Image-based estimation of ventricular fiber orientations for personalized modeling of cardiac electrophysiology

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Computational Modeling and Simulation of the Fibrotic Human Atria

Patient-specific modeling of atrial electrical activity enables the execution of simulations that can provide mechanistic insights and provide novel solutions to vexing clinical problems. The geometry and fibrotic remodeling of the heart can be reconstructed from clinical-grade medical scans and used to inform personalized models with detail incorporated at the cell- and tissue-scale to represent changes in image-identified diseased regions. Here, we provide a rubric for the reconstruction of realistic atrial models from pre-segmented 3D renderings of the left atrium with fibrotic tissue regions delineated, which are the output from clinical-grade systems for quantifying fibrosis. We then provide a roadmap for using those models to carry out patient-specific characterization of the fibrotic substrate in terms of its potential to harbor reentrant drivers via cardiac electrophysiology simulations.

Slice-specific tracking for free-breathing diffusion tensor cardiac MRI

BACKGROUND

Diffusion tensor cardiac magnetic resonance (DT-CMR) imaging has great potential to characterize myocardial microarchitecture. However, its accuracy is limited by respiratory and cardiac motion and long scan times. Here, we develop and evaluate a slice-specific tracking method to improve the efficiency and accuracy of DT-CMR acquisition during free breathing.

METHODS

Coronal images were obtained along with signals from a diaphragmatic navigator. Respiratory and slice displacements were obtained from the navigator signals and coronal images, respectively, and these displacements were fitted with a linear model to obtain the slice-specific tracking factors. This method was evaluated in DT-CMR examinations of 17 healthy subjects, and the results were compared with those obtained using a fixed tracking factor of 0.6. DT-CMR with breath-holding was used for reference. Quantitative and qualitative evaluation methods were used to analyze the performance of the slice-specific tracking method and the consistency between the obtained diffusion parameters.

RESULTS

In the study, the slice-specific tracking factors showed an upward trend from the basal to the apical slice. Residual in-plane movements were lower in slice-specific tracking than in fixed-factor tracking (RMSE: 2.748 ± 1.171 versus 5.983 ± 2.623, P < 0.001). The diffusion parameters obtained using slice-specific tracking were not significantly different from those obtained from breath-holding acquisition (P > 0.05).

CONCLUSION

In free-breathing DT-CMR imaging, the slice-specific tracking method reduced misalignment of the acquired slices. The diffusion parameters obtained using this approach were consistent with those obtained with the breath-holding technique.

Efficient identification of scars using heterogeneous model hierarchies

AIMS

Detection and quantification of myocardial scars are helpful for diagnosis of heart diseases and for personalized simulation models. Scar tissue is generally characterized by a different conduction of excitation. We aim at estimating conductivity-related parameters from endocardial mapping data. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. We aim at accelerating the estimation by combining electrophysiology models of different complexity.

METHODS AND RESULTS

Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the monodomain model and regularization. We formulate this optimization problem, including the modelling of scar tissue and different regularizations, and design an efficient solver. We consider grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. With numerical examples, efficiency and estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface.

CONCLUSION

In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more involved monodomain model for this purpose. Eikonal models can accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data.

A 3D personalized cardiac myocyte aggregate orientation model using MRI data-driven low-rank basis functions

Cardiac myocyte aggregate orientation has a strong impact on cardiac electrophysiology and mechanics. Studying the link between structural characteristics, strain, and stresses over the cardiac cycle and cardiac function requires a full volumetric representation of the microstructure. In this work, we exploit the structural similarity across hearts to extract a low-rank representation of predominant myocyte orientation in the left ventricle from high-resolution magnetic resonance ex-vivo cardiac diffusion tensor imaging (cDTI) in porcine hearts. We compared two reduction methods, Proper Generalized Decomposition combined with Singular Value Decomposition and Proper Orthogonal Decomposition. We demonstrate the existence of a general set of basis functions of aggregated myocyte orientation which defines a data-driven, personalizable, parametric model featuring higher flexibility than existing atlas and rule-based approaches. A more detailed representation of microstructure matching the available patient data can improve the accuracy of personalized computational models. Additionally, we approximate the myocyte orientation of one ex-vivo human heart and demonstrate the feasibility of transferring the basis functions to humans.

Area Available for Atrial Fibrillation to Propagate Is an Important Determinant of Recurrence After Ablation

OBJECTIVES

This study sought to evaluate atrial fibrillation (AF) ablation outcomes based on scar patterns and contiguous area available for AF wavefronts to propagate.

BACKGROUND

The relevance of ablation scar pattern acting as a barrier for electrical propagation in recurrence after catheter ablation for persistent AF is unknown.

METHODS

Three-month post-ablation atrial cardiac magnetic resonance was used to determine post-ablation scar. The left atrium (LA) was divided into 5 areas based on anatomical landmarks and scar patterns. The length of gaps in scar on the area boundaries was used to calculate fibrillatory areas (FAs) by adding the weighted contribution of adjacent areas. Cylindrical as well as patient-specific computational models were used to further confirm findings.

RESULTS

A total of 75 patients that underwent an initial ablation for AF with 2 years of follow-up were included. The average maximum FA was 7,896 ± 1,988 mm² in patients with recurrence (n = 40) and 6,559 ± 1,784 mm² in patients without recurrence (n = 35) (p < 0.008). After redo ablation in 19 patients with recurrence, average maximum FA was 7,807 ± 1,392 mm² in 9 patients with recurrence and 5,030 ± 1,765 mm² in 10 without recurrence (p < 0.007). LA volume and total scar were not significant predictors of recurrence after the first ablation. In the cylindrical model, AF self-terminated after reducing the FAs. In the patient-specific models, simulation matched the clinical outcomes with larger FAs associated with post-ablation arrhythmia recurrences.

CONCLUSIONS

This data provides mechanistic insights into AF recurrence, suggesting that post-ablation scar pattern dividing the atria into smaller regions is an important and better predictor than LA volume and total scar, with improved long-term outcomes in persistent AF.

