Cardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation

Abstract

Mathematical models can provide useful insights explaining behavior observed in experimental data; however, rigorous analysis is needed to select a subset of model parameters that can be informed by available data. Here we present a method to estimate an identifiable set of parameters based on baseline left ventricular pressure and volume time series data. From this identifiable subset, we then select, based on current understanding of cardiovascular control, parameters that vary in time in response to blood withdrawal, and estimate these parameters over a series of blood withdrawals. These time-varying parameters are first estimated using piecewise linear splines minimizing the mean squared error between measured and computed left ventricular pressure and volume data over four consecutive blood withdrawals. As a final step, the trends in these splines are fit with empirical functional expressions selected to describe cardiovascular regulation during blood withdrawal. Our analysis at baseline found parameters representing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility to be identifiable. Of these parameters, vascular resistance and cardiac contractility were varied in time. Data used for this study were measured in a control Sprague-Dawley rat. To our knowledge, this is the first study to analyze the response to multiple blood withdrawals both experimentally and theoretically, as most previous studies focus on analyzing the response to one large blood withdrawal. Results show that during each blood withdrawal both systemic vascular resistance and contractility decrease acutely and partially recover, and they decrease chronically across the series of blood withdrawals.

Control theory in biology and medicine

“…One paper [24] discusses optimizing a new approach to regulation of blood sugar in a diabetes model. Another broad theme concerns parameter identifiability and parameter estimation: both esti-mating physiological parameters from experimental data [8,32] and exploring how an organism might estimate parameters related to the stability of its own movements [15]. Controllability of systems with nonlinear dynamics is discussed in the context of ultrasensitivity and robust rhythm generation [10], and robust generation of waves in excitable media [3].…”

“…We turn next to a series of articles addressing different aspects of system identification and parameter estimation for a critical physiological control system: the regulation of blood pressure. In Cardiovascular regulation in response to multiple hemorrhages: analysis and parameter estimation, Ciocanel et al [8] study the cardiovascular response to a succession of blood withdrawals, analyzing the identifiability of different parameters in a quantitative physiologically based model of the cardiac regulatory system. They find that the identifiable parameters include those governing timing of cardiac contraction, systemic vascular resistance, and cardiac contractility.…”