The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates

Abstract

Objectives

Opening wedge high tibial osteotomy (HTO) is an established surgical procedure for the treatment of early-stage knee arthritis. Other than infection, the majority of complications are related to mechanical factors – in particular, stimulation of healing at the osteotomy site. This study used finite element (FE) analysis to investigate the effect of plate design and bridging span on interfragmentary movement (IFM) and the influence of fracture healing on plate stress and potential failure.

Materials and Methods

A 10° opening wedge HTO was created in a composite tibia. Imaging and strain gauge data were used to create and validate FE models. Models of an intact tibia and a tibia implanted with a custom HTO plate using two different bridging spans were validated against experimental data. Physiological muscle forces and different stages of osteotomy gap healing simulating up to six weeks postoperatively were then incorporated. Predictions of plate stress and IFM for the custom plate were compared against predictions for an industry standard plate (TomoFix).

Results

For both plate types, long spans increased IFM but did not substantially alter peak plate stress. The custom plate increased axial and shear IFM values by up to 24% and 47%, respectively, compared with the TomoFix. In all cases, a callus stiffness of 528 MPa was required to reduce plate stress below the fatigue strength of titanium alloy.

Conclusion

We demonstrate that larger bridging spans in opening wedge HTO increase IFM without substantially increasing plate stress. The results indicate, however, that callus healing is required to prevent fatigue failure.

Cite this article: A. R. MacLeod, G. Serrancoli, B. J. Fregly, A. D. Toms, H. S. Gill. The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates: An experimental and finite element study. Bone Joint Res 2018;7:639–649. DOI: 10.1302/2046-3758.712.BJR-2018-0035.R1.

Article focus

• The influence of working length when using different opening wedge designs of high tibial osteotomy (HTO) plates.

• The influence of healing on HTO plate stress reduction when using different plate designs.

Key messages

• Larger bridging spans in opening wedge HTO increase interfragmentary movement (IFM) without substantially increasing plate stress.

• Osteotomy gap healing is required to prevent plate fatigue failure.

Strengths and limitations

• This is an experimentally validated computational study.

• Several situations were evaluated involving different screw configurations and stages of healing.

Introduction

The lifetime risk of knee osteoarthritis (OA) is estimated to be as high as 45%¹ and is becoming more common.² Although the demand for knee arthroplasty is predicted to double by 2030,³ it is only suitable for end-stage disease.⁴ High tibial osteotomy (HTO) is an established treatment for early-stage knee arthritis. The procedure uses an opening or closing wedge osteotomy to change the varus alignment to a more valgus alignment, thereby altering the mechanical axis of the leg and reducing the load in the painful compartment.⁵ The osteotomy is then stabilized using an osteosynthesis plate. Plates with angularly stable ‘locking’ screws are generally used to ensure the osteotomy angle is maintained, since conventional screws have been shown to subside after the operation.^6,7 Opening wedge HTO procedures are more popular⁸ due to the simpler surgical approach, lower risk of peroneal nerve damage,^9,10 and better postoperative flexion scores.¹⁰ Unfortunately, the overall complication rate is still relatively high at 31%.¹¹ Infection is generally the most common complication (approximately 10%),¹¹ while reported rates of nonunion and delayed union range from 4.3% to 8.2%,^11-13 and rates of implant breakage range from 4.4% to 10%.^14,15 Patients with delayed consolidation of the osteotomy have been reported to have a significantly (p < 0.05) greater likelihood of complications.¹⁴ Therefore, due to the importance of preventing nonunions and delayed unions from occurring, promotion of fracture healing should be a priority in HTO surgery.¹⁶

In studies by Spahn¹⁵ and Nelissen et al,¹⁷ more plate breakages occurred in the non- or restricted-weight-bearing groups than in the fully weight-bearing groups. This observation implies that the loads imposed on the plate are not the only factor influencing plate breakage. While weight-bearing loads cause plate deformation, they also induce interfragmentary movement (IFM), stimulating healing at the fracture site, which in turn reduces stress on the plate.¹⁸ It is well known that wider fracture gaps require larger movements to achieve the same strain environment,¹⁹ and, unsurprisingly, the likelihood of HTO complications is related to the size of the osteotomy angle.¹⁵ Therefore, with the exception of infection, the most common complications in opening wedge HTO are related to mechanical factors and, in particular, the stimulation of healing at the osteotomy site.

