Experimental and probabilistic analysis of distal femoral periprosthetic fracture: a comparison of locking plate and intramedullary nail fixation. Part B: probabilistic investigation

The following is Part B of a two-part study. Part A evaluated, biomechanically, intramedullary (IM) nails versus locking plates for fixation of an extra-articular, metaphyseal wedge fracture in synthetic osteoporotic bone. Part B of this study introduces deterministic finite element (FE) models of each construct type in synthetic osteoporotic bone and investigates the probability of periprosthetic fracture of the locking plate compared with the retrograde IM nail using Monte Carlo simulation. Deterministic FE models of the fractured femur implanted with IM nail and locking plate, respectively, were developed and validated using experimental data presented in Part A of this study. The models were validated by comparing the load-displacement curve of the experimental data with the load-displacement curve of the FE simulation with a root-mean square error of less than 3?mm. The validated FE models were then modified by defining the cortical and cancellous bone modulus of elasticity as uncertain variables that could be assumed to vary randomly. Monte Carlo simulation was used to evaluate the probability of fracture (POF) of each fixation. The POF represents the cumulative probability that the predicted shear stresses in the cortical bone will exceed the expected shear strength of the cortical bone. This investigation provides information regarding the significance of post-operative damage accumulation on the POF of the implanted bones when the two fixations are used. The probabilistic analysis found the locking plate fixation to have a higher POF than the IM nail fixation under the applied loading conditions (locking plate 21.8% versus IM nail 0.019%).     

Impact response and simulation of damaged ulna with internal fixation

The objectives of this work were to explore a methodology that combines static and dynamic finite element (FE) analysis, linear elastic fracture mechanics (LEFM) and experimental methods to investigate a worst-case scenario in which a previously damaged bone plate system is subjected to an impact load. Cadaver ulnas with and without midshaft dynamic compression plates are subjected to a static three-point bend test and loaded such that subcritical crack growth occurs as predicted by a hybrid method that couples LEFM and static FE. The plated and unplated bones are then unloaded and subsequently subjected to a midshaft transverse impact test. A dynamic strain-based FE model is also developed to model the midshaft transverse impact test. The average value of the impact energy required for failure was observed to be 10.53% greater for the plated set. There appears to be a trade-off between impact damage and impact resistance when ulnas are supported by fixation devices. Predictions from the dynamic FE model are shown to corroborate inferences from the experimental approach.     

Biomechanical comparison of conventional and optimised locking plates for the fixation of intraarticular calcaneal fractures: a finite element analysis

Intraarticular calcaneal fractures can result in poor prognosis. Although operative fixation can improve the functional outcomes in most cases, surgical complications such as loss of reduction and wound healing problems may increase the risk of reoperation. Hence, this study aimed to design calcaneal locking plate with a lower profile and better biomechanical performance and to compare the redesigned plate with the traditional calcaneal plate via the finite element method. A Sanders’ type II-C intraarticular calcaneal fracture was simulated. Two fixation models utilising the branch-like calcaneal locking plate and the full plate were constructed. Topology optimisation was conducted to generate a new calcaneal plate design. A biomechanical comparison among the three groups of plates was performed using the finite element method. For the fracture simulated in this study, the optimised plate was superior to the traditional plate in terms of fixation stability and safety but was reduced in volume by approximately 12.34%. In addition, more rational stress distributions were observed in the redesigned plate, underscoring the superiority of this new design in terms of fatigue strength. These results demonstrate that the topology optimisation can be used to design a new implant with a minimised profile and no loss of fixation stability.     

基于有限元的第5 掌骨颈骨折钢板螺钉内固定的生物力学分析

目的：应用有限元方法建立三种不同的治疗第5 掌骨颈骨折的钢板螺钉内固定模型,比较三种模型的生物力学稳定性,为 第5 掌骨颈骨折的临床早期功能康复提供参考。方法：选取一名健康青年志愿者,将CT 扫描数据导入三维有限元软件建立第5 掌骨颈骨折模型,并选取三种钢板螺钉内固定方法进行骨折固定。对三种模型施加外力荷载并进行生物力学有限元分析,对比骨 折断端的最大位移和钢板螺钉的应力分布情况。结果：方法一、二、三的第5 掌骨骨折端的最大位移分别为0.189775 mm、 0.181428 mm、0.224299 mm,以方法二的骨折端位移最小;内固定材料的最大应力分别为1.20 KPa、1.00 KPa、1.39 KPa,以方法二 的钢板螺钉应力最小。结论：采用近端三颗螺钉远端两颗螺钉的直型钢板内固定方法治疗第五掌骨颈骨折的生物力学稳定性更 好,术后早期功能锻炼的安全性更高,是治疗第5 掌骨颈骨折的理想内固定方法。     

