Rabbit-specific ventricular model of cardiac electrophysiological function including specialized conduction system

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

Ventricular anatomical complexity and sex differences impact predictions from electrophysiological computational models

The aim of this work was to analyze the influence of sex hormones and anatomical details (trabeculations and false tendons) on the electrophysiology of healthy human hearts. Additionally, sex- and anatomy-dependent effects of ventricular tachycardia (VT) inducibility are presented. To this end, four anatomically normal, human, biventricular geometries (two male, two female), with identifiable trabeculations, were obtained from high-resolution, ex-vivo MRI and represented by detailed and smoothed geometrical models (with and without the trabeculations). Additionally one model was augmented by a scar. The electrophysiology finite element model (FEM) simulations were carried out, using O'Hara-Rudy human myocyte model with sex phenotypes of Yang and Clancy. A systematic comparison between detailed vs smooth anatomies, male vs female normal hearts was carried out. The heart with a myocardial infarction was subjected to a programmed stimulus protocol to identify the effects of sex and anatomical detail on ventricular tachycardia inducibility. All female hearts presented QT-interval prolongation however the prolongation interval in comparison to the male phenotypes was anatomy-dependent and was not correlated to the size of the heart. Detailed geometries showed QRS fractionation and increased T-wave magnitude in comparison to the corresponding smoothed geometries. A variety of sustained VTs were obtained in the detailed and smoothed male geometries at different pacing locations, which provide evidence of the geometry-dependent differences regarding the prediction of the locations of reentry channels. In the female phenotype, sustained VTs were induced in both detailed and smooth geometries with RV apex pacing, however no consistent reentry channels were identified. Anatomical and physiological cardiac features play an important role defining risk in cardiac disease. These are often excluded from cardiac electrophysiology simulations. The assumption that the cardiac endocardium is smooth may produce inaccurate predictions towards the location of reentry channels in in-silico tachycardia inducibility studies.

Cardiac biophysical detailed synergetic modality rendering and visible correlation

The heart is a vital organ in the human body. Research and treatment for the heart have made remarkable progress, and the functional mechanisms of the heart have been simulated and rendered through the construction of relevant models. The current methods for rendering cardiac functional mechanisms only consider one type of modality, which means they cannot show how different types of modality, such as physical and physiological, work together. To realistically represent the three-dimensional synergetic biological modality of the heart, this paper proposes a WebGL-based cardiac synergetic modality rendering framework to visualize the cardiac physical volume data and present synergetic correspondence rendering of the cardiac electrophysiological modality. By constructing the biological detailed interactive histogram, users can implement local details rendering for the heart, which could reveal the cardiac biology details more clearly. We also present cardiac physical-physiological correlation visualization to explore cardiac biological association characteristics. Experimental results show that the proposed framework can provide favorable cardiac biological detailed synergetic modality rendering results in terms of both effectiveness and efficiency. Compared with existing methods, the framework can facilitate the study of the internal mechanism of the heart and subsequently deduce the process of initiation, development, and transformation from a healthy heart to an ill one, and thereby improve the diagnosis and treatment of cardiac disorders.

Rate dependence of early afterdepolarizations in the His-Purkinje system: A simulation study

BACKGROUND AND OBJECTIVE

Early afterdepolarizations (EADs) are associated with a variety of arrhythmias and have the property of rate dependence. EADs can occur in Purkinje cells while the effect of rate dependence of EADs in the His-Purkinje system has not been fully investigated. In order to reveal the rate dependence of EADs in the His-Purkinje system and its effect on ventricular electrical activities, the simulation research was carried out in this manuscript.

METHODS

This manuscript first studied the relationship between the occurrence of EADs and stimulation cycle length on the DiFranNoble cell model. Then, the relationship between the rate dependence of EADs and the conduction block of the His-Purkinje system at slow heart rates was studied on the rabbit whole ventricular model including the His-Purkinje system, and its mechanism was analyzed from multiple angles.

RESULTS

① The rate dependence of EADs is related to the inconsistency of EADs occurrence in the His-Purkinje system. When the stimulation cycle length is long or short enough, EADs either occur or not occur stably in the His-Purkinje system, while in a certain stimulation cycle length window, the chaotic state of EADs will be observed. ② The key subcellular factors x-gate is an important mechanism involved to the rate dependence of EADs in the His-Purkinje system. ③ The discrete distribution of x-gate values and the "source-sink" mechanism lead to the inconsistency of EADs in the His-Purkinje system. The prolonged action potential duration caused by EADs can lead to conduction block at slow heart rates.

CONCLUSION

The rate dependence of EADs in Purkinje system can lead to disordered ventricular electrical activity.

