A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices

Iterated Residual Graph Convolutional Neural Network for Personalized Three-Dimensional Reconstruction of Left Myocardium from Cardiac MR Images

Three-dimensional reconstruction of the left myocardium is of great significance for the diagnosis and treatment of cardiac diseases. This paper proposes a personalized 3D reconstruction algorithm for the left myocardium using cardiac MR images by incorporating a residual graph convolutional neural network. The accuracy of the mesh, reconstructed using the model-based algorithm, is largely affected by the similarity between the target object and the average model. The initial triangular mesh is obtained directly from the segmentation result of the left myocardium. The mesh is then deformed using an iterated residual graph convolutional neural network. A vertex feature learning module is also built to assist the mesh deformation by adopting an encoder-decoder neural network to represent the skeleton of the left myocardium at different receptive fields. In this way, the shape and local relationships of the left myocardium are used to guide the mesh deformation. Qualitative and quantitative comparative experiments were conducted on cardiac MR images, and the results verified the rationale and competitiveness of the proposed method compared to related state-of-the-art approaches.

Rule-based definition of muscle bundles in patient-specific models of the left atrium

Atrial fibrillation (AF) is the most common arrhythmia encountered clinically, and as the population ages, its prevalence is increasing. Although the CHA2DS2- VASc score is the most used risk-stratification system for stroke risk in AF, it lacks personalization. Patient-specific computer models of the atria can facilitate personalized risk assessment and treatment planning. However, a challenge faced in creating such models is the complexity of the atrial muscle arrangement and its influence on the atrial fiber architecture. This work proposes a semi-automated rule-based algorithm to generate the local fiber orientation in the left atrium (LA). We use the solutions of several harmonic equations to decompose the LA anatomy into subregions. Solution gradients define a two-layer fiber field in each subregion. The robustness of our approach is demonstrated by recreating the fiber orientation on nine models of the LA obtained from AF patients who underwent WATCHMAN device implantation. This cohort of patients encompasses a variety of morphology variants of the left atrium, both in terms of the left atrial appendages (LAAs) and the number of pulmonary veins (PVs). We test the fiber construction algorithm by performing electrophysiology (EP) simulations. Furthermore, this study is the first to compare its results with other rule-based algorithms for the LA fiber architecture definition available in the literature. This analysis suggests that a multi-layer fiber architecture is important to capture complex electrical activation patterns. A notable advantage of our approach is the ability to reconstruct the main LA fiber bundles in a variety of morphologies while solving for a small number of harmonic fields, leading to a comparatively straightforward and reproducible approach.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Forward-Solution Noninvasive Computational Arrhythmia Mapping: The VMAP Study

BACKGROUND

The accuracy of noninvasive arrhythmia source localization using a forward-solution computational mapping system has not yet been evaluated in blinded, multicenter analysis. This study tested the hypothesis that a computational mapping system incorporating a comprehensive arrhythmia simulation library would provide accurate localization of the site-of-origin for atrial and ventricular arrhythmias and pacing using 12-lead ECG data when compared with the gold standard of invasive electrophysiology study and ablation.

METHODS

The VMAP study (Vectorcardiographic Mapping of Arrhythmogenic Probability) was a blinded, multicenter evaluation with final data analysis performed by an independent core laboratory. Eligible episodes included atrial and ventricular: tachycardia, fibrillation, pacing, premature atrial and ventricular complexes, and orthodromic atrioventricular reentrant tachycardia. Mapping system results were compared with the gold standard site of successful ablation or pacing during electrophysiology study and ablation. Mapping time was assessed from time-stamped logs. Prespecified performance goals were used for statistical comparisons.

RESULTS

A total of 255 episodes from 225 patients were enrolled from 4 centers. Regional accuracy for ventricular tachycardia and premature ventricular complexes in patients without significant structural heart disease (n=75, primary end point) was 98.7% (95% CI, 96.0%-100%; P<0.001 to reject predefined H0 <0.80). Regional accuracy for all episodes (secondary end point 1) was 96.9% (95% CI, 94.7%-99.0%; P<0.001 to reject predefined H0 <0.75). Accuracy for the exact or neighboring segment for all episodes (secondary end point 2) was 97.3% (95% CI, 95.2%-99.3%; P<0.001 to reject predefined H0 <0.70). Median spatial accuracy was 15 mm (n=255, interquartile range, 7-25 mm). The mapping process was completed in a median of 0.8 minutes (interquartile range, 0.4-1.4 minutes).

