Effect of local density changes on the failure load of the proximal femur

Finite element analysis of fixation effect for femoral neck fracture under different fixation configurations

In this study, the biomechanical differences among three internal fixation configurations for treatment of Pauwels type II and III femoral neck fractures were analyzed. Using finite element analysis, the femur displacement and stress distributions of the internal fixation device and fracture section were obtained for different patients and movement conditions. The results show that patients with osteoporosis are more prone to femoral varus and femoral neck shortening, and the fracture probability of the device for these patients is higher than that for patients with normal bone. The treatment effect of the inverted-triangle screw (ITS) fixation and proximal femoral nail anti-rotation (PFNA) fixation is better than that of dynamic hip screw (DHS) fixation. The ITS fixation is more suitable for the treatment of the normal bone patients with Pauwels II femur neck fracture. However, the PFNA fixation has better biomechanical advantages and better capability for anti-femoral neck shortening. Therefore, it is suitable for the treatment of femoral neck fracture patients with osteoporosis.

Assessment of femoral neck strength and bone mineral density changes following exercise using 3D-DXA images

Physical exercise induces spatially heterogeneous bone changes in the proximal femur. Recent advances have enabled 3D dual-energy X-ray Absorptiometry (DXA)-based finite element (FE) models to estimate bone strength. However, its ability to detect exercise-induced BMD and strength changes is unclear. The aim of this study was to quantify the repeatability of vBMD and femoral neck strength obtained from 3D-DXA images and determine the changes due an exercise intervention. The DXA scans included pairs of same-day repeated scans from ten healthy females and pre- and post-exercise intervention scans of 26 males. FE models with element-by-element correspondence were generated by morphing a template mesh to each bone. BMD and femoral strength under single-leg-stance and sideways fall loading configurations were obtained for both groups and compared. In the repeated images, the total hip vBMD difference was 0.5 ± 2.5%. Element-by-element BMD differences reached 30 ± 50%. The strength difference in single-leg stance was 2.8 ± 13% and in sideways fall was 4.5% ± 19%. In the exercise group, strength changes were 6 ± 19% under single-leg stance and 1 ± 18% under sideways fall. vBMD parameters were weakly correlated to strength (R² < 0.31). The exercise group had a mean bone accrual exceeding repeatability values in the femoral head and cortical regions. The case with the highest vBMD change (6.4%) caused 18% and -7% strength changes under single-leg stance and sideways fall. 3D-DXA technology can assess the effect of exercise interventions in large cohorts but its validity in individual cases should be interpreted with caution.

Assessment of finite element models for prediction of osteoporotic fracture

With increasing life expectancy and mortality rates, the burden of osteoporotic hip fractures is continually on an upward trend. In terms of prevention, there are several osteoporosis treatment strategies such as anti-resorptive drug treatments, which attempt to retard the rate of bone resorption, while promoting the rate of formation. With respect to prediction, several studies have provided insights into obtaining bone strength by non-invasive means through the application of FE analysis. However, what valuable information can we obtain from FE studies that have focused on osteoporosis research, with respect to the prediction of osteoporotic fractures? This paper aims to fine studies that have used FE analysis to predict fractures in the proximal femur through a systematic search of literature using PUBMED, with the main objective of supporting the diagnosis of osteoporosis. The focus of these FE studies is first discussed, and the methodological aspects are summarized, by mainly comparing and contrasting their meshing properties, material properties, and boundary conditions. The implications of these methodological differences in FE modelling processes and propositions with the aim of consolidating or minimalizing these differences are further discussed. We proved that studies need to start converging in terms of their input parameters to make the FE method applicable to clinical settings. This, in turn, will decrease the time needed for in vitro tests. Current advancements in FE analysis need to be consolidated before any further steps can be taken to implement engineering analysis into the clinical scenario.

Bone mechanical properties and changes with osteoporosis

This review will define the role of collagen and within-bone heterogeneity and elaborate the importance of trabecular and cortical architecture with regard to their effect on the mechanical strength of bone. For each of these factors, the changes seen with osteoporosis and ageing will be described and how they can compromise strength and eventually lead to bone fragility.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Fracture prevention by prophylactic femoroplasty of the proximal femur--metallic compared with cemented augmentation

OBJECTIVES

To compare 2 different femoral neck augmentation techniques at improving the mechanical strength of the femoral neck.

METHODS

Twenty pairs of human cadaveric femora were randomly divided into 2 groups. In 1 group, the femora were augmented with a steel spiral; the other group with the cemented technique. The untreated contralateral side served as an intraindividual control. Fracture strength was evaluated using an established biomechanical testing scenario mimicking a fall on the greater trochanter (Hayes fall).

RESULTS

The peak load to failure was significantly higher in the steel spiral group (P = 0.0024) and in the cemented group (P = 0.001) compared with the intraindividual controls. The peak load to failure showed a median of 3167 N (1825-5230 N) in the spiral group and 2485 N (1066-4395 N) in the spiral control group. The peak load to failure in the cemented group was 3698 N (SD ± 1249 N) compared with 2763 N (SD ± 1335 N) in the cement control group. Furthermore, fracture displacement was clearly reduced in the steel spiral group.

CONCLUSIONS

Femoral augmentations using steel spirals or cement-based femoroplasty are technically feasible procedures. Our results demonstrate that a prophylactic reinforced proximal femur has higher strength when compared with the untreated contralateral limb. Prophylactic augmentation has potential to become an auxiliary treatment option to protect the osteoporotic proximal femur against fracture.