Identification to cardiac conduction cells in humans and pigs according to their zonal distribution, using histological, immunohistochemical and morphometric study

Histologically, the cardiac conduction network is formed of electrically isolated subendocardial fibers that comprise specialized cells with fewer myofibrils and mitochondria than cardiomyocytes. Our aim is to uncover regional variations of cardiac conduction fibers through histological and morphometric study in a porcine and human model. We analyzed five male adult human hearts and five male pig hearts. The left ventricles were dissected and sectioned in the axial plane into three parts: basal, middle third and apex regions. Cardiac conduction fibers study was carried out using hematoxylin-eosin and Masson's trichrome staining, and cardiac conduction cells and their junctions were identified using desmin, and a PAS method. Cardiac conduction fibers were difficult to pinpoint in humans, mostly showing a darker color or equal to cardiomyocytes. Cardiac conduction fibers in humans were in the subendocardium and in pigs in the myocardium and subendocardium. Cardiac conduction fibers were located mainly in the septal region in both humans and pigs. In our morphometric analysis, we were able to determine that cardiac conduction cells in humans (18.52 +/- 5.41 μm) and pigs (21.32 +/- 6.45 μm) were large, compared to cardiomyocytes. Conduction fiber-myocardial junctions were present in 10% in humans and 24.2% in pigs. The performance of immunohistochemical methods made it possible to improve the identification of cardiac conduction cells in the species studied. Study of cardiac conduction fibers and cells and their myocardial junctions is vital to gain insight into their normal distribution in the species analyzed, and thus advance the use of pigs in experimental models of the cardiac conduction system in humans.

Morphometric analysis of cardiac conduction fibers in horses and dogs, a comparative histological and immunohistochemical study with findings in human hearts

The principal function of the ventricular conduction system is rapid electrical activation of the ventricles. The aim of this study is to conduct a morphometric study to pinpoint the morphological parameters that define cardiac conduction cells, allowing us to distinguish them from other cells. Five male horse hearts and five male dog hearts were used in the study. The hearts were fixed in a 5% formaldehyde solution. Histological sections of 5 μm thickness were acquired and stained with hematoxylin-eosin and Masson's trichrome and cardiac conduction cells and their junctions were identified by desmin, connexin 40 and a PAS method. We found statistically significant differences in cardiac conduction fibers density and thickness, which was much higher in horses than in dogs (p = 0.000 for both values). By comparing the measured parameters of the cells in both species, we determined that cardiac conduction cells area and diameters were greater in horses than in dogs (p = 0.000 for all values). In dogs there are more junctions (30.8%) than in horses (26.1%), a statistically significant difference (p = 0.041). Our findings regarding the cardiac conduction fibers distribution in the animal species studied becomes new knowledge that contributes to the morphological study of this component of the cardiac conduction system and also makes it possible to locate exactly the site with the highest density of cardiac conduction fibers as a contribution to the cardiological study of these structures that lead to the prevention of ventricular arrhythmias and the identification of their treatment site.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

OPTIMIZATION OF RABBIT VENTRICULAR ELECTROPHYSIOLOGICAL MODEL AND SIMULATION OF SYNTHETIC ELECTROCARDIOGRAM

This study aimed to use computer simulation method to study the mechanism of cardiac electrical activities. We optimized an electrophysiological rabbit ventricular model, including myocardial segmentation, heterogeneity and a realistic His-Purkinje network. Simulations of normal state, several types of ventricular premature contractions (VPC), conduction system pacing and right ventricular apical pacing were performed and the detailed cardiac electrical activities were studied from cell level to electrocardiogram (ECG) level. A detailed multiscale optimized ventricular model was obtained. The model effectively simulated various types of electrical activities. The synthetic ECG results were very similar to the real clinical ECG. The duration of QRS of typical VPC is 58[Formula: see text]ms, 71% longer than that of a normal-state synthetic QRS and the amplitude of the QRS is 35% larger, while the QRS duration and amplitude of the real clinical ECG of typical VPC are 69% longer and 36% larger than those of the real normal QRS. The duration of QRS of ventricular fusion beat is 31[Formula: see text]ms, 91% of that of a normal-state synthetic QRS and the amplitude of the QRS is 36% larger, while the QRS duration of the real clinical ECG of a ventricular fusion beat is 92% of the real normal QRS and the amplitude is 37% larger. Therefore, the results indicate that this model is effective and reliable in studying the detailed process of cardiac excitation and pacing.

Integration of activation maps of epicardial veins in computational cardiac electrophysiology

In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac electro-physiology of the left ventricle. To this aim, we consider four patients who suffered from Left Bundle Branch Block (LBBB). We use activation maps performed at the septum as input data for the model and maps at the epicardial veins for the validation. In particular, a first set (half) of the latter are used to estimate the conductivities of the patient and a second set (the remaining half) to compute the errors of the numerical simulations. We find an excellent agreement between measures and numerical results. Our validated computational tool could be used to accurately predict activation times at the epicardial veins with a short mapping, i.e. by using only a part (the most proximal) of the standard acquisition points, thus reducing the invasive procedure and exposure to radiation.

