Ilizarov ring-wire fixators are used to treat fractures that are comminuted or near articular surfaces.1 They are also widely used in the corrective treatment of non-unions, post-trauma residual misalignment, and limb deformities (by distraction osteogenesis).2–5 The Ilizarov method of fracture fixation makes use of pre-tensioned, thin wires (1.5–1.8 mm diameter) that transfix the bone, supported by circular rings, which are connected using stiff longitudinal bars. Unlike other fixation methods, Ilizarov fixators are characterized by non-linear stiffness in the axial direction.6–8 The pre-tensioned wires behave like beams and cables simultaneously, but with increasing load the cable behavior dominates, and their load carrying capacity changes non-linearly with the sagging of the wires. This results in a geometrically non-linear response in the form of a non-linear load-deflection curve.
A major complication of external fixation is loosening at the bone-implant interface.9 Ilizarov wires are thin compared to other fixation implants, so high stresses/strains arise at wire-bone interfaces causing the bone to yield.10 This risk of wire loosening should be exacerbated with age-related loss of bone mass as interface stresses would be more likely to exceed the strength of weaker, lower-density osteoporotic bone. Paradoxically, in spite of their thinness, Ilizarov wires are associated with low rates of loosening at epiphyseal and metaphyseal locations.11, 12 However, the mean age of patients receiving fracture fixation is relatively low (<50 years).11 Therefore, loosening rates might be higher if treatment with fine wire fixation was extended to older groups.
Analytical8, 13 and finite element (FE)14–16 studies investigated the mechanics of Ilizarov fixation. Previous studies focused on fixator stiffness.17–19 While it has been noted in some studies that8, 13 Ilizarov fixator stiffness cannot be quantified by a single value, but requires a full specification of the (geometrically) non-linear response; other studies appear to neglect the critical role of non-linearity. While yielding of the wires14 and slippage15 has been discussed, bone yielding has not been considered previously. All previous modeling studies assumed that the wire is bonded to the bone it traverses, i.e., a tied contact has been employed at the wire-bone interface. This assumption, made to simplify numerical modeling, unrealistically prevents sliding of wires. Furthermore, the tied contact does not allow separation between the wire and bone. As a result during loading, where separation between part of the wire and bone would be expected, the tied contact model compels the bone to be pulled with the wire, thereby predicting unrealistic tensile stresses in the bone. None of the previous FE studies included the substantial reduction of bone stiffness and strength associated with age-related bone loss.20, 21 The extent to which aging and osteoporosis could reduce fixation stability remains unclear. Our aim was to determine the location and extent of bone yielding when an Ilizarov frame is applied to the tibial shaft taking into account age-related changes in bone structure and properties.
A reference tibial cross-section was taken from the midshaft of a standardized tibia from the BEL repository (www.biomedtown.org). This was used to create cross-sectional profiles for: (a) Young, (b) middle-aged, and (c) old/osteoporotic bone (Fig. 1). The cross-sections in Figure 1a,b were identical (material properties were different as discussed later), while Figure 1c incorporated the increase in bone diameter that occurs with aging, consistent with female tibial data.22 These cross-sections were extruded longitudinally for 3D modeling (Fig. 2). We considered a single midshaft fracture. This choice avoided the complications encountered near articular surfaces and simplified the modeling process by eliminating any substantial presence of cancellous bone; only cortical bone was included. Ilizarov wires are typically installed such that two wires cross on each ring. Two-wire (one ring on each side of the fracture) and four-wire (two rings on each side of the fracture) configurations were modeled. The wire arrangements in the transverse plane matched typical installations at the tibial midshaft using an external ring of 155 mm diameter with wires restricted to safe corridors (Fig. 3). To simplify the simulation process, only half of the fracture site was