Modeling of mechanical dysfunction in regional stunned myocardium of the left ventricle

A mathematical model of human heart including the effects of heart contractility varying with heart rate changes

Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications.

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.

Numerical modeling of heart valves using resistive Eulerian surfaces

The goal of this work is the development and numerical implementation of a mathematical model describing the functioning of heart valves. To couple the pulsatile blood flow with a highly deformable thin structure (the valve's leaflets), a resistive Eulerian surfaces framework is adopted. A lumped-parameter model helps to couple the movement of the leaflets with the blood dynamics. A reduced circulation model describes the systemic hemodynamics and provides a physiological pressure profile at the downstream boundary of the valve. The resulting model is relatively simple to describe for a healthy valve and pathological heart valve functioning while featuring an affordable computational burden. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method, and we report several numerical experiments for both two-dimensional and three-dimensional cases with the aim of illustrating its accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

Left Ventricle-Arterial System Interaction in Heart Failure

Ejection fraction (EF) has been viewed as an important index in assessing the contractile state of the left ventricle (LV). However, it is frequently inadequate for the diagnosis and management of heart failure (HF), as a significant subset of HF patients have been found to have reduced EF (HFrEF) whereas others have preserved EF (HFpEF). It should be noted that the function of the LV is dependent on both preload and afterload, as well as its intrinsic contractile state. Furthermore, stroke volume (SV) is dependent on the properties of the arterial system (AS). Thus, the LV-arterial system interaction plays an important role in those patients with HF. This aspect is investigated through the analysis of the specific parameters involved in the coupling of the LV and AS. This includes contractility and the systolic/diastolic indices of the LV. Furthermore, AS afterload parameters such as vascular stiffness and arterial compliance, and their derived coupling coefficient, are also investigated. We conclude that those parameters, which relate to LV structural changes, are most appropriate in quantifying the LV-AS interaction.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

Cardiac force and muscle shortening in regional ischemia: asynchronization and possible uncoupling

Acute myocardial ischemia affects both cardiac muscle force development and shortening in the affected regions. The exact mechanisms are unclear. We investigated myocardial function during ischemia and reperfusion both experimentally and with a muscle fiber model. The model was subjected to perturbations in contractility and force activation. Results show that the cardiac muscle model reflects many of the physiological changes observed in myocardial ischemia and reperfusion. Asynchronization between force generation and muscle shortening observed during regional ischemia and reperfusion may be dependent on the extent of their uncoupling.

Cardiac parametric variations in post-ischemic myocardium

Mechanisms governing post-ischemic ventricular function after episodes of acute myocardial ischemia are still unclear. We investigated this stunned myocardial function with a computer model in conjunction with animal experiments. A modified lumped cardiac muscle model was subjected to parametric changes similar to regionally recorded ventricular parameters. The model was perturbed by alterations in contractility and rates of activation and deactivation. Results show that the cardiac muscle model can mimic many of the physiological changes observed in a stunned myocardium.

Mechanisms leading to reversible mechanical dysfunction in severe CAD: alternatives to myocardial stunning

Patients with severe chronic coronary artery disease (CAD) exhibit a highly altered myocardial pattern of perfusion, metabolism, and mechanical performance. In this context, the diagnosis of stunning remains elusive not only because of methodological and logistic considerations, but also because of the pathophysiological characteristics of the myocardium of these patients. In addition, a number of alternative pathophysiological mechanisms may act by mimicking the functional manifestations usually attributed to stunning. The present review describes three mechanisms that could theoretically lead to reversible mechanical dysfunction in these patients: myocardial wall stress, the tethering effect, and myocardial expression and release of auto- and paracrine agents. Attention is focused on the role of these mechanisms in scintigraphically “normal” regions (i.e., regions usually showing normal perfusion, glucose metabolism, and cellular integrity as assessed by nuclear imaging techniques), in which stunning is usually considered, but these mechanisms could also operate throughout the viable myocardium. We hypothesize that reversion of these three mechanisms could partially explain the unexpected functional benefit after reperfusion recently highlighted by high-spatial-resolution imaging techniques.

Effects of atrial contraction, atrioventricular interaction and heart valve dynamics on human cardiovascular system response

Various simulation models of different complexity have been proposed to model the dynamic response of the human cardiovascular system. In a related paper we proposed an improved numerical model to study the dynamic response of the cardiovascular system, and the pressures, volumes and flow-rates in the four chambers of the heart, which included the effects of atrial contraction, atrioventricular interaction, and heart valve dynamics. This paper investigates the effects of each one of these aspects of the model on the overall dynamic system response. The dynamic response is studied under different situations, with and without including the effect of various features of the model, and these situations are studied and compared among themselves and to detailed aspects of expected healthy-system response. As an important contribution with potential clinical applications, this paper examines the corresponding effects of atrioventricular interaction, and heart valve opening and closing dynamics to the general system dynamic response. This isolation of physical cause-effect relationships is difficult to study with purely experimental methods. The simulation results agree well with results in the open literature. Comparison shows that introduction of these new features greatly improves the simulation accuracy of the effects of a, v and c waves, and in predicting regurgitant valve flow, the dichrotic notch, and E/A velocity ratio.

A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction

Numerical modeling of the human cardiovascular system has always been an active research direction since the 19th century. In the past, various simulation models of different complexities were proposed for different research purposes. In this paper, an improved numerical model to study the dynamic function of the human circulation system is proposed. In the development of the mathematical model, the heart chambers are described with a variable elastance model. The systemic and pulmonary loops are described based on the resistance-compliance-inertia concept by considering local effects of flow friction, elasticity of blood vessels and inertia of blood in different segments of the blood vessels. As an advancement from previous models, heart valve dynamics and atrioventricular interaction, including atrial contraction and motion of the annulus fibrosus, are specifically modeled. With these improvements the developed model can predict several important features that were missing in previous numerical models, including regurgitant flow on heart valve closure, the value of E/A velocity ratio in mitral flow, the motion of the annulus fibrosus (called the KG diaphragm pumping action), etc. These features have important clinical meaning and their changes are often related to cardiovascular diseases. Successful simulation of these features enhances the accuracy of simulations of cardiovascular dynamics, and helps in clinical studies of cardiac function.

Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves

This paper presents a new concentrated parameter model for cardiovascular dynamics that includes an innovative model of heart valve dynamics, which is embedded in the overall model of the four chambers of the heart and the systemic and pulmonary circulation loops. The heart chambers are described with a variable elastance model, and the systemic and pulmonary loops are described with modified Windkessel models. In modelling the heart valve dynamics, the various factors that influence the valve motion are examined, and the governing differential equation for valve motion is derived. The heart valve model includes the influence of the blood pressure effect, the friction effect from the tissue, and from blood motion. As improvement from previous works, the contribution of the blood vortex effect in the vicinity of the valve leaflets to valve motion is specially considered. The proposed model is then used in simulation of healthy and certain pathological conditions such as mitral valve stenosis and aortic regurgitation. The predicted results agree well with results illustrated in cardiology textbooks.