Development of an animal fracture model for evaluation of cement augmentation femoroplasty: an in vitro biomechanical study

Osteoporotic hip fracture is the most severe kind of fracture with high morbidity and mortality. Patients' ambulation and quality of life are significantly affected by the fracture because only 50% regain their prefracture functional status, even if they undergo surgeries. There are many issues associated with the current preventive methods e.g., cost, side effects, patient compliance, and time for onset of action. Femoroplasty, the injection of bone cement into the proximal femur to augment femoral strength and to prevent fracture, has been an option with great potential. However, until now femoroplasty has remained at the stage of biomechanical testing. No in vivo study has evaluated its safety and effectiveness; there is not even an animal model for such investigations. The objective of this study was to develop a proximal femur fracture goat model that consistently fractures at the proximal femur when subject to vertical load, simulating osteoporotic hip fractures in human. Six pairs of fresh frozen mature Chinese goats' femora were obtained and randomly assigned into two groups. For the experimental group, a cylindrical bone defect was created at the proximal femur, while the control was left untreated. In addition, a configuration to mimic the mechanical axis of the goat femur was developed. When subjected to load along the mechanical axis, all the specimens from the bone defect group experienced femoral neck fractures, while fractures occurred at the femoral neck or other sites of the proximal femur in the control group. The biomechanical property (failure load) of the bone defect specimens was significantly lower than that of the control specimens (p<0.05). Osteoporotic hip fractures of humans were simulated by a goat fracture model, which may serve as a reference for future femoroplasty studies in vivo. The newly developed configuration simulating a femoral mechanical axis for biomechanical tests was practicable during the study.

PREDICTION OF PROXIMAL FEMORAL FRACTURE IN SIDEWAYS FALLS USING NONLINEAR DYNAMIC FINITE ELEMENT ANALYSIS

Hip fracture incidence caused by sideways falls is increasing year by year. The high morbidity and mortality not only cast a gloom over the life, but also increase the medical cost of the country. From a biomechanical perspective, hip fractures are related to different loading directions. The main purpose of this study is to investigate how different hip fracture types are affected by impact directions. The geometry of a proximal femur was obtained from the CT scan data of a 67-year-old Chinese male. Mimics and Ansys softwares were applied to establish the cortical bone and cancellous bone models. Six different loading cases, i.e., SW1 (α = 120°, β = 0°), SW2 (α = 90°, β = 0°), SW3 (α = 60°, β = 0°), SW4 (α = 20°, β = 0°), SW5 (α = 120°, β = 15°), SW6 (α = 120°, β = 45°) were defined as the angle α with reference to the long axis of the femur in the frontal plane, and β with reference to the femoral neck axis in the horizontal plane. They were established to simulate sideways falls by explicit dynamic nonlinear finite element analyses in ANSYS-LS-DYNA software. The impact speed was 3.17 m/s. Stress and strain analyses with time history of the fracture sites were taken to find the relationships between fracture types and impact directions. SW1–SW4 caused femoral neck fractures, and the maximum principal stresses were 4.5, 6, 5 and 4.8 MPa, respectively. SW5 caused compound fractures including neck fracture and trochanteric fracture, and the maximum principal stresses were 6.8 MPa and 6.5 MPa, respectively. SW6 caused trochanteric fracture, and the maximum principal stress was 4.2 MPa. The maximum principal strains of neck fracture (0.075, 0.135, 0.175, 0.092) and trochanteric fracture (0.045) increased to the maximum values in 10 ms after impact, and were much higher than the ultimate compressive strain of cancellous bone. These results were consistent with the clinical findings. This study showed that falling posture was an important factor leading to different types of fracture. Dynamic simulation was more effective in explaining the fracture mechanism and determining the load direction that caused hip fracture. The study also provided a theoretical basis for more targeted preventive measures for different types of hip fracture in clinics.

A NEW PARADIGM FOR THE IN VITRO SIMULATION OF SIDEWAYS FALL LOADING OF THE PROXIMAL HUMAN FEMUR

Although the direction of loads applied to the proximal human femur is unpredictable during sideways fall, most in vitro and numerical simulations refer to a single loading condition (15° internal rotation; 10° adduction), which has been anecdotally suggested in the 1950s. The aim of the present study was to improve in vitro simulations of sideways falls on the proximal femur.

An in vitro setup was developed that allowed exploring a range of loading directions +/-90° internal–external rotation; 0°–50° adduction). To enable accurate control of the loading conditions (direction and magnitude of all load components applied to the femur), the setup included a number of low-friction linear and rotary bearings. The setup was instrumented with an axial and a torsional load cell, three displacement transducers and a rotation transducer to monitor the most significant components of load/displacement during testing. The strain distribution was measured on the bone surface (16 triaxial strain gauges, 2,000 Hz). Fracture was recorded with a high-speed camera.

The setup was successfully tested on a cadaveric femur non-destructively (12 loading configurations) and destructively (15° internal rotation; 10° adduction). All measurements were highly repeatable (the displacements of the femoral head varied by < 2% between repetitions; the tilt in the frontal plane by < 0.05°; and strain varied on average 0.34% between repetitions). The displacement of the femoral head varied by over 50% when the same force was applied in different directions. Principal strains at the same location varied by over 70%, depending on the direction of the applied force. The high-speed video enabled the identification of the point of fracture initiation.

