Mathematical models and optimization methods in biomedical applications

Abstract

This thesis introduces computational design approaches for denture reinforcement and personalized drug delivery. The work focuses on three objectives: (1) strengthening dentures by using reinforcement material in critical regions; (2) simulating drug release profiles for arbitrary shapes by understanding the drug release mechanism; (3) optimizing drug material compositions to enable robust, erosion-driven release that produces specific target profiles.

Solid Isotropic Material with Penalization (SIMP)-based topology optimization involves material distribution via element-wise densities and penalizes intermediate values to produce solid–void solutions. In the reinforcement approach, SIMP is adapted to replace void regions with weak material to reinforce the denture. Computational design of the threedimensional (3D) reinforced dentures minimizes compliance and supports reinforcement fabrication within the field of prosthodontics.

Drug release mechanisms are complex; kinetic models such as Higuchi and Korsmeyer- Peppas characterize the drug mechanisms. These kinetic models are fitted to experimental data to obtain rapid mechanism insight. Under diffusion-release assumptions, two diffusion-driven models are fitted to the experimental data, and computational model parameters are estimated using maximum-likelihood methods. Building on this, a computational drug design method is introduced that specifies the optimal material compositions for a target release profile, assuming drug release via erosion. In the proposed design framework, the SIMP method is used for nonparametric structural optimization.

The simulations and proposed optimization methods contribute to economic (reduced costs), environmental (material efficiency), and social (patient-specific devices) sustainability, because the outputs enable the manufacture of personalized drugs and reinforceddenture designs.