Fractal-fractional partial differential models for plasma cell cancer progression

Abstract. Plasma cell cancer is a malignant blood cancer that develops in the bone marrow, affecting plasma cells and leading to abnormal
cell proliferation. Mathematical modeling provides a valuable approach
to understanding the dynamics of cancer growth and predicting disease
progression. In this study, a two-dimensional partial differential equation
(PDE) model was developed to simulate the temporal and spatial evolution of plasma cell cancer cells within the bone marrow. The model
incorporates parameters representing cell proliferation, diffusion, and interaction within the tissue environment. Numerical simulations allowing
visualization of how the cancer cell count changes over time and how
the overall tumor size expands. Results indicate a clear correlation between elapsed time and increased cancer cell density, demonstrating the
progressive nature of plasma cell. This study highlights the effectiveness of PDE-based modeling in capturing the spatiotemporal behavior
of cancer growth and provides a computational framework for future
research in predicting tumor development and evaluating potential therapeutic strategies. Using the box-counting method, the fractal dimension
of cancerous tissue can be quantified from digital images. Higher fractal
dimension values correspond to larger and more irregular cancer growth,
providing a measure of tumor size and progression.