The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing: A finite element study based on sheep experiments

Novel approach to estimate distraction forces in distraction osteogenesis and application in the human lower leg

PURPOSE

In distraction osteogenesis (DO) of long bones, new bone tissue is distracted to lengthen limbs or reconstruct bone defects. However, mechanical boundary conditions in human application such as arising forces are mainly based on limited empirical data. Our aim was the numerical determination of the callus distraction force (CDF) and the total distraction force (TDF) during DO in the tibia of adults to advance the understanding of callus tissue behavior and optimize DO procedures.

METHOD

We implemented a mathematical model based on an animal experiment to enable the calculation of forces arising while distracting callus tissue, excluding the influence of surrounding soft tissue (muscles, skin etc.). The CDF progression for the distraction period was calculated using the implemented model and varying distraction parameters (initial gap, area, step size, time interval, length). Further, we estimated the CDF based on reported forces in humans and compared the results to our model predictions. In addition, we calculated the TDF based on our CDF predictions in combination with reported resisting forces due to soft tissue presence in human cadavers. Finally, we compared the progressions to in vivo TDF measurements for validation.

RESULTS

Due to relaxation, a peak and resting CDF is observable for each distraction step. Our biomechanical results show a non-linear degressive increase of the resting and peak CDF at the beginning and a steady non-linear increase thereafter. The calculated resting and peak CDF in the tibial metaphysis ranged from 0.00075 to 0.0089 N and 0.22-2.6 N at the beginning as well as 20-25 N and 70-75 N at the end of distraction. The comparison to in vivo data showed the plausibility of our predictions and resulted in a 10-33% and 10-23% share of resting CDF in the total resting force for bone transport and elongation, respectively. Further, the percentage of peak CDF in total peak force was found to be 29-58% and 27-55% for bone transport and elongation, respectively. Moreover, our TDF predictions were valid based on the comparison to in vivo forces and resulted in a degressive increase from 6 to 125 N for the peak TDF and from 5 to 76 N for the resting TDF.

CONCLUSION

Our approach enables the estimation of forces arising due to the distraction of callus tissue in humans and results in plausible force progressions as well as absolute force values for the callus distraction force during DO. In combination with measurements of resisting forces due to the presence of soft tissue, the total distraction force in DO may also be evaluated. We thus propose the application of this method to approximate the behavior of mechanical callus properties during DO in humans as an alternative to in vivo measurements.

Morphology of bony callus growth in healing of a sheep tibial osteotomy

Long bone fractures typically heal via formation of an external callus, which helps stabilise the bone fragments. Callus composition and morphology influence the mechanical environment, which in turn regulates the progression of healing. Therefore characterising callus development over time is crucial in understanding this mechanobiological regulation. Although bony callus is often assumed to grow towards the fracture from either side, this is not consistent with observations from large animal studies and clinical cases. Therefore, we sought to quantify the morphology of bony callus over time in a large animal model. Sheep tibiae were x-rayed weekly over eight weeks following an osteotomy (n=5), with fixation allowing up to 10% axial displacement under normal weight-bearing. After scaling radiographs by known landmarks and normalising greyscales, bony callus boundaries were defined by manual segmentation. The lateral callus area and coordinates of its centroid were calculated from each image. The external callus initially formed adjacent to the osteotomy site. Over the first four weeks, callus growth from its outer surfaces was characterised by its centre of area moving outwards and away from the osteotomy, on both proximal and distal fragments. Subsequent weeks showed consolidation and resorption from the outer surface of the callus. Our approach allowed bony callus development to be tracked in individuals throughout healing. Contrary to the view that periosteal bone formation originates distant from the fracture, our data showed bony callus adjacent to the defect from early stages, followed by approximately concentric growth. This discrepancy highlights the need for data specific to experimental conditions, and particularly early stages of healing, for evaluating theoretical models of mechanical regulation.

Elastic Modulus of Woven Bone: Correlation with Evolution of Porosity and X-ray Greyscale

The woven bone created during the healing of bone regeneration processes is characterized as being extremely inhomogeneous and having a variable stiffness that increases with time. Therefore, it is important to study how the mechanical properties of woven bone are dependent on its microarchitecture and especially on its porosity and mineral content. The porosity and the x-ray greyscale of specimens taken from bone transport studies in sheep were assessed by means of ex vivo imaging. Our study demonstrates that the porosity of the woven bone in the distraction area diminishes during the healing process from 73.3% 35 days after surgery to 31.9% 525 days after surgery. In addition, the woven bone's porosity is negatively correlated with its Young's modulus. The x-ray greyscale, was measured as an indicator of the level of mineralization of the woven bone. Greyscale index has been demonstrated to be inversely proportional to porosity and to increase to up to 60-80% of the level in cortical bone. The results of this study may contribute to the development of micromechanical models of woven bone and improvements in in silico modelling.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C(Micro) of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C(Meso) were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c33 measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1-21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R(2) ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

