Creation and application of virtual patient cohorts of heart models.

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

A rule-based method for predicting the electrical activation of the heart with cardiac resynchronization therapy from non-invasive clinical data.

BACKGROUND: Cardiac Resynchronization Therapy (CRT) is one of the few effective treatments for heart failure patients with ventricular dyssynchrony. The pacing location of the left ventricle is indicated as a determinant of CRT outcome. OBJECTIVE: Patient specific computational models allow the activation pattern following CRT implant to be predicted and this may be used to optimize CRT lead placement. METHODS: In this study, the effects of heterogeneous cardiac substrate (scar, fast endocardial conduction, slow septal conduction, functional block) on accurately predicting the electrical activation of the LV epicardium were tested to determine the minimal detail required to create a rule based model of cardiac electrophysiology. Non-invasive clinical data (CT or CMR images and 12 lead ECG) from eighteen patients from two centers were used to investigate the models. RESULTS: Validation with invasive electro-anatomical mapping data identified that computer models with fast endocardial conduction were able to predict the electrical activation with a mean distance errors of 9.2 ±â€¯0.5 mm (CMR data) or (CT data) 7.5 ±â€¯0.7 mm. CONCLUSION: This study identified a simple rule-based fast endocardial conduction model, built using non-invasive clinical data that can be used to rapidly and robustly predict the electrical activation of the heart. Pre-procedural prediction of the latest electrically activating region to identify the optimal LV pacing site could potentially be a useful clinical planning tool for CRT procedures.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling.

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Accelerating cardiac bidomain simulations using graphics processing units.

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility.

A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models.

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

Biophysical modeling to simulate the response to multisite left ventricular stimulation using a quadripolar pacing lead.

BACKGROUND: Response to cardiac resynchronization therapy (CRT) is reduced in patients with posterolateral scar. Multipolar pacing leads offer the ability to select desirable pacing sites and/or stimulate from multiple pacing sites concurrently using a single lead position. Despite this potential, the clinical evaluation and identification of metrics for optimization of multisite CRT (MCRT) has not been performed. METHODS: The efficacy of MCRT via a quadripolar lead with two left ventricular (LV) pacing sites in conjunction with right ventricular pacing was compared with single-site LV pacing using a coupled electromechanical biophysical model of the human heart with no, mild, or severe scar in the LV posterolateral wall. RESULT: The maximum dP/dt(max) improvement from baseline was 21%, 23%, and 21% for standard CRT versus 22%, 24%, and 25% for MCRT for no, mild, and severe scar, respectively. In the presence of severe scar, there was an incremental benefit of multisite versus standard CRT (25% vs 21%, 19% relative improvement in response). Minimizing total activation time (analogous to QRS duration) or minimizing the activation time of short-axis slices of the heart did not correlate with CRT response. The peak electrical activation wave area in the LV corresponded with CRT response with an R(2) value between 0.42 and 0.75. CONCLUSION: Biophysical modeling predicts that in the presence of posterolateral scar MCRT offers an improved response over conventional CRT. Maximizing the activation wave area in the LV had the most consistent correlation with CRT response, independent of pacing protocol, scar size, or lead location.

Inter-model consistency and complementarity: learning from ex-vivo imaging and electrophysiological data towards an integrated understanding of cardiac physiology.

Computational models of the heart at various scales and levels of complexity have been independently developed, parameterised and validated using a wide range of experimental data for over four decades. However, despite remarkable progress, the lack of coordinated efforts to compare and combine these computational models has limited their impact on the numerous open questions in cardiac physiology. To address this issue, a comprehensive dataset has previously been made available to the community that contains the cardiac anatomy and fibre orientations from magnetic resonance imaging as well as epicardial transmembrane potentials from optical mapping measured on a perfused ex-vivo porcine heart. This data was used to develop and customize four models of cardiac electrophysiology with different level of details, including a personalized fast conduction Purkinje system, a maximum a posteriori estimation of the 3D distribution of transmembrane potential, the personalization of a simplified reaction-diffusion model, and a detailed biophysical model with generic conduction parameters. This study proposes the integration of these four models into a single modelling and simulation pipeline, after analyzing their common features and discrepancies. The proposed integrated pipeline demonstrates an increase prediction power of depolarization isochrones in different pacing conditions.

A finite element formulation for atrial tissue monolayer.

