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Contractions of the uterus play an important role in menstruation and fertility, and contractile dysfunction can lead to chronic diseases such as endometriosis. However, the structure and function of the uterus are difficult to interrogate in humans, and thus animal studies are often employed to understand its function. In rats, anatomical studies of the uterus have typically been based on histological assessment, have been limited to small segments of the uterine structure, and have been time-consuming to reconstruct at the organ scale. This study used micro-computed tomography imaging to visualise the muscle structures in the entire non-pregnant rat uterus and assess its use for 3D virtual histology. An assessment of the rodent uterus is presented to (i) quantify muscle thickness variations along the horns, (ii) identify predominant fibre orientations of the muscles and (iii) demonstrate how the anatomy of the uterus can be mapped to 3D volumetric meshes via virtual histology. Micro-computed tomography measurements were validated against measurements from histological sections. The average thickness of the myometrium was found to be 0.33 ± 0.11 mm and 0.31 ± 0.09 mm in the left and right horns, respectively. The micro-computed tomography and histology thickness calculations were found to correlate strongly at different locations in the uterus: at the cervix, r = 0.87, and along the horn from the cervical end to the ovarian end, respectively, r = 0.77, r = 0.89 and r = 0.54, with p < 0.001 in every location. This study shows that micro-computed tomography can be used to quantify the musculature in the whole non-pregnant uterus and can be used for 3D virtual histology., (© 2024 The Author(s). Journal of Anatomy published by John Wiley & Sons Ltd on behalf of Anatomical Society.)

This study aimed to use multi-scale atrial models to investigate pulmonary arterial hypertension (PAH)-induced atrial fibrillation mechanisms. The results of our computer simulations revealed that, at the single-cell level, PAH-induced remodelling led to a prolonged action potential (AP) (ΔAPD: 49.6 ms in the right atria (RA) versus 41.6 ms in the left atria (LA)) and an increased calcium transient (CaT) (ΔCaT: 7.5 × 10 -2 µM in the RA versus 0.9 × 10 -3 µM in the LA). Moreover, heterogeneous remodelling increased susceptibility to afterdepolarizations, particularly in the RA. At the tissue level, we observed a significant reduction in conduction velocity (CV) (ΔCV: -0.5 m s -1 in the RA versus -0.05 m s -1 in the LA), leading to a shortened wavelength in the RA, but not in the LA. Additionally, afterdepolarizations in the RA contributed to enhanced repolarization dispersion and facilitated unidirectional conduction block. Furthermore, the increased fibrosis in the RA amplified the likelihood of excitation wave breakdown and the occurrence of sustained re-entries. Our results indicated that the RA is characterized by increased susceptibility to afterdepolarizations, slow conduction, reduced wavelength and upregulated fibrosis. These findings shed light on the underlying factors that may promote atrial fibrillation in patients with PAH., Competing Interests: The authors have declared that no competing interests exist., (© 2023 The Author(s).)

The right-ventricular (RV) outflow tract (RVOT) and the transition to the RV free wall are recognized sources of arrhythmia in human hearts. However, we do not fully understand myocardial tissue structures in this region. Human heart tissue was processed for optical clarity, labelled with wheat-germ agglutin (WGA) and anti-Cx43, and imaged on a custom-built line scanning confocal microscope. The 3D images were analyzed for myocyte gross structures and cell morphology. There were regions of high organization as well as rapid changes to more heterogeneous regions. Preliminary cell segmentations were used to estimate cell morphology. Observed RVOT/RV structure is consistent with known arrhythmic substrates.Clinical Relevance- New views of human tissue structure enable clearer clinical understanding of arrhythmogenic activation pathways and targets for invasive treatment such as RF ablation.

Hypertensive heart disease (HHD) increases risk of ventricular tachycardia (VT) and ventricular fibrillation (VF). The roles of structural vs. electrophysiological remodelling and age vs. disease progression are not fully understood. This cross-sectional study of cardiac alterations through HHD investigates mechanistic contributions to VT/VF risk. Risk was electrically assessed in Langendorff-perfused, spontaneously hypertensive rat hearts at 6, 12 and 18 months, and paced optical membrane voltage maps were acquired from the left ventricular (LV) free wall epicardium. Distributions of LV patchy fibrosis and 3D cellular architecture in representative anterior LV mid-wall regions were quantified from macroscopic and microscopic fluorescence images of optically cleared tissue. Imaging showed increased fibrosis from 6 months, particularly in the inner LV free wall. Myocyte cross-section increased at 12 months, while inter-myocyte connections reduced markedly with fibrosis. Conduction velocity decreased from 12 months, especially transverse to the myofibre direction, with rate-dependent anisotropy at 12 and 18 months, but not earlier. Action potential duration (APD) increased when clustered by age, as did APD dispersion at 12 and 18 months. Among 10 structural, functional and age variables, the most reliably linked were VT/VF risk, general LV fibrosis, a measure quantifying patchy fibrosis, and non-age clustered APD dispersion. VT/VF risk related to a quantified measure of patchy fibrosis, but age did not factor strongly. The findings are consistent with the notion that VT/VF risk is associated with rate-dependent repolarization heterogeneity caused by structural remodelling and reduced lateral electrical coupling between LV myocytes, providing a substrate for heterogeneous intramural activation as HHD progresses. KEY POINTS: There is heightened arrhythmic risk with progression of hypertensive heart disease. Risk is related to increasing left ventricular fibrosis, but the nature of this relationship has not been quantified. This study is a novel systematic characterization of changes in active electrical properties and fibrotic remodelling during progression of hypertensive heart disease in a well-established animal disease model. Arrhythmic risk is predicted by several left ventricular measures, in particular fibrosis quantity and structure, and epicardial action potential duration dispersion. Age alone is not a good predictor of risk. An improved understanding of links between arrhythmic risk and fibrotic architectures in progressive hypertensive heart disease aids better interpretation of late gadolinium-enhanced cardiac magnetic resonance imaging and electrical mapping signals., (© 2022 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.)

The value of digital twins for prototyping controllers or interventions in a sandbox environment are well-established in engineering and physics. However, this is challenging for biophysics trying to seamlessly compose models of multiple spatial and temporal scale behavior into the digital twin. Two challenges stand out as constraining progress: (i) ensuring physical consistency of conservation laws across composite models and (ii) drawing useful and timely clinical and scientific information from conceptually and computationally complex models. Challenge (i) can be robustly addressed with bondgraphs. However, challenge (ii) is exacerbated using this approach. The complexity question can be looked at from multiple angles. First from the perspective of discretizations that reflect underlying biophysics (functional tissue units) and secondly by exploring maximum entropy as the principle guiding multicellular biophysics. Statistical mechanics, long applied to understanding emergent phenomena from atomic physics, coupled with the observation that cellular architecture in tissue is orchestrated by biophysical constraints on metabolism and communication, shows conceptual promise. This architecture along with cell specific properties can be used to define tissue specific network motifs associated with energetic contributions. Complexity can be addressed based on energy considerations and finding mean measures of dependent variables. A probability distribution of the tissue's network motif can be approximated with exponential random graph models. A prototype problem shows how these approaches could be implemented in practice and the type of information that could be extracted., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Hussan, Trew and Hunter.)

