Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Influence of intramedullary pressure on Lacuno-Canalicular fluid flow: A systematic review

While most of current models investigating bone remodelling are based on matrix deformation, intramedullary pressure also plays a role. Bone remodelling is orchestrated by the Lacuno-Canalicular Network (LCN) fluid-flow. The aim of this review was hence to assess the influence of intramedullary pressure on the fluid circulation within the LCN. Three databases (Science Direct, Web of Science, and PubMed) were used. The first phase of the search returned 731 articles, of which 9 respected the inclusion/exclusion criteria and were included. These studies confirm the association between intramedullary pressure and fluid dynamics in the LCN. Among the included studies, 7 experimental studies using animal models and 2 numerical models were found. The studies were then ranked according to the nature of the applied loading, either axial compression or direct cyclic intramedullary pressure. The current review revealed that there is an influence of intramedullary pressure on LCN fluid dynamics and that this influence depends on the magnitude and the frequency of the applied pressure. Two studies confirmed that the influence was effective even without bone matrix deformation. While intramedullary pressure is closely associated with LCN fluid, there is a severe lack of studies on this topic. STATEMENT OF SIGNIFICANCE: Since the 1990's, numerical models developed to investigate fluid flow in bone submicrometric porous network are based on the flow induced by matrix deformation. Bone fluid flow is known to be involved in cells stimulation and hence directly influences bone remodeling. Different studies have shown that intramedullary pressure is also associated with bone mechanosensitive adaptation. This pressure is developed in bone due to blood circulation and is increased during loading or muscle stimulation. The current article reviews the studies investigating the influence of this pressure on bone porous fluid flow. They show that fluid flow is involved by this pressure even without bone matrix deformation. The current review article highlights the severe lack of studies about this mechanism.

A lumped model for long bone behavior based on poroelastic deformation and Darcy flow

The present paper provides a simplified model for compact bone behavior by accounting for bone fluid flow coupled to the elasticity of the porous structure. The lumped model considers the bone material as a layered poroelastic structure and predicts normal pressure versus displacement, i.e, a stress-strain curve. There is a parametric dependency on porosity and permeability but, in addition, on pressure history. Specifically, the pressure impulse (the integral of pressure versus time) plays a key role. This factor is alluded to in several past studies, but not highlighted in a simplified fashion. Based on a global flow balance, bone displacement depends on the fluid flow in a channel according to the classical Darcy model of 1856, and on the rate of change of fluid within the porous solid according to the 1941 classical model of Biot. The present results agree with those of Perrin et al. which, in turn, agree with results of a detailed numerical simulation.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

Effect of saturation on the viscoelastic properties of dentin

This paper focuses on the analysis and quantitative characterization of the effect of saturation on the viscoelastic properties of human root dentin. Uniaxial compression tests under creep conditions have been performed on root molar dentin with tubules fully saturated with a viscous physiological fluid, as well as samples with non-saturated tubules (dry dentin samples). Blair-Rabotnov (BR) fraction-exponential model is used to characterize the overall viscoelastic properties of dentin and correlate them to the level of saturation. Experimental data are compared with theoretical predictions that interrelate the viscoelastic properties of saturated and dry specimens. The results show that saturation increases the viscous creep strains of dentin, which indicates a reduced capacity for stress relief. The uniaxial compression test under creep conditions, in combination with the BR kernel model, allows us to analyze the creep-relaxation behavior of dentin.

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.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.