Ken C. L. Wong

Physiological-Model-Constrained Noninvasive Reconstruction of Volumetric Myocardial Transmembrane Potentials

Personalized noninvasive imaging of subject-specific cardiac electrical activity can guide and improve preventive diagnosis and treatment of cardiac arrhythmia. Compared to body surface potential (BSP) recordings and electrophysiological information reconstructed on heart surfaces, volumetric myocardial transmembrane potential (TMP) dynamics is of greater clinical importance in exhibiting arrhythmic details and arrythmogenic substrates inside the myocardium. This paper presents a physiological-model-constrained statistical framework to reconstruct volumetric TMP dynamics inside the 3-D myocardium from noninvasive BSP recordings. General knowledge of volumetric TMP activity is incorporated through the modeling of cardiac electrophysiological system, and is used to constrain TMP reconstruction. This physiological system is reformulated into a stochastic state-space representation to take into account model and data uncertainties, and nonlinear data assimilation is developed to estimate volumetric myocardial TMP dynamics from personal BSP data. Robustness of the presented framework to practical model and data errors is evaluated. Comparison of epicardial potential reconstructions with classical regularization-based approaches is performed on computational phantom regarding right bundle branch blocks. Further, phantom experiments on intramural focal activities and an initial real-data study on postmyocardial infarction demonstrate the potential of the framework in reconstructing local arrhythmic details and identifying arrhythmogenic substrates inside the myocardium.

Noninvasive Computational Imaging of Cardiac Electrophysiology for 3-D Infarct

Myocardial infarction (MI) creates electrophysiologically altered substrates that are responsible for ventricular ar rhythmias, such as tachycardia and fibrillation. The presence, size, location, and composition of infarct scar bear significant prognostic and therapeutic implications for individual subjects. We have developed a statistical physiological model-constrained framework that uses noninvasive body-surface-potential data and tomographic images to estimate subject-specific transmembrane potential (TMP) dynamics inside the 3-D myocardium. In this paper, we adapt this framework for the purpose of noninvasive imaging, detection, and quantification of 3-D scar mass for postMI patients: the framework requires no prior knowledge of MI and converges to final subject-specific TMP estimates after several passes of estimation with intermediate feedback; based on the primary features of the estimated spatiotemporal TMP dynamics, we provide 3-D imaging of scar tissue and quantitative evaluation of scar location and extent. Phantom experiments were performed on a computational model of realistic heart-torso geometry, considering 87 transmural infarct scars of different sizes and locations inside the myocardium, and 12 compact infarct scars (extent between 10% and 30%) at different transmural depths. Real data experiments were carried out on BSP and magnetic resonance imaging (MRI) data from four postMI patients, validated by gold standards and existing results. This framework shows unique advantage of noninvasive, quantitative, computational imaging of subject-specific TMP dynamics and infarct mass of the 3-D myocardium, with the potential to reflect details in the spatial structure and tissue composition/heterogeneity of 3-D infarct scar.

Personalization of Cardiac Motion and Contractility From Images Using Variational Data Assimilation

Personalization is a key aspect of biophysical models in order to impact clinical practice. In this paper, we propose a personalization method of electromechanical models of the heart from cine-MR images based on the adjoint method. After estimation of electrophysiological parameters, the cardiac motion is estimated based on a proactive electromechanical model. Then cardiac contractilities on two or three regions are estimated by minimizing the discrepancy between measured and simulation motion. Evaluation of the method on three patients with infarcted or dilated myocardium is provided.

Inter-Model Consistency and Complementarity: Learning from ex-vivo Imaging and Electrophysiological Data towards an Integrated Understanding of Cardiac Physiology

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

Meshfree implementation of individualized active cardiac dynamics.

The cardiac physiome model has been proven to be useful for cardiac simulation, and has been more recently utilized to medical image analysis. To perform individualized analysis, structural images are necessary to provide subject-specific cardiac geometries. Although finite element methods have been extensively used for the spatial discretization of the myocardium, their complicated meshing procedures and element-based interpolation functions often result in algorithms which are either easy to implement but numerically inaccurate, or accurate but labor-intensive. In consequence, we have adopted the meshfree platform which provides element-free approximations for computational cardiology. Complicated volume meshing procedures are excluded, and no re-meshing is needed for improving spatial accuracy when deformation occurs. Furthermore, the polynomial bases for spatial approximation are not limited by the element structure. As a result, the meshfree platform is more adaptive to different cardiac geometries and thus beneficial to individualized analysis. In this paper, the cardiac physiome model tailored for medical image analysis is presented with its detailed 3D implementation using the meshfree methods. Experiments were performed to compare the meshfree methods with the finite element methods, and simulations were done on a cubical object to investigate the local behaviors of the cardiac physiome model, and on a human heart geometry extracted from a magnetic resonance image to verify its physiological plausibility.