modeled, assuming a symmetry plane through the fracture site such that the results can be equally applied to wires superior or inferior to the fracture. Wires were modeled with a crossing angle of 30°. A spacing of ≥30 mm (∼2 finger breadths are left between the skin and the ring in clinical practice) was left between the ring and the bone fragment for access. Thus, the tibial placement was eccentric to the ring centroid (Fig. 3), resulting in a different distance from the edge of the tibia to the inner edge of the ring at each of the four wire-bone intersections. These distances, termed exposed wire lengths, were designated lA, lB, lC, and lD for lengths from the tibial edge to the ring at A, B, C, and D, respectively (Fig. 3). Wires in each pair were separated by 10 mm. In the case of the four-wire models, the two pairs of wires (and the rings they were attached to) were separated by 40 mm. Fixator rings and vertical supports were not modeled. The stiffness of these members greatly exceeds that of pre-tensioned thin wires and can be assumed to contribute little to the flexibility of the overall construct. Wires of 1.8 mm diameter were used in all analyses. Wires and bone fragments were modeled as separate, untied entities with interaction between them governed by contact mechanics with no friction. Both bone and implants were meshed using 10-noded tetrahedral elements. Meshes consisted of ∼100,000 elements. The geometry of the models necessitated the use of a fine mesh resolution to achieve solution. The average element edge length was 0.4 mm at the wire-bone interface. Analysis of a model meshed with elements of half the edge length was made to check for mesh dependency. The yielded bone volume and bone fragment displacement changed by 3.3 and 0.3%, respectively, confirming that the selected mesh resolution was adequate.
Three groups of bone properties based on a previous study21 were created to capture the range of variability in patients (Table 1). These properties, based on a study of female femoral midshaft21 were assumed to be a reasonable approximation for the tibia. Since porosity is a more powerful determinant of mechanical resistance than age,21 it is useful to consider the groups as “porosity groups” rather than “age groups”. The orthotropic elasticity tensor was available near the periosteum and endosteum21 and was interpolated for intermediate locations.23
Table 1. The Orthotropic Elastic Constants Assigned at the Periosteum and Endosteum
Young's and shear moduli are in GPa.
Values were tensor interpolated at intermediate locations.
Several studies showed that the mechanical behavior of bone can be described using elasto-plasticity,24, 25 wherein with increasing loads an initial elastic phase is followed by plastic phase that includes yielding and development of irreversible plastic strains. Bone yielding can signify opening of microcracks, slip at microcracks, or crushing of the porous structure. Yielding was used as an indicator of local failure and risk of loosening. Bone yielding was modeled with a strain-based criterion. Commercial FE codes generally only incorporate stress-based yield criteria. Strain-based criteria exploit the fact that due to anisotropy, bone yield strengths are anisotropic, while yield strains are approximately uniform.24, 25 This study used a maximum (tension) and minimum (compression) principal elastic strain criterion, in which yield strains were assumed to be 0.5 and 0.7% in tension and compression, respectively, based on a recent experimental study.25 Previously reported values for tensile yield strain vary from 0.38 to 0.73%. The Young's modulus and Poisson's ratio of the wires were 151 GPa and 0.3, respectively.14 The wires were modeled as elastic. A wire pre-tension of 1,000 N was applied for most analyses. Additional analyses were used to investigate the effect of wire pre-tension on bone yielding by varying it from 0 to 2,000 N in 500 N increments. Wire pre-tension was applied as a preliminary analysis step; both ends of the wires were displaced along the wire axis to induce the required tensile force. Following the application of pre-tension, wire ends were fully restrained. All analyses were geometrically non-linear; this response was verified by comparing it to analytical predictions8 (Supplementary Fig. 3). Vertical loading of 700 N was applied as a pressure load to the superior face of the bone fragment, representing body weight during single-legged stance.
