The objective of this research plan is to develop mathematical foundations and geometric computational algorithms to bio-mimetically model fully customized and complex three-dimensional (3D) heterogeneous (multi-material) structures with controlled material composition and distribution. The proposed work will be used to model active multi-functional porous structures with controlled micro-architecture to satisfy different and sometimes conflicting functional requirements.First, computational algorithms are proposed to optimally design multi-material with bio-active molecules spatially in porous structures. A new design methodology is proposed to relate material and bioactive distribution to 3D shape (geometry). The internal micro-architecture of porous structures is also optimized based on biological and mechanical requirements. Second, a novel bio-fabrication processed is proposed to fabricate designed multi-functional active porous structures with various biodegradable materials embedded with active bio-molecules directly from the computer models. The proposed methodologies will be applied to 3D tissue scaffolds. Cell migration into design 3D scaffold will be tested in-vitro to assess and optimize the proposed methodologies. The proposed methods will make more advanced active scaffold systems possible. These active multi-functional porous structures could be used to arrange cells in an appropriate 3D configuration and present molecular signals in a spatial and temporal fashion so that the individual cells will grow and form the desired tissue structures.The results from this research would enable use of active implants, tissue/organ substitutes and micro-scale bio-sensors in many new applications in medicine and biomedical engineering. This project will also advance the knowledge in heterogeneous object modelling in computer-aided design, layered-based fabrication methodologies and biomaterials.