Transmural Imaging of Ventricular Action Potentials and Post-Infarction Scars in Swine Hearts

The problem of using surface data to reconstruct transmural electrophysiological (EP) signals is intrinsically ill-posed without a unique solution in its unconstrained form. Incorporating physiological spatiotemporal priors through probabilistic integration of dynamic EP models, we have previously developed a Bayesian approach to transmural electrophysiological imaging (TEPI) using body-surface electrocardiograms. In this study, we generalize TEPI to using electrical signals collected from heart surfaces, and we test its feasibility on two pre-clinical swine models provided through the STACOM 2011 EP simulation Challenge. Since this new application of TEPI does not require whole-body imaging, there may be more immediate potential in EP laboratories where it could utilize catheter mapping data and produce transmural information for therapy guidance. Another focus of this study is to investigate the consistency among three modalities in delineating scar after myocardial infarction: TEPI, electroanatomical voltage mapping (EAVM), and magnetic resonance imaging (MRI). Our preliminary data demonstrate that, compared to the low-voltage scar area in EAVM, the 3-D electrical scar volume detected by TEPI is more consistent with anatomical scar volume delineated in MRI. Furthermore, TEPI could complement anatomical imaging by providing EP functional features related to both scar and healthy tissue.

Physiological Fusion of Functional and Structural Images for Cardiac Deformation Recovery

The recent advances in meaningful constraining models have resulted in increasingly useful quantitative information recovered from cardiac images. Nevertheless, as most frameworks utilize either functional or structural images, the analyses cannot benefit from the complementary information provided by the other image sources. To better characterize subject-specific cardiac physiology and pathology, data fusion of multiple image sources is essential. Traditional image fusion strategies are performed by fusing information of commensurate images through various mathematical operators. Nevertheless, when image data are dissimilar in physical nature and spatiotemporal quantity, such approaches may not provide meaningful connections between different data. In fact, as different image sources provide partial measurements of the same cardiac system dynamics, it is more natural and suitable to utilize cardiac physiological models for the fusions. Therefore, we propose to use the cardiac physiome model as the central link to fuse functional and structural images for more subject-specific cardiac deformation recovery through state-space filtering. Experiments were performed on synthetic and real data for the characteristics and potential clinical applicability of our framework, and the results show an increase of the overall subject specificity of the recovered deformations.

Velocity-based cardiac contractility personalization from images using derivative-free optimization

Model personalization is a key aspect for biophysical models to impact clinical practice, and cardiac contractility personalization from medical images is a major step in this direction. Existing gradient-based optimization approaches show promising results of identifying the maximum contractility from images, but the contraction and relaxation rates are not accounted for. A main reason is the limited choices of objective functions when their gradients are required. For complicated cardiac models, analytical evaluations of gradients are very difficult if not impossible, and finite difference approximations are computationally expensive and may introduce numerical difficulties. By removing such limitations with derivative-free optimization, we found that a velocity-based objective function can properly identify regional maximum contraction stresses, contraction rates, and relaxation rates simultaneously with intact model complexity. Experiments on synthetic data show that the parameters are better identified using the velocity-based objective function than its position-based counterpart, and the proposed framework is insensitive to initial parameters with the adopted derivative-free optimization algorithm. Experiments on clinical data show that the framework can provide personalized contractility parameters which are consistent with the underlying physiologies of the patients and healthy volunteers.

Cardiac motion estimation using a proactive deformable model: evaluation and sensitivity analysis

To regularize cardiac motion recovery from medical images, electromechanical models are increasingly popular for providing a priori physiological motion information. Although these models are macroscopic, there are still many parameters to be specified for accurate and robust recovery. In this paper, we provide a sensitivity analysis of a proactive electromechanical model-based cardiac motion tracking framework by studying the impacts of its model parameters. Our sensitivity analysis differs from other works by evaluating the motion recovery through a synthetic image sequence with known displacement field as well as cine and tagged MRI sequences. This analysis helps to identify which parameters should be estimated from patient-specific data and which ones can have their values set from the literature.

Computational Complexity Reduction for Volumetric Cardiac Deformation Recovery

Cardiac deformation recovery is to estimate displacements and thus strains of the myocardium from patient’s medical measurements, which can then be used to locate possible areas of cardiac diseases such as infarction. In order to properly couple a priori cardiac physiological models with measurements from medical images, different state-space based filtering algorithms have been proposed for physically meaningful and statistically optimal estimations with promising results demonstrated. Nevertheless, as the filtering procedures include matrix multiplications and inversions of dense matrices which sizes increase exponentially with the number of nodes representing the heart, the computational complexities of these algorithms are very large and thus their scalability and practicability are limited. In order to alleviate the computational requirements while minimizing the loss of accuracy, the mode superposition approach is adopted in this paper. Mode superposition transforms the origin cardiac system dynamics into a mathematically equivalent space spanned by shape vectors of different modes, with each mode representing a particular frequency of the displacements. As only relatively few frequencies are required for a good approximation of the system, many shape vectors can be discarded and results in a space of much lower dimension. With the proper transformations of the filtering components derived in this paper, the filtering procedures can then be performed in this space with largely reduced computational complexity. Experiments have been performed on synthetic data to show the benefits and costs of using the proposed framework, and also on a magnetic resonance image sequence to show its effects and performance on real data.