Objective: To develop, train and test neural networks for predicting heart surface potentials (HSPs) from body surface potentials (BSPs). The method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions., Methods: Impulse HSPs were generated with single Gaussian basis functions at discrete heart surface locations and projected to corresponding BSPs using a volume conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to regular 2D surface meshes and used to train a neural network. Predictive capabilities of the network were tested with unseen synthetic and experimental data., Results: A dense full connected single hidden layer neural network was trained to map body surface impulses to heart surface Gaussian basis functions for reconstructing HSP. Synthetic pulses moving across the heart surface were predicted from the neural network with root mean squared error of 9.1±1.4%. Predicted signals were robust to noise up to 20 dB and errors due to displacement and rotation of the heart within the torso were bounded and predictable. A shift of the heart 40 mm toward the spine resulted in a 4% increase in signal feature localization error. The set of training impulse function data could be reduced, and prediction error remained bounded. Recorded HSPs from in-vitro pig hearts were reliably decomposed using space-time Gaussian basis functions. Activation times calculated from predicted HSPs for left-ventricular pacing had a mean absolute error of 10.4±11.4 ms. Other pacing scenarios were analyzed with similar success., Conclusion: Impulses from Gaussian basis functions are potentially an effective and robust way to train simple neural network data models for reconstructing HSPs from decomposed BSPs., Significance: The HSPs predicted by the neural network can be used to generate activation maps that non-invasively identify features of cardiac electrical dysfunction and can guide subsequent treatment options.

Recent developments in clearing and microscopy enable 3D imaging with cellular resolution up to the whole organ level. These methods have been used extensively in neurobiology, but their uptake in other fields has been much more limited. Application of this approach to the human heart and effective use of the data acquired present challenges of scale and complexity. Four interlinked issues need to be addressed: 1) efficient clearing and labelling of heart tissue, 2) fast microscopic imaging of human-scale samples, 3) handling and processing of multi-terabyte 3D images, and 4) extraction of structural information in computationally tractable structure-based models of cardiac function. Preliminary studies show that each of these requirements can be achieved with the appropriate application and development of existing technologies., Competing Interests: Declaration of competing interest The authors declare that they have no conflict of interest., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Cardiac electrophysiological disorders, in particular arrhythmias, are a key cause of morbidity and mortality throughout the world. There are two basic requirements for arrhythmogenesis: an underlying substrate and a trigger. Altered conduction velocity (CV) provides a key substrate for arrhythmogenesis, with slowed CV increasing the probability of re-entrant arrhythmias by reducing the length scale over which re-entry can occur. In this review, we examine methods to measure cardiac CV in vivo and ex vivo, discuss underlying determinants of CV, and address how pathological variations alter CV, potentially increasing arrhythmogenic risk. Finally, we will highlight future directions both for methodologies to measure CV and for possible treatments to restore normal CV.

Objective: Cardiovascular Implantable Electronic Devices (CIEDs) are used extensively for treating life-threatening conditions such as bradycardia, atrioventricular block and heart failure. The complicated heterogeneous physical dynamics of patients provide distinct challenges to device development and validation. We address this problem by proposing a device testing framework within the in-silico closed-loop context of patient physiology., Methods: We develop an automated framework to validate CIEDs in closed-loop with a high-level physiologically based computational heart model. The framework includes test generation, execution and evaluation, which automatically guides an integrated stochastic optimization algorithm for exploration of physiological conditions., Conclusion: The results show that using a closed loop device-heart model framework can achieve high system test coverage, while the heart model provides clinically relevant responses. The simulated findings of pacemaker mediated tachycardia risk evaluation agree well with the clinical observations. Furthermore, we illustrate how device programming parameter selection affects the treatment efficacy for specific physiological conditions., Significance: This work demonstrates that incorporating model based closed-loop testing of CIEDs into their design provides important indications of safety and efficacy under constrained physiological conditions.

Objective: Evaluating and testing cardiac electrical devices in a closed-physiologic-loop can help design safety, but this is rarely practical or comprehensive. Furthermore, in silico closed-loop testing with biophysical computer models cannot meet the requirements of time-critical cardiac device systems, while simplified models meeting time-critical requirements may not have the necessary dynamic features. We propose a new high-level (abstracted) physiologically-based computational heart model that is time-critical and dynamic., Methods: The model comprises cardiac regional cellular-electrophysiology types connected by a path model along a conduction network. The regional electrophysiology and paths are modeled with hybrid automata that capture non-linear dynamics, such as action potential and conduction velocity restitution and overdrive suppression. The hierarchy of pacemaker functions is incorporated to generate sinus rhythms, while abnormal automaticity can be introduced to form a variety of arrhythmias such as escape ectopic rhythms. Model parameters are calibrated using experimental data and prior model simulations., Conclusion: Regional electrophysiology and paths in the model match human action potentials, dynamic behavior, and cardiac activation sequences. Connected in closed loop with a pacing device in DDD mode, the model generates complex arrhythmia such as atrioventricular nodal reentry tachycardia. Such device-induced outcomes have been observed clinically and we can establish the key physiological features of the heart model that influence the device operation., Significance: These findings demonstrate how an abstract heart model can be used for device validation and to design personalized treatment.

