My graduate work is in multiscale modeling of microtubule and protein dynamics following neuronal axotomy. I am working with a variety of models including agent based models, Markov Chains models, and partial differential equations to describe known intracellular dynamics and investigate mechanisms hypothesized to support neuronal regeneration. Broadly, I am interested in mathematical biology research especially as it relates to human physiology. I am motivated by the application of mathematical techniques including modeling, dynamical systems, numerical simulations and analysis to problems in medicine and public health. I plean to pursue an industry based career in pharmaceutical and/or biotechnology development.
2. Epidemic Conditions with Temporary Link Deactivation on a Network SIR Disease Model,
with John Gemmer
Spora: A Journal of Biomathematics (2021). 7: 72–85.
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network model in which individuals probabilistically deactivate connections to infected individuals and later reconnect to the same individuals upon recovery. To analyze this network model, a mean field approximation consisting of a system of fourteen ordinary differential equations for the number of nodes and edges is developed. This system of equations is closed using a moment closure approximation for the number of triple links. By analyzing the differential equations, it is shown that, in addition to force of infection and recovery rate, the probability of deactivating edges and the average node degree of the underlying network determine if an epidemic occurs.
pdf arXiv 1. Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation,
with
Julia Arciero,
Brendan Fry, Amanda Albright, Grace Mattingly, Mandy Abernathy, Brent Siesky,
Alice Verticchio, Alon Harris
Photonics (2021). 8(10), 409.
Impaired blood flow and oxygenation have been implicated as contributors to many ocular pathologies including glaucomatous damage in the retina. In this study, a mathematical model is presented that combines an image-based heterogeneous representation of the retinal arteriolar vasculature with a compartmental description of the downstream capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model used to predict blood flow and oxygenation throughout the entire retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels and is conducted upstream to communicate the metabolic status of the retina to the arterioles. As expected, the model results indicate that a higher average metabolic signal is generated in pathways with a lower average oxygen level at the terminal arteriole. In addition, the model predicts a wide range of metabolic signals generated throughout the microvascular network, dependent both on oxygen levels and location within the network. For example, for a high level of oxygen demand, an approximately threefold range in metabolic signal is predicted in the terminal arterioles despite nearly identical PO2 levels. These results demonstrate that a whole-network approach that includes a spatially non-uniform structure is needed to yield an accurate description of the metabolic status of the retinal vasculature. This model provides the geometric and hemodynamic framework necessary to predict blood flow regulation in the human retina and will ultimately be used for early detection and treatment of ischemic and metabolic disorders of the eye.
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