Animal models of arrhythmia: classic electrophysiology to genetically modified large animals

Arrhythmias are common and contribute substantially to cardiovascular morbidity and mortality. The underlying pathophysiology of arrhythmias is complex and remains incompletely understood, which explains why mostly only symptomatic therapy is available. The evaluation of the complex interplay between various cell types in the heart, including cardiomyocytes from the conduction system and the working myocardium, fibroblasts and cardiac immune cells, remains a major challenge in arrhythmia research because it can be investigated only in vivo. Various animal species have been used, and several disease models have been developed to study arrhythmias. Although every species is useful and might be ideal to study a specific hypothesis, we suggest a practical trio of animal models for future use: mice for genetic investigations, mechanistic evaluations or early studies to identify potential drug targets; rabbits for studies on ion channel function, repolarization or re-entrant arrhythmias; and pigs for preclinical translational studies to validate previous findings. In this Review, we provide a comprehensive overview of different models and currently used species for arrhythmia research, discuss their advantages and disadvantages and provide guidance for researchers who are considering performing in vivo studies.

Opportunities and Challenges of Whole-Cell and -Tissue Simulations of the Outer Retina in Health and Disease

Visual processing starts in the outer retina, where photoreceptor cells sense photons that trigger electrical responses. Retinal pigment epithelial cells are located external to the photoreceptor layer and have critical functions in supporting cell and tissue homeostasis and thus sustaining a healthy retina. The high level of specialization makes the retina vulnerable to alterations that promote retinal degeneration. In this review, we discuss opportunities and challenges in proposing whole-cell and -tissue simulations of the human outer retina. An implicit position taken throughout this review is that mapping diverse data sets onto integrative computational models is likely to be a pivotal approach to understanding complex disease and developing novel interventions.

Effect of ventricular myocardium characteristics on the defibrillation threshold

Myocardium characteristics differ markedly among individuals and play an important role in defibrillation threshold. The accuracy of simulation models used in most published studies are still have room to be improved and most of them only discussed the effect of myocardial anisotropy on defibrillation threshold. In our manuscript, a rabbit ventricular finite-element (FE) volume conductor model with high precision was constructed. Ventricular myocardium characteristics include cardiomyocyte coupling and the degree of myocardial anisotropy, which are represented as the value and the ratio of anisotropic conductivity, respectively. Quantitative analysis was performed simultaneously in terms of cardiomyocyte coupling and the degree of myocardial anisotropy. Based on this, the combined effects of these two factors were further discussed. The electric field distributions of shocks and the defibrillation thresholds under different myocardial characteristics were simulated on this model. The simulation results revealed that as the degree of myocardial anisotropy increases, defibrillation threshold increases, and cardiomyocyte decoupling (decrease in electrical conductivity) can considerably increase the defibrillation threshold.

Predicting drug-induced arrhythmias by multiscale modeling

Drugs often have undesired side effects. In the heart, they can induce lethal arrhythmias such as torsades de pointes. The risk evaluation of a new compound is costly and can take a long time, which often hinders the development of new drugs. Here, we establish a high-resolution, multiscale computational model to quickly assess the cardiac toxicity of new and existing drugs. The input of the model is the drug-specific current block from single cell electrophysiology; the output is the spatio-temporal activation profile and the associated electrocardiogram. We demonstrate the potential of our model for a low-risk drug, ranolazine, and a high-risk drug, quinidine: For ranolazine, our model predicts a prolonged QT interval of 19.4% compared with baseline and a regular sinus rhythm at 60.15 beats per minute. For quinidine, our model predicts a prolonged QT interval of 78.4% and a spontaneous development of torsades de pointes both in the activation profile and in the electrocardiogram. Our model reveals the mechanisms by which electrophysiological abnormalities propagate across the spatio-temporal scales, from specific channel blockage, via altered single cell action potentials and prolonged QT intervals, to the spontaneous emergence of ventricular tachycardia in the form of torsades de pointes. Our model could have important implications for researchers, regulatory agencies, and pharmaceutical companies on rationalizing safe drug development and reducing the time-to-market of new drugs.

