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.

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.

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.

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.

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On behalf: GIGA-Cardiovascular Sciences Topic(s):Cardiac biology, other Citation:European Heart Journal ( 2013 ) 34 ( Abstract Supplement ), 602Purpose: The time-varying elastance theory has been widely used to describe left atrial and ventricular behaviors.However, the applicability of this theory to the left atrium is not fully established. Therefore, we used a different type of model, based on a description of sarcomere contraction. We aim to observe if the model behaves similarly to experimental observations during inferior vena cava occlusion (IVCO) experiments. Methods:We used a multi-scale model of the cardiovascular system in which left ventricular and atrial pressures are inferred from a sarcomere model. In this model, we reproduced IVCO experiments by a fourfold increase of the vena cava resistance. As in experimental settings, we observed the variation of measurements before and 5 heartbeats after modification of the resistance. These measurements were: maximum a and v wave pressures, minimum and end-diastolic ventricular pressures, slopes of a and v waves and maximum transmitral pressure gradients during early and late ventricular filling.Results: Among the 8 measurements, in the model, 7 followed a similar decrease as experimentally observed. The only measurement that increased is the slope of the v wave. A possible reason for this discrepancy could be that in experimental protocols, vena cava is obstructed far from the heart. In our model, since the vena cava is only represented by a windkessel model, this geographical difference cannot be accounted for. Conclusion:The developed multi-scale model inferring ventricular and atrial contraction from a sarcomere model correctly represents the left atrial behavior and responds to IVCO experiments as physiologically expected.

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. Keywords: Mathematical model, lumped-parameter system, parameter estimation, physiological model. BACKGROUNDCardiovascular diseases cause the highest mortality in Europe (Statistics-Explained (2011)) and in the USA (Xu et al. (2010)). They are also a major cause of admissions in intensive care units (ICU). Even with a proper amount of data, patients in ICU are difficult to treat, this is in part due to the fact that a diagnostic is hard to establish because of the limited amount of measurements available. In addition, these measurements are mainly external (e.g. central venous pressure, arterial pressure, electrocardiogram...) and thus do not provide any accurate information on the internal functioning of the heart, as, for example, the flow in the heart valves. Yet, this kind of information is of extreme interest in the study of many diseases, such as valvular dysfunctions.A mathematical model of the heart can yield a clear physiological picture from data hard to understand at first. Such a model should be usable at bedside and, consequently, should not require an important amount of measurements. Second, it should provide a reasonably correct picture of the intrinsic hemodynamic, which cannot be seen on the ICU monitors. Finally, the model has to be This work was financially supported by the French Community of Belgium (Actions de Recherches Concertées -Académie WallonieEurope).robust, in order to give correct predictions for all patients and conditions, and fast, to predict changes in real-time.Simple lumped models will be prefered to more detailed finite-elements approaches. Such models do not perfectly reproduce the reality but focus more on the macrophysiological trends. Thanks to their simplicity, the involved equations can be solved in a few minutes on a classic computer.The s...