**5.3.2 Clinical methodology**

796 Biomedical Science, Engineering and Technology

In another study [6], we assessed the capacity of *dσ\*/dtmax* to diagnose heart failure in patients with normal ejection fraction (HFNEF) and with reduced ejection fraction (HFREF).

Heart failure (HF) is a major health care burden: it is the leading cause of hospitalization in persons older than 65 years, and confers an annual mortality of 10%. HF can occur with either normal or reduced LV ejection fraction (EF), depending on different degrees of ventricular remodeling. Both heart failure with normal ejection fraction (HFNEF) and heart failure with reduced ejection fraction (HFREF), also commonly known as diastolic and systolic heart failure respectively, have equally poor prognosis [7]. Medical therapy targets to reduce load, by using vasodilators and/or to alter contractile strength using inotropic agents. Alternatively, some therapies target to affect cardiac remodeling, such as passive cardiac support devices, surgical restoration of LV shape (i.e. the Dor procedure), and stem

Assessment of left ventricular (LV) contractility is important for HF management and evaluation of the heart's response to medical and surgical therapies. Although approaches based on pressure-volume analysis, stress-strain analysis, and *dP/dtmax*-EDV relations [8]can provide assessments of contractile function, these relations generally require invasive data measured at several chamber loads and thus are difficult to apply in routine or long-term clinical studies. This is an important limitation, because heart failure often requires longitudinal evaluation. The ideal measure of contractility should have the following characteristics: sensitivity to inotropic changes, independence from loading conditions as well as heart size and mass, ease of application, and proven usefulness in the clinical setting. LV ejection fraction (EF) is the index overwhelmingly used to assess cardiac function in both clinical and experimental studies, despite the fact that it is highly dependent upon preload and afterload. Based on the National Heart Lung and Blood Institute's Framingham Heart Study, an LVEF50% as cut-off for the presence of normal LVEF has been used in the present

**Usefulness of** *dσ\*/dtmax* **as Contractility Index:** During LV systole, LV wall stress is generated intrinsically by sarcomere contraction and results in the development of extrinsic LV pressure. We have shown earlier that our novel LV contractility index, *dσ\*/dtmax* (maximal change rate of pressure-normalized wall stress) correlates well with LV *dP/dtmax* [3]. We have proposed and validated a new LV contractility index, *dσ\*/dtmax* **,**based on the maximal rate of development of LV wall stress with respect to LV pressure. From the righthand side of equation (8), this index is also seen to represent the maximal flow rate from the

This index is easily measured non-invasively (i.e. from echocardiography or magnetic resonance imaging), is sensitive to LV inotropic changes, and has been demonstrated by us to be preload and afterload independent [3]. Importantly, it is measured at a single steadystate condition, as opposed to the multiple variably loaded cardiac cycles required for many of the other indices. Thus *dσ\*/dtmax*has several qualities that make it a useful LV contractility index. This study [6] has constituted an important step toward establishing the clinical utility of *dσ\*/dtmax* as a tool for diagnosis of HF (both HFNEF and HFREF) as well as for

ventricle (cardiac output) normalized to myocardial volume (or mass).

**5.3 Use of cardiac contractility index** *dσ\*/dtmax* **to diagnose heart failure with normal** 

**ejection fraction (HFNEF) and with reduced ejection fraction (HFREF)** 

**5.3.1 Introduction** 

cells therapies.

study [9].

Patients referred to our echocardiography service with symptoms and signs of heart failure underwent echocardiography and electrocardiography (ECG). Patients with atrial fibrillation, more than mild mitral or aortic valvular regurgitation, and unsatisfactory echocardiographic images were excluded. Clinical signs of heart failure were defined as presence of at least one of the following: raised jugular venous pressure, peripheral pedema, hepatomegaly, basal inspiratory crepitation or gallop rhythm. Patients with LVEF ≥ 50% and LVEF < 50% on echocardiography were classified into HFNEF and HFREF, respectively.

*Echocardiography Study:* With the subject in the left lateral decubitus position, 2D examinations, M-mode measurements and Doppler recordings were performed from the standard left parasternal long- and short-axis as well as the apical four chamber views with simultaneous ECG. The LVEF was assessed by using a 2-dimensional method by an experienced observer; normal LVEF was defined as greater or equal to 50%. Mitral flow velocities were obtained from the apical 4-chamber view using pulsed wave Doppler technique with the sample volume at the tips of the corresponding valve leaflets. LV outflow tract velocity was obtained from apical 5-chamber view, using pulsed wave Doppler technique with the sample volume at the aortic valve level.

The measurements included peak E (peak early trans-mitral filling velocity during early diastole) and A (peak trans-mitral atrial filling velocity during late diastole); wave velocities (cm/s) were measured and E/A ratio was calculated. The E wave deceleration time (DT) was also calculated as the time elapsed between peak E velocity and the point where the extrapolation of the deceleration slope of E velocity crosses the zero baseline measured in milliseconds. LVOT maximal velocity *Vpeak* was measured, and LV mass was calculated by using ASE methods [10, 11]. Myocardial tissue Doppler (TDI) velocities were also estimated at the atrioventricular ring, septal positions, in the apical 4 chamber view. All measurements were averaged over two or three cardiac cycle.