Efficient Computational Modeling of Human Ventricular Activation and Its Electrocardiographic Representation: A Sensitivity Study

Patient-specific models of the ventricular myocardium, combined with the computational power to run rapid simulations, are approaching the level where they could be used for personalized cardiovascular medicine. A major remaining challenge is determining model parameters from available patient data, especially for models of the Purkinje-myocardial junctions (PMJs): the sites of initial ventricular electrical activation. There are no non-invasive methods for localizing PMJs in patients, and the relationship between the standard clinical ECG and PMJ model parameters is underexplored. Thus, this study aimed to determine the sensitivity of the QRS complex of the ECG to the anatomical location and regional number of PMJs. The QRS complex was simulated using an image-based human torso and biventricular model, and cardiac electrophysiology was simulated using Cardioid. The PMJs were modeled as discrete current injection stimuli, and the location and number of stimuli were varied within initial activation regions based on published experiments. Results indicate that the QRS complex features were most sensitive to the presence or absence of four “seed” stimuli, and adjusting locations of nearby “regional” stimuli provided finer tuning. Decreasing number of regional stimuli by an order of magnitude resulted in virtually no change in the QRS complex. Thus, a minimal 12-stimuli configuration was identified that resulted in physiological excitation, defined by QRS complex feature metrics and ventricular excitation pattern. Overall, the sensitivity results suggest that parameterizing PMJ location, rather than number, be given significantly higher priority in future studies creating personalized ventricular models from patient-derived ECGs.

Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology

Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including various types of validation results, underlying theory, evidence supporting model assumptions, evidence from model calibration, all at a variety of scales from ion channel to cell to organ. Consequently, it is often unclear, or a matter for debate, the extent to which a CEP model can be trusted for a given application. The aim of this article is to clarify potential rationale for the trustworthiness of CEP models by reviewing evidence that has been (or could be) presented to support their credibility. We specifically address the complexity and multi-scale nature of CEP models which makes traditional model evaluation difficult. In addition, we make explicit some of the credibility justification that we believe is implicitly embedded in the CEP modeling literature. Overall, we provide a fresh perspective to CEP model credibility, and build a depiction and categorisation of the wide-ranging body of credibility evidence for CEP models. This paper also represents a step toward the extension of model evaluation methodologies that are currently being developed by the medical device community, to physiological models.

Predicting the cardiac toxicity of drugs using a novel multiscale exposure-response simulator

A common but serious side effect of many drugs is torsades de pointes, a rhythm disorder that can have fatal consequences. Torsadogenic risk has traditionally been associated with blockage of a specific potassium channel and an increased recovery period in the electrocardiogram. However, the mechanisms that trigger torsades de pointes remain incompletely understood. Here we establish a computational model to explore how drug-induced effects propagate from the single channel, via the single cell, to the whole heart level. Our mechanistic exposure-response simulator translates block-concentration characteristics for arbitrary drugs into three-dimensional excitation profiles and electrocardiogram recordings to rapidly assess torsadogenic risk. For the drug of dofetilide, we show that this risk is highly dose-dependent: at a concentration of 1x, QT prolongation is 55% but the heart maintains its regular sinus rhythm; at 5.7x, QT prolongation is 102% and the heart spontaneously transitions into torsades de points; at 30x, QT prolongation is 132% and the heart adapts a quasi-depolarized state with numerous rapidly flickering local excitations. Our simulations suggest that neither potassium channel blockage nor QT interval prolongation alone trigger torsades de pointes. The underlying mechanism predicted by our model is early afterdepolarization, which translates into pronounced U waves in the electrocardiogram, a signature that is correctly predicted by our model. Beyond the risk assessment of existing drugs, our exposure-response simulator can become a powerful tool to optimize the co-administration of drugs and, ultimately, guide the design of new drugs toward reducing life threatening drug-induced rhythm disorders in the heart.

Three Dimensional Visualization of Human Cardiac Conduction Tissue in Whole Heart Specimens by High-Resolution Phase-Contrast CT Imaging Using Synchrotron Radiation

BACKGROUND

The feasibility of synchrotron radiation-based phase-contrast computed tomography (PCCT) for visualization of the atrioventricular (AV) conduction axis in human whole heart specimens was tested using four postmortem structurally normal newborn hearts obtained at autopsy.

METHODS

A PCCT imaging system at the beamline BL20B2 in a SPring-8 synchrotron radiation facility was used. The PCCT imaging of the conduction system was performed with "virtual" slicing of the three-dimensional reconstructed images. For histological verification, specimens were cut into planes similar to the PCCT images, then cut into 5-μm serial sections and stained with Masson's trichrome.

RESULTS

In PCCT images of all four of the whole hearts of newborns, the AV conduction axis was distinguished as a low-density structure, which was serially traceable from the compact node to the penetrating bundle within the central fibrous body, and to the branching bundle into the left and right bundle branches. This was verified by histological serial sectioning.

CONCLUSION

This is the first demonstration that visualization of the AV conduction axis within human whole heart specimens is feasible with PCCT.