Previous biomechanical studies have investigated the static strength and fatigue resistance of HTO plates. TomoFix HTO plates (DePuy Synthes, Zuchwil, Switzerland) have been shown to have lower stiffness and migrate more with cyclical loading than iBalance (Arthrex GmbH, Munich, Germany), Contour Lock (Arthrex), and PEEKPower (Arthrex) implants.²⁰ Despite these findings, TomoFix implants (without wedge blocks) are still the gold standard in HTO treatment and have lower complication rates than short spacer plates designed by competitors.²¹ In laboratory-based studies, implants that produce higher construct stiffness also generally have greater fatigue resistance.^20,22,23 Clinically, however, more flexible implants can perform better in terms of healing,²⁴ indicating that mechanical properties such as strength and, more importantly, stiffness do not necessarily translate into improved clinical performance.

It is difficult to recreate the in vivo biomechanical environment in vitro. For example, it is not practical to incorporate muscle forces in laboratory experiments. Additionally, fatigue tests in a laboratory setting ignore the fact that the osteotomy will heal over time, making it difficult to predict medium- or long-term in vivo performance.²⁰ Computer simulation allows the prediction of variables that would be difficult or impossible to measure experimentally. However, the model must be thoroughly validated to ensure it represents reality²⁵, and minimum reporting guidelines aid reproduction and improve standards.²⁶ Some previous computational studies have investigated implant stress,^27-29 IFM within the osteotomy,^28,29 and the influence of plate design.³⁰ A major limitation of previous computational studies using locking plates, however, is the use of bonded plate-screw interfaces. This assumption dramatically increases the construct stiffness while also lowering predictions of plate stress.³¹ Additionally, previous HTO computational studies have not considered the influence of healing at the fracture site.

The aim of this study was to create and validate a computational model of a tibia following an HTO procedure in order to compare predictions of IFM, plate stresses, and bone strains for different plate spans and designs. The three main goals of the investigation were: 1) to evaluate the influence of different screw arrangements – in particular, to assess whether a longer bridging span using fewer screws could be used safely; 2) to compare a custom HTO plate against an existing design; and 3) to investigate the influence of callus healing on the predictions of plate stress and bone strain.

Materials and Methods

The study was performed in three stages: 1) experimental testing; 2) creation of a finite element (FE) model validated for the intact condition and for an HTO procedure performed using a custom plate design and two different screw configurations; and 3) investigation of the influence of different plate configurations under physiological loading and including healing fracture callus.

Experimental testing.

A composite surrogate tibia was selected for use in the study (third-generation Sawbones model 3302, Biomechanical Test Materials; Pacific Research Laboratories, Malmö, Sweden). The specimen was instrumented with tri-axial strain gauges (SGD-2/350-RY63; Omega Engineering Ltd, Manchester, UK) at five locations of interest (Fig. 1a) based on a preliminary computational study. The composite tibia was potted using a low melting point alloy (Wood's Metal (70°C); Lowden Metals Ltd, Halesowen, United Kingdom) and mounted in a materials testing machine (Series 5965; Instron, Norwood, Massachusetts). The distal tibia was restrained using a 20 mm diameter spherical bearing positioned at the centre of the ankle joint. A unicondylar knee arthroplasty femoral component (Medium Oxford Partial Knee; Zimmer Biomet, Swindon, United Kingdom) with a radius of 23 mm was used to secure the specimen proximally and apply the loading to the medial condyle (Fig. 1a). The load was applied along the axis from the medial condyle to the ankle (Fig. 1a) in increments of 50 N up to 500 N. Strain readings were recorded using data acquisition software (LabVIEW 2010; National Instruments Corporation (U.K.) Ltd, Newbury, United Kingdom). Maximum and minimum principal strains were calculated from the measured directional surface strains (Matlab R2015b; The Mathworks Inc., Natick, Massachusetts). Each test was repeated ten times and the average was calculated.

a) The location of the five strain gauges used on the intact sawbones specimen in the testing machine. b) The osteotomized and plated sawbones specimen. c) The geometry of the osteotomy.

