A 3D computational simulation of fracture callus formation: influence of the stiffness of the external fixator

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500 N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150 N/mm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.     

Three-dimensional load measurements in an external fixator

On the basis of a six-degree-of-freedom adjustable fracture reduction hexapod external fixator, a system which can be used for measuring axial and shear forces as well as torsion and bending moments in the fixator in vivo was developed. In a pilot study on 9 patients (7 fresh fractures and 2 osteotomies of the tibia), the load in the fixator during the healing process was measured after 2, 4, 8 and 12 weeks and at fixator removal. The measured values enabled both the type of fracture to be determined as well as the monitoring of the healing process. In well-reduced type A3 fractures small axial (direction of the bone axis) forces were found in the fixator. A2, B2 and C3 fractures showed distinct axial forces, which decreased during the healing process, according to an increasing load transfer over the bone. Bending moments in the fixator showed good correspondence with the clinical healing process, except in the case of a C3 fracture. A combination of bending moment and axial force proved to be particularly suitable to assess fracture healing. In transverse fractures, the well-known resorption phenomenon of bone in the fracture gap at approximately 4 weeks was detected by the system. Compared with other external fixator load measurements in vivo, the hexapod offers the advantage of being able to measure all forces and moments in the fixator separately and with a relatively simple mechanical arrangement. In our opinion, it will be possible to control fracture healing using this system, thereby minimizing radiation exposure from radiographs. Furthermore, the measurement system is a step towards the development of external fixator systems that enable automatic adjustments of the callus mechanical situation ("automatic dynamization") and inform the patients about the optimal weight bearing of their extremity ("intelligent fixator").     

A rigorous method for evaluation of the 6D compliance of external fixators

External fixators are standard devices to stabilize bone fractures and their compliance aims at producing an interfragmentary motion that promotes rapid and successful healing. While evaluation of their axial compliance is a routine test, the quantification and interpretation of their full 6 × 6 compliance matrix is an extensive and delicate task. In this context, the objective of this study was to develop, validate and demonstrate the potential of a rigorous method to quantify their 6 × 6 compliance matrix. An experimental system was developed to apply six independent static forces and moments to an external fixator in the field of view of two infrared cameras quantifying the induced motion. The system was then tested with a calibration structure which compliance could be calculated analytically and numerically. Finally, the system was applied to compare three configurations of a commercial external wrist fixator. The results of the method proved to be reproducible and highly consistent with the linear elasticity theory in the physiological range of small deformations. A rigorous method for evaluation of the 6D compliance becomes therefore available for research in mechanobiology of fracture healing by external fixation.     

Evaluation of linear finite-element analysis models' assumptions for external fixation devices.

Linear finite-element models (FEMs) have enjoyed an increased use in orthopaedic research, including the use for modeling external fixation devices. These fixator FEMs depend on a number of basic assumptions concerning the overall fixation frame stability and the components' rigidity. Among the more important ones are: (i) rigid fixation at both ends of the pin and sidebar; (ii) that the sidebar can be treated essentially as a rigid entity, with all bending occurring in the bone pins; and (iii) that the system can be treated as linearly elastic. Prior work done by the authors questions some of these assumptions. Thus, this study sought an empirical evaluation of the validity of some of these a priori assumptions. A Hoffmann single half-frame was tested in its standard form and then according to a stepwise protocol wherein the frame was welded to eliminate any possible points of instability. These tests looked at the stability and rigidity in various modes (axial compression, torsion, and medial-lateral and anterior-posterior four-point bending). The basic assumptions concerning the frame stability, frame rigidity and the frame's response to loads were found to be erroneous. Component failure was common under minimal loads and statistically significant differences (p less than 0.05) of up to 75% were noted in frame rigidity among the various frame forms tested. Thus, considerable caution must be exercised when employing the FEM technique for evaluating the fixator properties.     

Development and clinical application of an external fixator monitoring system

A monitoring system for measuring movement occurring in a dynamic external fixator used to treat fractures is described. The system measures shortening during fracture healing, micromovement at the fracture site on weight bearing and detects pin loosening. The method of calibration including cadaver experiments is presented. The clinical application is described and the reasons for measuring movement are discussed.     