Altered electrical behavior alongside healed myocardial infarcts (MIs) is associated with increased risk of sudden cardiac death. However, the multidimensional mechanisms are poorly understood and described. This study characterizes, for the first time, the intramural spread of electrical activation in the peri-infarct region of chronic reperfusion MIs. Four sheep were studied 13 wk after antero-apical reperfusion infarction. Extracellular potentials (ECPs) were recorded in a ~20 × 20-mm 2 region adjacent to the infarct boundary (25 plunge needles <0.5-mm diameter with 15 electrodes at 1-mm centers) during multisite stimulation. Infarct geometry and electrode locations were reconstructed from magnetic resonance images. Three-dimensional activation spread was characterized by local activation times and interpolated ECP fields ( n = 191 records). Control data were acquired in 4 non-infarcted sheep ( n = 96 records). Electrodes were distributed uniformly around 15 ± 5% of the intramural infarct boundary. There were marked changes in pacing success and ECP morphology across a functional border zone (BZ) ±2 mm from the boundary. Stimulation adjacent to the infarct boundary was associated with low-amplitude electrical activity within the BZ and delayed activation of surrounding myocardium. Bulk tissue depolarization occurred 3.5-14.6 mm from the pacing site for 39% of stimuli with delays of 4-37 ms, both significantly greater than control ( P < 0.0001). Conduction velocity (CV) adjacent to the infarct was not reduced compared with control, consistent with structure-only computer model results. Insignificant CV slowing, irregular stimulus-site specific activation delays, and obvious indirect activation pathways strongly suggest that the substrate for conduction abnormalities in chronic MI is predominantly structural in nature. NEW & NOTEWORTHY Intramural in vivo measurements of peri-infarct electrical activity were not available before this study. We use pace-mapping in a three-dimensional electrode array to show that a subset of stimuli in the peri-infarct region initiates coordinated myocardial activation some distance from the stimulus site with substantial associated time delays. This is site dependent and heterogeneous and occurs for <50% of ectopic stimuli in the border zone. Furthermore, once coordinated activation is initiated, conduction velocity adjacent to the infarct boundary is not significantly different from control. These results give new insights to peri-infarct electrical activity and do not support the widespread view of uniform electrical remodeling in the border zone of chronic myocardial infarcts, with depressed conduction velocity throughout.

Key Points: Vagal reflexes slow heart rate and can change where the heartbeat originates within the sinoatrial node (SAN). The mechanisms responsible for this process - termed leading pacemaker (LP) shift - have not been investigated fully. We used optical mapping to measure the effects of baroreflex, chemoreflex and carbachol on pacemaker entrainment and electrical conduction across the SAN. All methods of stimulation triggered shifts in LP site from the central SAN to one or two caudal pacemaker regions. These shifts were associated with reduced current generation capacity centrally and increased electrical load caudally. Previous studies suggest LP shift is a rate-dependent phenomenon whereby acetylcholine slows central pacemaker rate disproportionately, enabling caudal cells that are less acetylcholine sensitive to assume control. However, our findings indicate the LP region is defined by both pacemaker rate and capacity to drive activation. Shifts in LP site provide an important homeostatic mechanism for rapid switches in heart rate., Abstract: Reflex vagal activity causes abrupt heart rate slowing with concomitant caudal shifts of the leading pacemaker (LP) site within the sinoatrial node (SAN). However, neither the mechanisms responsible nor their dynamics have been investigated fully. Therefore, the objective of this study was to elucidate the mechanisms driving cholinergic LP shift. Optical maps of right atrial activation were acquired in a rat working heart-brainstem preparation during baroreflex and chemoreflex stimulation or with carbachol. All methods of stimulation triggered shifts in LP site from the central SAN to caudal pacemaker regions, which were positive for HCN4 and received uniform cholinergic innervation. During baroreflex onset, the capacity of the central region to drive activation declined with a decrease in amplitude and gradient of optical action potentials (OAPs) in the surrounding myocardium. Accompanying this decline, there was altered entrainment in the caudal SAN as shown by decreased conduction velocity, OAP amplitude, gradient and activation time. Atropine abolished these responses. Chemoreflex stimulation produced similar effects but central capacity to drive activation was preserved before the LP shift. In contrast, carbachol produced a prolonged period of reduced capacity to drive and altered entrainment. Previous studies suggest LP shift is a rate-dependent phenomenon whereby acetylcholine slows central pacemaker rate disproportionately, enabling caudal cells that are less acetylcholine sensitive to assume control. Our findings indicate that cholinergic LP shifts are also determined by altered electrical source-to-sink balance in the SAN. We conclude that the LP region is defined by both rate and capacity to drive atrial activation., (© 2019 The Authors. The Journal of Physiology © 2019 The Physiological Society.)

Organ level simulation of bioelectric behavior in the body benefits from flexible and efficient models of cellular membrane potential. These computational organ and cell models can be used to study the impact of pharmaceutical drugs, test hypotheses, assess risk and for closed-loop validation of medical devices. To move closer to the real-time requirements of this modeling a new flexible Fourier based general membrane potential model, called as a Resonant model, is developed that is computationally inexpensive. The new model accurately reproduces non-linear potential morphologies for a variety of cell types. Specifically, the method is used to model human and rabbit sinoatrial node, human ventricular myocyte and squid giant axon electrophysiology. The Resonant models are validated with experimental data and with other published models. Dynamic changes in biological conditions are modeled with changing model coefficients and this approach enables ionic channel alterations to be captured. The Resonant model is used to simulate entrainment between competing sinoatrial node cells. These models can be easily implemented in low-cost digital hardware and an alternative, resource-efficient implementations of sine and cosine functions are presented and it is shown that a Fourier term is produced with two additions and a binary shift., Competing Interests: The authors have declared that no competing interests exist.

Whole electrocardiogram (ECG) waveform analysis is a technique for evaluating aggregate arrhythmic risks of drugs. In this paper, we propose methods for exploring changes to ECG morphology due to drug effects using Gaussian model parameters, and predict patient specific post-drug ECG based on pre-drug ECG. We evaluate the proposed methods using clinical ECG recordings from subjects under the effect of anti-arrhythmic drugs Dofetilide, Quinidine, Ranolazine, and Verapamil, from the ECGRVDQ database on PhysioNet. Paired-sample t-test p-values (>0.05) suggest the proposed method can achieve similar results when compared to expert annotated J to T peak and T peak to T end intervals for all four drug states. We employed a leave-one-out cross validation strategy to train the prediction model and produce the results. Mean Pearson correlations between all predicted and recorded post-drug waveform morphologies for all drug states across both the vector magnitude lead and Lead II is 0.94±0.05, with p-values <0.01 for all predictions; indicating significant predictions. Parameters from ECG models with Gaussian basis can be used to calculate clinically useful information and to capture or predict changes in cardiac signals due to drug effects., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

The arrangement of cardiac cells into strand and sheet-like structures within the heart wall, confers important electrical properties onto heart tissue. Unraveling cardiomyocyte architecture in both healthy and diseased hearts is fundamental to understanding the mechanisms generating normal rhythm and arrhythmia. We analyzed five extended volume serial image stacks of normal pig left ventricular tissue. Analysis included: (1) reconstruction of original tissue volume and shape with non-linear correction maps; (2) segmentation and higher-order descriptions, areas and orientations of laminar structures through the heart wall; (3)computation of fiber directions; (4) computation of tissue connectivity using a shell filter. These measures contributed to a deeper and more objective understanding of cardiac tissue structures and their spatial variation than previously possible.

