A reverse stroke characterizes the force generation of cardiac myofilaments, leading to an understanding of heart function.

Changes in the molecular properties of cardiac myosin strongly affect the interactions of myosin with actin that result in cardiac contraction and relaxation. However, it remains unclear how myosin molecules work together in cardiac myofilaments and which properties of the individual myosin molecules impact force production to drive cardiac contractility. Here, we measured the force production of cardiac myofilaments using optical tweezers. The measurements revealed that stepwise force generation was associated with a higher frequency of backward steps at lower loads and higher stall forces than those of fast skeletal myofilaments. To understand these unique collective behaviors of cardiac myosin, the dynamic responses of single cardiac and fast skeletal myosin molecules, interacting with actin filaments, were evaluated under load. The cardiac myosin molecules switched among three distinct conformational positions, ranging from pre- to post-power stroke positions, in 1 mM ADP and 0 to 10 mM phosphate solution. In contrast to cardiac myosin, fast skeletal myosin stayed primarily in the post-power stroke position, suggesting that cardiac myosin executes the reverse stroke more frequently than fast skeletal myosin. To elucidate how the reverse stroke affects the force production of myofilaments and possibly heart function, a simulation model was developed that combines the results from the single-molecule and myofilament experiments. The results of this model suggest that the reversal of the cardiac myosin power stroke may be key to characterizing the force output of cardiac myosin ensembles and possibly to facilitating heart contractions.

Transition mechanisms from atrial flutter to atrial fibrillation during anti-tachycardia pacing therapy.

BACKGROUND: Atrial anti-tachycardia pacing (aATP) has been shown to be effective for the termination of atrial tachyarrhythmias, but its success rate is still not high enough. OBJECTIVE: The main objective of this study was to investigate the mechanisms of atrial flutter (AFL) termination by aATP and the transition from AFL to atrial fibrillation (AF) during aATP. METHODS: We developed a multi-scale model of the human atrium based on magnetic resonance images and examined the atrial electrophysiology of AFL during aATP with a ramp protocol. RESULTS: In successful cases of aATP, paced excitation entered the excitable gap and collided with the leading edge of the reentrant wave front. Furthermore, the excitation propagating in the opposite direction collided with the trailing edge of the reentrant wave to terminate AFL. The second collision was made possible by the distribution of the wave propagation velocity in the atria. The detailed analysis revealed that the slowing of propagation velocity occurred at the exit of the sub-Eustachian isthmus, probably due to source-sink mismatch. During the transition from AFL to AF, the excitation collided with the refractory zone of the preceding wave and broke into multiple wave fronts to induce AF. A similar observation was made for the transition from AF to sinus rhythm. In both cases, the complex anatomy of the atria played an essential role. CONCLUSION: The complex anatomy of atria plays an essential role in the maintenance of stable AFL and its termination by aATP, which were revealed by the realistic three-dimensional simulation model.

Low-energy defibrillation using a base-apex epicardial electrode.

BACKGROUND: Current implantable cardioverter defibrillators (ICDs) require electric conduction with high voltage and high energy, which can impair cardiac function and induce another malignant arrhythmia. As a result, there has been a demand for an ICD that can effectively operate with lower energy to mitigate the risks of a strong electric shock. METHODS: A pair of sheet-shaped electrodes covering the heart were analyzed in three configurations (top-bottom, left-right, and front-back) using a heart simulator. We also varied the distance between the two electrodes (clearance) to identify the electrode shape with the lowest defibrillation threshold (DFT). We also investigated the ICD shock waveform, shock direction, and the effect of the backside insulator of the electrode. RESULTS: The DFT was high when the clearance was too small and the DFT was high even when the clearance was too large, suggesting that an optimal value clearance. The top-bottom electrodes with optimal clearance showed the lowest DFT when the biphasic shocks set the top electrode to a high potential first and then the bottom electrode was set to a high potential. An interval between a first shock waveform and a second shock waveform should be provided for low-energy defibrillation. Because the insulator prevents unnecessary current flow to the backside, the DFT of the electrodes with insulators is less than those without insulators. CONCLUSION: Painless defibrillation using sheet-shaped electrodes on the epicardium is predicated on the basis of results using a heart simulator.

An application of a patient-specific cardiac simulator for the prediction of outcomes after mitral valve replacement: a pilot study.