Estimating cardiomyofiber strain in vivo by solving a computational model

Since heart contraction results from the electrically activated contraction of millions of cardiomyocytes, a measure of cardiomyocyte shortening mechanistically underlies cardiac contraction. In this work we aim to measure preferential aggregate cardiomyocyte ("myofiber") strains based on Magnetic Resonance Imaging (MRI) data acquired to measure both voxel-wise displacements through systole and myofiber orientation. In order to reduce the effect of experimental noise on the computed myofiber strains, we recast the strains calculation as the solution of a boundary value problem (BVP). This approach does not require a calibrated material model, and consequently is independent of specific myocardial material properties. The solution to this auxiliary BVP is the displacement field corresponding to assigned values of myofiber strains. The actual myofiber strains are then determined by minimizing the difference between computed and measured displacements. The approach is validated using an analytical phantom, for which the ground-truth solution is known. The method is applied to compute myofiber strains using in vivo displacement and myofiber MRI data acquired in a mid-ventricular left ventricle section in N=8 swine subjects. The proposed method shows a more physiological distribution of myofiber strains compared to standard approaches that directly differentiate the displacement field.

Quantification of left ventricular contribution to stroke work by longitudinal and radial force-length loops

Left ventricular (LV) stroke work (SW) is calculated from the pressure-volume (PV) loop. PV loops do not contain information on longitudinal and radial pumping, leaving their contributions to SW unknown. A conceptual framework is proposed to derive the longitudinal and radial contributions to SW, using ventricular force-length loops reflecting longitudinal and radial pumping. The aim of this study was to develop and validate this framework experimentally and to explore these contributions in healthy controls and heart failure patients. Thirteen swine underwent cardiovascular magnetic resonance (CMR) and LV pressure catheterization at baseline (n = 7) or 1 wk after myocardial infarction (n = 6). CMR and noninvasive PV loop quantification were performed on 26 human controls and 14 patients. Longitudinal and radial forces were calculated as LV pressure multiplied by the myocardial surface areas in the respective directions. Length components were defined as the atrioventricular plane and epicardial displacements, respectively. Contributions to SW were calculated as the area within the respective force-length loop. Summation of longitudinal and radial SW had excellent agreement with PV loop-derived SW (ICC = 0.95, R = 0.96, bias ± SD = −4.5 ± 5.4%) in swine. Longitudinal and radial contributions to SW were ~50/50% in swine and human controls, and 44/56% in patients. Longitudinal pumping required less work than radial to deliver stroke volume in swine (6.8 ± 0.8 vs. 8.7 ± 1.2 mJ/mL, P = 0.0002) and in humans (11 ± 2.1 vs. 17 ± 4.7 mJ/mL, P < 0.0001). In conclusion, longitudinal and radial pumping contribute ~50/50% to SW in swine and human controls and 44/56% in heart failure patients. Longitudinal pumping is more energy efficient than radial pumping in delivering stroke volume.

NEW & NOTEWORTHY A novel method for quantifying the contributions of longitudinal and radial pumping to stroke work using global left ventricular force-length loops was proposed and validated, which can be quantified noninvasively using cardiovascular magnetic resonance and brachial cuff pressure. We found that longitudinal and radial pumping contributes equally to stroke work in controls and 44/56% in heart failure patients, and that the longitudinal pumping is more energy efficient in delivering stroke volume than radial pumping.

Multimodal cross-registration and quantification of metric distortions in marmoset whole brain histology using diffeomorphic mappings

Whole brain neuroanatomy using tera-voxel light-microscopic data sets is of much current interest. A fundamental problem in this field is the mapping of individual brain data sets to a reference space. Previous work has not rigorously quantified in-vivo to ex-vivo distortions in brain geometry from tissue processing. Further, existing approaches focus on registering unimodal volumetric data; however, given the increasing interest in the marmoset model for neuroscience research and the importance of addressing individual brain architecture variations, new algorithms are necessary to cross-register multimodal data sets including MRIs and multiple histological series. Here we present a computational approach for same-subject multimodal MRI-guided reconstruction of a series of consecutive histological sections, jointly with diffeomorphic mapping to a reference atlas. We quantify the scale change during different stages of brain histological processing using the Jacobian determinant of the diffeomorphic transformations involved. By mapping the final image stacks to the ex-vivo post-fixation MRI, we show that (a) tape-transfer assisted histological sections can be reassembled accurately into 3D volumes with a local scale change of 2.0 ± 0.4% per axis dimension; in contrast, (b) tissue perfusion/fixation as assessed by mapping the in-vivo MRIs to the ex-vivo post fixation MRIs shows a larger median absolute scale change of 6.9 ± 2.1% per axis dimension. This is the first systematic quantification of local metric distortions associated with whole-brain histological processing, and we expect that the results will generalize to other species. These local scale changes will be important for computing local properties to create reference brain maps.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Arrhythmia dynamics in computational models of the atria following virtual ablation of re-entrant drivers

Aims

Efforts to improve ablation success rates in persistent atrial fibrillation (AF) patients by targeting re-entrant driver (RD) sites have been hindered by weak mechanistic understanding regarding emergent RDs localization following initial fibrotic substrate modification. This study aimed to systematically assess arrhythmia dynamics after virtual ablation of RD sites in computational models.

Methods and results

Simulations were conducted in 12 patient-specific atrial models reconstructed from pre-procedure late gadolinium-enhanced magnetic resonance imaging scans. In a previous study involving these same models, we comprehensively characterized pre-ablation RDs in simulations conducted with either 'average human AF'-based electrophysiology (i.e. EPavg) or ±10% action potential duration or conduction velocity (i.e. EPvar). Re-entrant drivers seen under the EPavg condition were virtually ablated and the AF initiation protocol was re-applied. Twenty-one emergent RDs were observed in 9/12 atrial models (1.75 ± 1.35 emergent RDs per model); these dynamically localized to boundary regions between fibrotic and non-fibrotic tissue. Most emergent RD locations (15/21, 71.4%) were within 0.1 cm of sites where RDs were seen pre-ablation in simulations under EPvar conditions. Importantly, this suggests that the level of uncertainty in our models' ability to predict patient-specific ablation targets can be substantially mitigated by running additional simulations that include virtual ablation of RDs. In 7/12 atrial models, at least one episode of macro-reentry around ablation lesion(s) was observed.

Conclusion

Arrhythmia episodes after virtual RD ablation are perpetuated by both emergent RDs and by macro-reentrant circuits formed around lesions. Custom-tailoring of ablation procedures based on models should take steps to mitigate these sources of AF recurrence.

