# Abstract

HRV analysis plays significant role in preclinical assessment of performance of cardiac performance in case of diabetic subjects. Nonlinear and linear HRV indices are computed for diabetic and control group. The results are found to be consistent with the literature survey. Linear and nonlinear HRV indices are correlated with each other. It can be concluded that nonlinear HRV indices can be used as early markers for cardiac performance deterioration.

**Introduction **

There is strong correlation between elevated carbohydrate and fat intake, sedentary lifestyle to diabetic and hypertensive diseases [2]. Cardiac disease have strong association in diabetic and hypertensive subjects[2]. Cardiac disease contribute to large number of global deaths.

Cardiac performance is the outcome of balancing action of sympathetic and parasympathetic autonomous responses. (SNS and PSNS) controls the heart rate. In diabetic subjects parasympathetic nervous system is more dominating than sympathetic nervous system. The variations in heart rate is helpful in studying the functioning of autonomous nervous system. Shift in the balance of ANS and cardiovascular performance have strong association [1]. Large number of paper discuss the significance of HRV in assessing cardiac health. The analysis of heart rate variability for assessing cardiac health has witnessed significant progress by advent in different methods for analysis and their different parameters, which can be used for detecting any early sign of disease. Heart rate variability analysis tool is simple, reliable, and inexpensive. The technique can control mortality and morbidity due to cardiac diseases in diabetic subjects. Inspite of the advantages, it is not used in clinical practice. The technique is used and studied in biomedical engineering domain and not in the clinician’s [3].

## Sympathetic Nervous System (SNS)

Sympathetic nervous system opposes the physiological effect of parasympathetic nervous system. SNS causes the heart rate to speed up and contraction of blood vessels.SNS is activated especially under stress condition. It is a part of autonomous nervous system that prepare body for emergency situations.

## Parasympathetic Nervous System (PSNS)

Sympathetic nervous system is dominating when body functions require quick response. Parasympathetic nervous system dominates when body does not require large blood supply. Both the types of control are required because heart functions regulation is required. Whenever there is no higher demand of blood heart muscles can relax and ensuring that heart muscles do not get fatigue and also are able to supply more blood whenever there is demand for more blood supply.

**Overview of daibetic and associated complications **

Deterioration in cardiac performance in diabetic and hypertensive condition leads to cardiac stroke. Diabetes causes disorder where glucose metabolism is changed to protein and fat metabolism due to which most of the organs are deprived of nutrients. Protein and fat metabolism cause atherosclerosis and dyslipidemia [9].

In diabetic patients parasympathetic nervous system is more dominating than sympathetic nervous system due to which sudden demand of blood requirement is not fulfilled by heart [2]. As a result diabetic patient experience morbidity.

**Overview of hr**

Electrocardiogram signal are highly subjective hence statistical tools are used for 3-5 minute ECG signal to compute the HRV analysis.

Study of variation in heart rate deals with analysis of biological signals generated by various physiological process in human body. Signals in their raw form do not provide much information hence analysis of HRV signal is done by extracting RR interval detail from input ECG signal. Pan-Tompkins algorithm as shown in figure 2, is used to detect the QRS peak to get RR interval [2].

x-axis in the waveform show time scale and y-axis represent voltage.

To be identified as QRS complex, a peak must be recognized as QRS in both integration and filtered waveform. Figure 3 shows the changes in each waveform after each and every signal transformation.

**Methods**

## Time Domain Measurement

Time domain measurements are simple for analyzing fluctuations in physiological parameters. In time domain analysis two type of HRV indices are studied one is Short term analysis (5 minute recording) and other is long term analysis (24 hour recording).

Short term variation in HR represent fast change in heart rate while long term variations represent slow change in heart rate. Both type of indices can be calculated from RR interval. QRS complex is detected in electrocardiogram. RR interval is time interval between two succesive peaks arising from sinus node polarization.

