**5. Diabetic autonomic neuropathy diagnosis from HRV power spectrum plots**

The RR interval files are processed to get HRV and HRVPS [Desai, K.D et al., 2011]. The sampling frequency used to get HRV form RR file is 2Hz. The power spectrum plots depict power in (BPM)2 versus Frequency (in Hertz). The auto regression statistics gives display of the following parameters:

Power under Low frequency range: frequency range from 000 to 0.04Hz

Power under Mid frequency range: frequency range from 0.04 to 0.15Hz

Power under High frequency range: frequency range from 0.15 to 0.40Hz

Sympatho/Vagal balance ratio: ratio of mid to high frequency powers

The Sympatho-Vagal ratio is found in the different frequency characteristics of the parasympathetic and sympathetic influences on heart rate. The HRVPS plots (for the supine, standing and deep breathing modes) are plotted with time-scale up to 150 seconds and heart rate scale in the range of 40 bpm to 140 bpm.

Fig. 10. HRVPS plots of a normal subject in supine, standing and deep breathing modes. The power statistics on the right side show the power in low, medium and high frequency bands. There is an increase in the mid frequency power in standing position and in high frequency power in deep breathing mode.

**5. Diabetic autonomic neuropathy diagnosis from HRV power spectrum plots**  The RR interval files are processed to get HRV and HRVPS [Desai, K.D et al., 2011]. The sampling frequency used to get HRV form RR file is 2Hz. The power spectrum plots depict power in (BPM)2 versus Frequency (in Hertz). The auto regression statistics gives display of

The Sympatho-Vagal ratio is found in the different frequency characteristics of the parasympathetic and sympathetic influences on heart rate. The HRVPS plots (for the supine, standing and deep breathing modes) are plotted with time-scale up to 150 seconds and heart

Fig. 10. HRVPS plots of a normal subject in supine, standing and deep breathing modes. The power statistics on the right side show the power in low, medium and high frequency bands. There is an increase in the mid frequency power in standing position and in high

Power under Low frequency range: frequency range from 000 to 0.04Hz Power under Mid frequency range: frequency range from 0.04 to 0.15Hz Power under High frequency range: frequency range from 0.15 to 0.40Hz Sympatho/Vagal balance ratio: ratio of mid to high frequency powers

the following parameters:

rate scale in the range of 40 bpm to 140 bpm.

frequency power in deep breathing mode.

Figure 10 displays the HRVPS of a typical normal subject in supine, standing and deep breathing modes. In this figure, the power statistics show the power in low, medium and high frequency bands. It can be noted that there is an increase in the mid-frequency power in standing position and in the high-frequency power in deep breathing mode. Figure 11 depicts the HRVPS plot of a typical diabetic subject in supine, standing and deep-breathing modes. Now, it can be seen that there is a decrease in mid-frequency power and in highfrequency power in deep-breathing mode compared to corresponding power levels of a normal subject (in Figure 10) [Desai, K.D et al., 2011].

Fig. 11. HRVPS plots of a diabetic subject in supine, standing and deep breathing modes. The power statistics on the right side show the power in low, medium and high frequency bands. There is a decrease in the mid frequency power in standing position and in high frequency power in deep breathing mode compared to corresponding power levels of normal subject as shown in Fig 10a[Desai, K.D et al., 2011].

### **5.1 Diagnostic indices (based on HRVPS)**

The analysis of HRV power spectra is commonly focused on the power in different frequency bands. In particular, the power in the high-frequency range reflects the fast parasympathetic never activity [Fallen et al., 1985], and the power in the mid-frequency range reflects both parasympathetic and sympathetic never activity [Akselrod, S., et al., 1981].

The ratio of the mid-frequency range power to the high-frequency range power is sometimes used as a relative index of the sympatho/vagal balance [Bianchi et al., 1990]. The high frequency range power ratio between supine and standing position is used as a parasympathetic index [Fallen et al., 1985]. The same ratio is used to study sympathetic function in standing position in the mid frequency range [Fallen et al., 1985]. Sympathetic vasomotor nerve function is quantified by the baro receptor oscillation frequency (i.e., the mid-peak frequency) in the HRVPS [Kamath et al., 1987].

In our study, autonomic function indices are defined in terms of spectral power indices and HRV period (or frequency) shift indices. The mid and high-frequency ranges are considered for defining indices. The diagnostic indices are based on parameters measured from the HRVPS. The values of diagnostic indices for the three groups of subjects have shown significant difference and can provide rational basis for selecting prognostic therapy before a diabetic patient develops cardiac arrhythmic complications.

