Research Statement
Motivation: Advancing Biomedicine by the Power of Computing
Recent years’ extraordinary advances in computational modeling, computing power and imaging technologies have opened great opportunities for biomedical research, empowering scientists to integrate unprecedented complexity and realism in their exploration of biological mechanisms. Essential to this emerging research trend are two paradigms of computation: the forward problem of simulating a complex biomedical system, and the inverse problem of estimating or optimizing a given system. Both paradigms call for computational methods able to overcome the challenge posed by ever-increasing system complexity and data size. My research interests lie in computational modeling, estimation and optimization of the bioelectromagnetic phenomena arising from the heart, with the goal of fostering the understanding, diagnosis and treatment of cardiac functions and diseases.
My dissertation concentrates on inverse electrocardiography (ECG), which aims to noninvasively estimate cardiac electrophysiological activities from the potentials measured at the body surface. The essence of my work is a synergy of two themes: cardiac bioelectromagnetics, and inverse problems involving partial differential equations (PDEs). My research philosophy adheres to two principles: theoretical foundation and practical efficacy. I deeply believe that great computational research should not only exploit, and be rigorously founded on, advanced mathematical theories, but also create practical solutions driven by experimental data and beneficial to real-world scientific and clinical practice. In theory, my research on inverse problems assimilates works from functional analysis, PDEs, statistics and large-scale optimization. In practice, my computational research on cardiac bioelectricity features subject-specific, image-based modeling and simulation, closely coupled with electrophysiological animal experiments. To achieve this interdisciplinary goal, I have obtained in-depth training in quantitative electrophysiology, image processing, image-based geometric modeling, and scientific visualization. I also have experience in animal experiments, processing experimental data and integrating data into computer models. My diverse background enables me to appreciate both the needs of biomedical research and the development of computing technology, and prepares me to translate technological developments into breakthroughs in scientific discovery and clinical practice.
Past and Current Research
PDE-Constrained Optimization. A frontier in scientific computing research, PDE-constrained optimization refers to the optimization of systems described by partial differential equations (PDEs). I developed a general PDE-constrained optimization framework to solve the inverse ECG problems (cite). This work is the first systematic application of PDE-constrained optimization to realistic inverse ECG problems. My framework enables users to optimize nonlinear objectives, to incorporate physically-based constraints in various forms, and to customize the constraints to specific physical quantities or regions. PDE-constrained optimization typically poses great computational challenges because of the size and complexity of discretized PDEs, convolved with the need to solve PDEs many times. To better tackle these challenges, my work differs from previous optimization-related ECG studies in its rigorous separation of optimization from numerical discretization – I derive optimality conditions in function spaces before employing finite element methods for numerical solution. Such separation not only yields consistent multi-resolution optimization results, enables individualized discretization for each variable, but also allows users to adaptively discretize PDEs between nonlinear iterations. These features effectively improve both the inverse solutions and the computational efficiency.
PDE-constrained optimization will improve the solutions to many types of inverse problems in cardiac bioelectricity – one just needs to adjust the mathematical models of the given problem. I have applied this method to a previously-intractable task of localizing cardiac ischemic disease, which is presented below.
Noninvasive Localization Myocardial Ischemia. A practical contribution achieved by my inverse ECG research is in localizing myocardial ischemia, the main cause of heart attack and a disease of high socio-economic cost, caused by insufficient blood supply to the heart. Localizing ischemic regions from body-surface measurements is important for clinical treatment but has not been attained by present inverse ECG techniques. The challenge lies in achieving two often-conflicting goals: forming a bioelectric source model sophisticated enough to characterize ischemia, and inversely recovering this model. Traditional inverse ECG source models, such as activation isochrones or epicardial potentials, are oversimplified for representing ischemia. Ischemia simulation commonly uses the bidomain heart model, which is the most realistic yet tractable description of heart tissue, but due to the bidomain’s complexity its inverse estimation has seen limited progress. My contribution was advancing the inverse bidomain solution by pioneering the use of PDE-constrained optimization.
In collaboration with Dr. Rob MacLeod’s team at the Cardiovascular Research and Training Institute at University of Utah, our work is the first bidomain-based ischemia localization based on real anatomy and ischemia data, featuring a close synergy of animal experiments, image-based simulation and inverse estimation. The experiment involves suspending a live canine heart in a human-torso-shaped electrolytic tank, inducing controlled ischemia to the heart, and recording potentials simultaneously at the heart surface, in the heart wall, and at the torso surface. We constructed the heart geometry from MRI scans and extracted heart fiber structure from diffusion tensor imaging, through a pipeline involving image segmentation, tissue-interface generation by a particle system, and geometric modeling. We then combined the heart anatomy and the measured voltage data to create a realistic condition for our simulation and validation.
Our inverse simulation not only obtained promising results on ischemia localization, but also made the results consistent over multi-resolution simulation, enabling scientists to use heart models 10-50 times finer than previous inverse ECG studies.
Optimizing Finite Element Formulation for Inverse ECG Problems. Successful simulation needs sensible numerical formulation of model equations, especially for ill-conditioned inverse problems. I studied how to optimize the numerical formulation specifically for the inverse ECG problem when finite element methods are used, aiming at minimizing the degree of ill-conditioning and approximation error. This study was motivated by my research finding that traditional discretization refinement schemes are oriented toward best solving model equations, but may become inappropriate for solving the inverse problems associated with those equations. By using Fourier analysis to quantify how discretization influences the ill-conditioning of the inverse problem, I proposed a set of guidelines for optimally discretizing the heart, torso and other anatomical structures. To fulfill the guidelines I developed two refinement methods. The hybrid finite element method satisfies different discretization requirements by integrating various elements such as tetrahedra, prisms and hexahedra. The truncated high-order finite element method fulfills refinement by taking high-order basis polynomials, but allows users to locally specify the element order based on their need, by hierarchically decomposing each element’s polynomial space. The efficacy of both methods was validated by realistic simulations with real heart data.
Catheter-Based Endocardial ECG Mapping. Catheter-based endocardial mapping is a new diagnostic technique with increasing clinical use, particularly for guiding therapy for cardiac rhythmic disorders. This technique involves inserting a multi-electrode catheter array into a heart chamber via blood vessels, measuring intracavitary potentials, and reconstructing the endocardial surface potentials (the source) based on inverse solution to the Laplace’s equation. A crucial step in this technique is to make inverse solution robust to geometric errors, as both the chamber geometry and the electrode locations vary due to heart beat. Current inverse solutions are based on boundary element methods, which encounter numerical problems when the endocardial surface is either non-smooth or too close to the electrodes. Working as a technical consultant with Dr. Eric Voth at St. Jude Medical, I developed a new inverse solution method using PDE-constrained optimization implemented by a finite element method. My method resolves the non-smooth geometry problem, and outperforms the boundary-element inverse solutions by more flexibly enabling constraints. I also investigated how to optimize the placement of electrodes, applying my thesis research on inverse-solution-oriented discretization.