CONCLUSIONS

Computational ECG mapping using a forward-solution approach exceeded prespecified accuracy goals for arrhythmia and pacing localization. Spatial accuracy analysis demonstrated clinically actionable results. This rapid, noninvasive mapping technology may facilitate catheter-based and noninvasive targeted arrhythmia therapies.

REGISTRATION

URL: https://www.

CLINICALTRIALS

gov; Unique identifier: NCT04559061.

High-Order Cardiomyopathy Human Heart Model and Mesh Generation

Faithful, accurate, and successful cardiac biomechanics and electrophysiological simulations require patient-specific geometric models of the heart. Since the cardiac geometry consists of highly-curved boundaries, the use of high-order meshes with curved elements would ensure that the various curves and features present in the cardiac geometry are well-captured and preserved in the corresponding mesh. Most other existing mesh generation techniques require computer-aided design files to represent the geometric boundary, which are often not available for biomedical applications. Unlike such methods, our technique takes a high-order surface mesh, generated from patient medical images, as input and generates a high-order volume mesh directly from the curved surface mesh. In this paper, we use our direct high-order curvilinear tetrahedral mesh generation method [1] to generate several second-order cardiac meshes. Our meshes include the left ventricle myocardia of a healthy heart and hearts with dilated and hypertrophic cardiomyopathy. We show that our high-order cardiac meshes do not contain inverted elements and are of sufficiently high quality for use in cardiac finite element simulations.

Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement

The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.

Structural Responses of Integrated Parametric Aortic Valve in an Electro-Mechanical Full Heart Model

The aortic valve (AV) is located between the left ventricle and the aorta and responsible for maintaining an outward unidirectional flow. Many AV hemodynamic and structural aspects of have been extensively studied, however, more sophisticated models are needed to better understand the AV biomechanical behavior. This study deals with integrating a new parametric AV structural model with the electro-mechanical Living Heart Human Model® (LHHM). The LHHM is a finite element model simulating human heart capable of realistic electro-mechanical simulations. Different geometric metrics of AV have been examined. New integrated structural AV model within the LHHM better predict local stresses during the cardiac cycle due to the realistic boundary condition derived from the LHHM. It was found that ellipticity index (EI), calculated as the ratio between the maximal (Max) and minimal (Min) aortic annulus (AA) diameters, well correlates with measured clinical data obtained from patients undergoing computed tomography (CT) while the annular perimeter (Perim) matches the same trend. This increases the confidence in the predicted kinematic behavior, leaflets coaptation, and the overall stresses. From the clinical aspect, the new proposed coupled and integrated AV modeling can serve as a platform for design and implementation of pre-transcatheter aortic valve replacement (TAVR) procedures.

Feature Enhancement in Medical Ultrasound Videos Using Contrast-Limited Adaptive Histogram Equalization

Speckle noise reduction algorithms are extensively used in the field of ultrasound image analysis with the aim of improving image quality and diagnostic accuracy. However, significant speckle filtering induces blurring, and this requires the enhancement of features and fine details. We propose a novel framework for both multiplicative noise suppression and robust contrast enhancement and demonstrate its effectiveness using a wide range of clinical ultrasound scans. Our approach to noise suppression uses a novel algorithm based on a convolutional neural network that is first trained on synthetically modeled ultrasound images and then applied on real ultrasound videos. The feature improvement stage uses an improved contrast-limited adaptive histogram equalization (CLAHE) method for enhancing texture features, contrast, resolvable details, and image structures to which the human visual system is sensitive in ultrasound video frames. The proposed CLAHE algorithm also considers an automatic system for evaluating the grid size using entropy, and three different target distribution functions (uniform, Rayleigh, and exponential), and interpolation techniques (B-spline, cubic, and Lanczos-3). An extensive comparative study has been performed to find the most suitable distribution and interpolation techniques and also the optimal clip limit for ultrasound video feature enhancement after speckle suppression. Subjective assessments by four radiologists and experimental validation using three quality metrics clearly indicate that the proposed framework generates superior performance compared with other well-established methods. The processing pipeline reduces speckle effectively while preserving essential information and enhancing the overall visual quality and therefore could find immediate applications in real-time ultrasound video segmentation and classification algorithms.

