## 1 Introduction
Usually bone marrow stromal cells (BMSC), mesenchymal stem cells (MSC), or preosteoblasts are combined with bone morphogenetic proteins (BMP) or growth factors such as transforming growth factor-\(\beta\) (TGF-\(\beta\)), within porous scaffolds with the use of a bioreactor. In particular, BMSC-seeded ceramics were implanted in a large tibial defect in ewes [15]. Mechanical stability at the defect site was obtained either by an internal plate or by external fixation. Results show around 10% of bone volume to total volume regeneration. [PERSON] et al. [16] also presented the same tissue engineering strategy for segmental tibial defect in sheep, resulting in a progressive scaffold resorption coincident with new bone deposition [16]. A comparison of bone regeneration in rabbits among BMSC-harvested poly(lactide-co-glycolide) scaffolds, non-harvested ones, and without scaffolds was presented in [17]. The defect consisted of a unilateral femoral osteotomy gap created surgically under general anesthetic and stabilized by a mandibular reconstruction plate fixated with three screws on either side of the osteotomy site. The obtained results showed that there were no significant differences between the use of the scaffold alone and the cell-seeded scaffold although faster in this case. On the contrary, the non-scaffold strategy presented less regenerated tissue. Using biodegradable scaffolds as well, [PERSON] et al. [18] performed a trabecular-like, three-dimensional structure to repair bone. BMCS-preseeded scaffolds were implanted in a non-healing rabbit segmental bone defect achieving bony union within eight weeks. Biodegradable scaffolds medical-grade polycaprolactone-calcium phosphate (mPCL-CaP) seeded with BMSC were implanted under the skin of nude rats. It presented neo cortical and well-vascularized cancellous bone up to 40% of bone volume [19]. [PERSON] et al. [20] presented a study involving the use of poly-\(e\)-caprolactone scaffolds (PCL) loaded with BMSC and BMP-4. PCL without cells showed scarce bone formation and scaffold resorption, whereas PCL seeded with BMSC stimulated new tissue formation. In conclusion, the combination of BMSC with BMP-4 strongly favored osteoinductivity of cellular constructs. Bone tissue undergoes a piezoelectric effect such that bone cells are stimulated to remodel by means of an electrical filed, induced by a strain field, which recruits and aggregates macromolecules and ions in the extracellular matrix [21]. This feature has been exploited in bone tissue regeneration using piezoelectric scaffolds which mimic the natural collagen matrix, such as piezopolymers. The reader is referred to [22] for a review of piezoelectric scaffolds. Mathematical modeling and computer simulation have been demonstrated to be a powerful tool both in the design and evaluation stages of scaffolds in BTE applications. In the design phase, the mechanical properties (elasticity modulus, strength, toughness) and fluidic properties (diffusivity and permeability) are essential for the overall success of the scaffold. Moreover, the degradation properties and characteristics are also of interest for a certain BTE experiment. The overall behavior during implantation of BTE processes has also been simulated through the incorporation of biomechanical and mechanobiological theories. In the next sections, the state-of-the-art of continuum approaches and simulation of the referred BTE phenomena are reviewed. The new challenges, perspectives, and some conclusions are drawn at the end of the paper.