This study has shown that a new paradigm for testing the proximal femur (including improved testing conditions and a variety of loading configurations) can provide more accurate and more extensive information about the state of strain.

Algorithms for a strain-based plasticity criterion for bone

A range of stress-based plasticity criteria have been employed in the finite element analysis of the post-elastic behaviour of bone. There is some recognition now that strain-based criteria are more suitable for this material because they better represent its behaviour. Moreover, because bone yields at relatively isotropic strains, a strain-based criterion requires fewer material parameters unlike those required for a stress-based criterion. Based on a minimum and maximum principal strain criterion, a robust strain-based plasticity algorithm is developed. As the criterion comprises six piecewise linear surfaces in principal strain space, it has a number of singular regions. Singularity indicators are developed to direct the algorithm to make appropriate plastic corrector returns when singularity regions are encountered. The developed algorithms permit a plastic corrector to be achieved in a single iterative step in all cases. A range of benchmark tests are developed and conducted after implementing the algorithm in a finite element package. These tests show that the constitutive behaviour is as expected.

Cortical bone finite element models in the estimation of experimentally measured failure loads in the proximal femur

Highly accurate nonlinear finite element (FE) models have been presented to estimate bone fracture load. However, these complex models require high computational capacity, which restricts their clinical applicability. The objective of this experimental FE study was to assess the predictive value of a more simple cortical bone simulation model in the estimation of experimentally measured fracture load of the proximal femur. The prediction was compared with that of DXA, and with the prediction of our previous, more complex FE model including trabecular bone. Sixty-one formalin-fixed cadaver femora (from 41 women and 20 men, age 55-100 years) were scanned using a multi-detector CT and were mechanically tested for failure in a sideways fall loading configuration. Trabecular bone was completely removed from the FE models and only cortical bone was analyzed. The training set FE models (N=21) was used to establish the stress and strain thresholds for the element failure criteria. Bi-linear elastoplastic FE analysis was performed based on the CT images. The validation set (N=40) was used to estimate the fracture load. The estimated fracture load values were highly correlated with the experimental data (r(2)=0.73; p<0.001). The slope was 1.128, with an intercept of -360 N, which was not significantly different from 1 and 0, respectively. DXA-based BMD and BMC correlated moderately with the fracture load (r(2)=0.41 and r(2)=0.40, respectively). The study shows that the proximal femoral failure load in a sideways fall configuration can be estimated with reasonable accuracy by using the CT-based bi-linear elastoplastic cortical bone FE model. This model was more predictive for fracture load than DXA and only slightly less accurate than a full bone FE model including trabecular bone. The accuracy and calculation time of the model give promises for clinical use.

Ct-based finite element models can be used to estimate experimentally measured failure loads in the proximal femur

The objective of this experimental finite element (FE) study was to assess the accuracy of a simulation model estimate of the experimentally measured fracture load of the proximal femur in a sideways fall. Sixty-one formalin-fixed cadaver femora (41 female and 20 male) aged 55-100 years (an average of 80 years) were scanned with a multi-detector CT scanner and were mechanically tested for failure in a sideways fall loading configuration. Twenty-one of these femurs were used for training purposes, and 40 femurs were used for validation purposes. The training set FE models were used to establish the strain threshold for the element failure criteria. Bi-linear elastoplastic FE analysis was performed based on the CT images. The validation set was used to estimate the fracture loads. The Drucker-Prager criterion was applied to determine the yielding and the maximum principal stress criteria and the minimum principal strain criteria for element failure in tension and in compression, respectively. The estimated fracture load values were highly correlated with the experimental data (r=0.931; p<0.001). The slope was 0.929, with an intercept of 258 N, which was not significantly different from 1 and 0, respectively. The study shows that it is possible to estimate the fracture load with relatively high accuracy in a sideways fall configuration by using the CT-based FE method. This method may therefore be applied for studying the biomechanical mechanisms of hip fractures.

What makes an accurate and reliable subject-specific finite element model? A case study of an elephant femur

Finite element modelling is well entrenched in comparative vertebrate biomechanics as a tool to assess the mechanical design of skeletal structures and to better comprehend the complex interaction of their form-function relationships. But what makes a reliable subject-specific finite element model? To approach this question, we here present a set of convergence and sensitivity analyses and a validation study as an example, for finite element analysis (FEA) in general, of ways to ensure a reliable model. We detail how choices of element size, type and material properties in FEA influence the results of simulations. We also present an empirical model for estimating heterogeneous material properties throughout an elephant femur (but of broad applicability to FEA). We then use an ex vivo experimental validation test of a cadaveric femur to check our FEA results and find that the heterogeneous model matches the experimental results extremely well, and far better than the homogeneous model. We emphasize how considering heterogeneous material properties in FEA may be critical, so this should become standard practice in comparative FEA studies along with convergence analyses, consideration of element size, type and experimental validation. These steps may be required to obtain accurate models and derive reliable conclusions from them.

