Two New Calibration Techniques of Lumped-Parameter Mathematical Models for the Cardiovascular System

Abstract

Cardiocirculatory mathematical models are valuable tools for investigating both physiological and pathological conditions of the circulatory system. To assess an individual's clinical condition, these models must be tailored through parameter calibration. This study introduces a novel calibration method for a lumped-parameter cardiocirculatory model, by leveraging on the correlation matrix between model parameters and outputs to adjust the latter based on observed data. We evaluate the performance of our method, both independently and in combination with the L-BFGS-B optimization algorithm (Limited memory Broyden–Fletcher–Goldfarb–Shanno with Bound constraints), and we compare our results with those of L-BFGS-B alone. Using synthetic data, we show that both the correlation matrix calibration method and the combined one reduce the loss function of the optimization problem more effectively than L-BFGS-B. Moreover, the correlation matrix calibration method exhibits greater robustness to the initial parameter guess than both the combined method and L-BFGS-B. When applied to noisy data, all three calibration methods achieve comparable results. Although the correlation matrix calibration method yields less accurate parameter estimates than L-BFGS-B, in a real-world clinical case, the two new calibration methods provide clinical insights comparable to L-BFGS-B. Notably, the correlation matrix calibration method is three times faster than the other two calibration methods. These findings highlight the effectiveness of our new calibration method for clinical applications.