During my Ph.D. studies, I concentrated on numerical PDEs and boundary condition treatments for elastic and plastic deformations. The purpose of the research was to develop a method that allowed for using mature single-medium solvers to solve wave-propagation problems in complex media with heterogeneity. The ghost-solid method that I developed enabled the solution of wave propagation in discontinuous solids and resulted in publication of multiple high-impact journal articles. Since then, other groups have used this method to include various types of discontinuities in deformation studies.
During my first post-doctoral position at the National University of Singapore, I was the chief developer for a fluid-solid interaction software package that was used in the offshore oil and gas industry. We used finite element methods for both fluid and solid solvers. The intended problems were kilometer-long pipes subject to oceanic flows and had huge computational costs that demanded high-performance computing. Parallelization of the code was performed at the mutli-node level via MPI, and the code was further parallelized within each node using OpenMP to benefit from the multi-core structure of computer clusters. The development was carried out in a hybrid programming environment to utilize legacy linear solvers that were written in Fortran 77 and Fortran 90, with our implementation of the fluid and solid solvers written in C. This period of my career was a great experience in a fast-paced development environment that pushed me to use all my training in numerical PDEs, high-performance computing, physics, programming, and more to develop codes that could handle industry-standard problems. My work was presented at multiple conferences and I also co-authored a highly cited article on the origins of wake-induced oscillations in tandem cylinders published by the Journal of Fluid and Structures. The study utilized the same software package to carry out simulations that elucidated the physics of tandem oscillations.
Over the past five years, I have been able to use my background along with techniques in applied computational science to solve new physical problems. In particular, I have used my computational background to investigate a new and interesting area, cardiac dynamics. I have studied how the heart develops deadly arrhythmias and have been able to interact with clinicians and researchers at the FDA to identify how to improve heart modeling in support of developing drug therapies for arrhythmias and to design improved defibrillation methods. I have also worked on other areas including fractal structures and crystal growth, fluid flow around obstacles and modeling of lava flow down irregular terrains.
One of the most important highlights of my recent research is the development of a highly efficient library ``Abubu.js'' to solve partial differential equations interactively in irregular domains with GPU acceleration using WebGL 2.0 (see https://abubujs.org). This library allowed users for the first time to perform interactive simulations of detailed complex cardiac cell models in 2D and 3D tissue (solving on the order of 50-100 differential equations per cell) without a supercomputer. Cardiac disease remains the leading cause of death in the US and globally, and this research is allowing us as well as many clinicians and research groups to perform studies of cardiac arrhythmias with local PCs, thereby enabling smaller and newer groups to compete with large established groups. In fact, several groups around the world are now developing codes for studying heart arrhythmias using this library, and I am collaborating with many of them. For example, with the aid of Abubu.js, I am currently working with the FDA to develop augmented reality (AR) and virtual reality (VR) platforms for ‘near real-time’ whole-heart computer simulations. Such developments are necessary for the FDA to have early concrete and in-depth working knowledge of innovative technology to enable them to formulate regulatory guidelines that ensure efficacy and safety in clinical research studies and medical device submissions involving AR/VR applications. My work with the FDA has led to a joint NSF grant award to expand on this project and to ensure that the FDA has a scientifically rigorous framework for evaluating computational modeling-based studies and devices submitted. Another example is my collaboration with members of the computer science department at Oxford University, in which we are developing an XML interface to the abubu.js library to be able to import and simulate the hundreds of biological cell models continuously added to the CellML repository (https://models.cellml.org). This integration allows not only cardiac cell models to be more accessible but also many other biological models including ones for gene regulation, neurobiology, immunology and other physiological processes.
While much of my interest lies in utilizing new methodologies combined with developing robust numerical methods to solve complex problems, I also have a strong interest in applying them for basic research. For example, I have used some of the high-performance WebGL codes I have developed along with the Abubu.js library to investigate pro-arrhythmic effects of the drugs hydroxychloroquine and azithromycin used experimentally to treat COVID-19. Because of the larger concentrations, almost an order of magnitude larger, used for COVID-19, clinicians have been worried of possible arrhythmic effects. We were able to use a combined approach of experiments with numerical simulations to show (in a recent publication and a second one currently under review) that there is indeed a pro-arrhythmic effect at the new dosages used and to describe a cellular mechanism that explains some of the arrhythmic effects already observed in several clinical studies.
Similarly, using these codes, we have been able to understand from a topological point of view how defibrillation actually works when a strong electric field is delivered to the heart. In a manuscript under review, we show the characteristics of a successful defibrillation shock and describe how to design a single low-energy defibrillation shock that can terminate all the complex waves driving the arrhythmia. We have successfully tested this method in a large number of models and expect to test it in experiments soon. I believe this method will lead to new and improved strategies for low-energy defibrillation.
Since the Abubu.js library has established the ground work for solving PDEs quickly and interactively, I have also been able to apply it to other areas including fractal structures, crystal growth, and fluid flow around obstacles. I am also currently involved in fast simulations of air flow around insect and bird wings. Such tools and numerical methods have applications in fundamental and applied research ranging from basic understanding of the physics of the problem to industrial applications with fast, accurate and realistic simulations that can be used in aerodynamic, offshore and oceanic engineering designs.