Degree Name

Master of Arts (MA)

Semester of Degree Completion


Thesis Director

Suhrit K. Dey


T-Lymphocytes (T-cells), one of the many different lymphocytes, are the precursors of disease detection. Their primary purpose is to maintain a healthy immune system. They use the blood vasculature (blood stream) and lymphatic system to circulate throughout the body. Study of a T-cells journey throughout the human blood stream is useful to understand how they can detect disease, such as cancer, in an efficient and effective manner. T-cells are to be thought of as the good cells in our body searching to destroy the bad cells (cancer/infectious cells). The thymus lies in the anterior mediastinum, which is directly behind the breast plate. Initially T-cells migrate from bone marrow to the thymus so that they may proliferate, mature, and become immunocompetent. Once immunocompetent they leave and journey throughout the body to help fight disease.

It is assumed that with a greater velocity in the blood stream, T-cells will circulate throughout the body much more efficiently. Hence, surveillance by faster T-cells will promote rapid detection of cancer cells. A steady-state 3-dimensional model has been coded to analyze and simulate the velocity of T-cells in the blood stream. This model is based upon the Newtonian properties of blood plasma. The mathematical properties of this model resemble those of the Navier-Stokes equation with some extra force terms added. These force terms are controlled by Beta and Gamma. Beta is the measure of an individuals quality of health. Gamma is the amount of stress an individual is exposed to. Depending on these variables, the velocity of Lymphocytes in the blood stream will vary. In an effort to achieve a steady-state model, a technique called Perturbed Functional Iterations (PFI) has been implemented.