Experimental and probabilistic analysis of distal femoral periprosthetic fracture: a comparison of locking plate and intramedullary nail fixation. Part A: experimental investigation

The following is a two-part study. Part A evaluates biomechanically intramedullary (IM) nails vs. locking plates for fixation of femoral fractures in osteoporotic bone. Part B of this study introduces a deterministic finite element model of each construct type and investigates the probability of periprosthetic fracture of the locking plate compared with the retrograde IM nail using Monte Carlo simulation. For Part A, an extra-articular, metaphyseal wedge fracture pattern was created in 11 osteoporotic fourth-generation composite femurs. Fixation was performed with a locking plate or a retrograde IM nail. Axial, torsion and bending cyclic loading to simulate post-operative damage accumulation were performed followed by ramped load to failure. Locking plates proved to be more stable (using stiffness as the determining factor) in osteoporotic bone as observed under low load cycle conditions. However, some of these advantages were offset by a greater incidence of sudden periprosthetic fracture observed under ramped loading conditions. Cadaveric, osteoporotic femurs included as a case study also exhibited periprosthetic fracture, but failure was accompanied by catastrophic comminution of the cortex. Periprosthetic failure at the implant end including bone comminution is difficult to salvage with revision fixation. The weakened trabecular matrix and thinned cortex of osteoporotic bone may increase the incidence of periprosthetic fracture. It is, therefore, essential for the surgeon to consider all possible loading scenarios when recommending an ideal implant for the osteoporotic patient.     

Reasons why dynamic compression plates are inferior to locking plates in osteoporotic bone: a finite element explanation

While locking plate fixation is becoming increasingly popular for complex and osteoporotic fractures, for many indications compression plating remains the standard choice. This study compares the mechanical behaviour of the more recent locking compression plate (LCP) device, with the traditional dynamic compression plates (DCPs) in bone of varying quality using finite element modelling. The bone properties considered include orthotropy, inhomogeneity, cortical thinning and periosteal apposition associated with osteoporosis. The effect of preloads induced by compression plating was included in the models. Two different fracture scenarios were modelled: one with complete reduction and one with a fracture gap. The results show that the preload arising in DCPs results in large principal strains in the bone all around the perimeter of the screw hole, whereas for LCPs large principal strains occur primarily on the side of the screw proximal to the load. The strains within the bone produced by the two screw types are similar in healthy bone with a reduced fracture gap; however, the DCP produces much larger strains in osteoporotic bone. In the presence of a fracture gap, the DCP results in a considerably larger region with high tensile strains and a slightly smaller region with high compressive strains. These findings provide a biomechanical basis for the reported improved performance of locking plates in poorer bone quality.     

Finite element analysis of acetabular fractures—development and validation with a synthetic pelvis

Acetabular fracture presents a challenging situation to trauma surgeons today due to its complexity. Finite element (FE) models can be of great help as they can improve the surgical planning and post surgery patient management for those with acetabular fractures. We have developed a non-linear finite element model of the pelvis and validated its fracture prediction capability with synthetic polyurethane pelves. A mechanical experiment was performed with the synthetic bones and fracture loads and patterns were observed for two different loading cases. Fracture loads predicted by our FE model were within one standard deviation of the experimental fracture loads for both loading cases. The incipient fracture pattern predicted by the model also resembled the actual pattern from the experiment. Although it is not a complete validation with human cadaver bones, the good agreement between model predictions and experimental results indicate the validity of our approach in using non-linear FE formulation along with contact conditions in predicting bone fractures.     

Specimen-specific modeling of hip fracture pattern and repair

Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants.     

Biomechanical comparison of locking plate and crossing metallic and absorbable screws fixations for intra-articular calcaneal fractures

The locking plate and percutaneous crossing metallic screws and crossing absorbable screws have been used clinically to treat intra-articular calcaneal fractures, but little is known about the biomechanical differences between them. This study compared the biomechanical stability of calcaneal fractures fixed using a locking plate and crossing screws. Three-dimensional finite-element models of intact and fractured calcanei were developed based on the CT images of a cadaveric sample. Surgeries were simulated on models of Sanders type III calcaneal fractures to produce accurate postoperative models fixed by the three implants. A vertical force was applied to the superior surface of the subtalar joint to simulate the stance phase of a walking gait. This model was validated by an in vitro experiment using the same calcaneal sample. The intact calcaneus showed greater stiffness than the fixation models. Of the three fixations, the locking plate produced the greatest stiffness and the highest von Mises stress peak. The micromotion of the fracture fixated with the locking plate was similar to that of the fracture fixated with the metallic screws but smaller than that fixated with the absorbable screws. Fixation with both plate and crossing screws can be used to treat intra-articular calcaneal fractures. In general, fixation with crossing metallic screws is preferable because it provides sufficient stability with less stress shielding.     

Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods

Trabecular plates play an important role in determining elastic moduli of trabecular bone. However, the relative contribution of trabecular plates and rods to strength behavior is still not clear. In this study, individual trabeculae segmentation (ITS) and nonlinear finite element (FE) analyses were used to evaluate the roles of trabecular types and orientations in the failure initiation and progression in human vertebral trabecular bone. Fifteen human vertebral trabecular bone samples were imaged using micro computed tomography (μCT), and segmented using ITS into individual plates and rods by orientation (longitudinal, oblique, and transverse). Nonlinear FE analysis was conducted to perform a compression simulation for each sample up to 1% apparent strain. The apparent and relative trabecular number and tissue fraction of failed trabecular plates and rods were recorded during loading and data were stratified by trabecular orientation. More trabecular rods (both in number and tissue fraction) failed at the initiation of compression (0.1–0.2% apparent strain) while more plates failed around the apparent yield point (>0.7% apparent strain). A significant correlation between plate bone volume fraction (pBV/TV) and apparent yield strength was found (r²=0.85). From 0.3% to 1% apparent strain, significantly more longitudinal trabecular plate and transverse rod failed than other types of trabeculae. While failure initiates at rods and rods fail disproportionally to their number, plates contribute significantly to the apparent yield strength because of their larger number and tissue volume. The relative failed number and tissue fraction at apparent yield point indicate homogeneous local failure in plates and rods of different orientations.     

Quantitative computed tomography-based finite element models of the human lumbar vertebral body: effect of element size on stiffness,damage, and fracture strength predictions

This study investigated the numerical convergence characteristics of specimen-specific "voxel-based" finite element models of 14 excised human cadaveric lumbar vertebral bodies (age: 37-87; M = 6, F = 8) that were generated automatically from clinical-type CT scans. With eventual clinical applications in mind, the ability of the model stiffness to predict the experimentally measured compressive fracture strength of the vertebral bodies was also assessed. The stiffness of "low"-resolution models (3 x 3 x 3 mm element size) was on average only 4% greater (p = 0.03) than for "high"-resolution models (1 x 1 x 1.5 mm) despite interspecimen variations that varied over four-fold. Damage predictions using low- vs high-resolution models were significantly different (p = 0.01) at loads corresponding to an overall strain of 0.5%. Both the high (r2 = 0.94) and low (r2 = 0.92) resolution model stiffness values were highly correlated with the experimentally measured ultimate strength values. Because vertebral stiffness variations in the population are much greater than those that arise from differences in voxel size, these results indicate that imaging resolution is not critical in cross-sectional studies of this parameter. However, longitudinal studies that seek to track more subtle changes in stiffness over time should account for the small but highly significant effects of voxel size. These results also demonstrate that an automated voxel-based finite element modeling technique may provide an excellent noninvasive assessment of vertebral strength.     

Structural parameters determining the strength of the porcine vertebral body affected by tumours

Spinal metastatic disease could lead to catastrophic consequences for the patient. However, the structural parameters that explain the weakening of vertebrae affected by tumours are not fully understood. In this study, we developed a specimen-specific finite element model to predict the strength of the porcine vertebra with simulated tumours and used it to find the structural parameters determining the strength. We validated our model with mechanical testing and then we analysed the compressive strength of intact vertebrae and seven defects with different size and shape. The results showed that the minimum bone mineral mass of the cross section and areal defect fraction were the best predictors of the normalized strength. We also found that areal parameters appeared to be better predictors than the volumetric ones. In conclusion, reduction in bone strength for vertebrae weakened by metastatic tumours is mostly associated with decrease in the mechanical properties of the cross section.     

Modal behaviour of bones during fracture

A common cause of human disability is related to the fracture of bones, complex structural materials whose properties vary with time. An analytical study (using ANSYS, a commercial finite element package) of bones under fracture conditions is presented, focusing on the frequency variation versus depth of crack, as well as on the evolution of strength in the fracture area.     