**Calculation of** *dσ\*/dtmax from Echocardiography:* The contractility index was computed by the above equation (8). M-mode echocardiographic measurements of the LV were obtained, and LV mass calculated using standardized methodology [10, 11]. Myocardial volume was calculated by dividing LV mass with myocardial density (assumed to be 1.05 g/ml). Furthermore, two-dimensional apical four- and two-chamber views of the LV were acquired, and end-diastolic and –systolic endocardial contours were manually outlined. The corresponding LVEDV were then automatically determined using biplane Simpson's method.

From Pulse-wave echo-Doppler interrogation of the LV outflow tract (LVOT), we calculated (in the absence of significant mitral regurgitation or aortic valve dysfunction) the maximal LV volume rate (*dV/dtmax*) during ejection: *dV/dtmax*=*Vpeak*\*AVA, where *Vpeak* is the peak velocity sampled at the LVOT and AVA is the aortic valve area (= *πD*2/4, where *D* is the LVOT diameter measured in the two-dimensional parasternal long-axis image of the heart), as shown in Figure 7. Upon substituting values of myocardial volume and *dV/dtmax* into equation (8), we determined the value of *dσ\*/dtmax* .

Fig. 7. Echocardiographic measurement on (a) peak velocity *Vpeak* sampled at the LVOT and (b) LVOT diameter *D* measured in the two-dimensional parasternal long-axis image of the heart. This figure is adopted from Ref. [6].

**Clinical Studies:** The study involved 26 age- and sex-matched subjects in each of the groups of normal controls, HFNEF and HFREF. The characteristics of 78 subjects are shown in Table 6. It summarizes the subjects' age, BSA, LVEF, peak E, peak A, E/A ratio, DT, heart rate (HR), septal E/E', lateral E/E' and our index *dσ\*/dtmax*. Mean *dσ\*/dtmax* was 3.91 s-1 (95%CI, 3.56-4.26 s-1) in control subjects; it was reduced in heart failure, HFNEF, to 2.90 s-1 (95%CI, 2.56-3.24 s-1); and in HFREF, to 1.84 s-1 (95%CI, 1.60-2.07 s-1). There exists no substantially difference between the average values of LVEF, peak E, peak A, E/A ratio, DT, heart rate (HR), septal E/E', and lateral E/E' in HENEF compared to normal controls, except for *dσ\*/dtmax* (2.90 ± 0.84 vs. 3.91 ± 0.87, *p*<0.001). However, there exists significant difference between the average values of LVEF, peak E, peak A, E/A ratio, DT, septal E/E', lateral E/E' and *dσ\*/dtmax* in HEREF compared to HFNEF.

**Discussion on the Usefulness of** *dσ\*/dtmax***:** During LV systole, LV wall stress is generated intrinsically by sarcomere contraction and results in the development of extrinsic LV pressure. LV wall stress is dependent on wall thickness, LV geometry and chamber pressure and sarcomere contraction. Hence, it is rational to quantify the LV wall stress as an intrinsic measure of myocardial contractility. We have proposed and validated a new LV contractility index, *dσ\*/dtmax***,**based on the maximal rate of development of LV wall stress with respect to LV pressure. From the right-hand side of equation (8),this index is also seen to represent the maximal flow rate from the ventricle (cardiac output) normalized to myocardial volume (or mass).

**Assessment of heart failure with normal ejection fraction (HFNEF) and reduced ejection fraction (HFREF):** Heart failure may be viewed as a progressive disorder that is initiated after an "index event" with a resultant loss of functioning cardiac myocytes, thereby preventing the heart from contracting normally. HF can occur with either normal or reduced LV ejection fraction (LVEF), depending on different degree of ventricular remodeling. Perhaps 50% of patients with heart failure have a normal or minimally impaired LVEF (HFNEF) [12, 13].

Although mechanisms for HFNEF remain incompletely understood, diastolic dysfunction is said to play a dominant role: impaired relaxation, increased passive stiffness, raised end-

(a) (b) Fig. 7. Echocardiographic measurement on (a) peak velocity *Vpeak* sampled at the LVOT and (b) LVOT diameter *D* measured in the two-dimensional parasternal long-axis image of the

*D*

**Clinical Studies:** The study involved 26 age- and sex-matched subjects in each of the groups of normal controls, HFNEF and HFREF. The characteristics of 78 subjects are shown in Table 6. It summarizes the subjects' age, BSA, LVEF, peak E, peak A, E/A ratio, DT, heart rate (HR), septal E/E', lateral E/E' and our index *dσ\*/dtmax*. Mean *dσ\*/dtmax* was 3.91 s-1 (95%CI, 3.56-4.26 s-1) in control subjects; it was reduced in heart failure, HFNEF, to 2.90 s-1 (95%CI, 2.56-3.24 s-1); and in HFREF, to 1.84 s-1 (95%CI, 1.60-2.07 s-1). There exists no substantially difference between the average values of LVEF, peak E, peak A, E/A ratio, DT, heart rate (HR), septal E/E', and lateral E/E' in HENEF compared to normal controls, except for *dσ\*/dtmax* (2.90 ± 0.84 vs. 3.91 ± 0.87, *p*<0.001). However, there exists significant difference between the average values of LVEF, peak E, peak A, E/A ratio, DT, septal E/E', lateral

