Mathematical Modeling of Biological and Biomedical Engineering Processes

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The PI will spend a year in the Program of Biomedical Engineering at her home institution, Louisiana Tech University, where she will work in two research areas while advising a PhD student in each area. The first project will integrate neuroscience, nano- and micro-technology engineering, mathematical modeling, and feedback control. Data sets of calcium ion dynamics will be the basis for mathematical analysis and modeling of brain cell network activity, to include development of a computational brain cell controller. As one of the most important secondary messengers in the body, calcium ions are involved in both intracellular and intercellular coordination. Mathematical model development of neuron dynamics will lay the foundation for design of a feedback controller to estimate calcium concentration in brain cells, which has the potential to further understanding of how the human body reacts to disorders of the brain and the predictive behavior of the brain.The second project will integrate nanotechnology engineering, mathematical modeling, and feedback control design. The mathematical modeling involved will result in the development of an accurate prediction of the amount of a nano-therapeutic agent that reaches a tumor site based on real-time estimates of drug bioavailability. This, in turn, will lay the groundwork for the design of a computational feedback controller that would be used to noninvasively measure and regulate drug concentration in the body. Although the current treatment of cancerous tumors can be very effective, there is no way of monitoring the therapy as it is being administered. In fact, the only way the amount of chemotherapy to be administered is determined by the patient's body mass. By joining together mathematical modeling and feedback control techniques, this project seeks to provide a mechanism for prediction of the effects of the nano-particle chemotherapy drugs in a patient's body, thus leading to better models for drug regimen and administration.