Imaging of subendocardial adipose tissue and fiber orientation distributions in the human left atrium using optical coherence tomography

Background

Optical coherence tomography (OCT) has the potential to provide real‐time imaging guidance for atrial fibrillation ablation, with promising results for lesion monitoring. OCT can also offer high‐resolution imaging of tissue composition, but there is insufficient cardiac OCT data to inform the use of OCT to reveal important tissue architecture of the human left atrium. Thus, the objective of this study was to define OCT imaging data throughout the human left atrium, focusing on the distribution of adipose tissue and fiber orientation as seen from the endocardium.

Methods and Results

Human hearts (n = 7) were acquired for imaging the left atrium with OCT. A spectral‐domain OCT system with 1325 nm center wavelength, 6.5 μm axial resolution, 15 μm lateral resolution, and a maximum imaging depth of 2.51 mm in the air was used. Large‐scale OCT image maps of human left atrial tissue were developed, with adipose thickness and fiber orientation extracted from the imaging data. OCT imaging showed scattered distributions of adipose tissue around the septal and pulmonary vein regions, up to a depth of about 0.43 mm from the endocardial surface. The total volume of adipose tissue detected by OCT over one left atrium ranged from 1.42 to 28.74 mm³. Limited fiber orientation information primarily around the pulmonary veins and the septum could be identified.

Conclusion

OCT imaging could provide adjunctive information on the distribution of subendocardial adipose tissue, particularly around thin areas around the pulmonary veins and septal regions. Variations in OCT‐detected tissue composition could potentially assist ablation guidance.

Cardiac wall mechanics analysis in hypertension-induced heart failure rats with preserved ejection fraction

Although cardiac wall mechanics is of importance for understanding heart failure with preserved ejection fraction (HFpEF), there is a lack of relevant mechanics studies. The aim of this study was to analyze the changes in stress and strain in the left ventricle (LV) in hypertension-induced HFpEF rats. Based on experimental measurements in DSS rats fed with high-salt (HS) and low-salt (LS) diets, LV stress and strain were computed throughout the cardiac cycle using Continuity software. HS-feeding increased myofiber stress and strain along both the transmural and longitudinal directions at the end-diastolic state but resulted in a lower absolute value of strain and relatively unchanged stress at the end-systolic state. Moreover, the end-diastolic stress and strain decreased with increasing radial position from the endocardial towards the epicardial walls despite negligible changes along the longitudinal direction. The changes in LV wall mechanics characterized the elevated diastolic LV stiffness and slow LV relaxation in HS-fed rats of HFpEF. These findings denote that a vicious cycle of increased stress and strain and diastolic dysfunction can prompt the development of HFpEF.

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly-fewer elements are needed to build the cardiac geometry-compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.

Revival and modification of the Mustard operation

OBJECTIVE

The neonatal arterial switch operation is currently the procedure of choice for patients with transposition of the great arteries. However, a large number of patients present too late for the arterial switch operation and are best managed with the atrial switch operation.

METHODS

We have used the Mustard operation in its original form or following a new modification designed to enhance the atrial functions and filling of the left ventricle in an attempt to improve long-term results.

RESULTS

Between July 2013 and November 2018, a total of 101 patients underwent the Mustard operation, 86 with the new modification. The median age at operation was 16 months (6 months to 27 years). A total of 75 patients (74.3%) were male. Median preoperative oxygen saturation was 71%. There were no early deaths and there were 3 late deaths during a median follow-up period of 24.2 months (all in patients with large ventricular septal defect and established pulmonary vascular disease). At the latest follow-up, all patients were in stable sinus rhythm. There were no baffle leaks. Seven patients had asymptomatic narrowing of the superior baffle, and 1 patient required balloon dilatation. Follow-up is 100% complete and includes computed tomography and magnetic resonance imaging at regular intervals (75 patients to date). Computerized analysis of representative subsets showed enhanced rate and pattern of filling of the left ventricle in the modified operation compared with the classic operation.