Automatic mapping of atrial fiber orientations for patient-specific modeling of cardiac electromechanics using image registration

Knowledge of appropriate local fiber architecture is necessary to simulate patient-specific electromechanics in the human heart. However, it is not yet possible to reliably measure in vivo fiber directions especially in human atria. Thus, we present a method that defines the fiber architecture in arbitrarily shaped atria using image registration and reorientation methods based on atlas atria with fibers predefined from detailed histological observations. Thereby, it is possible to generate detailed fiber families in every new patient-specific geometry in an automated, time-efficient process. We demonstrate the good performance of the image registration and fiber definition on 10 differently shaped human atria. Additionally, we show that characteristics of the electrophysiological activation pattern that appear in the atlas atria also appear in the patients' atria. We arrive to analogous conclusions for coupled electro-mechano-hemodynamical computations.

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Computational cardiac modelling is a mature area of biomedical computing and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key factor for clinical use, and uncertainty quantification (UQ) and sensitivity analysis are important parts of such an assessment. In this study, we apply UQ in computational heart mechanics to study uncertainty both in material parameters characterizing global myocardial stiffness and in the local muscle fiber orientation that governs tissue anisotropy. The uncertainty analysis is performed using the polynomial chaos expansion (PCE) method, which is a nonintrusive meta-modeling technique that surrogates the original computational model with a series of orthonormal polynomials over the random input parameter space. In addition, in order to study variability in the muscle fiber architecture, we model the uncertainty in orientation of the fiber field as an approximated random field using a truncated Karhunen-Loéve expansion. The results from the UQ and sensitivity analysis identify clear differences in the impact of various material parameters on global output quantities. Furthermore, our analysis of random field variations in the fiber architecture demonstrate a substantial impact of fiber angle variations on the selected outputs, highlighting the need for accurate assignment of fiber orientation in computational heart mechanics models.

Imaging technologies for cardiac fiber and heart failure: a review

There has been an increasing interest in studying cardiac fibers in order to improve the current knowledge regarding the mechanical and physiological properties of the heart during heart failure (HF), particularly early HF. Having a thorough understanding of the changes in cardiac fiber orientation may provide new insight into the mechanisms behind the progression of left ventricular (LV) remodeling and HF. We conducted a systematic review on various technologies for imaging cardiac fibers and its link to HF. This review covers literature reports from 1900 to 2017. PubMed and Google Scholar databases were searched using the keywords "cardiac fiber" and "heart failure" or "myofiber" and "heart failure." This review highlights imaging methodologies, including magnetic resonance diffusion tensor imaging (MR-DTI), ultrasound, and other imaging technologies as well as their potential applications in basic and translational research on the development and progression of HF. MR-DTI and ultrasound have been most useful and significant in evaluating cardiac fibers and HF. New imaging technologies that have the ability to measure cardiac fiber orientations and identify structural and functional information of the heart will advance basic research and clinical diagnoses of HF.

ESTIMATING DIFFEOMORPHIC MAPPINGS BETWEEN TEMPLATES AND NOISY DATA: VARIANCE BOUNDS ON THE ESTIMATED CANONICAL VOLUME FORM

Anatomy is undergoing a renaissance driven by the availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by regularized estimation of a diffeomorphic transformation between the coordinate systems of the individual data and the template, building the transformation incrementally by integrating a smooth flow field. The canonical volume form of this transformation is used to quantify local growth, atrophy, or cell density. While multiple implementations exist for this estimation, less attention has been paid to the variance of the estimated diffeomorphism for noisy data. Notably, there is an infinite dimensional unobservable space defined by those diffeomorphisms which leave the template invariant. These form the stabilizer subgroup of the diffeomorphic group acting on the template. The corresponding flat directions in the energy landscape are expected to lead to increased estimation variance. Here we show that a least-action principle used to generate geodesics in the space of diffeomor-phisms connecting the subject brain to the template removes the stabilizer. This provides reduced-variance estimates of the volume form. Using simulations we demonstrate that the asymmetric large deformation diffeomorphic mapping methods (LDDMM), which explicitly incorporate the asymmetry between idealized template images and noisy empirical images, provide lower variance estimators than their symmetrized counterparts (cf. ANTs). We derive Cramer-Rao bounds for the variances in the limit of small deformations. Analytical results are shown for the Jacobian in terms of perturbations of the vector fields and divergence of the vector field.

Application of Patient-Specific Computational Fluid Dynamics in Coronary and Intra-Cardiac Flow Simulations: Challenges and Opportunities

The emergence of new cardiac diagnostics and therapeutics of the heart has given rise to the challenging field of virtual design and testing of technologies in a patient-specific environment. Given the recent advances in medical imaging, computational power and mathematical algorithms, patient-specific cardiac models can be produced from cardiac images faster, and more efficiently than ever before. The emergence of patient-specific computational fluid dynamics (CFD) has paved the way for the new field of computer-aided diagnostics. This article provides a review of CFD methods, challenges and opportunities in coronary and intra-cardiac flow simulations. It includes a review of market products and clinical trials. Key components of patient-specific CFD are covered briefly which include image segmentation, geometry reconstruction, mesh generation, fluid-structure interaction, and solver techniques.

Patient-Specific Cardiovascular Computational Modeling: Diversity of Personalization and Challenges

Patient-specific computer models have been developed representing a variety of aspects of the cardiovascular system spanning the disciplines of electrophysiology, electromechanics, solid mechanics, and fluid dynamics. These physiological mechanistic models predict macroscopic phenomena such as electrical impulse propagation and contraction throughout the entire heart as well as flow and pressure dynamics occurring in the ventricular chambers, aorta, and coronary arteries during each heartbeat. Such models have been used to study a variety of clinical scenarios including aortic aneurysms, coronary stenosis, cardiac valvular disease, left ventricular assist devices, cardiac resynchronization therapy, ablation therapy, and risk stratification. After decades of research, these models are beginning to be incorporated into clinical practice directly via marketed devices and indirectly by improving our understanding of the underlying mechanisms of health and disease within a clinical context.

