F.E. Donaldson

Bone properties affect loosening of half-pin external fixators at the pin–bone interface

INTRODUCTION Local bone yielding at the pin-bone interface of external fixation half-pins has been known to initiate fixator loosening. Deterioration of bone properties due to ageing and disease can lead to an increase in the risk of pin loosening. This study determines the extent, locations and mechanics of bone yielding for unilateral external fixation systems at the tibial midshaft with changes in age-related bone structure and properties. The study also evaluates the effect of the number of pins used in the fixation system and use of titanium pins (in place of steel) on bone yielding. METHODS We employ nonlinear finite element (FE) simulations. Strain-based plasticity is used to simulate bone yielding within FE analyses. Our analyses also incorporate contact behaviour at pin-bone interfaces, orthotropic elasticity and periosteal-endosteal variation of bone properties. RESULTS The results show that peri-implant yielded bone volume increases by three times from young to old-aged cases. The use of three, rather than two half-pins (on either side of the fracture), reduces the volume of yielded bone by 80% in all age groups. The use of titanium half-pins resulted in approximately 60-65% greater volumes of yielded bone. CONCLUSIONS We successfully simulate half-pin loosening at the bone-implant interface which has been found to occur clinically. Yielding across the full cortical thickness may explain the poor performance of these devices for old-aged cases. The models are able to identify patients particularly at risk of half-pin loosening, who may benefit from alternative fixator configurations or techniques such as those using pre-tensioned fine wires.

Investigation of factors affecting loosening of ilizarov ring‐wire external fixator systems at the bone‐wire interface

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.

Algorithms for a strain‐based plasticity criterion for bone

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.

Modeling microdamage behavior of cortical bone

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.

An Automated Step-Wise Micro-Compression Device for 3D Dynamic Image-Guided Failure Assessment of Bone Tissue on a Microstructural Level Using Time-Lapsed Tomography

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 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.