Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

Experimental and computational analysis of energy absorption characteristics of three biomimetic lattice structures under compression

The objective of this study is to evaluate the mechanical properties and energy absorption characteristics of the gyroid, dual-lattice and spinodoid structures, as biomimetic lattices, through finite element analysis and experimental characterisation. As part of the study, gyroid and dual-lattice structures at 10% volume fraction were 3D-printed using an elastic resin, and mechanically tested under uniaxial compression. Computational models were calibrated to the observed experimental data and the response of higher volume fraction structures were simulated in an explicit finite element solver. Stress-strain data of groups of lattices at different volume fractions were studied and energy absorption parameters including total energy absorbed per unit volume, energy absorption efficiency and onset of densification strain were calculated. Also, the structures were characterized into bending-dominant and stretch-dominant structures, according to their nodal connectivity and Gibson-and-Ashby's law. The results of the study showed that the dual-lattice is capable of absorbing more energy at each volume fraction cohort. However, gyroid structures showed higher energy absorption efficiency and the onset of densification at higher strains. The spinodoid structure was found to be the poorest structure in terms of energy absorption, specifically at low volume fractions. Also, the results showed that the dual-lattice was a stretch dominated structure, while the gyroid structure was a bending dominated structure, which may be a reason that it is a better candidate for energy absorption applications.

Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design

Porous biomaterials design for bone repair is still largely limited to regular structures (e.g. rod-based lattices), due to their easy parameterization and high controllability. The capability of designing stochastic structure can redefine the boundary of our explorable structure-property space for synthesizing next-generation biomaterials. We hereby propose a convolutional neural network (CNN) approach for efficient generation and design of spinodal structure-an intriguing structure with stochastic yet interconnected, smooth, and constant pore channel conducive to bio-transport. Our CNN-based approach simultaneously possesses the tremendous flexibility of physics-based model in generating various spinodal structures (e.g. periodic, anisotropic, gradient, and arbitrarily large ones) and comparable computational efficiency to mathematical approximation model. We thus successfully design spinodal bone structures with target anisotropic elasticity via high-throughput screening, and directly generate large spinodal orthopedic implants with desired gradient porosity. This work significantly advances stochastic biomaterials development by offering an optimal solution to spinodal structure generation and design.

A morphological, topological and mechanical investigation of gyroid, spinodoid and dual-lattice algorithms as structural models of trabecular bone

In this study, we evaluate the performance of three algorithms as computational models of trabecular bone architecture, through systematic evaluation of morphometric, topological, and mechanical properties. Here, we consider the widely-used gyroid lattice structure, the recently-developed spinodoid structure and a structure similar to Voronoi lattices introduced here as the dual-lattice. While all computational models were calibrated to recreate the trabecular tissue volume (e.g. BV/TV), it was found that both the gyroid- and spinodoid-based structures showed substantial differences in many other morphometric and topological parameters and, in turn, showed lower effective mechanical properties compared to trabecular bone. The newly-developed dual-lattice structures better captured both morphometric parameters and mechanical properties, despite certain differences being evident their topological configuration compared to trabecular bone. Still, these computational algorithms provide useful platforms to investigate trabecular bone mechanics and for designing biomimetic structures, which could be produced through additive manufacturing for applications that include bone substitutes, scaffolds and porous implants. Furthermore, the software for the creation of the structures has been added to the open source toolbox GIBBON and is therefore freely available to the community.

Bone: An Outstanding Composite Material

Bone is an outstanding, well-designed composite. It is constituted by a multi-level structure wherein its properties and behavior are dependent on its composition and structural organization at different length scales. The combination of unique mechanical properties with adaptive and self-healing abilities makes bone an innovative model for the future design of synthetic biomimetic composites with improved performance in bone repair and regeneration. However, the relation between structure and properties in bone is very complex. In this review article, we intend to describe the hierarchical organization of bone on progressively greater scales and present the basic concepts that are fundamental to understanding the arrangement-based mechanical properties at each length scale and their influence on bone’s overall structural behavior. The need for a better understanding of bone’s intricate composite structure is also highlighted.

Inverting the structure-property map of truss metamaterials by deep learning

Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained on millions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10-20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Multiscale design of artificial bones with biomimetic elastic microstructures

Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.