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Thomas Howard

Abstract/Description

Alzheimer’s disease is a condition linked to plaque aggregation in the brain. Despite being the focus of many studies, current treatments are of questionable significance in the overall improvement of a patient’s condition. In recent years, computer models have been used to better understand complex biological systems and simulate the effects of various treatments. In the following paper we present a mathematical model studying the effects of plaque aggregation on the neuronal pathways of the human brain. To create our mathematical model we employ tools from the theory of dynamical systems and stochastic processes, and simulate the passage of a signal through a healthy and a plaque-affected brain. Moreover, our model simulates the increased resistance of the neuronal network to plaque disruption as a result of cognitive stimulation through learning and cerebral exercises, and measures the increased connectivity in a plaque-affected neuronal network when cognitive stimulation is present. Our mathematical model shows promise as a first step in modeling the complex interactions of plaque deposits in the human brain and studying the influence of behavioral treatments on Alzheimer patients.

Note on the Author

Thomas Howard graduated in May 2012 from BSU with a BS in Mathematics and is currently a graduate student earning an MS in Computer Science at BSU. This research was developed as part of an ATP Summer Research Grant under the direction of Dr. Irina Seceleanu. Tom presented his research at the Joint Mathematics Meeting, the largest annual mathematics meeting in the world, and at the National Conference on Undergraduate Research in the spring of 2012.

Rights Statement

Articles published in The Undergraduate Review are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.

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