This paper presents a novel computer-aided modeling of 3D tissue scaffolds with a controlled internal architecture. The complex internal architecture of scaffolds is biomimetically modeled with controlled micro-architecture to satisfy different and sometimes conflicting functional requirements. A functionally gradient porosity function is used to vary the porosity of the designed scaffolds spatially to mimic the functionality of tissues or organs. The three-dimensional porous structures of the scaffold are geometrically partition into functionally uniform porosity regions with a novel offsetting operation technique described in this paper. After determining the functionally uniform porous regions, an optimized deposition-path planning is presented to generate the variational internal porosity architecture with enhanced control of interconnected channel networks and continuous filament deposition. The presented methods are implemented, and illustrative examples are presented in this paper. Moreover, a sample optimized tool path for each example is fabricated layer-by-layer using a micronozzle biomaterial deposition system.