Simulation of Left Atrial Function Using a Multi-Scale Model of the Cardiovascular System

Abstract

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors.

Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

“…Even severe stenosis caused only a slight decrease in cardiac output although the mean systolic pressure gradient between LV and aorta achieved 50 mmHg. The good match of the results of the simulation with clinical recommendations showed that simple Equations (11) to (13) for pressure drop across the valve provided a reasonable quantitative fit of major integral hydrodynamic characteristics of complicated nonsteady blood flow through a stenotic aortic valve.…”

“…This model was used to simulate normal circulation and acute or chronic pulmonary hypertension. Pironet and colleagues suggested multiscale models in that 0D multiscale models of the LV, alone or combined with a model of the left atrium, were based on a sarcomere model . Using these models, they simulated the dependence of the end‐systolic pressure‐volume relations on preload and afterload, mitral valve resistance, etc., and estimated the contribution of the left atrium to the LV function.…”

Effects of Choice of Medical Imaging Modalities on a Non-invasive Diagnostic and Monitoring Computational Framework for Patients With Complex Valvular, Vascular, and Ventricular Diseases Who Undergo Transcatheter Aortic Valve Replacement

“…where, P LV (t), V(t), and V 0 are the LV time-varying pressure, time-varying volume, and unloaded volume, respectively (Keshavarz-Motamed et al, 2016). As explained by Keshavarz-Motamed (2020), to represent the normalized elastance function of the LV, we observed that among summation of Gaussian functions (Pironet et al, 2013;Chaudhry, 2015), Boltzmann Distribution (McDowell, 1999), double Hill function (Mynard et al, 2012;Broomé et al, 2013), and the latter provided the most physiologically accurate results (e.g., pressure, volume, and flow waveforms). The double Hill function which is a cooperative process (Moss et al, 2004), as physiologically expected from myocyte recruitment during preload and is modeled by a sigmoidal Hill function.…”

Patient-Specific Monitoring and Trend Analysis of Model-Based Markers of Fluid Responsiveness in Sepsis: A Proof-of-Concept Animal Study

“…It has not yet been shown that the time varying elastance theory can be applied to the atria as it is done to the ventricle. Other authors have developed alternate methods to represent the atria such as the multi-scale model [26]. However, the large number of parameters required for such methods to work cannot be identified using the limited data clinically available, making it unsuitable to apply in this work.…”