CONCLUSIONS

The use of the Mustard operation, particularly the modified technique should play an important role in treating late-presenting patients with transposition of the great arteries. Improving the pattern of filling of the left ventricle could enhance the long-term results of the Mustard operation.

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

Atrial fibrillation (AF) is a supraventricular tachyarrhythmia characterized by complete absence of coordinated atrial contraction and is associated with an increased morbidity and mortality. Personalized computational modeling provides a novel framework for integrating and interpreting the role of atrial electrophysiology (EP) including the underlying anatomy and microstructure in the development and sustenance of AF. Coronary computed tomography angiography data were segmented using a statistics-based approach and the smoothed voxel representations were discretized into high-resolution tetrahedral finite element (FE) meshes. To estimate the complex left atrial myofiber architecture, individual fiber fields were generated according to morphological data on the endo- and epicardial surfaces based on local solutions of Laplace’s equation and transmurally interpolated to tetrahedral elements. The influence of variable transmural microstructures was quantified through EP simulations on 3 patients using 5 different fiber interpolation functions. Personalized geometrical models included the heterogeneous thickness distribution of the left atrial myocardium and subsequent discretization led to high-fidelity tetrahedral FE meshes. The novel algorithm for automated incorporation of the left atrial fiber architecture provided a realistic estimate of the atrial microstructure and was able to qualitatively capture all important fiber bundles. Consistent maximum local activation times were predicted in EP simulations using individual transmural fiber interpolation functions for each patient suggesting a negligible effect of the transmural myofiber architecture on EP. The established modeling pipeline provides a robust framework for the rapid development of personalized model cohorts accounting for detailed anatomy and microstructure and facilitates simulations of atrial EP.

Atlas-Based Computational Analysis of Heart Shape and Function in Congenital Heart Disease

Approximately 1% of all babies are born with some form of congenital heart defect. Many serious forms of CHD can now be surgically corrected after birth, which has led to improved survival into adulthood. However, many patients require serial monitoring to evaluate progression of heart failure and determine timing of interventions. Accurate multidimensional quantification of regional heart shape and function is required for characterizing these patients. A computational atlas of single ventricle and biventricular heart shape and function enables quantification of remodeling in terms of z scores in relation to specific reference populations. Progression of disease can then be monitored effectively by longitudinal evaluation of z scores. A biomechanical analysis of cardiac function in relation to population variation enables investigation of the underlying mechanisms for developing pathology. Here, we summarize recent progress in this field, with examples in single ventricle and biventricular congenital pathologies.

Non-invasive, model-based measures of ventricular electrical dyssynchrony for predicting CRT outcomes

AIMS

Left ventricular activation delay due to left bundle branch block (LBBB) is an important determinant of the severity of dyssynchronous heart failure (DHF). We investigated whether patient-specific computational models constructed from non-invasive measurements can provide measures of baseline dyssynchrony and its reduction after CRT that may explain the degree of long-term reverse ventricular remodelling.

METHODS AND RESULTS

LV end-systolic volume reduction (ΔESV_LV) measured by 2D trans-thoracic echocardiography in eight patients following 6 months of CRT was significantly (P < 0.05) greater in responders (26 ± 20%, n = 4) than non-responders (11 ± 16%, n = 4). LV reverse remodelling did not correlate with baseline QRS duration or its change after biventricular pacing, but did correlate with baseline LV endocardial activation measured by electroanatomic mapping (R²=0.71, P < 0.01). Patient-specific models of LBBB ventricular activation with parameters obtained by matching model-computed vectorcardiograms (VCG) to those derived from standard patient ECGs yielded LV endocardial activation times that correlated well with those measured from endocardial maps (R²=0.90). Model-computed 3D LV activation times correlated strongly with the reduction in LVESV (R²=0.93, P < 0.001). Computed decreases due to simulated CRT in the time delay between LV septal and lateral activation correlated strongly with ΔESV_LV (R²=0.92, P < 0.001). Models also suggested that optimizing VV delays may improve resynchronization by this measure of activation delay.

