Two new calibration techniques of lumped-parameter mathematical models for the cardiovascular system

TL;DR

This paper introduces two novel calibration techniques for lumped-parameter cardiovascular models, demonstrating their robustness, efficiency, and clinical relevance through in silico and real data tests.

Contribution

The study proposes a new correlation matrix-based calibration method and its combination with L-BFGS-B, improving parameter estimation in cardiovascular models.

Findings

The new methods effectively reduce the optimization loss function.

The correlation matrix method is robust to noise and initial guesses.

The methods perform well on real clinical data.

Abstract

Cardiocirculatory mathematical models serve as valuable tools for investigating physiological and pathological conditions of the circulatory system. To investigate the clinical condition of an individual, cardiocirculatory models need to be personalized by means of calibration methods. In this study we propose a new calibration method for a lumped-parameter cardiocirculatory model. This calibration method utilizes the correlation matrix between parameters and model outputs to calibrate the latter according to data. We test this calibration method and its combination with L-BFGS-B (Limited memory Broyden - Fletcher - Goldfarb - Shanno with Bound constraints) comparing them with the performances of L-BFGS-B alone. We show that the correlation matrix calibration method and the combined one effectively reduce the loss function of the associated optimization problem. In the case of in silico generated data, we show that the two new calibration methods are robust with respect to the initial guess of parameters and to the presence of noise in the data. Notably, the correlation matrix calibration method achieves the best results in estimating the parameters in the case of noisy data and it is faster than the combined calibration method and L-BFGS-B. Finally, we present real test case where the two new calibration methods yield results comparable to those obtained using L-BFGS-B in terms of minimizing the loss function and estimating the clinical data. This highlights the effectiveness of the new calibration methods for clinical applications.