic function provides important information about the alteration of the sympathetic-parasympathetic, altered balance in critically ill patients with or without multiple organ failure. The proven tools are heart rate variability, baroreflex sensitivity, and, with limitations, cardiac chemoreflex sensitivity [38]. The R-R interval functions as a substitute for the sympathovagal balance and represents the net result of all autonomic influences in the sinus node. Both the sympathetic and parasympathetic inputs to the sinus node can be characterized by a tonic level of activity and by the modulation of this activity (e.g., by respiration in the case of the parasympathetic input). Heart rate variability most reliably provides a

measure of the modulation of the sympathetic and parasympathetic inputs to the sinus node, although a more precise way to characterize the sympathovagal balance is unknown [41, 42]. With new, nonlinear methods being evaluated, the risk (with prognostic implications) could be predicted more accurately by providing additional information on autonomic heart rate control in critically ill patients [29].

## 6. Conclusions

Note that there is a clear separation between the dimensions of correlation for sick and healthy behaviors. Finally, we note that small-dimensional correlation magnitudes are related to less complex behaviors than those with high correlation dimensions. It is important to note that in our database are records of people who were healthy and became in serious condition, as well

The neural regulation of cardiac bioelectric signal has been explored in the frequency domain, showing the complexity of the sympathovagal balance which is tonically and phasically modulated by the interaction of at least three major factors: (a) central neural integration, (b) peripheral inhibitory reflex mechanisms (with negative-feedback characteristics), and (c) peripheral excitatory reflex mechanisms (with positive-feedback characteristics) [29]. Parasympathetic efferent nerve fibers come through the parasympathetic ganglia positioned in the periaortic and epicardial fat pad. Efferent sympathetic innervation arrives from superior, middle, and inferior cervical and the upper four or five thoracic ganglia. Medullary nuclei and reticular formation give both excitatory and inhibitory preganglionic efferent fibers as well as accept afferent fibers. Afferent pathways from baroreceptors and the so-called cardiopulmonary receptors to the brain stem are closing the loop assuring a feedback mechanism. These baroreceptors are located in the wall of aortic arch and great arteries arising from it, and in the carotid sinus. The hypothalamus is considered the most important supramedullary compound that integrates autonomic, somatic,

The applications of entropy on human physiological signals were developed earlier for analyzing the heart rate and beat-to-beat blood pressure. Heart rate is influenced by numerous factors including the liquid metabolism, hormonal and temperature variations, physical activity, circadian rhythms, and autonomic nervous system. As a result, heart rate variations are

The entropy of heart rate was linked to neurological system since the modulation of heart beat was associated with the two components of autonomic nervous system: sympathetic and parasympathetic nerves [38]. Rhythmical oscillations of both heart rate and blood pressure have been indicated to reflect the sympathetic and parasympathetic modulation [39, 40].

The evaluation of the autonomic function provides important information about the alteration of the sympathetic-parasympathetic, altered balance in critically ill patients with or without multiple organ failure. The proven tools are heart rate variability, baroreflex sensitivity, and, with limitations, cardiac chemoreflex sensitivity [38]. The R-R interval functions as a substitute for the sympathovagal balance and represents the net result of all autonomic influences in the sinus node. Both the sympathetic and parasympathetic inputs to the sinus node can be characterized by a tonic level of activity and by the modulation of this activity (e.g., by respiration in the case of the parasympathetic input). Heart rate variability most reliably provides a

mental, and emotional information via its extensive associations [29].

extremely complex in healthy individuals [37].

as people who were sick and recovered later.