Mineral and matrix contributions to rigidity in fracture healing

The purpose of this study was to investigate the relationships among selected properties of fracture callus: bending rigidity, tissue density, mineral density, matrix density and mineral-to-matrix ratio. The experimental model was an osteotomized canine radius in which the development of the fracture callus was modified by electrical stimulation with various levels of direct current. This resulted in a range of values for the selected properties of the callus, determined post mortem at 7 weeks after osteotomy. We found that the rigidity (R) of the bone-callus combination obeyed relationships of the form R = axb, where x is the tissue density, mineral density, matrix density or the mineral-to-matrix ratio of the repair tissue. These are analogous to power-law relationships found in studies of compact and cancellous bone. The results suggest that fracture callus at 7 weeks after osteotomy in canine radius behaves more like immature compact bone than cancellous bone in its mechanical and physicochemical properties. The present study demonstrates the feasibility of developing non-invasive in vivo densitometric methods to monitor fracture healing, since models may be developed that can predict mechanical properties from densitometric data. Further studies are needed to develop a refined model based on experimental data on the mechanical and physicochemical properties and microstructure of fracture callus at different stages of healing.     

The influence of mechanical stimulus on the pattern of tissue differentiation in a long bone fracture--an FEM study

2D, coronal plane, finite elements models (FEMs) were developed from orthogonal radiographs of a diaphyseal tibial fracture and its reparative tissue at four different time points during healing. Each callus was separated into regions of common tissue histology by computerised radiographic analysis. Starting point values of tissue material properties from the literature were refined by the model to simulate exactly the mechanical behaviour of the subject's callus and bone during loading. This was achieved by matching measured inter-fragmentary displacements with calculated inter-fragmentary forces. Stress and strain distributions in the callus and bone were calculated from peak inter-fragmentary displacements measured during natural walking activity, and were correlated with the subsequently observed pattern of tissue differentiation and maturation of the callus. The growth and stiffening of the external callus progressively reduced the inter-fragmentary gap strain. Partial maturation of the gap tissue was apparent only one week before fixator removal. Principal stresses in the callus were compared with 'yield stresses' in corresponding tissue from the literature. This indicated the presence of stress concentrations medial and lateral to the fracture gap, which probably caused tissue damage during normal activity levels. Tissue damage may also have precipitated partial structural failure of the callus, both of which were believed to have delayed healing during the middle third of the fixation period. Had the fixation device provided greater inter-fragmentary support during early healing, this may have prevented callus failure and the consequent delay in healing. A further benefit of this would have been the reduction of the initially high intra-gap tissue strains to a magnitude more conducive to earlier maturation of the bridging tissue that united the bone.     

Kinematic adjustability of unilateral external fixators for fracture reduction and alignment of axial dynamization

Bone fracture reduction and bone axial dynamization are important operations which effectiveness can be further enhanced by the use of a unilateral external fixator. By design, axial dynamization can be performed through reciprocating one of its translational joints. However, non-axial dynamization may occur after correcting residual fracture deformity. To explore and to maximize its full potential, the joint adjustment constraint equations for fracture reduction and alignment of axial dynamization under unilateral external fixation are derived. Their physical implications and criteria on the kinematic structure of a fixator are then established. In order to correctly make the alignment of axial dynamization with the proper fracture reduction, this study shows that the linkage of a bone–fixator system should have a minimum of eight degrees-of-freedom (DOFs) with at least two nonparallel rotational DOFs adjacent to both ends of the designated single translational DOF for axial dynamization. Thus, the adjustment of the connection between bone pin/pin clamp of Othofix^® fixator is required, while the alignment of one of the translational joints of Dynafix^® fixator with its bone segment axis during fracture stabilization procedure is a crucial step. A conceptual fixator that requires neither an adjustment of the pin/pin clamp connection nor special pre-alignment is demonstrated. Based on the constraint equations and criteria developed throughout this study, the creation of an effective frame design of external fixation device becomes feasible.     