The **diagnosis indices** are defined as follows:

$$\mathbf{I}\_1 = \text{Relative synapticathetic} - \text{to} - \text{vagal balance index} = \mathbf{P}\_2 / \text{P3} \,\tag{22}$$

where

(P2)=area under HRVPS spectral plot between 0.04 Hz and 0.15 Hz (P3)=area under HRVPS spectral plot between 0.15 and 0.4 Hz.

$$\mathbf{I}\_2 = \text{Orthosstatic Stress Index} \tag{2} \\ \text{(P2sta - P2sup)} / \text{P2sup} \tag{23}$$

where

(P2)=area under HRVPS spectral plot between 0.04 Hz and 0.15 Hz, and subscripts 'sta' and 'sup' refer to standing supine positions.

$$\mathbf{I}\_3 = \text{Symbolo} - \text{Vagal Integrity Index} = \sum (\text{Hirmax} - \text{Hrimin}) / \text{n} \,\tag{24}$$

where

HRmax = Local maximum heart rate (beats per minute) during one breathing cycle.

HRmin = Local minimum heart rate (beats per minute) prior to local maximum in the same breathing cycle.

n=number of breathing cycles.

4std ( ) ( ) std 2 I Sympathetic HRV – Spectral Frequency Shift Index standing F2 0.1 /0.1, where F Frequency of the Baroreceptor reflex peak = = − <sup>=</sup> . (25)

5sup ( ) ( ) supine I =Sympathetic HRV – Spectral Frequency Shift Index supine = − F2 0.1 /0.1 (26)

$$\mathbf{I}\_6 = \text{Respiratory Stress Index} = \left( \mathbf{P}\_{\text{3db}} - \mathbf{P}\_{\text{3supine}} \right) \tag{27}$$

where

$$\begin{aligned} \left(\text{P}\_{2\text{supine}}\right) &= \text{area under HRVPS spectral plot} \\ \text{frequency } 0.04 \text{ Hz and } 0.15 \text{ Hz in stripe position } . \end{aligned} \tag{28}$$

The ratio of the mid-frequency range power to the high-frequency range power is sometimes used as a relative index of the sympatho/vagal balance [Bianchi et al., 1990]. The high frequency range power ratio between supine and standing position is used as a parasympathetic index [Fallen et al., 1985]. The same ratio is used to study sympathetic function in standing position in the mid frequency range [Fallen et al., 1985]. Sympathetic vasomotor nerve function is quantified by the baro receptor oscillation frequency (i.e., the

In our study, autonomic function indices are defined in terms of spectral power indices and HRV period (or frequency) shift indices. The mid and high-frequency ranges are considered for defining indices. The diagnostic indices are based on parameters measured from the HRVPS. The values of diagnostic indices for the three groups of subjects have shown significant difference and can provide rational basis for selecting prognostic therapy before

(P2)=area under HRVPS spectral plot between 0.04 Hz and 0.15 Hz, and subscripts 'sta' and

HRmin = Local minimum heart rate (beats per minute) prior to local maximum in the same

5sup ( ) ( ) supine I =Sympathetic HRV – Spectral Frequency Shift Index supine = − F2 0.1 /0.1 (26)

frequency 0.04 Hz and 0.15 Hz in supine position

HRmax = Local maximum heart rate (beats per minute) during one breathing cycle.

4std ( ) ( ) std

= = −

I Sympathetic HRV – Spectral Frequency Shift Index standing F2 0.1 /0.1,

1 2 I Relative sympathetic to vagal balance index P /P3 = − − = , (22)

I Orthostatic Stress Index P2sta – P2sup /P2sup <sup>2</sup> = = ( ) , (23)

I3 = − Sympatho Vagal Integrity Index Hrmax – Hrmin / n <sup>=</sup> ∑( ) , (24)

<sup>=</sup> . (25)

6 3 ( ) db 3supine I Respiratory Stress Index P – P = = , (27)

.

(28)

mid-peak frequency) in the HRVPS [Kamath et al., 1987].

a diabetic patient develops cardiac arrhythmic complications.

(P2)=area under HRVPS spectral plot between 0.04 Hz and 0.15 Hz (P3)=area under HRVPS spectral plot between 0.15 and 0.4 Hz.

The **diagnosis indices** are defined as follows:

'sup' refer to standing supine positions.

where F Frequency of the Baroreceptor reflex peak

( ) P2supine area under HRVPS spectral plot

=

where

where

where

where

breathing cycle.