178 Interpreting Cardiac Electrograms - From Skin to Endocardium

5. Discussion

The results obtained allow us to arrive at the following conclusions: if the time windows studied belong to a person who is sick, the complexity of the time series is low, the dimension of embedding is small (below 6), and the dimension of correlation is low (below 2). For healthy people, the dimension of embedding is higher (above 7), the correlation dimension is also higher (above 2). The transition from a completely healthy to a completely sick behavior and vice versa occurs continuously. If the temporary moving windows corresponding to stages of transit between completely healthy and completely diseased behavior had been included in the analysis, such marked differences in the distributions of the correlation dimensions in each of these cases do not happen suddenly. In general, the heart electrical signal of a healthy person is more complex than that of a sick person. Results similar to these have been obtained by other methods [25]. In the aforementioned work, the authors affirm that the results obtained by them show that the cardiac dynamics of a healthy subject is more complex and random compared to the same for a heart failure patient, whose dynamics is more deterministic [43]. Our results are more general because we have managed to classify temporary windows in "healthy" or "diseased" (even for the same person) in terms of the complexity of the time series from their embedding dimension or their correlation dimension.

Our work opens the possibility of observing with these tools patients, for example, under anesthesia and relaxation in the operating room and critical care unit where patients often have no possibility of spoken communication, opening another way to evaluate and monitor the increase or decrease in the complexity of the cardiac bioelectrical signal, with the future possibility to evaluate the severity of the sick state or the reduction of this, analyzing in real time the behavior of the dynamics of that bioelectrical signal by means of the observation of the loss or recovery of the dimension of that bioelectrical signal, which is getting a numeric value that suggests the severity of the patient.

The implications of this for the early warning of the episodes of dysfunction are clear. Once the embedding dimension or the correlation dimension falls below a preset threshold, we may consider that we are facing an emergency.

Finally, the algorithms must deliver the results in real time in order for early warning to be effective and this is a challenge that must be faced. The ever-increasing speed of digital devices will certainly help this goal. On the other hand, the thresholds for early warnings should be obtained from careful statistical experiments.

## Author details

Pedro Eduardo Alvarado Rubio<sup>1</sup> , Ricardo Mansilla Corona<sup>2</sup> , Lizette Segura Vimbela<sup>1</sup> \*, Alejandro González Mora<sup>1</sup> , Roberto Brugada Molina<sup>3</sup> , Cesar Augusto González López<sup>3</sup> and Laura Yavarik Alvarado Avila<sup>4</sup>

\*Address all correspondence to: merida\_timucuy@yahoo.com.mx

1 Critical Care Unit Hospital Regional Lic., Adolfo López Mateos Social Security Institute for State Workers (ISSSTE), National Autonomous University of Mexico (UNAM), Mexico City, Mexico

2 Center for Interdisciplinary Research in the Sciences and Humanities (CEIICH), National Autonomous University of Mexico (UNAM), Mexico City, Mexico

3 Intensive Care Unit, Regional Hospital Lic, Adolfo López Mateos ISSSTE, Mexico City, Mexico

4 National Autonomous University of Mexico - Faculty of Veterinary Medicine, UNAM, Mexico City, Mexico

#### References


[9] Small M, et al. Automatic identification and recording of cardiac arrhythmia. Computers in Cardiology. 2000;27:355-358

Author details

Mexico

Mexico

Mexico City, Mexico

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Pedro Eduardo Alvarado Rubio<sup>1</sup>

180 Interpreting Cardiac Electrograms - From Skin to Endocardium

Laura Yavarik Alvarado Avila<sup>4</sup>

Alejandro González Mora<sup>1</sup>

, Ricardo Mansilla Corona<sup>2</sup>

1 Critical Care Unit Hospital Regional Lic., Adolfo López Mateos Social Security Institute for State Workers (ISSSTE), National Autonomous University of Mexico (UNAM), Mexico City,

2 Center for Interdisciplinary Research in the Sciences and Humanities (CEIICH), National

3 Intensive Care Unit, Regional Hospital Lic, Adolfo López Mateos ISSSTE, Mexico City,

4 National Autonomous University of Mexico - Faculty of Veterinary Medicine, UNAM,

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, Roberto Brugada Molina<sup>3</sup>

\*Address all correspondence to: merida\_timucuy@yahoo.com.mx

Autonomous University of Mexico (UNAM), Mexico City, Mexico

, Lizette Segura Vimbela<sup>1</sup>

, Cesar Augusto González López<sup>3</sup> and

\*,


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