Clinical Applications of Patient-Specific Models: The Case for a Simple Approach

Over the past several decades, increasingly sophisticated models of the heart have provided important insights into cardiac physiology and are increasingly used to predict the impact of diseases and therapies on the heart. In an era of personalized medicine, many envision patient-specific computational models as a powerful tool for personalizing therapy. Yet the complexity of current models poses important challenges, including identifying model parameters and completing calculations quickly enough for routine clinical use. We propose that early clinical successes are likely to arise from an alternative approach: relatively simple, fast, phenomenologic models with a small number of parameters that can be easily (and automatically) customized. We discuss examples of simple yet foundational models that have already made a tremendous impact on clinical education and practice, and make the case that reducing rather than increasing model complexity may be the key to realizing the promise of patient-specific modeling for clinical applications.

Universal ventricular coordinates: A generic framework for describing position within the heart and transferring data

Being able to map a particular set of cardiac ventricles to a generic topologically equivalent representation has many applications, including facilitating comparison of different hearts, as well as mapping quantities and structures of interest between them. In this paper we describe Universal Ventricular Coordinates (UVC), which can be used to describe position within any biventricular heart. UVC comprise four unique coordinates that we have chosen to be intuitive, well defined, and relevant for physiological descriptions. We describe how to determine these coordinates for any volumetric mesh by illustrating how to properly assign boundary conditions and utilize solutions to Laplace's equation. Using UVC, we transferred scalar, vector, and tensor data between four unstructured ventricular meshes from three different species. Performing the mappings was very fast, on the order of a few minutes, since mesh nodes were searched in a KD tree. Distance errors in mapping mesh nodes back and forth between meshes were less than the size of an element. Analytically derived fiber directions were also mapped across meshes and compared, showing  < 5° difference over most of the ventricles. The ability to transfer gradients was also demonstrated. Topologically variable structures, like papillary muscles, required further definition outside of the UVC framework. In conclusion, UVC can aid in transferring many types of data between different biventricular geometries.

Termination of re-entrant atrial tachycardia via optogenetic stimulation with optimized spatial targeting: insights from computational models

KEY POINTS

Optogenetics has emerged as a potential alternative to electrotherapy for treating heart rhythm disorders, but its applicability for terminating atrial arrhythmias remains largely unexplored. We used computational models reconstructed from clinical MRI scans of fibrotic patient atria to explore the feasibility of optogenetic termination of atrial tachycardia (AT), comparing two different illumination strategies: distributed vs. targeted. We show that targeted optogenetic stimulation based on automated, non-invasive flow-network analysis of patient-specific re-entry morphology may be a reliable approach for identifying the optimal illumination target in each individual (i.e. the critical AT isthmus). The above-described approach yields very high success rates (up to 100%) and requires dramatically less input power than distributed illumination We conclude that simulations in patient-specific models show that targeted light pulses lasting longer than the AT cycle length can efficiently and reliably terminate AT if the human atria can be successfully light-sensitized via gene delivery of ChR2.

ABSTRACT

Optogenetics has emerged as a potential alternative to electrotherapy for treating arrhythmia, but feasibility studies have been limited to ventricular defibrillation via epicardial light application. Here, we assess the efficacy of optogenetic atrial tachycardia (AT) termination in human hearts using a strategy that targets for illumination specific regions identified in an automated manner. In three patient-specific models reconstructed from late gadolinium-enhanced MRI scans, we simulated channelrhodopsin-2 (ChR2) expression via gene delivery. In all three models, we attempted to terminate re-entrant AT (induced via rapid pacing) via optogenetic stimulation. We compared two strategies: (1) distributed illumination of the endocardium by multi-optrode grids (number of optrodes, N_opt  = 64, 128, 256) and (2) targeted illumination of the critical isthmus, which was identified via analysis of simulated activation patterns using an algorithm based on flow networks. The illuminated area and input power were smaller for the targeted approach (19-57.8 mm² ; 0.6-1.8 W) compared to the sparsest distributed arrays (N_opt  = 64; 124.9 ± 6.3 mm² ; 3.9 ± 0.2 W). AT termination rates for distributed illumination were low, ranging from <5% for short pulses (1/10 ms long) to ∼20% for longer stimuli (100/1000 ms). When we attempted to terminate the same AT episodes with targeted illumination, outcomes were similar for short pulses (1/10 ms long: 0% success) but improved for longer stimuli (100 ms: 54% success; 1000 ms: 90% success). We conclude that simulations in patient-specific models show that light pulses lasting longer than the AT cycle length can efficiently and reliably terminate AT in atria light-sensitized via gene delivery. We show that targeted optogenetic stimulation based on analysis of AT morphology may be a reliable approach for defibrillation and requires less power than distributed illumination.

Sensitivity of reentrant driver localization to electrophysiological parameter variability in image-based computational models of persistent atrial fibrillation sustained by a fibrotic substrate

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia, causing morbidity and mortality in millions worldwide. The atria of patients with persistent AF (PsAF) are characterized by the presence of extensive and distributed atrial fibrosis, which facilitates the formation of persistent reentrant drivers (RDs, i.e., spiral waves), which promote fibrillatory activity. Targeted catheter ablation of RD-harboring tissues has shown promise as a clinical treatment for PsAF, but the outcomes remain sub-par. Personalized computational modeling has been proposed as a means of non-invasively predicting optimal ablation targets in individual PsAF patients, but it remains unclear how RD localization dynamics are influenced by inter-patient variability in the spatial distribution of atrial fibrosis, action potential duration (APD), and conduction velocity (CV). Here, we conduct simulations in computational models of fibrotic atria derived from the clinical imaging of PsAF patients to characterize the sensitivity of RD locations to these three factors. We show that RDs consistently anchor to boundaries between fibrotic and non-fibrotic tissues, as delineated by late gadolinium-enhanced magnetic resonance imaging, but those changes in APD/CV can enhance or attenuate the likelihood that an RD will anchor to a specific site. These findings show that the level of uncertainty present in patient-specific atrial models reconstructed without any invasive measurements (i.e., incorporating each individual's unique distribution of fibrotic tissue from medical imaging alongside an average representation of AF-remodeled electrophysiology) is sufficiently high that a personalized ablation strategy based on targeting simulation-predicted RD trajectories alone may not produce the desired result.

