Mateusz Juszczyk

Mechanical testing of bones: the positive synergy of finite-element models and in vitro experiments

Bone biomechanics have been extensively investigated in the past both with in vitro experiments and numerical models. In most cases either approach is chosen, without exploiting synergies. Both experiments and numerical models suffer from limitations relative to their accuracy and their respective fields of application. In vitro experiments can improve numerical models by: (i) preliminarily identifying the most relevant failure scenarios; (ii) improving the model identification with experimentally measured material properties; (iii) improving the model identification with accurately measured actual boundary conditions; and (iv) providing quantitative validation based on mechanical properties (strain, displacements) directly measured from physical specimens being tested in parallel with the modelling activity. Likewise, numerical models can improve in vitro experiments by: (i) identifying the most relevant loading configurations among a number of motor tasks that cannot be replicated in vitro; (ii) identifying acceptable simplifications for the in vitro simulation; (iii) optimizing the use of transducers to minimize errors and provide measurements at the most relevant locations; and (iv) exploring a variety of different conditions (material properties, interface, etc.) that would require enormous experimental effort. By reporting an example of successful investigation of the femur, we show how a combination of numerical modelling and controlled experiments within the same research team can be designed to create a virtuous circle where models are used to improve experiments, experiments are used to improve models and their combination synergistically provides more detailed and more reliable results than can be achieved with either approach singularly.

Accuracy of finite element predictions in sideways load configurations for the proximal human femur

Subject-specific finite element models have been used to predict stress-state and fracture risk in individual patients. While many studies analysed quasi-axial loading configurations, only few works simulated sideways load configurations, such as those arising in a fall. The majority among these latter directly predicted bone strength, without assessing elastic strain prediction accuracy. The aim of the present work was to evaluate if a subject-specific finite element modelling technique from CT data that accurately predicted strains in quasi-axial loading configurations is suitable to accurately predict strains also when applying low magnitude loads in sideways configurations. To this aim, a combined numerical-experimental study was performed to compare finite element predicted strains with strain-gauge measurements from three cadaver proximal femurs instrumented with sixteen strain rosettes and tested non-destructively under twelve loading configurations, spanning a wide cone (0-30° for both adduction and internal rotation angles) of sideways fall scenarios. The results of the present study evidenced a satisfactory agreement between experimentally measured and predicted strains (R(2) greater than 0.9, RMSE% lower than 10%) and displacements. The achieved strain prediction accuracy is comparable to those obtained in state of the art studies in quasi-axial loading configurations. Still, the presence of the highest strain prediction errors (around 30%) in the lateral neck aspect would deserve attention in future studies targeting bone failure.

The human proximal femur behaves linearly elastic up to failure under physiological loading conditions

It has not been demonstrated whether the human proximal femur behaves linearly elastic when loaded to failure. In the present study we tested to failure 12 cadaveric femurs. Strain was measured (at 5000Hz) on the bone surface with triaxial strain gages (up to 18 on each femur). High-speed videos (up to 18,000frames/s) were taken during the destructive test. To assess the effect of tissue preservation, both fresh-frozen and formalin-fixed specimens were tested. Tests were carried out at two strain-rates covering the physiological range experienced during daily motor tasks. All specimens were broken in only two pieces, with a single fracture surface. The high-speed videos showed that failure occurred as a single abrupt event in less than 0.25ms. In all specimens, fracture started on the lateral side of the neck (tensile stress). The fractured specimens did not show any sign of permanent deformation. The force-displacement curves were highly linear (R(2)>0.98) up to 99% of the fracture force. When the last 1% of the force-displacement curve was included, linearity slightly decreased (minimum R(2)=0.96). Similarly, all force-strain curves were highly linear (R(2)>0.98 up to 99% of the fracture force). The slope of the first part of the force-displacement curve (up to 70% fracture force) differed from the last part of the curve (from 70% to 100% of the fracture force) by less than 17%. Such a difference was comparable to the fluctuations observed between different parts of the curve. Therefore, it can be concluded that the proximal femur has a linear-elastic behavior up to fracture, for physiological strain-rates.

Strain distribution in the proximal human femoral metaphysis

Abstract There is significant interest in the stress—strain state in the proximal femoral metaphysis, because of its relevance for hip fractures and prosthetic replacements. The scope of this work was to provide a better understanding of the strain distribution, and of its correlation with the different directions of loading, and with bone quality. A total of 12 pairs of human femurs were instrumented with strain gauges. Six loading configurations were designed to cover the range of directions spanned by the hip joint force. Inter-specimen variability was reduced if paired specimens were considered. The principal strain magnitude varied greatly between loading configurations. This suggests that different loading configurations need to be simulated in vitro. The strain magnitude varied between locations but, on average, was compatible with the strain values measured in vivo. The strain magnitudes and the direction of principal tensile strain in the head and neck were compatible with the spontaneous fractures of the proximal femur reported in some subjects. The principal tensile strain was significantly larger where the cortical bone was thinner; the compressive strain was larger where the cortical bone was thicker. The direction of the principal strain varied significantly between measurement locations but varied little between loading configurations. This suggests that the anatomy and the distribution of anisotropic material properties enable the proximal femur to respond adequately to the changing direction of daily loading.

