UCLA

Heart failure is the leading cause of death in the world and yet the mechanisms of disease progression are not well understood. Validated computer models which simulate physiologically accurate biomechanics can help provide insight into these mechanisms. Cardiac modeling is a multiphysics problem consisting of electrophysiology (EP), solid mechanics, and fluid mechanics. In this thesis, we develop a multiscale model of congestive heart failure, formulate a novel constitutive viscoactive model for contraction, and examine the necessary boundary conditions for replicating a physiological deformation profile during the cardiac cycle.

The congestive heart failure model was developed using a previous validated healthy EP model of a rabbit heart and modifying the cell model properties to capture the observed phenomena such as a longer action potential duration and lower amplitude calcium transient. Next, the failing cell model was incorporated into homogeneous and heterogeneous (transmural and apex-to-base gradients) cables and the conduction velocity was decreased from normal values to account for Connexin 43 downregulation. The cable with the failing cell model showed the presence of alternans and full conduction block at rapid pacing. The biventricular heart simulations with the failing cell model had significantly higher T-wave alternans and developed QRS alternans at high heart rates. Wavebreak and reentry were induced in the presence of premature ventricular stimuli: a train of 200ms beats followed by two 180ms beats. The mechanism of VF presented here is not due to a steepening of the restitution curve but rather due to a conduction block at the basal region of the ventricles. The failing cell model developed in this work shows that the heart is more susceptible to arrhythmias and potential drug therapies, such as the upregulation of SERCA, have shown to reduce the risk of the block-induced VF.

The heart undergoes two distinct phases during every beat: diastole, which is the passive filling of the chambers with blood, followed by systole, which is the muscle contraction to force the blood out of the ventricles. The presence of calcium in the cell initiates cross-bridge cycling and force generation in cardiac muscle. In this work, the passive and active phases of the heart are modeled using a Hill-like three element model. The hyperelastic behavior of tissue during filling and contraction is captured through the parallel and serial elements, respectively. The motion of the contractile element is parametrized by a set of internal variables, which are the stretch ratios in the fiber, cross-fiber, and the sheet normal directions. The evolution of these internal variables is governed by a kinetic potential, which is derived from experimental force-velocity relationships. For the three-element model, a single variational principle is developed from which incremental stress-strain relations are derived. In this model, we make the assumption that the amount of isometric tension developed in the fiber is directly proportional to the magnitude of intracellular calcium, obtained from the rabbit EP model. The model, when tested at a single material point, shows how active tension can develop in the model due to the shortening of the contractile element even when there is no visible deformation (F = I). Further, when simulating a strip of tissue with transmural fiber distribution, the model develops wall thickening and twist which are features observed in reality.

Boundary conditions in cardiac mechanics must capture the interaction of the outer surface of the heart with the pericardium and the other surrounding organs. Here, we explore those conditions and validate our model qualitatively and quantitatively using criteria from experimental literature. The geometry and microstructure of an ex-vivo swine heart are obtained using diffusion tensor magnetic resonance imaging (DTMRI). The model was constructed using 6109 quadratic tetrahedral elements and fiber orientations were interpolated at each quadrature point. The basal surface is allowed to translate in the longitudinal direction but rotation of the surface out of plane is penalized. The mesh for the pericardium boundary condition is constructed by projecting the epicardial nodes along the normal. The interaction between the pericardium and epicardium allows for free sliding along the surface but a resisting force is applied for inward and outward motions. Only this boundary condition showed the correct motion of the basal surface: during inflation the base moved upward with upward with minimal epicardial wall motion while in systole, there is apex-to-base shortening with significant wall thickening.