Effect of Threshold Value r on Multiscale Entropy based Heart Rate Variability

Effects of ECG Data Length on Heart Rate Variability among Young Healthy Adults

The relationship between the robustness of HRV derived by linear and nonlinear methods to the required minimum data lengths has yet to be well understood. The normal electrocardiography (ECG) data of 14 healthy volunteers were applied to 34 HRV measures using various data lengths, and compared with the most prolonged (2000 R peaks or 750 s) by using the Mann-Whitney U test, to determine the 0.05 level of significance. We found that SDNN, RMSSD, pNN50, normalized LF, the ratio of LF and HF, and SD1 of the Poincaré plot could be adequately computed by small data size (60-100 R peaks). In addition, parameters of RQA did not show any significant differences among 60 and 750 s. However, longer data length (1000 R peaks) is recommended to calculate most other measures. The DFA and Lyapunov exponent might require an even longer data length to show robust results. Conclusions: Our work suggests the optimal minimum data sizes for different HRV measures which can potentially improve the efficiency and save the time and effort for both patients and medical care providers.

Age induced interactions between heart rate variability and systolic blood pressure variability using approximate entropy and recurrence quantification analysis: a multiscale cross correlation analysis

The purpose of this study is to study the effect of age on the correlation between heart rate variability (HRV) and blood pressure variability (BPV). To meet this end, multi-scale cross correlation (CC) analysis of HRV and systolic blood pressure variability (SBPV) was performed. The Approximate Entropy (ApEn) and Recurrence Quantification Analysis (RQA) derived indices, calculated from RR interval series (RRi) and systolic blood pressure (SBP) series at multiple temporal scales, are the basis of this CC analysis. For the computation of ApEn and RQA indices, the tolerance threshold (r) is chosen by either: (i) selecting any arbitrary value (0.2) within the recommended range (0.1-0.25) times standard deviation (SD) of time series, and (ii) taking the 'r' (r_opt) corresponding to maximum ApEn (ApEn_max) as tolerance threshold. It is found that (i) at each time scale (τ), a lower SD is observed when indices are computed using r_opt than [Formula: see text] (r_0.2), for RRi as well as SBP series, (ii) descriptive indices of RRi are found significant (p < 0.05) at all scales (τ), however for SBP, these are found insignificant (p > 0.05) at most of the scales, (iii) CC values of descriptive statistics viz., mean and SD are not significant (p > 0.05) irrespective of τ, barring τ = 1, (iv) CC values of ApEn and RQA indices, found using r_opt, are found significant (p < 0.05) and provide enhanced stratification at τ = 1, 2 and 3, whereas this significant correlation and strong classification is missing for indices calculated using r_0.2, and (v) Lastly as τ increases, ApEn and RQA indices, computed with r_opt, reverse their trend but manage to provide significant difference in elder and younger subjects. It is concluded that HRV and SBPV interactions gets altered with age. Descriptive indicators however are not enough to capture these changes. These complex interactions can only be deciphered using complexity-based methods such as approximate entropy and that too at the multiple scale level.

A joint application of optimal threshold based discrete cosine transform and ASCII encoding for ECG data compression with its inherent encryption

In this paper, a joint use of the discrete cosine transform (DCT), and differential pulse code modulation (DPCM) based quantization is presented for predefined quality controlled electrocardiogram (ECG) data compression. The formulated approach exploits the energy compaction property in transformed domain. The DPCM quantization has been applied to zero-sequence grouped DCT coefficients that were optimally thresholded via Regula-Falsi method. The generated sequence is encoded using Huffman coding. This encoded series is further converted to a valid ASCII code using the standard codebook for transmission purpose. Such a coded series possesses inherent encryption capability. The proposed technique is validated on all 48 records of standard MIT-BIH database using different measures for compression and encryption. The acquisition time has been taken in accordance to that existed in literature for the fair comparison with contemporary state-of-art approaches. The chosen measures are (1) compression ratio (CR), (2) percent root mean square difference (PRD), (3) percent root mean square difference without base (PRD1), (4) percent root mean square difference normalized (PRDN), (5) root mean square (RMS) error, (6) signal to noise ratio (SNR), (7) quality score (QS), (8) entropy, (9) Entropy score (ES) and (10) correlation coefficient (r _x,y ). Prominently the average values of CR, PRD and QS were equal to 18.03, 1.06, and 17.57 respectively. Similarly, the mean encryption metrics i.e. entropy, ES and r _x,y were 7.9692, 0.9962 and 0.0113 respectively. The novelty in combining the approaches is well justified by the values of these metrics that are significantly higher than the comparison counterparts.