Fracture prevention by femoroplasty--cement augmentation of the proximal femur

The prevention of hip fractures is a desirable goal to reduce morbidity, mortality, and socio-economic burden. We evaluated the influence on femoral strength of different clinically applicable cementing techniques as "femoroplasty." Twenty-eight human cadaveric femora were augmented by means of four clinically applicable percutaneous cementing techniques and then tested biomechanically against their native contralateral control to determine fracture strength in an established biomechanical model mimicking a fall on the greater trochanter. The energy applied until fracture could be significantly increased by two of the methods by 160% (53.1 Nm vs. 20.4 Nm, p < 0.001) and 164% (47.1 Nm vs. 17.8 Nm, p = 0.008), respectively. The peak load to failure was significantly increased by three of the methods by 23% (3818.3 N vs. 3095.7 N, p = 0.003), 35% (3698.4 N vs. 2737.5 N, p = 0.007), and 12% (3056.8 N vs. 2742.8 N, p = 0.005), respectively. The femora augmented with cemented double drill holes had a lower fracture strength than the single drilled ones. Experimental femoroplasty is a technically feasible procedure for the prophylactic reinforcement of the osteoporotic proximal femur and, hence, could be an auxiliary treatment option to protect the proximal femur against osteoporotic fractures.

Performance of modified anatomic plates is comparable to proximal femoral nail, dynamic hip screw and anatomic plates: finite element and biomechanical testing

AIM

To establish whether the modified anatomic plate (MAP) performs as well as the anatomic plate (AP), dynamic hip screw (DHS) and proximal femoral nail (PFN) from a biomechanical perspective.

MATERIALS AND METHODS

The, AP, MAP, DHS and PFN were assessed using finite element (FE) methods and biomechanical tests. A solid model was created based on the fracture lines and results were assessed using analyses of variance.

MAIN OUTCOME MEASUREMENTS

Independent variables were the implants (n=4) and axial loads: 0-1000 Newton (N) in 100 N increments. Dependent variables were loads at the intertrochanteric fracture line as measured by load cells.

RESULTS

Axial loads ≤400 N generated significantly (p<0.05) greater stress at the fracture line in both the FE model and biomechanical settings: the PFN generated the highest forces at the fracture line followed by the AP, MAP and DHS. For axial loads ≥400 N, the AP and DHS generated nonsignificant (p>0.5) lower forces (almost 50% less) compared with the MAP and PFN. At 1000 N, the DHS generated the highest (p<0.05) load at the fracture line.

CONCLUSION

The biomechanical features of the MAP were similar to those of the PFN. The MAP generated optimal loads at both the fracture site and the proximal femur. FE methods and biomechanical tests revealed that the MAP is associated with both intra- and extra-medullary fixation features, even though the load was applied as an extramedullary stimulus.

Development of a parametric finite element model of the proximal femur using statistical shape and density modelling

Skeletal fractures associated with bone mass loss are a major clinical problem and economic burden, and lead to significant morbidity and mortality in the ageing population. Clinical image-based measures of bone mass show only moderate correlative strength with bone strength. However, engineering models derived from clinical image data predict bone strength with significantly greater accuracy. Currently, image-based finite element (FE) models are time consuming to construct and are non-parametric. The goal of this study was to develop a parametric proximal femur FE model based on a statistical shape and density model (SSDM) derived from clinical image data. A small number of independent SSDM parameters described the shape and bone density distribution of a set of cadaver femurs and captured the variability affecting proximal femur FE strength predictions. Finally, a three-dimensional FE model of an 'unknown' femur was reconstructed from the SSDM with an average spatial error of 0.016 mm and an average bone density error of 0.037 g/cm(3).

Assessment of the bilateral asymmetry of human femurs based on physical, densitometric, and structural rigidity characteristics

The purpose of this study was to perform a comprehensive geometric, densitometric, biomechanical, and statistical analysis of paired femurs for an adult population over a wide age range using three imaging modalities to quantify the departure from symmetry in size, bone mineral density, and cross-sectional structural rigidities. Femur measurements were obtained from 20 pairs of cadaveric femurs. Dimensions of these anatomic sites were measured using calipers directly on the bone and plain radiographs. Dual energy X-ray absorptiometry was used to measure bone mineral density. Bone mineral content and axial and bending rigidities were determined from the CT imaging. No differences were observed between the geometric measurements, DXA based bone mineral density and axial and bending rigidities of left and right femurs (P>0.05 for all cases). Left and right proximal femurs are not significantly different based on geometric, densitometric, and structural rigidity measurements. However, absolute left-right differences for individual patients can be substantial. When using the contralateral femur as a control, the number of femur pairs required to assess significant changes in anatomic dimensions and structural properties induced by a tumor, infection, fracture, or implanted device can range from 3 to 165 pairs depending on the desired effect size or sensitivity (5% or 10% difference). This information is important both for femoral arthroplasty implant design and the use of the contralateral femur as an intra-subject control for clinical assessment and research studies. In addition, our statistical analysis provides sample size estimates for planning future orthopedic research studies.

A biomechanical evaluation of femoroplasty under simulated fall conditions

OBJECTIVES

To test the hypotheses that, compared with controls: 1) femoroplasty (the injection of bone cement into the proximal femur in an attempt to prevent fragility fracture) increases the yield and ultimate loads, yield and ultimate energies, and stiffness of the proximal osteoporotic femur in a simulated fall model; and 2) the manner in which the cement distributes in the proximal femur affects the extent to which those mechanical properties are altered.

