Computational Biology, Geometric Modeling, Image Processing, Computational Geometry, Computer Graphics, Compression, Mesh Generation, Scientific Computation, and Visualization

My research interests span the algorithmic and mathematics underpinnings of Structural Biology and Biophysics, Image Processing, Geometric Modeling, Computer Graphics, and Visualization. Current research initiatives include (a) structure elucidation and reconstruction of spatially realistic models of molecules, organelles, cells, tissues, and organs, from electron microscopy, and bio-imaging, (b) fast high-dimensional search engine for identifying energetically favorable molecular binding conformations (e.g virtual screening for anti-viral drugs), and (c) integrated approaches to computational modeling, mathematical analysis and interrogative visualization, in particular, of the dynamics of electrical signaling and oscillations (3–10 Hz) amongst neurons in the hippocampus (the central area of learning and memory).

One of my principal research aims are to develop and implement efficient algorithms for determining structural features of macromolecules from 3D-EM (Electron Microscopy) maps at multiple resolutions, and for generating hierarchical, volumetric spline approximations of the determined structural features to facilitate fast Fourier based matching of geometry and imaging. My 3D EM biology collaborators in this endeavour are Dr. Manfred Auer, Lawrence Berkeley National Labs, Dr. Timothy Baker, Univ. of California San Diego, Dr. Joachim Frank of Columbia University, Dr. Steve Ludtke of Baylor College of Medicine, and Dr. Sriram Subramaniam, Center for Cancer Research, National Institutes of Health. The principal aims of another research project are to develop, implement and test novel mathematical algorithms that speed up computational protein-protein docking search and scoring, as well as to significantly improve the predictive models of inter-molecular recognition and electrodynamically dominated interactions. My collaborators here are Drs. Art Olson and Michael Sanner of The Scripps Research Institute, Professor Andrew McCammon of the University of California, San Diego, Professor Nathan Baker of Washington University St. Louis, and Professors Ron Elber and Peter Rossky of the University of Texas at Austin.

I also have a very active collaboration with Professors Kristen Harris and Dan Johnston of the UT Austin, Department of Neurobiology and the Institute of Learning and Memory (ILM) on developing multiscale biophysical models of structural plasticity in the hippocampus. We have undertaken a comprehensive approach to the computational (finite element) modeling, simulation, calibration of intrinsic electrical oscillations (3–10 Hz) in the hippocampus. using spatially realistic domain models of hippocampus CA1, CA3 neurons with their synaptic connections, reconstructed from serial section Transmission Electron Microscopy.

For the past four years Ive been involved in a multi-disciplinary NSF project “Dynamic Data-Driven System for Laser Treatment of Cancer,” with active collaboration with Professor Tinsley Oden and Jim Brown of the UT Austin Institute for Computational Engineering and Sciences, Prof. Ken Diller of Biomedical Engineering, and Dr. J. Hazle of MD Anderson Cancer Center,. The principal aim here is to develop a dynamic data-driven planning, control, and visualization system for the laser treatment of cancer. The proposed research includes development of a family of mathematical and computational models of bio-heat transfer, tissue damage, and tumor viability, dynamic calibration, verification and validation processes based protocols using model predictions.

I also collaborate actively with Professors Luis Caffarelli, John Luecke , Lexing Ying of the UT Austin Mathematics department , Professors Inderjit Dhillon and Tom Hughes of the Institute for Computational Engineering and Sciences, and Professors Alberto Paoluzzi and Antonio DiCarlo of the University of Roma, on a number of intertwined topics related to pure and applied geometry, and topology.

My research is currently sponsored by grants from the National Science Foundation (NSF) and the National Institutes of Health (NIH), and include

 
My research publications are available here, as is my Curriculum Vitae.