Editorial: Bone integrity in patients with osteoporosis: Evaluation of fracture risk and influence of pharmacological treatments and mechanical aspects

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Coupling systems biology with multiscale mechanics, for computer simulations of bone remodeling

Bone remodeling is a process involving removal of mature bone tissue and subsequent formation of new bone tissue. This process is driven by complex actions of biological cells and biochemical factors, and it is sensitive to the loads applied onto the skeleton. Herein, we develop a mathematical framework describing this process at the (macroscopic) level of cortical bone, by combining, for the first time, bone cell population kinetics with multiscale bone mechanics. Key variables are concentrations of biological cells (osteoclasts, osteoblasts and their progenitors) and biochemical factors (RANK, RANKL, OPG, PTH, and TGF-beta), as well as mechanical strains, both at the ("macroscopic") level of cortical bone and at the ("microscopic") level of the extravascular bone matrix. Multiscale bone mechanics delivers, as a function of the vascular porosity, the relation between the macroscopic strains resulting from the loads, and the microscopic strains, which are known to modulate, either directly, or via poromechanical couplings such as hydrostatic pressure or fluid flow, the expression or proliferation behavior of the biological cells residing in, or attached to the extravascular bone matrix. Hence, these microscopic strains enter the biochemical kinetics laws governing cell expression, proliferation, differentiation, and apoptosis. Without any additional phenomenologically motivated paradigm, this novel approach is able to explain the experimentally observed evolutions of bone mass in postmenopausal osteoporosis and under microgravity conditions: namely, a decrease of bone loss over time

Computational Modeling of Interactions between Multiple Myeloma and the Bone Microenvironment

Multiple Myeloma (MM) is a B-cell malignancy that is characterized by osteolytic bone lesions. It has been postulated that positive feedback loops in the interactions between MM cells and the bone microenvironment form reinforcing ‘vicious cycles’, resulting in more bone resorption and MM cell population growth in the bone microenvironment. Despite many identified MM-bone interactions, the combined effect of these interactions and their relative importance are unknown. In this paper, we develop a computational model of MM-bone interactions and clarify whether the intercellular signaling mechanisms implemented in this model appropriately drive MM disease progression. This new computational model is based on the previous bone remodeling model of Pivonka et al. [1], and explicitly considers IL-6 and MM-BMSC (bone marrow stromal cell) adhesion related pathways, leading to formation of two positive feedback cycles in this model. The progression of MM disease is simulated numerically, from normal bone physiology to a well established MM disease state. Our simulations are consistent with known behaviors and data reported for both normal bone physiology and for MM disease. The model results suggest that the two positive feedback cycles identified for this model are sufficient to jointly drive the MM disease progression. Furthermore, quantitative analysis performed on the two positive feedback cycles clarifies the relative importance of the two positive feedback cycles, and identifies the dominant processes that govern the behavior of the two positive feedback cycles. Using our proposed quantitative criteria, we identify which of the positive feedback cycles in this model may be considered to be ‘vicious cycles’. Finally, key points at which to block the positive feedback cycles in MM-bone interactions are identified, suggesting potential drug targets

