Development of a Mathematical Model for the Left Ventricle to Analyze Stiffness Variations During the Cardiac Cycle

Cardiovascular diseases are currently the leading cause of death worldwide, and prevention remains critical in addressing this global health issue. One of the emerging approaches to cardiac health assessments involves analyzing the mechanical properties of the heart, which can serve as a powerful tool for evaluating its overall condition. While modern methods to quantify these mechanical characteristics often rely on invasive procedures, numerous non-invasive imaging techniques are already used to assess the heart’s geometric features. The aim of this thesis is to develop a mathematical model for the left ventricle that enables the estimation of the tissue stiffness throughout the cardiac cycle using geometric data, such as volume changes. Following a review of the existing literature on this topic, a spring-mass model was selected due to its simplicity and its ability to directly calculate stiffness values from positional data derived from the volume changes. Multiple methods were applied to estimate stiffness across different cardiac cycles, focusing on two primary strategies, the first one involved the computation of the stiffness by the model equation and the second one computing the stiffness resolving an optimization problem. The results demonstrate that, despite the simplicity of the model, it was possible to capture variations in stiffness during the cardiac cycle. These variations were consistent across different techniques and aligned with the physiological behavior of heart tissues. In conclusion, this work demonstrate that is possible to obtain mechanical information from geometrical data obtained through non-invasive techniques, and that the use of a simple spring-mass system proved to be an effective method for estimating changes in stiffness over the course of a cardiac cycle. Increasing the model’s complexity could enhance the accuracy of these evaluations and this research can highlight the potential for mathematical modeling to play a significant role in non-invasive cardiac diagnostics and monitoring.