Maximum likelihood estimation of cardiac fiber bundle orientation from arbitrarily spaced diffusion weighted images

We propose an estimation scheme for local fiber bundle direction in the left ventricle directly from gray values of arbitrarily spaced cardiac diffusion weighted images (DWI). The approach is based on a parametric and space-dependent mathematical representation of the myocardial fiber bundle orientation and hence the diffusion tensor (DT) for the ventricular geometry. By solving a nonlinear inverse problem derived from a maximum likelihood estimator, the degrees of freedom of the fiber and DT model can be estimated from the measured gray values of the DWIs. The continuity of the DT model allows to relax the restriction to the individual DWIs to match spatially like for voxelwise DT calculation. Hence, the spatial misalignment between image slices with different diffusion encoding directions, that is encountered in-vivo cardiac imaging practice can be integrated into the estimation scheme. This feature results then in a negligible impact of the spatial misalignment on the reconstructed solution. We illustrate the methodology using synthetic data and compare it against a previously reported fiber bundle reconstruction technique. To show the potential for real data, we also present results for multi-slice data constructed from ex-vivo cardiac diffusion weighted measurements in both mono- and bi-ventricular configurations.

Determinants of biventricular cardiac function: a mathematical model study on geometry and myofiber orientation

In patient-specific mathematical models of cardiac electromechanics, usually a patient-specific geometry and a generic myofiber orientation field are used as input, upon which myocardial tissue properties are tuned to clinical data. It remains unclear to what extent deviations in myofiber orientation and geometry between model and patient influence model predictions on cardiac function. Therefore, we evaluated the sensitivity of cardiac function for geometry and myofiber orientation in a biventricular (BiV) finite element model of cardiac mechanics. Starting out from a reference geometry in which myofiber orientation had no transmural component, two new geometries were defined with either a 27 % decrease in LV short- to long-axis ratio, or a 16 % decrease of RV length, but identical LV and RV cavity and wall volumes. These variations in geometry caused differences in both local myofiber and global pump work below 6 %. Variation of fiber orientation was induced through adaptive myofiber reorientation that caused an average change in fiber orientation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim }8^\circ $$\end{document}∼8∘ predominantly through the formation of a component in transmural direction. Reorientation caused a considerable increase in local myofiber work \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\sim }18\,\%)$$\end{document}(∼18%) and in global pump work \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\sim }17\,\%)$$\end{document}(∼17%) in all three geometries, while differences between geometries were below 5 %. The findings suggest that implementing a realistic myofiber orientation is at least as important as defining a patient-specific geometry. The model for remodeling of myofiber orientation seems a useful approach to estimate myofiber orientation in the absence of accurate patient-specific information.

Spatial reproducibility of complex fractionated atrial electrogram depending on the direction and configuration of bipolar electrodes: an in-silico modeling study

Although 3D-complex fractionated atrial electrogram (CFAE) mapping is useful in radiofrequency catheter ablation for persistent atrial fibrillation (AF), the directions and configuration of the bipolar electrodes may affect the electrogram. This study aimed to compare the spatial reproducibility of CFAE by changing the catheter orientations and electrode distance in an in-silico left atrium (LA). We conducted this study by importing the heart CT image of a patient with AF into a 3D-homogeneous human LA model. Electrogram morphology, CFAE-cycle lengths (CLs) were compared for 16 different orientations of a virtual bipolar conventional catheter (conv-cath: size 3.5 mm, inter-electrode distance 4.75 mm). Additionally, the spatial correlations of CFAE-CLs and the percentage of consistent sites with CFAE-CL<120 ms were analyzed. The results from the conv-cath were compared with that obtained using a mini catheter (mini-cath: size 1 mm, inter-electrode distance 2.5 mm). Depending on the catheter orientation, the electrogram morphology and CFAE-CLs varied (conv-cath: 11.5±0.7% variation, mini-cath: 7.1±1.2% variation), however the mini-cath produced less variation of CFAE-CL than conv-cath (p<0.001). There were moderate spatial correlations among CFAE-CL measured at 16 orientations (conv-cath: r=0.3055±0.2194 vs. mini-cath: 0.6074±0.0733, p<0.001). Additionally, the ratio of consistent CFAE sites was higher for mini catheter than conventional one (38.3±4.6% vs. 22.3±1.4%, p<0.05). Electrograms and CFAE distribution are affected by catheter orientation and electrode configuration in the in-silico LA model. However, there was moderate spatial consistency of CFAE areas, and narrowly spaced bipolar catheters were less influenced by catheter direction than conventional catheters.

Myocardial Infarct Segmentation From Magnetic Resonance Images for Personalized Modeling of Cardiac Electrophysiology

Accurate representation of myocardial infarct geometry is crucial to patient-specific computational modeling of the heart in ischemic cardiomyopathy. We have developed a methodology for segmentation of left ventricular (LV) infarct from clinically acquired, two-dimensional (2D), late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) images, for personalized modeling of ventricular electrophysiology. The infarct segmentation was expressed as a continuous min-cut optimization problem, which was solved using its dual formulation, the continuous max-flow (CMF). The optimization objective comprised of a smoothness term, and a data term that quantified the similarity between image intensity histograms of segmented regions and those of a set of training images. A manual segmentation of the LV myocardium was used to initialize and constrain the developed method. The three-dimensional geometry of infarct was reconstructed from its segmentation using an implicit, shape-based interpolation method. The proposed methodology was extensively evaluated using metrics based on geometry, and outcomes of individualized electrophysiological simulations of cardiac dys(function). Several existing LV infarct segmentation approaches were implemented, and compared with the proposed method. Our results demonstrated that the CMF method was more accurate than the existing approaches in reproducing expert manual LV infarct segmentations, and in electrophysiological simulations. The infarct segmentation method we have developed and comprehensively evaluated in this study constitutes an important step in advancing clinical applications of personalized simulations of cardiac electrophysiology.

Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology

PURPOSE

Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need.

METHODS

The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitly represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method.

RESULTS

The accuracy of the LogOdds method in reconstructing 3D infarct geometry, as measured by the Dice similarity coefficient, was 82.10% ± 6.58%, a significantly higher value than those of the alternative reconstruction methods. Among outcomes of electrophysiological simulations with infarct reconstructions generated by various methods, the simulation results corresponding to the LogOdds method showed the smallest deviation from those corresponding to the manual reconstructions, as measured by metrics based on both activation maps and pseudo-ECGs.