A comparison of stereology, structural rigidity and a novel 3D failure surface analysis method in the assessment of torsional strength and stiffness in a mouse tibia fracture model

In attempting to develop non-invasive image based measures for the determination of the biomechanical integrity of healing fractures, traditional μCT based measurements have been limited. This study presents the development and evaluation of a tool for assessment of fracture callus mechanical properties through determination of the geometric characteristics of the fracture callus, specifically along the surface of failure identified during destructive mechanical testing. Fractures were created in tibias of ten male mice and subjected to μCT imaging and biomechanical torsion testing. Failure surface analysis, along with previously described image based measures was calculated using the μCT image data, and correlated with mechanical strength and stiffness. Three-dimensional measures along the surface of failure, specifically the surface area and torsional rigidity of bone, were shown to be significantly correlating with mechanical strength and stiffness. It was also shown that surface area of bone along the failure surface exhibits stronger correlations with both strength and stiffness than measures of average and minimum torsional rigidity of the entire callus. Failure surfaces observed in this study were generally oriented at 45° to the long axis of the bone, and were not contained exclusively within the callus. This work represents a proof of concept study, and shows the potential utility of failure surface analysis in the assessment of fracture callus stability.     

新型可透X线骨外固定器的研制

目的治疗近关节骨折、复杂骨折、骨缺损及骨不连等的一种新型可透x线骨外固定器。方法由固定部件、连接杆、万向头、连接杆锁紧螺帽、骨折固定螺钉、固定螺钉锁紧螺帽构成,通过x线能够全方位地观察骨折情况,调整骨外固定器使骨折对位对线。结果可避免因传统金属骨外固定器对术后骨折愈合情况观察,固定安全可靠,特别适用于战时、紧急情况下对骨折的固定,固定不超关节,故可以术后即刻关节功能锻炼。结论固定器设计合理,构思新颖,值得推广应用。     

The impact of low-magnitude high-frequency vibration on fracture healing is profoundly influenced by the oestrogen status in mice

Fracture healing is impaired in aged and osteoporotic individuals. Because adequate mechanical stimuli are able to increase bone formation, one therapeutical approach to treat poorly healing fractures could be the application of whole-body vibration, including low-magnitude high-frequency vibration (LMHFV). We investigated the effects of LMHFV on fracture healing in aged osteoporotic mice. Female C57BL/6NCrl mice (n=96) were either ovariectomised (OVX) or sham operated (non-OVX) at age 41 weeks. When aged to 49 weeks, all mice received a femur osteotomy that was stabilised using an external fixator. The mice received whole-body vibrations (20 minutes/day) with 0.3 g peak-to-peak acceleration and a frequency of 45 Hz. After 10 and 21 days, the osteotomised femurs and intact bones (contra-lateral femurs, lumbar spine) were evaluated using bending-testing, micro-computed tomography (μCT), histology and gene expression analyses. LMHFV disturbed fracture healing in aged non-OVX mice, with significantly reduced flexural rigidity (−81%) and bone formation (−80%) in the callus. Gene expression analyses demonstrated increased oestrogen receptor β (ERβ, encoded by Esr2) and Sost expression in the callus of the vibrated animals, but decreased β-catenin, suggesting that ERβ might mediate these negative effects through inhibition of osteoanabolic Wnt/β-catenin signalling. In contrast, in OVX mice, LMHFV significantly improved callus properties, with increased flexural rigidity (+1398%) and bone formation (+637%), which could be abolished by subcutaneous oestrogen application (0.025 mg oestrogen administered in a 90-day-release pellet). On a molecular level, we found an upregulation of ERα in the callus of the vibrated OVX mice, whereas ERβ was unaffected, indicating that ERα might mediate the osteoanabolic response. Our results indicate a major role for oestrogen in the mechanostimulation of fracture healing and imply that LMHFV might only be safe and effective in confined target populations.KEY WORDS: Whole-body vibration, LMHFV, Fracture healing, Oestrogen receptor signalling, Wnt signalling     

Adjustable Stiffness,External Fixator for the Rat Femur Osteotomy and Segmental Bone Defect Models

The mechanical environment around the healing of broken bone is very important as it determines the way the fracture will heal. Over the past decade there has been great clinical interest in improving bone healing by altering the mechanical environment through the fixation stability around the lesion. One constraint of preclinical animal research in this area is the lack of experimental control over the local mechanical environment within a large segmental defect as well as osteotomies as they heal. In this paper we report on the design and use of an external fixator to study the healing of large segmental bone defects or osteotomies. This device not only allows for controlled axial stiffness on the bone lesion as it heals, but it also enables the change of stiffness during the healing process in vivo. The conducted experiments have shown that the fixators were able to maintain a 5 mm femoral defect gap in rats in vivo during unrestricted cage activity for at least 8 weeks. Likewise, we observed no distortion or infections, including pin infections during the entire healing period. These results demonstrate that our newly developed external fixator was able to achieve reproducible and standardized stabilization, and the alteration of the mechanical environment of in vivo rat large bone defects and various size osteotomies. This confirms that the external fixation device is well suited for preclinical research investigations using a rat model in the field of bone regeneration and repair.     

