Using Kalman Filtering to Predict Time-Varying Parameters in a Model Predicting Baroreflex Regulation During Head-Up Tilt

Abstract

The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet noninvasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility, and a number of other factors. Given that numerous factors contribute to changing these quantities, it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, it requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during head-up tilt. Similar to the study by Williams et al. [51], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1], [11], [12], [33]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.

Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models

“…Results in this study were obtained using a piecewise linear function to estimate time-varying parameters. While this approach works [31,16], it has the disadvantage that results critically depend on node placement. In a previous study [16], we used an ensemble Kalman filter to predict the time-varying parameters.…”

“…While this approach works [31,16], it has the disadvantage that results critically depend on node placement. In a previous study [16], we used an ensemble Kalman filter to predict the time-varying parameters. The advantage of this method is that it in addition to the instantaneous value provide a measure of uncertainty, though uncertainty can also be calculated for the spline method, e.g.…”

An optimal control approach for blood pressure regulation during head-up tilt

“…Here we compared results to a piecewise linear spline approach, other options would have been to compare predictions to Kalman filtering, e.g. used in our previous study [14] predicting the same parameters using a pulsatile model. Figures 3 and 5 validate that predicting R aup and E m with an optimal control approach using GPOPS can render almost equivalent dynamics for HUT, compared to using a piecewise linear spline approach coupled with gradient-based optimization.…”

“…Previous efforts to regulate vascular resistance and cardiac contractility included parametrizing these variables using piecewise linear splines in the context of nonlinear leastsquares problem formulation [31] and nonlinear filtering [14]. The spline method proved to be computationally expensive, as well as requiring a priori knowledge of the system for placement of the nodes for the splines.…”

A Numerical Model for Simulating the Hemodynamic Effects of Enhanced External Counterpulsation on Coronary Arteries

“…In addition to the above method, there are other contemporary modeling methods of baroreflex regulation that can be adopted. (Olufsen et al, 2006;Matzuka et al, 2015).…”