Cut-through renderings of the bone fragments are shown in Figure 4. Bone regions that yielded are highlighted in red for sites A and C. For the proximal rings, periosteal yielding occurred on the superior (loaded) side of the wires; endosteal yielding occurred on the inferior side. Sagging of the wires (on the proximal side of the fracture) caused them to become inclined in their tracks such that high compressive strains were experienced by the bone at the superior side of the track at the periosteum and inferior side at the endosteum. Similarly, on the distal side of the fracture the predicted response would be high compressive strains on the inferior side of the track at the periosteum and superior side of the track at the endosteum. Periosteal and endosteal yielded regions did not connect in any analyses. The periosteal yielded region appeared to be larger than the endosteal, particularly at site A and in the longitudinal direction. More extensive yielding was observed at site A than site C in all analyses. The former corresponded to the shortest exposed wire length, and the latter with the longest (Fig. 3). Two-wire fixation (Fig. 4a–c) resulted in more extensive yielding than four-wire fixation (Fig. 4d–f); yielded bone extended further radially and longitudinally. The volume of yielded bone at locations A to D is plotted in Figure 5 for two- and four-wire fixation. Considerable variation of the volume of yielded bone was observed between different entrance sites. A similar hierarchy was observed in all analyses; the largest yielded volume occurred at A, the smallest at C, and sites B and D were intermediate. The exposed length of the wires at each site followed the opposite hierarchy; lA < lD < lB < lC. Hence, the largest volume of yielded bone occurred at the site with the shortest exposed wire length. Yielded bone volume increased substantially with aging; yielded volumes in the old-aged group were ∼1.7 and 2.2 times greater than the young group with two- and four-wire fixation, respectively. Two-wire fixation produced larger volumes of yielded bone at all sites than four-wire fixation. At the critical wire entrance site (A), ∼2.5–2.8 times more yielded bone was observed in two-wire fixation than four-wire fixation of equivalent groups. An approximately linear variation was observed between wire pre-tension and the volume of yielded bone (Fig. 6); increased pre-tension corresponded to reduced yielded bone volume.
We predicted wire loosening by the volume and location of yielded bone. The volume of yielded bone cannot be predicted using elastic analyses as considered in some previous studies.9, 10 Bone yielding was observed at both the periosteum and the endosteum in all analyses. As wires sagged due to loading the exposed wires became inclined to their tracks in the bone. The angles between the wires and their tracks at the periosteum can be referred to as intersection angles. In two-wire fixation of the old-aged model, the intersection angles were ∼3.7°, 2.8°, 1.7°, 2.0° at sites A, B, C, and D, respectively. Combined with Figure 5, these data indicate that greater volumes of yielded bone occurred at sites with larger intersection angles. Further, since the wires were not aligned with the wire-track once deformed, contact with the bone was concentrated at the corners formed by the ends of the wire tracks; superior to the wire at the periosteum and inferior to the wire at the endosteum. Stresses were thus concentrated at these corner sites leading to amplified strains and yielding. In addition to stress concentrations at corner sites, the inclination of wires in their tracts increased the wire-bone stresses required to resist the applied loading. The applied loading acted vertically downwards and was therefore resisted by compressive contact stresses on the superior side of the wires. However, as the wires became inclined with loading, additional stresses were transferred to the endosteum from the inferior side of the wires. To satisfy equilibrium, these additional stresses were resisted by increased compressive stresses on the periosteum from the superior side of the wires. Indeed, in the old-aged, two-wire fixation model, contact forces at the endosteum accounted for ∼20% of those at the periosteum.
Differences in the exposed wire lengths can account for the noted variation of intersection angles. The exposed length at each site was inversely proportional to the associated volume of yielded bone, suggesting that yielding could be reduced by increasing the total wire length (increasing exposed wire length). However, increased wire length would reduce the fixator stiffness and produce greater deflections.8 The results indicate that yielding could be reduced at the critical site by minimizing the difference in exposed lengths of the same wire on opposite sides of the limb, i.e., to locate the bone fragment near the mid-point of the wire. This strategy would not adversely affect fixator stiffness or the mechanical environment at the callus. Since the tibia is generally located eccentrically to the ring to accommodate the surrounding soft tissues, achieving this clinically may be difficult. In severely osteoporotic bone, these results may motivate the use of greater ring diameters, combined with more wires to enable central positioning of the bone fragment.