HR/min. = 1/ (NN interval *60)

Statistical parameters used for variability study in time domain methods are,

## Mean HR

It is the average value of RR interval. It is denoted by µ. It is given by,

µ = 1/N Ʃ RRi

RR1, RR2, RR3…….. (Specified period, RR value)

## SDNN

It is the standard deviation of NN interval. SDNN measures the variation in the value of NN interval. It is written as,

SDNN =

In normal subjects SDNN is high while for pathophysiological condition variations are less.The statistical parameters such as standard error of the mean (SENN), square root of mean squared differences of successive NN interval (RMSSD) and percentage of successive heart beat which differs by more than 50% (PNN50%) can be used as time domain parameters [1].

## Frequency Domain Measurement

Time domain analysis is mathematical function of signal with respect to time, continuous or discrete time. It shows changes in signal with time.

Frequency domain analysis shows how much of the signal lies within each given frequency domain over a range of frequency.

Heart rate is defined as the number of pulse per unit time that’s why we use frequency domain measurement. In frequency domain analysis, number of times each peak (R wave) arrives over entire time period of recording, is recorded.

Frequency domain analysis is much easier compared to time domain analysis as it can help in knowing the key points in total time interval. Time domain method lack the ability to discriminate between sympathetic and parasympathetic contribution of HRV.

In frequency domain HRV study is based on FFT for estimating power spectral density, PSD.

Parameters of method are estimated by the given data sequence. Then from these estimation, the power spectral density is computed [1]. But these method suffer from spectral leakage. The parametric power spectrum estimation method avoid the problem of leakage and give better frequency resolution.

In AR method, AR parameter can be done easily by solving linear equation.

AR method can be expressed as,

Where a(k) are AR coefficients and w(n) is white noise of variance equal to ϭ2. The important aspect of AR method is selection of order P. The order of the AR model p = 16 can be taken [8].

In frequency domain, ratio of low frequency to high frequency ratio is high for pathophysiological condition because of less variation in RR interval. So this ratio LF/HF can either increase or decrease from normal range.

## Limitations of Linear Techniques

Linear techniques of HRV analysis assumes ECG is a stationary signal. HRV techniques using linear methods are computationally simple. Cardiac functions are complex and nonlinear owing to multiple control loops [4] Linear HRV analysis does not identify or analyze the information content in the RR interval.

## Nonlinear Method

Physiological processes are highly nonlinear and complex due to several closed loops. Goldberger et al. have shown the evidence of nonlinearity in cardiac patients [11]. The heart rate represents the complex interplay between various control loops. The physiological data is much more complicated as it involve various factors influencing heart rate, mental pressure, respiration etc. hence the long term sequence of RR interval contains information about the different physiological states owing to different interacting systems. Long term and short term heart rate variability, information content in the regulation of RR interval due to the complex interplay between the sympathetic and parasympathetic stimulation can be detected by nonlinear HRV techniques.

## Correlation dimension

The nonlinear technique are based on chaos theory and it has been shown that nonlinear parameter like correlation dimension is useful indicator of pathology. It is a measure of fractal dimension.

Correlation dimension value is high for chaotic data and it decreases with the decrease in RR signal variation i.e. CD decreases with cardiac disease.

## Detrended fluctuation analysis

The root mean square fluctuations of an integrated and detrended time series is measured at different windows and plotted against the size of window on a log-log scale [1].

RR time series is integrated using equation,

This integrated time series is divided into window of equal length then it is detrended, root mean square fluctuations can be expressed as,

This root mean square fluctuations are calculated for all window to obtain relation between F(n) and window size ‘n’ (number of beats in a window). F(n) increases with increase in window size.

Slope of the line relating log F(n) to log(n) is being represented by scaling exponent α. α is indicator which shows larger the α smaller the time series (less variation)

## Approximate entropy (ApEn)

ApEn is the measures the irregulation and disorder in heart rate signal. It gives the knowledge of irregulation and complexity of time series.

ApEn value falls with decrease in RR variation. Sample entropy (SampEn) is improved tool compared to ApEn for measuring complexity and study of cardiovascular physiology.

## Poincare geometry

It is a plot in which RR interval is plotted as a function of previous RR interval.

