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This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

Implantation of cardioverter defibrillators is the most widely used primary preventive care for sudden cardiac death (SCD). Current clinical practice of using a left-ventricular ejection fraction threshold as the sole criterion for defibrillator insertion results in many unnecessary implantations. To address the need for alternative criteria, we seek three-dimensional shape metrics of the left ventricle derived from clinical cardiac magnetic resonance images that can predict SCD risk. The present study is a proof-of-concept, where we have combined image-processing and computational anatomy techniques to develop a processing pipeline to statistically compare localized left ventricular shape metrics between patient groups. We tested the methodology with data from a small cohort of patients, classified into two groups based on SCD risk. The results demonstrate that our approach is able to locate systematic wall thickness differences between the two groups.

Defibrillation efficacy is decreased in infarcted hearts, but the mechanisms by which infarcted hearts are more vulnerable to electric shocks than healthy hearts remain poorly understood. The goal of this study was to provide insight into the 3D mechanisms for the increased vulnerability to electric shocks in infarcted hearts. We hypothesized that changes in virtual electrode polarizations (VEPs) and propagation delay through the peri-infarct zone (PZ) were responsible. We developed a micro anatomically detailed rabbit ventricular model with chronic myocardial infarction from magnetic resonance imaging and enriched the model with data from optical mapping experiments. We further developed a control model without the infarct. The simulation protocol involved apical pacing followed by biphasic shocks. Simulation results from both models were compared.The upper limit of vulnerability(ULV) was 8 V cm(-1) in the infarction model and 4 V cm(-1) in the control model. VEPs were less pronounced in the infarction model, providing a larger excitable area for postshock propagation but smaller transmembrane potential gradients to initiate new wavefronts. Initial post-shock transmural activation occurred at a later time in the infarction model, and the PZ served to delay propagation in subsequent beats. The presence of the PZ was found to be responsible for the increased vulnerability.

Atrial fibrillation (AF), a very common cardiac arrhythmia, has recently emerged as a new interdisciplinary epicenter of clinical, engineering, and basic science research. This emergence is fueled by new results from experiments, animal models of the disease, and multimodal measurements in patients, catalyzed by rapid developments in interventional approaches to treatment. Our understanding of the disease is growing but still inadequate to provide satisfactory patient care and so there is enormous opportunity for a range of research approaches. Some attributes of the disease also make it a simultaneously compelling, accessible, and challenging target for inquiry; AF emerges only as a result of long term changes in tissue substrate, is triggered by remote ectopic activity, involves one or more mechanisms of cardiac arrhythmias, has a variable time course in individuals, and is both damaging to immediate quality of life and a major risk for secondary disease.

Technological limitations pose a major challenge to acquisition of myocardial fiber orientations for patient-specific modeling of cardiac (dys)function and assessment of therapy. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4° . Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.

Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace–Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.

Left ventricular-assist devices (LVADs) are used to supply blood to the body of patients with heart failure. Pressure unloading is greater for counter-pulsating LVADs than for continuous LVADs. However, several clinical trials have demonstrated that myocardial recovery is similar for both types of LVAD. This study examined the contractile energy consumption of the myocardium with continuous and counter-pulsating LVAD support to ascertain the effect of the different LVADs on myocardial recovery. We used a three-dimensional electromechanical model of canine ventricles, with models of the circulatory system and an LVAD. We compared the left ventricular peak pressure (LVPP) and contractile ATP consumption between pulsatile and continuous LVADs. With the continuous and counter-pulsating LVAD, the LVPP decreased to 46 and 10%, respectively, and contractile ATP consumption decreased to 60 and 50%. The small difference between the contractile ATP consumption of these two types of LVAD may explain the comparable effects of the two types on myocardial recovery.

A long-sought, and thus far elusive, goal has been to develop drugs to manage diseases of excitability. One such disease that affects millions each year is cardiac arrhythmia, which occurs when electrical impulses in the heart become disordered, sometimes causing sudden death. Pharmacological management of cardiac arrhythmia has failed because it is not possible to predict how drugs that target cardiac ion channels, and have intrinsically complex dynamic interactions with ion channels, will alter the emergent electrical behavior generated in the heart. Here, we applied a computational model, which was informed and validated by experimental data, that defined key measurable parameters necessary to simulate the interaction kinetics of the anti-arrhythmic drugs flecainide and lidocaine with cardiac sodium channels. We then used the model to predict the effects of these drugs on normal human ventricular cellular and tissue electrical activity in the setting of a common arrhythmia trigger, spontaneous ventricular ectopy. The model forecasts the clinically relevant concentrations at which flecainide and lidocaine exacerbate, rather than ameliorate, arrhythmia. Experiments in rabbit hearts and simulations in human ventricles based on magnetic resonance images validated the model predictions. This computational framework initiates the first steps toward development of a virtual drug-screening system that models drug-channel interactions and predicts the effects of drugs on emergent electrical activity in the heart.