Structural behaviour and strain distribution of the long bones of the human lower limbs

Although stiffness and strength of lower limb bones have been investigated in the past, information is not complete. While the femur has been extensively investigated, little information is available about the strain distribution in the tibia, and the fibula has not been tested in vitro. This study aimed at improving the understanding of the biomechanics of lower limb bones by: (i) measuring the stiffness and strain distributions of the different low limb bones; (ii) assessing the effect of viscoelasticity in whole bones within a physiological range of strain-rates; (iii) assessing the difference in the behaviour in relation to opposite directions of bending and torsion. The structural stiffness and strain distribution of paired femurs, tibias and fibulas from two donors were measured. Each region investigated of each bone was instrumented with 8-16 triaxial strain gauges (over 600 grids in total). Each bone was subjected to 6-12 different loading configurations. Tests were replicated at two different loading speeds covering the physiological range of strain-rates. Viscoelasticity did not have any pronounced effect on the structural stiffness and strain distribution, in the physiological range of loading rates explored in this study. The stiffness and strain distribution varied greatly between bone segments, but also between directions of loading. Different stiffness and strain distributions were observed when opposite directions of torque or opposite directions of bending (in the same plane) were applied. To our knowledge, this study represents the most extensive collection of whole-bone biomechanical properties of lower limb bones.

Stress shielding and stress concentration of contemporary epiphyseal hip prostheses

Abstract After the first early failures, proximal femoral epiphyseal replacement is becoming popular again. Prosthesis-to-bone load transfer is critical for two reasons: stress shielding is suspected of being responsible for a number of failures of early epiphyseal prostheses; stress concentration is probably responsible of the relevant number of early femoral neck fractures in resurfaced patients. The scope of this work was to experimentally investigate the load transfer of a commercial epiphyseal prosthesis (Birmingham Hip Replacement (BHR)) and an innovative prototype proximal epiphyseal replacement. To investigate bone surface strain, ten cadaveric femurs were instrumented with 15 triaxial strain gauges. In addition the cement layer of the prototype was instrumented with embedded gauges to estimate the strain in the adjacent trabecular bone. Six different loading configurations were investigated, with and without muscles. For the BHR prosthesis, significant stress shielding was observed on the posterior side of the head—neck region (the strain was halved); a pronounced stress concentration was observed on the anterior surface (up to five times in some specimens); BHR was quite sensitive to the different loading configurations. For the prototype, the largest stress shielding was observed in the neck region (lower than the BHR; alteration less than 20 per cent); some stress concentration was observed at the head region, close to the rim of the prosthesis (alteration less than 20 per cent); the different loading configurations had similar effects. Such large alterations with respect to the pre-operative conditions were found only in regions where the strain level was low. Conversely, alterations were moderate where the strain was higher. Thus, prosthesis-to-bone load transfer of both devices has been elucidated; the prototype preserved a stress distribution closer to the physiological condition.

Accurate in vitro identification of fracture onset in bones: Failure mechanism of the proximal human femur

Bone fractures have extensively been investigated, especially for the proximal femur. While failure load can easily be recorded, and the fracture surface is readily accessible, identification of the point of fracture initiation is difficult. Accurate location of fracture initiation is extremely important to understand the multi-scale determinants of bone fracture. In this study, a recently developed technique based on electro-conductive lines was applied to the proximal femoral metaphysis to elucidate the fracture mechanism. Eight cadaveric femurs were prepared with 15-20 electro-conductive lines (crack-grid) covering the proximal region. The crack-grid was connected to a dedicated data-logger that monitored electrical continuity of each line at 700 kHz. High-speed videos (12,000 frames/s, 0.1-0.2 mm pixel size) of the destructive tests were acquired. Most crack-grid-lines failed in a time-span of 0.08-0.50 ms, which was comparable to that identified in the high-speed videos, and consistent with previous video recordings. However, on all specimens 1-3 crack-grid-lines failed significantly earlier (2-200 ms) than the majority of the crack-grid-lines. The first crack-grid-line to fail was always the closest one to the point of fracture initiation identified in the high-speed videos (superior-lateral neck region). Then the crack propagated simultaneously, at comparable velocity on the anterior and posterior sides of the neck. Such a failure pattern has never been observed before, as spatial resolution of the high-speed videos prevented from observing the initial opening of a crack. This mechanism (fracture onset, time-lag, followed by catastrophic failure) can be explained with a transfer of load to the internal trabecular structure caused by the initial fracture of the thin cortical shell. This study proves the suitability of the crack-grid method to investigate bone fractures associated to tensile stress. The crack-grid method enables significantly faster sampling than high-speed cameras. The present findings elucidate some aspects of the failure mechanism of the proximal human femoral metaphysis.

