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

TL;DR

The paper addresses parameter calibration for patient-specific lumped-parameter cardiovascular models by introducing Correlation Matrix Calibration (CMC), a gradient-free method that leverages parameter-output correlations. It compares CMC and a CMC-L-BFGS-B hybrid against the gradient-based L-BFGS-B on in silico and clinical data, finding higher success rates and faster performance for CMC, with the hybrid improving accuracy. CMC shows strong robustness to noisy data and initial guesses, while clinical calibrations yield plausible hemodynamic states and PV loops comparable to conventional optimization. The work demonstrates practical potential for rapid, reliable personalization of cardiovascular models in clinical settings, particularly when data are noisy or limited.

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.

Figures (7)

• Figure 1: Lumped-parameter model. We depict pressures and flow rates in red and blue, respectively, and parameters in black.
• Figure 2: RLC Windkessel circuit used for the arterial and venous compartments (a) and RC Windkessel circuit used for capillary compartments (b).
• Figure 3: Total-effect Sobol indices between parameters and model outputs related to data. A detailed definition of parameters and model outputs is provided in Table \ref{['table:params']} and Table \ref{['table:qoi']}.
• Figure 4: Test 1. Number of successful calibration procedures for each calibration method (a) and $RMSE$ between estimated and real parameters for each sample (b). Only succesful calibrations are reported in the figure.
• Figure 5: Test 2. Number of successful calibration procedures for each calibration method (a), $RMSE$ between estimated and real parameters for each initial guess of parameters (b) and relative standard deviations of the estimated parameters (c). Only succesful calibrations are reported in the figure.