**Discussion on the Usefulness of** *dσ\*/dtmax***:** During LV systole, LV wall stress is generated intrinsically by sarcomere contraction and results in the development of extrinsic LV pressure. LV wall stress is dependent on wall thickness, LV geometry and chamber pressure and sarcomere contraction. Hence, it is rational to quantify the LV wall stress as an intrinsic measure of myocardial contractility. We have proposed and validated a new LV contractility index, *dσ\*/dtmax***,**based on the maximal rate of development of LV wall stress with respect to LV pressure. From the right-hand side of equation (8),this index is also seen to represent the maximal flow rate from the ventricle (cardiac output) normalized to myocardial volume (or

**Assessment of heart failure with normal ejection fraction (HFNEF) and reduced ejection fraction (HFREF):** Heart failure may be viewed as a progressive disorder that is initiated after an "index event" with a resultant loss of functioning cardiac myocytes, thereby preventing the heart from contracting normally. HF can occur with either normal or reduced LV ejection fraction (LVEF), depending on different degree of ventricular remodeling. Perhaps 50% of patients with heart failure have a normal or minimally impaired LVEF

Although mechanisms for HFNEF remain incompletely understood, diastolic dysfunction is said to play a dominant role: impaired relaxation, increased passive stiffness, raised end-

heart. This figure is adopted from Ref. [6].

*Vpeak*

E/E' and *dσ\*/dtmax* in HEREF compared to HFNEF.

mass).

(HFNEF) [12, 13].

diastolic pressure (EDP) [14]. The diagnostic standard for HFNEF is cardiac catheterization, which demonstrates increased EDP. However, a more practical noninvasive alternative is echocardiography. Our study has shown that E/A ratio (1.26 ± 0.90 vs. 0.96 ± 0.38, p<0.05) and DT (157 ± 41 ms vs. 214 ± 47 ms, p<0.05) are significantly different between HFREF and normal controls, and not so between HFNEF and normal controls (Table 6).

Our contractility index, of change rate of normalized wall stress index *dσ\*/dtmax*, is dependent on lumen and wall volume of LV chamber and represents an integrated assessment of LV systolic performance [3], based on our findings relating *dσ\*/dtmax* with HFNEF and HFREF [6]. In this study, as shown in Table 7, we find that there exists significant difference in *dV/dtmax* between HFREF and HFNEF (233±48 ml/s vs. 355±65 ml/s, *p*<0.05), while there exists no difference between HFNEF and normal controls (355±65 ml/s vs. 353±80 ml/s, *NS*). Similarly, there exists significant difference in LV mass between normal controls and HFNEF (147±41 g vs. 202±47 g, *p*<0.05), while there is no difference between HFREF and HFNEF (213±60 g vs. 202±47 g, *NS*).

Our *dσ\*/dtmax* index, using *dV/dtmax* normalized with LV mass, can clearly differentiate HFREF, HFNEF and normal controls (p<0.05) (Table 7). The average value of *dσ\*/dtmax* decreases in HFNEF and HFREF, in relation to normal controls. The mean value of *dσ\*/dtmax* was found to be 3.91 s-1 (95%CI, 3.56-4.26 s-1) in control subjects; the index was reduced in heart failure patients: in HFNEF, to 2.90 s-1 (95%CI, 2.56-3.24 s-1) and in HFREF, to 1.84 s-1 (95%CI, 1.60-2.07 s-1). This suggests that poor systolic function of LV is associated with lower *dσ\*/dtmax* values. Therefore, it can again be concluded that *dσ\*/dtmax* is an appropriate index for representing assessment of LV contractile function in heart failure with/without preserved LV ejection fraction.


A, mitral atrial flow velocity on echo-Doppler; BSA, body surface area; DT, mitral E deceleration time; E, mitral early velocity; E', septal mitral annular myocardial velocity on tissue Doppler imaging; HR, heart rate, LVEF, let ventricular ejection fraction.

The values are expressed as mean ± SD. § and \* denote statistically significant difference of HF compared to controls, HFREF compared to HFNEF patients, respectively (Bonferroni pairwise test, *p* value <0.05)

Table 6. Patients characteristics and echocardiographic measurements in Group 1 (Controls), Group 2 (HFNEF) and Group 3 (HFREF). This table is related to our work in Ref [6].


§ and \* denote statistically significant difference of HF compared to controls, HFREF compared to HFNEF patients, respectively

Table 7. Comparison of the maximal flow rate *dV/dtmax*, *Vpeak*, LV mass, and *dσ\*/dtmax* in Group 1 (Controls), Group 2 (HFNEF) and Group 3 (HFREF). This table is related to our work in Ref [6].