Despite advancements in preoperative prediction of patient outcomes, determination of the most appropriate surgical treatments for patients with severely impaired cardiac function remains a challenge. "UT-Heart" is a multi-scale, multi-physics heart simulator, which can be used to assess the effects of treatment without imposing any burden on the patients. This retrospective study aimed to assess whether UT-Heart can function as a tool that aids decision making for performing mitral valve replacements (MVR) in patients with severe mitral regurgitation (MR) and impaired left ventricular (LV) function. We used preoperative clinical data to create a patient-specific heart model using UT-Heart for a patient who had dilated cardiomyopathy with severe MR. After confirming that this heart model reproduced the preoperative state of the patient, we performed an in silico MVR operation without changing any parameters, such as the end-diastolic volume of the left ventricle, systemic vascular resistance, and the number of myocardiocytes. Among the functional changes introduced by in silico surgery, we found two indices, forward flow and the mechanical efficiency of the work done to the systemic circulation, which may relate positively to the favorable outcome observed in the real world. Thus, multi-scale, multi-physics heart simulators can reproduce the pathophysiology of MR with impaired LV function. By performing in silico MVR and examining the resultant functional changes, we identified two indices, whose usefulness should be tested in future studies.

Patient-specific heart simulation can identify non-responders to cardiac resynchronization therapy.

To identify non-responders to cardiac resynchronization therapy (CRT), various biomarkers have been proposed, but these attempts have not been successful to date. We tested the clinical applicability of computer simulation of CRT for the identification of non-responders. We used the multi-scale heart simulator "UT-Heart," which can reproduce the electrophysiology and mechanics of the heart based on a molecular model of the excitation-contraction mechanism. Patient-specific heart models were created for eight heart failure patients who were treated with CRT, based on the clinical data recorded before treatment. Using these heart models, bi-ventricular pacing simulations were performed at multiple pacing sites adopted in clinical practice. Improvement in pumping function measured by the relative change of maximum positive derivative of left ventricular pressure (%ΔdP/dtmax) was compared with the clinical outcome. The operators of the simulation were blinded to the clinical outcome. In six patients, the relative reduction in end-systolic volume exceeded 15% in the follow-up echocardiogram at 3 months (responders) and the remaining two patients were judged as non-responders. The simulated %ΔdP/dtmax at the best lead position could identify responders and non-responders successfully. With further refinement of the model, patient-specific simulation could be a useful tool for identifying non-responders to CRT.

Longitudinal dissociation and transition in thickness of the His-Purkinje system cause various QRS waveforms of surface ECG under His bundle pacing: A simulation study based on clinical observations.

AIMS: His bundle pacing (HBP) is a feasible and reliable alternative to conventional right ventricular pacing (RVP), but associated ECG (electrocardiogram) changes have not been well-studied. This study aimed to determine the mechanisms underlying ECG changes associated with HBP using patient-specific multiscale heart simulations. METHODS: ECGs were recorded in two patients who were treated by HBP under a native rhythm and HBP at high and low voltages. We created patient-specific multiscale simulation heart models of these patients and performed ECG simulation under these conditions. Using these results and detailed information on the electrical field around the pacing lead, we investigated mechanisms underlying the observed ECG changes. RESULTS: Heart simulations successfully reproduced ECGs under a native rhythm for both cases. In case 1, nonselective HBP produced a left bundle branch (LBB) block pattern, which was reproduced as a selective right bundle branch (RBB) pacing. However, in case 2, ECG under nonselective HBP showed an RBB block pattern, which could not be reproduced by the commonly used framework. Findings on the electrical field and anatomy of the His bundle and its branches suggested that longitudinal dissociation of the His bundle and transition of thickness in the stem of the LBB caused a conduction delay in the RBB to produce these ECG changes in this patient. CONCLUSION: Variations in the anatomy of the His bundle and its branches may underlie the diverse ECG responses to HBP. These variations should be taken into account when performing this therapy.

Clinical and pharmacological application of multiscale multiphysics heart simulator, UT-Heart.

