Martin J. Bishop

Generation of histo−anatomically representative models of the individual heart: tools and application

This paper presents methods to build histo-anatomically detailed individualized cardiac models. The models are based on high-resolution three-dimensional anatomical and/or diffusion tensor magnetic resonance images, combined with serial histological sectioning data, and are used to investigate individualized cardiac function. The current state of the art is reviewed, and its limitations are discussed. We assess the challenges associated with the generation of histo-anatomically representative individualized in silico models of the heart. The entire processing pipeline including image acquisition, image processing, mesh generation, model set-up and execution of computer simulations, and the underlying methods are described. The multifaceted challenges associated with these goals are highlighted, suitable solutions are proposed, and an important application of developed high-resolution structure–function models in elucidating the effect of individual structural heterogeneity upon wavefront dynamics is demonstrated.

Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function

Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: ∼125 μm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 × 43 × 36 μm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.

Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations

In this paper, we illustrate how advanced computational modelling and simulation can be used to investigate drug-induced effects on cardiac electrophysiology and on specific biomarkers of pro-arrhythmic risk. To do so, we first perform a thorough literature review of proposed arrhythmic risk biomarkers from the ionic to the electrocardiogram levels. The review highlights the variety of proposed biomarkers, the complexity of the mechanisms of drug-induced pro-arrhythmia and the existence of significant animal species differences in drug-induced effects on cardiac electrophysiology. Predicting drug-induced pro-arrhythmic risk solely using experiments is challenging both preclinically and clinically, as attested by the rise in the cost of releasing new compounds to the market. Computational modelling and simulation has significantly contributed to the understanding of cardiac electrophysiology and arrhythmias over the last 40 years. In the second part of this paper, we illustrate how state-of-the-art open source computational modelling and simulation tools can be used to simulate multi-scale effects of drug-induced ion channel block in ventricular electrophysiology at the cellular, tissue and whole ventricular levels for different animal species. We believe that the use of computational modelling and simulation in combination with experimental techniques could be a powerful tool for the assessment of drug safety pharmacology.

Modeling the Role of the Coronary Vasculature During External Field Stimulation

The exact mechanisms by which defibrillation shocks excite cardiac tissue far from both the electrodes and heart surfaces require elucidation. Bidomain theory explains this phenomena through the existence of intramural virtual electrodes (VEs), caused by discontinuities in myocardial tissue structure. In this study, we assess the modeling components essential in constructing a finite-element cardiac tissue model including blood vessels from high-resolution magnetic resonance data and investigate the specific role played by coronary vasculature in VE formation, which currently remains largely unknown. We use a novel method for assigning histologically based fiber architecture around intramural structures and include an experimentally derived vessel lumen wall conductance within the model. Shock-tissue interaction in the presence of vessels is assessed through comparison with a simplified model lacking intramural structures. Results indicate that VEs form around blood vessels for shocks >8 V/cm. The magnitude of induced polarizations is attenuated by realistic representation of fiber negotiation around vessel cavities, as well as the insulating effects of the vessel lumen wall. Furthermore, VEs formed around large subepicardial vessels reduce epicardial polarization levels. In conclusion, we have found that coronary vasculature acts as an important substrate for VE formation, which may help interpretation of optical mapping data.

Representing Cardiac Bidomain Bath-Loading Effects by an Augmented Monodomain Approach: Application to Complex Ventricular Models

Although the cardiac bidomain model has been widely used in the simulation of electrical activation, its relatively computationally expensive nature means that monodomain approaches are generally required for long-duration simulations (for example, investigations of arrhythmia mechanisms). However, the presence of a conducting bath surrounding the tissue is known to induce wavefront curvature (surface leading bulk), a phenomena absent in standard monodomain approaches. Here, we investigate the bio physical origin of the bidomain bath-loading induced wavefront curvature and present a novel augmented monodomain-equivalent bidomain approach faithfully replicating all aspects of bidomain wavefront morphology and conduction velocity, but with a fraction of the computational cost. Bath-loading effects are shown to be highly dependent upon specific conductivity parameters, but less dependent upon the thickness or conductivity of the surrounding bath, with even relatively thin surrounding fluid layers (~ 0.1 mm) producing significant wavefront curvature in bidomain simulations. We demonstrate that our augmented monodomain approach can be easily adapted for different conductivity sets and applied to anatomically complex models, thus facilitating fast and accurate simulation of cardiac wavefront dynamics during long-duration simulations, further aiding the faithful comparison of simulations with experiments.

The role of fine-scale anatomical structure in the dynamics of reentry in computational models of the rabbit ventricles.

•  The specific mechanisms by which fine‐scale structures within the heart may interact with complex excitation wavefronts during cardiac arrhythmias to increase their stability, and how this interaction may differ between species are currently incompletely understood. •  Computational models provide an important basic science tool in mechanistic arrhythmia enquiry. Recent advances in cardiac imaging have allowed the generation of highly anatomically detailed computational ventricular models including fine‐scale features such as blood vessels and endocardial structures. •  Using such an anatomically detailed MR‐derived rabbit ventricular model, in conjunction with a simplified equivalent model, we assessed the role played by fine‐scale anatomy in the sustenance of different types of simulated arrhythmias. •  Our simulation results suggest that, in the rabbit, anatomical structures such as the vasculature and endocardial structures play little role in the maintenance of cardiac arrhythmias, although their role becomes marginally more important with increasing arrhythmia complexity. •  Consequently, in the rabbit, constructing computational models which represent the vasculature and endocardial structures may not be necessary for mechanistic investigation of arrhythmia maintenance.

