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

Abstract

BackgroundValve 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.MethodsA 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.ResultsSimulations 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.ConclusionsThe 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.

Extract of Spatholobus suberctus Dunn ameliorates ischemia-induced injury by targeting miR-494

“…The neuroprotective effects of SSCE on ischemic stroke were verified both in vitro and in vivo . Overwhelming evidence suggests cell death was observed and considered as the predominant phenomenon of ischemia-induced damage [ 23 , 24 ]. In our study, OGD-induced decrease of cell viability and increase of cell apoptosis were all decreased by 2–5 μg/μl SSCE, suggesting the neuroprotective roles of SSCE in vitro .…”

Closed-loop real-time simulation model of hemodynamics and oxygen transport in the cardiovascular system

“…Models focusing on particular aspects of hemodynamics such as mitral valve dynamics [4], remodeling of heart and vessels [5], individual drug effects [6] and effects of therapeutic measures such as positive end-expiratory pressure (PEEP) [7] offer good examples of how cardiovascular simulation models can be validated in specific situations and used clinically. It is however difficult to know to what extent these models can be used in clinical situations other than those described in the articles.…”

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

“…This model was first described by Smith et al [5] and has already been validated in silico and in several animal model studies [8,10,[13][14][15][16]. In Figure 1, resistances (R), inductors (L) and diodes respectively model the resistance of the flows through the arteries, the effects of inertia, and the cardiac valves.…”

“…Improving the Heaviside formulation of cardiac valves law used in the minimal cardiovascular system (CVS) model has already be done previously [10,11]. This model accounts for valve dynamics using a second order differential equation to simulate the physiological opening valve law.…”