Saulo Martelli

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

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.

Biomechanics Modeling of the Musculoskeletal Apparatus: Status and Key Issues

The aim of this review paper is to report on the current state of the art in creating in silico humans able to simulate the biomechanics of the human body at all scales of interest. The focus is on the musculoskeletal apparatus, although much of what is written is valid also for the biomechanical modeling of other organs. The state of the art of computational biomechanics at body, organ, tissue, and cell levels is briefly described and the most recent achievements in the area of multiscale models are discussed. In conclusion, the challenges to be faced to realize a true living human model are summarized. It is evident that the demands associated with some of these challenges greatly exceed the potential currently possessed by the computational biomechanics research community. Thus, to tackle them it will be necessary not only to coordinate all efforts in a coherent way,but also to mobilize much greater financial and human resources than are currently available.

Are spontaneous fractures possible? An example of clinical application for personalised, multiscale neuro-musculo-skeletal modelling

Elderly frequently present variable degrees of osteopenia, sarcopenia, and neuromotor control degradation. Severely osteoporotic patients sometime fracture their femoral neck when falling. Is it possible that such fractures might occur without any fall, but rather spontaneously while the patient is performing normal movements such as level walking? The aim of this study was to verify if such spontaneous fractures are biomechanically possible, and in such case, which conditions of osteoporosis, sarcopenia, and neuromotor degradation could produce them. To the purpose, a probabilistic multiscale body-organ model validated against controlled experiments was used to predict the risk of spontaneous fractures in a population of 80-years old women, with normal weight and musculoskeletal anatomy, and variable degree of osteopenia, sarcopenia, and neuromotor control degradation. A multi-body inverse dynamics sub-model, coupled to a probabilistic neuromuscular sub-model, and to a femur finite element sub-model, formed the multiscale model, which was run within a Monte Carlo stochastic scheme, where the various parameters were varied randomly according to well defined distributions. The model predicted that neither extreme osteoporosis, nor extreme neuromotor degradation alone are sufficient to predict spontaneous fractures. However, when the two factors are combined an incidence of 0.4% of spontaneous fractures is predicted for the simulated population, which is consistent with clinical reports. When the model represented only severely osteoporotic patients, the incidence of spontaneous fractures increased to 29%. Thus, is biomechanically possible that spontaneous femoral neck fractures occur during level walking, due to a combination of severe osteoporosis and severe neuromotor degradation.

Effect of sub-optimal neuromotor control on the hip joint load during level walking

Skeletal forces are fundamental information in predicting the risk of bone fracture. The neuromotor control system can drive muscle forces with various task- and health-dependent strategies but current modelling techniques provide a single optimal solution of the muscle load sharing problem. The aim of the present work was to study the variability of the hip load magnitude due to sub-optimal neuromotor control strategies using a subject-specific musculoskeletal model. The model was generated from computed tomography (CT) and dissection data from a single cadaver. Gait kinematics, ground forces and electromyographic (EMG) signals were recorded on a body-matched volunteer. Model results were validated by comparing the traditional optimisation solution with the published hip load measurements and the recorded EMG signals. The solution space of the instantaneous equilibrium problem during the first hip load peak resulted in 10(5) dynamically equivalent configurations of the neuromotor control. The hip load magnitude was computed and expressed in multiples of the body weight (BW). Sensitivity of the hip load boundaries to the uncertainty on the muscle tetanic stress (TMS) was also addressed. The optimal neuromotor control induced a hip load magnitude of 3.3 BW. Sub-optimal neuromotor controls induced a hip load magnitude up to 8.93 BW. Reducing TMS from the maximum to the minimum the lower boundary of the hip load magnitude varied moderately whereas the upper boundary varied considerably from 4.26 to 8.93 BW. Further studies are necessary to assess how far the neuromotor control can degrade from the optimal activation pattern and to understand which sub-optimal controls are clinically plausible. However we can consider the possibility that sub-optimal activations of the muscular system play a role in spontaneous fractures not associated with falls.

Femoral shaft strains during daily activities: Implications for atypical femoral fractures.

BACKGROUND Atypical femoral fractures are low-energy fractures initiating in the lateral femoral shaft. We hypothesized that atypical femoral fracture onset is associated with daily femoral strain patterns. We examined femoral shaft strains during daily activities. METHODS We analyzed earlier calculations of femoral strain during walking, sitting and rising from a chair, stair ascent, stair descent, stepping up, and squatting based on anatomically consistent musculoskeletal and finite-element models from a single donor and motion recordings from a body-matched volunteer. Femoral strains in the femoral shaft were extracted for the different activities and compared. The dependency between femoral strains in the lateral shaft and kinetic parameters was studied using multi-parametric linear regression analysis. FINDINGS Tensile strain in the lateral femoral shaft varied from 327 με (squatting) to 2004 με (walking). Walking and stair descent imposed tensile loading on the lateral shaft, whereas the other activities mainly imposed tensile loads on the anterior shaft. The multi-parametric linear regression showed a moderately strong correlation between tensile strains in the lateral shaft and the motion kinetic (joint moments and ground reaction force) in the proximal (R(2)=0.60) and the distal shaft (R(2)=0.46). INTERPRETATION Bone regions subjected to tensile strains are associated with atypical femoral fractures. Walking is the daily activity that induces the highest tensile strain in the lateral femoral shaft. The kinetics of motion explains 46%-50% of the tensile strain variation in the lateral shaft, whereas the unexplained part is likely to be attributed to the way joint moments are decomposed into muscle forces.