CONCLUSIONS

The authors have developed a novel method for reconstructing 3D infarct geometry from segmented slices of Lo-res clinical 2D LGE-CMR images. This method outperformed alternative approaches in reproducing expert manual 3D reconstructions and in electrophysiological simulations.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Feasibility of using patient-specific models and the "minimum cut" algorithm to predict optimal ablation targets for left atrial flutter

BACKGROUND

Left atrial flutter (LAFL) occurs in patients after atrial fibrillation ablation. Identification of optimal ablation targets to terminate LAFL remains challenging.

OBJECTIVE

The purpose of this study was to use patient-specific models to simulate LAFL and predict optimal ablation targets using a novel approach based on flow network theory.

METHODS

Late gadolinium-enhanced cardiac magnetic resonance scans from 10 patients with LAFL were used to construct atrial models incorporating fibrosis by investigators blinded to procedural findings. Rapid pacing was applied in silico to induce LAFL. In each LAFL, we represented reentrant wave propagation as an electric flow network and identified the "minimum cut" (MC), which was the smallest amount of tissue that separated the flow into 2 discontinuous components. In silico ablation was applied at MCs, and targets were compared to those that terminated LAFL during catheter ablation.

RESULTS

Patient-specific atrial models were successfully generated from patient scans. LAFL was induced in 7 of 10 models. Ablation of MCs terminated LAFL in 4 models and produced new, slower LAFL morphologies in the other 3. For the latter cases, flow analysis was repeated to identify MCs of emergent LAFLs. Ablation of these MCs terminated emergent LAFLs. The MC-based ablation lesions in simulations were similar in length and location to ablation targets that terminated LAFL during catheter ablation for these 7 patients.

CONCLUSION

Personalized atrial simulations can predict ablation targets for LAFL. These simulations provide a powerful tool for planning ablation procedures and may reduce procedural times and complications.

DTI template-based estimation of cardiac fiber orientations from 3D ultrasound

PURPOSE

Cardiac muscle fibers directly affect the mechanical, physiological, and pathological properties of the heart. Patient-specific quantification of cardiac fiber orientations is an important but difficult problem in cardiac imaging research. In this study, the authors proposed a cardiac fiber orientation estimation method based on three-dimensional (3D) ultrasound images and a cardiac fiber template that was obtained from magnetic resonance diffusion tensor imaging (DTI).

METHODS

A DTI template-based framework was developed to estimate cardiac fiber orientations from 3D ultrasound images using an animal model. It estimated the cardiac fiber orientations of the target heart by deforming the fiber orientations of the template heart, based on the deformation field of the registration between the ultrasound geometry of the target heart and the MRI geometry of the template heart. In the experiments, the animal hearts were imaged by high-frequency ultrasound, T1-weighted MRI, and high-resolution DTI.

RESULTS

The proposed method was evaluated by four different parameters: Dice similarity coefficient (DSC), target errors, acute angle error (AAE), and inclination angle error (IAE). Its ability of estimating cardiac fiber orientations was first validated by a public database. Then, the performance of the proposed method on 3D ultrasound data was evaluated by an acquired database. Their average values were 95.4% ± 2.0% for the DSC of geometric registrations, 21.0° ± 0.76° for AAE, and 19.4° ± 1.2° for IAE of fiber orientation estimations. Furthermore, the feasibility of this framework was also performed on 3D ultrasound images of a beating heart.

CONCLUSIONS

The proposed framework demonstrated the feasibility of using 3D ultrasound imaging to estimate cardiac fiber orientation of in vivo beating hearts and its further improvements could contribute to understanding the dynamic mechanism of the beating heart and has the potential to help diagnosis and therapy of heart disease.

Determining Cardiac Fiber Orientation Using FSL and Registered Ultrasound/DTI volumes

Accurate extraction of cardiac fiber orientation from diffusion tensor imaging is important for determining heart structure and function. However, the acquisition of magnetic resonance (MR) diffusion tensor images is costly and time consuming. By comparison, cardiac ultrasound imaging is rapid and relatively inexpensive, but it lacks the capability to directly measure fiber orientations. In order to create a detailed heart model from ultrasound data, a three-dimensional (3D) diffusion tensor imaging (DTI) with known fiber orientations can be registered to an ultrasound volume through a geometric mask. After registration, the cardiac orientations from the template DTI can be mapped to the heart using a deformable transformation field. This process depends heavily on accurate fiber orientation extraction from the DTI. In this study, we use the FMRIB Software Library (FSL) to determine cardiac fiber orientations in diffusion weighted images. For the registration between ultrasound and MRI volumes, we achieved an average Dice similarity coefficient (DSC) of 81.6±2.1%. For the estimation of fiber orientations from the proposed method, we achieved an acute angle error (AAE) of 22.7±3.1° as compared to the direct measurements from DTI. This work provides a new approach to generate cardiac fiber orientation that may be used for many cardiac applications.

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

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.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Accuracy of prediction of infarct-related arrhythmic circuits from image-based models reconstructed from low and high resolution MRI

Identification of optimal ablation sites in hearts with infarct-related ventricular tachycardia (VT) remains difficult to achieve with the current catheter-based mapping techniques. Limitations arise from the ambiguities in determining the reentrant pathways location(s). The goal of this study was to develop experimentally validated, individualized computer models of infarcted swine hearts, reconstructed from high-resolution ex-vivo MRI and to examine the accuracy of the reentrant circuit location prediction when models of the same hearts are instead reconstructed from low clinical-resolution MRI scans. To achieve this goal, we utilized retrospective data obtained from four pigs ~10 weeks post infarction that underwent VT induction via programmed stimulation and epicardial activation mapping via a multielectrode epicardial sock. After the experiment, high-resolution ex-vivo MRI with late gadolinium enhancement was acquired. The Hi-res images were downsampled into two lower resolutions (Med-res and Low-res) in order to replicate image quality obtainable in the clinic. The images were segmented and models were reconstructed from the three image stacks for each pig heart. VT induction similar to what was performed in the experiment was simulated. Results of the reconstructions showed that the geometry of the ventricles including the infarct could be accurately obtained from Med-res and Low-res images. Simulation results demonstrated that induced VTs in the Med-res and Low-res models were located close to those in Hi-res models. Importantly, all models, regardless of image resolution, accurately predicted the VT morphology and circuit location induced in the experiment. These results demonstrate that MRI-based computer models of hearts with ischemic cardiomyopathy could provide a unique opportunity to predict and analyze VT resulting for from specific infarct architecture, and thus may assist in clinical decisions to identify and ablate the reentrant circuit(s).

