Assessing the strength of cardiac and sympathetic baroreflex controls via transfer entropy during orthostatic challenge

Abstract

The study assesses the strength of the causal relation along baroreflex (BR) in humans during an incremental postural challenge soliciting the BR. Both cardiac BR (cBR) and sympathetic BR (sBR) were characterized via BR sequence approaches from spontaneous fluctuations of heart period (HP), systolic arterial pressure (SAP), diastolic arterial pressure (DAP) and muscle sympathetic nerve activity (MSNA). A model-based transfer entropy method was applied to quantify the strength of the coupling from SAP to HP and from DAP to MSNA. The confounding influences of respiration were accounted for. Twelve young healthy subjects (20-36 years, nine females) were sequentially tilted at 0°, 20°, 30° and 40°. We found that (i) the strength of the causal relation along the cBR increases with tilt table inclination, while that along the sBR is unrelated to it; (ii) the strength of the causal coupling is unrelated to the gain of the relation; (iii) transfer entropy indexes are significantly and positively associated with simplified causality indexes derived from BR sequence analysis. The study proves that causality indexes are complementary to traditional characterization of the BR and suggests that simple markers derived from BR sequence analysis might be fruitfully exploited to estimate causality along the BR.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Mathematical methods in medicine: neuroscience, cardiology and pathology

“…-better data analysis and diagnoses [9,12,16,17]; -better therapies or instrumentation [15,[19][20][21]; -better understanding of biological processes [10,13,14]; and -better understanding of medical disorders [11,18].…”

“…Thus, one can find in the literature biomarkers ranging from the traditional statistics, several sorts of entropy, the count of some kind of symbols, to even properties of graphs constructed from the data. Concrete implementations of this strategy can be found in [16,17], as we explain in the following. Given L consecutive (or, more generally, equidistant) data of a time series, one can assign a symbol to them.…”

“…The paper by Porta et al [17] is related to [16] in that it also uses an entropy-like quantity (transfer entropy, a popular measure of causality), but this time to assess the strength of cardiac and sympathetic baroreflex. Causality analysis provides an ideal framework to assess the strength of the physiological interactions aiming at the maintenance of arterial blood pressure during an orthostatic challenge in the presence of relevant nonlinear relations and confounding factors blurring the causal link from sympathetic neural activity to arterial blood pressure (e.g.…”

“…This theme issue on the applications of mathematics to medicine is composed of six papers belonging to the area of neuroscience [9][10][11][12][13][14], three papers belonging to cardiology [15][16][17] and four papers belonging to pathology [18][19][20][21], totalling 13 papers from collaborations among 55 scientists.…”

“…direct effect of respiration on both variables). Porta et al [17] exploit and compare a model-based and a model-free approach to transfer entropy estimation grounded, respectively, on multivariate autoregressive model and k-nearest neighbour technique to evaluate the strength of the causal relation from sympathetic activity to arterial blood pressure and vice versa in a multivariate framework accounting for heart rate and respiration as covariates.…”