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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Modeling Vascular Diffusion Of Oxygen In Breast Cancer, Tina Giorgadze
Modeling Vascular Diffusion Of Oxygen In Breast Cancer, Tina Giorgadze
Senior Projects Spring 2023
Oxygen is a vital nutrient necessary for tumor cells to survive and proliferate. Oxygen is diffused from our blood vessels into the tissue, where it is consumed by our cells. This process can be modeled by partial differential equations with sinks and sources. This project focuses on adding an oxygen diffusion module to an existing 3D agent-based model of breast cancer developed in Dr. Norton’s lab. The mathematical diffusion module added to an existing agent-based model (ABM) includes deriving the 1-dimensional and multi-dimensional diffusion equations, implementing 2D and 3D oxygen diffusion models into the ABM, and numerically evaluating those equations …
Simulating An Immune Response With A Combined Agent-Based Model Of A Triple-Negative Breast Cancer Tumor And Vascular Network, Michael J. Ventoso
Simulating An Immune Response With A Combined Agent-Based Model Of A Triple-Negative Breast Cancer Tumor And Vascular Network, Michael J. Ventoso
Senior Projects Fall 2019
Cytotoxic T-cells (CTLs) are one mechanism the immune system employs to eliminate cancer cells. In this study, I expand upon a previous 3-dimmensional agent-based model of triple-negative breast cancer to include a therapy simulating an immune response in the form of a CTL insertion into the tumor. The model consists of the tumor, comprised of progenitor cells, cancer stem cells, and tumor-associated macrophages, as well as an expanding vascular network. I investigate the effects of inserting different amounts of CTLs into the space, and their effect on tumor size in the short and longer terms. The results show that while …
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
Senior Projects Spring 2018
Mathematical models are finding increased use in biology, and partuculary in the field of cancer research. In relation to cancer, systems of differential equations have been proven to model tumor growth for many types of cancer while taking into account one or many features of tumor growth. One feature of tumor growth that models must take into account is that tumors do not grow exponentially. One model that embodies this feature is the Gomperts Model of Cell Growth. By fitting this model to long-term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor …