Introduction

The need for replacement organs and tissue substitutes is on the rise. At present, there is an insufficient amount of tissue replacements for failed or damaged organs, due to the lack of donors. In the USA alone, over twenty million patients per year suffer from some form of tissue- and/or organ-related malady, and are awaiting a replacement. The financial cost of health care for these patients has been estimated to be over $400 billion annually [1, 2]. Computer-aided tissue engineered substitutes are one of the most promising applications of tissue replacements to address this issue. These tissue arrays are fabricated using techniques from a variety of science and engineering disciplines to create the optimum tissue replacement (in terms of the targeted functionality). Additionally, these tissue constructs play a vital role as pre-formed extracellular matrices to which cells can readily attach, whereupon they can rapidly multiply and form new tissue [3, 4]. In recent decades, scientists have proven that these fields are evolving into one of the most promising therapeutic approaches in regenerative medicine [5–9].

Three-dimensional tissue scaffolds are designed with a preferred internal architecture, wherein porosity and material connectivity provide the required structural integrity, mass transport, and comprehensive microenvironment for cell and tissue growth. A literature survey has shown that cell survival and proliferation within the tissue scaffold are dependent on oxygen, vital molecules, and the micro-architecture of the scaffolds [10, 11]. The complexity of tissue scaffolds requires novel approaches and computational algorithms to match the desired criteria for internal architecture, permeability, pore size, and connectivity. The dynamics of a tissue scaffold is governed by its structural and topological configuration defined by porosity, pore interconnectivity, tortuosity, and scaffold material permeability and diffusivity [12–14]. The scaffold tortuosity characterizes the diffusion path length of fluid molecules through the scaffold, which shapes the internal architecture of the scaffold and plays a major role in tissue growth and proliferation [15–19]. Many cells respond more favorably to a three-dimensional (3D) microenvironment (than to a two-dimensional (2D) microenvironment) with intricate intracellular architectures where the cell’s morphological shape, behavior, and gene expression are richer, more robust, and more similar to in-vivo responses [20–22].