Zero-Dimensional Cardiovascular Modeling: A Personalized Approach to Non-Invasive Measurement and Sensitivity Analysis

TL;DR

This study investigates how parameter sensitivity in zero-dimensional cardiovascular models depends on model granularity by comparing a simplified single-ventricle model with a four-chamber model. Global sensitivity analyses using Sobol indices ($S_1$, $S_T$) and Morris method reveal that parameter importance shifts with model structure and output availability, with $E_{min}$, $C_{sa}$, and $R_s$ dominating the simple model, and timing and chamber elastance parameters becoming prominent in the detailed model. The work demonstrates convergence behavior and highlights the potential for sensitivity-driven model reduction, especially under non-invasive measurement constraints, to enable scalable, patient-friendly cardiovascular simulations. These findings support targeted parameter fixing to reduce computational load and guide non-invasive clinical applications, while acknowledging the need for broader ranges and higher-order analyses to capture interactions in more extreme physiologic states.

Abstract

Zero-dimensional cardiovascular models provide a computationally efficient framework for studying global hemodynamic behavior, yet the influence of model complexity on parameter sensitivity remains insufficiently understood. This work investigates two lumped-parameter cardiovascular models, a simplified single-ventricle configuration and a detailed four-chamber representation, to examine how physiological parameter sensitivities vary with model structure. Time-varying elastance functions are used to represent cardiac dynamics, and global sensitivity analysis is performed using Sobol and Morris methods to quantify the impact of key physiological parameters, including venous return, myocardial contractility, total peripheral resistance, and arterial compliance. The results demonstrate that sensitivity rankings differ substantially between the two models, highlighting the role of model granularity and parameter interactions in shaping cardiovascular responses. These findings support sensitivity-driven model reduction and provide a foundation for scalable, non-invasive cardiovascular simulation frameworks.

Figures (9)

• Figure 1: Model 1 outputs with sub-interval from 8s to 10s. Figure a) illustrates the pressure outputs of the left ventricle as well as the pressures of system arteries and veins. Figure b) and c) are the volume of the left ventricle over time and the flow rate over time respectively. Figure d) contains the Pressure-Volume Loop which compares pressure and volume of left ventricle for each cardiac cycle
• Figure 2: Model 2 outputs of ventricle volumes and atrial volumes, compared with the pressure of each compartment, with sub-interval from 8s to 9s
• Figure 3: The convergence pattern of each parameter across different sample sizes of [300, 500, 1000, 1500, 2500, 4000, 6000, 12000]. The x-axis is the number of sample sizes and the y-axis is the value of the Sobol indices under each parameter size
• Figure 4: Sobol Method Result of Model 1: figure(a) is the first-order sensitivity indices of Model 1 and figure(b) is the total-effect sensitivity indices. Figure(c) is the rank of parameter importance of figure a) according to the mean value of each column, and figure(d) is the rank of parameter importance of figure(b)
• Figure 5: Morris Method Result for Model 1: figure(a) is the mean elementary effect; the values are normalized into range of $[-1,1]$ to show their relative effect as well as directions. Figure(b) is the standard deviation of the elementary effects, normalized into range of $[0,1]$. Figure(c) is the rank of parameter importance, based on the absolute average value of each parameter from figure(a)