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A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.
Bone fracture healing is a complex process which is still under research. Computer-aided patient-specific prediction of bone development, fracture risk, prevention and treatment approaches promises a significant milestone in clinical practice. With this long-term goal in mind, a novel model is presented and examined in this work in the context of continuum bone remodelling. Therein, a clear distinction is made between external mechanical stimulation and the biological healing process of an injured bone tissue. The model is implemented within a finite element framework and investigated for the example of a fractured proximal femur head. The results show promising perspectives for further application. Besides, the model offers the possibility of easily integrating other factors like age-dependency and the availability of nutrition. For the future, further studies with large clinical datasets are essential for validation.
Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution.
This manuscript aims at a particular (simple) geometrically nonlinear formulation of poromechanics which is inspired by the format of thermo-mechanics. Thereby the motivation is two-fold: the formulation allows, on the one hand, to design a non-dissipative version of poro-elasticity as opposed to the classical dissipative Darcy-type version and, on the other hand, to derive and analyse the configurational setting
of poro-mechanics in an easy and transparent fashion. Thus, this contribution intends to alleviate studies of defects and fracture in two-phase solid/fluid mixtures based on the concepts of configurational mechanics.
We propose a novel two-scale (meso-macro-scale) approach to computationally capture cancellous bone remodelling allowing for efficient and effective numerical implementation. Therein, the macro-scale is governed by the well-established kinematics and kinetics of one-scale continuum bone remodelling. However, the constitutive behaviour is not postulated phenomenologically at the macro-scale, but rather follows from the meso-scale. There, for the sake of computational efficiency, the trabecular architecture is idealised as a truss network with the cross-sectional area of the trabeculae adapting to mechanical loading. Then, the meso- and the macro-scale are coupled through up- and down-scaling. Computational results on benchmark problems from bio-mechanics demonstrate that the proposed two-scale approach is effective from a modelling perspective and efficient from a computational perspective. In particular, it automatically captures anisotropy resulting from the irregular trabecular architecture at the meso-scale, and, most importantly, enables the direct investigation of different trabecular structures at the meso-scale, thereby serving as a virtual “magnifiying glass”. As an outlook, the proposed two-scale approach to cancellous bone remodelling provides an excellent launch pad for further extension, e.g., by considering more complex trabecular architectures and/or through inclusion of micro-scale bone cellular activities.
Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.
Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach toward continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics.
Remodelling of cancellous bone due to the combined activity of osteoclasts and osteoblasts at the cellular scale has notable repercussions both at the meso (tissue) as well as the macro (organ) scale. At the meso scale, trabeculae adapt their geometry, typically in terms of their cross section, whereas the nominal bone density evolves at the macro scale, all in response to habitual mechanical loading and its perturbations. To capture this intricate scale coupling, we here propose a novel conceptual three-scale approach to the remodelling of cancellous bone. Therein, we combine a detailed bone cell population model at the cellular scale with an idealised trabecular truss network model with adaptive cross sections, that are driven by the cell population model, at the meso scale, which is eventually upscaled to a continuum bone density adaption model at the macro scale. Algorithmically, we solve the meso and macro problems concurrently within a finite element setting and update the cell activity in a staggered fashion. Our benchmark simulations demonstrate the applicability and effectivity of the three-scale approach to analyse bone remodelling in health and disease (here exemplified for the example of osteoporosis) with rich details, e.g. evolving anisotropy, resolved at each scale.