## **6. Coronary Arterial Bypass Grafting (CABG) to salvage ischemic myocardial segments**

As is well known, coronary artery bypass graft (CABG) surgery has been the standard treatment for serious blockages in the coronary arteries and for re-perfusing myocardial ischemic segments to restore them to normal contractile state. During the surgery, one end of the graft is sewn to the aorta (or its subsidiary branches) to create proximal anastomosis, while the other end is attached to coronary artery below the area of blockage to create distal anastomosis. In this way, the oxygen-rich blood is taken directly from the aorta, bypasses the obstruction, and flows through the graft to perfuse and nourish the heart muscle. The most commonly used graft is the saphenous vein. Besides this vein graft, some arterial conduits (such as internal mammary artery, gastroepiploic artery and radial artery etc), and synthetic veins (such as Dacron, Teflon and Polytetrafluoroethylene-PTFE veins) are also suitable for CABG.

Although the number of bypass operations keeps increasing, the CABG has not been without complications. Approximately 15% to 20% vein grafts occlude in the first year, and 22.5% to 30% occlude within the first 2 years. At 10 years, approximately 60% of vein grafts are patent; only 50% of these vein grafts remain free of significant stenosis. In order to intensively investigate the coronary arterial stenosis symptom, numerous research works have been carried out. One direction of these studies is to investigate the pathogenic mechanism of bypass graft failure. In this regard, vascular injury and biomechanical factors (such as wall shear stress related factors, compliance mismatch, etc.) are believed to stimulate cellular responses for pathological changes. In particular, hemodynamic flow patterns of CABG have considerable relevance to the causes and sites of pathogenesis. Hence, we have carried out simulation of hemodynamic flow patterns in CABG models, to look into the hemodynamic causes and mechanisms of lesions in coronary bypass grafts.

The flow characteristics and hemodynamic parameters distributions in a complete CABG model (as shown in Figure 8) have been investigated computationally by us [15]. It is found that disturbed flow (flow separation and reattachment, vortical and secondary flows) patterns occur at both proximal and distal anastomoses, especially at the distal anastomosis. In addition, regions of high-OSI & low-WSS and low-OSI & high-WSS are found in the proximal and distal anastomoses, especially at the toe and heel regions of distal anastomosis. These regions are suspected to initiate the atherosclerotic lesions and are further worsened by the increasing permeability of low-density lipoprotein as indicated by high WSSG. The comparisons of segmental average of HPs (in the Table of Figure 8) further

*dV/dtmax* (ml/s) 353 (320, 385) 355 (329, 381) 233 (213, 252)§\* *Vpeak*(cm/s) 106 (98, 115) 112 (104, 119) 73 (68, 78) §\* LV mass (g) 147 (131, 164) 202 (183, 221)§ 213 (189, 297)§ *dσ\*/dtmax* (s-1) 3.91 (3.56, 4.26) 2.90 (2.56, 3.24)§\* 1.84 (1.60, 2.07)§\* § and \* denote statistically significant difference of HF compared to controls, HFREF compared to

Table 7. Comparison of the maximal flow rate *dV/dtmax*, *Vpeak*, LV mass, and *dσ\*/dtmax* in Group 1 (Controls), Group 2 (HFNEF) and Group 3 (HFREF). This table is related to our

**6. Coronary Arterial Bypass Grafting (CABG) to salvage ischemic myocardial** 

As is well known, coronary artery bypass graft (CABG) surgery has been the standard treatment for serious blockages in the coronary arteries and for re-perfusing myocardial ischemic segments to restore them to normal contractile state. During the surgery, one end of the graft is sewn to the aorta (or its subsidiary branches) to create proximal anastomosis, while the other end is attached to coronary artery below the area of blockage to create distal anastomosis. In this way, the oxygen-rich blood is taken directly from the aorta, bypasses the obstruction, and flows through the graft to perfuse and nourish the heart muscle. The most commonly used graft is the saphenous vein. Besides this vein graft, some arterial conduits (such as internal mammary artery, gastroepiploic artery and radial artery etc), and synthetic veins (such as Dacron, Teflon and Polytetrafluoroethylene-PTFE veins) are also

Although the number of bypass operations keeps increasing, the CABG has not been without complications. Approximately 15% to 20% vein grafts occlude in the first year, and 22.5% to 30% occlude within the first 2 years. At 10 years, approximately 60% of vein grafts are patent; only 50% of these vein grafts remain free of significant stenosis. In order to intensively investigate the coronary arterial stenosis symptom, numerous research works have been carried out. One direction of these studies is to investigate the pathogenic mechanism of bypass graft failure. In this regard, vascular injury and biomechanical factors (such as wall shear stress related factors, compliance mismatch, etc.) are believed to stimulate cellular responses for pathological changes. In particular, hemodynamic flow patterns of CABG have considerable relevance to the causes and sites of pathogenesis. Hence, we have carried out simulation of hemodynamic flow patterns in CABG models, to look into the hemodynamic causes and mechanisms of lesions in coronary bypass grafts. The flow characteristics and hemodynamic parameters distributions in a complete CABG model (as shown in Figure 8) have been investigated computationally by us [15]. It is found that disturbed flow (flow separation and reattachment, vortical and secondary flows) patterns occur at both proximal and distal anastomoses, especially at the distal anastomosis. In addition, regions of high-OSI & low-WSS and low-OSI & high-WSS are found in the proximal and distal anastomoses, especially at the toe and heel regions of distal anastomosis. These regions are suspected to initiate the atherosclerotic lesions and are further worsened by the increasing permeability of low-density lipoprotein as indicated by high WSSG. The comparisons of segmental average of HPs (in the Table of Figure 8) further

HFNEF patients, respectively

work in Ref [6].