Invasive cardiac catheterisation is a precursor to ablation therapy for ventricular tachycardia. Invasive cardiac diagnostics are fraught with risks. Decades of research has been conducted on the inverse problem of electrocardiography, which can be used to reconstruct Heart Surface Potentials (HSPs) from Body Surface Potentials (BSPs), for non-invasive cardiac diagnostics. State of the art solutions to the inverse problem are unsatisfactory, since the inverse problem is known to be ill-posed. In this paper we propose a novel approach to reconstructing HSPs from BSPs using a Time-Delay Artificial Neural Network (TDANN). We first design the TDANN architecture, and then develop an iterative search space algorithm to find the parameters of the TDANN, which results in the best overall HSP prediction. We use recorded BSPs and HSPs from individuals suffering from serious cardiac conditions to validate our TDANN. The results are encouraging, in that the predicted and recorded HSPs have an average correlation coefficient of 0.7 under diseased conditions.

Objective: A flexible, efficient, and verifiable pacemaker cell model is essential to the design of real-time virtual hearts that can be used for closed-loop validation of cardiac devices. A new parametric model of pacemaker action potential is developed to address this need., Methods: The action potential phases are modeled using hybrid automaton with one piecewise-linear continuous variable. The model can capture rate-dependent dynamics, such as action potential duration restitution, conduction velocity restitution, and overdrive suppression by incorporating nonlinear update functions. Simulated dynamics of the model compared well with previous models and clinical data., Conclusion: The results show that the parametric model can reproduce the electrophysiological dynamics of a variety of pacemaker cells, such as sinoatrial node, atrioventricular node, and the His-Purkinje system, under varying cardiac conditions., Significance: This is an important contribution toward closed-loop validation of cardiac devices using real-time heart models.

Virtual heart models have been proposed to enhance the safety of implantable cardiac devices through closed loop validation. To communicate with a virtual heart, devices have been driven by cardiac signals at specific sites. As a result, only the action potentials of these sites are sensed. However, the real device implanted in the heart will sense a complex combination of near and far-field extracellular potential signals. Therefore many device functions, such as blanking periods and refractory periods, are designed to handle these unexpected signals. To represent these signals, we develop an intracardiac electrogram (IEGM) model as an interface between the virtual heart and the device. The model can capture not only the local excitation but also far-field signals and pacing afterpotentials. Moreover, the sensing controller can specify unipolar or bipolar electrogram (EGM) sensing configurations and introduce various oversensing and undersensing modes. The simulation results show that the model is able to reproduce clinically observed sensing problems, which significantly extends the capabilities of the virtual heart model in the context of device validation.

Introduction: Extracellular potentials measured on the heart surfaces are used to infer events that originate deep within the heart wall. We have reconstructed intramural potentials in three dimensions for the first time, and compare these with epicardial and endocardial surface potentials and cardiac microstructure., Methods and Results: Extracellular potentials from intramural point stimulation were measured from a high density 3-D electrode array in the in vivo pig LV. MR and extended volume imaging were used to register electrode locations and characterize fiber and laminar orientations throughout the recording volume. Measured potentials were compared with predictions of tissue-specific bidomain computer activation models. Positive potentials recorded in the LV wall preceded the depolarization wavefront as it spread in the fiber direction. Transverse to this, passive and active potentials spread preferentially in the laminar direction (anisotropy ratio ∼1.6:1). Epicardial surface potentials reflect initial intramural propagation at the stimulus location, but endocardial potentials do not, particularly adjacent to papillary muscles. Measured 3-D potentials were consistently better captured by computer models that incorporate three distinct conductivities aligned with local microstructural axes, but the preferential spread of potentials in the laminar direction was not fully predicted., Conclusions: This study provides evidence for preferential transmural conduction and raises questions about the extent to which intramural electrical events can be inferred from endocardial potentials., (© 2017 Wiley Periodicals, Inc.)

Background: Gastric slow waves regulate peristalsis, and gastric dysrhythmias have been implicated in functional motility disorders. To accurately define slow wave patterns, it is currently necessary to collect high-resolution serosal recordings during open surgery. We therefore developed a novel gastric slow wave mapping device for use during laparoscopic procedures., Methods: The device consists of a retractable catheter constructed of a flexible nitinol core coated with Pebax. Once deployed through a 5-mm laparoscopic port, the spiral head is revealed with 32 electrodes at 5 mm intervals. Recordings were validated against a reference electrode array in pigs and tested in a human patient., Results: Recordings from the device and a reference array in pigs were identical in frequency (2.6 cycles per minute; p = 0.91), and activation patterns and velocities were consistent (8.9 ± 0.2 vs 8.7 ± 0.1 mm s -1 ; p = 0.2). Device and reference amplitudes were comparable (1.3 ± 0.1 vs 1.4 ± 0.1 mV; p = 0.4), though the device signal-to-noise ratio was higher (17.5 ± 0.6 vs 12.8 ± 0.6 dB; P < 0.0001). In the human patient, corpus slow waves were recorded and mapped (frequency 2.7 ± 0.03 cycles per minute, amplitude 0.8 ± 0.4 mV, velocity 2.3 ± 0.9 mm s -1 )., Conclusion: In conclusion, the novel laparoscopic device achieves high-quality serosal slow wave recordings. It can be used for laparoscopic diagnostic studies to document slow wave patterns in patients with gastric motility disorders., Competing Interests: RB, MT and JW report no conflict of interest or financial ties to disclose.

High-resolution (HR) mapping has been used to study gastric slow-wave activation; however, the specific characteristics of antral electrophysiology remain poorly defined. This study applied HR mapping and computational modeling to define functional human antral physiology. HR mapping was performed in 10 subjects using flexible electrode arrays (128-192 electrodes; 16-24 cm 2 ) arranged from the pylorus to mid-corpus. Anatomical registration was by photographs and anatomical landmarks. Slow-wave parameters were computed, and resultant data were incorporated into a computational fluid dynamics (CFD) model of gastric flow to calculate impact on gastric mixing. In all subjects, extracellular mapping demonstrated normal aboral slow-wave propagation and a region of increased amplitude and velocity in the prepyloric antrum. On average, the high-velocity region commenced 28 mm proximal to the pylorus, and activation ceased 6 mm from the pylorus. Within this region, velocity increased 0.2 mm/s per mm of tissue, from the mean 3.3 ± 0.1 mm/s to 7.5 ± 0.6 mm/s (P < 0.001), and extracellular amplitude increased from 1.5 ± 0.1 mV to 2.5 ± 0.1 mV (P < 0.001). CFD modeling using representative parameters quantified a marked increase in antral recirculation, resulting in an enhanced gastric mixing, due to the accelerating terminal antral contraction. The extent of gastric mixing increased almost linearly with the maximal velocity of the contraction. In conclusion, the human terminal antral contraction is controlled by a short region of rapid high-amplitude slow-wave activity. Distal antral wave acceleration plays a major role in antral flow and mixing, increasing particle strain and trituration., (Copyright © 2016 the American Physiological Society.)