Design and experimental evaluation of adjustable bone plates for mandibular fracture fixation

Conventional bone plates are commonly used for surgical mandibular fracture fixation. Improper alignment between bone segments, however, can result in malocclusion. Current methods of fixation require a surgeon to visually align segments of bone and affix a metal plate using bone screws, after which little can be done to adjust alignment. A method of adjusting fracture alignment after plate placement, without screw removal, presents an improvement over costly and risky revision surgery. A modified bone plate has been designed with a deformable section to give surgeons the ability to reduce misalignments at the fracture site. The mechanics of deformation for various adjustment mechanisms was explored analytically, numerically, and experimentally to ensure that the adjustable plate is comparable to conventional bone plates. A static force of 358.8 N is required to deform the adjustable bone plate, compared with predicted values of 351 N using numerical simulation and 362 N using a simple beam theory. Dynamic testing was performed to simulate in vivo loading conditions and evaluate load-capacity in both deformed and un-deformed bone plates. Results indicate that bending stiffness of a rectangular bone plate is 709 N/mm, compared with 174 N/mm for an octagonal plate and 176 N/mm for standard plates. Once deformed, the rectangular and octagonal plates had a stiffness of 323 N/mm and 228 N/mm, respectively. Un-deformed and deformed adjustable bone plates have efficacy in bone segment fixation and healing.     

Mesh-morphing algorithms for specimen-specific finite element modeling

Despite recent advances in software for meshing specimen-specific geometries, considerable effort is still often required to produce and analyze specimen-specific models suitable for biomechanical analysis through finite element modeling. We hypothesize that it is possible to obtain accurate models by adapting a pre-existing geometry to represent a target specimen using morphing techniques. Here we present two algorithms for morphing, automated wrapping (AW) and manual landmarks (ML), and demonstrate their use to prepare specimen-specific models of caudal rat vertebrae. We evaluate the algorithms by measuring the distance between target and morphed geometries and by comparing response to axial loading simulated with finite element (FE) methods.

First a traditional reconstruction process based on μCT was used to obtain two natural specimen-specific FE models. Next, the two morphing algorithms were used to compute mappings from the surface of one model, the source, to the other, the target, and to use this mapping to morph the source mesh to produce a target mesh. The μCT images were then used to assign element-specific material properties. In AW the mappings were obtained by wrapping the source and target surfaces with an auxiliary triangulated surface. In ML, landmarks were manually placed on corresponding locations on the surfaces of both source and target.

Both morphing algorithms were successful in reproducing the shape of the target vertebra with a median distance between natural and morphed models of 18.8 and 32.2 μm, respectively, for AW and ML. Whereas AW–morphing produced a surface more closely resembling that of the target, ML guaranteed correspondence of the landmark locations between source and target. Morphing preserved the quality of the mesh producing models suitable for FE simulation. Moreover, there were only minor differences between natural and morphed models in predictions of deformation, strain and stress. We therefore conclude that it is possible to use mesh-morphing techniques to produce accurate specimen-specific FE models of caudal rat vertebrae. Mesh morphing techniques provide advantages over conventional specimen-specific finite element modeling by reducing the effort required to generate multiple target specimen models, facilitating intermodel comparisons through correspondence of nodes and maintenance of connectivity, and lends itself to parametric evaluation of “artificial” geometries with a focus on optimizing reconstruction.     

Chondrocyte apoptosis enhanced at the growth plate: a physeal response to a diaphyseal fracture

Post-traumatic overgrowth of growing long bones is a common clinical phenomenon in paediatric traumatology and is the result of an enhanced stimulation of the nearby growth plate after fracture. To date, the exact post-fractural reactions of the growth plate are poorly understood. The aim of this study has been to determine the impact of fracture on the frequency of chondrocyte apoptosis of the growth plate. Rats sustained a mid-diaphyseal closed fracture of the left tibia or were left untreated. All animals were killed 3, 10, 14 or 29 days after trauma. The left and right tibiae were harvested and apoptotic chondrocytes of the proximal tibial growth plate were detected by TUNEL staining. The apoptosis percentage of physeal chondrocytes was statistically compared among fractured bones, intact contra-lateral bones and control bones. The physeal apoptosis rate of the fractured bone was significantly higher than that of the contra-lateral intact bone (valid for all evaluated days) and the control bone (valid from day 10 onwards). Contra-lateral intact tibiae never showed significantly higher apoptosis rates compared with control tibiae. Thus, mid-diaphyseal fracture influences the nearby growth plate by stimulating chondrocyte programmed cell death, which is associated with cartilage resorption and bone replacement. The lack of a significant difference between the intact contra-lateral and the intact control bone suggests that fracture only has a local effect that contributes to the greater apoptosis rate of the adjacent physis.     