A heart simulator, UT-Heart, is a finite element model of the human heart that can reproduce all the fundamental activities of the working heart, including propagation of excitation, contraction, and relaxation and generation of blood pressure and blood flow, based on the molecular aspects of the cardiac electrophysiology and excitation-contraction coupling. In this paper, we present a brief review of the practical use of UT-Heart. As an example, we focus on its application for predicting the effect of cardiac resynchronization therapy (CRT) and evaluating the proarrhythmic risk of drugs. Patient-specific, multiscale heart simulation successfully predicted the response to CRT by reproducing the complex pathophysiology of the heart. A proarrhythmic risk assessment system combining in vitro channel assays and in silico simulation of cardiac electrophysiology using UT-Heart successfully predicted druginduced arrhythmogenic risk. The assessment system was found to be reliable and efficient. We also developed a comprehensive hazard map on the various combinations of ion channel inhibitors. This in silico electrocardiogram database (now freely available at http://ut-heart.com/) can facilitate proarrhythmic risk assessment without the need to perform computationally expensive heart simulation. Based on these results, we conclude that the heart simulator, UT-Heart, could be a useful tool in clinical medicine and drug discovery.

Multi-scale, tailor-made heart simulation can predict the effect of cardiac resynchronization therapy.

BACKGROUND: The currently proposed criteria for identifying patients who would benefit from cardiac resynchronization therapy (CRT) still need to be optimized. A multi-scale heart simulation capable of reproducing the electrophysiology and mechanics of a beating heart may help resolve this problem. The objective of this retrospective study was to test the capability of patient-specific simulation models to reproduce the response to CRT by applying the latest multi-scale heart simulation technology. METHODS AND RESULTS: We created patient-specific heart models with realistic three-dimensional morphology based on the clinical data recorded before treatment in nine patients with heart failure and conduction block treated by biventricular pacing. Each model was tailored to reproduce the surface electrocardiogram and hemodynamics of each patient in formats similar to those used in clinical practice, including electrocardiography (ECG), echocardiography, and hemodynamic measurements. We then performed CRT simulation on each heart model according to the actual pacing protocol and compared the results with the clinical data. CRT simulation improved the ECG index and diminished wall motion dyssynchrony in each patient. These results, however, did not correlate with the actual response. The best correlation was obtained between the maximum value of the time derivative of ventricular pressure (dP/dtmax) and the clinically observed improvement in the ejection fraction (EF) (r=0.94, p<0.01). CONCLUSIONS: By integrating the complex pathophysiology of the heart, patient-specific, multi-scale heart simulation could successfully reproduce the response to CRT. With further verification, this technique could be a useful tool in clinical decision making.

Biomechanical simulation of thorax deformation using finite element approach.

BACKGROUND: The biomechanical simulation of the human respiratory system is expected to be a useful tool for the diagnosis and treatment of respiratory diseases. Because the deformation of the thorax significantly influences airflow in the lungs, we focused on simulating the thorax deformation by introducing contraction of the intercostal muscles and diaphragm, which are the main muscles responsible for the thorax deformation during breathing. METHODS: We constructed a finite element model of the thorax, including the rib cage, intercostal muscles, and diaphragm. To reproduce the muscle contractions, we introduced the Hill-type transversely isotropic hyperelastic continuum skeletal muscle model, which allows the intercostal muscles and diaphragm to contract along the direction of the fibres with clinically measurable muscle activation and active force-length relationship. The anatomical fibre orientations of the intercostal muscles and diaphragm were introduced. RESULTS: Thorax deformation consists of movements of the ribs and diaphragm. By activating muscles, we were able to reproduce the pump-handle and bucket-handle motions for the ribs and the clinically observed motion for the diaphragm. In order to confirm the effectiveness of this approach, we simulated the thorax deformation during normal quiet breathing and compared the results with four-dimensional computed tomography (4D-CT) images for verification. CONCLUSIONS: Thorax deformation can be simulated by modelling the respiratory muscles according to continuum mechanics and by introducing muscle contractions. The reproduction of representative motions of the ribs and diaphragm and the comparison of the thorax deformations during normal quiet breathing with 4D-CT images demonstrated the effectiveness of the proposed approach. This work may provide a platform for establishing a computational mechanics model of the human respiratory system.

Distinct functional roles of cardiac mitochondrial subpopulations revealed by a 3D simulation model.

