Using Approximate Bayesian Computation to Calibrate the Model Parameters Characterizing the Autoregulatory Behavior of Microvessels

Abstract

This study aims to leverage available experimental data on the myogenic and endothelial responses of the microvessels to calibrate the parameters and refine the functional form of the compliance feedback model. The experimental data used in this study trace the changes in the vessel calibre of individual arteriolar vessels in response to changes in the intraluminal pressure and/or the pressure gradient, which correspond to the myogenic and endothelial mechanisms, respectively. The compliance feedback model was previously developed to characterize the elastic and autoregulatory behavior of microvessels. We devise and employ a two-stage sequential Monte Carlo (MC) approximate Bayesian computation (ABC) scheme to obtain the posterior distribution of the model's parameters, such that the final parameter space distribution integrates information from any prior knowledge of the parameters, the model dynamics, and the available experimental data. Furthermore, the calibration scheme provides key insights into the underlying mechanistic features of the dynamical system; namely, the ABC scheme reveals that there is a marked difference in the time constants between the myogenic-induced dilation and constriction. Overall, upon parameter calibration, the computationally low-cost compliance feedback model achieves very good agreement with the experimental measurements, despite limited data availability, demonstrating that the model provides a simple, compact, yet robust and physiologically grounded characterization of the autoregulatory response, all of which are essential attributes to increase the translatability of hemodynamic models into the clinical environment for future clinical applications.