Speaker: Luis J. Gomez
Affiliation: University of Michigan at Ann Arbor
Abstract: As we enter the era of personalized medicine, electromagnetic (EM) and wireless performance become increasingly essential to the control and functionality of implantable devices, imaging modalities, and non-invasive stimulation techniques. The optimal and patient specific performance of future biomedical technologies calls for co-design processes that involve computational scientists and applied mathematicians working alongside biomedical experts and system engineers to render informed decisions about features and tradeoffs in hardware and software, and their underlying algorithms.
I describe an innovative computational framework that I developed in close collaboration with medical scientists and bio-engineers for designing next-generation, patient-reconfigurable Transcranial Magnetic Stimulation (TMS) coil applicators. TMS is a noninvasive technique used both as a research tool for cognitive neuroscience and as a FDA-approved treatment for depression. TMS uses coils driven by low-frequency currents to magnetically induce fields inside targeted regions of the brain and disrupt neuronal function. My design framework integrates a new integral equation (IE) solver with high dimensional model reduction (HDMR), uncertainty quantification (UQ) and Pareto optimization techniques.
- The new IE solver permits the fast forward analysis of TMS-induced EM fields in inhomogeneous media. It uses a new volume/Lippmann-Schwinger and surface IE construct that unlike all its predecessors results in well-conditioned systems of equations in both the high-contrast (HC) and low frequency (LF) limit. To achieve these properties boundary elements are introduced on interfaces between media with strongly disparate material properties and integral operators are judiciously combined to cancel out hypersingular terms that are responsible for the HC and LF breakdown phenomena that plague conventional formulations. The solver has many uses beyond TMS, and already has been applied to the analysis of MRI imaging modalities, neuromuscular therapies, and negative permittivity plasmas.
- Hybridization of this EM solver with HDMR methods allows for the quantification of uncertainty in TMS observables due to system setup and patient variability. This UQ study identified important contributors to TMS uncertainty and proposals for procedural refinements to limit variability in coil location and orientation.
- Finally, the EM solver was coupled with a Pareto genetic algorithm technique for designing TMS coil arrays that generate fields that penetrate the brain 3x deeper than existing ones (patent pending). Experimental validation of the coil performance is in progress.
Time permitting, I will discuss the mapping of the above design philosophy and computational technology onto other emerging applications.
Biography: Luis J. Gomez is a Post-doctoral Fellow at the Radiation Laboratory, University of Michigan at Ann Arbor, Ann Arbor, Michigan, where he is currently developing fast-integral equation methods for analyzing scattering by highly-heterogeneous media, uncertainty quantification methods and inverse scattering methods. He received his B.S. degrees in electrical engineering and mathematics from the University of Florida, Gainesville, Florida, in 2008, and M.S. degrees in electrical engineering and applied math and Ph.D. degrees in electrical engineering, from the University of Michigan, Ann Arbor, in 2014 and 2015, respectively. In 2008, Dr. Gomez was the recipient of the National Science Foundation Graduate Fellowship (NSF-GRFP).
Date(s) - Apr 18, 2016
11:00 am - 12:15 pm
EE-IV Shannon Room #54-134
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095