Assessment of femoral neck fracture risk for a novel proximal epiphyseal hip prosthesis

BACKGROUND This study addresses the risk of femoral neck fracture associated with resurfacing hip prostheses. A novel cemented Proximal Epiphyseal Replacement (PER) featuring a short curved stem was investigated. METHODS Seven pairs of femurs were in vitro tested. One femur of each pair was randomly assigned for PER implantation. The contralateral femur was tested intact. All femurs were loaded to failure in a validated, physiological configuration. High-speed videos (10,000-12,000 frames/s) were acquired to identify the location of fracture initiation. For comparison, data were included from Birmingham Hip Resurfacing previously tested in an identical fashion (N=3). FINDINGS Relative to the contralateral intact femurs, the failure load of the PER and Birmingham implants was 15.4% higher and 10.0% lower, respectively. In six of the seven PER implants, fracture initiation (neck or inter-trochanteric) was similar to the contralateral intact femurs, suggesting comparable stress distribution. Conversely, fracture initiation in the Birmingham implants occurred at the lateral prosthesis rim, which differed substantially from the intact femurs. No correlation existed between bone quality and strengthening/weakening effect of the PER (failure load of implant as a percentage of intact: R^2=0.067). Conversely, Birmingham implantation weakened the femurs with lower density (R^2=0.92). Therefore, unlike most resurfacing prostheses, the PER seems suitable also for osteoporotic subjects. INTERPRETATION This study seems to confirm that resurfacing with a Birmingham Hip tends to reduce the strength of the proximal femur. The opposite seemed to happen with the PER, which slightly reduced the risk of neck fracture, also in low-quality bones.

Biomechanical Testing of the Proximal Femoral Epiphysis: Intact and Implanted Condition

There is renewed interest in resurfacing hip prostheses. While stemmed prostheses have been extensively studied in the past, little is known about the biomechanics of epiphyseal prostheses. Our aim was to develop a combined experimental-numerical tool to study the intact and operated epiphysis. Bone and implant stress, relative micromotion and failure mode in the intact and implanted bone were investigated. Twelve pairs of cadaver human femurs were studied intact, to fully characterize the proximal epiphysis. Four were then implanted with a commercial resurfacing prosthesis. They were tested in the elastic range, while strains were measured with 15 rosettes. Implant micromotions were measured in the operated condition. A total of 7 loading scenarios were simulated to cover the range of typical motor tasks. Additionally, Finite Element (FE) models were built using a validated procedure for assigning inhomogeneous material properties based on CT data. To allow extensive validation of the FE model, additional measurements were taken in vitro: bone deflection in various points, indirect measurement of load application point, digitizing of the bone surface and gauge locations. The FE models were also used to identify the most critical load scenario to recreate in vitro spontaneous head-neck fractures. Strain measurements were successfully obtained in intact and implanted femurs, providing the natural strain pattern, and indicating moderate stress-shielding in the operated condition. Results on the 6 femurs that were modeled showed that FE can predict overall displacements with an accuracy of 0.4mm, and principal stress with an accuracy of 10% (Root Mean Squared, RMSE). In vitro failure tests were successful: all specimens fractured, with a variety of failures ranging from sub-capital to trans-trochanteric. This confirms the suitability of this test model to replicate spontaneous fractures in elderly subjects. In conclusion, an experimentally validated FE method was developed, that run in parallel with an optimized in vitro simulation. These tools can successfully predict the stress distribution and the failure mode in the proximal femur both in its natural condition and with a resurfacing prosthesis.Copyright

Shape and function of the diaphysis of the human tibia

There is an agreement about the principle that bones are optimized to resist daily loads. This has never been ascertained for the human tibia. One of the main load components in the tibia in vivo is a cantilever load (with a linearly varying bending moment, with its largest component in the sagittal plane). investigated if the cross-section of the diaphysis and its variation along the tibia make it an optimized structure with respect to such loads. Six cadaveric tibias were CT-scanned. The geometry and material properties were extracted from the CT-scans, and analyzed along the tibias. A linear variation along the tibia was found for the second moments of area and inertia, and the section modulus in the sagittal plane (slightly less linear in the frontal plane). Conversely, the other properties (polar moments and cross-section are) were much less linear. This suggests that the structure is optimized to resist a bending moment that varies linearly along the tibia. The tibias were instrumented with 28 triaxial straingauges each. Strain was measured under cantilever loading in the sagittal and frontal planes, under quasi-constant-bending in the sagittal and frontal planes, under torsional loading, and with an axial force. The strain distribution was remarkably uniform when cantilever loading was applied in the sagittal plane and slightly less uniform when cantilever loading was applied in the frontal plane. Strain variations were one order of magnitude larger for all other loading configurations. This shows that the tibia is a uniform-stress structure (i.e. optimized) for cantilever loading.