Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Young's modulus and compression loading acting on the scaffold upper surface.Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Young's modulus are preferable.The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.

Functionally Graded Scaffolds (FGSs) are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young’s modulus values. For each combination of these variables, the explicit equation of the porosity distribution law–i.e the law that describes the pore dimensions in function of the spatial coordinates–was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards optimizing geometry of functionally graded scaffolds based on mechanobiological criteria.

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The aims of this study were to analyse the stress distribution developing around an orthodontic miniscrew (OM) inserted into the maxilla and to determine the stress field changes for different screw lengths and for different levels of osseointegration occurring at the bone/screw interface. An integrated experimental/numerical approach was adopted. Using the photoelastic technique, the stress field arising in the bone after screw insertion and the application of the initial orthodontic load was assessed. The finite element (FE) method was used to determine the stress acting in the bony tissue after a given time following screw application, when, for the viscoelastic relaxation effects, the only stress field remaining was that due to the application of the orthodontic load. Different levels of osseointegration were hypothesized. Photoelastic analyses showed that stress distribution does not change significantly for moderate initial orthodontic loads. From the FE simulations, it was found that critical conditions occur for screws 14 mm long with an orthodontic load of 2 N. The optimal screw length seems to be 9 mm. For such a dimension, small stress values were found as well as low risk of lesion to the anatomical structures.

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The zona pellucida (ZP) is an extracellular membrane surrounding mammalian oocytes. The so-called zona hardening plays a key role in fertilization process, as it blocks polyspermy, which may also be caused by an increase in the mechanical stiffness of the ZP membrane. However, structural reorganization mechanisms leading to ZP's biomechanical hardening are not fully understood yet. Furthermore, a correct estimate of the elastic properties of the ZP is still lacking. Therefore, the aim of the present study was to investigate the biomechanical behaviour of ZP membranes extracted from mature and fertilized bovine oocytes to better understand the mechanisms involved in the structural reorganization of the ZP that may lead to the biomechanical hardening of the ZP. For that purpose, a hybrid procedure is developed by combining atomic force microscopy nanoindentation measurements, nonlinear finite element analysis and nonlinear optimization. The proposed approach allows us to determine the biomechanical properties of the ZP more realistically than the classical analysis based on Hertz's contact theory, as it accounts for the nonlinearity of finite indentation process, hyperelastic behaviour and material heterogeneity. Experimental results show the presence of significant biomechanical hardening induced by the fertilization process. By comparing various hyperelastic constitutive models, it is found that the Arruda -Boyce eight-chain model best describes the biomechanical response of the ZP. Fertilization leads to an increase in the degree of heterogeneity of membrane elastic properties. The Young modulus changes sharply within a superficial layer whose thickness is related to the characteristic distance between cross-links in the ZP filamentous network. These findings support the hypothesis that biomechanical hardening of bovine ZP is caused by an increase in the number of inter-filaments cross-links whose density should be higher in the ZP inner side.

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