Histomorphometry-based modeling and simulation of multiple myeloma bone disease

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.