2

n=number of breathing cycles.


 $\left(\mathbf{P}\_{\text{3supine}}\right)$ =area under HRVPS spectral plot between  $\mathbf{V}$  frequency 0.15 Hz and 0.4 Hz, in spite position  $\mathbf{I}$ .

The following Table 2 shows the calculated indices, for a sample normal subject, obtained from the HRVPS parameters.


Table 2. Computed Indices for a typical normal subject.

In this Table 2, I1(sp) = P2/P3 (equation 22) in supine position; I2(st) = P2/P3 (equation 22) in standing position; I2(db) = P2/P3 (equation 22) in deep – breathing mode.

Now, diagnosis based on six indices makes it somewhat difficult to track in a patient as regards how much each index varies from its normal value, for making an appropriate diagnosis. So now we will adopt the novel approach, as in Ghista [Ghsta, 2004; 2009a], of formulating an index by combining the parameters in such a way that the index values are distinctly different for normal subjects, diabetics, and diabetics with ischemic heart disease. Hence, we are proposing that, from a diagnostic and classification viewpoint, it would be more convenient to formulate a DAN Integrated Index (DAN-IID) [Desai, K.D et al., 2011], as :

$$\text{IDAN} - \text{IID} = \left[ \left( \text{I1,st} \right) + \left( \text{I1,d1b} \right) + \left( \text{I2} \right) + \left( \text{I3} \right) + \left( \text{I6} \right) \right] - \dots \left[ \left( \text{I4} \right) + \left( \text{I5} \right) \right] \tag{31}$$

### **5.2 Results and analysis: HRVPS of normal subjects, diabetic subjects, and diabetic subjects with ischemic heart disease**

The instantaneous heart rate average (IHRav), average of difference between maximum and minimum heart rate over a cycle (ΔHrav), power and frequency measurements (P,F) measured from HRVPS are determined. There from the diagnostic indices are computed (as per equation 22-27).

### **Descriptive Statistics of Indices of the Three Groups**

The computed indices for the three categories of subjects are displayed in the following Tables

Table 3 for normal subject group.

Table 4 for diabetic subject group.


Table 5 for IHF subject group.

Then, using the values in Tables (2), (3) and (4), the mean and standard deviation values of three groups are calculated and presented in the Table 6.

Table 3. Results of Indices for normal subject group.


Table 4. Results of Indices for diabetic subject group.

Then, using the values in Tables (2), (3) and (4), the mean and standard deviation values of

Name I1sp(N) I1,st(N) I1,db(N) I2(N) I3(N) I4(N) I5(N) I6(N) DAN-IID Ahamidm 2.08 14.57 0.51 3.78 3.26 -0.1 -0.07 16.26 38.55 Awmeah 2.07 7.83 0.33 1.64 6.62 -0.05 -0.1 16.7 33.27 Fahmia 1.88 2.67 0.36 2.04 8.56 0.13 -0.1 17.81 31.41 Fatimah 0.47 7.46 0.84 1.08 4.9 -0.57 0.07 0.24 15.02 Gitakr 1.93 3.93 2.49 2.66 9.51 0.03 -0.07 2.8 21.43 Indvai 1.63 8.25 0.26 2.01 3.86 -0.4 -0.07 16.14 30.85 Kploga 1.4 2.31 0.3 2.32 7.66 -0.12 0.5 10.67 22.88 Mattarh 1.21 9.17 2.02 2.2 3.59 -0.52 -0.07 1.53 19.1 Mohdsae 3.09 1.47 0.3 -0.65 4.43 -0.08 0.13 1.81 7.31 Mohsed 5.78 9.95 0.75 1.36 6.63 -0.02 0.1 21.87 40.48 Ramial 8.95 3.53 0.18 0.92 11.73 0.3 0.1 8.69 24.65 Sekarm 2.15 5.19 0.25 0.02 3.29 -0.05 0.3 9.88 18.38

Table 5 for IHF subject group.

Average 2.72

Average 2.26

±1.36

5.03 ±6.31

Table 4. Results of Indices for diabetic subject group.

1.05 ±1.17 8.66E-02±0.9 2.43 ±1.32 0.43 ±0.2 -.455 ±0.29 5.29 ±7.94 14.804 ±9.43

±2.36

6.36 ±3.87

Table 3. Results of Indices for normal subject group.

