Computational Models of the Embryonic Heart

Congenital heart defects (CHDs) are the most common form of congenital malformations present in humans and the leading cause of congenital malformation deaths in the US. Research has been overwhelmingly oriented towards defining genetic variants underlying the emergence of CHDs. But because the interactions of cardiac tissue with the surrounding environment directly impact the developement of the heart, understanding the role of biomechanical conditions, such as intracardiac blood flow and contractility, is necessary to link genetics and molecular interactions with tissue deformations and shapes in CHDs. In many cases physical experiments are difficult, unethical, or even impossible to perform at the early stages of embryonic development, and therefore mathematical and computational models are crucial tools to investigate how mechanical forces impact morphogenesis. I am creating a mathematical modeling framework integrating experimental and imaging techniques that links biomechanical forces and macroscopic organ function in embryonic heart development including both electromechanical coupling and hemodynamics.

Whole-mount Imaging of the Chick Embryonic Heart

Computational studies of heart development have been limited by the paucity of comprehensive imaging data. For this reason, I am presently working to establish the the first atlases of three-dimensional models of the heart suitable for computational modeling at various stages of embryonic development. The creation of computational models on image-based representations of the embryonic heart will give access to the detailed valuation of wall shear stresses and tissue strains giving insights to the mechanistic processes that control development.

I use light-sheet fluorescent microscopy to create the first three-dimensional atlas of chick heart development.

Developement of the Cardiac Conduction System

Normal pacemaking in the heart depends on the coordinated discharge frequency of thousands of pacemaker cells comprising the sinoatrial (SA) region. Coordinated behavior is essential to generate rhythmic activity and produce a single impulse with each cardiac cycle. When residing within the sinoatrial node tissue environment, the clock periods of individual pacemaker cells become mutually entrained via cell-to-cell communication, in part due to electrotonic and mechanical interactions, and generate spontaneous beating intervals that exhibit fractal-like behavior. Dysfunction in the sinoatrial node is associated with increased risk of cardiovascular events including syncope, overt heart failure, and poorly tolerated atrial arrhythmias. Models exploring the mechanisms of synchronization of cardiac pacemakers cells assumed the presence of gap junctions as the mechanism which controls cellular interactions. But the number of gap junctions between the pacemaking cells is not sufficient to explain this type of communication. Under severe reduction in gap junction conductance, cell-to-cell interaction can still be mediated by ephaptic coupling. Ephaptic coupling is the result of ionic concentration effects in the extracellular space and it contributes to synchronization in neurons.

Modeling Total Heart Function

I am creating of a fluid--structure interaction (FSI) model of the entire adult human heart including the great vessels, the four heart chambers, and the four valves. The FSI system is approximated using the immersed boundary finite element method. In this approach the momentum equation and mass conservation for incompressible motion is solved on a fixed Cartesian grid using a Marker and Cell (MAC) finite difference approximation. Structural displacements and forces are evaluated on a Lagrangian finite element mesh immersed within the Cartesian grid. Velocities and forces are exchanged between the Cartesian and FE representations by means of discrete delta functions. This allows to account for the complex geometry of the heart without creating a conforming discretization of the fluid and solid domains.

Patient-specific computational models

An essential component of patient-specific models is the ability to run simulations based on medical images. For 8 patients with atrial fibrillation, I reconstructed three dimensional volumetric finite element meshes to study the influence of left atrial appendage (LAA) morphology on the formation of blood clots. Differences in LAA morphology has been correlated with an increased risk of thromboembolism. To prevent stroke some patients undergo implantation of the WATCHMAN device.

Cardiac Electromechanics

An electrical stimulus propagates in the four chambers of the heart signaling the muscle cells to contract. My work focused on linking single cardiac cell contraction to organ-scale deformations. The contraction model I developed, known as the orthotropic active strain forulation, is based on a multiplcative decomposition of the deformation gradient tensor.

The muscle cells in the ventricular chambers have a helicoidal structure. The cardiac muscle cells are also separated in layers by collagen proteins that strongly influence the global contraction of the heart. Since inextensible collagen proteins constrain the possible deformations of the heart even during contraction, my computational models integrated a rearrangement of muscle cells necessary to capture the systolic blood ejection. I used the model to simulate the electromechanics of the heart in a biventricular domain under physiological and pathological (left bundle branch block) conditions. The model has been extended to capture atrial contraction under sinus rhythm and atrial fibrillation.

Atrial Fibrillation and Fibrosis

Atrial firbrillation is associated with progressive changes to the underlying structural and ionic properties of the atrial tissue. Aging and disease contribute to this progression by giving rise to diffuse or regional fibrosis, cell death, fat deposition, and down-regulation of sodium and potassium currents . Considering electric potentials in the extracellular space as well as in the surrounding tissues, I developed a model of fibrosis. This model is used to define a novel electro-biomarker combining high-resolution velocity vector mapping and local extracellular electrograms morphology to determine the degree, type and boundaries of fibrosis.

Mathematical and Numerical Methods for Computational Biomechanics.

Typical behavior of biomaterials, which are predominately made of aqueous solutions, is often approximated as incompressible. In most biomedical engineering applications, the design geometry may be quite complex, and often automatic meshing is confined to simplicial grids, i.e. triangular and tetrahedral grids. But there are no simple tetrahedral finite element formulations that are robust and accurate, particularly in the time-dependent, nearly or fully incompressible cases. Defining J as the determinant of the Jacobian transformation between the reference and the deformed configuration of a continuum, local volume conservation is defined by the constraint J = 1. When this constraint is applied in electrodynamics, common computational methods for incompressible elasticity become unstable. To overcome this, I used a variational multiscale (VMS) approach to develop mixed velocity-pressure formulation for incompressible elastodynamics.