CONCLUSIONS

Patient-specific computational models constructed from non-invasive measurements can compute estimates of LV dyssynchrony and their changes after CRT that may be as good as or better than electroanatomic mapping for predicting long-term reverse remodelling.

Rotors exhibit greater surface ECG variation during ventricular fibrillation than focal sources due to wavebreak, secondary rotors, and meander

INTRODUCTION

Ventricular fibrillation is a common life-threatening arrhythmia. The ECG of VF appears chaotic but may allow identification of sustaining mechanisms to guide therapy.

HYPOTHESIS

We hypothesized that rotors and focal sources manifest distinct features on the ECG, and computational modeling may identify mechanisms of such features.

METHODS

VF induction was attempted in 31 patients referred for ventricular arrhythmia ablation. Simultaneous surface ECG and intracardiac electrograms were recorded using biventricular basket catheters. Endocardial phase maps were used to mechanistically classify each VF cycle as rotor or focally driven. ECGs were analyzed from patients demonstrating both mechanisms in the primary analysis and from all patients with induced VF in the secondary analysis. The ECG voltage variation during each mechanism was compared. Biventricular computer simulations of VF driven by focal sources or rotors were created and resulting ECGs of each VF mechanism were compared.

RESULTS

Rotor-based VF exhibited greater voltage variation than focal source-based VF in both the primary analysis (n = 8, 110 ± 24% vs. 55 ± 32%, P = 0.02) and the secondary analysis (n = 18, 103 ± 30% vs. 67 ± 34%, P = 0.009). Computational VF simulations also revealed greater voltage variation in rotors compared to focal sources (110 ± 19% vs. 33 ± 16%, P = 0.001), and demonstrated that this variation was due to wavebreak, secondary rotor initiation, and rotor meander.

CONCLUSION

Clinical and computational studies reveal that quantitative criteria of ECG voltage variation differ significantly between VF-sustaining rotors and focal sources, and provide insight into the mechanisms of such variation. Future studies should prospectively evaluate if these criteria can separate clinical VF mechanisms and guide therapy.

Automated classification of optical coherence tomography images of human atrial tissue

Tissue composition of the atria plays a critical role in the pathology of cardiovascular disease, tissue remodeling, and arrhythmogenic substrates. Optical coherence tomography (OCT) has the ability to capture the tissue composition information of the human atria. In this study, we developed a region-based automated method to classify tissue compositions within human atria samples within OCT images. We segmented regional information without prior information about the tissue architecture and subsequently extracted features within each segmented region. A relevance vector machine model was used to perform automated classification. Segmentation of human atrial ex vivo datasets was correlated with trichrome histology and our classification algorithm had an average accuracy of 80.41% for identifying adipose, myocardium, fibrotic myocardium, and collagen tissue compositions.

Comparison of Detailed and Simplified Models of Human Atrial Myocytes to Recapitulate Patient Specific Properties

Computer studies are often used to study mechanisms of cardiac arrhythmias, including atrial fibrillation (AF). A crucial component in these studies is the electrophysiological model that describes the membrane potential of myocytes. The models vary from detailed, describing numerous ion channels, to simplified, grouping ionic channels into a minimal set of variables. The parameters of these models, however, are determined across different experiments in varied species. Furthermore, a single set of parameters may not describe variations across patients, and models have rarely been shown to recapitulate critical features of AF in a given patient. In this study we develop physiologically accurate computational human atrial models by fitting parameters of a detailed and of a simplified model to clinical data for five patients undergoing ablation therapy. Parameters were simultaneously fitted to action potential (AP) morphology, action potential duration (APD) restitution and conduction velocity (CV) restitution curves in these patients. For both models, our fitting procedure generated parameter sets that accurately reproduced clinical data, but differed markedly from published sets and between patients, emphasizing the need for patient-specific adjustment. Both models produced two-dimensional spiral wave dynamics for that were similar for each patient. These results show that simplified, computationally efficient models are an attractive choice for simulations of human atrial electrophysiology in spatially extended domains. This study motivates the development and validation of patient-specific model-based mechanistic studies to target therapy.

