Methodology and Data Analysis

2. Methodology and Data Analysis

Three sets of RR interval data of CHF subjects, NHH subjects and of Atrial Fibrillations (AF) subjects of different age groups each recorded at different points of time of a day is obtained from Physionet [13, 14]. Multi-scale entropy (MSE) estimated [9, 10] requires minimum data length as 30,000 and scale-1 represented that entire data. The data is divided by the respective scale value, such that the scale 20 has 1,500 data values, and for each scale data the entropy was estimated. The values of MSE can’t indicate the behaviour at various points of time [12].

In order to overcome these limitations and to further monitor the dynamism of heart throughout the length of the recoded data, multiple scale (segment) entropy technique is applied (MPE) where in nearly 35,000 samples of RR intervals have been considered for the NHH, CHF subjects obtained from Physionet [13, 14]. The entire data is divided into 7 segments each segment having ~5,000 values of RR intervals, and each segment is denoted by a scale, and MPE was estimated using sample entropy [12, 14]. The limitation of this method is that the duration of each segment may not be the same for different data lengths as the sampling frequency of each data may be different. To overcome this, a new method called modified multiple scale/segment entropy (MMPE) is introduced where nearly 35,000 samples of RR intervals have been considered for all the three NHH, CHF and AF subjects obtained from Physionet [13, 14]. The entire data is divided into 8 segments each segment having values of RR intervals recorded for 15 minutes, and each segment is denoted by a scale. The segments are divided based on the data recorded intervals. For every one hour data recorded for 15 minutes, a segment or scale is assigned. This classification is essential for studying the nonlinear dynamic behaviour of the data over the entire period of the recorded data. The data samples taken in different scales (segments) are shown in Table 1. The first column of Table 1 indicates the data sample duration/range. Column 2 is the corresponding scales

Table 1 Classification of data into different ranges and scale index.

RR interval data duration Scale(segment) index

0 - 15 minutes

1hr - 1hr 15minutes

2hr - 2hr 15minutes

3hr - 3hr 15minutes

4hr - 4hr 15 minutes

5hr - 5hr 15minutes

6hr - 6hr 15minutes

7hr - 7hr 15minutes

Modified Multiple Scale/Segment Entropy (MMPE) Analysis of Heart Rate Variability

of NHH, CHF & AF Subjects

for each range of data. The value of ApEn estimated in AF data in all the intervals representing different scales. each scale or segment are defined as modified

It is possible to use these results for monitoring multiple scale/segment entropy (MMPE). The ApEn

different dynamic status of the heart. For NHH subjects is computed using concepts of Pincus [5-8].

ApEn values are high and the functioning of the heart is Approximate entropy (ApEn) is a measure used to

very dynamic and HRV is not very regular. For the quantify regularity in data about which no knowledge

CHF subjects the ApEn values remain low indicating about the system generating the data is available. ApEn

that the heart is less active and HRV becomes more is found to be useful parameter for finding the hidden

regular. But for the AF data the ApEn values being changes which could not be detected by the time series

high and fluctuating around the same value indicates analysis. It detects changes in underlying dynamic

the fibrillations and erratic heart behaviour. It is nature not seen in the signal measurements. The

reported in the Refs. [1-6] that the heart rate variations algorithm is implemented in C++ language and

are not regular for healthy subjects indicating a highly MATLAB. The algorithm is capable of handling 1024

dynamic heart and become more regular and indicate or more data points. With m = 2 considering two

uncorrelated random behaviour for disease subjects. elements the correlation integral C m (i) is calculated

In order to consolidate the significance of the results, then its logarithm value is estimated and Øm(r) is

the mean MMPE values have been calculated using the calculated as Eq. (1) given below [5-8, 11, 12]:

data over all the scales/segments for NHH, CHF and

Φ AF data which is shown in Fig. 2. It can be seen that for

m ( r ) = 1 ( N − m + 1 ) ∑ InC r ( i )

i = 1 NHH subjects the mean ApEn ~1.3, for AF subjects the The correlation integral is calculated using m = 3 and

mean ApEn ~1.1 and for CHF subjects mean ApEn Ø m+1 (r) is estimated using Eq. (1) replacing m = m+1.

~0.6. The MMPE value for NHH subjects is Finally, the ApEn value is calculated from the Eq. (2):

significantly high suggesting that for normal subjects ApEn(m,r,N) = Øm(r) – Øm+1(r) (2)