After testing in the intact condition, a wedge osteotomy was created (AO classification: 31-A1 / 31-A2). The proximal plane of the resulting osteotomy was inclined 15° to the joint line at the knee, and the gap angle was 10° (Figs 1b and 1c). A custom HTO locking plate was designed to match the surface profile of the composite tibia and manufactured using titanium alloy (Ti-6Al-4V) (EOS M:280 laser sintering; Mario Nava S.p.A., Bosisio Parini, Italy). The profile of the plate used locations on the surface of the specimen obtained from a micro-CT scan of the composite tibia (Nikon XTH225 ST CT-scanning unit; Nikon UK Ltd, Kingston upon Thames, United Kingdom). Locking screws were also manufactured; the threads were tapped/threaded as post-processing operations. The plate was located against the bone using a custom positioning jig to ensure it was placed exactly as planned in the virtual environment. Tri-axial strain gauges were also applied to the top and bottom surfaces of the locking plate (Fig. 1b). The plated, osteotomized tibia was then tested in an identical manner to the intact specimen. In total, three scenarios were examined: A) an intact tibia; B) an osteotomized tibia stabilized with the custom plate using a short bridging span with four distal locking screws; and C) an osteotomized tibia stabilized with the custom plate using a long bridging span with three distal locking screws (Fig. 2). The working lengths for the short and long bridging spans considered in our study were 33 mm and 50 mm, respectively, for both plate types. As we were limited to recording 15 strain readings simultaneously (three per strain gauge), during the testing of conditions B and C, two of the bone strain gauges were unused during testing of the implanted tibia. In order to measure IFM in a non-contact manner, the net displacement of two tracking markers was determined using digital image correlation software (Ncorr v1.2; Georgia Institute of Technology, Atlanta, Georgia). The tracking markers were applied to the surface of the bone above and below the osteotomy, and photographs were taken every 100 N during loading (Matlab R2016b; The MathWorks, Inc.) using a digital camera (DFK 23GP031, Resolution: 2592×1944 (5 MP); Imaging Source Europe GmbH, Bremen, Germany).

The different scenarios examined experimentally, showing: a) the intact tibia; b) the first screw configuration with a short bridging span annotated (plate superimposed for clarity); and c) the second screw configuration with a longer bridging span annotated.

Finite element modelling: validation

For validation purposes, FE models were created to replicate the three experimental cases A, B, and C (Abaqus 2017, Simulia; Dassault Systèmes, Paris, France). The Sawbones tibia geometry was created from the previously acquired CT scan using image processing software (ScanIP version M-2017.06; Synopsys, Mountain View, California). Material properties of the surrogate cortical and cancellous bone were assigned based on the manufacturer’s information (Pacific Research Laboratories). Linear elastic isotropic material properties were used with Young’s moduli (Poisson’s ratio) equal to 7.6 GPa (0.24) and 157 MPa (0.3) for cortical and cancellous bone, respectively.

Screws were modelled as cylinders with an outer diameter of 5.0 mm. As the interest of the study was primarily the IFM and plate stress, the screw-bone interaction was modelled as tied for simplification.³² The screw-plate interface was modelled as a penalty-based interaction with a tabulated contact stiffness (Table I) and a standard Coulomb friction model with coefficient of friction equal to 0.8 to represent the macro-interlock of the plate and screw threads mating. Similar values of friction have been used previously to represent rough screw-bone interfaces.³³

Table I.

The pressure-overclosure relationship of the plate-screw contact

Pressure (MPa)	Overclosure (mm)
0	-0.01
10	0.05
100	0.1
1000	1

Reference points representing the experimental proximal and distal centres of rotation (knee and ankle) were defined. These reference points were rigidly connected to the bone surface using a multi-point constraint. The proximal reference point was restrained against transverse movement but allowed to move along the mechanical axis. The distal reference point was restrained against all translations. The load was applied proximally in the same manner as the experimental tests.