**segments** 

suitable for CABG.

Controls (95% CI) HFNEF (95% CI) HFREF (95% CI)

imply that intimal hyperplasia is more prone to form in the distal anastomosis than the proximal anastomosis, especially along the suture line at the toe and heel of distal anastomosis, which was in line with the in-vivo observations.

We then investigated the fluid dynamics of blood flow in two complete models of CABG for the right and left coronary artery separately, as shown in Figure 9 [16]. The results reveal that blood flow through the coronary artery bypass graft primarily occurs only during the diastolic phase of the cardiac cycle, which is in agreement with the physiological observation. However, at the onset of ejection, some backflow from the coronary artery into the bypass graft is found for the CABG to left coronary artery, which is absent for the right coronary artery. This reversal of flow during systole can be explained by the predominant intra-cardiac course of the left coronary artery system. As the same time, this study also found a low WSS region near the heel and a high WSS in the toe region of the anastomosis domain.

Fig. 8. (a) The configuration to mimic complete CABG; (b) sketch maps of areas investigated for segmental averages of hemodynamic parameters (HPs) in proximal and distal anastomoses;


Fig. 8. (c) the segmental averages of HPs at these locations. This figure is adopted from our work in Ref 15 (Zhang et al., 2008).

Fig. 9. Geometry (plane view) and dimensions (in mm) of the bypass models of: (a) The aorta-right coronary artery bypass model; (b) The aorta-left coronary artery bypass model (PSCA-Perfused Segment of the Coronary Artery; OSCA-Occluded Segment of the Coronary Artery; T-Toe; H-Heel). This figure is adopted from our work in Ref 16: (Sankaranarayanan et al., 2005).

(c) Fig. 8. (c) the segmental averages of HPs at these locations. This figure is adopted from our

(a)

(b) Fig. 9. Geometry (plane view) and dimensions (in mm) of the bypass models of: (a) The aorta-right coronary artery bypass model; (b) The aorta-left coronary artery bypass model (PSCA-Perfused Segment of the Coronary Artery; OSCA-Occluded Segment of the Coronary Artery; T-Toe; H-Heel). This figure is adopted from our work in Ref 16: (Sankaranarayanan

Proximal anastomosis

Distal anastomosis

et al., 2005).

work in Ref 15 (Zhang et al., 2008).

Name Labels in maps Area (mm2) <WSS> (Pa) <WSSG> <OSI>

heel A 4.23 4.48 11.88 0.41 toe B 1.59 8.58 20.24 0.36 part3 C 9.46 3.17 3.24 0.49 part4 D 25.50 6.56 14.25 0.07 suture\_line E 12.00 5.06 9.01 0.29

heel F 0.55 2.92 12.75 0.24 toe G 0.55 **28.04 147.17 0.02**  part3 H 9.70 **14.63 64.24 0.07**  part4 I 6.81 0.85 3.59 0.22 suture\_line J 3.18 **9.20 41.43 0.11** 

CABG performance is based on flow characteristics at both the proximal and distal anastomoses. So then, let us summarise the optimal geometrical parameters for proximal and distal anastomoses. For proximal anastomosis, a detailed study, on the effect of three grafting angles (viz. 45° forward facing, 45° backward facing, and 90°), has been carried out by Chua et al. [17]. The results show a flow separation region along the graft inner wall immediately after the heel at peak flow phase, which decreases in size with the grafting angle shifting from 45° forward facing to 45° backward facing. The existence of nearly fixed stagnating location, flow separation, vortex, high-WSS-low-OSI, low-WSS-high-OSI, and high WSSG is suspected to lead to graft stenosis. Among these three models, the 45° backward-facing graft is found to have the lowest variation range of time-averaged WSS and the lowest segmental average of WSSG, as shown in Figure 10; these parameters are then recommended for obtaining higher expected patency rates in bypass operations.

Fig. 10. Contours of HPs: (a) time-averaged WSS; (b) time-averaged WSSG; and (c) OSI, on the surfaces of 45° forward-facing, 90°, and 45° backward-facing models ('H' means the region has high value, 'L' means the region has low values. This figure is adopted from our work in Ref 17 (Chua et al., 2005b).