Age-related bone loss increased the volume of yielded bone in both two- and four-wire fixation. Since the loading was identical between age groups, the increase in yielded bone volume resulted from the reduced yield stress and cross-sectional area in the older models. The choice of yield strains affects the volume of yielded bone. We considered a 15% decrease in yield strains, which resulted in a 24% increase in yielded volume at site A for the young model. However, the pattern of yielded regions remained unchanged. Thus, a relatively small decrease in yield strain resulted in a relatively larger increase in the volume of yielded bone. Further, the sensitivity of this parameter can be indirectly estimated by comparing the yielded volumes for different age groups, as reduction in Young's modulus (for older models) could alternatively be viewed as a proportional reduction of yield strain without a change in Young's modulus. Stress concentration at the corners formed by the ends of the wire tracts also resulted in considerable radial stresses within the bone. The Young's modulus (and hence strength) in this direction reduces most rapidly with aging.21 The relative preservation of axial, over transverse, bone stiffness with aging would therefore appear to amplify the corner-site loading effect in elderly/osteoporotic patients. Indeed, in the old-aged models, a considerably greater proportion of the cortical thickness yielded than in younger models. However, while the volume increased with aging, it remained concentrated at the periosteum and endosteum separately (superior and inferior to the wire, respectively) and did not progress through the cortex. A substantial proportion of the cortical thickness remained in the elastic regime and would continue to provide stable support to the wires. The absence of through-thickness yielding, even in the old-aged cases, implies that the risk of wire loosening may be lower than is implied merely by the volumes of yielded bone. This offers an explanation for the good clinical performance of Ilizarov fixation.
Due to the geometric and material non-linearity of the system the use of twice the number of wires did not produce half the displacement. Indeed, axial displacements in four-wire fixation were 64% of those observed with two-wire fixation. However, the use of twice the number of wires did result in a reduction of yielded bone volume by ∼60%. The fact that yielded bone volume reduced by a greater proportion than the increase in wire numbers implies that the use of more wires is particularly effective to reduce the risk of loosening.
Increased wire pre-tension reduced the volume of yielded bone (Fig. 6). Increased pre-tension enhances fixator stiffness, resulting in lower deflections and hence smaller intersection angles. As discussed, smaller intersection angles imply lower yielded volumes, i.e., reduced risk of loosening. However, wire plasticity and slippage occur at pre-tensions of 1,28714 and 1,250 N,26 respectively. Improved material properties and wire-end fixing techniques would be required to realize substantial reductions of yielded bone volume by increasing pre-tension.
Our study has limitations. We incorporated both geometrical non-linearity and material non-linearity of the bone, so all responses varied non-linearly with load magnitude. So the responses cannot be linearly extrapolated for magnitudes other than those applied. However, an increase in load is akin to reduction in elastic moduli (as considered for older models) and thus a reduction in yield stress. So a relatively small increase in load will lead to a relatively larger increase in the volume of yielded bone, i.e., for a 20% increase in applied load there would be an increase in yielded volume >20%. The location of yielded regions and thereby the mechanics of loosening would not change with small increases or decreases in load. We did not consider the effect of cyclic loads. With the formulation adopted, load removal would result in permanent deformation and reloading would cause the same response as that seen at the end of the first load step, i.e., no increase in yielded bone volumes. We believe this reflects reality for a small number of load cycles; however some further yielding would be expected due to fatigue as the number of load cycles becomes large. We assumed that all loading was carried through the fixator, representative of a patient bearing load on an immature or absent callus. Previous studies reported both higher27 and lower28, 29 loading. The rings to which wires are attached and longitudinal bars were not modeled in our study. As these components have considerably larger stiffness30 and the compliance is primarily determined by the wires (thickness, pre-tension, length), the exclusion of ring and frame components simplifies the modeling process17, 31 and is unlikely to affect the results.
In conclusion, we showed that increasing the number and pre-tension of Ilizarov wires reduces bone yielding. The volume of yielded bone increased with age-related bone loss. We found that Ilizarov fixation does not cause continuous through-cortex yielding even in the old-aged group. This may explain why Ilizarov fixators have fewer clinical complications in comparison to unilateral fixators.9
Funding from The Carnegie Trust for the Universities of Scotland is gratefully acknowledged.