0.71 ±0.75 1.61 ±1.19

Name I1sp(D) I1,st(D) I1,db(D) I2(D) I3(D) I4(D) I5(D) I6(D) DAN-IID Ahmedn 3.54 7.09 0.19 -0.06 2.83 -0.08 -0.57 1.88 12.58 Altmoh 2.07 4.95 0.31 -0.32 2.47 -0.57 -0.57 5.40 13.95 Aminaha 1.34 2.11 0.70 -0.28 2.94 -0.57 -0.57 1.08 7.69 Bakmh 4.25 2.45 0.52 -0.35 1.66 -0.57 -0.57 25.00 30.42 Elmamol 0.51 0.49 0.44 -0.41 2.25 -0.57 -0.57 -0.47 3.44 Fikria 3.57 12.72 0.16 0.78 1.51 -0.57 -0.57 16.89 33.2 Ghyarh 3.78 7.75 1.56 -0.36 2.81 -0.52 -0.57 0.20 13.05 Humoya 3.58 3.78 0.68 2.80 3.68 -0.35 -0.57 4.59 16.45 Kmilmo 2.84 5.30 0.59 0.11 2.38 -0.30 -0.57 1.15 10.4 Krshpr 0.85 0.59 0.13 -0.36 1.86 -0.57 -0.57 20.42 23.78 Kurubrl 1.55 1.74 3.08 0.03 1.44 -0.57 -0.57 3.78 11.21 Mahabs 1.54 5.78 1.06 0.51 6.91 -0.57 -0.57 1.28 16.68 Mohdosb 4.39 1.92 0.32 -0.76 2.01 0.03 0.01 1.32 4.77 Mohikat 2.41 0.55 0.29 -0.29 1.87 -0.57 -0.23 13.25 16.47 Muisdr 0.86 1.08 3.30 -0.30 2.98 -0.10 -0.57 0.34 8.07 Nasah 2.59 26.95 1.19 1.83 2.09 -0.32 0.57 0.44 32.25 Naya 0.75 3.51 3.92 -0.71 1.36 -0.57 -0.57 -0.58 8.64 Salmm 0.35 1.89 0.54 -0.30 0.78 -0.57 -0.57 -0.59 3.43

6.17 ±2.76 -0.12 ±0.25 6.0E-02 ±0.18

10.36 ±7.45 25.277 ±9.88

three groups are calculated and presented in the Table 6.


Table 5. Results of Indices for ischemic heart disease subject group.


Table 6. Descriptive Statistics of indices of the three groups.

### **Diagnostically significant indices**

In order to demonstrate the effectiveness of the diagnostic indices (I1 to I6) to distinguish the three groups, the diagnostically significant indices are calculated using Mann Whitney Wilicoxon Rank test (Non-Parametric Tests), and the p values(<0.05)are tabulated in Table 7 below[Desai, K.D et al., 2011].


Table 7. Diagnostically Significant Indices.

### **5.3 Physiological relevance of the computed indices**

The computed indices reflect the sympatho-vagal interactions that modulate cardiovascular function. The low-frequency component (in the 0.04Hz to 0.15Hz range) of the HRV power spectrum (F2 peak) is an indicator of sympathetic modulation, and the high frequency component (in the 0.15Hz to 0.4Hz range) in the HRV power spectrum (F3 peak) is a marker of vagal modulation.

**The index I1 (= P2/P3) represents** relative sympathetic-to-vagal balance, I1 is found to be reduced to a very low value, from 6.361 to 0.155 in standing position in the case of diabetics with ischemic heart disease. This indicates that diabetics with ischemic heart disease are not able to withstand orthostatic stress or load. Patients recovering from an acute myocardial infarction can be expected to have an increased I1 index during early convalescence, and a return to a normal value by 6 to 12 months

**The orthostatic stress index I2** shows significant reduction from a normal value of 1.614 to 0.085 in diabetics, and, to 0.155 in diabetics with ischemic heart disease. A similar trend is noted for **the sympatho-vagal integrity index I3,** showing reduction in the index value from a normal value of 6.19 to 2.43 in the case of diabetics, and to 2.16 in diabetics with ischemic heart disease. This is indicative of damage to the sympathetic and parasympathetic systems controlling the SA node pacing activity

The sympathetic HRVRS frequency-shift Index in standing position (I4sd) and Sympathetic HRVPS frequency-shift Index in supine position (I5sup) are found to be decreased in diabetics as well as in diabetics with ischemic heart disease patients, compared to the normal subject group. This is indicative of the increased delay (of more than 10 seconds) in case of diabetics as well as diabetics with ischemic heart disease, due to demyelination of their nervous control system controlling the heart rate.