At the distal anastomosis junction of CABG, the important geometrical parameters for smooth flow are the angle (α) and the diameter ratio (φ) between the graft and host artery. The hemodynamics associated with these parametric were investigated by Xiong and Chong [18], over a range of φ (1:1, 1.5:1 and 2:1) and α (15°, 30°, 45° and 60°) in physiological coronary flow conditions. It is found that increasing φ from 1:1 to 1.5:1 almost eliminates both low WSS and high OSI at the toe. However, further increasing φ to 2:1 causes elevated OSI for most of the host artery segment in the anastomotic region and in almost the entire graft. On the other hand, varying α is also found to change certain aspects of hemodynamics, although less than those changes related with different values of φ. A smaller value of α is found to be associated with a higher OSI in the anastomotic region, whereas a larger α causes higher WSSG on the artery floor. Therefore, it is suggested that for distal coronary anastomosis (with a 20:80 proximal to distal flow division ratio maintained in the host artery), the geometry associated with φ = 1.5 and α = 30–45° is favorable for enhancing long-term performance.

## **7. Surgical Ventricular Restoration (SVR), combined with CABG, restores LV shape and improves cardiac contractility**

### **7.1 Introduction**

Ischemic heart disease is one of the most widely spread, progressive and prognostically unfavorable diseases of the cardiovascular system. In ischemic dilated cardiomyopathy (IDC) patients, the remodeling process involves a lesser systolic LV curved shape, increase of peak wall stress, and decrease of contractile functional index, compared with normal subjects. Surgical ventricular restoration (SVR) is performed in chronic ischemic heart disease patients with large non-aneurysmal or aneurysmal post-myocardial infarction zones. It involves operative methods, that reduce LV volume and 'restore' ventricular ellipsoidal shape, by exclusion of anteroseptal, apical, and anterolateral LV scarred segments by means of intra-cardiac patch or direct closure.

For patients in heart failure (HF) resulting from serious myocardial diseases of ischemic dilated cardiomyopathy and myocardial infarction (MI), surgical ventricular restoration (SVR), designed to restore the LV to its normal shape (reversal of LV remodeling), is performed usually in conjunction with coronary artery bypass grafting (CABG). In our study [19], in 40 ischemic dilated cardiomyopathy (IDC) patients who underwent SVR and CABG, there was found to be: (i) decrease in end-diastolic volume from 318 ± 63 ml to 206 ± 59 ml (p<0.01) and in end-systolic volume from 228 ± 58 ml to 133 ± 61 ml (p<0.01), (ii) increase in LV ejection fraction from 26 ± 7% to 31 ± 8% (p<0.01), (iii) decrease in LV mass (from 204 ± 49 g to 187 ± 53 g, p<0.01), (iv) decrease in peak normalized wall stress (PNWS) (from 4.30 ± 0.95 to 3.31 ± 0.75, p<0.01) , (v) increase in end-systolic sphericity index SI (from 0.57 ± 0.094 to 0.67 ± 0.13, p<0.01), (vi) increased value of shape (S) index (from 0.44 ± 0.085 to 0.54 ± 0.089, p<0.01) during end-systole indicating that LV became more spherical after SVR, and most importantly (vii) improvement in LV contractility index *d*σ*\*/dtmax* (from 2.69 ± 0.74 s-1 to 3.23 ± 0.73 s-1, p<0.01).

Thus, in IDC patients, surgical ventricular restoration (in combination with CABG) aiming to reverse LV remodeling, has shown to (i) improve ventricular function and decrease wall stress, along with making a more curved apex, and (ii) improve cardiac contractility. It is not the LV shape alone that defines LV contractility. Rather, a complex interaction of the rate of change of shape factor (*dS/dtmax*) along with LV maximal flow rate and LV mass may explain the improvement in LV contractility.

## **7.2 Clinical study**

804 Biomedical Science, Engineering and Technology

At the distal anastomosis junction of CABG, the important geometrical parameters for smooth flow are the angle (α) and the diameter ratio (φ) between the graft and host artery. The hemodynamics associated with these parametric were investigated by Xiong and Chong [18], over a range of φ (1:1, 1.5:1 and 2:1) and α (15°, 30°, 45° and 60°) in physiological coronary flow conditions. It is found that increasing φ from 1:1 to 1.5:1 almost eliminates both low WSS and high OSI at the toe. However, further increasing φ to 2:1 causes elevated OSI for most of the host artery segment in the anastomotic region and in almost the entire graft. On the other hand, varying α is also found to change certain aspects of hemodynamics, although less than those changes related with different values of φ. A smaller value of α is found to be associated with a higher OSI in the anastomotic region, whereas a larger α causes higher WSSG on the artery floor. Therefore, it is suggested that for distal coronary anastomosis (with a 20:80 proximal to distal flow division ratio maintained in the host artery), the geometry associated with φ = 1.5 and α = 30–45° is favorable for

**7. Surgical Ventricular Restoration (SVR), combined with CABG, restores LV** 

Ischemic heart disease is one of the most widely spread, progressive and prognostically unfavorable diseases of the cardiovascular system. In ischemic dilated cardiomyopathy (IDC) patients, the remodeling process involves a lesser systolic LV curved shape, increase of peak wall stress, and decrease of contractile functional index, compared with normal subjects. Surgical ventricular restoration (SVR) is performed in chronic ischemic heart disease patients with large non-aneurysmal or aneurysmal post-myocardial infarction zones. It involves operative methods, that reduce LV volume and 'restore' ventricular ellipsoidal shape, by exclusion of anteroseptal, apical, and anterolateral LV scarred