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.

Fibroblasts are electrophysiologically quiescent in the healthy heart. Evidence suggests that remodeling following myocardial infarction may include coupling of myofibroblasts (Mfbs) among themselves and with myocytes via gap junctions. We use a magnetic resonance imaging-based, three-dimensional computational model of the chronically infarcted rabbit ventricles to characterize the arrhythmogenic substrate resulting from Mfb infiltration as a function of Mfb density. Mfbs forming gap junctions were incorporated into both infarct regions, the periinfarct zone (PZ) and the scar; six scenarios were modeled: 0%, 10%, and 30% Mfbs in the PZ, with either 80% or 0% Mfbs in the scar. Ionic current remodeling in PZ was also included. All preparations exhibited elevated resting membrane potential within and near the PZ and action potential duration shortening throughout the ventricles. The unique combination of PZ ionic current remodeling and different degrees of Mfb infiltration in the infarcted ventricles determines susceptibility to arrhythmia. At low densities, Mfbs do not alter arrhythmia propensity; the latter arises predominantly from ionic current remodeling in PZ. At intermediate densities, Mfbs cause additional action potential shortening and exacerbate arrhythmia propensity. At high densities, Mfbs protect against arrhythmia by causing resting depolarization and blocking propagation, thus overcoming the arrhythmogenic effects of PZ ionic current remodeling.

The extraction of the cardiac Purkinje system (PS) from intensity images is a critical step toward the development of realistic structural models of the heart. Such models are important for uncovering the mechanisms of cardiac disease and improving its treatment and prevention. Unfortunately, the manual extraction of the PS is a challenging and error-prone task due to the presence of image noise and numerous fiber junctions. To deal with these challenges, we propose a framework that estimates local fiber orientations with high accuracy and reconstructs the fibers via tracking. Our key contribution is the development of a descriptor for estimating the orientation distribution function (ODF), a spherical function encoding the local geometry of the fibers at a point of interest. The fiber/branch orientations are identified as the modes of the ODFs via spherical clustering and guide the extraction of the fiber centerlines. Experiments on synthetic data evaluate the sensitivity of our approach to image noise, width of the fiber, and choice of the mode detection strategy, and show its superior performance compared to those of the existing descriptors. Experiments on the free-running PS in an MR image also demonstrate the accuracy of our method in reconstructing such sparse fibrous structures.

Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computation physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single cell models and the second half addresses organ models. At the subcelluar level, myofilament models represent actin-myosin interaction and Ca-based activation. Myofilament models and their refinements represent an overview of the development in the field. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered the cellular basis of the Frank-Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction-diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

This article reviews the development of patient-specific image-based models of the heart and the circulatory system. The goal of these types of models is to provide better assessment of cardiovascular function under the patient-specific pathophysiological conditions and to serve as a testbed for improved cardiovascular therapies that are tailored to the patient. These new models constitute a part of the growing trend towards the development of new computational approaches (i.e., computational medicine) that can aid treatment and prevention of human disease.

A mathematical model describing electrical stimulation of the heart is developed, in which a uniform electric field is applied to a spherical shell of cardiac tissue. The electrical properties of the tissue are characterized using the bidomain model. Analytical expressions for the induced transmembrane potential are derived for the cases of equal anisotropy ratios in the intracellular and interstitial (extracellular) spaces, and no transverse coupling between fibers. Numerical calculations of the transmembrane potential are also performed using realistic electrical conductivities. The model illustrates several mechanisms for polarization of the cell membrane, which can be divided into two categories, depending on if they polarize fibers at the heart surface only or if they polarize fibers both at the surface and within the bulk of the tissue. The latter mechanisms can be classified further according to whether they originate from continuous or discrete properties of cardiac tissue. If cardiac tissue had equal anisotropy ratios, a large membrane polarization would be induced at the heart surface that would become negligible a few length constants into the tissue. If cardiac tissue were continuous and had no transverse coupling between fibers, a membrane polarization would be induced throughout the bulk that would arise from an "activating function" similar to the one used to describe neural stimulation. Polarization would occur if the fibers were curving, if the cross-sectional area of the tissue were changing (fiber branching), or both. The numerically calculated transmembrane potential is intermediate between those predicted using the assumptions of equal anisotropy ratios and no transverse coupling between fibers. Although discrete properties of cardiac tissue are not incorporated into this model, an estimate of their effect indicates that the amplitude of the polarization caused by the resistance of the cellular junctions is similar to that caused by fiber curvature and branching. The spatial distribution of the polarization, however, is quite different.