Cardiac image modelling: Breadth and depth in heart disease

With the advent of large-scale imaging studies and big health data, and the corresponding growth in analytics, machine learning and computational image analysis methods, there are now exciting opportunities for deepening our understanding of the mechanisms and characteristics of heart disease. Two emerging fields are computational analysis of cardiac remodelling (shape and motion changes due to disease) and computational analysis of physiology and mechanics to estimate biophysical properties from non-invasive imaging. Many large cohort studies now underway around the world have been specifically designed based on non-invasive imaging technologies in order to gain new information about the development of heart disease from asymptomatic to clinical manifestations. These give an unprecedented breadth to the quantification of population variation and disease development. Also, for the individual patient, it is now possible to determine biophysical properties of myocardial tissue in health and disease by interpreting detailed imaging data using computational modelling. For these population and patient-specific computational modelling methods to develop further, we need open benchmarks for algorithm comparison and validation, open sharing of data and algorithms, and demonstration of clinical efficacy in patient management and care. The combination of population and patient-specific modelling will give new insights into the mechanisms of cardiac disease, in particular the development of heart failure, congenital heart disease, myocardial infarction, contractile dysfunction and diastolic dysfunction.

Lessons from computer simulations of ablation of atrial fibrillation

This paper reviews the simulations of catheter ablation in computer models of the atria, from the first attempts to the most recent anatomical models. It describes how postulated substrates of atrial fibrillation can be incorporated into mathematical models, how modelling studies can be designed to test ablation strategies, what their current trade-offs and limitations are, and what clinically relevant lessons can be learnt from these simulations. Drawing a parallel between clinical and modelling studies, six ablation targets are considered: pulmonary vein isolation, linear ablation, ectopic foci, complex fractionated atrial electrogram, rotors and ganglionated plexi. The examples presented for each ablation target illustrate a major advantage of computer models, the ability to identify why a therapy is successful or not in a given atrial fibrillation substrate. The integration of pathophysiological data to create detailed models of arrhythmogenic substrates is expected to solidify the understanding of ablation mechanisms and to provide theoretical arguments supporting substrate-specific ablation strategies.

Biomechanics Simulations Using Cubic Hermite Meshes with Extraordinary Nodes for Isogeometric Cardiac Modeling

Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >= 5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Creating shape templates for patient specific biventricular modeling in congenital heart disease

Survival rates for infants with congenital heart disease (CHD) are improving, resulting in a growing population of adults with CHD. However, the analysis of left and right ventricular function is very time-consuming owing to the variety of congenital morphologies. Efficient customization of patient geometry and function depends on high quality shape templates specifically designed for the application. In this paper, we combine a method for creating finite element shape templates with an interactive template customization to patient MRI examinations. This enables different templates to be chosen depending on patient morphology. To demonstrate this pipeline, a new biventricular template with 162 elements was created and tested in place of an existing 82-element template. The method was able to provide fast interactive biventricular analysis with 0.31 sec per edit response time. The new template was customized to 13 CHD patients with similar biventricular topology, showing improved performance over the previous template and good agreement with clinical indices.

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.

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.

High-order finite element methods for cardiac monodomain simulations

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

Structural contributions to fibrillatory rotors in a patient-derived computational model of the atria

AIMS

The aim of this study was to investigate structural contributions to the maintenance of rotors in human atrial fibrillation (AF) and possible mechanisms of termination.

METHODS AND RESULTS

A three-dimensional human biatrial finite element model based on patient-derived computed tomography and arrhythmia observed at electrophysiology study was used to study AF. With normal physiological electrical conductivity and effective refractory periods (ERPs), wave break failed to sustain reentrant activity or electrical rotors. With depressed excitability, decreased conduction anisotropy, and shorter ERP characteristic of AF, reentrant rotors were readily maintained. Rotors were transiently or permanently trapped by fibre discontinuities on the lateral wall of the right atrium near the tricuspid valve orifice and adjacent to the crista terminalis, both known sites of right atrial arrhythmias. Modelling inexcitable regions near the rotor tip to simulate fibrosis anchored the rotors, converting the arrhythmia to macro-reentry. Accordingly, increasing the spatial core of inexcitable tissue decreased the frequency of rotation, widened the excitable gap, and enabled an external wave to impinge on the rotor core and displace the source.