For patients in heart failure (HF) resulting from serious myocardial diseases of ischemic dilated cardiomyopathy and myocardial infarction (MI), surgical ventricular restoration (SVR), designed to restore the LV to its normal shape (reversal of LV remodeling), is performed usually in conjunction with coronary artery bypass grafting (CABG). In our study [19], in 40 ischemic dilated cardiomyopathy (IDC) patients who underwent SVR and CABG, there was found to be: (i) decrease in end-diastolic volume from 318 ± 63 ml to 206 ± 59 ml (p<0.01) and in end-systolic volume from 228 ± 58 ml to 133 ± 61 ml (p<0.01), (ii) increase in LV ejection fraction from 26 ± 7% to 31 ± 8% (p<0.01), (iii) decrease in LV mass (from 204 ± 49 g to 187 ± 53 g, p<0.01), (iv) decrease in peak normalized wall stress (PNWS) (from 4.30 ± 0.95 to 3.31 ± 0.75, p<0.01) , (v) increase in end-systolic sphericity index SI (from 0.57 ± 0.094 to 0.67 ± 0.13, p<0.01), (vi) increased value of shape (S) index (from 0.44 ± 0.085 to 0.54 ± 0.089, p<0.01) during end-systole indicating that LV became more spherical after

Thus, in IDC patients, surgical ventricular restoration (in combination with CABG) aiming to reverse LV remodeling, has shown to (i) improve ventricular function and decrease wall stress, along with making a more curved apex, and (ii) improve cardiac contractility. It is not the LV shape alone that defines LV contractility. Rather, a complex interaction of the rate of change of shape factor (*dS/dtmax*) along with LV maximal flow rate and LV mass may

σ

*\*/dtmax* (from 2.69

enhancing long-term performance.

± 0.74 s-1 to 3.23 ± 0.73 s-1, p<0.01).

explain the improvement in LV contractility.

**7.1 Introduction** 

**shape and improves cardiac contractility** 

segments by means of intra-cardiac patch or direct closure.

SVR, and most importantly (vii) improvement in LV contractility index *d*

The study was carried to retrospectively evaluate (with cardiac MRI) the changes on systolic function and LV wall stress, the relationships between LV geometry (shape) and dimensions and systolic function after SVR performed in chronic ischemic heart disease patients with aneurismal postmyocardial infarction zones. The study consisted of 40 patients with ischemic dilated cardiomyopathy who had SVR; the age of the patients averaged 69 years (range, 52-84 years). MRI scans were performed 2 weeks before surgery (pre-surgery) and 1 week after the surgery; the details of the MRI procedure are reported in our earlier work [19].

Cardiac magnetic resonance imaging (MRI) provides the means to study heart structure and function: the ventricular systolic and diastolic volumes (and hence ejection fraction) are easily assessed reproducibly and accurately; the regional wall motion of the asynergy area and the remote myocardium can be measured by several quantitative means, including with myocardial tagging; the presence or absence of nonviable, irreversible scar can be detected with gadolinium-based interstitial contrast agents.

**Data Analysis, 3-dimensional modeling of LV:**For analysis, the images were displayed on a computer monitor in a cine-loop mode using CMRtools, to reconstruct the 3-dimensional model of the left ventricle (LV). The LV epicardial and endocardial borders were outlined, and all the frames were delineated to produce a volume curve from end-diastolic and endsystolic phases. These measurements were used to determine the end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV), ejection fraction (EF), and LV mass.

*Ellipsoidal Shape factor, Eccentricity (E) and sphericity index and normalized wall stress*: The LV is modeled as a prolate spheroid, truncated 50% of the distance from equator to base, as shown in figure 11 [20, 21]. Then, the left ventricular cavity wall volume is calculated, from the endocardial anterior-posterior (AP) and base-apex (BA) lengths [20], as:

$$V\_m = \frac{9}{8} \left[ \left( \frac{BA}{1.5} + h \right) \left( \frac{AP}{2} + h \right)^2 - \left( \frac{BA}{1.5} \right) \left( \frac{AP}{2} \right)^2 \right] \tag{9}$$

wherein the BA and AP dimensions are identified in figure 12. The mean wall thickness (h) is calculated at each cavity volume, from the above equation, by assuming that myocardial wall volume (*Vm* ) remains constant throughout the cardiac cycle. The endocardial minor axis dimension (SA) and major axis dimension (LA), shape factor (S), eccentricity (E) and sphericity index (SI) were then calculated as follows (refer figures 11 and 12):

$$\text{ASA} = \text{AP } / 2 \text{; LA} = \text{BA } / 1.5 \text{, S} = \text{SA } / \text{LA} \text{, } \to \left(\frac{\text{BA}^2 - \text{AP}^2}{\text{BA}^2}\right)^{0.5}, \text{ SI} = \text{AP } / \text{BP} \tag{10}$$

wherein BA (the LV long axis) is defined as the longest distance from the apex to the base of the LV (defined as the mitral annular plane), as measured on the four-chamber cine MRI view of the heart; AP is defined as the widest LV minor axis **(**Figure 12). A small value of SI implies an ellipsoid LV, whereas values approaching "1" suggest a more spherical LV. The SI at end-diastole (SIed) and end-systole (SIes), the % shortening of the long and minor axes, as well as the difference between end-diastolic and end-systolic values of SI, (SIed - SIes) were calculated and are tabulated in Table 10 below.

