Failure of Myocardial Tissue: Simulation of Blood Perfusion

Technological advances in computational mechanics allow to simulate failure of any part of airplanes, pumps, compressors, electric power stations, foundations, bridges, etc. Billions of dollars have been invested to calculate 3D stress configuration in engineering structures. Because the criterion of failure in engineering structures is generally exceeds stress. Failure of the human heart is responsible for 6 million deaths per year worldwide. Models of cardiac mechanics have been developed to analyse cardiac pump function from tissue to organ scale. All of these models focus on stress and strain. However, heart failure is not associated with fracture. Failure of a heart is usually induced by a mismatch between blood perfusion and metabolic needs of the cardiomyocytes. Because failure is associated with blood perfusion and present day models do not address this failure mechanism, there is an urgent need for a computational strategy for blood perfusion in deforming myocardial tissue. Upscaling of the vessel trees to a continuum opens the way to computation of coronary blood flow in a multi compartment poro-mechanical model of the beating heart. Arterial, arteriolar, capillary, venular and venous blood are treated as separate compartments. As a result, the supply of oxygen to the tissue is modelled. The present interest in tissue engineering as means to support heart function, and the great difficulties associated with angiogenesis in myocardial tissue engineering, calls for a virtual environment for testing cardiac interventions, so that the time to market of newly designed devices and therapies can be shortened substantially

Strain-controlled electrophysiological wave propagation alters in silico scar-based substrate for ventricular tachycardia

Introduction: Assessing a patient’s risk of scar-based ventricular tachycardia (VT) after myocardial infarction is a challenging task. It can take months to years after infarction for VT to occur. Also, if selected for ablation therapy, success rates are low. Methods: Computational ventricular models have been presented previously to support VT risk assessment and to provide ablation guidance. In this study, an extension to such virtual-heart models is proposed to phenomenologically incorporate tissue remodeling driven by mechanical load. Strain amplitudes in the heart muscle are obtained from simulations of mechanics and are used to adjust the electrical conductivity. Results: The mechanics-driven adaptation of electrophysiology resulted in a more heterogeneous distribution of propagation velocities than that of standard models, which adapt electrophysiology in the structural substrate from medical images only. Moreover, conduction slowing was not only present in such a structural substrate, but extended in the adjacent functional border zone with impaired mechanics. This enlarged the volumes with high repolarization time gradients (≥ 10 ms/mm). However, maximum gradient values were not significantly affected. The enlarged volumes were localized along the structural substrate border, which lengthened the line of conduction block. The prolonged reentry pathways together with conduction slowing in functional regions increased VT cycle time, such that VT was easier to induce, and the number of recommended ablation sites increased from 3 to 5 locations. Discussion: Sensitivity testing showed an accurate model of strain-dependency to be critical for low ranges of conductivity. The model extension with mechanics-driven tissue remodeling is a potential approach to capture the evolution of the functional substrate and may offer insight into the progression of VT risk over time.<br/

An isogeometric analysis framework for ventricular cardiac mechanics

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the Isogeometric Analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4,700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders

Dependence of Intramyocardial Pressure and Coronary Flow on Ventricular Loading and Contractility: A Model Study

The phasic coronary arterial inflow during the normal cardiac cycle has been explained with simple (waterfall, intramyocardial pump) models, emphasizing the role of ventricular pressure. To explain changes in isovolumic and low afterload beats, these models were extended with the effect of three-dimensional wall stress, nonlinear characteristics of the coronary bed, and extravascular fluid exchange. With the associated increase in the number of model parameters, a detailed parameter sensitivity analysis has become difficult. Therefore we investigated the primary relations between ventricular pressure and volume, wall stress, intramyocardial pressure and coronary blood flow, with a mathematical model with a limited number of parameters. The model replicates several experimental observations: the phasic character of coronary inflow is virtually independent of maximum ventricular pressure, the amplitude of the coronary flow signal varies about proportionally with cardiac contractility, and intramyocardial pressure in the ventricular wall may exceed ventricular pressure. A parameter sensitivity analysis shows that the normalized amplitude of coronary inflow is mainly determined by contractility, reflected in ventricular pressure and, at low ventricular volumes, radial wall stress. Normalized flow amplitude is less sensitive to myocardial coronary compliance and resistance, and to the relation between active fiber stress, time, and sarcomere shortening velocity

Evaluation of stimulus-effect relations in left ventricular growth using a simple multiscale model

\u3cp\u3eCardiac growth is the natural capability of the heart to change size in response to changes in blood flow demand of the growing body. Cardiac diseases can trigger the same process leading to an abnormal type of growth. Prediction of cardiac growth would be clinically valuable, but so far published models on cardiac growth differ with respect to the stimulus-effect relation and constraints used for maximum growth. In this study, we use a zero-dimensional, multiscale model of the left ventricle to evaluate cardiac growth in response to three valve diseases, aortic and mitral regurgitation along with aortic stenosis. We investigate how different combinations of stress- and strain-based stimuli affect growth in terms of cavity volume and wall volume and hemodynamic performance. All of our simulations are able to reach a converged state without any growth constraint, with the most promising results obtained while considering at least one stress-based stimulus. With this study, we demonstrate how a simple model of left ventricular mechanics can be used to have a first evaluation on a designed growth law.\u3c/p\u3

Stimulus–effect relations for left ventricular growth obtained with a simple multi-scale model: the influence of hemodynamic feedback

Cardiac growth is an important mechanism for the human body to respond to changes in blood flow demand. Being able to predict the development of chronic growth is clinically relevant, but so far models to predict growth have not reached consensus on the stimulus–effect relation. In a previously published study, we modeled cardiac and hemodynamic function through a lumped parameter approach. We evaluated cardiac growth in response to valve disease using various stimulus–effect relations and observed an unphysiological decline pump function. Here we extend that model with a model of hemodynamic feedback that maintains mean arterial pressure and cardiac output through adaptation of peripheral resistance and circulatory unstressed volume. With the combined model, we obtain stable growth and restoration of pump function for most growth laws. We conclude that a mixed combination of stress and strain stimuli to drive cardiac growth is most promising since it (1) reproduces clinical observations on cardiac growth well, (2) requires only a small, clinically realistic adaptation of the properties of the circulatory system and (3) is robust in the sense that results were fairly insensitive to the exact choice of the chosen mechanics loading measure. This finding may be used to guide the choice of growth laws in more complex finite element models of cardiac growth, suitable for predicting the response to spatially varying changes in tissue load. Eventually, the current model may form a basis for a tool to predict patient-specific growth in response to spatially homogeneous changes in tissue load, since it is computationally inexpensive

Evaluation of stimulus-effect relations in left ventricular growth using a simple multiscale model

Cardiac growth is the natural capability of the heart to change size in response to changes in blood flow demand of the growing body. Cardiac diseases can trigger the same process leading to an abnormal type of growth. Prediction of cardiac growth would be clinically valuable, but so far published models on cardiac growth differ with respect to the stimulus-effect relation and constraints used for maximum growth. In this study, we use a zero-dimensional, multiscale model of the left ventricle to evaluate cardiac growth in response to three valve diseases, aortic and mitral regurgitation along with aortic stenosis. We investigate how different combinations of stress- and strain-based stimuli affect growth in terms of cavity volume and wall volume and hemodynamic performance. All of our simulations are able to reach a converged state without any growth constraint, with the most promising results obtained while considering at least one stress-based stimulus. With this study, we demonstrate how a simple model of left ventricular mechanics can be used to have a first evaluation on a designed growth law