Spin echo versus stimulated echo diffusion tensor imaging of the in vivo human heart

Purpose

To compare signal‐to‐noise ratio (SNR) efficiency and diffusion tensor metrics of cardiac diffusion tensor mapping using acceleration‐compensated spin‐echo (SE) and stimulated echo acquisition mode (STEAM) imaging.

Methods

Diffusion weighted SE and STEAM sequences were implemented on a clinical 1.5 Tesla MR system. The SNR efficiency of SE and STEAM was measured (b = 50–450 s/mm²) in isotropic agar, anisotropic diffusion phantoms and the in vivo human heart. Diffusion tensor analysis was performed on mean diffusivity, fractional anisotropy, helix and transverse angles.

Results

In the isotropic phantom, the ratio of SNR efficiency for SE versus STEAM, SNR_t(SE/STEAM), was 2.84 ± 0.08 for all tested b‐values. In the anisotropic diffusion phantom the ratio decreased from 2.75 ± 0.05 to 2.20 ± 0.13 with increasing b‐value, similar to the in vivo decrease from 2.91 ± 0.43 to 2.30 ± 0.30. Diffusion tensor analysis revealed reduced deviation of helix angles from a linear transmural model and reduced transverse angle standard deviation for SE compared with STEAM. Mean diffusivity and fractional anisotropy were measured to be statistically different (P < 0.001) between SE and STEAM.

Conclusion

Cardiac DTI using motion‐compensated SE yields a 2.3–2.9× increase in SNR efficiency relative to STEAM and improved accuracy of tensor metrics. The SE method hence presents an attractive alternative to STEAM based approaches. Magn Reson Med 76:862–872, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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.

Higher-Order Motion-Compensation for In Vivo Cardiac Diffusion Tensor Imaging in Rats

Motion of the heart has complicated in vivo applications of cardiac diffusion MRI and diffusion tensor imaging (DTI), especially in small animals such as rats where ultra-high-performance gradient sets are currently not available. Even with velocity compensation via, for example, bipolar encoding pulses, the variable shot-to-shot residual motion-induced spin phase can still give rise to pronounced artifacts. This study presents diffusion-encoding schemes that are designed to compensate for higher-order motion components, including acceleration and jerk, which also have the desirable practical features of minimal TEs and high achievable b-values. The effectiveness of these schemes was verified numerically on a realistic beating heart phantom, and demonstrated empirically with in vivo cardiac diffusion MRI in rats. Compensation for acceleration, and lower motion components, was found to be both necessary and sufficient for obtaining diffusion-weighted images of acceptable quality and SNR, which yielded the first in vivo cardiac DTI demonstrated in the rat. These findings suggest that compensation for higher order motion, particularly acceleration, can be an effective alternative solution to high-performance gradient hardware for improving in vivo cardiac DTI.

Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.

Under normal conditions, the electrical activation of the heart is almost synchronous, leading to uniform contraction. Due to either pathology or electrical pacing, the heart can be activated asynchronously. The result is discoordinated contraction and a reduction in the ability to pump blood. There is considerable interest in using computer simulations to understand how asynchronous electrical activation affects cardiac deformation, and how pathologies of the cardiac conduction system can be treated by pacing the heart. We present the MultiPatch module for simulating the effects of asynchronous electrical activation on cardiac contraction in the relatively simple CircAdapt model of the heart and circulation. We quantitatively compare model simulations to deformation patterns recorded during an experimental study of pacing-induced electrical asynchrony. We then demonstrate a ‘patient-specific’ simulation of deformation in a patient with a conduction disorder called left bundle-branch block. We use timings from endocardial mapping of electrical activation in a patient as an input for the model, and compare the resulting simulated deformation patterns to tagged magnetic resonance imaging recordings from the same patient. The model qualitatively reproduces deformation as observed in the patient. We conclude that the MultiPatch module makes CircAdapt appropriate for simulation of dyssynchronous heart failure in patients.

Register cardiac fiber orientations from 3D DTI volume to 2D ultrasound image of rat hearts

Two-dimensional (2D) ultrasound or echocardiography is one of the most widely used examinations for the diagnosis of cardiac diseases. However, it only supplies the geometric and structural information of the myocardium. In order to supply more detailed microstructure information of the myocardium, this paper proposes a registration method to map cardiac fiber orientations from three-dimensional (3D) magnetic resonance diffusion tensor imaging (MR-DTI) volume to the 2D ultrasound image. It utilizes a 2D/3D intensity based registration procedure including rigid, log-demons, and affine transformations to search the best similar slice from the template volume. After registration, the cardiac fiber orientations are mapped to the 2D ultrasound image via fiber relocations and reorientations. This method was validated by six images of rat hearts ex vivo. The evaluation results indicated that the final Dice similarity coefficient (DSC) achieved more than 90% after geometric registrations; and the inclination angle errors (IAE) between the mapped fiber orientations and the gold standards were less than 15 degree. This method may provide a practical tool for cardiologists to examine cardiac fiber orientations on ultrasound images and have the potential to supply additional information for diagnosis of cardiac diseases.

3D in vivo imaging of rat hearts by high frequency ultrasound and its application in myofiber orientation wrapping

Cardiac ultrasound plays an important role in the imaging of hearts in basic cardiovascular research and clinical examinations. 3D ultrasound imaging can provide the geometry or motion information of the heart. Especially, the wrapping of cardiac fiber orientations to the ultrasound volume could supply useful information on the stress distributions and electric action spreading. However, how to acquire 3D ultrasound volumes of the heart of small animals in vivo for cardiac fiber wrapping is still a challenging problem. In this study, we provide an approach to acquire 3D ultrasound volumes of the rat hearts in vivo. The comparison between both in vivo and ex vivo geometries indicated 90.1% Dice similarity. In this preliminary study, the evaluations of the cardiac fiber orientation wrapping errors were 24.7° for the acute angle error and were 22.4° for the inclination angle error. This 3D ultrasound imaging and fiber orientation estimation technique have potential applications in cardiac imaging.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Effects of fibrosis morphology on reentrant ventricular tachycardia inducibility and simulation fidelity in patient-derived models

