Speaker
Description
The Cahn-Hilliard equation is used to describe the dynamics of two phases interacting across a thin region known as the interface. This framework naturally lends itself to the formulation of tumor growth models.
In this work we deal with parameter estimation for a phase-field model of tumor evolution coupled with nutrient dynamics. The mathematical model consists of a Cahn-Hilliard type equation describing the tumor phase field coupled with a diffusion equation for the nutrient concentration, including chemotactic effects and reaction terms. The resulting system captures key mechanisms such as tumor proliferation, nutrient consumption and chemotactic interactions.
The forward problem is solved numerically using isogeometric analysis with second order B-spline basis functions, which naturally provide the $C^1$ regularity required by the fourth-order operator appearing in the Cahn-Hilliard equation. Time integration is performed using a generalized-$\alpha$ scheme combined with Newton iterations to handle nonlinearities.
The inverse problem is formulated as a PDE-constrained optimization problem aimed at identifying model parameters from observed tumor configurations. The gradient of the objective functional is computed through sensitivity equations derived from the linearization of the governing system. The resulting optimization algorithm combines a weighted gradient descent and a quasi-Newton method with Gauss-Newton Hessian approximation.
The proposed framework provides a computational approach for calibrating phase-field tumor growth models and represents a step toward patient-specific simulations based on medical imaging data.