Advances in Computational Techniques for Bio-Inspired Cellular Materials in the Field of Biomechanics: Current Trends and Prospects.

Cellular materials have a wide range of applications, including structural optimization and biomedical applications. Due to their porous topology, which promotes cell adhesion and proliferation, cellular materials are particularly suited for tissue engineering and the development of new structural solutions for biomechanical applications. Furthermore, cellular materials can be effective in adjusting mechanical properties, which is especially important in the design of implants where low stiffness and high strength are required to avoid stress shielding and promote bone growth. The mechanical response of such scaffolds can be improved further by employing functional gradients of the scaffold's porosity and other approaches, including traditional structural optimization frameworks; modified algorithms; bio-inspired phenomena; and artificial intelligence via machine learning (or deep learning). Multiscale tools are also useful in the topological design of said materials. This paper provides a state-of-the-art review of the aforementioned techniques, aiming to identify current and future trends in orthopedic biomechanics research, specifically implant and scaffold design.

Computationally modelling cell proliferation: A review.

Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.

Computational simulation of cellular proliferation using a meshless method.

BACKGROUND AND OBJECTIVE: During cell proliferation, cells grow and divide in order to obtain two new genetically identical cells. Understanding this process is crucial to comprehend other biological processes. Computational models and algorithms have emerged to study this process and several examples can be found in the literature. The objective of this work was to develop a new computational model capable of simulating cell proliferation. This model was developed using the Radial Point Interpolation Method, a meshless method that, to the knowledge of the authors, was never used to solve this type of problem. Since the efficiency of the model strongly depends on the efficiency of the meshless method itself, the optimal numbers of integration points per integration cell and of nodes for each influence-domain were investigated. Irregular nodal meshes were also used to study their influence on the algorithm. METHODS: For the first time, an iterative discrete model solved by the Radial Point Interpolation Method based on the Galerkin weak form was used to establish the system of equations from the reaction-diffusion integro-differential equations, following a new phenomenological law proposed by the authors that describes the growth of a cell over time while dependant on oxygen and glucose availability. The discretization flexibility of the meshless method allows to explicitly follow the geometric changes of the cell until the division phase. RESULTS: It was found that an integration scheme of 6 × 6 per integration cell and influence-domains with only seven nodes allows to predict the cellular growth and division with the best balance between the relative error and the computing cost. Also, it was observed that using irregular meshes do not influence the solution. CONCLUSIONS: Even in a preliminary phase, the obtained results are promising, indicating that the algorithm might be a potential tool to study cell proliferation since it can predict cellular growth and division. Moreover, the Radial Point Interpolation Method seems to be a suitable method to study this type of process, even when irregular meshes are used. However, to optimize the algorithm, the integration scheme and the number of nodes inside the influence-domains must be considered.

Load adaptation through bone remodeling: a mechanobiological model coupled with the finite element method.

This work proposes a novel tissue-scale mechanobiological model of bone remodeling to study bone's adaptation to distinct loading conditions. The devised algorithm describes the mechanosensitivity of bone and its impact on bone cells' functioning through distinct signaling factors. In this study, remodeling is mechanically ruled by variations of the strain energy density (SED) of bone, which is determined by performing a linear elastostatic analysis combined with the finite element method. Depending on the SED levels and on a set of biological signaling factors ([Formula: see text] parameters), osteoclasts and osteoblasts can be mechanically triggered. To reproduce this phenomenon, this work proposes a new set of [Formula: see text] parameters. The combined response of osteoclasts and osteoblasts will then affect bone's apparent density, which is correlated with other mechanical properties of bone, through a phenomenological law. Thus, this novel model proposes a constant interplay between the mechanical and biological components of the process. The spatiotemporal simulation used to validate this new approach is a benchmark example composed by two distinct phases: (1) pre-orientation and (2) load adaptation. On both of them, bone is able to adapt its morphology according to the loading condition, achieving the required trabecular distribution to withstand the applied loads. Moreover, the equilibrium morphology reflects the orientation of the load. These preliminary results support the new approach proposed in this study.

A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method.

Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach - the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.

Application of an enhanced homogenization technique to the structural multiscale analysis of a femur bone.

Bone is a complex hierarchical material that can be characterized from the microscale to macroscale. This work demonstrates the application of an enhanced homogenization methodology to the multiscale structural analysis of a femoral bone. The use of this homogenization technique allows to remove subjectivity and reduce the computational cost associated with the iterative process of creating a heterogeneous mesh. Thus, it allows to create simpler homogenized meshes with its mechanical properties defined using information directly from the mesh source: the medical images. Therefore, this methodology is capable to accurately predict bone mechanical behavior in a fraction of the time required by classical approaches. The results show that using the homogenization technique, despite the differences between the used homogeneous and heterogeneous meshes, its mechanical behavior is similar. The proposed homogenization technique is useful for a multiscale modelling and it is computationally efficient.

A new numerical approach to mechanically analyse biological structures.

In this work, an advanced discretization meshless technique is used to study the structural response of a human brain due to an impact load. The 2D and 3D brain geometrical models, and surrounding structures, were obtained through the processing of medical images, allowing to achieve a realistic geometry for the virtual model and to define the distribution of the mechanical properties accordingly with the medical images colour scale. Additionally, a set of essential and natural boundary conditions were assumed in order to reproduce a sudden impact force applied to the cranium. Then, a structural numerical analysis was performed using the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The obtained results were compared with the finite element method (FEM) and a solution available in the literature. This work shows that the NNRPIM is a robust and accurate numerical technique, capable to produce results very close to other numerical approaches. In addition, the variable fields obtained with the meshless method are much smoother than the FEM corresponding solution.

A Global Numerical analysis of the "central incisor/local maxillary bone" system using a meshless method.

In this work the maxillary central incisor is numerically analysed with an advance discretization technique--Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM permits to organically determine the nodal connectivity, which is essential to construct the interpolation functions. The NNRPIM procedure, based uniquely in the computational nodal mesh discretizing the problem domain, allows to obtain autonomously the required integration mesh, permitting to numerically integrate the differential equations ruling the studied physical phenomenon. A numerical analysis of a tooth structure using a meshless method is presented for the first time. A two-dimensional model of the maxillary central incisor, based on the clinical literature, is established and two distinct analyses are performed. First, a complete elasto-static analysis of the incisor/maxillary structure using the NNRPIM is evaluated and then a non-linear iterative bone tissue remodelling analysis of the maxillary bone, surrounding the central incisive, is performed. The obtained NNRPIM solutions are compared with other numerical methods solutions available in the literature and with clinical cases. The results show that the NNRPIM is a suitable numerical method to analyse numerically dental biomechanics problems.