Mathematical modeling and simulation of tissue engineering: A comprehensive study of nutrient flow, nutrient dynamics and scaffold elasticity

This dissertation explores the critical aspects of scaffold design in tissue engineering through a combination of elasticity, nutrient concentration, and network modeling. The first chapter presents an introduction to tissue engineering and the foundational concepts underlying this field, providing historical context and emphasizing the significance of tissue engineering for medical applications. This chapter also outlines the motivation for the study, focusing on the fundamental principles crucial to advancing scaffold design and mathematical modeling. It reviews essential concepts in nutrient transport, mechanical stress distribution, scaffold architecture, and mathematical tools, including Partial Differential Equations and the Laplacian matrix, which are pivotal for our research on optimizing scaffold environments for tissue regeneration. The second chapter investigate the effects of scaffold elasticity and nutrient concentration on cell proliferation within a single channel. Utilizing mathematical models, the research highlights how mechanical properties and nutrient availability significantly influence tissue growth. Chapter three extends this analysis to a network model, optimizing scaffold designs using a Random Geometric Graph (RGG) method. This model simulates nutrient flow, mechanical stress distribution, and cellular migration within scaffold pores, integrating fluid dynamics and elasticity principles to capture laminar flow and scaffold deformation. The findings underscore the pivotal role of scaffold architecture in promoting effective tissue regeneration. By providing a comprehensive analysis of single-channel and network models, this dissertation offers actionable insights for designing scaffolds that enhance tissue growth and regeneration.