OBJECTIVES: Using computer models for the study of complex atrial arrhythmias such as atrial fibrillation is computationally demanding as long observation periods in the order of tens of seconds are required. A well established approach for reducing computational workload is to approximate the thin atrial walls by curved monolayers. On the other hand, the finite element method (FEM) is a well established approach to solve the underlying partial differential equations. METHODS: A generalized 2D finite element method (FEM) is presented which computes the corresponding stiffness and coupling matrix for arbitrarily shaped monolayers (ML). Compared to standard 2D FEM, only one additional coordinate transformation is required. This allows the use of existing FEM software with minor modifications. The algorithm was tested to simulate wave propagation in benchmark geometries and in a model of atrial anatomy. RESULTS: The ML model was able to simulate electric activation in curved tissue with anisotropic conductivity. Simulations in branching tissue yielded slightly different patterns when compared to a volumetric model with finite thickness. In the model of atrial anatomy the computed activation times for five different pacing protocols displayed a correlation of 0.88 compared to clinical data. CONCLUSIONS: The presented method provides a useful and easily implemented approach to model wave propagation in MLs with a few restrictions to volumetric models.

Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions.

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Solvers for the cardiac bidomain equations.

The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue. They are especially important for accurately modeling extracellular stimulation, as evidenced by their prediction of virtual electrode polarization before experimental verification. However, solution of the equations is computationally expensive due to the fine spatial and temporal discretization needed. This limits the size and duration of the problem which can be modeled. Regardless of the specific form into which they are cast, the computational bottleneck becomes the repeated solution of a large, linear system. The purpose of this review is to give an overview of the equations and the methods by which they have been solved. Of particular note are recent developments in multigrid methods, which have proven to be the most efficient.

A new floating sensor array to detect electric near fields of beating heart preparations.

A new flexible sensor for in vitro experiments was developed to measure the surface potential, Phi, and its gradient, E (electric near field), at given sites of the heart. During depolarisation, E describes a vector loop from which direction and magnitude of local conduction velocity theta can be computed. Four recording silver electrodes (14 microm x 14 microm) separated by 50 microm, conducting leads, and solderable pads were patterned on a 50 microm thick polyimide film. The conductive structures, except the electrodes, were isolated with polyimide, and electrodes were chlorided. Spacer pillars mounted on the tip fulfil two functions: they keep the electrodes 70 microm from the tissue allowing non-contact recording of Phi and prevent lateral slipping. The low mass (9.1 mg) and flexibility (6.33 N/m) of the sensor let it easily follow the movement of the beating heart without notable displacement. We examined the electrodes on criteria like rms-noise of Phi, signal-to-noise ratio of Phi and E, maximum peak-slope recording dPhi/dt, and deviation of local activation time (LAT) from a common signal and obtained values of 24-28 microV, 46 and 41 dB, 497-561 V/s and no differences, respectively. With appropriate data acquisition (sampling rate 100 kHz, 24-bit), we were able to record Phi and to monitor E and theta on-line from beat-to-beat even at heart rates of 600 beats/min. Moreover, this technique can discriminate between uncoupled cardiac activations (as occur in fibrotic tissue) separated by less than 1 mm and 1 ms.

Cardiac near-field morphology during conduction around a microscopic obstacle--a computer simulation study.

In a recent paper, we described the behavior of the cardiac electric near-field, E, parallel to the tissue surface during continuous conduction. We found that the tip of E describes a vector-loop during depolarization with the peak field, E, pointing opposite to the direction of propagation, phiI(m). Experimentally recorded loop morphologies of E, however, frequently showed significant deviations from the theoretically predicted behavior. We hypothesized that this variety of morphologies might be caused by conduction obstacles at a microscopic size scale. This study examines the influence of obstacles on the morphology of vector loops of E and whether the peak of distorted loops remains a reliable indicator for the direction of propagation. We used a computer model of a sheet of cardiac tissue with a central conduction obstacle immersed in an unbounded volume conductor. We studied the loop morphologies of E and the differences between the intracellularly determined direction of propagation, phiI(m), and the direction of E, phiE. Distortions of the vector loop were morphologically similar to those observed experimentally. Differences between phiI(m) and phiE were less than 18 degrees at all observation sites. The obstacle led to deformations of the loop morphology, particularly during the initial and terminal phases, and to a lesser degree near the instant of E. We concluded that E is a reliable indicator of phiI(m).

Use of cardiac electric near-field measurements to determine activation times.