BACKGROUND Electromechanical wave imaging (EWI) is an entirely noninvasive, ultrasound-based imaging method capable of mapping the electromechanical activation sequence of the ventricles in vivo. Given the broad accessibility of ultrasound scanners in the clinic, the application of EWI could constitute a flexible surrogate for the 3-dimensional electrical activation. OBJECTIVE The purpose of this report is to reproduce the electromechanical wave (EW) using an anatomically realistic electromechanical model, and establish the capability of EWI to map the electrical activation sequence in vivo when pacing from different locations. METHODS EWI was performed in 1 canine during pacing from 3 different sites. A high-resolution dynamic model of coupled cardiac electromechanics of the canine heart was used to predict the experimentally recorded electromechanical wave. The simulated 3-dimensional electrical activation sequence was then compared with the experimental EW. RESULTS The electrical activation sequence and the EW were highly correlated for all pacing sites. The relationship between the electrical activation and the EW onset was found to be linear, with a slope of 1.01 to 1.17 for different pacing schemes and imaging angles. CONCLUSION The accurate reproduction of the EW in simulations indicates that the model framework is capable of accurately representing the cardiac electromechanics and thus testing new hypotheses. The one-to-one correspondence between the electrical activation and the EW sequences indicates that EWI could be used to map the cardiac electrical activity. This opens the door for further exploration of the technique in assisting in the early detection, diagnosis, and treatment monitoring of rhythm dysfunction.

One of the most important components of mechano-electric coupling is stretch-activated channels, sarcolemmel channels that open upon mechanical stimuli. Uncovering the mechanisms by which stretch-activated channels contribute to ventricular arrhythmogenesis under a variety of pathological conditions is hampered by the lack of experimental methodologies that can record the three-dimensional electromechanical activity simultaneously at high spatiotemporal resolution. Computer modeling provides such an opportunity. This goal of this review is to illustrate the utility of sophisticated, physiologically realistic, whole heart computer simulations in determining the role of mechano-electric coupling in ventricular arrhythmogeneisis. We first present the various ways by which stretch-activated channels have been modeled and demonstrate how these channels affect cardiac electrophysiological properties. Next, we employ an electrophysiological model of the rabbit ventricles to understand how so-called commotio cordis, the mechanical impact to the pre-cordial region of the heart, can initiate ventricular tachycardia via the recruitment of stretch-activated channels. Using the same model, we also provide mechanistic insight to the termination of arrhythmias by precordial thump under normal and globally-ischemic conditions. Lastly, we employ a novel anatomically-realistic dynamic 3D coupled electromechanical model of the rabbit ventricles to gain insight into the role of electromechanical dysfunction in arrhythmogenesis during acute regional ischemia.

Background After near-defibrillation threshold (DFT) shocks from an implantable cardioverter-defibrillator (ICD), the first postshock activation that leads to defibrillation failure arises focally after an isoelectric window (IW). The mechanisms underlying the IW remain incompletely understood. Objective The goal of this study was to provide mechanistic insight into the origins of postshock activations and IW after ICD shocks, and to link shock outcome to the preshock state of the ventricles. We hypothesized that the nonuniform ICD field results in the formation of an intramural excitable area (tunnel) only in the left ventricular (LV) free wall, through which both pre-existing and new shock-induced wavefronts propagate during the IW. Methods Simulations were conducted using a realistic three dimensional (3D) model of defibrillation in the rabbit ventricles. Biphasic ICD shocks of varying strengths were delivered to 27 different fibrillatory states. Results After near-DFT shocks, regardless of preshock state, the main postshock excitable area was always located within LV free wall, creating an intramural tunnel. Either pre-existing fibrillatory or shock-induced wavefronts propagated during the IW (duration of up to 74 ms) in this tunnel and emerged as breakthroughs on LV epicardium. Preshock activity within the LV played a significant role in shock outcome: a large number of preshock filaments resulted in an IW associated with tunnel propagation of pre-existing rather than shock-induced wavefronts. Furthermore, shocks were more likely to succeed if the LV excitable area was smaller. Conclusion The LV intramural excitable area is the primary reason for near-DFT failure. Any intervention that decreases the extent of this area will improve the likelihood of defibrillation success.

The practice of cardiovascular care has seen significant advances in the past 40 years with dramatic reduction of mortality from heart diseases. Nevertheless, cardiac diseases remain the leading cause of morbidity and mortality in the developed world and are on the rise in developing countries [37]. It is well recognized that the conventional clinical practice of using population-based metrics to prescribe “one size fits all” treatment methods does not provide optimal health care for many patients because of the individual variability in pathophysiology. Moreover, in many situations, physicians do not have a way of predicting patient responses to various therapeutic interventions, and therefore have to rely on “trial and error” to identify the treatment-response relationship. An emerging paradigm that addresses these challenges is the so-called personalized medicine, which seeks to develop diagnosis and treatment methods that can be tailored by the physician a priori according to the specific needs of an individual patient [25, 44, 52]. Application of such personalized approach to cardiac care can dramatically improve the treatment of heart diseases. To fully utilize the quality and diversity of clinically available data for personalized cardiac care, it is necessary to integrate structural and functional data at molecular, cellular, tissue, and organ level into a consistent framework which can be used to predict the outcomes of therapeutic interventions. Computational modeling provides a powerful tool to perform this data integration [29, 32].