Virtual heart models have been proposed for closed loop validation of safety-critical embedded medical devices, such as pacemakers. These models must react in real-time to off-the-shelf medical devices. Real-time performance can be obtained by implementing models in computer hardware, and methods of compiling classes of Hybrid Automata (HA) onto FPGA have been developed. Models of ventricular cardiac cell electrophysiology have been described using HA which capture the complex nonlinear behavior of biological systems. However, many models that have been used for closed-loop validation of pacemakers are highly abstract and do not capture important characteristics of the dynamic rate response. We developed a new HA model of cardiac cells which captures dynamic behavior and we implemented the model in hardware. This potentially enables modeling the heart with over 1 million dynamic cells, making the approach ideal for closed loop testing of medical devices.

Goal: Gastric motility disorders have been associated with abnormal slow wave electrical activity (gastric dysrhythmias). Gastric pacing is a potential therapy for gastric dysrhythmias; however, new pacing protocols are required that can effectively modulate motility patterns, while being power efficient. This study presents a novel comprehensive 3-D multiscale modeling framework of the human stomach, including anisotropic conduction, capable of evaluating pacing strategies., Methods: A high-resolution anatomically realistic mesh was generated from CT images taken from a human stomach. Principal conduction axes were calculated and embedded within this model based on a modified Laplace-Dirichlet rule-based algorithm. A continuum-based tridomain formulation was implemented and evaluated for performance and used to model the slow-wave propagation, which takes into account the two main cell types present in gastric musculature. Model parameters were found by matching predicted normal slow-wave activity to experimental observation and data. These simulation parameters were applied while modeling an external pacing event to entrain slow-wave patterns., Results: The proposed formulation was found to be two times more efficient than a previous formulation for a normal slow-wave simulation. Convergence analysis showed that a mesh resolution of [Formula: see text] is required for an accurate solution process., Conclusion: The effect of different pacing frequencies on entrainment demonstrated that the pacing protocols are limited by the frequency of the native propagation and the refractory period of the cellular activity., Significance: The model is expected to become an important tool in studying pacing protocols for both efficiency and effectiveness.

Ectopic electrical activity that originates in the peri-infarct region can give rise to potentially lethal re-entrant arrhythmias. The spatial variation in electrotonic loading that results from structural remodelling in the infarct border zone may increase the probability that focal activity will trigger electrical capture, but this has not previously been investigated systematically. This study uses in-silico experiments to examine the structural modulation of effective refractory period on ectopic beat capture. Informed by 3-D reconstructions of myocyte organization in the infarct border zone, a region of rapid tissue expansion is abstracted to an idealized representation. A novel metric is introduced that defines the local electrotonic loading as a function of passive tissue properties and boundary conditions. The effective refractory period correlates closely with local electrotonic loading, while the action potential duration, conduction, and upstroke velocity reduce in regions of increasing electrotonic load. In the presence of focal ectopic stimuli, spatial variation in effective refractory period can cause unidirectional conduction block providing a substrate for reentrant arrhythmias. Consequently, based on the observed results, a possible novel mechanism for arrhythmogenesis in the infarct border zone is proposed.

Background: The electric response of myocardial tissue to periodic field stimuli has attracted significant attention as the basis for low-energy antifibrillation pacing, potentially more effective than traditional single high-energy shocks. In conventional models, an electric field produces a highly nonuniform response of the myocardial wall, with discrete excitations, or hot spots (HS), occurring at cathodal tissue surfaces or large coronary vessels. We test this prediction using novel 3-dimensional tomographic optical imaging., Methods and Results: Experiments were performed in isolated coronary perfused pig ventricular wall preparations stained with near-infrared voltage-sensitive fluorescent dye DI-4-ANBDQBS. The 3-dimensional coordinates of HS were determined using alternating transillumination. To relate HS formation with myocardial structures, we used ultradeep confocal imaging (interrogation depths, >4 mm). The peak HS distribution is located deep inside the heart wall, and the depth is not significantly affected by field polarity. We did not observe the strong colocalization of HS with major coronary vessels anticipated from theory. Yet, we observed considerable lateral displacement of HS with field polarity reversal. Models that de-emphasized lateral intracellular coupling and accounted for resistive heterogeneity in the extracellular space showed similar HS distributions to the experimental observations., Conclusions: The HS distributions within the myocardial wall and the significant lateral displacements with field polarity reversal are inconsistent with standard theories of defibrillation. Extended theories based on enhanced descriptions of cellular scale electric mechanisms may be necessary. The considerable lateral displacement of HS with field polarity reversal supports the hypothesis of biphasic stimuli in low-energy antifibrillation pacing being advantageous., (© 2015 American Heart Association, Inc.)

Optical mapping, with membrane-bound, voltage-sensitive dyes, is widely used for in vitro recording of cardiac electrical activity. The spatial registration of such maps is lost when the heart moves with respect to a fixed photodetector array and contraction can generate substantial artifact if background fluorescence is not uniformly distributed. While motion artifact is commonly suppressed with electromechanical uncoupling agents, there are circumstances where these are undesirable. This study outlines a novel image-based approach for retrospective motion artifact correction. Isolated Langendorff-supported rat hearts (n = 8), stained with di-4-ANEPPS, were illuminated at 516 ± 14 nm and fluorescent emission (>565 ± 10 nm) was acquired with a charge multiplying CCD camera. Background fluorescence was segmented in successive frames and stabilized using a non-rigid image registration algorithm. The resultant image deformation was used to estimate material point movement on the heart surface, so that total fluorescence could be mapped frame-by-frame to appropriate reference pixels. Finally, residual motion artifact was identified and removed. The effectiveness of this correction method was evaluated over 18 experimental datasets. Signal-to-noise ratio was increased more than fourfold, and activation time and action potential duration (APD) could be estimated at 24% more pixels than in the raw data. The variability of all APD measures was substantially reduced (i.e. APD50 estimated as 83.8 ± 45.8 ms before correction was 52.1 ± 4.7 ms afterward). This approach provides a robust means of recovering optical action potentials in the presence of substantial motion artifact.

