Document Type


Date of Degree

Spring 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Ayati, Bruce

First Committee Member

Camillo, Victor

Second Committee Member

Martin, James

Third Committee Member

Mitchell, Colleen

Fourth Committee Member

Stroyan, Keith


Multiple myeloma is a plasma cell cancer that affects the bones, immune system, and kidneys. In this thesis, we focus on the impact on the bone, specifically routine bone remodeling. The bone remodeling process is governed by chemical signaling between several cell populations. In multiple myeloma patients, this process is out of balance. Bone destruction outpaces bone replacement, leaving patients with bone lesions. We describe the cell-signaling network that regulates bone remodeling and explain how it is impacted by multiple myeloma. We then present a series of mathematical models describing the bone remodeling process. We lay a thorough mathematical foundation, starting with the derivation of Savageau's power law approximations. Next, we introduce a novel one-dimensional moving-boundary partial differential equation model of this biological system. Our model improves upon models from the literature by including new cell populations, specifically osteoclast precursors, stromal cells, and tumor cells. We also discuss the model's computational results and their significance. We then discuss image processing techniques that can be used on bone marrow biopsies to gather data on the growth of a multiple myeloma tumor. By analyzing these medical images, we can extract tumor cell counts. In particular, we give the results of such an analysis for one patient using color unmixing. Image processing techniques, such as the ones presented here, could be used for validation of the models we present. The long-term goal of this project is the creation of a diagnostic tool that will aid oncologists in selecting the best treatment plan for their patients with multiple myeloma.

Public Abstract

Cancer is a lot like a hurricane; you can see it coming, but you don't know exactly where it will go or how much damage it will do. However, by combining a mathematical model with patient data, we can predict how a patient's cancer will develop. This thesis focuses on multiple myeloma, a plasma cell cancer that disrupts the bone remodeling process. In multiple myeloma patients, bone destruction outpaces bone replacement, producing bone lesions. Here we describe biological factors that regulate the bone remodeling process. We then explain how this process is impacted by multiple myeloma. We give a thorough background of mathematical methods for representing this disease and we use these techniques to create a new model. We also describe mathematical tools that can be used to analyze patients' medical images. By analyzing these images, we can track the growth of the patient's tumor. The long-term goal of our work is the creation of a diagnostic tool that will aid oncologists in selecting the best treatment plan for their patients with multiple myeloma.


publicabstract, bone, modeling, myeloma, PDE


xi, 115 pages


Includes bibliographical references (pages 109-115).


Copyright 2016 Catherine Elizabeth Patterson