Experimental characterization of two cardiac mitochondrial subpopulations, namely, subsarcolemmal mitochondria (SSM) and interfibrillar mitochondria (IFM), has been hampered by technical difficulties, and an alternative approach is eagerly awaited. We previously developed a three-dimensional computational cardiomyocyte model that integrates electrophysiology, metabolism, and mechanics with subcellular structure. In this study, we further developed our model to include intracellular oxygen diffusion, and determined whether mitochondrial localization or intrinsic properties cause functional variations. For this purpose, we created two models: one with equal SSM and IFM properties and one with IFM having higher activity levels. Using these two models to compare the SSM and IFM responses of [Ca(2+)], tricarboxylic acid cycle activity, [NADH], and mitochondrial inner membrane potential to abrupt changes in pacing frequency (0.25-2 Hz), we found that the reported functional differences between these subpopulations appear to be mostly related to local [Ca(2+)] heterogeneity, and variations in intrinsic properties only serve to augment these differences. We also examined the effect of hypoxia on mitochondrial function. Under normoxic conditions, intracellular oxygen is much higher throughout the cell than the half-saturation concentration for oxidative phosphorylation. However, under limited oxygen supply, oxygen is mostly exhausted in SSM, leaving the core region in an anoxic condition. Reflecting this heterogeneous oxygen environment, the inner membrane potential continues to decrease in IFM, whereas it is maintained to nearly normal levels in SSM, thereby ensuring ATP supply to this region. Our simulation results provide clues to understanding the origin of functional variations in two cardiac mitochondrial subpopulations and their differential roles in maintaining cardiomyocyte function as a whole.

Mitochondrial colocalization with Ca2+ release sites is crucial to cardiac metabolism.

In cardiomyocyte subcellular structures, colocalization of mitochondria with Ca2+ release sites is implicated in regulation of cardiac energetics by facilitating Ca2+ influx into mitochondria to modulate the tricarboxylic acid (TCA) cycle. However, current experimental techniques limit detailed examination of this regulatory mechanism. Earlier, we developed a three-dimensional (3D) finite-element cardiomyocyte model featuring a subcellular structure that integrates excitation-contraction coupling and energy metabolism. Here, using this model, we examined the influence of distance between mitochondria and Ca2+ release sites by comparing a normal (50-nm) distance model and a large (200-nm) distance model (LD). The influence of distance was minimal under a low pacing rate (0.25 Hz), but under a higher pacing rate (2 Hz), lower levels of mitochondrial Ca2+ and NADH, elevated phosphate, and suppressed force generation became apparent in the LD model. Such differences became greater when functional impairments (reduced TCA cycle activity, uncoupling effect, and failing excitation-contraction coupling) were additionally imposed. We concluded that juxtaposition of the mitochondria and the Ca2+ release sites is crucial for rapid signal transmission to maintain cardiac-energy balance. The idealized 3D model of cardiac excitation-contraction and metabolism is a powerful tool to study cardiac energetics.

Effects of an hERG activator, ICA-105574, on electrophysiological properties of canine hearts.

In short QT syndrome, inherited gain-of-function mutations in the human ether a-gogo-related gene (hERG) K(+) channel have been associated with development of fatal arrhythmias. This implies that drugs that activate hERG as a side effect may likewise pose significant arrhythmia risk. hERG activators have been found to have diverse mechanisms of activation, which may reflect their distinct binding sites. Recently, the new hERG activator ICA-105574 was introduced, which disables inactivation of the hERG channel with very high potency. We explored characteristics of this new drug in several experimental models. Patch clamp experiments were used to verify activation of hERG channels by ICA-105574 in human embryonic kidney cells stably-expressing hERG channels. ICA-105574 significantly shortened QT and QTc intervals and monophasic action potential duration (MAP(90)) in Langendorff-perfused guinea-pig hearts. We also administered ICA-105574 to anesthetized dogs while recording ECG and drug plasma concentrations. ICA-105574 (10 mg/kg) significantly shortened QT and QTc intervals, with a free plasma concentration of approximately 1.7 µM at the point of maximal effect. Our data showed that unbound ICA-105574 caused QT shortening in dogs at concentrations comparable to the half maximal effective concentration (EC(50), 0.42 µM) of hERG activation in the patch clamp studies.

Patient specific simulation of body surface ECG using the finite element method.

