Sabine Paeme

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

BackgroundThe 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.MethodsIn 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.ResultsExperiments 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.ConclusionsWe 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.

Simulation of left atrial function using a multi-scale model of the cardiovascular system

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.

A simplified model for mitral valve dynamics

Located between the left atrium and the left ventricle, the mitral valve controls flow between these two cardiac chambers. Mitral valve dysfunction is a major cause of cardiac dysfunction and its dynamics are little known. A simple non-linear rotational spring model is developed and implemented to capture the dynamics of the mitral valve. A measured pressure difference curve was used as the input into the model, which represents an applied torque to the anatomical valve chords. A range of mechanical model hysteresis states were investigated to find a model that best matches reported animal data of chord movement during a heartbeat. The study is limited by the use of one dataset found in the literature due to the highly invasive nature of getting this data. However, results clearly highlight fundamental physiological issues, such as the damping and chord stiffness changing within one cardiac cycle, that would be directly represented in any mitral valve model and affect behaviour in dysfunction. Very good correlation was achieved between modeled and experimental valve angle with 1-10% absolute error in the best case, indicating good promise for future simulation of cardiac valvular dysfunction, such as mitral regurgitation or stenosis. In particular, the model provides a pathway to capturing these dysfunctions in terms of modeled stiffness or elastance that can be directly related to anatomical, structural defects and dysfunction.

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

Abstract The atria play an important role in cardiac function. The introduction of two chambers representing the atria in an existing model of the cardiovascular system could provide useful information. A previously validated cardiovascular system model is modified to include the atria, whose behaviour is modelled in an original way. An a wave pressure independent of the volume is introduced to make the model more realistic. This is one of the ten new parameters that are introduced in the atrial model. Six of these parameters are identified with an extension of the previously existing parameter identification method. A method to infer important atrial pressure characteristics from the ventricular pressure waveform is also developed. Identification of the model parameters with and without atria are performed using data sets from a pulmonary embolism pig trial. The error is bigger in the model containing the atria, but remains of the order of measurement errors. The model with atria provides useful information about these two new compartments, without requiring the need for new measurements. This work is a useful improvement of the already existing model and identification methods as it now allows characterization of atrial function.

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

Abstract A minimal cardiovascular system (CVS) model including mitral valve dynamics has been previously validated in silico. It accounts for valve dynamics using a second order differential equation to simulate the physiological opening valve law. This second order equation is based on output heart signals and is very difficult to match its anatomical or physiological parameters, making this model difficult to interpret and to particularise to pathological situations. In contrast, a simple non-linear rotational spring model of the motion of the mitral valve, located between the left atrium and ventricle, has been validated. A measured pressure difference curve was the model input, which provides an applied torque to the valve chords. Various damping and hysteresis states were investigated to find a model that best matches reported animal data of chord movement during a heartbeat. This model is based on simple physiological behavior modeling, defining parameters that are directly linked with physiological or anatomical data, and is thus more physiologically relevant. This research describes a new closed-loop CVS model integrating the simple non-linear rotational spring model. This new model is shown to fit the static and dynamic heart behaviour observed, as an initial validation of its relevance in a larger CVS model.