Rationale : Although ventricular premature beats (VPBs) during acute regional ischemia have been linked to mechanical stretch of ischemic tissue, whether and how ischemia-induced mechanical dysfunction can induce VPBs and facilitate their degradation into reentrant arrhythmias has not been yet addressed. Objective : This study used a novel multiscale electromechanical model of the rabbit ventricles to investigate the origin of and the substrate for spontaneous arrhythmias arising from ischemia-induced electrophysiological and mechanical changes. Methods and Results : Two stages of ischemia were simulated. Dynamic mechanoelectrical feedback was modeled as spatially and temporally nonuniform membrane currents through mechanosensitive channels, the conductances of which depended on local strain rate. Our results reveal that both strains and strain rates were significantly larger in the central ischemic zone than in the border zone. However, in both ischemia stages, a VPB originated from the ischemic border in the left ventricular apical endocardium because of mechanically induced suprathreshold depolarizations. It then traveled fully intramurally until emerging from the ischemic border on the anterior epicardium. Reentry was formed only in the advanced ischemia stage as the result of a widened temporal excitable gap. Mechanically induced delayed afterdepolarization-like events contributed to the formation of reentry by further decreasing the already reduced-by-hyperkalemia local excitability, causing extended conduction block lines and slowed conduction in the ischemic region. Conclusions : Mechanically induced membrane depolarizations in the ischemic region are the mechanism by which mechanical activity contributes to both the origin of and substrate for spontaneous arrhythmias under the conditions of acute regional ischemia.

In the intact heart, the distribution of electromechanical delay (EMD), the time interval between local depolarization and myocyte shortening onset, depends on the loading conditions. The distribution of EMD throughout the heart remains, however, unknown because current experimental techniques are unable to evaluate three-dimensional cardiac electromechanical behavior. The goal of this study was to determine the three-dimensional EMD distributions in the intact ventricles for sinus rhythm (SR) and epicardial pacing (EP) by using a new, to our knowledge, electromechanical model of the rabbit ventricles that incorporates a biophysical representation of myofilament dynamics. Furthermore, we aimed to ascertain the mechanisms that underlie the specific three-dimensional EMD distributions. The results revealed that under both conditions, the three-dimensional EMD distribution is nonuniform. During SR, EMD is longer at the epicardium than at the endocardium, and is greater near the base than at the apex. After EP, the three-dimensional EMD distribution is markedly different; it also changes with the pacing rate. For both SR and EP, late-depolarized regions were characterized with significant myofiber prestretch caused by the contraction of the early-depolarized regions. This prestretch delays myofiber-shortening onset, and results in a longer EMD, giving rise to heterogeneous three-dimensional EMD distributions.

Ongoing investigation of the electrophysiology and pathophysiology of the human atria requires an accurate representation of the membrane dynamics of the human atrial myocyte. However, existing models of the human atrial myocyte action potential do not accurately reproduce experimental observations with respect to the kinetics of key repolarizing currents or rate dependence of the action potential and fail to properly enforce charge conservation, an essential characteristic in any model of the cardiac membrane. In addition, recent advances in experimental methods have resulted in new data regarding the kinetics of repolarizing currents in the human atria. The goal of this study was to develop a new model of the human atrial action potential, based on the Nygren et al. model of the human atrial myocyte and newly available experimental data, that ensures an accurate representation of repolarization processes and reproduction of action potential rate dependence and enforces charge conservation. Specifically, the transient outward K+current ( It) and ultrarapid rectifier K+current ( IKur) were newly formulated. The inwardly recitifying K+current ( IK1) was also reanalyzed and implemented appropriately. Simulations of the human atrial myocyte action potential with this new model demonstrated that early repolarization is dependent on the relative conductances of Itand IKur, whereas densities of both IKurand IK1underlie later repolarization. In addition, this model reproduces experimental measurements of rate dependence of It, IKur, and action potential duration. This new model constitutes an improved representation of excitability and repolarization reserve in the human atrial myocyte and, therefore, provides a useful computational tool for future studies involving the human atrium in both health and disease.

The inclusion of the free-running Purkinje network in computational simulations provides a significant insight into understanding the mechanisms of cardiac pathophysiologies. However, its automatic extraction is challenging due to the presence of abundant local complexities. We thereby introduce a novel algorithm to track the Purkinje fibers in high resolution magnetic resonance (MR) images. Our formulation successively identifies local fiber orientations by using a nonlinear oriented filter. Specifically, the filter is used to compute several local profiles, from which one can estimate the orientation distribution function (ODF). The algorithm then determines the directions to be followed by detecting the modes of the local ODF using different spherical clustering methods. We quantitatively compare the accuracy of the tracked fibers with manually delineated anatomical structures.