BACKGROUND: Recent studies, supported by advances in computer science, have successfully simulated the excitation and repolarization processes of the heart, based on detailed cell models of electrophysiology and implemented with realistic morphology. METHODS: In this study, we extend these approaches to simulate the body surface electrocardiogram (ECG) of specific individuals. Patient-specific finite element models of the heart and torso are created for four patients with various heart diseases, based on clinical data including computer tomography, while the parallel multi-grid method is used to solve the dynamic bi-domain problem. Personalization procedures include demarcation of nonexcitable tissue, allocation of the failing myocyte model of electrophysiology, and modification of the excitation sequence. In particular, the adjustment of QRS morphology requires iterative computations, facilitated by the simultaneous visualization of the propagation of excitation in the heart, average QRS vector in the torso, and 12-lead ECG. RESULTS: In all four cases we obtained reasonable agreement between the simulated and actual ECGs. Furthermore, we also simulated the ECGs of three of the patients under bi-ventricular pacing, and once again successfully reproduced the actual ECG morphologies. Since no further adjustments were made to the heart models in the pacing simulations, the good agreement provides strong support for the validity of the models. CONCLUSIONS: These results not only help us understand the cellular basis of the body surface ECG, but also open the possibility of heart simulation for clinical applications.

Discordance of the areas of peak wall shear stress and tissue stress in coronary artery plaques as revealed by fluid-structure interaction finite element analysis: a case study.

Simulation studies have been performed in attempts to elucidate the signifi cance of shear and tissue stresses in the progression and rupture of coronary artery plaques, but few studies have analyzed both stresses simultaneously. We analyzed the distributions of shear stress and tissue stress in a model of coronary artery plaque based on intravascular ultrasound data by fluid-structure interaction finite element analysis under physiological pressure and flow. As shown in previous studies, the region of peak shear stress was observed at the proximal side of the plaque where flow velocity was high but its value was at most 10 Pa. On the other hand, 1000-10,000 times greater tissue stress was located in the stenotic region but the location of peak tissue stress was different from that of shear stress. We also found that stenting not only stabilizes the stented segment but also reduces the stress in the adjacent region. Fluid-structure interaction analysis revealed discordance in the distribution of shear and tissue stresses. These two stresses exert distinct influences on the coronary plaque, rupture of which may occur where tissue stress exceeds the plaque strength, which is weakened by pathological processes triggered by shear stress.

Structural heterogeneity in the ventricular wall plays a significant role in the initiation of stretch-induced arrhythmias in perfused rabbit right ventricular tissues and whole heart preparations.

RATIONALE: Mechanical stress is known to alter the electrophysiological properties of the myocardium and may trigger fatal arrhythmias when an abnormal load is applied to the heart. OBJECTIVE: We tested the hypothesis that the structural heterogeneity of the ventricular wall modulates globally applied stretches to create heterogeneous strain distributions that lead to the initiation of arrhythmias. METHODS AND RESULTS: We applied global stretches to arterially perfused rabbit right ventricular tissue preparations. The distribution of strain (determined by marker tracking) and the transmembrane potential (measured by optical mapping) were simultaneously recorded while accounting for motion artifacts. The 3D structure of the preparations was also examined using a laser displacement meter. To examine whether such observations can be translated to the physiological condition, we performed similar measurements in whole heart preparations while applying volume pulses to the right ventricle. At the tissue level, larger stretches (> or = 20%) caused synchronous excitation of the entire preparation, whereas medium stretches (10% and 15%) induced focal excitation. We found a significant correlation between the local strain and the local thickness, and the probability for focal excitation was highest for medium stretches. In the whole heart preparations, we observed that such focal excitations developed into reentrant arrhythmias. CONCLUSIONS: Global stretches of intermediate strength, rather than intense stretches, created heterogeneous strain (excitation) distributions in the ventricular wall, which can trigger fatal arrhythmias.

UT-Heart: A Finite Element Model Designed for the Multiscale and Multiphysics Integration of our Knowledge on the Human Heart.

To fully understand the health and pathology of the heart, it is necessary to integrate knowledge accumulated at molecular, cellular, tissue, and organ levels. However, it is difficult to comprehend the complex interactions occurring among the building blocks of biological systems across these scales. Recent advances in computational science supported by innovative high-performance computer hardware make it possible to develop a multiscale multiphysics model simulating the heart, in which the behavior of each cell model is controlled by molecular mechanisms and the cell models themselves are arranged to reproduce elaborate tissue structures. Such a simulator could be used as a tool not only in basic science but also in clinical settings. Here, we describe a multiscale multiphysics heart simulator, UT-Heart, which uses unique technologies to realize the abovementioned features. As examples of its applications, models for cardiac resynchronization therapy and surgery for congenital heart disease will be also shown.

