Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

Hierarchical nanomechanics of collagen microfibrils

Collagen constitutes one third of the human proteome, providing mechanical stability, elasticity and strength to connective tissues. Collagen is also the dominating material in the extracellular matrix (ECM) and is thus crucial for cell differentiation, growth and pathology. However, fundamental questions remain with respect to the origin of the unique mechanical properties of collagenous tissues, and in particular its stiffness, extensibility and nonlinear mechanical response. By using x-ray diffraction data of a collagen fibril reported by Orgel et al. (Proceedings of the National Academy of Sciences USA, 2006) in combination with protein structure identification methods, here we present an experimentally validated model of the nanomechanics of a collagen microfibril that incorporates the full biochemical details of the amino acid sequence of the constituting molecules. We report the analysis of its mechanical properties under different levels of stress and solvent conditions, using a full-atomistic force field including explicit water solvent. Mechanical testing of hydrated collagen microfibrils yields a Young’s modulus of ≈300 MPa at small and ≈1.2 GPa at larger deformation in excess of 10% strain, in excellent agreement with experimental data. Dehydrated, dry collagen microfibrils show a significantly increased Young’s modulus of ≈1.8 to 2.25 GPa (or ≈6.75 times the modulus in the wet state) owing to a much tighter molecular packing, in good agreement with experimental measurements (where an increase of the modulus by ≈9 times was found). Our model demonstrates that the unique mechanical properties of collagen microfibrils can be explained based on their hierarchical structure, where deformation is mediated through mechanisms that operate at different hierarchical levels. Key mechanisms involve straightening of initially disordered and helically twisted molecules at small strains, followed by axial stretching of molecules, and eventual molecular uncoiling at extreme deformation. These mechanisms explain the striking difference of the modulus of collagen fibrils compared with single molecules, which is found in the range of 4.8±2 GPa or ≈10-20 times greater. These findings corroborate the notion that collagen tissue properties are highly scale dependent and nonlinear elastic, an issue that must be considered in the development of models that describe the interaction of cells with collagen in the extracellular matrix. A key impact the atomistic model of collagen microfibril mechanics reported here is that it enables the bottom-up elucidation of structure-property relationships in the broader class of collagen materials such as tendon or bone, including studies in the context of genetic disease where the incorporation of biochemical, genetic details in material models of connective tissue is essential

Biomedical modeling: the role of transport and mechanics

This issue contains a series of papers that were invited following a workshop held in July 2011 at the University of Notre Dame London Center. The goal of the workshop was to present the latest advances in theory, experimentation, and modeling methodologies related to the role of mechanics in biological systems. Growth, morphogenesis, and many diseases are characterized by time dependent changes in the material properties of tissues—affected by resident cells—that, in turn, affect the function of the tissue and contribute to, or mitigate, the disease. Mathematical modeling and simulation are essential for testing and developing scientific hypotheses related to the physical behavior of biological tissues, because of the complex geometries, inhomogeneous properties, rate dependences, and nonlinear feedback interactions that it entails

Cancellous bone and theropod dinosaur locomotion. Part II—a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single ‘characteristic posture’ for a given species—one in which bone continuum-level principal stresses best align with cancellous bone fabric—and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well

Continuum Modeling and Simulation in Bone Tissue Engineering

Bone tissue engineering is currently a mature methodology from a research perspective. Moreover, modeling and simulation of involved processes and phenomena in BTE have been proved in a number of papers to be an excellent assessment tool in the stages of design and proof of concept through in-vivo or in-vitro experimentation. In this paper, a review of the most relevant contributions in modeling and simulation, in silico, in BTE applications is conducted. The most popular in silico simulations in BTE are classified into: (i) Mechanics modeling and sca old design, (ii) transport and flow modeling, and (iii) modeling of physical phenomena. The paper is restricted to the review of the numerical implementation and simulation of continuum theories applied to di erent processes in BTE, such that molecular dynamics or discrete approaches are out of the scope of the paper. Two main conclusions are drawn at the end of the paper: First, the great potential and advantages that in silico simulation o ers in BTE, and second, the need for interdisciplinary collaboration to further validate numerical models developed in BTE.Ministerio de Economía y Competitividad del Gobierno España DPI2017-82501-