Biomechanics and Modeling in Mechanobiology

In this study, 3D finite element analyses (FEA) are conducted to quantify the orthotropic elastic properties and investigate the load transfer mechanism of bone at the sub-lamellar level. Three finite element (FE) unit cells with periodic boundary conditions are presented to model a two-scale microstructure of bone including a mineralized collagen fibril (MCF), the extrafibrillar matrix (EFM) and the resulting fibril array (FAY) under arbitrary loading. The axial and transverse elastic properties of the FAY computed by FEA are calibrated with unique experimental results on ovine micro-samples showing a coherent fibril orientation. They are then systematically compared with those calculated using analytical methods including the basic Voigt, Reuss and shear-lag models, the Mori–Tanaka scheme and the upper and lower bounds by Hashin and Shtrikman. The predicted axial strain ratios between the two-scales are discussed with respect to a recent small-angle X-ray scattering and wide-angle X-ray diffraction study. Beyond apparent elastic properties, the FE models provide stress distributions at both hierarchical levels, confirm the shear lag mechanisms within the MCF and between MCF and EFM and identify potential damage sites under arbitrary loading conditions. A comprehensive sensitivity analysis shows that mineral volume fraction in the fibril array is the dominant parameter on the axial and transverse elastic moduli, while the MCF volume fraction in FAY is the most sensitive variable for the ratio of axial versus transverse elastic modulus followed by the elastic moduli of hydroxyapatite and collagen. The FE model of the FAY developed and calibrated in the current study represents an anatomically realistic, experimentally validated and computationally efficient basis for investigating the apparent yield, post-yield and failure behaviors of lamellar bone in future research.

There are two main approaches to unraveling the mechanisms involved in the regulation of collective cell movement. On the one hand, “in vitro” tests try to represent “in vivo” conditions. On the other hand, “in silico” tests aim to model this movement through the use of complex numerically implemented mathematical methods. This paper presents a simple cell-based mathematical model to represent the collective movement phenomena. This approach is used to better understand the different interactive forces which guide cell movement, focusing mainly on the role of the cell propulsion force with the substrate. Different applications are simulated for 2D cell cultures, wound healing, and collective cell movement in substrates with different degrees of stiffness. The model provides a plausible explanation of how cells work together in order to regulate their movement, showing the significant influence of the propulsive force exerted by the cell to the substrate on guiding the collective cell movement and its interplay with other cell forces.

Axisymmetric nonlinear finite models of accommodation incorporating the posteriorly sloped force and vitreous effects have been studied by means of their effectiveness in mechanical and optical performances. All materials were assumed to be linearly elastic, vitreous and lens matrices were incompressible. The present model is subjected to certain indicated shortcomings, however, the behavior of the model is predictable, reasonable and favourably consistent with different published data, supporting the Helmholtz theory of accommodation.

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load–displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53–0.65, average error of 13–17%). A lower correlation was found for failure load (R2 = 0.21–0.48, average error of 9–15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75–0.80 for stiffness, R2 = 0.55–0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin ‘transient’ layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection. The proposed representative volume element together with the multiscale finite element is used to simulate the wave propagation and to evaluate the attenuation coefficient for samples with different effective densities in the dependence of the applied excitation frequency. The obtained numerical values show a very good agreement with the experimental results. Moreover, the model enables the determination of the upper and the lower bound for the attenuation coefficient.

Cell entry into a micro-channel has potential applications in cell sorting and cancer diagnostics. In this paper, we numerically model breast cancer cell entry into a constricted micro-channel. Our results indicate that the cell velocity decreases during entry and increases after entry, an observation in agreement with experiments. We found that the cell entry time depend strongly on the cortical stiffness and is minimum at some critical cortical elasticity. In addition, we found that for the same entry time, a stiff nucleus is displaced toward the cell front, whereas a viscous nucleus is displaced toward the rear. In comparison, the nucleus is less sensitive to the viscosity of the cytoplasm. These observations suggest that specific intra-cellular properties can be deduced non-invasively during cell entry, through the inspection of the nucleus using suitable illumination techniques, such as fluorescent labeling.

The purpose of this study was to determine suture-holding properties of tissue-engineered neocartilage relative to native articular cartilage. To this end, suture pull-out strength was quantified for native articular cartilage and for neocartilages possessing various mechanical properties. Suture-holding properties were examined in vitro and in vivo. Neocartilage from bovine chondrocytes was engineered using two sets of exogenous stimuli, resulting in neotissue of different biochemical compositions. Compressive and tensile properties and glycosaminoglycan, collagen, and pyridinoline cross-link contents were assayed (study 1). Suture pull-out strength was compared between neocartilage constructs, and bovine and leporine native cartilage. Uniaxial pull-out test until failure was performed after passing 6-0 Vicryl through each tissue (study 2). Subsequently, neocartilage was implanted into a rabbit model to examine short-term suture-holding ability in vivo (study 3). Neocartilage glycosaminoglycan and collagen content per wet weight reached $$4.55 \pm 1.62\,\%$$ and $$4.21 \pm 0.77\,\%$$ , respectively. Tensile properties for neocartilage constructs reached $$2.6 \pm 0.77$$  MPa for Young’s modulus and $$1.39 \pm 0.63$$  MPa for ultimate tensile strength. Neocartilage reached $$\sim $$ 33 % of suture pull-out strength of native articular cartilage. Neocartilage cross-link content reached 50 % of native values, and suture pull-out strength correlated positively with cross-link content $$(R^{2}=0.74)$$ . Neocartilage sutured into rabbit osteochondral defects was successfully maintained for 3 weeks. This study shows that pyridinoline cross-links in neocartilage may be vital in controlling suture pull-out strength. Neocartilage produced in vitro with one-third of native tissue pull-out strength appears sufficient for construct suturing and retention in vivo.