In this study we develop a methodology to accurately extract and visualize cardiac microstructure from experimental Diffusion Tensor (DT) data. First, a test model was constructed using an image-based model generation technique on Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. These images were derived from a dataset having 122x122x500 um 3 voxel resolution. De-noising and image enhancement was applied to this high-resolution dataset to clearly define anatomical boundaries within the images. The myocardial tissue was segmented from structural images using edge detection, region growing, and level set thresholding. The primary eigenvector of the diffusion tensor for each voxel, which represents the longitudinal direction of the fiber, was calculated to generate a vector field. Then an advanced locally regularizing nonlinear anisotropic filter, termed Perona-Malik (PEM), was used to regularize this vector field to eliminate imaging artifacts inherent to DT-MRI from volume averaging of the tissue with the surrounding medium. Finally, the vector field was streamlined to visualize fibers within the segmented myocardial tissue to compare the results with unfiltered data. With this technique, we were able to recover locally regularized (homogenized) fibers with a high accuracy by applying the PEM regularization technique, particularly on anatomical surfaces where imaging artifacts were most apparent. This approach not only aides in the visualization of noisy complex 3D vector fields obtained from DT-MRI, but also eliminates volume averaging artifacts to provide a realistic cardiac microstructure for use in electrophysiological modeling studies.

The objective of this article is to present a set of methods for constructing realistic computational models of cardiac structure from high-resolution structural and diffusion tensor magnetic resonance images and to demonstrate the applicability of the models in simulation studies. The structural image is segmented to identify various regions such as normal myocardium, ventricles, and infarct. A finite element mesh is generated from the processed structural data, and fiber orientations are assigned to the elements. The Purkinje system, when visible, is modeled using linear elements that interconnect a set of manually identified points. The methods were applied to construct 2 different models; and 2 simulation studies, which demonstrate the applicability of the models in the analysis of arrhythmia and defibrillation, were performed. The models represent cardiac structure with unprecedented detail for simulation studies.

We introduce and compare three different modalities to study seismocardiogram (SCG) and its correlation with cardiac events. We used an accelerometer attached to the subject sternum to get a reference measure. Cardiac events were then approximately identified using echocardiography. As an alternative approximation, we used consecutive Cine-MRI images of the heart to capture cardiac movements and compared them with the experimental SCG. We also employed an anatomically accurate, finite element base electromechanical model with geometry built completely from DT-MRI to simulate a portion of the cardiac cycle as observed in the SCG signal. The preliminary results demonstrate the usability of these newly proposed methods to investigate the mechanism of SCG waves and also demonstrate the usability of echocardiograph in interpretation of these results in terms of correlating them to underlying cardiac cycle events.

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease.

The paper compares the rigorous and the conventional approximate line source solution of Laplace's equation used to evaluate the potential of a single cylindrical fibre. Particular attention is given to the solutions for a radially restricted circular cylindrical volume conductor. The effect of the extent of the volume conductor b on the difference between the potentials evaluated according to the different models is examined. For values of b larger than 10 times the fibre radius, the relative difference is less than 1 per cent and the values of b around 2 times the fibre radii, the error reaches as much as 17 per cent.

Previous models based on a cylindrical bidomain assumed either that the ratio of intracellular and interstitial conductivities in the principal directions were the same or that there was no radial variation in potential (i.e., a planar front, ∂V m ⧸ ∂p = 0). This paper presents a formulation and the expressions for the intracellular, interstitial, extracellular, and transmembrane potentials arising from nonplanar propagation along a cylindrical bundle of cardiac tissue represented as a bidomain with arbitrary anisotropy. For unequal anisotropy, the transmembrane current depends not only on the local change of the transmembrane potential but also on the nature of the transmembrane potential throughout the volume.

Atrial fibrosis has been implicated in the development and maintenance of atrial arrhythmias, and is characterized by expansion of the extracellular matrix and an increased number of fibroblasts (Fbs). Electrotonic coupling between atrial myocytes and Fbs may contribute to the formation of an arrhythmogenic substrate. However, the role of these cell-cell interactions in the function of both normal and diseased atria remains poorly understood. The goal of this study was to gain mechanistic insight into the role of electrotonic Fb-myocyte coupling on myocyte excitability and repolarization. To represent the system, a human atrial myocyte (hAM) coupled to a variable number of Fbs, we employed a new ionic model of the hAM, and a variety of membrane representations for atrial Fbs. Simulations elucidated the effects of altering the intercellular coupling conductance, electrophysiological Fb properties, and stimulation rate on the myocyte action potential. The results demonstrate that the myocyte resting potential and action potential waveform are modulated strongly by the properties and number of coupled Fbs, the degree of coupling, and the pacing frequency. Our model provides mechanistic insight into the consequences of heterologous cell coupling on hAM electrophysiology, and can be extended to evaluate these implications at both tissue and organ levels.