A thermodynamically consistent monte carlo cross-bridge model with a trapping mechanism reveals the role of stretch activation in heart pumping.

Changes in intracellular calcium concentrations regulate heart beats. However, the decline in the left ventricular pressure during early diastole is much sharper than that of the Ca2+ transient, resulting in a rapid supply of blood to the left ventricle during the diastole. At the tissue level, cardiac muscles have a distinct characteristic, known as stretch activation, similar to the function of insect flight muscles. Stretch activation, which is a delayed increase in force following a rapid muscle length increase, has been thought to be related to autonomous control in these muscles. In this numerical simulation study, we introduced a molecular mechanism of stretch activation and investigated the role of this mechanism in the pumping function of the heart, using the previously developed coupling multiple-step active stiffness integration scheme for a Monte Carlo (MC) cross-bridge model and a bi-ventricular finite element model. In the MC cross-bridge model, we introduced a mechanism for trapping the myosin molecule in its post-power stroke state. We then determined the rate constants of transitions for trapping and escaping in a thermodynamically consistent manner. Based on our numerical analysis, we draw the following conclusions regarding the stretch activation mechanism: (i) the delayed force becomes larger than the original isometric force because the population of trapped myosin molecules and their average force increase after stretching; (ii) the delayed force has a duration of more than a few seconds owing to a fairly small rate constant of escape from the trapped state. For the role of stretch activation in heart pumping, we draw the following conclusions: (iii) for the regions in which the contraction force decreases earlier than the neighboring region in the end-systole phase, the trapped myosin molecules prevent further lengthening of the myocytes, which then prevents further shortening of neighboring myocytes; (iv) as a result, the contraction forces are sustained longer, resulting in a larger blood ejection, and their degeneration is synchronized.

A three-dimensional simulation model of cardiomyocyte integrating excitation-contraction coupling and metabolism.

Recent studies have revealed that Ca(2+) not only regulates the contraction of cardiomyocytes, but can also function as a signaling agent to stimulate ATP production by the mitochondria. However, the spatiotemporal resolution of current experimental techniques limits our investigative capacity to understand this phenomenon. Here, we created a detailed three-dimensional (3D) cardiomyocyte model to study the subcellular regulatory mechanisms of myocardial energetics. The 3D cardiomyocyte model was based on the finite-element method, with detailed subcellular structures reproduced, and it included all elementary processes involved in cardiomyocyte electrophysiology, contraction, and ATP metabolism localized to specific loci. The simulation results were found to be reproducible and consistent with experimental data regarding the spatiotemporal pattern of cytosolic, intrasarcoplasmic-reticulum, and mitochondrial changes in Ca(2+); as well as changes in metabolite levels. Detailed analysis suggested that although the observed large cytosolic Ca(2+) gradient facilitated uptake by the mitochondrial Ca(2+) uniporter to produce cyclic changes in mitochondrial Ca(2+) near the Z-line region, the average mitochondrial Ca(2+) changes slowly. We also confirmed the importance of the creatine phosphate shuttle in cardiac energy regulation. In summary, our 3D model provides a powerful tool for the study of cardiac function by overcoming some of the spatiotemporal limitations of current experimental approaches.

Transmural and apicobasal gradients in repolarization contribute to T-wave genesis in human surface ECG.

The cellular basis of the T-wave morphology of surface ECG remains controversial in clinical cardiology. We examined the effect of action potential duration (APD) distribution on T-wave morphology using a realistic model of the human ventricle and torso. We developed a finite-element model of the ventricle consisting of ∼26 million elements, including the conduction system, each implemented with the ion current model of cardiomyocytes. This model was embedded in a torso model with distinct organ structures to obtain the standard ECG leads. The APD distribution was changed in the transmural direction by locating the M cells in either the endocardial or epicardial region. We also introduced apicobasal gradients by modifying the ion channel parameters. Both the transmural gradient (with M cells on the endocardial side) and the apicobasal gradient produced positive T waves, although a very large gradient was required for the apicobasal gradient. By contrast, T waves obtained with the transmural gradient were highly symmetric and, therefore, did not represent the true physiological state. Only combination of the transmural and the moderate apicobasal gradients produced physiological T waves in surface ECG. Positive T waves in surface ECG mainly originated from the transmural distribution of APD with M cells on the endocardial side, although the apicobasal gradient was also required to attain the physiological waveform.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation.

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.