Mathematical modeling od the mitral valve. From local to global hemodynamics

Mitral valve dysfunction is a relatively common heart disease which typically requires mechanical valve replacement, with consequent high social and economic costs. More specifically, ischemic mitral insufficiency following myocardial infarction has a dynamic behavior that can lead to failure in its detection in certain patients, creating a situation with increased risk of morbidity and mortality. Improving the tracking and the control of valvular pathologies is therefore crucial, as it offers significant opportunities to improve care, costs and prognosis for patients with this disease. To study heart and cardiac valve dysfunction, cardiologists need information about detailed pressure and flow dynamics around and through the valves, atria and ventricles. However, non-invasive information about pressure is currently limited to indices at specific times and invasive catheterization data, which is more traumatic for the patient, is not usually routinely available. One alternative to this involves mathematical modeling of the cardiovascular system which offers a non-invasive and inexpensive way of studying cardiac and circulatory dynamics. This is particularly beneficial where detailed, continuous measurements may not be practicable. This study consisted of the development of a multi-scale closed-loop model of the cardiovascular system that accounted for progressive mitral valve aperture area over the entire cardiac cycle. This multi-scale model, which included detailed mitral valve and left atrium models, was tested over a range of physiological situations and clinical data. The goal was to validate the model’s ability to reproduce clinically measured physiological and pathophysiological behavior in a manner that would enable a model to be made patient-specific using available data. The resulting model was designed to be made patient-specific, and thus capture and reproduce the patient’s unique hemodynamic state on both global and local scales. In particular, it was shown to provide significant information about the patient’s mitral valve dynamics and the detailed flow dynamics and pressure around it. These data are not currently available without extensive, invasive measurements, and this therefore represents a significant step forward in model-based sensing and diagnosis. It is hoped that the model and methods developed in this study will be a powerful tool in assisting medical teams in investigating, tracking, diagnosing and controlling the cardiovascular system. More specifically, the mitral valve, as well as other similar valves, could be directly monitored to improve the diagnosis, costs and prognosis of valvular dysfunction. Furthermore, the overall results justify detailed in vivo animal experiments to thoroughly validate these models and methods in advance of clinical trials