Simulating distal radius fracture strength using biomechanical tests: a modeling study examining the influence of boundary conditions

Distal radius fracture strength has been quantified using in vitro biomechanical testing. These tests are frequently performed using one of two methods: (1) load is applied directly to the embedded isolated radius or (2) load is applied through the hand with the wrist joint intact. Fracture loads established using the isolated radius method are consistently 1.5 to 3 times greater than those for the intact wrist method. To address this discrepancy, a validated finite element modeling procedure was used to predict distal radius fracture strength for 22 female forearms under boundary conditions simulating the isolated radius and intact wrist method. Predicted fracture strength was highly correlated between methods (r = 0.94; p < 0.001); however, intact wrist simulations were characterized by significantly reduced cortical shell load carriage and increased stress and strain concentrations. These changes resulted in fracture strength values less than half those predicted for the isolated radius simulations (2274 ± 824 N for isolated radius, 1124 ± 375 N for intact wrist; p < 0.001). The isolated radius method underestimated the mechanical importance of the trabecular compartment compared to the more physiologically relevant intact wrist scenario. These differences should be borne in mind when interpreting the physiologic importance of mechanical testing and simulation results.     

Three-dimensional design optimisation of patient-specific femoral plates as a means of bone remodelling reduction

Previous investigations into the optimisation of internal plates have mostly focused on the material properties of the implant. In this work, we optimise the shape, size and placement of the plate for successfully minimising bone remodelling around the implant. A design optimisation algorithm based on strain energy density criterion, combined with the finite element analysis, has been used in this study. The main optimisation goal was to reduce this change and keep it close to the conditions of an intact femur. The results suggest that the anterolateral side of the bone would be the optimum location for the plate, as for the geometry, the optimum moves towards having a thick, wide and short plate. These important results could be directly applicable to orthopaedic surgeons treating a femur fracture with internal plates. Since the optimisation algorithm remains the same for any patient, this advancement provides the surgeon with a tool to minimise the post surgery remodelling by trying to maintain the natural structure of the bone.     

Long bone torsion: II. A combined experimental and computational method for determining an effective shear modulus

A technique is established which allows an effective torsional shear modulus to be determined for long bones, while remaining nondestructive to whole bone specimens. Strain gages are bonded to the diaphysis of the bone. Strains are then recorded under pure torsional loads. Theoretical stress predictions are combined with experimental strain recordings to arrive at a modulus value. Shear modulus calculations for four canine radii are reported using theoretical stress predictions from circular, elliptical and finite element models of the transverse bone geometry. The effective shear modulus, obtained from an average of the shear moduli determined at strain gage locations, serves to average the heterogeneous shear modulus distribution over the cross section. The shear modulus obtained is that associated with the "circumferential" direction in transverse planes.     

Virtual structural analysis of tibial fracture healing from low-dose clinical CT scans

Quantitative assessment of bone fracture healing remains a significant challenge in orthopaedic trauma research. Accordingly, we developed a new technique for assessing bone healing using virtual mechano-structural analysis of computed tomography (CT) scans. CT scans from 19 fractured human tibiae at 12 weeks after surgery were segmented and prepared for finite element analysis (FEA). Boundary conditions were applied to the models to simulate a torsion test that is commonly used to access the structural integrity of long bones in animal models of fracture healing. The output of each model was the virtual torsional rigidity (VTR) of the healing zone, normalized to the torsional rigidity of each patient’s virtually reconstructed tibia. This provided a structural measure to track the percentage of healing each patient had undergone. Callus morphometric measurements were also collected from the CT scans. Results showed that at 12 weeks post-op, more than 75% of patients achieved a normalized VTR (torsional rigidity relative to uninjured bone) of 85% or above. The predicted intact torsional rigidities compared well with published cadaveric data. Across all patients, callus volume and density were weakly and non-significantly correlated with normalized VTR and time to clinical union. Conversely, normalized VTR was significantly correlated with time to union (R² = 0.383, p = 0.005). This suggests that fracture scoring methods based on the visual appearance of callus may not accurately predict mechanical integrity. The image-based structural analysis presented here may be a useful technique for assessment of bone healing in orthopaedic trauma research.