A quantitative structural and morphometric analysis of the Purkinje network and the Purkinje-myocardial junctions in pig hearts

The morpho-functional properties of the distal section of the cardiac Purkinje network (PN) and the Purkinje-myocardial junctions (PMJs) are fundamental to understanding the sequence of electrical activation in the heart. The overall structure of the system has already been described, and several computational models have been developed to gain insight into its involvement in cardiac arrhythmias or its interaction with implantable devices, such as pacemakers. However, anatomical descriptions of the PN in the literature have not enabled enough improvements in the accuracy of anatomical-based electrophysiological simulations of the PN in 3D hearts models. In this work, we study the global distribution and morphological properties of the PN, with special emphasis on the cellular and architectural characterization of its intramural branching structure, mesh-like sub-endocardial network, and the PMJs in adult pig hearts by both histopathological and morphometric evaluation. We have defined three main patterns of PMJ: contact through cell bodies, contact through cell prolongations either thick or piliform, and contact through transitional cells. Moreover, from hundreds of micrographs, we quantified the density of PMJs and provided data for the basal/medial/apical regions, anterior/posterior/septal/lateral regions and myocardial/sub-endocardial distribution. Morphometric variables, such as Purkinje cell density and thickness of the bundles, were also analyzed. After combining the results of these parameters, a different septoanterior distribution in the Purkinje cell density was observed towards the cardiac apex, which is associated with a progressive thinning of the conduction bundles and the posterolateral ascension of intramyocardial terminal scattered fibers. The study of the PMJs revealed a decreasing trend towards the base that may anatomically explain the early apical activation. The anterolateral region contains the greatest number of contacts, followed by the anterior and septal regions. This supports the hypothesis that thin distal Purkinje bundles create a junction-rich network that may be responsible for the quick apical depolarization. The PN then ascends laterally and spreads through the anterior and medial walls up to the base. We have established the first morphometric study of the Purkinje system, and provided quantitative and objective data that facilitate its incorporation into the development of models beyond gross and variable pathological descriptions, and which, after further studies, could be useful in the characterization of pathological processes or therapeutic procedures.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

Analysis of Microstructure of the Cardiac Conduction System Based on Three-Dimensional Confocal Microscopy

The specialised conducting tissues present in the ventricles are responsible for the fast distribution of the electrical impulse from the atrio-ventricular node to regions in the subendocardial myocardium. Characterisation of anatomical features of the specialised conducting tissues in the ventricles is highly challenging, in particular its most distal section, which is connected to the working myocardium via Purkinje-myocardial junctions. The goal of this work is to characterise the architecture of the distal section of the Purkinje network by differentiating Purkinje cells from surrounding tissue, performing a segmentation of Purkinje fibres at cellular scale, and mathematically describing its morphology and interconnections. Purkinje cells from rabbit hearts were visualised by confocal microscopy using wheat germ agglutinin labelling. A total of 16 3D stacks including labeled Purkinje cells were collected, and semi-automatically segmented. State-of-the-art graph metrics were applied to estimate regional and global features of the Purkinje network complexity. Two types of cell types, tubular and star-like, were characterised from 3D segmentations. The analysis of 3D imaging data confirms the previously suggested presence of two types of Purkinje-myocardium connections, a 2D interconnection sheet and a funnel one, in which the narrow side of a Purkinje fibre connect progressively to muscle fibres. The complex network analysis of interconnected Purkinje cells showed no small-world connectivity or assortativity properties. These results might help building more realistic computational PK systems at high resolution levels including different cell configurations and shapes. Better knowledge on the organisation of the network might help in understanding the effects that several treatments such as radio-frequency ablation might have when the PK system is disrupted locally.

Generating Purkinje networks in the human heart

The Purkinje network is an integral part of the excitation system in the human heart. Yet, to date, there is no in vivo imaging technique to accurately reconstruct its geometry and structure. Computational modeling of the Purkinje network is increasingly recognized as an alternative strategy to visualize, simulate, and understand the role of the Purkinje system. However, most computational models either have to be generated manually, or fail to smoothly cover the irregular surfaces inside the left and right ventricles. Here we present a new algorithm to reliably create robust Purkinje networks within the human heart. We made the source code of this algorithm freely available online. Using Monte Carlo simulations, we demonstrate that the fractal tree algorithm with our new projection method generates denser and more compact Purkinje networks than previous approaches on irregular surfaces. Under similar conditions, our algorithm generates a network with 1219±61 branches, three times more than a conventional algorithm with 419±107 branches. With a coverage of 11±3mm, the surface density of our new Purkije network is twice as dense as the conventional network with 22±7mm. To demonstrate the importance of a dense Purkinje network in cardiac electrophysiology, we simulated three cases of excitation: with our new Purkinje network, with left-sided Purkinje network, and without Purkinje network. Simulations with our new Purkinje network predicted more realistic activation sequences and activation times than simulations without. Six-lead electrocardiograms of the three case studies agreed with the clinical electrocardiograms under physiological conditions, under pathological conditions of right bundle branch block, and under pathological conditions of trifascicular block. Taken together, our results underpin the importance of the Purkinje network in realistic human heart simulations. Human heart modeling has the potential to support the design of personalized strategies for single- or bi-ventricular pacing, radiofrequency ablation, and cardiac defibrillation with the common goal to restore a normal heart rhythm.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

