Cardiac electrophysiology and mechanoelectric feedback : modeling and simulation

Cardiac arrhythmia such as atrial and ventricular fibrillation are characterized by rapid and irregular electrical activity, which may lead to asynchronous contraction and a reduced pump function. Besides experimental and clinical studies, computer simulations are frequently applied to obtain insight in the onset and perpetuation of cardiac arrhythmia. In existing models, the excitable tissue is often modeled as a continuous two-phase medium, representing the intracellular and interstitial domains, respectively. A possible drawback of continuous models is the lack of flexibility when modeling discontinuities in the cardiac tissue. We introduce a discrete bidomain model in which the cardiac tissue is subdivided in segments, each representing a small number of cardiac cells. Active membrane behavior as well as intracellular coupling and interstitial currents are described by this model. Compared with the well-known continuous bidomain equations, our Cellular Bidomain Model is better aimed at modeling the structure of cardiac tissue, in particular anisotropy, myofibers, fibrosis, and gap junction remodeling. An important aspect of our model is the strong coupling between cardiac electrophysiology and cardiomechanics. Mechanical behavior of a single segment is modeled by a contractile element, a series elastic element, and a parallel elastic element. Active force generated by the sarcomeres is represented by the contractile element together with the series elastic element. The parallel elastic element describes mechanical behavior when the segment is not electrically stimulated. Contractile force is related to the intracellular calcium concentration, the sarcomere length, and the velocity of sarcomere shortening. By incorporating the influence of mechanical deformation on electrophysiology, mechanoelectric feedback can be studied. In our model, we consider the immediate influence of stretch on the action potential by modeling a stretch-activated current. Furthermore, we consider the adap- tation of ionic membrane currents triggered by changes in mechanical load. The strong coupling between cardiac electrophysiology and cardiac mechanics is a unique property of our model, which is reflected by its application to obtain more insight in the cause and consequences of mechanical feedback on cardiac electrophysiology. In this thesis, we apply the Cellular Bidomain Model in five different simulation studies to cardiac electrophysiology and mechanoelectric feedback. In the first study, the effect of field stimulation on virtual electrode polarization is studied in uniform, decoupled, and nonuniform cardiac tissue. Field stimulation applied on nonuniform tissue results in more virtual electrodes compared with uniform tissue. Spiral waves can be terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increases and spiral waves can be terminated. We conclude that the clinical success of defibrillation may be explained by intracellular decoupling and spatial heterogeneity present in normal and in pathological cardiac tissue. In the second study, the role of the hyperpolarization-activated inward current If is investigated on impulse propagation in normal and in pathological tissue. The effect of diffuse fibrosis and gap junction remodeling is simulated by reducing cellular coupling nonuniformly. As expected, the conduction velocity decreases when cellular coupling is reduced. In the presence of If, the conduction velocity increases both in normal and in pathological tissue. In our simulations, ectopic activity is present in regions with high expression of If and is facilitated by cellular uncoupling. We also found that an increased If may facilitate propagation of the action potential. Hence, If may prevent conduction slowing and block. Overexpression of If may lead to ectopic activity, especially when cellular coupling is reduced under pathological conditions. In the third study, the influence of the stretch-activated current Isac is investigated on impulse propagation in cardiac fibers composed of segments that are electrically and mechanically coupled. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and Isac under stretch. Conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria. In the fourth study, we investigate the hypothesis that electrical remodeling is triggered by changes in mechanical work. Stroke work is determined for each segment by simulating the cardiac cycle. Electrical remodeling is simulated by adapting the L-type Ca2+ current ICa,L such that a homogeneous distribution of stroke work is obtained. With electrical remodeling, a more homogeneous shortening of the fiber is obtained, while heterogeneity in APD increases and the repolarization wave reverses. These results are in agreement with experimentally observed distributions of strain and APD and indicate that electrical remodeling leads to more homogeneous shortening during ejection. In the fifth study, we investigate the effect of stretch on the vulnerability to AF. The human atria are represented by a triangular mesh obtained from MRI data. To model acute dilatation, overall stretch is applied to the atria. In the presence of Isac, the membrane potential depolarizes, which causes inactivation of the sodium channels and results in conduction slowing or block. Inducibility of AF increases under stretch, which is explained by an increased dispersion in refractory period, conduction slowing, and local conduction block. Our observations explain the large differences in intra-atrial conduction measured in experiments and provide insight in the vulnerability to AF in dilated atria. In conclusion, our model is well-suited to describe cardiac electrophysiology and mechanoelectric feedback. For future applications, the model may be improved by taking into account new insights from cellular physiology, a more accurate geometry, and hemodynamics.