Biomechanical influences of pin placement and elbow angle on hinge alignment and joint distraction of bridged elbow-pin-fixator construct

Joint distraction and mobilization with a hinged external fixator preserves elbow stability and mobility. However, the alignment of both elbow and fixator hinges was the initial prerequisite of the arthrodiatasis technique. The main goal of this study was to numerically evaluate the kinematic influence of the device, surgery, and joint factors on hinge alignment. The kinetic effects of the pins placement and elbow angle on concentric distraction and mobilization were also discussed. A unilaterally hinged elbow-fixator system with a 14 links and 10 degrees-of-freedom was instrumented into a humeroulnar model. The Denavit–Hartenberg method with the homogeneous transformation matrixes was applied to perform kinematic analysis of the linkage system. The predicted results revealed that the concurrence of hinge alignment (i.e., kinematic) and concentric distraction (i.e., kinetic) necessitates two telescopic tubes orthogonal to the elbow hinge. The degrees-of-freedom arrangement of the fixator articulators plays a significant role in hinge alignment. After joint distraction, two hinges might be misaligned due to the difference in the structural rigidity of the pins, fixator, and stiffened elbow. Furthermore, those two prerequisite are interactive and sensitive to elbow angle, fixator design, and pin placement of the bridged elbow-pin-fixator construct. In addition, the ideally concentric distraction might occur only at an elbow angle of 120° owing to the ulnar anatomy. Meticulous planning is necessary for such highly technically demanding surgery.     

A new device to control mechanical environment in bone defect healing in rats

Mechanical conditions have a significant influence on the biological processes of bone healing. Small animal models that allow controlling the mechanical environment of fracture and bone defect healing are needed. The aim of this study was to develop a new animal model that allows to reliably control the mechanical environment in fracture and bone defect healing in rats using different implant materials. An external fixator was designed and mounted in vitro to rat femurs using four Kirschner-wires (titanium (T) or steel (S)) of 1.2mm diameter. The specimens were distracted to a gap of 1.5mm. Axial and torsional stiffness of the device was tested increasing the offset (distance between bone and fixator crossbar) from 5 to 15mm. In vivo performance (well-being, infection, breaking of wires and bone healing) was evaluated in four groups of 24 Sprague-Dawley rats varying in offset (7.5 and 15mm) and implant material (S/T) over 6 weeks. Torsional and axial stiffness were higher in steel compared to titanium setups. A decrease in all configurations was observed by increasing the offset. The offset 7.5mm showed a significantly higher torsional (S: p<0.01, T: p<0.001) and axial in vitro stiffness (S: p<0.001, T: p<0.001) compared to 15mm offset of the fixator. Although in vitro designed to be different in mechanical stiffness, no difference was found between the groups regarding complication rate. The overall-complication rate was 5.2%. In conclusion, we were able to establish a small animal model for bone defect healing which allows modeling the mechanical conditions at the defect site in a defined manner.     

Design and performance of a fracture monitoring transducer

The answer to the question, ‘when is a fracture healed?’ is not simple, since the healing process is progressive and it is not possible to specify a time when the fracture can be said to have healed. In the past the assessment of fracture healing has, in the main, been subjective, relying upon the skill of the interpreter. A more objective method would be an advantage for many reasons, and since the bone is intended to be load bearing it is reasonable to assess healing by measuring the mechanical integrity of the bone. to do this a ‘clamp on’ transducer has been developed which, when fitted to the support column of an external fixator, enables the stiffness of a fracture to be determined during the healing process. Over the past 6 years this system has been used for both clinical and research work. It has enabled various forms of treatment to be evaluated in terms of ‘rate of healing’ and it also indicates the safe point at which the fixator can be removed.     

Modelling the effects of different fracture geometries and healing stages on ultrasound signal loss across a long bone fracture

The effect on the signal amplitude of ultrasonic waves propagating along cortical bone plates was modelled using a 2D Finite Difference code. Different healing stages, represented by modified fracture geometries were introduced to the plate model. A simple transverse and oblique fracture filled with water was introduced to simulate the inflammatory stage. Subsequently, a symmetric external callus surrounding a transverse fracture was modelled to represent an advanced stage of healing. In comparison to the baseline (intact plate) data, a large net loss in signal amplitude was produced for the simple transverse and oblique cases. Changing the geometry to an external callus with different mechanical properties caused the net loss in signal amplitude to reduce significantly. This relative change in signal amplitude as the geometry and mechanical properties of the fracture site change could potentially be used to monitor the healing process.     

