Honors Program


Document Type


Date of this Version

Spring 2021


Cruikshank, A. 2021. A Mathematical Model of Pancreatic Cancer Growth and Response to Treatment. Undergraduate Honors Thesis. University of Nebraska-Lincoln.


Copyright Allison Cruikshank 2021.


Pancreatic cancer is one of the leading causes of death due to cancer in the United States. Analyzing the effects of radiation is extremely valuable in determining when a patient is allowed surgical resection, which is, presently, the only potentially curative treatment for pancreatic cancer. This study examines pancreatic tumor growth and shrinkage to predict tumor response and change of resectability for pancreatic cancer patients undergoing radiation therapy. This is done using ordinary differential equations as a mathematical model. Mathematical models have increasingly been applied to various biological systems/processes to analyze the principles involved. In our project, a population dynamical model is used along with suitable assumptions to study the tumor growth, and the model parameters are carefully calculated from references. To model the tumor response under radiotherapy treatment, a linear- quadratic (LQ) model is incorporated with the tumor growth model. The coupled model is used to observe the mechanisms involved in pancreatic cancer growth and radioresistance. Numerical analysis of the model takes place using modeling soft- ware (MATLAB). We found that the implementation of higher doses of radiation in a smaller amount of fractions more effectively decreases the cancer cell size with and without a radioresistance factor.