Femoral loads during gait in a patient with massive skeletal reconstruction

BACKGROUND Biological massive skeletal reconstructions in tumours adopt a long rehabilitation protocol aimed at minimising the fracture risk. To improve rehabilitation and surgical procedures it is important to fully understand the biomechanics of the reconstructed limb. The aim of the present study was to develop a subject-specific musculoskeletal model of a patient with a massive biological skeletal reconstruction, to investigate the loads acting on the femur during gait, once the rehabilitation protocol was completed. METHODS A personalised musculoskeletal model of the patients lower limbs was built from a CT exam and registered with the kinematics recorded in a gait analysis session. Predicted activations for major muscles were compared to EMG signals to assess the models predictive accuracy. FINDINGS Gait kinematics showed only minor discrepancies between the two legs and was compatible with normality data. External moments showed slightly higher differences and were almost always lower on the operated leg exhibiting a lower variability. In the beginning of the stance phase, the joint moments were, conversely, higher on the operated side and showed a higher variability. This pattern was reflected and amplified on the femoral forces where the differences became important: on the hip, a maximum difference of 1.6 BW was predicted. The variability of the forces seemed, generally, lower on the operated leg than on the contralateral one. INTERPRETATION Small asymmetries in kinematic patterns might be associated, in massive skeletal reconstruction, to significant difference in the skeletal loads (up to 1.6 BW for the hip joint reaction) during gait.

Strain energy in the femoral neck during exercise

Physical activity is recommended to mitigate the incidence of hip osteoporotic fractures by improving femoral neck strength. However, results from clinical studies are highly variable and unclear about the effects of physical activity on femoral neck strength. We ranked physical activities recommended for promoting bone health based on calculations of strain energy in the femoral neck. According to adaptive bone-remodeling theory, bone formation occurs when the strain energy (S) exceeds its homeostatic value by 75%. The potential effectiveness of activity type was assessed by normalizing strain energy by the applied external load. Tensile strain provided an indication of bone fracture. External force and joint motion data for 15 low- and high-load weight-bearing and resistance-based activities were used. High-load activities included weight-bearing activities generating a ground force above 1 body-weight and maximal resistance exercises about the hip and the knee. Calculations of femoral loads were based on musculoskeletal and finite-element models. Eight of the fifteen activities were likely to trigger bone formation, with isokinetic hip extension (ΔS=722%), one-legged long jump (ΔS=572%), and isokinetic knee flexion (ΔS=418%) inducing the highest strain energy increase. Knee flexion induced approximately ten times the normalized strain energy induced by hip adduction. Strain and strain energy were strongly correlated with the hip-joint reaction force (R(2)=0.90-0.99; p<0.05) for all activities, though the peak load location was activity-dependent. None of the exercises was likely to cause fracture. Femoral neck mechanics is activity-dependent and maximum isokinetic hip-extension and knee-flexion exercises are possible alternative solutions to impact activities for improving femoral neck strength.

Sensitivity of a subject-specific musculoskeletal model to the uncertainties on the joint axes location

Subject-specific musculoskeletal models have become key tools in the clinical decision-making process. However, the sensitivity of the calculated solution to the unavoidable errors committed while deriving the model parameters from the available information is not fully understood. The aim of this study was to calculate the sensitivity of all the kinematics and kinetics variables to the inter-examiner uncertainty in the identification of the lower limb joint models. The study was based on the computer tomography of the entire lower-limb from a single donor and the motion capture from a body-matched volunteer. The hip, the knee and the ankle joint models were defined following the International Society of Biomechanics recommendations. Using a software interface, five expert anatomists identified on the donors images the necessary bony locations five times with a three-day time interval. A detailed subject-specific musculoskeletal model was taken from an earlier study, and re-formulated to define the joint axes by inputting the necessary bony locations. Gait simulations were run using OpenSim within a Monte Carlo stochastic scheme, where the locations of the bony landmarks were varied randomly according to the estimated distributions. Trends for the joint angles, moments, and the muscle and joint forces did not substantially change after parameter perturbations. The highest variations were as follows: (a) 11° calculated for the hip rotation angle, (b) 1% BW × H calculated for the knee moment and (c) 0.33 BW calculated for the ankle plantarflexor muscles and the ankle joint forces. In conclusion, the identification of the joint axes from clinical images is a robust procedure for human movement modelling and simulation.

Biomechanical robustness of a new proximal epiphyseal hip replacement to patient variability and surgical uncertainties: A FE study

The biomechanical behaviour of current hip epiphyseal replacements is notably sensitive to the typical variability of conditions following a standard surgery. The aim of the present study was to assess the biomechanical robustness to the variability of post-operative conditions of an innovative proximal epiphyseal replacement (PER) hip device featuring a short, curved and cemented stem. The risk of femoral neck fractures, prosthesis fractures and aseptic loosening were assessed through a validated finite element procedure following a systematic approach. Risk changes due to anatomical variations were assessed mimicking extreme conditions in terms of femoral size and level of osteoporosis. Failure risks associated with surgical uncertainties were assessed mimicking extreme conditions in terms of uncertainties on the prosthesis position/alignment, cement-bone interdigitation depth, and friction between the prosthesis and the hosting cavity. The femoral neck strength increased after implantation from 9% to 49% and was most sensitive to changes of the anatomo-physiological variables. The risk of stem fractures was low in all studied configurations. The risk of stem loosening was low and most sensitive to surgical uncertainties. In conclusion, the new device can be considered an effective alternative to current epiphyseal replacements. Care is recommended in a proper seating of the prosthesis in the femur.