Blood Pressure Complexity Discriminates Pathological Beat‐to‐Beat Variability as a Marker of Vascular Aging

Background Beat‐to‐beat blood pressure variability (BPV) is associated with an increased risk of stroke but can be driven by both healthy physiological processes and failure of compensatory mechanisms. Blood pressure (BP) complexity measures structured, organized variations in BP, as opposed to random fluctuations, and its reduction may therefore identify pathological beat‐to‐beat BPV. Methods and Results In the prospective, population‐based OXVASC (Oxford Vascular Study) Phenotyped Cohort with transient ischemic attack or minor stroke, patients underwent at least 5 minutes of noninvasive beat‐to‐beat monitoring of BP (Finometer) and ECG to derive the following: BPV (coefficient of variation) and complexity (modified multiscale entropy) of systolic BP and diastolic BP, heart rate variability (SD of R‐R intervals), and baroreflex sensitivity (BRS; Welch's method), in low‐ (0.04–0.15 Hz) and high‐frequency (0.15–0.4 Hz) bands. Associations between BPV or BP complexity with autonomic indexes and arterial stiffness were determined (linear regression), unadjusted, and adjusted for age, sex, and cardiovascular risk factors. In 908 consecutive, consenting patients, BP complexity was inversely correlated with BPV coefficient of variation (P<0.001) and was similarly reduced in patients with hypertension or diabetes (P<0.001). However, although BPV coefficient of variation had a U‐shaped relationship with age, BP complexity fell systematically across age quintiles (quintile 1: 15.1 [14.0–16.1] versus quintile 5: 13.8 [12.4–15.1]) and was correlated with markers of autonomic dysfunction (heart rate variability SD of R‐R intervals: r = 0.20; BRS low frequency: 0.19; BRS high frequency: 0.26) and arterial stiffness (pulse wave velocity: −0.21; all P<0.001), even after adjustment for clinical variables (heart rate variability SD of R‐R intervals: 0.12; BRS low frequency and BRS high frequency: 0.13 and 0.17; and pulse wave velocity: −0.07; all P<0.05). Conclusions Loss of BP complexity discriminates BPV because of pathological failure of compensatory mechanisms and may represent a less confounded and potentially modifiable risk factor for stroke.


A1. Modified multiscale entropy (ModMSE)
The code for ModMSE can be found in the Appendix in the original publication by Wu et al. 2013. Physica A. 2013. doi:10.1016/j.physa.2013 Entropy has been proposed as an estimate to quantify the degree of irregularity (or randomness) of a signal, and sample entropy (SampEn) is one of the methods commonly used, originally proposed by Richman andMoorman in 2000 (Am J Physiol Heart Circ Physiol. 2000;278:H2039-49. doi: 10.1152/ajpheart.2000. Its calculation is based on the negative logarithm of the number of the occurrence of repeating patterns (match components) that have distance smaller than the tolerance in the signal (figure A1). Given the time-series data = { 1 , 2 , 3 , … }, the SampEn first constructs the similarity index (i.e., the th template vector) of length , ( ) = { , +1 , +2 , +3 , … ( + −1) }, as well as match vector of length ( + 1), +1 ( ). Sample entropy can then be described and calculated as follows: ( , , , ) = − ln [ ] where parameters represent the dimension of constructing the template vector pairs; indicates the tolerance threshold; is the length of the signal; is the number of the matches (i.e., the template vector) of length( + 1) that has a distance smaller than times the standard deviation (SD) of the signal, expressed as: [ +1 ( ), +1 ( )] < ( × ℎ ) and is the number of the matches of length( ) that has a distance smaller than tolerance times the SD of the signal: Later, Govindan et al., 2007 (Physica A 376;158-164) further modified the definition of the original SampEn and incorporated a time-delay in calculating the match template vectors, where the SampEn with time-delay can thus be expressed as: where  is the time-delay between the successive match components when constructing the match templates: () = { , + , … ( −1) } Similarly, the distances for each match components are calculated by deriving the number of matches in this modified version of SampEn (Wu et al. 2013), as determined by: and are the same parameters used for the dimension vector and tolerance threshold respectively. Costa et al., 2002, 2005(Phys Rev Let. 200289(6):068102) proposed an extended method, termed the multiscale entropy (MSE) method 19,20 , to determine the complexity of the signal. The process of this conventional MSE is: (i) to coarse-grain the signal by averaging the neighbouring data-points with non-overlapping window by the scale factor (i.e., ); and (ii) to calculate the SampEn of each coarse-grained time-series; and (iii) by plotting the SampEn against scale factor, the MSE curve can be obtained. The coarse-grained time-series, , can be expressed as follows: where represents the scale factor and is the data length. For both original SampEn and conventional MSE, a unity-delay was applied ( = 1) 38 .
However, the coarse-graining process in the conventional MSE shortens the data length, which may result in inaccurate estimates, particularly in short-term time-series. In 2013, Wu et al., 2013 38 thus proposed the modified multiscale entropy (ModMSE). The modMSE applies the sample entropy with time-delay and replace the coarse-graining process in the conventional MSE algorithm with a moving-average procedure. The moving-averaged timeseries at scale factor is therefore expressed as: The size of the moving-average window is set for both the time-delay and the scale factor to overcome the limitation of shortened data length, and the ModMSE is expressed as follows: ( , , , ) = ( , ,  = , ) as described previously (Wu et al., 2013). Similarly, by plotting sample entropy against the scale factor , the ModMSE curve can be obtained. Figure A2 demonstrates the simulation of modMSE with short-term time series signals using length of 500 data points. In this study, we set the parameters of r = 0.2, m = 2, and the scale from 1 -10, which are the commonly selected numbers with better statistical validity 24 ; and the complexity index is defined as the integration of the area under the modMSE curves, as described in previous studies 28-32 . references [19,20,32]. Parameter r is set for the threshold for the tolerance for accepting matches; m, the dimension parameter (m = 2 in this case). Solid circles and dash circles are the match templates of (m+1) and (m) dimensions, respectively. Sample Entropy

(C)
White noise 1/f noise  The association was determined by general linear model with a log-transformation. Three invalid quality of HRV recordings and those who do not meet the statistical criterion of BRS coherence were not included in the analysis of HRV and BRS. All analyses are statistically significant, except for analyses with a *. Adjusted (A+S), adjusted for age and sex; Adjusted (A+S+RF), adjusted for age, sex and cardiovascular risk factors of hypertension, diabetes, and smoking habit.   Data are presented as mean ± standard error of the mean (SEM) and regression line with 95% CI. Pearson's r = -0.51; p <0.001 Figure S5. Values of complexity of DBP, stratified by quartiles of parameters of (A)

SDRR and (B) RMSSD of R-R intervals; and BRS in (C) LF and (D) HF, respectively.
Three invalid quality of HRV recordings and those do not meet the statistical criterion of BRS coherence were not included.
Data are presented as mean with 95% CI. Data are presented as mean with 95% CI.