Background: Cardiovascular magnetic resonance (CMR) can through the two methods 3D FLASH and diffusion tensor imaging (DTI) give complementary information on the local orientations of cardiomyocytes and their laminar arrays., Methods: Eight explanted rat hearts were perfused with Gd-DTPA contrast agent and fixative and imaged in a 9.4T magnet by two types of acquisition: 3D fast low angle shot (FLASH) imaging, voxels 50 × 50 × 50 μm, and 3D spin echo DTI with monopolar diffusion gradients of 3.6 ms duration at 11.5 ms separation, voxels 200 × 200 × 200 μm. The sensitivity of each approach to imaging parameters was explored., Results: The FLASH data showed laminar alignments of voxels with high signal, in keeping with the presumed predominance of contrast in the interstices between sheetlets. It was analysed, using structure-tensor (ST) analysis, to determine the most (v1(ST)), intermediate (v2(ST)) and least (v3(ST)) extended orthogonal directions of signal continuity. The DTI data was analysed to determine the most (e1(DTI)), intermediate (e2(DTI)) and least (e3(DTI)) orthogonal eigenvectors of extent of diffusion. The correspondence between the FLASH and DTI methods was measured and appraised. The most extended direction of FLASH signal (v1(ST)) agreed well with that of diffusion (e1(DTI)) throughout the left ventricle (representative discrepancy in the septum of 13.3 ± 6.7°: median ± absolute deviation) and both were in keeping with the expected local orientations of the long-axis of cardiomyocytes. However, the orientation of the least directions of FLASH signal continuity (v3(ST)) and diffusion (e3(ST)) showed greater discrepancies of up to 27.9 ± 17.4°. Both FLASH (v3(ST)) and DTI (e3(DTI)) where compared to directly measured laminar arrays in the FLASH images. For FLASH the discrepancy between the structure-tensor calculated v3(ST) and the directly measured FLASH laminar array normal was of 9 ± 7° for the lateral wall and 7 ± 9° for the septum (median ± inter quartile range), and for DTI the discrepancy between the calculated v3(DTI) and the directly measured FLASH laminar array normal was 22 ± 14° and 61 ± 53.4°. DTI was relatively insensitive to the number of diffusion directions and to time up to 72 hours post fixation, but was moderately affected by b-value (which was scaled by modifying diffusion gradient pulse strength with fixed gradient pulse separation). Optimal DTI parameters were b = 1000 mm/s(2) and 12 diffusion directions. FLASH acquisitions were relatively insensitive to the image processing parameters explored., Conclusions: We show that ST analysis of FLASH is a useful and accurate tool in the measurement of cardiac microstructure. While both FLASH and the DTI approaches appear promising for mapping of the alignments of myocytes throughout myocardium, marked discrepancies between the cross myocyte anisotropies deduced from each method call for consideration of their respective limitations.

Gastrointestinal motility is facilitated by specialized pacemaker cells called Interstitial Cells of Cajal (ICC). ICC play a critical role in coordinating normal motility and its degradation in the gastrointestinal tract is associated with many functional motility disorders. Nonetheless, the degree of degradation and associated clinical impact remains unclear. Continuum modeling frameworks offers a virtual mean to simulate the electrical activity, and analyze the ICC activity in both normal and diseased states. Confocal images of the ICC networks were obtained from the intestine of normal mice. In this study, a new approach is presented where meshes of ICC networks were generated using a Delaunay triangulation and used to solve finite-element based reaction-diffusion equations describing gastrointestinal electrophysiology. The electrical activity was simulated on the ICC network and solutions were compared to those of a regular mesh based on individual pixel locations. The simulation results showed the proposed approach to be approximately 80% more efficient than a pixel-based mesh. The difference in activation time for the entire network between the different methods was observed to be around 4% (about 20 ms). The proposed approach will enable efficient examination of the ICC slow wave activity in larger networks and for longer temporal duration that has been previously impossible. This will provide valuable insights relating ICC degradation to gastrointestinal motility disorders.

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems.

Gastrointestinal motility is coordinated by slow waves (SWs) generated by the interstitial cells of Cajal (ICC). Experimental studies have shown that SWs spontaneously activate at different intrinsic frequencies in isolated tissue, whereas in intact tissues they are entrained to a single frequency. Gastric pacing has been used in an attempt to improve motility in disorders such as gastroparesis by modulating entrainment, but the optimal methods of pacing are currently unknown. Computational models can aid in the interpretation of complex in vivo recordings and help to determine optimal pacing strategies. However, previous computational models of SW entrainment are limited to the intrinsic pacing frequency as the primary determinant of the conduction velocity, and are not able to accurately represent the effects of external stimuli and electrical anisotropies. In this paper, we present a novel computationally efficient method for modeling SW propagation through the ICC network while accounting for conductivity parameters and fiber orientations. The method successfully reproduced experimental recordings of entrainment following gastric transection and the effects of gastric pacing on SW activity. It provides a reliable new tool for investigating gastric electrophysiology in normal and diseased states, and to guide and focus future experimental studies.

Impulse propagation in the heart depends on the excitability of individual cardiomyocytes, impulse transmission between adjacent myocytes, and the 3-dimensional arrangement of those cells. Here, we review the role of each of these factors in normal and aberrant cardiac electric activation, with particular emphasis on the effects of 3-dimensional myocyte architecture at the tissue scale. The analysis draws on findings from in vivo and in vitro experiments, as well as biophysically based computer models that have been used to integrate and interpret these experimental data. It indicates that discontinuous arrangement of myocytes and extracellular connective tissue at the tissue scale can give rise to current source-to-sink mismatch, spatiotemporal distribution of refractoriness, and rate-sensitive electric instability, which contribute to the initiation and maintenance of reentrant cardiac arrhythmia. This exacerbates the risk of rhythm disturbance associated with heart disease. We conclude that structure-based, multiscale computer models that incorporate accurate information about local cellular electric activity provide a powerful platform for investigating the basis of reentrant cardiac arrhythmia. However, it is important that these models capture key features of structure and related electric function at the tissue scale.

Vagal nerve activity has been shown to play a role in the formation and maintenance of atrial fibrillation (AF). Nerves on the atria are now increasingly being targeted using ablation-based therapies for the treatment of paroxysmal AF. In vivo, changes in vagal activity are part of an integrated autonomic profile that invariably involves accompanying modulations in sympathetic activity. To date, it has not been possible to replicate endogenous profiles of autonomic activity with the experimental set-ups used to study the effects of vagal stimulation on AF development. In this paper, we describe an experimental set-up using an in situ preparation that addresses these challenges for the first time. A high resolution surface electrode array has been used to make recordings of atrial electrograms during baroreflex activation from a preparation with intact innervation from brainstem to heart. This provides a novel framework for relating reflex-mediated autonomic activity to altered regional impulse propagation and electrical rhythm in the atria.