In a recent paper, we described the behavior of the cardiac electric near-field, E, parallel to the tissue surface during continuous conduction. We found that T(E), the time at which the peak near-field, E, occurs, is an accurate marker of local activation time. Examination of experimentally recorded E vector loops revealed a large variety of morphologies. We postulated that propagation around an obstacle could lead to the observed deviations in loop morphology. The purpose of this study was to determine if this was plausible, and if so, whether T(E) remains an accurate time marker of local activation under these conditions. We used a monodomain computer model of a sheet of cardiac tissue with a central conduction obstacle immersed in an unbounded volume conductor. Activation times T(Im), T(phi), and T(E) were derived from the transmembrane current I(m), the extracellular potential phi(e), and E, respectively. The obstacle led to deformations of the vector loops, morphologically similar to those observed experimentally, particularly during the initial and terminal phases, and to a lesser degree near the time of E. Despite these loop deformations, T(E) was an accurate time marker of local activation. We found that T(E) was significantly closer to T(Im) than T(phi). We concluded that isochrone maps computed from T(E) better reflect intracellular activation patterns than those computed from T(phi). For a given electrode spacing of 60 microm, the sensitivity to noise of E was significantly less than that of phi(e). Hence, T(E) was less affected by noise than T(phi).

Computational tools for modeling electrical activity in cardiac tissue.

Computer models offer many attractive benefits. However, the modeling of cardiac tissue is computationally expensive due to several physical constraints which result in fine spatiotemporal discretization over large spatiotemporal regions. Our laboratory has been actively trying to develop new techniques to make large scale cardiac simulations tractable over the past 15 years. This paper describes the latest modeling software that our group has developed, called Carp (Cardiac arrhythmias research package). It is designed to run in both shared memory and clustered computing environments. Carp aims to be modular and flexible by following a plug-in framework. This allows the latest models and most efficient solvers to be incorporated as well as enabling run-time selection of techniques. Performance results are given for a large-scale simulation which utilized a comprehensive membrane ionic current description.

Application of the Cross Battery Approach in the assessment of American Indian children: a viable alternative.

This article examines current psychometric and testing practices that appear to do a limited job of assessing the intelligence of American Indian individuals. For several reasons, contemporary approaches are found to be inadequate. Unfortunately, these practices are then employed in making educational decisions and placing these same children into Special Education programs. Alternative methods of testing, including the Gf-Gc Cross-Battery Approach, are discussed and evaluated in terms of usefulness in the evaluation of American Indian children and adolescents. The cross-battery method of testing was found to provide more in-depth procedures for bypassing both language and cultural differences among American Indian individuals.

Model study of vector-loop morphology during electrical mapping of microscopic conduction in cardiac tissue.

The large variety in loop morphology of potential differences recorded at the cardiac surface has been generally attributed to structural discontinuities of the tissue. The aim of this work was to examine if the diversity of vector loops of the electric field E found experimentally may also arise during continuous anisotrope conduction. For this purpose a monodomain computer model was used, consisting of a two-dimensional sheet of excitable tissue surrounded with an unbounded volume conductor. Close to the tissue surface our computations predicted a narrow biphasic course of phi(e) with peak-to-peak separation of less than 400 microm. We examined how accurately E could be reconstructed from measurements recorded with four-element electrode arrays and how activation sequence, interelectrode spacing, and probe orientation affects the results. We found "closed" vector loops of E in planar, and at the apex of elliptical wave fronts, whereas outside of these regions vector loops were "open." Varying probe orientation and size resulted in substantial changes of vector-loop morphology. We concluded that close to the cardiac current sources accurate measurement of E would require interelectrode distances of less than 100 microm.

A new real-time mapping system to detect microscopic cardiac excitation patterns.

A new fast, high-resolution measurement system has been developed to analyze the propagation of cardiac excitation on a microscopic scale. The instrument uses a microsensor array to detect microscopic excitation patterns at the cardiac surface. Ninety-six epicardial signals are recorded simultaneously with 14-bit resolution at 200-kHz samples per second per channel. The system operates like a digital oscilloscope. Preprocessing routines (offset, gain, and triggering) are executed within a sampling interval of 5 microseconds by 48 digital signal processors. Analog-to-digital (A/D) converters are provided with 12 Mb of buffer memory, allowing continuous recording of up to 64-k samples x 96 channels. The recorded dataset is transferred rapidly (8 Mb/sec) to the memory of the integrated computer system via VXIbus. Analysis and visualization of the propagating excitation are computed by custom-designed software. The performance of the system allows recording as well as visualization of the cardiac excitation spread in a beat-to-beat manner.

Comparison between the role of discontinuities in cardiac conduction and in a one-dimensional hardware model.

In real electrophysiological experiments, irregularities in the extracellular excitation spread are believed to depend on cardiac tissue microstructure. An electronic hardware model was developed to analyze this dependence by placing some inhomogeneities (slow propagation areas) in the medium. The position of such inhomogeneities is correlated with abnormal delays and irregularities measured in signal propagation.