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Modeling blood vessels and oxygen diffusion into brain tissue

Caldwell, Mark Alexander
http://rave.ohiolink.edu/etdc/view?acc_num=osu1565276066111476

Abstract Details

2019, Master of Mathematical Sciences, Ohio State University, Mathematics.
The delivery of oxygen by blood through blood vessels is a critical process that enables cells and tissue to maintain functionality. This thesis focuses on this process at a small scale in the body. In particular, it examines the flow of blood through capillaries in the brain and how that blood diffuses oxygen into the surrounding tissue. These two models, blood flow and oxygen diffusion, are modeled and the two models are coupled. Two different implementations of this coupled model are used to solve the partial differential equation (PDE). First, an implementation in MATLAB based on the Finite Element Method (FEM) was written for this paper. Additionally, an implementation in C++ is used which is based on Green’s Function Methods. This implementation was written by Secomb and can be found at github [3]. These implementations are used to examine oxygen transport and the effects of heterogeneity on it (differences in oxygen content of blood vessels that are close to each other). Heterogeneity tends to occur alongside diseases. We aim to show that this heterogeneity decreases the total oxygen in surrounding tissue. Additionally, we aim to show what the consequences of heterogeneity and the decrease in oxygen in the tissue would be on nearby neurons.
David Terman (Advisor)
Yulong Xing (Committee Member)
Biology; Computer Science; Mathematics
Blood Flow; Oxygen Transport; Oxygen Diffusion; Heterogeneity, Homogeneity

Recommended Citations

Citations

  • Caldwell, M. A. (2019). Modeling blood vessels and oxygen diffusion into brain tissue [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1565276066111476

    APA Style (7th edition)

  • Caldwell, Mark. Modeling blood vessels and oxygen diffusion into brain tissue. 2019. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1565276066111476.

    MLA Style (8th edition)

  • Caldwell, Mark. "Modeling blood vessels and oxygen diffusion into brain tissue." Master's thesis, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1565276066111476

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.