Mathematical model of the mitral valve and the cardiovascular system, application for studying, monitoring and in the diagnosis of valvular pathologies

peer reviewedA cardiovascular and circulatory system (CVS) model has been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiological accurate “open on pressure, close on flow” law. Thus, it does not consider the real time scale of the valve aperture dynamics and thus doesn’t fully capture valve dysfunction particularly where the dysfunction involves partial closure. This research describes a new closed-loop CVS model including a model describing the progressive aperture of the mitral valve and valid over the full cardiac cycle. This new model is solved for a healthy and diseased mitral valve

Development and Identification of a Closed-Loop Model of the Cardiovascular System Including the Atria

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Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

Valve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions. A cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate “open on pressure, close on flow” law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle. Simulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends. The resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves

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

A Multi­‐Scale Computer Model of the Cardiovascular System Can Account for the Three Roles of the Left Atrium

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Parameter Identification in a Model of the Cardiovascular System Including the Atria

Peer reviewe

Structural model of the mitral valve included in a cardiovascular closed loop model. Static and dynamic validation

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non invasive estimation of left atrial pressure and mitral valve area waveforms during an entire cardiac cycle

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A multi-scale cardiovascular system model can account for the load-dependence of the end-systolic pressure-volume relationship.

ABSTRACT: BACKGROUND: The end-systolic pressure-volume relationship is often considered as a load-independent property of the heart and, for this reason, is widely used as an index of ventricular contractility. However, many criticisms have been expressed against this index and the underlying time-varying elastance theory: first, it does not consider the phenomena underlying contraction and second, the end-systolic pressure volume relationship has been experimentally shown to be load-dependent. METHODS: In place of the time-varying elastance theory, a microscopic model of sarcomere contraction is used to infer the pressure generated by the contraction of the left ventricle, considered as a spherical assembling of sarcomere units. The left ventricle model is inserted into a closed-loop model of the cardiovascular system. Finally, parameters of the modified cardiovascular system model are identified to reproduce the hemodynamics of a normal dog. RESULTS: Experiments that have proven the limitations of the time-varying elastance theory are reproduced with our model: (1) preload reductions, (2) afterload increases, (3) the same experiments with increased ventricular contractility, (4) isovolumic contractions and (5) flow-clamps. All experiments simulated with the model generate different end-systolic pressure-volume relationships, showing that this relationship is actually load-dependent. Furthermore, we show that the results of our simulations are in good agreement with experiments. CONCLUSIONS: We implemented a multi-scale model of the cardiovascular system, in which ventricular contraction is described by a detailed sarcomere model. Using this model, we successfully reproduced a number of experiments that have shown the failing points of the time-varying elastance theory. In particular, the developed multi-scale model of the cardiovascular system can capture the load-dependence of the end-systolic pressure-volume relationship

Minimal cardiovascular system model including physiological mitral valve opening

This research describes a new closed-loop cardiovascular system (CVS) model including a model of the left atrium and a model describing the progressive aperture of the mitral valv