Application of dynamic point process models to cardiovascular control

Abstract

The development of statistical models that accurately describe the stochastic structure of biological signals is a fast growing area in quantitative research. In developing a novel statistical paradigm based on Bayes' theorem applied to point processes, we are focusing our recent research on characterizing the physiological mechanisms involved in cardiovascular control. Results from a Tilt Table study point at our statistical framework as a valid model for the heart beat, as generated from complex mechanisms underlying cardiovascular control. The point process analysis provides new quantitative indices that could have important implications for research studies of cardiovascular and autonomic regulation and for monitoring of heart rate and heart rate variability measures in clinical settings.

Predicting Bradycardia in Preterm Infants Using Point Process Analysis of Heart Rate

“…Thus, the corresponding R-R time interval at time k is given by the set H k = { w k , w k −1 ,, … ․, w k − p +1 }, where w k = u k − u k −1 and 0 ≤ p ≤ k . Because heart rate is a serial procedure, we can estimate a heartbeat at time k with a p -order linear regression [34]: $$\mu true(H_k,\theta false(\mathrm{normalt}false)true)={\theta }_o+{\sum }_{j=1}^p{\theta }_j{w}_{k-j+1}$$where θ (t) = { θ o , …, θ j , …, θ k } is the estimation vector of optimized model parameters.…”

“…To compute optimal estimates of θ ( t ) and σ ( t ), we define a local joint probability density of u t − l : t , with u t − l : t being the collection of R-wave peaks on the interval ( t − l, t ] that are generated with the previous p R-R intervals [31, 34]. We define the maximum likelihood estimate (MLE) of θ ( t ) and σ ( t ) on ( t − l, t ] to be θ̂ and σ̂ , respectively.…”

“…Infant heart rate is innately nonstationary, and conventional analysis methods may not fully capture the idiosyncratic fluctuations of heartbeat signals. Point process analysis can be used to generate real-time, stochastic measures from discrete observables of continuous biological mechanisms [29–34]. Introducing a stochastic estimation of heart rate can capture the fleeting instabilities (e.g.…”

Bayesian estimation of renewal function for inverse Gaussian renewal process

“…Barbien and Brown [7] used IG as a renewal model for cardiovascular activities. It is assumed that given any R-wave event, the waiting time until the next R-wave event, or equivalently, the length of the next R-R interval has IG distribution.…”

A Model-Based Machine Learning Approach to Probing Autonomic Regulation From Nonstationary Vital-Sign Time Series

“…Traditional techniques assume time series stationarity, and cannot properly model transient phenomena or track evolving dynamics effectively. More recently, time varying autoregressive and point process based techniques have been developed to quantify the relationship between multiple variables in nonstationary physiological time series and to extract spectral indices of autonomic control [17], [18]. However, these techniques model each time series individually, and as a result, it is not clear how they can be applied to identify phenotypic dynamic behaviors exhibited across a patient cohort.…”