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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.

Background: P waves reported in electrocardiology literature uniformly appear smooth. Computer simulation and signal analysis studies have shown much more complex shapes., Objective: We systematically investigated P-wave complexity in normal volunteers using high-fidelity electrocardiographic techniques without filtering., Methods: We recorded 5-min multichannel ECGs in 16 healthy volunteers. Noise and interference were reduced by averaging over 300 beats per recording. In addition, normal P waves were simulated with a realistic model of the human atria., Results: Measured P waves had an average of 4.1 peaks (range 1-10) that were reproducible between recordings. Simulated P waves demonstrated similar complexity, which was related to structural discontinuities in the computer model of the atria., Conclusion: The true shape of the P wave is very irregular and is best seen in ECGs averaged over many beats., (Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2015 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

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 Ca(2+) 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., (Copyright © 2014 the American Physiological Society.)

Background: The transition from persistent to permanent atrial fibrillation (AF) is associated with increased complexity of fibrillatory conduction. We have investigated the spatial distribution of fibrillation waves and structural alterations in the atrial free walls in a goat model of AF., Methods and Results: AF was maintained for 3 weeks (short term [ST], persistent AF) or 6 months (long term [LT], permanent AF). Fibrillation patterns were assessed with epicardial mapping. The origin of fibrillation waves and sites of conduction abnormalities were more homogeneously distributed in LT than in ST goats. Histologically, the total area fraction occupied by fibrous tissue and the degree of perimysial fibrosis (separation between myocyte bundles) were not significantly different between groups. However, endomysial fibrosis (distance between myocytes within bundles) was significantly larger in LT goats, particularly in the outer millimeter of the atria. By contrast, myocyte diameters were larger in LT goats throughout the atrial walls. High-resolution optical mapping showed that epicardial wavefront expansion was slower and more anisotropic in LT than in ST goats. Finally, a mathematical model of a simplified atrial architecture confirmed the potential impact of epicardial endomysial fibrosis on AF complexity., Conclusions: Altered propagation after 6 months of AF is consistent with homogeneous structural remodeling in the outer millimeter of the atria. Loss of continuity of the epicardial layer because of endomysial fibrosis may reduce its synchronizing effect, thereby increasing the complexity of fibrillatory conduction pathways. The exact distribution of fibrosis may be more important for the occurrence of conduction disturbances than the overall quantity.

Aims: Structural alterations during atrial fibrillation (AF) not only lead to electrical dissociation within the epicardial layer, but also between the epicardial layer and the endocardial bundle network. The aim of the study was to investigate the role of transmural conduction in the stability of AF episodes using a dual-layer computer model., Methods and Results: A proof-of-principle dual-layer model was developed in which connections between the layers can be introduced or removed at any time during the simulation. Using an S1-S2 protocol, a spiral wave was initiated in one of the layers, which degenerated into a complex AF pattern after connection with the other layer at six randomly chosen sites. After 6 s, connections were either retained (dual-layer simulations) or removed (single-layer simulations). Dual-layer simulations were more complex, as indicated by the higher number of waves and phase singularities. Tracking waves through both layers revealed that the number of waves in dual-layer simulations was significantly higher than in the single-layer simulations, reflecting more opportunities for reentry and a concomitant increase in AF stability. In the dual-layer model, only 12% of the AF episodes died out within 6 s, while 59% died out in the single-layer model., Conclusion: Atrial fibrillation patterns are more complex and AF episodes are more stable in a dual-layer model. This study indicates an important role for endo-epicardial conduction for the stabilization of AF.

In the ECG, T- and R-wave are concordant during normal sinus rhythm (SR), but discordant after a period of ventricular pacing (VP). Experiments showed that the latter phenomenon, called T-wave memory, is mediated by a mechanical stimulus. By means of a mathematical model, we investigated the hypothesis that slow acting mechano-electrical feedback (MEF) explains T-wave memory. In our model, electromechanical behavior of the left ventricle (LV) was simulated using a series of mechanically and electrically coupled segments. Each segment comprised ionic membrane currents, calcium handling, and excitation-contraction coupling. MEF was incorporated by locally adjusting conductivity of L-type calcium current (g(CaL)) to local external work. In our set-up, g(CaL) could vary up to 25%, 50%, 100% or unlimited amount around its default value. Four consecutive simulations were performed: normal SR (with MEF), acute VP, sustained VP (with MEF), and acutely restored SR. MEF led to T-wave concordance in normal SR and to discordant T-waves acutely after restoring SR. Simulated ECGs with a maximum of 25-50% adaptation closely resembled those during T-wave memory experiments in vivo and also provided the best compromise between optimal systolic and diastolic function. In conclusion, these simulation results indicate that slow acting MEF in the LV can explain a) the relatively small differences in systolic shortening and mechanical work during SR, b) the small dispersion in repolarization time, c) the concordant T-wave during SR, and d) T-wave memory. The physiological distribution in electrophysiological properties, reflected by the concordant T-wave, may serve to optimize cardiac pump function., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

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.