The FE models were solved using geometric non-linearity with an implicit solver and automatic incrementation (Abaqus 2017). The models were meshed using fully integrated quadratic tetrahedral elements (C3D10), with an average element edge length of 0.8 mm for the plate, 0.8 mm for the screws, 1.4 mm for the cancellous foam, 1.2 mm for the cortical shell, and 2.0 mm for the callus. In contacting regions, the average element edge length was refined to 0.5 mm. The total number of nodes and elements was 1 050 282 and 769 227, respectively. A mesh convergence study was conducted (convergence criteria, 5%). For the selected mesh resolution, doubling the mesh size altered the prediction of IFM by 3.20%, plate stress by 0.54%, and principal strain in the bone around screw holes by 3.89%.

The predicted principal strains and IFM from the FE models were compared against the experimentally measured values using linear regression.

Finite element modelling: incorporating physiological loading

After validation, a physiological loading case was incorporated. We chose to use the instance of the gait cycle where the medial knee joint contact forces are highest, corresponding to 19% of the gait cycle.³⁴ Muscle and joint contact forces for a 70 kg patient from a previous study³⁴ were registered to our geometry (Matlab R2016b). All forces were applied at reference points and distributed over the surface of the bone within a 10 mm to 12 mm radius (Fig. 3). In these models, the most distal part of the tibial shaft was constrained in all directions and no other restraint was applied (Fig. 3). The muscle force and joint reaction vectors are given in Table II.

a) The measurement locations used to determine the interfragmentary movement (IFM) experimentally and in the finite element (FE) models; b) the locations of the applied muscle force vectors (not to scale).

Table II.

Joint contact and muscle forces applied to the model; the coordinate system is shown in Figure 3b

Force description	Directional force component (n)
	x	y	z
Medial knee joint contact force	45.35	8.84	-984.14
Lateral knee joint contact force	16.09	3.14	-349.25
Biceps femoris (long head)	1.13	-5.59	4.65
Biceps femoris (short head)	1.41	-3.47	6.00
Gracilis	1.30	-23.30	23.45
Rectus femoris	24.36	21.93	74.34
Sartorius	1.16	-0.01	3.35
Semimembranosus	-0.69	-31.74	29.12
Semitendinosus	0.15	-5.71	5.38
Soleus	-7.15	-3.31	-26.39
Tensor fasciae latae	39.34	24.63	191.36
Vastus intermedius	22.83	27.63	78.72
Vastus lateralis	3.11	4.01	13.25
Vastus medialis	52.57	48.36	141.60

Finite element modelling: structural optimization of plate

The shape of the custom plate was structurally optimized for the short and long configurations under physiological loading (Tosca Structure 2017, Simulia; Dassault Systèmes). The optimization process iteratively modified the envelope of the geometry in order to satisfy prescribed optimization functions. Our intention was to reduce the maximum plate stress while increasing the average plate strain to generate IFM. Two equally weighted design optimization functions were used: 1) the maximum strain energy density (SED) anywhere in the plate; and 2) the negative of the minimum SED in the bridging span of the plate. The maximum values of both functions were minimized until the combined SED function was deemed to have converged; at 20 design cycles there was 0.12% change from the previous iteration. Geometric restrictions were placed on the screw holes, and the volume of the plate was constrained to a fraction of 0.9 of the original plate to help reduce underused material. The resulting shape of the optimized plate mesh was smoothed and re-exported.

Finite element modelling: comparison of different plate types with callus healing

The FE model was modified to replace the custom plate with a widely used commercial HTO device (TomoFix; DePuy Synthes). The geometry of the TomoFix plate was obtained by reconstructing micro-CT scan data in a similar manner to the bone geometry. Other than the plate geometry, all aspects of the TomoFix model were identical to the custom plate model. For both plate types, predictions were made for short and long bridging spans. The fracture callus was represented by filling the osteotomy gap with a linearly elastic isotropic homogeneous material. Three stages of early callus healing were incorporated into the models: connective tissue formation; fibrous tissue formation; and immature woven bone formation. Young’s modulus and Poisson’s ratios for each stage are given in Table III.^35,36

Table III.