An adaptive technique for multiscale approximate entropy (MAEbin) threshold (r) selection: application to heart rate variability (HRV) and systolic blood pressure variability (SBPV) under postural stress

Multiscale approximate entropy (MAE) is used to quantify the complexity of a time series as a function of time scale τ. Approximate entropy (ApEn) tolerance threshold selection 'r' is based on either: (1) arbitrary selection in the recommended range (0.1-0.25) times standard deviation of time series (2) or finding maximum ApEn (ApEnmax) i.e., the point where self-matches start to prevail over other matches and choosing the corresponding 'r' (rmax) as threshold (3) or computing rchon by empirically finding the relation between rmax, SD1/SD2 ratio and N using curve fitting, where, SD1 and SD2 are short-term and long-term variability of a time series respectively. None of these methods is gold standard for selection of 'r'. In our previous study [1], an adaptive procedure for selection of 'r' is proposed for approximate entropy (ApEn). In this paper, this is extended to multiple time scales using MAEbin and multiscale cross-MAEbin (XMAEbin). We applied this to simulations i.e. 50 realizations (n = 50) of random number series, fractional Brownian motion (fBm) and MIX (P) [1] series of data length of N = 300 and short term recordings of HRV and SBPV performed under postural stress from supine to standing. MAEbin and XMAEbin analysis was performed on laboratory recorded data of 50 healthy young subjects experiencing postural stress from supine to upright. The study showed that (i) ApEnbin of HRV is more than SBPV in supine position but is lower than SBPV in upright position (ii) ApEnbin of HRV decreases from supine i.e. 1.7324 ± 0.112 (mean ± SD) to upright 1.4916 ± 0.108 due to vagal inhibition (iii) ApEnbin of SBPV increases from supine i.e. 1.5535 ± 0.098 to upright i.e. 1.6241 ± 0.101 due sympathetic activation (iv) individual and cross complexities of RRi and systolic blood pressure (SBP) series depend on time scale under consideration (v) XMAEbin calculated using ApEnmax is correlated with cross-MAE calculated using ApEn (0.1-0.26) in steps of 0.02 at each time scale in supine and upright position and is concluded that ApEn0.26 has highest correlation at most scales (vi) choice of 'r' is critical in interpreting interactions between RRi and SBP and in ascertaining true complexity of the individual RRi and SBP series.

An alternative approach to approximate entropy threshold value (r) selection: application to heart rate variability and systolic blood pressure variability under postural challenge

This study presents an alternative approach to approximate entropy (ApEn) threshold value (r) selection. There are two limitations of traditional ApEn algorithm: (1) the occurrence of undefined conditional probability (CPu) where no template match is found and (2) use of a crisp tolerance (radius) threshold 'r'. To overcome these limitations, CPu is substituted with optimum bias setting ɛ opt which is found by varying ɛ from (1/N - m) to 1 in the increments of 0.05, where N is the length of the series and m is the embedding dimension. Furthermore, an alternative approach for selection of r based on binning the distance values obtained by template matching to calculate ApEnbin is presented. It is observed that ApEnmax, ApEnchon and ApEnbin converge for ɛ opt = 0.6 in 50 realizations (n = 50) of random number series of N = 300. Similar analysis suggests ɛ opt = 0.65 and ɛ opt = 0.45 for 50 realizations each of fractional Brownian motion and MIX(P) series (Lu et al. in J Clin Monit Comput 22(1):23-29, 2008). ɛ opt = 0.5 is suggested for heart rate variability (HRV) and systolic blood pressure variability (SBPV) signals obtained from 50 young healthy subjects under supine and upright position. It is observed that (1) ApEnbin of HRV is lower than SBPV, (2) ApEnbin of HRV increases from supine to upright due to vagal inhibition and (3) ApEnbin of BPV decreases from supine to upright due to sympathetic activation. Moreover, merit of ApEnbin is that it provides an alternative to the cumbersome ApEnmax procedure.