CONCLUSION

These model findings highlight the importance of structural features in rotor dynamics and suggest that regions of fibrosis may anchor fibrillatory rotors. Increasing extent of fibrosis and scar may eventually convert fibrillation to excitable gap reentry. Such macro-reentry can then be eliminated by extending the obstacle or by external stimuli that penetrate the excitable gap.

Modeling Pathologies of Diastolic and Systolic Heart Failure

Chronic heart failure is a medical condition that involves structural and functional changes of the heart and a progressive reduction in cardiac output. Heart failure is classified into two categories: diastolic heart failure, a thickening of the ventricular wall associated with impaired filling; and systolic heart failure, a dilation of the ventricles associated with reduced pump function. In theory, the pathophysiology of heart failure is well understood. In practice, however, heart failure is highly sensitive to cardiac microstructure, geometry, and loading. This makes it virtually impossible to predict the time line of heart failure for a diseased individual. Here we show that computational modeling allows us to integrate knowledge from different scales to create an individualized model for cardiac growth and remodeling during chronic heart failure. Our model naturally connects molecular events of parallel and serial sarcomere deposition with cellular phenomena of myofibrillogenesis and sarcomerogenesis to whole organ function. Our simulations predict chronic alterations in wall thickness, chamber size, and cardiac geometry, which agree favorably with the clinical observations in patients with diastolic and systolic heart failure. In contrast to existing single- or bi-ventricular models, our new four-chamber model can also predict characteristic secondary effects including papillary muscle dislocation, annular dilation, regurgitant flow, and outflow obstruction. Our prototype study suggests that computational modeling provides a patient-specific window into the progression of heart failure with a view towards personalized treatment planning.

Optimization of catheter ablation of atrial fibrillation: insights gained from clinically-derived computer models

Atrial fibrillation (AF) is the most common heart rhythm disturbance, and its treatment is an increasing economic burden on the health care system. Despite recent intense clinical, experimental and basic research activity, the treatment of AF with current antiarrhythmic drugs and catheter/surgical therapies remains limited. Radiofrequency catheter ablation (RFCA) is widely used to treat patients with AF. Current clinical ablation strategies are largely based on atrial anatomy and/or substrate detected using different approaches, and they vary from one clinical center to another. The nature of clinical ablation leads to ambiguity regarding the optimal patient personalization of the therapy partly due to the fact that each empirical configuration of ablation lines made in a patient is irreversible during one ablation procedure. To investigate optimized ablation lesion line sets, in silico experimentation is an ideal solution. 3D computer models give us a unique advantage to plan and assess the effectiveness of different ablation strategies before and during RFCA. Reliability of in silico assessment is ensured by inclusion of accurate 3D atrial geometry, realistic fiber orientation, accurate fibrosis distribution and cellular kinetics; however, most of this detailed information in the current computer models is extrapolated from animal models and not from the human heart. The predictive power of computer models will increase as they are validated with human experimental and clinical data. To make the most from a computer model, one needs to develop 3D computer models based on the same functionally and structurally mapped intact human atria with high spatial resolution. The purpose of this review paper is to summarize recent developments in clinically-derived computer models and the clinical insights they provide for catheter ablation.

Left Ventricular Diastolic and Systolic Material Property Estimation from Image Data: LV Mechanics Challenge

Cardiovascular simulations using patient-specific geometries can help researchers understand the mechanical behavior of the heart under different loading or disease conditions. However, to replicate the regional mechanics of the heart accurately, both the nonlinear passive and active material properties must be estimated reliably. In this paper, automated methods were used to determine passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Two different approaches were used to model systole. In the first, a physiologically-based active contraction model [1] coupled to a hemodynamic three-element Windkessel model of the circulation was used to simulate ventricular ejection. In the second, developed active tension was directly adjusted to match ventricular volumes at end-systole while prescribing the known end-systolic pressure. These methods were tested in four normal dogs using the data provided for the LV mechanics challenge [2]. The resulting end-diastolic and end-systolic geometry from the simulation were compared with measured image data.

