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Multiple myeloma is a plasma cell cancer that leads to a dysregulated bone remodeling process. We present a partial differential equation model describing the dynamics of bone remodeling with the presence of myeloma tumor cells. The model explicitly takes into account the roles of osteoclasts, osteoblasts, precursor cells, stromal cells, osteocytes, and tumor cells. Previous models based on ordinary differential equations make the simplifying assumption that the bone and tumor cells are adjacent to each other. However, in actuality, these cell populations are separated by the bone marrow. Our model takes this separation into account by including the diffusion of chemical factors across the marrow, which can be viewed as communication between the tumor and bone. Additionally, this model incorporates the growth of the tumor and the diminishing bone mass by utilizing a ``moving boundary. We present numerical simulations that qualitatively validate our models description of the cell population dynamics.
Multiple myeloma (MM), a plasma cell cancer, is associated with many health challenges, including damage to the kidney by tubulointerstitial fibrosis. We develop a mathematical model which captures the qualitative behavior of the cell and protein pop
Mechanics has an important role during morphogenesis, both in the generation of forces driving cell shape changes and in determining the effective material properties of cells and tissues. Drosophila dorsal closure (DC) has emerged as a model system
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios
Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles, and predict the collective ce
Agent-based models have been employed to describe numerous processes in immunology. Simulations based on these types of models have been used to enhance our understanding of immunology and disease pathology. We review various agent-based models relev