Using Modified Sample Entropy to Characterize Aging-Associated Microvascular Dysfunction

Fuyuan Liao, Yih-Kuen Jan

Cutaneous microvascular function can be assessed by skin blood flow (SBF) response to thermal stimuli. Usually, the activities of the regulatory mechanisms are quantified by means of spectral analysis of the response. However, spectral measures are unable to characterize the nonlinear dynamics of SBF signal. Sample entropy (SampEn) is a commonly used nonlinear measure of the degree of regularity of time series. However, SampEn value depends on the relationship between the frequency of the studied dynamics and sampling rate. Hence, when time series data are oversampled, SampEn may give misleading results. We modified the definition of SampEn by including a lag between successive data points of the vectors to be compared to address the oversampled issue. The lag could be chosen as the first minimum of the auto mutual information function of the time series. We tested the performance of modified SampEn using simulated signals and SBF data in the young and old groups. The results indicated that modified SampEn yields consistent results for different sampling rates in simulated data, but SampEn cannot. Blood flow data showed a higher degree of regularity during the maximal vasodilation period as compared to the baseline in both groups and a higher degree of regularity in the older group as compared to the young group. Furthermore, our results showed that during the second peak the more regular behavior of blood flow oscillations (BFO) is mainly attributed to enhanced cardiac oscillations. This study suggests that the modified SampEn approach may be useful for assessing microvascular function.