**The Respiratory Stress Index I6** denotes the effectiveness of vagal control on heart rate variation, and is found to be considerably reduced from a normal value of 10.36 to 5.26 in diabetics, and to 5.29 in diabetics with ischemic heart disease.

Thus the indices derived from the HRV power spectrum represent non-invasive signatures of the balance between sympathetic and parasympathetic components of the autonomic nervous system. These indices are shown to characterize diabetic autonomic neuropathy state, and to hence distinguish diabetics and diabetics with ischemic heart disease.

The computed indices reflect the sympatho-vagal interactions that modulate cardiovascular function. The low-frequency component (in the 0.04Hz to 0.15Hz range) of the HRV power spectrum (F2 peak) is an indicator of sympathetic modulation, and the high frequency component (in the 0.15Hz to 0.4Hz range) in the HRV power spectrum (F3 peak) is a marker

**The index I1 (= P2/P3) represents** relative sympathetic-to-vagal balance, I1 is found to be reduced to a very low value, from 6.361 to 0.155 in standing position in the case of diabetics with ischemic heart disease. This indicates that diabetics with ischemic heart disease are not able to withstand orthostatic stress or load. Patients recovering from an acute myocardial infarction can be expected to have an increased I1 index during early convalescence, and a

**The orthostatic stress index I2** shows significant reduction from a normal value of 1.614 to 0.085 in diabetics, and, to 0.155 in diabetics with ischemic heart disease. A similar trend is noted for **the sympatho-vagal integrity index I3,** showing reduction in the index value from a normal value of 6.19 to 2.43 in the case of diabetics, and to 2.16 in diabetics with ischemic heart disease. This is indicative of damage to the sympathetic and parasympathetic systems

The sympathetic HRVRS frequency-shift Index in standing position (I4sd) and Sympathetic HRVPS frequency-shift Index in supine position (I5sup) are found to be decreased in diabetics as well as in diabetics with ischemic heart disease patients, compared to the normal subject group. This is indicative of the increased delay (of more than 10 seconds) in case of diabetics as well as diabetics with ischemic heart disease, due to demyelination of their nervous

**The Respiratory Stress Index I6** denotes the effectiveness of vagal control on heart rate variation, and is found to be considerably reduced from a normal value of 10.36 to 5.26 in

Thus the indices derived from the HRV power spectrum represent non-invasive signatures of the balance between sympathetic and parasympathetic components of the autonomic nervous system. These indices are shown to characterize diabetic autonomic neuropathy

state, and to hence distinguish diabetics and diabetics with ischemic heart disease.

Index Significance Between Two Groups P-value(<0.05)

I1 (standing) N & H 0.0109 I2 N & H 0.0253 I3 N & H 0.0004 I4 N & H 0.0025 I5 N & H 0.0083 I2 N & D 0.0020 I3 N & D 0.0000 I4 N & D 0.0015 I5 N & D 0.0000 I6 N & D 0.0422 I5 H & D 0.0105

Table 7. Diagnostically Significant Indices.

return to a normal value by 6 to 12 months

controlling the SA node pacing activity

control system controlling the heart rate.

diabetics, and to 5.29 in diabetics with ischemic heart disease.

of vagal modulation.

**5.3 Physiological relevance of the computed indices** 

### **Integrated index composed of power-spectral indices**

We have shown how well the HRVPS indices differentiate normal subjects from diabetics and diabetics with ischemic heart disease.

We now compute the values of this integrated Index (DAN-IID) for normal subjects (in Table 3), diabetic subjects (in Table 4), and diabetic patients with ischemic heart disease (in Table 5) . From these Index values, we compute its mean values and standard deviations, for normals, diabetics, and diabetics with ischemic heart disease (IHD). These values are tabulated in Table 6. It can be clearly seen, from this Table 6, that our integrated Index can be employed to effectively differentiate and diagnose diabetic subjects and diabetics with IHD. The Index can also be employed to assess the efficacy of diabetic medication and insulin administration.

We next make a distribution plot of this Integrated Index for normals, diabetics, and diabetics with IHD, in Figure 12. This plot graphically illustrates how well this integrated Index separates normal subjects, diabetic patients, and diabetic patients with ischemic heart disease[Desai, K.D et al., 2011].

Fig. 12. Variation of DAN-IID for (N) normal subjects, (D) diabetic patients, and (H) diabetics with IHD. It can be noted that this DAN-IID clearly separates diabetics and diabetics with IHD from normal subjects.