Comparison of Rule-Based and DTMRI-Derived Fibre Architecture in a Whole Rat Ventricular Computational Model

The anisotropic electrical conduction within myocardial tissue due to preferential cardiac myocyte orientation (`fibre orientation) is known to impact strongly in electrical wavefront dynamics, particularly during arrhythmogenesis. Faithful representation of cardiac fibre architecture within computational cardiac models which seek to investigate such phenomena is thus imperative. Drawbacks in derivation of fibre structure from imaging modalities often render rule-based representations based on a priori knowledge preferential. However, the validity of using such rule-based approaches within whole ventricular models remains unclear. Here, we present the development of a generic computational framework to directly compare the fibre architecture predicted by rule-based methods used within whole ventricular models against fibre structure derived from DTMRI data, and assess how relative differences influence propagation dynamics throughout the ventricles. Results demonstrate the close overall match between the methods within the rat ventricles, and highlight regions for potential rule-adaption.

Three-dimensional atrial wall thickness maps to inform catheter ablation procedures for atrial fibrillation

AIMS Transmural lesion formation is critical to success in atrial fibrillation ablation and is dependent on left atrial wall thickness (LAWT). Pre- and peri-procedural planning may benefit from LAWT measurements. METHODS AND RESULTS To calculate the LAWT, the Laplace equation was solved over a finite element mesh of the left atrium derived from the segmented computed tomographic angiography (CTA) dataset. Local LAWT was then calculated from the length of field lines derived from the Laplace solution that spanned the wall from the endocardium or epicardium. The method was validated on an atrium phantom and retrospectively applied to 10 patients who underwent routine coronary CTA for standard clinical indications at our institute. The Laplace wall thickness algorithm was validated on the left atrium phantom. Wall thickness measurements had errors of <0.2 mm for thicknesses of 0.5-5.0 mm that are attributed to image resolution and segmentation artefacts. Left atrial wall thickness measurements were performed on 10 patients. Successful comprehensive LAWT maps were generated in all patients from the coronary CTA images. Mean LAWT measurements ranged from 0.6 to 1.0 mm and showed significant inter and intra patient variability. CONCLUSIONS Left atrial wall thickness can be measured robustly and efficiently across the whole left atrium using a solution of the Laplace equation over a finite element mesh of the left atrium. Further studies are indicated to determine whether the integration of LAWT maps into pre-existing 3D anatomical mapping systems may provide important anatomical information for guiding radiofrequency ablation.

Efficient simulation of cardiac electrical propagation using high-order finite elements II: Adaptive p-version

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

Progressive changes in T₁, T₂ and left-ventricular histo-architecture in the fixed and embedded rat heart.

Chemical tissue fixation, followed by embedding in either agarose or Fomblin, is common practice in time‐intensive MRI studies of ex vivo biological samples, and is required to prevent tissue autolysis and sample motion. However, the combined effect of fixation and sample embedding may alter tissue structure and MRI properties. We investigated the progressive changes in T1 and T2 relaxation times, and the arrangement of locally prevailing cardiomyocyte orientation determined using diffusion tensor imaging, in embedded ex vivo rat hearts fixed using Karnovskys solution (glutaraldehyde–formaldehyde mix). Three embedding media were investigated: (i) standard agarose (n = 3 hearts); (ii) Fomblin (n = 4 hearts); and (iii) iso‐osmotic agarose (n = 3 hearts); in the latter, the osmolarity of the fixative and embedding medium was adjusted to 300 mOsm to match more closely that of native tissue. The T1 relaxation time in the myocardium showed a pronounced decrease over a 48‐h period following embedding in Fomblin (−11.3 ± 6.2%; mean ± standard deviation), but was stable in standard agarose‐ and iso‐osmotic agarose‐embedded hearts. The mean myocardial T2 relaxation time increased in all embedded hearts: by 35.1 ± 14.7% with standard agarose embedding, 13.1 ± 5.6% with Fomblin and 13.3 ± 1.4% with iso‐osmotic agarose. Deviation in the orientation of the primary eigenvector of the diffusion tensor occurred in all hearts (mean angular changes of 6.6°, 3.2° and 1.9° per voxel after 48 h in agarose‐, Fomblin‐ and iso‐osmotic agarose‐embedded hearts, respectively), indicative of progressive structural changes in myocardial histo‐architecture, in spite of previous exposure to fast‐acting tissue fixation. Our results suggest that progressive structural changes occur in chemically fixed myocardium, and that the extent of these changes is modulated by the embedding medium, and by osmotic gradients between the fixative in the tissue and the surrounding medium. Copyright