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ABSTRACT:The potential for peri-implant bone yielding and subsequent loosening of Ilizarov ring-wire external fixation systems was investigated using non-linear finite element (FE) analyses. A strain-based plasticity model was employed to simulate bone yielding. FE models also incorporated contact behavior at the wire-bone interface, orthotropic elasticity, and periosteal-endosteal variation of bone properties. These simulations were used to determine the extent and location of yielding with change in age-related bone structure and properties for the bone-Ilizarov construct at the tibial midshaft. At critical wire-bone interfaces, the predicted volume of yielded bone with four wires (on either side of the fracture) was 40% of that with two wires. Old-aged cases showed considerably greater bone yielding at the wire-bone interface than young cases (1.7-2.2 times greater volumes of yielded bone). The volume of yielded bone at all wire-bone interfaces decreased with an increase in wire pre-tension. The absence of continuous through-thickness yielding offers an explanation for the clinical observation that Ilizarov ring-wire fixation can provide stable fracture fixation even in bone with high porosity. ß

Homogenized elastic properties are often assumed for macro-finite element (FE) models used in orthopaedic biomechanics. The accuracy of material property assignments may have a strong effect on the ability of these models to make accurate predictions. For cortical bone, most macro-scale FE models assume isotropic elastic material behaviour and do not include variation of material properties due to bone micro-architecture. The first aim of the present study was to evaluate the variation of apparent-level (homogenized) orthotropic elastic constants of cortical bone with age and indices of bone micro-architecture. Considerable age-dependent differences in porosity were noted across the cortical thickness in previous research. The second aim of the study was to quantify the resulting differences in elastic constants between the periosteum and endosteum. Specimens were taken from the anterior femoral midshaft of 27 female donors (age 53.4 +/- 23.6 years) and micro-FE (gFE) analysis was used to derive orthotropic elastic constants. The variation of orthotropic elastic constants (Young's moduli, shear moduli, and Poisson's ratios) with various cortical bone micro-architectural indices was investigated. The ratio of canal volume to tissue volume, Ca.V/TV, analogous to porosity, was found to be the strongest predictor (r2(ave) = 0.958) of the elastic constants. Age was less predictive (r2(ave) = 0.385) than Ca.V/TV. Elastic anisotropy increased with increasing Ca.V/TV, leading to lower elastic moduli in the transverse, typically less frequently loaded, directions. Increased Ca.V/TV led to a more substantial reduction in elastic constants at the endosteal aspect than at the periosteal aspect. The results are expected to be most applicable in similar midshaft locations of long bones; specific analysis of other sites would be necessary to evaluate elastic properties elsewhere. It was concluded that Ca.V/TV was the most predictive of cortical bone elastic constants and that considerable periosteal-endosteal variations in these constants can develop with bone loss.

A range of stress-based plasticity criteria have been employed in the finite element analysis of the post-elastic behaviour of bone. There is some recognition now that strain-based criteria are more suitable for this material because they better represent its behaviour. Moreover, because bone yields at relatively isotropic strains, a strain-based criterion requires fewer material parameters unlike those required for a stress-based criterion. Based on a minimum and maximum principal strain criterion, a robust strain-based plasticity algorithm is developed. As the criterion comprises six piecewise linear surfaces in principal strain space, it has a number of singular regions. Singularity indicators are developed to direct the algorithm to make appropriate plastic corrector returns when singularity regions are encountered. The developed algorithms permit a plastic corrector to be achieved in a single iterative step in all cases. A range of benchmark tests are developed and conducted after implementing the algorithm in a finite element package. These tests show that the constitutive behaviour is as expected.

Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.

Microstructural bone phenotypes, such as the intracortical canal network, could be directly linked to the mechanical failure behavior of cortical bone tissue. In addition, high accumulation of microdamage can significantly increase bone brittleness and thus, is a precursor of mechanical failure. Here, we discuss the development and validation of an automated step-wise micro-compression device (MCD) for dynamic image-guided failure assessment (DIGFA) of intracortical bone microstructure and bone microdamage. The device was found to be highly accurate and precise with positioning errors of less than 1 µm and force errors of less than 1.25 N. In addition, the results of a first biological study using DIGFA and time-lapsed computed tomography are presented. In short, whole mouse femora from mature C57BL/6 (B6) and C3H/He (C3H) mice with mid-diaphyseal notches were tested in step-wise compression and concomitantly imaged until failure. DIGFA was performed at the TOMCAT beamline of the Swiss Light Source (SLS) using synchrotron radiation-based computed tomography (SR CT). Following the experiment, intracortical porosity was separated into the canal network, osteocyte lacunae, and microcracks for subsequent morphometric evaluation. The thicker cortex of C3H was penetrated by a dense canal network, whereas in B6 only a few scattered canals were observed. For B6, the first occurrence of crack was noted at 1.45% local strain, while for C3H, crack initiation took place only at 2.66% local strain. In addition, we were able to relate whole bone mechanics to local failure events by deriving correlations between microstructural porosity and microdamage propagation. In conclusion, initiation and accumulation of microcracks were investigated for two mouse phenotypes demonstrating that DIGFA in combination with SR CT is a suitable technique for time-lapsed three-dimensional assessment of bone morphology and bone fracture behavior down to the cellular level.

The study of the mechanical behaviour of trabecular bone has extensively employed micro-level finite element (microFE) models generated from images of real bone samples. It is now recognized that the key determinants of the mechanical behaviour of bone are related to its micro-architecture. The key indices of micro-architecture, in turn, depend on factors such as age, anatomical site, sex, and degree of osteoporosis. In practice, it is difficult to acquire sufficient samples that encompass these variations. In this preliminary study, a method of generating virtual finite element (FE) samples of trabecular bone is considered. Virtual samples, calibrated to satisfy some of the key micro-architectural characteristics, are generated computationally. The apparent level elastic and post-elastic mechanical behaviour of the generated samples is examined: the elastic mechanical response of these samples is found to compare well with natural trabecular bone studies conducted by previous investigators; the post-elastic response of virtual samples shows that material non-linearities have a much greater effect in comparison with geometrical non-linearity for the bone densities considered. Similar behaviour has been reported by previous studies conducted on real trabecular bone. It is concluded that virtual modelling presents a potentially valuable tool in the study of the mechanical behaviour of trabecular bone and the role of its micro-architecture.