Research Projects

Tissue engineering offers a transformative pathway to regenerate organs and biological structures, addressing the scarcity of viable donors and improving patient compatibility through scaffold-based tissue cultivation. Despite significant advances, experimental models remain costly and limited in clinical applicability. This project aims to bridge that gap by developing rigorous multiscale mathematical frameworks to analyze and predict tissue growth within engineered scaffolds, using homogenization techniques to upscale micro-scale interactions to effective macroscopic behavior. The research focuses on modeling biphasic mixture systems that treat biological tissues as deformable porous media. It proposes three distinct fluid-solid models—steady-state viscous-inviscid, one-way coupled, and two-way coupled dynamics—to analyze interphase interactions, nutrient transport, and tissue deformation. Each model is designed for increasing biological realism and mathematical complexity, involving systems of partial differential equations derived from continuum mechanics and poroelastic theory. The novelty lies in coupling analytical methods with homogenization (two-scale convergence and periodic unfolding) to extract effective parameters that inform scaffold design. A key innovation is the rigorous analysis of scaffold-mediated tissue growth under varied fluid-structure assumptions. This includes modeling flow and deformation in periodic fiber-hydrogel systems, resolving the existence and uniqueness of weak solutions, and generating numerical simulations mimicking bioreactor environments. Simulations, if time permits, will explore tumor shapes and scaffold geometries such as hollow fiber membrane constructs. Through this approach, the project will yield predictive insights into how microstructural features of scaffolds influence cellular behavior, nutrient dispersion, and macroscopic tissue mechanics. The interdisciplinary relevance is underscored by collaborations across mathematics, bioengineering, and clinical sciences, with potential applications in regenerative medicine, drug delivery, and tumor modeling. Dissemination plans include journal publications, conference presentations, educational modules, and public engagement via digital platforms. Long-term goals involve refining these models for clinical translation and integrating them into experimental frameworks at IIT Kharagpur's School of Medical Science and Technology. With expertise in PDE analysis, multiscale modeling, and biological physics, the PI and Co-PI bring methodological depth and academic leadership. The proposal’s strategic combination of mathematical rigor, simulation fidelity, and biomedical relevance positions it as a vital contribution to the advancement of computational tissue engineering.