A thermodynamics framework to describe bone remodeling: a 2D study

Introduction Bone is a living material which is continuously reorganized by bone cells in response to their mechanical and biochemical environment. This process, known as bone remodeling, is of major importance in everyday life, in case of fractures and to allow osseointegration phenomena around implants. Bone remodeling can be described as a stress- and chemistry-driven evolution of the mechanical properties of bone tissue. The interplay between mechanics and biochemistry, as well as the multiple scales involved in this process, represent serious challenges for the development of realistic bone adaptation models. This study describes a novel, thermodynamically sound model of bone remodeling which, while being mechanistic in nature, is able to account for the above issues.   Methods The theory of material remodeling [1] offers a firm basis to build a model of bone remodeling. Bone is described as an orthotropic elastic medium whose elastic properties evolve in time according to the prevailing mechanical and chemical stimuli. In this study, we focus on a special class of evolution, namely the stress-driven rotation of the elastic principal axes of the bony material. Our model is based on balance laws derived through a suitable statement of the virtual power principle, as well as the description of a constitutive theory. The latter is based on the definition of a strain-energy density depending only on the elastic strain, and on a formulation of the dissipation principle incorporating the dissipation due to remodeling. This modeling framework leads to a remodeling evolution law giving an explicit relationship coupling the dissipation related to the remodeling, the stress and strain tensors, the rotation of the material axes and its evolution. Remodeling equilibrium is achieved when material properties no longer evolve, corresponding to a stationary state of the rotation. It is worth noting that this model predicts the principal axes of the strain and stress tensors to be collinear at the remodeling equilibrium [2]. Thus, a physically sound condition for remodeling equilibrium [3] is recovered without any ad-hoc assumption.   Results and Discussion The model was studied in 2D where the rotation of the elastic principal axes is parameterized by an angle. In case of uniform stress/strain conditions, stable remodeling equilibrium states were found to correspond to strain energy minima (imposed displacements). Finite element simulations were also performed to study the evolution of the elastic principal axes resulting from different boundary conditions. The prediction of the rotation of the principal axes of the material in simple loading configurations is consistent with the superimposed boundary conditions confirming the ability of the model to simulate the material response to non-uniform stress configurations.   Conclusion A novel, thermodynamically sound model of bone remodeling was proposed. Preliminary results obtained in 2D are promising and show the potential of this approach. Model predictions for in vivo biomechanical loading configurations need to be further tested. Suitable experimental data will be identified. The particular case of tissue surrounding an implant will be also studied. Our model can also integrate the mechanobiological phenomena regulating bone remodeling. However, this would require a reliable description of the biochemical stimuli of bone remodeling. This matter is out of the scope of this paper and will be addressed in future works.   Acknowledgement This project has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation program (grant agreement No 682001, project ERC Consolidator Grant 2015 BoneImplant).   References [1] DiCarlo A, Naili S, and Quiligotti S (2006) C. R. Mecanique, 334:651-661 [2] Sansalone V, Naili S, and Di Carlo A (2011) Comput Methods Biomech Biomed Engin, 14(s1):203-204 [3] Cowin S (1986) J Biomech Eng, 108:83-8

Cortical Thickness Adaptive Response to Mechanical Loading Depends on Periosteal Position and Varies Linearly With Loading Magnitude

The aim of the current study was to quantify the local effect of mechanical loading on cortical bone formation response at the periosteal surface using previously obtained μCT data from a mouse tibia mechanical loading study. A novel image analysis algorithm was developed to quantify local cortical thickness changes (ΔCt.Th) along the periosteal surface due to different peak loads (0N ≤ F ≤ 12N) applied to right-neurectomised mature female C57BL/6 mice. Furthermore, beam analysis was performed to analyse the local strain distribution including regions of tensile, compressive, and low strain magnitudes. Student’s paired t-test showed that ΔCt.Th in the proximal (25%), proximal/middle (37%), and middle (50%) cross-sections (along the z-axis of tibia) is strongly associated with the peak applied loads. These changes are significant in a majority of periosteal positions, in particular those experiencing high compressive or tensile strains. No association between F and ΔCt.Th was found in regions around the neutral axis. For the most distal cross-section (75%), the association of loading magnitude and ΔCt.Th was not as pronounced as the more proximal cross-sections. Also, bone formation responses along the periosteum did not occur in regions of highest compressive and tensile strains predicted by beam theory. This could be due to complex experimental loading conditions which were not explicitly accounted for in the mechanical analysis. Our results show that the bone formation response depends on the load magnitude and the periosteal position. Bone resorption due to the neurectomy of the loaded tibia occurs throughout the entire cross-sectional region for all investigated cortical sections 25, 37, 50, and 75%. For peak applied loads higher than 4 N, compressive and tensile regions show bone formation; however, regions around the neutral axis show constant resorption. The 50% cross-section showed the most regular ΔCt.Th response with increased loading when compared to 25 and 37% cross-sections. Relative thickness gains of approximately 70, 60, and 55% were observed for F = 12 N in the 25, 37, and 50% cross-sections. ΔCt.Th at selected points of the periosteum follow a linear response with increased peak load; no lazy zone was observed at these positions