METHODS

In 10 pairs of osteoporotic human cadaveric femora, we injected one femur of each pair with 40 to 50 mL of polymethylmethacrylate bone cement; the noninjected femur served as the control. The filling percentage was calculated in four anatomic regions of the femur: head, neck, trochanter, and subtrochanter. All specimens were biomechanically tested in a configuration that simulated a fall on the greater trochanter. Student t test, linear regression, and multinomial logistic regression statistical analyses were conducted where appropriate with significant difference defined as P < 0.05.

RESULTS

Femoroplasty significantly increased yield load (22.0%), ultimate load (37.3%), yield energy (79.6%), and ultimate energy (154%) relative to matched controls but did not significantly change stiffness (-10.9%). There was a strong (r = 0.7) correlation between yield load and filling percentage in the femoral neck.

CONCLUSIONS

This study showed that 1) femoroplasty significantly increased fracture load and energy to fracture when osteoporotic femora were loaded in simulated fall conditions, and 2) cement filling in the femoral neck may have an important role in the extent to which femoroplasty affects mechanical strength of the proximal femur.

Shockwave exerts osteogenic effect on osteoporotic bone in an ovariectomized goat model

Our recent in vitro study showed that extracorporeal shock wave (ESW) stimulated calcium deposition in human periosteal cells. In this study, we hypothesized that the use of ESW could induce new bone formation in osteoporotic bone. Using our established osteoporotic goat model, the calcaneus, distal radius and femoral condyle of the left limb were treated with ESW once per month; the contralateral side served as the control. Bone mineral density (BMD), microarchitecture and dynamic histomorphometric index were evaluated after 9 months. Trabecular BMD of the calcaneus increased significantly by 2.90%. This finding was substantiated by micro-computed tomography findings showing that trabecular bone volume fraction and trabecular thickness of the treated calcaneus were enhanced compared with the contralateral control. However, significant difference could not be detected in the other two weight-bearing skeletal sites. Mineral apposition rates of all ESW-treated regions were also consistently higher than those of the control. These findings suggest that ESW treatment could enhance local BMD by inducing new bone formation, yet the effect was more apparent in non-weight-bearing sites.

Effects of trochanteric soft tissue thickness and hip impact velocity on hip fracture in sideways fall through 3D finite element simulations

A major worldwide health problem is hip fracture due to sideways fall among the elderly population. The effects of sideways fall on the hip are required to be investigated thoroughly. The objectives of this study are to evaluate the responses to trochanteric soft tissue thickness (T) variations and hip impact velocity (V) variations during sideways fall based on a previously developed CT scan derived 3D non-linear and non-homogeneous finite element model of pelvis-femur-soft tissue complex with simplified biomechanical representation of the whole body. This study is also aimed at quantifying the effects [peak impact force (F(max)), time to F(max), acceleration and peak principal compressive strain (epsilon(max))] of these variations (T,V) on hip fracture. It was found that under constant impact energy, for 81% decrease in T (26-5mm), F(max) and epsilon(max) increased by 38% and 97%, respectively. Hence, decrease in T (as in slimmer persons) strongly correlated to risk for hip fracture (phi) and strain ratio (SR) by 0.972 and 0.988, respectively. Also under same T and body weight, for 75% decrease in V (4.79-1.2m/s), F(max) and epsilon(max) decreased by 70% and 86%, respectively. Hence, increase in V (as in taller persons) strongly correlated to phi and SR by 0.995 and 0.984, respectively. For both variations in T and V, inter-trochanteric fracture situations were well demonstrated by phi as well as by SR and strain contours, similar to clinically observed fractures. These quantifications would be helpful for effective design of person-specific hip protective devices.

A modified method for assigning material properties to FE models of bones

The aim of the present study is to compare the results from subject-specific finite element analysis (FEA) of a human femur to experimental measurements, using two different methods for assigning material properties to the FE models. A modified material mapping strategy allowing for spatial variation of material properties within the elements and Young's modulus surface corrections is presented and compared to a more conventional strategy, whereby constant material properties are assigned to each element. The accuracy of the superficial stress-strain predictions was evaluated against experimental results from 13 strain gauges and five different load cases. Both methods predicted stresses with acceptable accuracy (R(2) = 0.92, root mean square error, RMSE < 10%), with the conventional method performing slightly better. The modified method performed better in strain prediction (R(2) = 0.85, RMSE = 23% versus R(2) = 0.79, RMSE = 31%).

The material mapping strategy influences the accuracy of CT-based finite element models of bones: An evaluation against experimental measurements

Aim of the present study was to evaluate the influence on the global model's accuracy of the strategy adopted to define the average element Young's modulus in subject-specific finite element models of bones from computed tomography data. The classic strategy of calculating the Young's modulus from an average element density and the one that averages the Young's moduli directly derived from each voxel Hounsfield Unit were considered. These strategies were applied to the finite element model of a real human femur. The accuracy of the superficial stress and strain predictions was evaluated against experimentally measured values in 13 strain-gauge locations for five different loading conditions. The results obtained for the two material distributions were statistically different. Both models predicted very accurately the superficial stresses, with regression coefficients higher than 0.9 and slopes not significantly different from unity. The second strategy definitely improved the strains prediction accuracy: the regression coefficient raised from 0.69 to 0.79; the average and peak errors decreased from 45.1% to 31.3% and from 228% to 134% of the maximum measured strain, respectively. The stress fields predicted inside the bone were also significantly different. A new software implementing the second strategy was made available in the public domain.