Defibrillation of the heart by high-intensity electric shocks is currently the only reliable procedure for termination of ventricular fibrillation. Despite the critical role that defibrillation therapy plays in saving human life, elucidating the mechanisms by which electric shocks halt life-threatening arrhythmias has been a long and arduous process. Uncovering how electric current delivered to the heart to terminate lethal arrhythmias traverses myocardial structures and interacts with the wavefronts of fibrillation has been enormously challenging. Of particular importance has been obtaining insight into the mechanisms by which the shock fails since reinitiation of fibrillation is related not only to the effect of the shock on the electrical state of the myocardium, but also to the intrinsic properties of the tissue that lead to destabilization of postshock activations and their degradation into electric turbulence. The complexity of the relationships and dependencies to be teased out and dissected in this quest has been staggering.

The delay in myofiber shortening (MS) onset between the endocardial and epicardial layers is greater than the electrical activation delay during sinus rhythm (SR) and decreases at the location of the pacing site during epicardial pacing (EP). The goal of this study is to demonstrate that increased transmural mechanical delay during SR is determined by the electrical activation sequence within the myocardial layers, rather than the transmural activation pattern. We employed a novel 3D anatomically-accurate electromechanical model of the rabbit ventricles that incorporated a detailed model of cardiac myofilament dynamics. MS was calculated throughout the ventricular volume during SR and for EP at the left ventricular anterior wall. Onset of MS followed the direction of electrical activation for both SR and EP, as shown in Figure . However, transmural delay in MS onset was greater during SR, consistent with experiments (28ms-SR vs. 19ms-EP). Difference in the MS delay could not be explained by changes in transmural electrical activation delay (19ms-SR vs. 25ms-EP). Examination of the mechanisms revealed a longer apex-to-base electrical activation delay on the epicardium as compared to that on the endocardium during SR. “Prestretching” of the late-activated epicardial myofibers at the base by the shortening of the early-activated apical region increased MS delay. No prestretching was observed following EP. This finding indicates that transmural MS delay strongly depends on the electrical and mechanical activation sequence within the myocardial layers. This research has received full or partial funding support from the American Heart Association, AHA Mid-Atlantic Affiliate (Maryland, North Carolina, South Carolina, Virginia & Washington, DC).

The role of the 3D infarct structure in arrhythmia generation and maintenance in hearts with myocardial infarction cannot be fully elucidated through experimental techniques alone. Our aim was to develop methodology to construct a high resolution computational model of the infarcted canine heart using magnetic resonance (MRI) and diffusion tensor images (DTI) and then to use the resulting model to study post-infarction ventricular tachycardia (VT). Segmentation of the MRI and DTI stacks using image processing techniques provided accurate representations of the myocardium, the infarct scar, and the border zone (BZ) surrounding the scar. Realistic electrophysiological properties were assigned to each region. Simulations using the novel model revealed that postinfarction VT is initiated and maintained by reentrant circuits located within the BZ.

The purpose of this study was to determine whether abnormalities of calcium cycling explain ventricular action potential (AP) oscillations and cause electrocardiogram T-wave alternans (TWA).Mechanisms explaining why heart failure patients are at risk for malignant ventricular arrhythmias (ventricular tachycardia [VT]/ventricular fibrillation [VF]) are unclear. We studied whether oscillations in human ventricular AP explain TWA and predict VT/VF, and used computer modeling to suggest potential cellular mechanisms.We studied 53 patients with left ventricular ejection fraction 28 +/- 8% and 18 control subjects. Monophasic APs were recorded in the right ventricle (n = 62) and/or left ventricle (n = 9) at 109 beats/min.Alternans of AP amplitude, computed spectrally, had higher magnitude in study patients than in controls (p = 0.03), particularly in AP phase II (p = 0.02) rather than phase III (p = 0.10). The AP duration and activation restitution (n = 11 patients) were flat at 109 beats/min and did not explain TWA. In computer simulations, only reduced sarcoplasmic reticulum calcium uptake explained our results, causing calcium oscillations, AP amplitude alternans, and TWA that were all abolished by calcium clamping. On prospective follow-up for 949 +/- 553 days, 17 patients had VT/VF. The AP amplitude alternans predicted VT/VF (p = 0.04), and was 78% concordant with simultaneous TWA (p = 0.003).Patients with systolic dysfunction show ventricular AP amplitude alternans that prospectively predicted VT/VF. Alternans in AP amplitude, but not variations in AP duration or conduction, explained TWA ator =109 beats/min. In computer models, these findings were best explained by reduced sarcoplasmic reticulum calcium uptake. Thus, in heart failure patients, in vivo AP alternans may reflect cellular calcium abnormalities and provide a mechanistic link with VT/VF.

