Proceedings of the Institution of Mechanical Engineers,Part H: Journal of Engineering in Medicine

Cortical bone fracture mechanisms are well studied under quasi-static loading. The influence of strain rate on crack propagation mechanisms needs to be better understood, however. We have previously shown that several aspects of the bone micro-structure are involved in crack propagation, such as the complete porosity network, including the Haversian system and the lacunar network, as well as biochemical aspects, such as the maturity of collagen cross-links. The aim of this study is to investigate the influence of strain rate on the toughness of human cortical bone with respect to its microstructure and organic non-collagenous composition. Two strain rates will be considered: quasi-static loading (10⁻⁴ s⁻¹), a standard condition, and a higher loading rate (10⁻¹ s⁻¹), representative of a fall. Cortical bone samples were extracted from eight female donors (age 50–91 years). Three-point bending tests were performed until failure. Synchrotron radiation micro-computed tomography imaging was performed to assess bone microstructure including the Haversian system and the lacunar system. Collagen enzymatic cross-link maturation was measured using a high performance liquid chromatography column. Results showed that that under quasi-static loading, the elastic contribution of the fracture process is correlated to both the collagen cross-links maturation and the microstructure, while the plastic contribution is correlated only to the porosity network. Under fall-like loading, bone organization appears to be less linked to crack propagation.

Osteosynthesis for canine long bones is a complex process requiring knowledge of biology, surgical techniques and (bio)mechanical principles. Subject-specific finite element analysis constitutes a promising tool to evaluate the effect of surgical intervention on the global properties of a bone–implant construct, but suffers from a lack of validation. In this study, the biomechanical behavior of 10 canine humeri was compared before and after creation of a 10 mm bone defect stabilized with an eight-hole locking compression plate (Synthes^®) and two locking screws on each fragment. The response under compression of both intact and plated samples was measured experimentally and reproduced with a finite element model. The experimental stiffness ratio between plated and intact bone was equal to 0.39 ± 0.06. A subject-specific finite element analysis including density-dependent elasto-plastic material properties for canine bone and automatic generation of orthopedic implants was then conducted to recover these experimental results. The stiffness of intact and plated samples could be predicted, with no significant differences with experimental data. The simulated stiffness ratio between plated and intact canine bone was equal to 0.43 ± 0.03. This study constitutes a first step toward the building of a virtual database of pre-computed cases, aiming at helping the veterinary surgeons to make decisions regarding the most suited orthopedic solution for a given dog and a given fracture.

The usage of finite element method techniques gives a possibility to replace time-consuming experiments or imitate physical process in the ear by numerical simulation. Especially, the research of spatial motion of ossicular chain in the middle ear is of high interest for the oto-surgeons and engineers. It is known that the most affected bone from the ossicular chain is the incus. After the cholesteatoma operation and tympanoplasty, the affected incus is removed or sacrificed; thus, the possibility of transducing noise lays on the stapes, new titanium or other material prosthesis. In this case, the affected incus was removed because of the cholesteatoma that was lying in front of it in the tympanic cavity. The removed incus with the affected long process passed micro–computed tomography. The computer-aided design systems allowed redesigning a ‘healthy’ incus with an intact long process. In this way, it was possible to evaluate the influence of damaged long process of incus in the vibrational analysis. This article analyses the problems of mechanical behaviour of injured and healthy human incus. The numerical simulation has demonstrated that the features of healthy incus and analysed injured incus do not differ significantly, especially at low (about 500 Hz) frequencies. It explains why there is no impact of cholesteatoma on hearing for a long time in the audiogram.

In this article, we summarize the developments in the mathematical modeling of the mechanics of bone and related biological phenomena. We will devote special attention to the results of the last 10–15 years, although we will cover some relevant classical work to better frame the more recent researches. We will propose a division of the literature based on the main aim of the model (mechanical/biomathematical) and the type of biological phenomena considered (stimulus, growth, cell population dynamics). Finally, we will suggest some possible directions for future investigations.

The trabecular bone can adapt its form to mechanical loads and form structures that are both lightweight and very stiff. In this sense, it is a problem similar to structural optimization, especially topology optimization. The natural phenomenon leading to mechanical optimization of the bone structures is called trabecular bone remodeling. The main assumption and the benchmark for the numerical models of the phenomenon is the observation that the strain energy density on the structural surface is constant. This constant value corresponds to the homeostatic strain energy density, the state of bone tissue with a perfect balance of the loss, and gain of the bone mass. We assumed that the trabecular bone can form an optimal structure. The idea behind the investigation is to carry out studies on the ground of mechanics and to interpret clinical observations in the context of the results obtained from the optimization studies. In this way, clinical observations have been confirmed by strict arguments based on mechanics, leading to the unequivocal conclusion that equalization of the strain energy density on the trabecular bone surface allows minimizing the strain energy in the whole structure of the bone. This proves the veracity of the assumption that the remodeling process leads to the formation of the structure with the highest stiffness. In addition, this article elaborates on two new aspects of the remodeling phenomenon resulting directly from the considerations in the field of shape optimization important for numerical simulation. The first one concerns the influence of surface curvature on the remodeling process. The second one concerns the role of the bone surface where different loads are analyzed. Both aspects show the need of actual trabecular bone geometry model for the simulation of the trabecular bone remodeling phenomenon.

In this study, deformation and failure mechanisms of mineralized tissue (bone) were investigated both experimentally and computationally by performing diametral compression tests on millimetric disk specimens and conducting finite element analysis in which a granular micromechanics-based nonlinear user-defined material model is implemented. The force–displacement relationship obtained in the simulation agreed well with the experimental results. The simulation was also able to capture location of the failure initiation observed in the experiment, which is inside out from the hole along the loading axis. Furthermore, propagation of micro-sized cracks into failure was observed both in the experiment using simultaneous slow-motion microscopy imaging and in the simulation analyzing the local distortion and local volume change within the specimen. The anisotropy evolution was found to be significant around the hole along the loading axis by evaluating the anisotropy index computed using finite element results. In conclusion, this work revealed that the prediction capability of granular micromechanics-based user-defined nonlinear material model (UMAT) is promising considering the match between the results and observations from the physical experiment and finite element analysis such as force–displacement relationship and failure initiation/pattern. This work has also shown that the tensile damage and failure of mineralized tissues can be characterized using diametral compression (split tension) test.

Bone aging involves structural and molecular modifications, especially at the level of type I tropocollagen. This macromolecule shows two main age-related alterations, which are the decrease of both molecular diameter (due to the loss of hydration) and number of hydrogen bonds. In this work, it is proposed to investigate the influence of these two parameters (molecular diameter and number of hydrogen bonds) on the mechanical behavior of tropocollagen using finite element method. To this end, a novel three-dimensional finite element model of collagen molecule accounting for hydrogen bonds was developed. Then, a numerical design of experiments for the diameter of tropocollagen and variations in the number of hydrogen bonds has been established. The mechanical properties (“load–strain” curve and apparent Young’s modulus) of the collagen molecule were obtained by employing the proposed model to uniaxial tensile tests. The parametric study demonstrates that the mechanical properties of tropocollagen are slightly affected by the rate of hydration but considerably affected by variation of the number of hydrogen bonds. Finally, a fitted analytical function was deduced from the above results showing effects of the two parameters (hydration rate and hydrogen bonds) on the apparent Young’s modulus of tropocollagen. This study could be useful to understand the influence of structural age modifications of tropocollagen on the macroscopic mechanical properties of bone.