Callus properties assumed for different stages of bone fracture healing^34,35

Approximate postoperative time, wks	Tissue type	Young’s modulus (MPa)	Poisson’s ratio
0	No callus	N/A	N/A
1	Connective tissue	1.4	0.33
2	Fibrous tissue	28.0	0.3
6	Woven bone	528.0	0.3

N/A, not applicable

Measured output variables

The main variables of interest in the study were the IFM and the peak von Mises stress within the plate. The IFM was defined as the difference in displacement between the measurement locations at the osteotomy site (Fig. 3). Axial IFM was calculated using displacement along the mechanical axis (z-direction), whereas transverse IFM was calculated using the magnitude of the transverse displacements (x- and y-directions). Additionally, the strain levels in the cortical bone around the screw holes were evaluated. A measure of strain concentration, termed εVOL, was used as an output variable, defined as the total volume of bone exposed to a principal strain larger than the cortical bone yield strain of either 0.5% in tension or 0.7% in compression.³⁷

Results

Evaluation of finite element model

The principal strain predictions of the FE models closely correlated with the experimentally measured data (Fig. 4). The linear regression slope (and R²) values for cases A, B, and C were 0.77 (R² = 0.96), 1.13 (R² = 0.98), and 1.06 (R² = 0.98), respectively. The values of measured and predicted axial interfragmentary displacement (IFM) were within 5% at 500 N with a root mean square error (RMSE) of 0.03 mm and 0.02 mm for the short and long bridging spans, respectively (Fig. 5a). Linear regression of the IFM predictions against measured values gave slope (and R²) values of 0.99 (0.996) and 0.94 (0.995) for cases B and C, respectively (Fig. 5b).

Maximum (blue) and minimum (red) principal strain at the five strain gauge locations for: a) the intact tibia; b) the stabilized osteotomized tibia with short span; and c) the stabilized osteotomized tibia with long span. FE, finite element.

a) Values of axial interfragmentary movement (IFM) measured experimentally and finite element (FE) predictions for two different screw arrangements. b) Linear regression of the predicted versus measured IFM values.

Comparison of TomoFix and optimized custom plate

The shape optimization process resulted in the custom plate becoming thicker and wider over the bridging span and around the two screw holes on either side of the osteotomy. Compared with the pre-optimized design, the average plate stress increased while the maximum stress decreased. The underside of the plate also became concave.

Comparing the optimized custom plate against the TomoFix plate, the pattern of IFM produced by the two devices was similar (Fig. 6). The custom plate produced a 4.8% smaller axial IFM than did the TomoFix device in the short bridging span but a 24.1% larger axial IFM in the long bridging span. In the custom plate, shear IFM was increased by 52.1% and 54.8% for short and long bridging spans, respectively (Fig. 6a). The values of IFM underneath the plate followed the same trends as those at the IFM measurement locations (Fig. 6b).

Net axial and transverse interfragmentary movement (IFM) for both plate types and spans under physiological loading with joint contact and muscle forces corresponding to 19% of the gait cycle, showing a) the IFM at the medial measurement locations (Fig. 3) and b) the IFM under the plate.

In both configurations, the TomoFix plate experienced peak plate stresses at the screw hole proximal to the osteotomy and the plate T-junction, whereas the custom plate distributed the stresses more evenly throughout the span bridging the osteotomy (Fig. 7). For the TomoFix plate, the peak von Mises stress was 656 MPa and 654 MPa for short and long bridging configurations, respectively. For the custom plate, the peak stress was 693 MPa for the short span and 715 MPa for the long span. The peak von Mises stress within the custom plate was 5% larger than with the TomoFix plate for the short span and 10% larger for the long span.

