Bayesian calibration of Arterial Windkessel Model

TL;DR

This paper introduces a Bayesian calibration framework for Windkessel models to improve parameter estimation and uncertainty quantification in personalized blood pressure modeling, validated through synthetic and real data.

Contribution

It develops a Bayesian approach for calibrating Windkessel models, enabling more accurate and interpretable parameter inference in cardiovascular modeling.

Findings

Successfully reconstructs blood pressure waveforms from noisy data.

Accurately estimates model parameters consistent with mathematical relationships.

Effective in both synthetic simulations and real clinical data.

Abstract

This work is motivated by personalized digital twins based on observations and physical models for treatment and prevention of Hypertension. The models commonly used are simplification of the real process and the aim is to make inference about physically interpretable parameters. To account for model discrepancy we propose to set up the estimation problem in a Bayesian calibration framework. This naturally solves the inverse problem accounting for and quantifying the uncertainty in the model formulation, in the parameter estimates and predictions. We focus on the inverse problem, i.e. to estimate the physical parameters given observations. The models we consider are the two and three parameters Windkessel models (WK2 and WK3). These models simulate the blood pressure waveform given the blood inflow and a set of physically interpretable calibration parameters. The third parameter in WK3 function as a tuning parameter. The WK2 model offers physical interpretable parameters and therefore we adopt it as a computer model choice in a Bayesian calibration formulation. In a synthetic simulation study, we simulate noisy data from the WK3 model. We estimate the model parameters using conventional methods, i.e. least squares optimization and through the Bayesian calibration framework. It is demonstrated that our formulation can reconstruct the blood pressure waveform of the complex model, but most importantly can learn the parameters according to known mathematical connections between the two models. We also successfully apply this formulation to a real case study, where data was obtained from a pilot randomized controlled trial study. Our approach is successful for both the simulation study and the real cases.