Modelling the effects of different fracture geometries and healing stages on ultrasound signal loss across a long bone fracture

The effect on the signal amplitude of ultrasonic waves propagating along cortical bone plates was modelled using a 2D Finite Difference code. Different healing stages, represented by modified fracture geometries were introduced to the plate model. A simple transverse and oblique fracture filled with water was introduced to simulate the inflammatory stage. Subsequently, a symmetric external callus surrounding a transverse fracture was modelled to represent an advanced stage of healing. In comparison to the baseline (intact plate) data, a large net loss in signal amplitude was produced for the simple transverse and oblique cases. Changing the geometry to an external callus with different mechanical properties caused the net loss in signal amplitude to reduce significantly. This relative change in signal amplitude as the geometry and mechanical properties of the fracture site change could potentially be used to monitor the healing process.     

Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing

Most long-bone fractures heal through indirect or secondary fracture healing, a complex process in which endochondral ossification is an essential part and bone is regenerated by tissue differentiation. This process is sensitive to the mechanical environment, and several authors have proposed mechano-regulation algorithms to describe it using strain, pore pressure and/or interstitial fluid velocity as biofeedback variables. The aim of this study was to compare various mechano-regulation algorithms' abilities to describe normal fracture healing in one computational model. Additionally, we hypothesized that tissue differentiation during normal fracture healing could be equally well regulated by the individual mechanical stimuli, e.g. deviatoric strain, pore pressure or fluid velocity. A biphasic finite element model of an ovine tibia with a 3mm fracture gap and callus was used to simulate the course of tissue differentiation during normal fracture healing. The load applied was regulated in a biofeedback loop, where the load magnitude was determined by the interfragmentary movement in the fracture gap. All the previously published mechano-regulation algorithms studied, simulated the course of normal fracture healing correctly. They predicted (1) intramembranous bone formation along the periosteum and callus tip, (2) endochondral ossification within the external callus and cortical gap, and (3) creeping substitution of bone towards the gap from the initial lateral osseous bridge. Some differences between the effects of the algorithms were seen, but they were not significant. None of the volumetric components, i.e. pore pressure or fluid velocity, alone were able to correctly predict spatial or temporal tissue distribution during fracture healing. However, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing. This suggests that the deviatoric component may be the most significant mechanical parameter to guide tissue differentiation during indirect fracture healing.     

Midkine-Deficiency Delays Chondrogenesis during the Early Phase of Fracture Healing in Mice

The growth and differentiation factor midkine (Mdk) plays an important role in bone development and remodeling. Mdk-deficient mice display a high bone mass phenotype when aged 12 and 18 months. Furthermore, Mdk has been identified as a negative regulator of mechanically induced bone formation and it induces pro-chondrogenic, pro-angiogenic and pro-inflammatory effects. Together with the finding that Mdk is expressed in chondrocytes during fracture healing, we hypothesized that Mdk could play a complex role in endochondral ossification during the bone healing process. Femoral osteotomies stabilized using an external fixator were created in wildtype and Mdk-deficient mice. Fracture healing was evaluated 4, 10, 21 and 28 days after surgery using 3-point-bending, micro-computed tomography, histology and immunohistology. We demonstrated that Mdk-deficient mice displayed delayed chondrogenesis during the early phase of fracture healing as well as significantly decreased flexural rigidity and moment of inertia of the fracture callus 21 days after fracture. Mdk-deficiency diminished beta-catenin expression in chondrocytes and delayed presence of macrophages during early fracture healing. We also investigated the impact of Mdk knockdown using siRNA on ATDC5 chondroprogenitor cells in vitro. Knockdown of Mdk expression resulted in a decrease of beta-catenin and chondrogenic differentiation-related matrix proteins, suggesting that delayed chondrogenesis during fracture healing in Mdk-deficient mice may be due to a cell-autonomous mechanism involving reduced beta-catenin signaling. Our results demonstrated that Mdk plays a crucial role in the early inflammation phase and during the development of cartilaginous callus in the fracture healing process.