DT-MRI has been widely used to quantify myocardial fiber and laminar orientations. These structural orientations influence both the spread of excitation and the reorganization of the myocardium during contraction and are altered in disease states. Studies have sought to validate DT-MRI but questions remain about the accuracy of the method and its sensitivity to the time post-fixation and imaging parameters, including b-value, number of diffusion directions and image voxel size. The advent of high-spatial resolution ex vivo MRI and structure tensor (ST) analysis provides a means of direct validation of DT-MRI and assessment of sensitivity to the b-value, the number of diffusion directions and the image voxel size. We find that, with the fixation method we used, structure does not change with time (up to 72 hours). We show that DT-MRI and ST/HR-MRI are markedly similar measures of fiber orientation but DT-MRI and ST are much less similar measures of laminar orientation. DT-MRI performance is not sensitive to the number of directions, with similar structural orientations measured with 6 or 12 directions. Likewise, DT-MRI performance is generally insensitive to b-value, but laminar measurement is moderately more accurate at b = 500 than for higher b-values.

A novel, anatomically-accurate model of a tibialis anterior muscle is used to investigate the electro-physiological properties of denervated muscles following functional electrical stimulation. The model includes a state-of-the-art description of cell electro-physiology. The main objective of this work is to develop a computational framework capable of predicting the effects of different stimulation trains and electrode configurations on the excitability and fatigue of skeletal muscle tissue. Utilizing a reduced but computationally amenable model, the effects of different electrode sizes and inter-electrode distances on the number of activated muscle fibers are investigated and qualitatively compared to existing literature. To analyze muscle fatigue, the sodium current, specifically the K+ ion concentrations within the t-tubule and the calcium release from the sarcoplasmic reticulum, is used to quantify membrane and metabolic fatigue. The simulations demonstrate that lower stimulation frequencies and biphasic pulse waveforms cause less fatigue than higher stimulation frequencies and monophasic pulses. A comparison between single and dual electrode configurations (with the same overall stimulation surface) is presented to locally investigate the differences in muscle fatigue. The dual electrode configuration causes the muscle tissue to fatigue quicker., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear., Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure., Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm(3) and 5.6 mm(3)) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 μm across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo-Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing., Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry.

A theoretical model of the cross-linking topology of ventricular muscle tissue is developed. Using parameter estimation the terms of the theoretical model are estimated for normal and pathological conditions. The model represents the anisotropic structure of the tissue, reproduces published experimental data and characterizes the role of different tissue components in the observed macroscopic behavior. Changes in the material parameters are consistent with expected structural changes and the model is extended to reproduce force-Calcium relationships. Model results are invoked to argue that semisoft behavior and the material axis anisotropy arise from the constraints on the extracellular matrix cross-linking topology.

The ventricular myocardium has a structure of branching laminae through which course regularly orientated myofibers, an architecture important in excitation and contraction. Quantifying this architecture is vital for understanding normal and disease states in the heart and for assessing their impact on electrical function. These data are also highly important in the construction of scientifically and clinically useful computer models of cardiac electrical behavior. Detailed structural information has previously been obtained from serial imaging. In this work we assess the potential for high-resolution (HR) MRI as a means to furnish useful myoarchitecture and compare and contrast this approach with the growing use of DT. Using rat hearts, we conclude that both approaches have strengths and weaknesses, however, HR-MRI may provide a consistently more robust picture of the myoarchitecture in small hearts.

A method is presented for registering 3D cardiac tissue images to reference data, for the purpose of analyzing recorded electrical activity. Following left-ventricular in vivo electrical mapping studies in pig hearts, MRI is used to define a reference geometry in the tissue segment around the recording electrodes. The segment is then imaged in 3D using a high-resolution serial imaging microscopy technique. The tissue processing required for this introduces segment-wide distortion. Piecewise-smooth maps are used to correct the tissue distortion and register the 3D images with the reference MRI data. The methods are validated and techniques for identifying the preferred maps are proposed. Recorded electrical activation is shown to map reliably onto cardiac tissue structure using this registration method.

Radiofrequency catheter ablation as a curative method for atrial fibrillation (AF) has become increasingly popular. Patients with paroxysmal AF have been treated by catheter ablation with great success, but so far this treatment has been less effective for patients with persistent AF. Usually there are multiple triggers or substrates during persistent AF and their exact locations are unclear. On the other hand, the non-contact mapping system (Ensite 3000, St Jude Medical) producing thousands of virtual endocardial electrograms, has gradually become accepted as a powerful tool to use on patients before and after ablation. Effective mathematical tools to detect the substrates of AF from unipolar electrograms produced by the non-contact mapping are few, though many methods are available for performing this task with bipolar electrograms. In this work, we introduce for the first time a simple and efficient approach to automatically and systematically determine the substrate of persistent AF in order to guide catheter ablation via the non-contact mapping.

Background: Marked changes in ventricular APD restitution and associated alternans rhythm have been demonstrated in structural heart disease (SHD). However, whether this is due to structural heterogeneity or regional variation in cellular properties remains uncertain. In this study, we address the hypothesis that the structural heterogeneity associated with SHD is sufficient to alter dynamic restitution and increase the probability of electric instability., Methods and Results: Activation was simulated in a 14x14 mm(2) domain in the presence and absence (control) of a central region containing nonuniform discontinuities resembling patchy fibrosis. A modified LR1 cardiac activation model was used in a bidomain formulation with isotropic conductivities. Bipolar stimulation was imposed above the central region with coupling intervals decreasing progressively from 500 ms and then maintained at 105 ms. Structural discontinuities had little effect on electric activation at low stimulus rates, but activation time and APD distributions became highly nonuniform within and adjacent to the discontinuous region at high rates. Discordant APD alternans occurred in both "fibrosis" and control, but at lower stimulus rates and with markedly greater extent in the former. Tortuous conduction through the discontinuous region resulted in large fluctuations of diastolic intervals giving rise to regional electric instability, which modulates dynamic conduction velocity and APD restitution. This led to heterogeneous conduction block and reentry not observed in control., Conclusions: We show that structural discontinuities can amplify discordant alternans and provide a rate-dependent substrate for reentry. This work provides new insights into the mechanisms by which fibrosis may contribute to arrhythmogenesis.