Predicted von Mises stress within the plate assuming no callus formation for: a) the TomoFix plate with a short bridging span; b) the TomoFix plate with a long bridging span; c) the custom plate with a short bridging span; and d) the custom plate with a long bridging span. Red regions have values higher than 600 MPa.

Strains in the bone around screw holes

The distribution of strain in the bone around screw locations was different for the two plate types (Fig. 8). For both bridging spans, the TomoFix plates produced larger εVOL around the metaphyseal screw holes compared with the custom plate (Fig. 9), particularly screw holes 1 and 3. The TomoFix plate also produced larger εVOL at the most distal screw (number 8). Compared with the TomoFix, the custom plate produced slightly larger εVOL around the screws adjacent to the osteotomy (numbers 4 and 5) compared with the TomoFix plate. Compared with the short span, the longer span produced 44.1% and 61.1% larger εVOL for the custom plate and the TomoFix, respectively. The εVOL for the custom plate was 32.5% smaller and 39.6% smaller than that of the TomoFix for the short and long spans, respectively. Considering only the screws in metaphyseal bone, the custom plate reduced εVOL by 61.2% and by 51.9% for the short and long spans, respectively.

Predicted absolute maximum principal strain on the surface of the tibia for: a) the TomoFix plate with a short bridging span; b) the TomoFix plate with a long bridging span; c) the custom plate with a short bridging span; and d) the custom plate with a long bridging span. Red and blue regions have values higher than 0.5% (tensile) and -0.7% (compressive) strain, respectively.

Fig. 9.

Predicted volume of elements exceeding the yield strain of cortical bone (εVOL) for the different plates and screw configurations examined in the study. Results shown are for complete osteotomy gap (no callus healing).

Influence of fracture callus

As the stiffness of the callus increased, the stress in both plate types decreased (Fig. 10). Peak von Mises stress in the TomoFix plate was very similar for both span lengths. The custom short span plate produced lower peak stress compared with the custom long span plate. The peak stress was higher than the fatigue strength of titanium for all cases, except when a callus stiffness of 528 MPa was used (corresponding to immature woven bone).

Fig. 10.

Predicted von Mises stress in the different plate types and configurations for different levels of callus formation.

Discussion

This study investigated the biomechanical environment produced by two HTO plate types under physiological loading. Different bridging spans were considered by changing the number of screws used. The study was performed using a validated FE model and demonstrated that longer bridging spans did not necessarily increase plate stress. When early callus formation was included in the models, the plate stress was similar or lower for the longer bridging spans compared with the shorter bridging spans.

By using an optimization algorithm to increase the average plate strain while minimizing the maximum plate strain, we designed a custom plate that produced higher IFM and smaller regions of high strain in the bone compared with the TomoFix design with similar levels of peak stress. It should be noted that if plate stress was the only specified optimization goal, the resulting plate stress could be substantially lower; however, the stiffness would be increased. To ensure the final plate design was flexible, we also included plate deformation as an equally weighted optimization goal.

Our study confirmed the findings of previous studies that increasing the bridging span increased the axial and transverse IFM.^38,39 Augat et al⁴⁰ demonstrated that transverse motion in the absence of axial motion can delay or prevent fracture healing. Park et al⁴¹ showed that oblique motion (a combination of axial and transverse motion) produced the best healing in terms of callus formation. It is also known that intramedullary nails perform very well despite producing larger transverse movements than axial movements at the fracture site.⁴² Therefore, provided that the device adequately stabilizes the fracture, the combination of transverse and axial IFM may be superior to predominantly or exclusively axial motion.

In previous studies that looked at locking plates, bridging span had a more pronounced influence on IFM than found in our study,^38,39 and we attributed this difference to two factors: 1) the orientation of the HTO plate with respect to the loading axis; and 2) the presence of the intact cortical hinge laterally. From the deformation observed in our models, it was clear that the plate bending was mainly around its major axis (the stiffer direction). Additionally, the intact lateral hinge resisted plate bending in the weak axis direction. It is likely that a complete osteotomy or a broken lateral hinge would substantially increase IFM.