Subject-specific finite element models can accurately predict strain levels in long bones

The prediction of the stress-state and fracture risk induced in bones by various loading conditions in individual patients using subject-specific finite element models still represents a challenge in orthopaedic biomechanics. The accuracy of the strain predictions reported in the literature is variable and generally not satisfactory. The aim of the present study was to evaluate if a proper choice of the density-elasticity relationship can lead to accurate strain predictions in the frame of an automatic subject-specific model generation strategy. To this aim, a combined numerical-experimental study was performed comparing finite element predicted strains with strain-gauges measurements obtained on eight cadaver proximal femurs, each instrumented with 15 rosettes mostly concentrated in the bone metaphyses, tested non-destructively in vitro under six different loading scenarios. Three different density-elasticity power relationships were selected from the literature and implemented in the finite element models derived from computed tomography data. The results of the present study confirm the great influence of the density-elasticity relationship used on the accuracy of numerical predictions. One of the tested constitutive laws provided a very good agreement (R(2)=0.91, RMSE lower than 10% of the maximum measured value) between numerical calculations and experimental measurements. The presented results show, in addition, that the adoption of a single density-elasticity relationship over the whole bone density range is adequate to obtain an accuracy that is already suitable for many applications.

Off-axis loads cause failure of the distal radius at lower magnitudes than axial loads: a finite element analysis

Distal radius (Colles') fractures are a common fall-related injury in older adults and frequently result in long-term pain and reduced ability to perform activities of daily living. Because the occurrence of a fracture during a fall depends on both the strength of the bone and upon the kinematics and kinetics of the impact itself, we sought to understand how changes in bone mineral density (BMD) and loading direction affect the fracture strength and fracture initiation location in the distal radius. A three-dimensional finite element model of the radius, scaphoid, and lunate was used to examine changes of +/-2% and +/-4% BMD, and both axial and physiologically relevant off-axis loads on the radius. Changes in BMD resulted in similar percent changes in fracture strength. However, modifying the applied load to include dorsal and lateral components (assuming a dorsal view of the wrist, rather than an anatomic view) resulted in a 47% decrease in fracture strength (axial failure load: 2752N, off-axis: 1448N). Loading direction also influenced the fracture initiation site. Axially loaded radii failed on the medial surface immediately proximal to the styloid process. In contrast, off-axis loads, containing dorsal and lateral components, caused failure on the dorsal-lateral surface. Because the radius appears to be very sensitive to loading direction, the results suggest that much of the variability in fracture strength seen in cadaver studies may be attributed to varying boundary conditions. The results further suggest that interventions focused on reducing the incidence of Colles' fractures when falls onto the upper extremities are unavoidable may benefit from increasing the extent to which the radius is loaded along its axis.

Finite-Element Modeling of Bones From CT Data: Sensitivity to Geometry and Material Uncertainties

The aim of this paper is to analyze how the uncertainties in modelling the geometry and the material properties of a human bone affect the predictions of a finite-element model derived from computed tomography (CT) data. A sensitivity analysis, based on a Monte Carlo method, was performed using three femur models generated from in vivo CT datasets, each subjected to two different loading conditions. The geometry, the density and the mechanical properties of the bone tissue were considered as random input variables. Finite-element results typically used in biomechanics research were considered as statistical output variables, and their sensitivity to the inputs variability assessed. The results showed that it is not possible to define a priori the influence of the errors related to the geometry definition process and to the material assignment process on the finite-element analysis results. The errors in the geometric representation of the bone are always the dominant variables for the stresses, as was expected. However, for all the variables, the results seemed to be dependent on the loading condition and to vary from subject to subject. The most interesting result is, however, that using the proposed method to build a finite-element model of a femur from a CT dataset of the quality typically achievable in the clinical practice, the coefficients of variation of the output variables never exceed the 9%. The presented method is hence robust enough to be used for investigating the mechanical behavior of bones with subject-specific finite-element models derived from CT data taken in vivo.

Femoroplasty--augmentation of the proximal femur with a composite bone cement--feasibility, biomechanical properties and osteosynthesis potential

BACKGROUND

Analogous to vertebroplasty, cement-augmentation of the proximal femur ("femoroplasty") could reinforce osteoporotic bones. This study was to evaluate (i) the feasibility of femoroplasty with a composite cement (Cortoss), (ii) its influence on femoral strength by mechanical testing and (iii) the feasibility of stable osteosynthesis of the augmented fractured bones.

METHODS

Nine human cadaveric femora were augmented with a composite bone cement, the surface heat generation monitored, and then tested biomechanically against their native contralateral control to determine fracture strength. Subsequently, thirteen reinforced and fractured femora were osteosynthetized by different implants and tested against their osteosynthetisized, non-augmented contralateral control.

FINDINGS

Cement could be injected easily, with a moderate temperature rise. A positive correlation between BMD and fracture load and a significant increase in fracture load (+43%) of the augmented femora compared to their native controls (6324 N and 4430 N, respectively) as well as a significant increase in energy-to-failure (+187%, 86 N m and 30 N m, respectively) was found. Osteosynthesis was possible in cement-augmented femora. Osteosynthetisized femora showed equivalent strength to the intact controls.

INTERPRETATION

Augmentation of the proximal femur with composite bone cement could be of use in prophylaxis of fractures in osteoporotic femurs. Osteosynthesis of the fractured augmented bones is a challenging procedure but has a good chance to restore strength.

