Date of Completion


Degree Type

Honors Thesis - Campus Access


Mathematics (MATH)

First Advisor

Robert Rovetti


Pancreatic beta cells are triggered to release insulin into the bloodstream by fast oscillations ("bursting") of their internal calcium (Ca), which can be mathematically modeled using a system of nonlinear ordinary differential equations. In the original Chay and Keizer model (1983), the dynamics of Ca depend on Ca currents flowing into and out of the cell, which are modified by changes in the cell's electrical potential (itself a function of Ca and potassium in the cell). Keizer and Magnus (1989) and Bertram and Sherman (2004) updated the model to include an ATP-sensitive potassium current as well as an internal Ca compartment (the endoplasmic reticulum).

However, none of these models account for changing levels of blood glucose (which is important, for instance, during a meal). Fridlyand and Philipson (2010) present modelling that connects the ADP/ATP ratio in the beta cells to blood glucose. We integrate their observations into the Bertram and Sherman model via a two-dimensional sigmoid function to establish a relationship between calcium bursting in pancreatic beta cells and glucose concentration. Through computer simulation, we demonstrate a bifurcation to periodic bursting behavior as glucose increases (and ADT/ATP decreases). We also find that there is a linear decreasing relationship between calcium conductance and the critical glucose concentration for the onset of bursting.

Our model can help us to better understand the dynamics of the body's insulin system, particularly in diabetic patients. It allows us to suggest ways to use drugs that alter channel conductance to ensure that beta cells will release enough insulin for a given dose of glucose.