Exercise-induced inhibition of remodelling is focally offset with fatigue fracture in racehorses

Bone remodelling is inhibited by high repetitive loading. However, in subchondral bone of racehorses in training, eroded surface doubled in association with fatigue fracture and there was greater surrounding trabecular bone volume suggesting trabecular modelling unloads the bone focally, allowing damage repair by remodelling.

INTRODUCTION

Remodelling replaces damaged bone with new bone but is suppressed during high magnitude repetitive loading when damage is most likely. However, in cortical bone of racehorses, at sites of fatigue fracture, focal porosity, consistent with remodelling, is observed in proportion to the extent of surrounding callus. Focal areas of porosity are also observed at sites of fatigue damage in subchondral bone. We hypothesised that fatigued subchondral bone, like damaged cortical bone, is remodelled focally in proportion to the modelling of surrounding trabecular bone.

METHODS

Eroded and mineralizing surfaces and bone area were measured using backscattered scanning electron microscopy of post-mortem specimens of the distal third metacarpal bone in 11 racehorses with condylar fractures (cases) and eight racehorses in training without fractures (controls).

RESULTS

Cases had a two-fold greater eroded surface per unit area at the fracture site than controls (0.81 ± 0.10 vs. 0.40 ± 0.12 mm(-1), P = 0.021) but not at an adjacent site (0.22 ± 0.09 vs. 0.30 ± 0.11 mm(-1), P = 0.59). Area fraction of surrounding trabecular bone was higher in cases than controls (81 ± 2 vs. 72 ± 2 %, P = 0.0020) and the eroded surface at the fracture site correlated with the surrounding trabecular area (adjusted R (2) = 0.63, P = 0.0010).

CONCLUSION

In conclusion, exercise-induced inhibition of remodelling is offset at sites of fatigue fracture. Modelling of trabecular bone may contribute to unloading these regions, allowing repair by remodelling.

Evaluation of methods and timing in nail dynamisation for treating delayed healing femoral shaft fractures

INTRODUCTION

Dynamisation is a simple method for treating femoral shaft fractures (FSFs) in patients with delayed healing after intramedullary nailing. However, only around half of patients with a slow-healing FSF have been successfully treated with this strategy. Although it is thought that dynamisation with a screw preserved in the dynamic locking hole improves treatment outcome in these patients, to date, no studies have demonstrated empirical evidence supporting this technique. In this study, we investigated the effects of dynamisation with and without rotation and length control as well as timing of dynamisation on treatment outcomes in FSF patients with delayed healing.

PATIENTS AND METHODS

Thirty-nine consecutive acute FSF patients with static locking intramedullary nails who subsequently underwent dynamisation were recruited between January 2000 and June 2011. The indication for dynamisation was the presence of gap caused by bone absorption or over-traction at the fracture site when the locking screws were placed. Age, gender, dynamisation method, fracture classification, duration from nail insertion to dynamisation (i.e., timing of dynamisation) and dynamisation outcome were included in the statistical analysis.

RESULTS

Patients whose nail was dynamised with a screw preserved in the dynamic locking hole had a significantly higher successful bone union rate (14/15 vs. 14/24, p=0.028) compared with those with all screws removed from one end of the nail. The patients treated in 10-24 weeks had a significantly increased chance of bone union than those treated after 24 weeks (p=0.027). A significantly higher bone union rate (p=0.036) was observed in 10-24 weeks (83.3%) than after 24 weeks (33.3%) in the group of dynamisation with all screws removed from one end of the nail. No statistical difference in bone union success rate was found between patients at 10-24 weeks and after 24 weeks in the group of dynamisation with a screw preserved in the dynamic locking hole. There were no significant differences in outcome based on other variables.

CONCLUSION

(1) Dynamisation with a screw preserved in the dynamic locking hole was associated with a higher success rate in bone union than all screws removed from one end of the nail for patients with delayed healing FSFs. (2) Early dynamisation (10-24 weeks) had a better outcome than late dynamisation (>24 weeks). Late dynamisation with all screws removed from one end of the nails resulted in a poor success rate. Alternative treatment should be considered if the latter approach is to be adopted.

The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3 mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.