Background: The anisotropy of cardiac tissue is a key determinant of 3D electric propagation and the stability of activation wave fronts in the heart. The electric properties of ventricular myocardium are widely assumed to be axially anisotropic, with activation propagating most rapidly in the myofiber direction and at uniform velocity transverse to this. We present new experimental evidence that contradicts this view., Methods and Results: For the first time, high-density intramural electric mapping (325 electrodes at approximately 4x4x1-mm spacing) from pig left ventricular tissue was used to reconstruct 3D paced activation surfaces projected directly onto 3D tissue structure imaged throughout the same left ventricular volume. These data from 5 hearts demonstrate that ventricular tissue is electrically orthotropic with 3 distinct propagation directions that coincide with local microstructural axes defined by the laminar arrangement of ventricular myocytes. The maximum conduction velocity of 0.67+/-0.019 ms(-1) was aligned with the myofiber axis. However, transverse to this, the maximum conduction velocity was 0.30+/-0.010 ms(-1), parallel to the myocyte layers and 0.17+/-0.004 ms(-1) normal to them. These orthotropic conduction velocities give rise to preferential activation pathways across the left ventricular free wall that are not captured by structurally detailed computer models, which incorporate axially anisotropic electric properties., Conclusions: Our findings suggest that current views on uniform side-to-side electric coupling in the heart need to be revised. In particular, nonuniform laminar myocardial architecture and associated electric orthotropy should be included in future models of initiation and maintenance of ventricular arrhythmia.

Introduction: Atrial fibrillation is prevalent in the elderly and contributes to mortality in congestive heart failure. Development of computer models of atrial electrical activation that incorporate realistic structures provides a means of investigating the mechanisms that initiate and maintain reentrant atrial arrhythmia. As a step toward this, we have developed a model of the right atrial appendage (RAA) including detailed geometry of the pectinate muscles (PM) and crista terminalis (CT) with high spatial resolution, as well as complete fiber architecture., Methods and Results: Detailed structural images of a pig RAA were acquired using a semiautomated extended-volume imaging system. The generally accepted anisotropic ratio of 10:1 was adopted in the computer model. To deal with the regional action potential duration heterogeneity in the RAA, a Courtemanche cell model and a Luo-Rudy cell model were used for the CT and PM, respectively. Activation through the CT and PM network was adequately reproduced with acceptable accuracy using reduced-order computer models. Using a train of reducing cycle length stimuli applied to a CT/PM junction, we observed functional block both parallel with and perpendicular to the axis of the CT., Conclusion: With stimulation from the CT at the junction of a PM, we conclude: (a) that conduction block within the CT is due to a reduced safety factor; and (b) that unidirectional block and reentry within the CT is due to its high anisotropy. Regional differences in effective refractive period do not explain the observed conduction block.

Detailed models of sample specific structures in pig left-ventricular tissue have been constructed. These models include epicardial and endocardial surfaces, fiber and sheet orientations, vessels and cleavage planes with significant dimensions. This work shows that it is possible to extract from 3D tissue images reduced dimension descriptions of cleavage planes in the heart wall. These descriptions are used to analyze the response of tissue to electrical shocks of varying strengths. The presence of explicit discontinuities in the heart significantly reduces the time required for transmural activation and provides a basis for understanding successful defibrillation.

The heart's response to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. Analysis of the microstructure of the heart predicts that three unique intracellular electrical conductances can be defined at any point in the ventricular wall; however, to date, there has been no experimental confirmation of this concept. We report the design, fabrication, and validation of a novel plunge electrode array capable of addressing this issue. A new technique involving nylon coating of 24G hypodermic needles is performed to achieve nonconductive electrodes that can be combined to give moderate-density multisite intramural measurement of extracellular potential in the heart. Each needle houses 13 silver wires within a total diameter of 0.7 mm, and the combined electrode array gives 137 sites of recording. The ability of the electrode array to accurately assess conductances is validated by mapping the potential field induced by a point current source within baths of saline of varying concentration. A bidomain model of current injection in the heart is then used to test an approximate relationship between the monodomain conductivities measured by the array, and the full set of bidomain conductivities that describe cardiac tissue.

Two-dimensional in silico models have been constructed for investigating electrical dynamics arising due to pacing rates and tissue discontinuities. Discontinuities (structures) are introduced explicitly through flux discontinuities in the intracellular space. These models use isotropic electrophysiological properties with heterogeneity arising solely from tissue structure. Both simplified and tissue-specific structures can be used together with membrane models with varying restitution properties. Stimuli are delivered at increasing pacing rates, and solution restarts enable the investigation of repeat stimulation at any of the rates. Investigations using these models are providing new insights into mechanisms leading to conduction block and arrhythmogenesis in cardiac tissue.

Experimental intramural recordings of electrical activity at high resolution have been made in the in-vivo pig LV free wall. To analyze features of these recordings experiment-specific 3D computer models of tissue structures and electrical behavior around the recording sites were constructed. The construction of the models used novel tissue image registration, correction and feature extraction methods. Appropriate model conductivity parameters were deduced from measurements and used to replicate features of experimental recordings.

We present a method to efficiently solve cardiac membrane models using a novel unsupervised clustering algorithm. The unsupervised clustering algorithm was designed to handle repeated clustering of multidimensional objects with rapidly changing properties. A Modified Trie datastructure that allowed efficient search, scalable and distributed assembly of the result was designed. The method was applied to solve monodomain models of cardiac tissue with highly non-linear reaction elements. We demonstrate the versatility and advantages of using the method by subjecting the tissue to various spatial excitation patterns.

The response of the heart to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. A long-held view of cardiac electrical anisotropy is that electrical conductivity is greatest along the myocyte axis allowing most rapid propagation of electrical activation in this direction, and that conductivity is isotropic transverse to the myocyte axis supporting a slower uniform spread of activation in this plane. In this context, knowledge of conductivity in two directions, parallel and transverse to the myofiber axis, is sufficient to characterize the electrical action of the heart. Here we present new experimental data that challenge this view. We have used a novel combination of intramural electrical mapping, and experiment-specific computer modeling, to demonstrate that left ventricular myocardium has unique bulk conductivities associated with three microstructurally-defined axes. We show that voltage fields induced by intramural current injection are influenced by not only myofiber direction, but also the transmural arrangement of muscle layers or myolaminae. Computer models of these experiments, in which measured 3D tissue structure was reconstructed in-silico, best matched recorded voltages with conductivities in the myofiber direction, and parallel and normal to myolaminae, set in the ratio 4:2:1, respectively. These findings redefine cardiac tissue as an electrically orthotropic substrate and enhance our understanding of how external shocks may act to successfully reset the fibrillating heart into a uniform electrical state. More generally, the mechanisms governing the destabilization of coordinated electrical propagation into ventricular arrhythmia need to be evaluated in the light of this discovery.

Significant tissue structures exist in cardiac ventricular tissue, which are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhythmogenesis, and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements, we use tissue-specific structure and mathematical modeling. Our models, which can incorporate ion channel models at the cell level into the reaction-diffusion equations at the tissue level, have enabled us to consider key hypotheses regarding discontinuous activation.

Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.