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.

Background: Acute atrial dilation increases the susceptibility to atrial fibrillation (AF). However, the mechanisms by which atrial stretch may contribute to the initiation and perpetuation of AF remain to be determined., Objective: The purpose of this study was to use a novel multiscale model of atrial electromechanics and mechanoelectrical feedback to test the hypothesis that acute stretch increases vulnerability to AF by heterogeneous activation of stretch-activated channels., Methods: Human atria were represented by a triangular mesh obtained from magnetic resonance imaging data. Atrial trabecular bundle structure was incorporated by varying thicknesses of the atrial wall. Atrial membrane behavior was modeled by the Courtemanche-Ramirez-Nattel model with the addition of a nonselective stretch-activated cation current (I(sac)). Mechanical behavior was modeled by a series elastic, a contractile, and a parallel elastic element in which contractile force was related to intracellular concentration of free calcium and sarcomere length., Results: Acute atrial dilation was simulated by increasing stretch throughout the atrial wall. Stimulation near the pulmonary vein ostia at an interval of 600 ms induced AF at an overall stretch ratio of 1.10. Initiation and perpetuation of AF in our model were related to increased dispersion of effective refractory period, conduction slowing, and local conduction block, all related to heterogeneous activation of I(sac). Upon local contraction, mechanoelectrical coupling affects perpetuation of AF by temporarily changing local excitability., Conclusion: During acute atrial dilation, heterogeneous activation of I(sac) enhances initiation and can affect perpetuation of AF., (Copyright © 2011 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

Regional variation in ionic membrane currents causes differences in action potential duration (APD) and is proarrhythmic. After several weeks of ventricular pacing, AP morphology and duration are changed due to electrical remodeling of the transient outward potassium current (I (to)) and the L-type calcium current (I (Ca,L)). It is not clear what mechanism drives electrical remodeling. By modeling the cardiac muscle as a string of segments that are electrically and mechanically coupled, we investigate the hypothesis that electrical remodeling is triggered by changes in mechanical load. Contractile force generated by the sarcomeres depends on the calcium transient and on the sarcomere length. Stroke work is determined for each segment by simulating the cardiac cycle. Electrical remodeling is simulated by adapting I (Ca,L) kinetics 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. Our results are in agreement with experimentally observed homogeneity in mechanics and heterogeneity in electrophysiology. In conclusion, electrical remodeling is a possible mechanism to reduce heterogeneity in cardiomechanics induced by ventricular pacing.

Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current (I(sac)) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca(2+) concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and I(sac) under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na(+) channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. 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.

Atrial fibrillation is the most common cardiac arrhythmia. Structural cardiac defects such as fibrosis and gap junction remodeling lead to a reduced cellular electrical coupling and are known to promote atrial fibrillation. It has been observed that the expression of the hyperpolarization-activated current If is increased under pathological conditions. Recent experimental data indicate a possible contribution of If to arrhythmogenesis. In this paper, the role of If in action potential propagation in normal and in pathological tissue is investigated by means of computer simulations. 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 conclude 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.

Aim: The aim of the present study is to investigate the origin and effect of virtual electrode polarization in uniform, decoupled and non-uniform cardiac tissue during field stimulation., Methods: A discrete bidomain model with active membrane behaviour was used to simulate normal cardiac tissue as well as cardiac tissue that is decoupled due to fibrosis and gap junction remodelling. Various uniform and non-uniform electric fields were applied to the external domain of uniform, decoupled and non-uniform resting cardiac tissue as well as cardiac tissue in which spiral waves were induced., Results: Field stimulation applied on non-uniform tissue results in more virtual electrodes compared with uniform tissue. The spiral waves were 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 increased and the spiral waves were terminated., Conclusion: Fast depolarization of the tissue after field stimulation may be explained by intracellular decoupling and spatial heterogeneity present in normal and pathological cardiac tissue. We demonstrated that termination of spiral waves by means of field stimulation can be achieved when the tissue is modelled as a non-uniform, anisotropic bidomain with active membrane behaviour.