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

Highlights - A representative volume element (RVE) size of 2 ×2 × 2 mm3 is sufficient to represent bovine trabecular bone microstructure and corresponding fluid flow properties. - Using periodic boundary conditions, with a mesh size >125,000 elements, provides the most accurate values for respective bone permeability data. - Comparison of bone specimens with respect to porosity does not provide accurate information about permeability. - For similarity between specimens based on mechanical properties, both magnitude of principal permeability and anisotropic ratio, need to be similar. - Comparison of permeabilities of our bovine sternum bone specimens with other bone samples from the literature, showed excellent agreement. Abstract In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 −8 m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies

Handheld Co-Axial Bioprinting: Application to in situ surgical cartilage repair

Three-dimensional (3D) bioprinting is driving major innovations in the area of cartilage tissue engineering. Extrusion-based 3D bioprinting necessitates a phase change from a liquid bioink to a semi-solid crosslinked network achieved by a photo-initiated free radical polymerization reaction that is known to be cytotoxic. Therefore, the choice of the photocuring conditions has to be carefully addressed to generate a structure stiff enough to withstand the forces phisiologically applied on articular cartilage, while ensuring adequate cell survival for functional chondral repair. We recently developed a handheld 3D printer called Biopen . To progress towards translating this freeform biofabrication tool into clinical practice, we aimed to define the ideal bioprinting conditions that would deliver a scaffold with high cell viability and structural stiffness relevant for chondral repair. To fulfill those criteria, free radical cytotoxicity was confined by a co-axial Core/Shell separation. This system allowed the generation of Core/Shell GelMa/HAMa bioscaffolds with stiffness of 200KPa, achieved after only 10seconds of exposure to 700mW/cm2 of 365nm UV-A, containing \u3e90% viable stem cells that retained proliferative capacity. Overall, the Core/Shell handheld 3D bioprinting strategy enabled rapid generation of high modulus bioscaffolds with high cell viability, with potential for in situ surgical cartilage engineering

Computational and experimental model of nanoengineered drug delivery system for trabecular bone

This paper describes fully coupled advective-diffusive transport of a drug through a trabecular bone sample in a perfused bioreactor. We used the analogy between heat transfer and mass transfer in order to derive the effective transport properties of the porous material such as effective diffusion coefficient and permeability. This allowed employing the heat transfer equations in Abaqus and they were solved using the finite element (FE) method. The average velocity was calculated using the Darcy-Brinkman-Forchheimer equation. Simulation results suggest that effective diffusivity plays a major role in the spatio-temporal distribution of the drug in the bone sample. Bone permeability was found less effective on manipulating the spatial distribution of drug. The bioreactor perfusion rate played a major role in the distribution of the drug throughout the bone sample. Increased perfusion rate leads to clearance of the drug towards the outlet of the bioreactor. It was found that even for moderate bioreactor perfusion rates the drug was concentrated towards the outlet, while zero concentration of drug was observed around the inlet. The numerical simulations showed that the essential effects of local drug release in bone can be captured using fluid flow through porous media theory. Our simulation results revealed that drug delivery is a multi-factorial phenomenon. Therefore, a mathematical model can enhance our understanding of this complicated problem that is difficult to characterize using experimental techniques alone

Investigation of bone resorption within a cortical basic multicellular unit using a lattice-based computational model

In this paper we develop a lattice-based computational model focused on bone resorption by osteoclasts in a single cortical basic multicellular unit (BMU). Our model takes into account the interaction of osteoclasts with the bone matrix, the interaction of osteoclasts with each other, the generation of osteoclasts from a growing blood vessel, and the renewal of osteoclast nuclei by cell fusion. All these features are shown to strongly influence the geometrical properties of the developing resorption cavity including its size, shape and progression rate, and are also shown to influence the distribution, resorption pattern and trajectories of individual osteoclasts within the BMU. We demonstrate that for certain parameter combinations, resorption cavity shapes can be recovered from the computational model that closely resemble resorption cavity shapes observed from microCT imaging of human cortical bone.Comment: 17 pages, 11 figures, 1 table. Revised version: paper entirely rewritten for a more biology-oriented readership. Technical points of model description now in Appendix. Addition of two new figures (Fig. 5 and Fig. 9) and removal of former Fig.