Computational Modeling of Cardiac Electromechanics

Cardiac arrhythmias are a leading cause of death worldwide. Notably, the electrophysiologiy and microstructural requirements for a fatal ventricular arrhythmia remain incompletely understood, thereby the treatment remains largely empirical. Standard antiarrhythmic drug therapy has failed to reduce, and in some instances has increased, the incidence of Sudden Cardiac Death (SCD). Hence, a more complete understanding of the mechanisms that foment a fatal arrhythmia is needed and computational models offer an excellent way to test hypotheses about various changes to cellular electrophysiology and myocardial microstructure in a manner not easily achieved in experiments. The understanding of associated deformation is also a longstanding research field; to some extent it provides the paradigm of a complex system, as it incorporates several mathematical issues such as geometric and material nonlinearity, complex geometrical and material data, fluid-structure interaction, that are already challenging by themselves without even mentioning the social relevance of the problem.This thesis is concerned with the development of a unified formulation of cardiac electromechanics. The computational requirements for physiologically and numerically accurate computational analysis of the coupled equations of cardiac electrophysiology and finite-deformation contractile mechanics are carefully examined. The validation criterion which needs to be satisfied by any generic model are laid out.The voltage evolution in the heart is obtained by solving the reaction diffusion monodomain equations. The convergence properties of finite-element procedures, employing various combinations of different shape functions, quadrature methods, and operator splitting strategies are studied which place the most stringent limitations on mesh resolution. Computational speedup is achieved preferential by row-sum lumping of the capacitance and mass matrices. However, selective lumping of these matrices can have noticeable effects on the convergence. Finite element model of a rabbit ventricle is developed using Diffusion Tensor(DT) - MRI images. His-Bundle is included in the model to provide the correct activation sequence. Different geometries of the conduction system are analyzed comparing the obtained activation pattern and six lead electrocardiogram (ECG). The ventricular model is further validated by reproducing scroll wave break up.Cardiac excitation coupling is modeled using an active deformation formulation based on Calcium dynamics. Analysis of the formulation of the active part of the deformation gradient and its dependence on Calcium concentration is studied. Effects of material models and inclusion of fiber anisotropy are also studied. Using a simplified ellipsoid model with assumed fiber orientation consistent with commonly used values in literature we successfully reproduce the twisting action and 60% volume reduction which is typically observed in experiments

Development of web application for shape and topology optimization of truss structure and gusset plates

by Amar Mandhyan, Gaurav Srivastava and Shankarjee Krishnamoorth

Web application for size and topology optimization of trusses and gusset plates

by Shankarjee Krishnamoorthi, Gaurav Srivastava and Amar Mandhya

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response.

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle

From cells to ventricles: understanding the mechanisms of ventricular fibrillation through multiscale modeling

by Shankarjee Krishnamoorthi et al.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology.

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

<div><p>We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.</p></div

Mahajan Cell Model Parameters.

<p>Mahajan cell model parameters used in the electrophysiology simulations. The description of each parameter is taken from Mahajan <i>et al.</i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114494#pone.0114494-Mahajan1" target="_blank">[25]</a></p><p>Mahajan Cell Model Parameters.</p