Different shape of the plot indicates the degree of heart failure in a subject [12]. SD1 and SD2 are two important parameters of plot. SD1 refers to fast beat to beat variation in data and SD2 refers longer variability of RRi. Ratio SD1/SD2 is of great interest.

**Materials and methods**

Data is acquired from diabetic camp. It is ensured that the diabetic group has varied range of diabetic pathology variation by inquiring the subject about duration of prevalence of diabetes and other associated complications. Control group data is collected from researcher’s college staff. Data acquisition is carried out in morning after breakfast to maintain uniform metabolic status. ECG samples are acquired for 15 minutes supine position at sampling rate of 500 samples/second. R-R interval sequence is computed after denoising the ECG acquired. Kubios HRV is an advanced tool for studying the inter-beat interval variations. It has wide variety of different analysis options which is easy to use, the software is suitable for researchers and clinicians for the analysis of ECG signal [6].

The RR interval file extracted from ECG is given as an input to the HRV simulator. The Simulator used is open source simulation software developed by PHYSIONET called as Kubios HRV simulator. It generates result sheet. The simulator gives various parameters related to the time domain, frequency domain and the nonlinear analysis index.

**Results and discussion**

Following results are compared for both diabetic and normal groups of subjects in supine position.

It can be seen from the figure 5, that heart rate in case of diabetic subjects is much higher compared to the control group. This condition is called as resting tachycardia is commonly found in diabetic subjects. The extent of increase is more indicating the peripheral blood supply is inadequate.

Figure 4 shows that the SDNN is reduced in case of diabetic subject indicating the loss of responsiveness of heart as. The extent of decrease indicates the decrease of heart’s ability to respond to the pathophysiological changes.

There are various non-linear parameters such as correlation dimension, largest lyapunov exponent (LLE), SD1/SD2 of Poincare plot, approximate entropy (ApEn), Fractal dimension, alpha slope (α) of detrended fluctuation analysis etc.

## SDNN

## Mean HR

## Nonlinear Domain Analysis

Sample Entropy (SampEn) Sample entropy is the information content of the present interval compared to the previous interval. If the heart is not responsive to the different changes, it indicates reduced complexity of heart. Sample entropy gives a measure of the information content in the succsessive R-R intervals. Lower value of sample entropy indicates that heart is not able to response to different changes in the physiollogical changes and hence there is less information content in the successive R-R intervals. Same can be observed in the results shown in figure 6.

SD1/SD2 The ratio SD1/SD2 denotes the ratio of long term heart rate variability to short term heart rate variability. The complexity of heart is indicated by the higher longterm vaiability. As showm in figure 7, the ratio is found to be higher in case of control group.

The table-1 shows the student’s t-table indicating the data between diabetic and control group subject is statistically independent for different indices considered.

Table-2 shows the Pearson’s correlation coefficient with the linear HRV indices- heart rate and SDNN to that with nonlinear HRV index- SD1/SD2.

It can be observed that the medium corraltion between SDNN and SD1/SD2 exists in normal cohort. The correlation is lost in case of diabetic subjects. This can be an early marker of reduced heart performance.

Table-3 shows the correlation of linear HRV indices- heart rate and SDNN to that with nonlinear HRV index-and sample entropy. It can be observed that heart rate and SDNN are correlated to sample entropy by medium range. The correlation is lost in case of diabetic subjects. This can be an early marker of reduced heart performance.

For all biological data medium correlation is considered to be a significant indication since all the biological processes are highly nonlinear and complex and also non statioary.[3]

## Sample entropy (SampEn)

## SD1/SD2

Sr. No. | HR Index | P Value for different chorts |
---|---|---|

1 | SDNN | 0.008593211 |

2 | Mean HR | 0.064452261 |

3 | SampEn | 0.000167568 |

4 | SD1/SD2 | 0.001021436 |

Heart Rate and SD1/SD2 | SDNN and SD1/SD2 | |
---|---|---|

normal | -0.27585 | -0.54863 |

diabetic | 0.167063 | -0.03215 |

Heart Rate and Sample entropy | SDNN and Sample Entropy | |
---|---|---|

normal | -0.31475 | 0.603483 |

diabetic | -0.15155 | 0.547064 |

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