Protective Role of False Tendon in Subjects with Left Bundle Branch Block: A Virtual Population Study

False tendons (FTs) are fibrous or fibromuscular bands that can be found in both the normal and abnormal human heart in various anatomical forms depending on their attachment points, tissue types, and geometrical properties. While FTs are widely considered to affect the function of the heart, their specific roles remain largely unclear and unexplored. In this paper, we present an in silico study of the ventricular activation time of the human heart in the presence of FTs. This study presents the first computational model of the human heart that includes a FT, Purkinje network, and papillary muscles. Based on this model, we perform simulations to investigate the effect of different types of FTs on hearts with the electrical conduction abnormality of a left bundle branch block (LBBB). We employ a virtual population of 70 human hearts derived from a statistical atlas, and run a total of 560 simulations to assess ventricular activation time with different FT configurations. The obtained results indicate that, in the presence of a LBBB, the FT reduces the total activation time that is abnormally augmented due to a branch block, to such an extent that surgical implant of cardiac resynchronisation devices might not be recommended by international guidelines. Specifically, the simulation results show that FTs reduce the QRS duration at least 10 ms in 80% of hearts, and up to 45 ms for FTs connecting to the ventricular free wall, suggesting a significant reduction of cardiovascular mortality risk. In further simulation studies we show the reduction in the QRS duration is more sensitive to the shape of the heart then the size of the heart or the exact location of the FT. Finally, the model suggests that FTs may contribute to reducing the activation time difference between the left and right ventricles from 12 ms to 4 ms. We conclude that FTs may provide an alternative conduction pathway that compensates for the propagation delay caused by the LBBB. Further investigation is needed to quantify the clinical impact of FTs on cardiovascular mortality risk.

Modeling the different sections of the cardiac conduction system to obtain realistic electrocardiograms

The cardiac conduction system is divided in different sections that play an important role in the cardiac depolarization sequence and define the morphology of the electrocardiogram. In this study we have built several configurations for each section based on anatomical descriptions. The effect of the morphology of the bundle branches, and the density of both Purkinje branches and Purkinje-myocardial junctions (PMJ) has been studied by comparing the pseudo-ECGs obtained with the standard precordial leads of the electrocardiogram. A functional model for the PMJs based on the existence of a conduction adaptation layer is also presented. Simulation results showed a large influence of the His bundle and bundle branches in the pseudo-ECG and helped to elucidate the most appropriate morphology. The functional PMJ model allowed bidirectional communication between the conduction system and the myocardium with realistic transmission delays between both mediums. These results can help to improve current conduction system models and improve depolarization sequences of activation in the ventricles.

Computational modeling of cardiac optogenetics: Methodology overview & review of findings from simulations

Cardiac optogenetics is emerging as an exciting new potential avenue to enable spatiotemporally precise control of excitable cells and tissue in the heart with low-energy optical stimuli. This approach involves the expression of exogenous light-sensitive proteins (opsins) in target heart tissue via viral gene or cell delivery. Preliminary experiments in optogenetically-modified cells, tissue, and organisms have made great strides towards demonstrating the feasibility of basic applications, including the use of light stimuli to pace or disrupt reentrant activity. However, it remains unknown whether techniques based on this intriguing technology could be scaled up and used in humans for novel clinical applications, such as pain-free optical defibrillation or dynamic modulation of action potential shape. A key step towards answering such questions is to explore potential optogenetics-based therapies using sophisticated computer simulation tools capable of realistically representing opsin delivery and light stimulation in biophysically detailed, patient-specific models of the human heart. This review provides (1) a detailed overview of the methodological developments necessary to represent optogenetics-based solutions in existing virtual heart platforms and (2) a survey of findings that have been derived from such simulations and a critical assessment of their significance with respect to the progress of the field.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient-specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models.