The Living Heart Project: A robust and integrative simulator for human heart function

The heart is not only our most vital, but also our most complex organ: Precisely controlled by the interplay of electrical and mechanical fields, it consists of four chambers and four valves, which act in concert to regulate its filling, ejection, and overall pump function. While numerous computational models exist to study either the electrical or the mechanical response of its individual chambers, the integrative electro-mechanical response of the whole heart remains poorly understood. Here we present a proof-of-concept simulator for a four-chamber human heart model created from computer topography and magnetic resonance images. We illustrate the governing equations of excitation-contraction coupling and discretize them using a single, unified finite element environment. To illustrate the basic features of our model, we visualize the electrical potential and the mechanical deformation across the human heart throughout its cardiac cycle. To compare our simulation against common metrics of cardiac function, we extract the pressure-volume relationship and show that it agrees well with clinical observations. Our prototype model allows us to explore and understand the key features, physics, and technologies to create an integrative, predictive model of the living human heart. Ultimately, our simulator will open opportunities to probe landscapes of clinical parameters, and guide device design and treatment planning in cardiac diseases such as stenosis, regurgitation, or prolapse of the aortic, pulmonary, tricuspid, or mitral valve.

Atlas-based quantification of cardiac remodeling due to myocardial infarction

Myocardial infarction leads to changes in the geometry (remodeling) of the left ventricle (LV) of the heart. The degree and type of remodeling provides important diagnostic information for the therapeutic management of ischemic heart disease. In this paper, we present a novel analysis framework for characterizing remodeling after myocardial infarction, using LV shape descriptors derived from atlas-based shape models. Cardiac magnetic resonance images from 300 patients with myocardial infarction and 1991 asymptomatic volunteers were obtained from the Cardiac Atlas Project. Finite element models were customized to the spatio-temporal shape and function of each case using guide-point modeling. Principal component analysis was applied to the shape models to derive modes of shape variation across all cases. A logistic regression analysis was performed to determine the modes of shape variation most associated with myocardial infarction. Goodness of fit results obtained from end-diastolic and end-systolic shapes were compared against the traditional clinical indices of remodeling: end-diastolic volume, end-systolic volume and LV mass. The combination of end-diastolic and end-systolic shape parameter analysis achieved the lowest deviance, Akaike information criterion and Bayesian information criterion, and the highest area under the receiver operating characteristic curve. Therefore, our framework quantitatively characterized remodeling features associated with myocardial infarction, better than current measures. These features enable quantification of the amount of remodeling, the progression of disease over time, and the effect of treatments designed to reverse remodeling effects.

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.

Atlas-based Anatomical Modeling and Analysis of Heart Disease

Heart shape and function are major determinants of disease severity and predictors of future morbidity and mortality. Many studies now rely on non-invasive cardiac imaging techniques to quantify structural and functional changes. Statistical anatomical modeling of heart shape and motion provides a new tool for the quantification and evaluation of heart disease. This review surveys recent progress in the evaluation of statistical shape measures across populations and sub-cohorts, and highlights collaborative efforts to facilitate data sharing and atlas-based shape analysis.

An automatic service for the personalization of ventricular cardiac meshes

Computational cardiac physiology has great potential to improve the management of cardiovascular diseases. One of the main bottlenecks in this field is the customization of the computational model to the anatomical and physiological status of the patient. We present a fully automatic service for the geometrical personalization of cardiac ventricular meshes with high-order interpolation from segmented images. The method is versatile (able to work with different species and disease conditions) and robust (fully automatic results fulfilling accuracy and quality requirements in 87% of 255 cases). Results also illustrate the capability to minimize the impact of segmentation errors, to overcome the sparse resolution of dynamic studies and to remove the sometimes unnecessary anatomical detail of papillary and trabecular structures. The smooth meshes produced can be used to simulate cardiac function, and in particular mechanics, or can be used as diagnostic descriptors of anatomical shape by cardiologists. This fully automatic service is deployed in a cloud infrastructure, and has been made available and accessible to the scientific community.