SIGNATURE WORK
CONFERENCE & EXHIBITION 2024

Our research is based on the Partial Differential Equation (PDE) model of tumor growth, with a primary objective to investigate the stability or instability of tumor growth boundaries after perturbations. This research holds significant importance as prior studies have indicated that the regularity or irregularity of tumor boundaries serves as a crucial indicator of malignancy or benignancy. My focus lies in extending the previous 2D models to 3D, which is a significant step in modeling tumor growth. This extension holds meaningful implications for medical treatments in cancer by offering valuable predictions and insights. The transition to a 3D framework introduces complexities requiring advanced techniques such as spherical harmonics, modified Bessel functions, and hyperbolic trigonometric functions. We then apply perturbation methods and asymptotic analysis to explore the tumor boundary stability/ instability. Our findings are dependent on the tumor’s nutrient consumption rate; higher consumption rates increase susceptibility to instability. Additionally, the perturbation wave number plays a crucial role in determining stability. Furthermore, stability outcomes differ between in vitro and in vivo models due to distinct boundary conditions, emphasizing the influence of nutrient concentration distributions, consumption rates, and wave numbers on results. We are also exploring scenarios involving the necrotic core of the tumor, where we have the inner and outer boundaries.