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ventricle is therefore important to account for the Purkinje fibers. Until now, the inclusion of such fibers has been obtained either by using surrogates such as space-dependent conduction properties or by generating a network based on an a priori anatomical knowledge. The aim of this work was to propose a new method for the generation of the Purkinje network using clinical measures of the activation times on the endocardium related to a normal electrical propagation, allowing to generate a patient-specific network. The measures were acquired by means of the EnSite NavX system. This system allows to measure for each point of the ventricular endocardium the time at which the activation front, that spreads through the ventricle, has reached the subjacent muscle. We compared the accuracy of the proposed method with the one of other strategies proposed so far in the literature for three subjects with a normal electrical propagation. The results showed that with our method we were able to reduce the absolute errors, intended as the difference between the measured and the computed data, by a factor in the range 9-25 %, with respect to the best of the other strategies. This highlighted the reliability of the proposed method and the importance of including a patient-specific Purkinje network in computational models.

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study

The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/ did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Computational methods to reduce uncertainty in the estimation of cardiac conduction properties from electroanatomical recordings

Cardiac imaging is routinely used to evaluate cardiac tissue properties prior to therapy. By integrating the structural information with electrophysiological data from e.g. electroanatomical mapping systems, knowledge of the properties of the cardiac tissue can be further refined. However, as in other clinical modalities, electrophysiological data are often sparse and noisy, and this results in high levels of uncertainty in the estimated quantities. In this study, we develop a methodology based on Bayesian inference, coupled with a computationally efficient model of electrical propagation to achieve two main aims: (1) to quantify values and associated uncertainty for different tissue conduction properties inferred from electroanatomical data, and (2) to design strategies to optimize the location and number of measurements required to maximize information and reduce uncertainty. The methodology is validated in an in silico study performed using simulated data obtained from a human image-based ventricular model, including realistic fibre orientation and a transmural scar. We demonstrate that the method provides a simultaneous description of clinically-relevant electrophysiological conduction properties and their associated uncertainty for various levels of noise. By using the developed methodology to investigate how the uncertainty decreases in response to added measurements, we then derive an a priori index for placing electrophysiological measurements in order to optimize the information content of the collected data. Results show that the derived index has a clear benefit in minimizing the uncertainty of inferred conduction properties compared to a random distribution of measurements, reducing the number of required measurements by over 50% in several of the investigated settings. This suggests that the methodology presented in this work provides an important step towards improving the quality of the spatiotemporal information obtained using electroanatomical mapping.

Computational assessment of drug-induced effects on the electrocardiogram: from ion channel to body surface potentials

Background and Purpose

Understanding drug effects on the heart is key to safety pharmacology assessment and anti-arrhythmic therapy development. Here our goal is to demonstrate the ability of computational models to simulate the effect of drug action on the electrical activity of the heart, at the level of the ion-channel, cell, heart and ECG body surface potential.

Experimental Approach

We use the state-of-the-art mathematical models governing the electrical activity of the heart. A drug model is introduced using an ion channel conductance block for the hERG and fast sodium channels, depending on the IC₅₀ value and the drug dose. We simulate the ECG measurements at the body surface and compare biomarkers under different drug actions.

Key Results

Introducing a 50% hERG-channel current block results in 8% prolongation of the APD₉₀ and 6% QT interval prolongation, hERG block does not affect the QRS interval. Introducing 50% fast sodium current block prolongs the QRS and the QT intervals by 12% and 5% respectively, and delays activation times, whereas APD₉₀ is not affected.

Conclusions and Implications

Both potassium and sodium blocks prolong the QT interval, but the underlying mechanism is different: for potassium it is due to APD prolongation; while for sodium it is due to a reduction of electrical wave velocity. This study shows the applicability of in silico models for the investigation of drug effects on the heart, from the ion channel to the ECG-based biomarkers.

Characterization and modeling of the peripheral cardiac conduction system

The development of biophysical models of the heart has the potential to get insights in the patho-physiology of the heart, which requires to accurately modeling anatomy and function. The electrical activation sequence of the ventricles depends strongly on the cardiac conduction system (CCS). Its morphology and function cannot be observed in vivo, and therefore data available come from histological studies. We present a review on data available of the peripheral CCS including new experiments. In order to build a realistic model of the CCS we designed a procedure to extract morphological characteristics of the CCS from stained calf tissue samples. A CCS model personalized with our measurements has been built using L-systems. The effect of key unknown parameters of the model in the electrical activation of the left ventricle has been analyzed. The CCS models generated share the main characteristics of observed stained Purkinje networks. The timing of the simulated electrical activation sequences were in the physiological range for CCS models that included enough density of PMJs. These results show that this approach is a potential methodology for collecting knowledge-domain data and build improved CCS models of the heart automatically.