Myocardial fibrosis detected via delayed-enhanced magnetic resonance imaging (MRI) has been shown to be a strong indicator for ventricular tachycardia (VT) inducibility. However, little is known regarding how inducibility is affected by the details of the fibrosis extent, morphology, and border zone configuration. The objective of this article is to systematically study the arrhythmogenic effects of fibrosis geometry and extent, specifically on VT inducibility and maintenance. We present a set of methods for constructing patient-specific computational models of human ventricles using in vivo MRI data for patients suffering from hypertension, hypercholesterolemia, and chronic myocardial infarction. Additional synthesized models with morphologically varied extents of fibrosis and gray zone (GZ) distribution were derived to study the alterations in the arrhythmia induction and reentry patterns. Detailed electrophysiological simulations demonstrated that (1) VT morphology was highly dependent on the extent of fibrosis, which acts as a structural substrate, (2) reentry tended to be anchored to the fibrosis edges and showed transmural conduction of activations through narrow channels formed within fibrosis, and (3) increasing the extent of GZ within fibrosis tended to destabilize the structural reentry sites and aggravate the VT as compared to fibrotic regions of the same size and shape but with lower or no GZ. The approach and findings represent a significant step toward patient-specific cardiac modeling as a reliable tool for VT prediction and management of the patient. Sensitivities to approximation nuances in the modeling of structural pathology by image-based reconstruction techniques are also implicated.

Methodology for image-based reconstruction of ventricular geometry for patient-specific modeling of cardiac electrophysiology

Patient-specific modeling of ventricular electrophysiology requires an interpolated reconstruction of the 3-dimensional (3D) geometry of the patient ventricles from the low-resolution (Lo-res) clinical images. The goal of this study was to implement a processing pipeline for obtaining the interpolated reconstruction, and thoroughly evaluate the efficacy of this pipeline in comparison with alternative methods. The pipeline implemented here involves contouring the epi- and endocardial boundaries in Lo-res images, interpolating the contours using the variational implicit functions method, and merging the interpolation results to obtain the ventricular reconstruction. Five alternative interpolation methods, namely linear, cubic spline, spherical harmonics, cylindrical harmonics, and shape-based interpolation were implemented for comparison. In the thorough evaluation of the processing pipeline, Hi-res magnetic resonance (MR), computed tomography (CT), and diffusion tensor (DT) MR images from numerous hearts were used. Reconstructions obtained from the Hi-res images were compared with the reconstructions computed by each of the interpolation methods from a sparse sample of the Hi-res contours, which mimicked Lo-res clinical images. Qualitative and quantitative comparison of these ventricular geometry reconstructions showed that the variational implicit functions approach performed better than others. Additionally, the outcomes of electrophysiological simulations (sinus rhythm activation maps and pseudo-ECGs) conducted using models based on the various reconstructions were compared. These electrophysiological simulations demonstrated that our implementation of the variational implicit functions-based method had the best accuracy.

Patient-specific modeling of ventricular activation pattern using surface ECG-derived vectorcardiogram in bundle branch block

Patient-specific computational models have promise to improve cardiac disease diagnosis and therapy planning. Here a new method is described to simulate left-bundle branch block (LBBB) and RV-paced ventricular activation patterns in three dimensions from non-invasive, routine clinical measurements. Activation patterns were estimated in three patients using vectorcardiograms (VCG) derived from standard 12-lead electrocardiograms (ECG). Parameters of a monodomain model of biventricular electrophysiology were optimized to minimize differences between the measured and computed VCG. Electroanatomic maps of local activation times measured on the LV and RV endocardial surfaces of the same patients were used to validate the simulated activation patterns. For all patients, the optimal estimated model parameters predicted a time-averaged mean activation dipole orientation within 6.7 ± 0.6° of the derived VCG. The predicted local activation times agreed within 11.5 ± 0.8 ms of the measured electroanatomic maps, on the order of the measurement accuracy.

Measuring myofiber orientations from high-frequency ultrasound images using multiscale decompositions

High-frequency ultrasound (HFU) has the ability to image both skeletal and cardiac muscles. The quantitative assessment of these myofiber orientations has a number of applications in both research and clinical examinations; however, difficulties arise due to the severe speckle noise contained in the HFU images. Thus, for the purpose of automatically measuring myofiber orientations from two-dimensional HFU images, we propose a two-step multiscale image decomposition method. It combines a nonlinear anisotropic diffusion filter and a coherence enhancing diffusion filter to extract myofibers. This method has been verified by ultrasound data from simulated phantoms, excised fiber phantoms, specimens of porcine hearts, and human skeletal muscles in vivo. The quantitative evaluations of both phantoms indicated that the myofiber measurements of our proposed method were more accurate than other methods. The myofiber orientations extracted from different layers of the porcine hearts matched the prediction of an established cardiac mode and demonstrated the feasibility of extracting cardiac myofiber orientations from HFU images ex vivo. Moreover, HFU also demonstrated the ability to measure myofiber orientations in vivo.

Effect of statistically derived fiber models on the estimation of cardiac electrical activation

Myocardial fiber orientation plays a critical role in the electrical activation and subsequent contraction of the heart. To increase the clinical potential of electrophysiological (EP) simulation for the study of cardiac phenomena and the planning of interventions, accurate personalization of the fibers is a necessary yet challenging task. Due to the difficulties associated with the in vivo imaging of cardiac fiber structure, researchers have developed alternative techniques to personalize fibers. Thus far, cardiac simulation was performed mainly based on rule-based fiber models. More recently, there has been a significant interest in data-driven and statistically derived fiber models. In particular, our predictive method in [1] allows us to estimate the unknown subject-specific fiber orientation based on the more easily available shape information. The aim of this work is to estimate the effect of using such statistical predictive models for the estimation of cardiac electrical activation times and patterns. To this end, we perform EP simulations based on a database of ten canine ex vivo diffusion tensor imaging (DTI) datasets that include normal and failing cases. To assess the strength of the fiber models under varying conditions, we consider both sinus rhythm and biventricular pacing simulations. The results show that 1) the statistically derived fibers improve the estimation of the local activation times by an average of 53.7% over traditional rule-based models, and that 2) the obtained electrical activations are consistently similar to those of the DTI-based fibers.