The time-varying circumferential normalized wall stress, NWS(t), is calculated from the instantaneous measurements of LV dimensions and wall thickness, by treating the LV as a prolate spheroid model truncated 50% of the distance from equator to base **[**20, 21]

$$NPVS(t) = \frac{AP(t)}{2h(t)} \left| 1 - \frac{\frac{9AP(t)}{32h(t)}(SI)^2}{\frac{AP(t)}{h(t)} + 1} \right| \tag{11}$$

The LV wall thickness, h(t), is calculated from the following formula (based on the above equation 9), by assuming that the myocardial wall volume (*Vm*) remains constant throughout the cardiac cycle:

Fig. 11. LV model geometry, showing the major and minor radii of the inner surface of the LV (LA & SA) and the wall-thickness (h).

**Cardicac Contractility** *dσ\*/dtmax***:**In order to compute the contractility index by employing the above equation (8), a 6-order polynomial function to curve-fit the volumes-time data to calculate the volume rate (*dV/dt*) by differentiating it. Then the contractility index *dσ\*/dtmax* is calculated as:

$$d\sigma^\* \left/ dt\_{\text{max}} = \left| \frac{d\left(\sigma\_{\theta} \,' \, P\right)}{dt} \right|\_{\text{max}} = \frac{3}{2V\_m} \left| \left(\frac{dV}{dt}\right) \right|\_{\text{max}}$$

where*Vm* is myocardial volume at the end-diastolic phase.

The time-varying circumferential normalized wall stress, NWS(t), is calculated from the instantaneous measurements of LV dimensions and wall thickness, by treating the LV as a

( ) 32 ( ) () 1 2 () ( ) <sup>1</sup>

The LV wall thickness, h(t), is calculated from the following formula (based on the above equation 9), by assuming that the myocardial wall volume (*Vm*) remains constant

> <sup>9</sup> () () 8 1.5 <sup>2</sup> 1.5 2 *<sup>m</sup> BA t AP t BA t AP t*

Fig. 11. LV model geometry, showing the major and minor radii of the inner surface of the

**Cardicac Contractility** *dσ\*/dtmax***:**In order to compute the contractility index by employing the above equation (8), a 6-order polynomial function to curve-fit the volumes-time data to calculate the volume rate (*dV/dt*) by differentiating it. Then the contractility index *dσ\*/dtmax* is

*max* <sup>2</sup> *<sup>m</sup> max*

⎝ ⎠

*dt V dt*

⎛ ⎞ = = ⎜ ⎟

/ <sup>3</sup> \* /

σθ

*d P dV d dt*

⎡ ⎤ <sup>⎛</sup> ⎞⎛ <sup>⎞</sup> ⎛ ⎞⎛ ⎞ ⎢ ⎥ <sup>⎜</sup> + + =+ ⎟⎜ <sup>⎟</sup> ⎜ ⎟⎜ ⎟ ⎢ ⎥ <sup>⎜</sup> ⎟⎜ <sup>⎟</sup> <sup>⎝</sup> ⎠⎝ <sup>⎠</sup> ⎝ ⎠⎝ ⎠ ⎣ ⎦

*ht ht V t*

*h t AP t*

= − <sup>⎢</sup> <sup>⎥</sup> <sup>⎢</sup> <sup>⎥</sup> <sup>+</sup> <sup>⎢</sup> <sup>⎥</sup> <sup>⎣</sup> <sup>⎦</sup>

( ) ( ) ( ) ( ) ( ) 2 2

( ) 9 () <sup>2</sup>

(11)

(12)

*AP t SI*

<sup>⎡</sup> <sup>⎤</sup> <sup>⎢</sup> <sup>⎥</sup>

( )

*h t*

prolate spheroid model truncated 50% of the distance from equator to base **[**20, 21]

*AP t h t NWS t*

throughout the cardiac cycle:

LV (LA & SA) and the wall-thickness (h).

( ) max

σ

where*Vm* is myocardial volume at the end-diastolic phase.

calculated as:

(a) Pre-SVR

(b) Post-SVR

Fig. 12. Short-axis (panels A and C) and long-axis (panels B and D) magnetic resonance images of patients, before (panels A and B) and after (panels C and D) surgical ventricular restoration (SVR). Multiple short-axis cines from the apex to the base of the heart (or orientated axial) and long-axis cines are used to quantify LV function. Anterior-posterior (AP) (panels A and C) and base-apex (BA) (panels B and D) were measured from 2-D CMR imaging before (panels A and B) and after (panels C and D) SVR during cardiac cycle. The shape factor S, eccentricity index and sphericity index (SI) were calculated from Equation (6). It can be noted that the long-axis decreased more dramatically compared with the shortaxis dimension, thereby producing a more spherical ventricle. This figure is adopted from our work presented in Ref 19.
