Simulation of Fractionated Electrograms at Low Spatial Resolution in Large-Scale Heart Models

Abstract To compute extracellular potentials from transmembrane potentials an elliptic boundary-value problem must be solved. This must be done at a spatial resolution of 0.2 mm or better to avoid artefacts in the form of large spikes before and after major deflections. For macroscopic heart models, this leads to very large linear systems. Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the sources from high to low resolution. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with weighted summation rather than simple injection. We tested this method in a model of the human ventricles. We found that using the proposed scheme, a good visual match could be obtained between electrograms computed at 1-mm and 0.2-mm resolution, even in regions where strong sub-millimeter heterogeneity in tissue conductivity was present. Introduction Computation of extracellular potentials from transmembrane potentials is a common problem in cardiac electrophysiology Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the source data from the high-resolution to the low-resolution mesh. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with regional summation rather than simple injection. The summation algorithm must fulfill the following criteria: • No contribution may be lost, otherwise a solution for the linear problem would not exist. • Contributions should remain as local as possible. • The summation should not introduce artefacts. We tested the performance of a summation method with trilinear weighting to fulfill these criteria. Methods An anatomic model of a human heart and torso was created from MRI data as described earlier The resulting model represented the subject's heart with 50 million cubic elements having sides of 0.2 mm. To each element, a local fiber orientation and cell type (subendocardial, subepicardial, or M cell) were assigned. Propagating action potentials (AP) were simulated with a monodomain reaction-diffusion equation, using software that has been described previously Computation of extracellular potentials (electrograms) from the simulated membrane potentials was based on the bidomain model for cardiac tissue where We evaluated I(x, t) at the full 0.2 mm resolution of the reaction-diffusion model. Uniform finite-difference meshes were used for both the simulation of propagation and for the computation of φ e (x, t). To solve equation where N is the ratio of fine to coarse grid resolution (N = 5 in this paper) and ∆x, ∆y, ∆z is the number of finemesh edges between the C node and the F node along the x, y, and z axis, respectively. Thus, both the sum of all weights for a single C node and the sum of the weights for a single F node were unity. To obtain a unique solution to equation Electrograms were computed at 1-mm resolution both for the isolated heart and for the in-situ heart. These simulations were performed with 1 million and with 42 million nodes, respectively. To test the validity of the lowresolution results, electrograms were also computed at the full 0.2-mm resolution in the isolated heart; this took 113 million nodes. Simulations were performed on 32-128 processors of an SGI Altix 4700 supercomputer. To create a situation where inhomogeneous tissue caused fractionated electrograms, fibrofatty replacement and Na-channel block were simulated as in previous work 3. Results Discussion and conclusions We have shown that using regionally summated transmembrane current as a source, electrograms may be computed at a resolution as low as 1 mm in a model of the human ventricles without introducing visible artefacts. Assuming that the transmembrane current itself is computed with a reaction-diffusion model at 0.2-mm to 0.1-mm resolution, this reduces the computational load associated with electrogram simulation by at least a factor 125 to 1000. The proposed method is easy to implement in an existing bidomain solver. It worked well even in the presence of sub-millimeter heterogeneity in tissue conductivity. The method is probably less accurate in small-scale simulations, where most of the electrogram shape originates from nearby tissue. We consider it useful for whole-heart and whole-body models of large mammals, especially man. It may also be valuable as a restriction operator in (geometric) multigrid methods

Atrial septostomy benefits severe pulmonary hypertension patients by increase of left ventricular preload reserve

Koeken Y, Kuijpers NH, Lumens J, Arts T, Delhaas T. Atrial septostomy benefits severe pulmonary hypertension patients by increase of left ventricular preload reserve. Am J Physiol Heart Circ Physiol 302: H2654-H2662, 2012. First published April 27, 2012; doi:10.1152/ajpheart.00072.2012.-At present, it is unknown why patients suffering from severe pulmonary hypertension (PH) benefit from atrial septostomy (AS). Suggested mechanisms include enhanced filling of the left ventricle, reduction of right ventricular preload, increased oxygen availability in the peripheral tissue, or a combination. A multiscale computational model of the cardiovascular system was used to assess the effects of AS in PH. Our model simulates beat-to-beat dynamics of the four cardiac chambers with valves and the systemic and pulmonary circulations, including an atrial septal defect (ASD). Oxygen saturation was computed for each model compartment. The acute effect of AS on systemic flow and oxygen delivery in PH was assessed by a series of simulations with combinations of different ASD diameters, pulmonary flows, and degrees of PH. In addition, blood pressures at rest and during exercise were compared between circulations with PH before and after AS. If PH did not result in a right atrial pressure exceeding the left one, AS caused a left-to-right shunt flow that resulted in decreased oxygenation and a further increase of right ventricular pump load. Only in the case of severe PH a right-to-left shunt flow occurred during exercise, which improved left ventricular preload reserve and maintained blood pressure but did not improve oxygenation. AS only improves symptoms of right heart failure in patients with severe PH if net right-to-left shunt flow occurs during exercise. This flow enhances left ventricular filling, allows blood pressure maintenance, but does not increase oxygen availability in the peripheral tissue