Microdamage propagation in trabecular bone due to changes in loading mode

Microdamage induced by falls or other abnormal loads that cause shear stress in trabecular bone could impair the mechanical properties of the proximal femur or spine. Existing microdamage may also increase the initiation and propagation of further microdamage during subsequent normal, on-axis, loading conditions, resulting in atraumatic or "spontaneous" fractures. Microdamage formation due to shear and compressive strains was studied in 14 on-axis cylindrical bovine tibial trabecular bone specimens. Microdamage was induced by a torsional overload followed by an on-axis compressive overload and quantified microscopically. Fluorescent agents were used to label microdamage and differentiate damage due to the two loading modes. Both the microcrack density and diffuse damage area caused by the torsional overload increased with increasing shear strain from the center to the edge of the specimen. However, the mean microcrack length was uniform across the specimen, suggesting that microcrack length is limited by microstructural features. The mean density of microcracks caused by compressive overloading was slightly higher near the center of the specimen, and the diffuse damage area was uniform across the specimen. Over 20% of the microcracks formed in the initial torsional overloading propagated during compression. Moreover the propagating microcracks were, on average, longer than microcracks formed by a single overload. As such, changes in loading mode can cause propagation of microcracks beyond the microstructural barriers that normally limit the length. Damage induced by in vivo off-axis loads such as falls may similarly propagate during subsequent normal loading, which could affect both remodeling activity and fracture susceptibility.

The Modified Super-Ellipsoid Yield Criterion for Human Trabecular Bone

Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micro-mechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through micro-computed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior, whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error±SD less than −0.04±5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error±SD<2.5±6.5%). We conclude that the four-parameter “Modified Super-Ellipsoid” yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.

Updating a 3-D vertebral body finite element model using 2-D images

In osteoporotic patients, vertebral strength is often evaluated in the clinical setting using bone densitometry methods, such as dual energy X-ray absorptiometry. Finite element models based on computed tomography (CT) have been shown to outperform such methods in predicting fracture strength, but repetitive use of CT scans may be impractical due to cost, availability, and radiation exposure. We propose a method of generating a vertebral model at an initial time point which can subsequently be updated using several digital radiographs by using an algebraic reconstruction technique (ART) to find the three-dimensional density distribution. The effectiveness of the algorithm was measured by comparison of the error of the reconstructed model to the error incurred by using the outdated model. Application of the ART was able to reduce density errors from 30% to under 7% and to reduce errors in calculated vertebral stiffness from 125% to under 10%. This preliminary study demonstrates that the method is valid and could potentially improve fracture risk diagnostics drastically.

Femoroplasty-augmentation of mechanical properties in the osteoporotic proximal femur: a biomechanical investigation of PMMA reinforcement in cadaver bones

OBJECTIVE

To determine the feasibility of polymethyl-methacrylate injection into the osteoporotic proximal femur and its effect on the mechanical properties.

DESIGN

In vitro pairwise comparison of non reinforced and reinforced bones in a load to failure loading mode.

BACKGROUND

Hip fractures represent an important public healthcare problem. Continued growth in the elderly population will raise the incidence of hip fractures and their associated costs dramatically in the near future.

METHODS

Twenty pairs of osteoporotic femurs were mechanically tested either in a single-limb stance configuration or simulating a fall on the greater trochanter. From each pair, one femur was augmented with bone cement, with the contralateral femur serving as a control. The surface temperature at the femoral neck was recorded until twenty minutes after injection. The fracture load and the energy absorption were calculated. The Wilcoxon signed rank test was used to test for differences in fracture load and energy absorption between the reinforced femurs and the native controls.

RESULTS

Volumes of 28-41 ml of cement (mean, 36 ml) could be injected. The increase of surface temperature at the femoral neck ranged from delta18.4 to delta29.8 degrees C. For the single limb stance configurations, the peak fracture load was increased by 21%, (P < 0.002) and for the simulated fall on the hip by 82%, (P < 0.002). The corresponding values for energy absorption were +48%; and +188% (P < 0.002) respectively.

CONCLUSIONS

The feasibility and mechanical effectiveness of the in vitro procedure could be demonstrated. The heat generation due to polymethyl-methacrylate polymerisation is high.

RELEVANCE

Prophylactic reinforcement of the femur could become a treatment option to solve the problems with osteoporotic hip fractures in patients at risk. Reinforcement materials with less exothermic reaction need to be evaluated further and also the feasibility of fracture repair after reinforcement.

Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load

Hip fracture is a serious and common injury that can lead to permanent disability, pneumonia, pulmonary embolism, and death. Research to help prevent these fractures is essential. Computed tomographic (CT) scan-based finite element (FE) modeling is a tool that can predict proximal femoral fracture loads in vitro. Because this tool might be used in vivo, this study examined whether FE models generated from CT scans in situ and in vitro yield comparable predictions of proximal femoral fracture load. CT scans of the left proximal femur of two human cadavers were obtained in situ and in vitro, and three-dimensional FE models employing nonlinear mechanical properties were generated from each CT scan. The models were evaluated under single-limb stance-type loading by applying displacements incrementally to the femoral head. The FE-predicted fracture load (F(FE)) was the maximum femoral head reaction force. F(FE) for the in situ-derived models for the two subjects were 5.2 and 13.3% greater than for the in vitro-derived models. These results demonstrate that using CT scan data obtained in situ instead of in vitro to generate FE models can lead to substantially different predicted fracture loads. This effect must be considered when using this technology in vivo.

