## 3 Transport and Flow Modeling  
Fluid circulation, transport of nutrients, and waste removal are essential processes that must take place inside the scaffold microstructure in a successful BTE product. In fact, vascularization, i.e., invasion of blood vessel and formation of new vasculature, is one of the main drawbacks in tissue engineering [75]. Moreover, fluid percolation and circulation is important as well in vitro in BTE assisted by bioreactors. Therefore, flow mechanics and diffusion mechanisms have been theoretically modeled and simulated during design of BTE scaffolds. Permeability is an overall parameter that (macroscopically) condenses the information about how a fluid penetrates in a porous medium. It is a clear design parameter in BTE scaffolds. Scaffold permeability has been measured experimentally in several papers using pumped water [76; 77], with a gravity-induced pressure using water [78; 79; 80] or using compressed air [81], to cite a few. Indeed, permeability was numerically validated using the homogenization theory versus an experimental gravity-induced pressure setup, for a specific commercial scaffold for BTE applications [27]. In the same context, [PERSON] et al. [82] validated the permeability values of Ti6 Al4V scaffolds using CFD simulations. An interesting study [83] obtained the permeability of simulated cancellous bone structure  
Figure 2: Multiscale computer simulation in BTE to predict new bone tissue growth in a unit cell of a predefined scaffold microstructure. (**a**) CT reconstruction of a rabbit femur, (**b**) model of the femur, scaffold implantation, loads and boundary conditions, (**c**) detailed mesh of the model, (**d**) unit cell microstructure of the scaffold solid domain, and (**e**) unit cell microstructure of the scaffold fluid domain. Reprinted with permission from [69]. by means of CFD analyses over a unit cell of the scaffold. Results concluded which waste best-suited scaffold microarchitecture for BTE in terms of blood circulation inside the microstructure. The study presented in [84], see Figure 3, shows a CFD analysis over a complex non regular microstructure of a poly(\(\iota\)-lactic acid) scaffold. The microstructural geometry was obtained by microCT and results analyzed both the permeability parameter as well as the wall shear stress, which is an important mechanobiological output as a mechanical stimulus [39], as seen before. The experimental results validated the simulations in the referred work. Similar studies were conducted for irregular pore geometries and regular ones [41; 46]. Homogeneous fluid flow distribution was found for irregular microstructures, in contrast to regular ones, due to irregular interconnection between the pores [85]. On the other hand, diffusion and transport of nutrients have been simulated in the design of scaffold microstructure. The macroscopic diffusivity of porous scaffolds, as an analogy to Darcian permeability, was analyzed as a function of the pore microarchitecture [68]. These results were used in a full multiscale model accounting for microstructural growth and resorption, and subsequent macroscopic evolution. [PERSON] et al. [86] showed finite element simulations of the diffusion and evolution of oxygen concentration along the interior of regular scaffold microstructures. The evolution of tissue growth coupled with nutrient supply and also including mechanistic effects has been mathematically modeled mostly for in vitro (bioreactor) conditions. In particular, [PERSON] et al. [87] proposed a continuum and multiphasic model including scaffold, cells, and water (medium) as the main phases. The model was applied to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. This model was extended in [88]. A similar approach, which includes coupling between tissue growth and nutrients consumption, was proposed in [89].