We consider the problems of extracting local fiber orientation and tracing tubular structures in 2-D medical images. We first present a nonlinear filter for detecting overlaid orientations at each pixel. The filter is used to build two profiles, the directional profile and the appearance profile, which are designed to give high responses along an oriented structure. The local orientation at a pixel is then obtained from the local maxima of the product of these two profiles. We also develop an algorithm for tracing tubular structures. Starting from a user-specified seed point on the fiber, we find the next point on the fiber by locating the maxima of the tracing profile, which favors the smoothness of the curve as well as its alignment with the estimated orientation. We evaluate the proposed method on different medical structures such as cardiac myofibers, vessels, and microtubules.

Background Delayed ventricular arrhythmias during acute myocardial ischemia (1B arrhythmias) are associated with an increase in tissue impedance and are most likely sustained in a thin subepicardial layer. Objective The goal of this study was to test the hypothesis that heterogeneous uncoupling between depolarized midmyocardium and surviving subepicardium results in heterogeneous refractoriness in the latter, providing the reentry substrate after a premature beat. Methods A 3-dimensional bidomain slab was constructed comprising a normal subepicardial layer coupled to a slightly depolarized (−80 to −60 mV) but inexcitable midmyocardium. Experimentally measured tissue impedance served as input for the model. Four stages of heterogeneous uncoupling between the 2 layers were simulated, each corresponding to an experimental ischemic impedance value. Effective refractory periods (ERP), conduction velocities, and inducibility of reentry were examined. Results Heterogeneous uncoupling resulted in subepicardial ERP dispersion, allowing reentry to occur. The minimum ERP dispersion needed to induce reentry was 28 ms. Reentry induction was only possible in this model at the 2 intermediate stages of uncoupling, and only when midmyocardial resting membrane potential was more negative than −60 mV. Complete uncoupling of the layers resulted in normal subepicardial conduction without arrhythmias. The minimum length of the reentrant pathway was 2.5 cm, comparable to 2.4 cm reported in previous experiments. Conclusion Heterogeneous uncoupling to a negative sink such as depressed inexcitable midmyocardium may be a substrate for ischemia 1B arrhythmias. Total uncoupling removes the arrhythmogenic substrate.

Comprehensive understanding of the ventricular response to shocks is the approach most likely to succeed in reducing defibrillation threshold. We propose a new theory of shock-induced arrhythmogenesis that unifies all known aspects of the response of the heart to monophasic (MS) and biphasic (BS) shocks. The central hypothesis is that submerged “tunnel” propagation of postshock activations through shock-induced intramural excitable areas underlies fibrillation induction and the existence of isoelectric window. We conducted simulations of fibrillation induction using a realistic bidomain model of rabbit ventricles. Following pacing, MS and BS of various strengths/timings were delivered. The results demonstrated that, during the isoelectric window, an activation originated deep within the ventricular wall, arising from virtual electrodes; it then propagated fully intramurally through an excitable tunnel induced by the shock, until it emerged onto the epicardium, becoming the earliest-propagated postshock activation. Differences in shock outcomes for MS and BS were found to stem from the narrower BS intramural postshock excitable area, often resulting in conduction block, and the difference in the mechanisms of origin of the postshock activations, namely intramural virtual electrode–induced phase singularity for MS and virtual electrode–induced propagated graded response for BS. This study provides a novel analysis of the 3D mechanisms underlying the origin of postshock activations in the process of fibrillation induction by MS and BS and the existence of isoelectric window. The tunnel propagation hypothesis could open a new avenue for interventions exploration to achieve significantly lower defibrillation threshold.

In the mammalian heart, myocytes and fibroblasts can communicate via gap junction, or connexin-mediated current flow. Some of the effects of this electrotonic coupling on the action potential waveform of the human ventricular myocyte have been analyzed in detail. The present study employs a recently developed mathematical model of the human atrial myocyte to investigate the consequences of this heterogeneous cell–cell interaction on the action potential of the human atrium. Two independent physiological processes which alter the physiology of the human atrium have been studied. i) The effects of the autonomic transmitter acetylcholine on the atrial action potential have been investigated by inclusion of a time-independent, acetylcholine-activated K + current in this mathematical model of the atrial myocyte. ii) A non-selective cation current which is activated by natriuretic peptides has been incorporated into a previously published mathematical model of the cardiac fibroblast. These results identify subtle effects of acetylcholine, which arise from the nonlinear interactions between ionic currents in the human atrial myocyte. They also illustrate marked alterations in the action potential waveform arising from fibroblast–myocyte source–sink principles when the natriuretic peptide-mediated cation conductance is activated. Additional calculations also illustrate the effects of simultaneous activation of both of these cell-type specific conductances within the atrial myocardium. This study provides a basis for beginning to assess the utility of mathematical modeling in understanding detailed cell–cell interactions within the complex paracrine environment of the human atrial myocardium.

