Speaker
Description
Colorectal cancer remains a major global health concern, and understanding the mechanisms of its progression is critical for advancing treatment and prevention strategies. In this presentation, we explore how PDE-based models can be applied to study tumor invasion and basement membrane dynamics, with an explicit focus on colorectal cancer. These models offer valuable insights into the interactions between tumor development and the surrounding tissue environment, providing insights into the complex mechanisms underlying cancer progression.
The colonic crypts, which are fundamental structures in the epithelial layer of the colon, play a critical role in regulating cell proliferation and differentiation. Disruptions to these processes can lead to the initiation and progression of colorectal cancer. In this context, mathematical modeling provides a powerful tool to examine the dynamics of tumor invasion, including how tumor development progresses and breaches the basement membrane, a key barrier in tissue architecture.This talk examines the application of partial differential equation (PDE) models to simulate tumor development and basement membrane dynamics at the crypt level in three dimensions. To address the complexities of colorectal cancer progression, we employ a combination of mathematical frameworks tailored to different aspects of the problem: diffuse-interface models to capture transitions between tumor and healthy tissue, geometry-tracking methods for evolving tumor boundaries, and mechanical models to represent the deformation and stresses within the crypt structure. Each framework addresses specific aspects of tumor dynamics, and their combination provides a more comprehensive representation of the underlying processes.
Preliminary simulation results will be presented, demonstrating how continuous mathematical models can capture the spatial progression of tumor development and the structural interactions with the basement membrane. These findings emphasize the role of crypt geometry and epithelial organization in shaping cancer dynamics. By calibrating model parameters, we aim to improve the predictive accuracy of these frameworks and enhance our understanding of tumor growth and invasion.