The study predicted peak plate stresses in both plate designs to be lower than the yield strength of Ti-6Al-4V (approximately 789 MPa to 1013 MPa⁴³). In our gap defect models, the plate stresses were much higher than the fatigue strength of titanium (approximately 150 MPa for fatigue fretting in phosphate-buffered saline⁴³), indicating that callus healing is required to prevent fatigue failure.

Strain levels around screws can be indicative of loosening risk.^44,45 When using the TomoFix plate, our study predicted the strains within the bone to be largest in the proximal tibial fragment. This is the location where screw loosening and breakage have been reported to occur clinically,⁴⁶ giving us confidence in the clinical relevance of the modelling predictions. The optimized custom plate reduced strain levels in the proximal tibia where the bone stock is weaker. We attributed this finding to the increased amount of material surrounding the screws compared with the TomoFix plate – higher rigidity screws are known to reduce strain at the screw-bone interface.⁴⁷ One previous study reported a 6.7% rate of tibial plateau fracture; we did not investigate this aspect in our models, however, as the authors attributed it to a technical error of leaving too much lateral cortex intact.⁴⁸

Martinez de Albornoz et al⁴⁹ conducted biomechanical experiments to evaluate IFM using different plate types and found larger values than the present study. Their study used low density synthetic bone and measured IFM at the loading actuator, making their results difficult to interpret. Other authors have measured much smaller displacements.^50,51 However, they used a highly constrained experimental setup, which is likely to have influenced the results.³¹ Additionally, Röderer et al⁵¹ measured very small values of IFM in one cadaveric model (0.05 mm at 1000 N) examining an alternative screw type, which they found dramatically increased the IFM to 0.16 mm at 1000 N. A previous experimental and computational study by Luo et al²⁸ used a similar loading regime to the present study and found IFM values for a TomoFix implant placed in the same orientation as the present study to be 0.93 mm at 2000 N.

This study has several important limitations. The operative technique for TomoFix includes the use of a compression screw to pull the plate closer to the bone, thus generating tensile preload in the plate and compressive preload in the lateral cortical hinge. We did not incorporate this phenomenon as it would be highly variable depending on the size of the hinge and the position of the plate. It would, however, alter predictions of plate stress, IFM, and εVOL. Validation was only conducted using the custom plate, and we assumed that the screw-plate contact parameters would be the same for the TomoFix plate. The experimental tests were primarily for validation purposes, with Sawbones selected for their consistent material properties.^25,52 Nevertheless, we only used a single specimen. It is difficult to compare our results with those of previous studies due to differences in loading regimes and geometrical variation such as the size of the lateral hinge, specimen dimensions, methods of restraining the specimens, and material properties. The material properties of third-generation Sawbones are different in compression and tension.⁵² We chose to use the compressive Young’s moduli as our test was a compression test, and implementing differing compressive and tensile moduli in FE codes is not straightforward. Moreover, the material properties of surrogate cortical bone may not be representative of human bone, particularly in osteoporotic cases. We considered the joint contact and muscle forces at 19% of the gait cycle. We also examined the influence of using forces corresponding to 44% of the gait cycle (second contact force peak) but found that it was not as critical for plate stress predictions. In our models, we evaluated the different plate types and configurations using predefined callus properties to represent different healing stages. It is known, however, that plates with larger IFM promote faster callus formation and thus also reduce plate stress more quickly.⁵³

In conclusion, we found that larger bridging spans, particularly transverse movements, have the potential to increase substantially the IFM produced at the fracture site. Our optimized plate design produced similar plate stress to the TomoFix plate for both short and long bridging spans while substantially reducing high strain regions within the bone. This study has shown that both plate types and spans produced very large plate stresses in the gap defect model. Substantial callus formation was required in all cases to reduce stress below the fatigue strength of titanium.

Funding Statement

We gratefully acknowledge the support of Arthritis Research UK (grant number: POC055) and Innovate UK (grant number: 102930). We also thank colleagues from the University of Bath including Stephen Coombes for help with instrumentation, Clare Ball for micro-CT scanning and Nick Waywell for experimental support.