A fully three-dimensional model of the ventricular or atrial free wall will involve a planar geometry of finite thickness. The governing equations for the interstitial and extracellular potential of a planar slab of cardiac tissue comprised of parallel fibers undergoing uniform plane-wave activation are presented. A comparison with a bidomain of cylindrical geometry with the same half-thickness shows that the potentials in the planar bidomain (as a function of depth) approach core-conductor behavior more quickly.

A method to localize the electrical axis of a motor unit (MU) and to simultaneously determine the anisotropy ratio (the ratio between the transverse and the longitudinal extracellular conductivity) of the muscle is proposed. The method is based on the use of Laplace's equation. Particular attention is paid to the theoretical consideration of an asymmetric MU. The method is tested utilizing simulation data on the extracellular potentials of a MU in which the propagation of two depolarized zones along a participant muscle fiber is accounted for. It is shown that the method is reliable and the calculation accurate mostly for the moments of time associated with small changes in the MU potential.

The mathematical description of the extracellular field generated by activity in an excitable fiber in an unbounded volume conductor will depend on assumptions made about the sources and the source-field relationship. This paper examines and compares the rigorous and conventional approximate solutions of Laplace's equation used to evaluate the extracellular potential of a single, cylindrical fiber. The single fiber is considered as both a prototypical element (such as a nerve or muscle fiber) and an elementary model of an entire multicellular preparation (e.g., nerve bundle or Purkinje strand). The effects of the fiber radius, the intracellular and extracellular conductivities, and the shape and extent of the source function (either the transmembrane potential or the intracellular potential) on the solutions are discussed. The results show that, in general, the approximate solutions are unsatisfactory for computing the surface extracellular potential when the single fiber is used to represent a large bundle (greater than 300 microns).

Although the majority of patients undergoing defibrillation suffer from coronary heart disease, little is known about defibrillation in the setting of ischemic disease. The goal of this study is to aid understanding of defibrillation failure in ischemic hearts by studying changes in cardiac vulnerability to electric shocks the first 10 min following LAD occlusion. To do so, a 3D anatomically-accurate electrophysiologically-detailed bidomain model of the regionally ischemic ventricles following LAD occlusion was developed based on experimental data. The ventricles were paced at the apex and truncated exponential monophasic shocks were applied over a range of coupling intervals to determine the upper limit of vulnerability (ULV) and the vulnerable window (VW) in normoxia and 10 min post-occlusion. Simulation results demonstrate that, despite the profound electrophysiological changes in the ischemic region, the ULV remains unchanged 10 min post-occlusion because following high shock strengths gesULV virtual electrode polarization and postshock behavior remain unaffected by ischemia. However, the range of coupling intervals comprising the VW increases from spanning 60 ms in normoxia to 90 ms at 10 min post-occlusion. The increased in vulnerability in regional ischemia stems from the fact that slow conduction and increased dispersion of refractoriness in the ischemic region increase the likelihood of the establishment of a reentrant circuit following shocks of strength

The mechanisms by which arrhythmias are generated in the heart remains a field of intensive research. Recent advances in computational biology and electrophysiology have enabled researchers to use an alternative tool in the study of arrhythmia mechanisms, the multi-scale modeling and simulation of cardiac arrhythmogenesis at the organ level. This article reviews the recent advances and achievements using this approach.

Existing models of myocardial membrane kinetics have not been able to reproduce the experimentally-observed negative bias in the asymmetry of transmembrane potential changes (DeltaVm) induced by strong electric shocks. The goals of this study are: 1) to demonstrate that this negative bias could be reproduced by the addition, to the membrane model, of electroporation and an outward current, Ia, part of the K+ flow through the L-type Ca2+-channel, and 2) to determine how such modifications in the membrane model affect shock-induced break excitation in a 2D preparation. We conducted simulations of shocks in bidomain fibers and sheets with membrane dynamics represented by the LRd'2000 model, to which electroporation (LRd+EP model) and the outward current, Ia , activated upon strong shock-induced depolarization (aLRd model) was added. Assuming Ia is a part of K+ flow through the L-type Ca2+-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive DeltaVm and the value of near 2 of the negative-to-positive deltaVm ratio. In the sheet, Ia not only contributed to the negative bias in DeltaVm asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaVm. Electroporation, in its turn, was responsible for the decrease in cathode-break excitation threshold in the aLRd sheet, as compared to the other two cases, as well as for the occurrence of the excitation after the shock-end rather than during the shock. The incorporation of electroporation and Ia in a membrane model ensures match between simulation results and experimental data. The use of the aLRd model results in a lower threshold for shock-induced break excitation

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.

There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high-resolution cardiac structure-function models. The current article presents a step in this general direction: it illustrates how whole-heart noninvasive imaging can be combined with whole-heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 x 26.4 x 24.4 microm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.