Modeling Cardiac Electromechanics and Mechanoelectrical Coupling in Dyssynchronous and Failing Hearts

Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation–contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy

How disruption of endo-epicardial electrical connections enhances endo-epicardial conduction during atrial fibrillation

Aims Loss of side-to-side electrical connections between atrial muscle bundles is thought to underlie conduction disturbances predisposing to atrial fibrillation (AF). Putatively, disruption of electrical connections occurs not only within the epicardial layer but also between the epicardial layer and the endocardial bundle network, thus impeding transmural conductions (‘breakthroughs’). However, both clinical and experimental studies have shown an enhancement of breakthroughs during later stages of AF. We tested the hypothesis that endo-epicardial uncoupling enhances endo-epicardial electrical dyssynchrony, breakthrough rate (BTR), and AF stability.Methods and results In a novel dual-layer computer model of the human atria, 100% connectivity between the two layers served as healthy control. Atrial structural remodelling was simulated by reducing the number of connections between the layers from 96 to 6 randomly chosen locations. With progressive elimination of connections, AF stability increased. Reduction in the number of connections from 96 to 24 resulted in an increase in endo-epicardial dyssynchrony from 6.6 ± 1.9 to 24.6 ± 1.3%, with a concomitant increase in BTR. A further reduction to 12 and 6 resulted in more pronounced endo-epicardial dyssynchrony of 34.4 ± 1.15 and 40.2 ± 0.52% but with BTR reduction. This biphasic relationship between endo-epicardial coupling and BTR was found independently from whether AF was maintained by re-entry or by ectopic focal discharges.Conclusion Loss of endo-epicardial coupling increases AF stability. There is a biphasic relation between endo-epicardial coupling and BTR. While at high degrees of endo-epicardial connectivity, the BTR is limited by the endo-epicardial synchronicity, at low degrees of connectivity, it is limited by the number of endo-epicardial connections

Mechano-electrical coupling as framework for understanding functional remodeling during LBBB and CRT

It is not understood why, after onset of left bundle-branch block (LBBB), acute worsening of cardiac function is followed by a further gradual deterioration of function, whereas most adverse cardiac events lead to compensatory adaptations. We investigated whether mechano-electrical coupling (MEC) can explain long-term remodeling with LBBB and cardiac resynchronization therapy (CRT). To this purpose, we used an integrative modeling approach relating local ventricular electrophysiology, calcium handling, and excitation-contraction coupling to global cardiovascular mechanics and hemodynamics. Each ventricular wall was composed of multiple mechanically and electrically coupled myocardial segments. MEC was incorporated by allowing adaptation of L-type Ca2+ current aiming at minimal dispersion of local external work, an approach that we previously applied to replicate T-wave memory in a synchronous heart after a period of asynchronous activation. LBBB instantaneously decreased left-ventricular stroke work and increased end-diastolic volume. During sustained LBBB, MEC reduced intraventricular dispersion of mechanical workload and repolarization. However, MEC-induced reduction in contractility in late-activated regions was larger than the contractility increase in early-activated regions, resulting in further decrease of stroke work and increase of end-diastolic volume. Upon the start of CRT, stroke work increased despite a wider dispersion of mechanical workload. During sustained CRT, MEC-induced reduction in dispersion of workload and repolarization coincided with a further reduction in end-diastolic volume. In conclusion, MEC may represent a useful framework for better understanding the long-term changes in cardiac electrophysiology and contraction following LBBB as well as CRT

Dynamic regulation of atrial coronary blood flow in healthy adult pigs

BACKGROUND There are several indications for a mismatch between atrial oxygen supply and demand during atrial fibrillation (AF), but atrial coronary flow regulation has not been investigated extensively. OBJECTIVE The purpose of this study was to characterize the dynamic regulation of atrial coronary flow in pigs. METHODS In anesthetized open-chest pigs, Doppler flow probes were placed around left atrial (LA) and left ventricular (LV) branches of the circumflex artery. Pressures and work indices were measured simultaneously. Systolic and diastolic flow contribution, flow response kinetics, and relationship between pressures, work, and flow were investigated during sinus rhythm, atrial pacing, and acute AF. RESULTS During atrial systole, LA flow decreased. Only 2% of total LA flow occurred during atrial systole. Pacing with 2:1 AV block and infusion of acetylcholine revealed that atrial contraction itself impeded atrial coronary flow. The response to sudden changes in heart rate was slower in LA compared to LV. Both LA and LV vascular conductance were positively correlated with work. After the cessation of acute AF, the LA showed a more pronounced phase of supranormal vascular conductance than the LV, indicating a period of atrial reactive hyperemia. CONCLUSION In healthy adult pigs, atrial coronary flow is impeded by atrial contraction. Although atrial coronary blood flow is positively correlated with atrial external work, it reacts more slowly to changes in rate than ventricular flow. The occurrence of a pronounced hyperemic phase after acute AF supports the notion of a significant supply-demand mismatch during AF