Mechanical strength of a femoral reconstruction in paediatric oncology: a finite element study

In 1997 the proximal femur of a four-year-old child affected by a Ewing sarcoma was reconstructed using a massive bone allograft in conjunction with a vascularized fibula autograft. During the first three years of follow-up the reconstruction underwent important morphological changes. The aim of the present study was to evaluate the risk of fracture of the reconstructed proximal femur, once the physiological loads are restored, associated with a short, slow but unprotected level walk. Subject-specific finite element models of the operated femur, and of the intact contralateral one, were generated from a computed tomography exam, taken for routine clinical monitoring at month 33 of follow-up. The material properties were mapped on to the mesh and a loading condition comprising the hip joint reaction and the abductor muscle force was simulated. The risk of fracture was locally estimated, for the operated and intact femur, using the ratio between the bone tissue strength and the predicted Von Mises equivalent stress, taking into account the different behaviours of the bone tissue in tension or compression. The results showed that although the fibula grew dramatically during follow-up, the reconstructed femur had not recovered the whole mechanical strength of a normal femur. The reconstructed femoral neck seemed to be weaker than the contralateral one and hence at a higher fracture risk. However, no region reached the failure limit, so the model predicted no fracture of the femur if a short, slow but unprotected walk were allowed. The model predictions found an indirect clinical validation when the child was allowed to perform short unprotected walks and did not experience any fracture.

Longitudinal changes in bone mineral density during normal pregnancy

Pregnancy is a common physiological event that could affect peak bone mass and the risk of developing osteoporosis later in life. There have been few longitudinal studies over a complete reproductive cycle of any size to show whether bone mineral density (BMD) changes. We have measured BMD by dual-energy X-ray absorptiometry in 46 normal women before conception and then again immediately after delivery and compared them with 30 control women who failed to conceive. Fifteen women were osteopenic in preconceptual BMD, but there was no difference between those who did or did not become pregnant. During pregnancy there was a small and statistically nonsignificant decline in BMD at all sites. The decrease at the trochanteric region was 4.2%, while losses at other sites were about 1%. The decline at the trochanter exceeded the least significant change between two measurements (5.04%) in 17 women (40.5%) with significant changes within individuals being much less common at the other measurement sites. The nonpregnant controls showed small increases in BMD of 0.3%-1.9% but no woman lost more than the least significant change. At the trochanter there was a significant difference (P = 0.013) between those who did and did not become pregnant. There was a good correlation between changes in BMD at all sites and no significant difference in the slope of these correlations between the pregnant and control groups. Correlations with lumbar spine were total hip, r = 0.46, P = 0.0001; femoral neck, r = 0.49, P = 0.0005; and trochanter, r = 0.66, P < 0.0001.

Biaxial failure behavior of bovine tibial trabecular bone

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.

Effect of force direction on femoral fracture load for two types of loading conditions

Identifying the loading conditions under which the femur is most likely to fracture may aid the prevention of hip fracture. This study quantified the effect of force direction on fracture load, a factor inherently associated with fracture risk. Finite element (FE) models of four femora were used to determine the force directions associated with the lowest fracture loads. Force directions were varied three-dimensionally for two types of loading, one representing impact from a fall and one similar to joint loading during daily activities (atraumatic loading). For the fall configuration, the force direction with lowest fracture load corresponded to an impact onto the posterolateral aspect of the greater trochanter. For atraumatic loading, the lowest fracture loads for the force directions analyzed occurred when posterior force components were relatively large or when posterior and lateral components were both small, similar to conditions while standing on one leg or climbing stairs. When both fall and atraumatic configurations are considered, the type of loading associated with greatest fracture risk, i.e., with the greatest applied force and lowest fracture load, is impact from a fall onto the posterolateral aspect of the greater trochanter. Therefore, evaluation of hip fracture risk and development of fracture prevention technologies should focus on this high-risk loading condition.

Improved prediction of proximal femoral fracture load using nonlinear finite element models

Hip fracture, which is often due to osteoporosis or other conditions affecting bone strength, can lead to permanent disability, pneumonia, pulmonary embolism, and/or death. Great effort has been directed toward developing noninvasive methods for evaluating proximal femoral strength (fracture load), with the goal of assessing fracture risk. Previously, computed tomographic scan-based, linear finite element (FE) models were used to estimate proximal femoral fracture loads ex vivo in two load configurations, one approximating joint loading during single-limb stance and the other simulating impact from a fall. Measured and computed fracture loads were correlated (stance, r=0.867; fall, r=0.949). However, precision for the stance configuration was insufficient to identify subjects with below average fracture loads reliably. The present study examined whether, for this configuration, nonlinear FE models could be used to identify these subjects. These models were found to predict fracture load within +/-2.0 kN (r=0.962). This level of precision is sufficient to identify 97.5% of femora with fracture loads 1.3 standard deviations below the mean as having below average fracture loads. Accordingly, 20% of subjects with below average fracture loads, i.e. those with the lowest fracture loads and likely to be at greatest risk of fracture, would be correctly identified with at least 97.5% reliability. This FE modeling method will be a powerful tool for studies of hip fracture.