Mathematical Theory and Numerical Methods for Microscale Biomedical Devices

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The Investigator and his colleagues study new activematerials and their possible use in micro-electro-mechanicalsystems (MEMS) for biomedical applications. The research projectis motivated by the biomedical revolution based on the use ofemerging materials and emerging mathematical methods of analysisand simulation for applications to noninvasive surgery and drugdelivery at nanoscale to milliscale. The work concerns the use ofsmall scale actuators based on smart materials, especiallyshape-memory and magnetostrictive materials. They study thegrowth of tissue on materials and the interactions withsurrounding tissue and biological fluids, as well as noveldesigns of actuator systems. They consider remote actuationbased on the use of a magnetic field applied external to thebody, and they explore the possible use of MRI. New active materials --- materials that can change shapeunder moderate stimuli, for example --- hold great promise forbuilding MEMS (micro-electro-mechanical systems) for a variety ofapplications. Opportunities in biomedical applications areparticularly intriguing; they include noninvasive surgery anddrug delivery at nanoscale to milliscale lengths. This project isaimed at biomedical MEMS based on the use of new activematerials. The investigators study the properties of activematerials, the behaviors of MEMS that could be built with them,and the interactions between the materials and surroundingbiological tissues and fluids. The work requires new mathematicalmethods of analysis and simulation. Investigators focus on theuse of small scale actuators based on shape-memory and emergingferromagnetic shape-memory materials, energized by a remotelyapplied magnetic field. They study the growth of tissue on thematerials and materials interactions with the elastoviscoussurrounding tissue, as well as novel designs of actuator systemsbased on molecular beam epitaxial growth of films. The use ofMRI for simultaneous imaging and actuation is explored.