Application of micro-computed tomography with iodine staining to cardiac imaging, segmentation, and computational model development

Micro-computed tomography (micro-CT) has been widely used to generate high-resolution 3-D tissue images from small animals nondestructively, especially for mineralized skeletal tissues. However, its application to the analysis of soft cardiovascular tissues has been limited by poor inter-tissue contrast. Recent ex vivo studies have shown that contrast between muscular and connective tissue in micro-CT images can be enhanced by staining with iodine. In the present study, we apply this novel technique for imaging of cardiovascular structures in canine hearts. We optimize the method to obtain high-resolution X-ray micro-CT images of the canine atria and its distinctive regions-including the Bachmann's bundle, atrioventricular node, pulmonary arteries and veins-with clear inter-tissue contrast. The imaging results are used to reconstruct and segment the detailed 3-D geometry of the atria. Structure tensor analysis shows that the arrangement of atrial fibers can also be characterized using the enhanced micro-CT images, as iodine preferentially accumulates within the muscular fibers rather than in connective tissues. This novel technique can be particularly useful in nondestructive imaging of 3-D cardiac architectures from large animals and humans, due to the combination of relatively high speed ( ~ 1 h/per scan of the large canine heart) and high voxel resolution (36 μm) provided. In summary, contrast micro-CT facilitates fast and nondestructive imaging and segmenting of detailed 3-D cardiovascular geometries, as well as measuring fiber orientation, which are crucial in constructing biophysically detailed computational cardiac models.

Computational cardiology: the heart of the matter

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.

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Structure-function relationship in the sinus and atrioventricular nodes

Recently published optical mapping studies of larger mammals, including humans, have identified functionally discrete sinoatrial exit pathways of activation. This is in line with earlier mapping studies of the dog and the human but in contrast with findings in the mouse and the rabbit, wherein a propagation wave front pattern of activation has been described. It underpins the complex three-dimensional (3D) organization of the cardiac pacemaking and conduction system in larger species, wherein sinoatrial and atrioventricular nodal physiologies both demonstrate identifiable activation pathways, which coincide with anatomic landmarks and histologic architecture, so that in addition to muscle fiber orientation and cell coupling, these intrinsic factors act to determine excitation pathways. This complex 3D organization increases the effect of source-to-sink mismatch both by greater variability in the space constant of tissue and by the 3D projection of this effect in all directions. Mathematical modeling provides a means to study these interactions, and newer models should incorporate these additional factors and their effect into the 3D structure of large mammal physiology.

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.

Contrast enhanced micro-computed tomography resolves the 3-dimensional morphology of the cardiac conduction system in mammalian hearts

The general anatomy of the cardiac conduction system (CCS) has been known for 100 years, but its complex and irregular three-dimensional (3D) geometry is not so well understood. This is largely because the conducting tissue is not distinct from the surrounding tissue by dissection. The best descriptions of its anatomy come from studies based on serial sectioning of samples taken from the appropriate areas of the heart. Low X-ray attenuation has formerly ruled out micro-computed tomography (micro-CT) as a modality to resolve internal structures of soft tissue, but incorporation of iodine, which has a high molecular weight, into those tissues enhances the differential attenuation of X-rays and allows visualisation of fine detail in embryos and skeletal muscle. Here, with the use of a iodine based contrast agent (I₂KI), we present contrast enhanced micro-CT images of cardiac tissue from rat and rabbit in which the three major subdivisions of the CCS can be differentiated from the surrounding contractile myocardium and visualised in 3D. Structures identified include the sinoatrial node (SAN) and the atrioventricular conduction axis: the penetrating bundle, His bundle, the bundle branches and the Purkinje network. Although the current findings are consistent with existing anatomical representations, the representations shown here offer superior resolution and are the first 3D representations of the CCS within a single intact mammalian heart.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria--the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project

The VPH/Physiome Project is developing the model encoding standards CellML (cellml.org) and FieldML (fieldml.org) as well as web-accessible model repositories based on these standards (models.physiome.org). Freely available open source computational modelling software is also being developed to solve the partial differential equations described by the models and to visualise results. The OpenCMISS code (opencmiss.org), described here, has been developed by the authors over the last six years to replace the CMISS code that has supported a number of organ system Physiome projects. OpenCMISS is designed to encompass multiple sets of physical equations and to link subcellular and tissue-level biophysical processes into organ-level processes. In the Heart Physiome project, for example, the large deformation mechanics of the myocardial wall need to be coupled to both ventricular flow and embedded coronary flow, and the reaction-diffusion equations that govern the propagation of electrical waves through myocardial tissue need to be coupled with equations that describe the ion channel currents that flow through the cardiac cell membranes. In this paper we discuss the design principles and distributed memory architecture behind the OpenCMISS code. We also discuss the design of the interfaces that link the sets of physical equations across common boundaries (such as fluid-structure coupling), or between spatial fields over the same domain (such as coupled electromechanics), and the concepts behind CellML and FieldML that are embodied in the OpenCMISS data structures. We show how all of these provide a flexible infrastructure for combining models developed across the VPH/Physiome community.