Parameter estimation for closed-loop lumped parameter models of the systemic circulation using synthetic data

Abstract

Physics-based models can be applied to describe mechanisms in both health and disease, which has the potential to accelerate the development of personalized medicine. The aim of this study was to investigate the feasibility of personalizing a model of systemic hemodynamics by estimating model parameters. We investigated the feasibility of estimating model parameters for a closed-loop lumped parameter model of the left heart and systemic circulation using the step-wise subset reduction method. This proceeded by first investigating the structural identifiability of the model parameters. Secondly, we performed sensitivity analysis to determine which parameters were most influential on the most relevant model outputs. Finally, we constructed a sequence of progressively smaller subsets including parameters based on their ranking by model output influence. The model was then optimized to data for each set of parameters to evaluate how well the parameters could be estimated for each subset. The subsequent results allowed assessment of how different data sets, and noise affected the parameter estimates. In the noiseless case, all parameters could be calibrated to less than 10^(-3)% error using time series data, while errors using clinical index data could reach over 100%. With 5% normally distributed noise the accuracy was limited to be within 10% error for the five most sensitive parameters, while the four least sensitive parameters were unreliably estimated for waveform data. The three least sensitive parameters were particularly challenging to estimate so these should be prioritized for measurement. Cost functions based on time series such as pressure waveforms, were found to give better parameter estimates than cost functions based on standard indices used in clinical assessment of the cardiovascular system, for example stroke volume (SV) and pulse pressure (PP). Averaged parameter estimate errors were reduced by several orders of magnitude by choosing waveforms for noiseless synthetic data. Also when measurement data were noisy, the parameter estimation procedure based on continuous waveforms was more accurate than that based on clinical indices. By application of the stepwise subset reduction method we demonstrated that by the addition of venous pressure to the cost function, or conversely fixing the systemic venous compliance parameter at an accurate value improved all parameter estimates, especially the diastolic filling parameters which have least influence on the aortic pressure.