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Computational Simulations of Bone Remodeling under Natural Mechanical Loading or Muscle Malfunction Using Evolutionary Structural Optimization Method

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... Calculations which take into account such a distribution of forces have been presented, among other, in (Latifi et al. 2014). A model so defined provides a reliable image of the internal state of the bone, similar to its actual behavior. ...
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The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database “Osteoporotic Virtual Physiological Human Project.” To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.
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Bone is able to react to changing mechanical demands by adapting its internal microstructure through bone forming and resorbing cells. This process is called bone modeling and remodeling. It is evident that changes in mechanical demands at the organ level must be interpreted at the tissue level where bone (re)modeling takes place. Although assumed for a long time, the relationship between the locations of bone formation and resorption and the local mechanical environment is still under debate. The lack of suitable imaging modalities for measuring bone formation and resorption in vivo has made it difficult to assess the mechanoregulation of bone three-dimensionally by experiment. Using in vivo micro-computed tomography and high resolution finite element analysis in living mice, we show that bone formation most likely occurs at sites of high local mechanical strain (p<0.0001) and resorption at sites of low local mechanical strain (p<0.0001). Furthermore, the probability of bone resorption decreases exponentially with increasing mechanical stimulus (R(2) = 0.99) whereas the probability of bone formation follows an exponential growth function to a maximum value (R(2) = 0.99). Moreover, resorption is more strictly controlled than formation in loaded animals, and ovariectomy increases the amount of non-targeted resorption. Our experimental assessment of mechanoregulation at the tissue level does not show any evidence of a lazy zone and suggests that around 80% of all (re)modeling can be linked to the mechanical micro-environment. These findings disclose how mechanical stimuli at the tissue level contribute to the regulation of bone adaptation at the organ level.
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It is proposed that the external asymmetric formation of callus tissues that forms naturally about an oblique bone fracture can be predicted computationally. We present an analysis of callus formation for two cases of bone fracture healing: idealised and subject-specific oblique bone fractures. Plane strain finite element (FE) models of the oblique fractures were generated to calculate the compressive strain field experienced by the immature callus tissues due to interfragmentary motion. The external formations of the calluses were phenomenologically simulated using an optimisation style algorithm that iteratively removes tissue that experiences low strains from a large domain. The resultant simulated spatial formation of the healing tissues for the two bone fracture cases showed that the calluses tended to form at an angle equivalent to the angle of the oblique fracture line. The computational results qualitatively correlated with the callus formations found in vivo. Consequently, the proposed methods show potential as a means of predicting callus formation in pre-clinical testing.
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The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175 μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized.
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A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.
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Cortical bone can be modeled as a complex hierarchical composite interrelating both structure and material properties on four levels of structural organization: molecular, ultrastructural, microscopic, and macroscopic. In young animals, the microstructural systems are long parallel lamellar units, plexiform bone, which in older or more mature animals converts by internal remodeling into multiple concentric lamellar units, secondary osteons, forming haversian bone. Ultrasonic wave propagation measurements performed on both plexiform and haversian bone clearly show a definitive relationship with microstructure; haversian bone can be described as a transversely symmetric material whereas plexiform bone appears to be orthotropic in nature. The anisotropy of the elastic constants are found to reflect the tissue symmetry; moreover, plexiform bone is stiffer and more rigid in all directions than is haversian bone. Similar experiments were performed on osteoporotic and osteopetrotic bone. While the results for osteoporotic bone are understandable in terms of the increased porosity, the results for the osteopetrotic bone are anomalous with respect to its density. Since Wolff, the remodeling of bone has been interpreted as a way of altering the mechanical properties to suit some need. For haversian remodeling from plexiform bone, the argument that adaptation occurs to optimize properties requires additional clarification since haversian bone appears to have inferior mechanical properties to plexiform bone.
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The three-dimensional microstructure of cancellous bone seems to be one of the key factors in the prediction of mechanical bone properties like bone strength or bone stiffness. In this paper trabecular bone structure was assessed nondestructively by means of high-resolution computed tomography (CT) with a spatial resolution of 250 microns. Mineralized bone was separated from bone marrow and muscle tissue with the help of a three-dimensional segmentation algorithm based on the analysis of directional derivatives. From the three-dimensional stack of CT slices a subvolume comparable in size (3.6 x 3.4 x 3.4 mm3) to standard histologic bone sections was selected. We refer to this subvolume as non-invasive bone biopsy. A new automated mesh generator was developed to create a three-dimensional finite element model of the non-invasive bone biopsy. Four-noded tetrahedron solid elements were used to guarantee a smooth surface representation. The aim of the presented work was to demonstrate the potential of high-resolution CT imaging in the prediction of the anisotropic material properties of cancellous bone. Preliminary results of the 3D finite element stress analysis are very promising. The predicted value of the apparent Young's modulus (564 MPa) is within the range reported for uniaxial compression testings of cancellous bone specimens.
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The loading parameters in the canine hip were determined from multiple studies, involving the collection of kinematic and force plate data in vivo joint reaction force from an instrumented hip replacement prosthesis, and in vivo femoral cortical bone strain gauge data in different dogs. In the middle of the stance phase of gait the canine femur was flexed 110 degrees with respect to the pelvis and formed a 20 degree angle relative to the floor. At this point in the gait cycle, a line passing from the superior to the inferior aspect of the pubic symphysis was parallel to the floor. The joint reaction force measurements showed that the net force vector during midstance was directed inferiorly, posteriorly, and laterally, with a peak magnitude of up to 1.65 times the body weight. A torsional moment of 1.6 N m is exerted about the femoral shaft. In vivo strain data showed that during gait peak compressive strains of -300 to -502 microstrain were produced on the medial aspect of the femoral cortex and peak tensile strains of +250 to +458 midstrain were produced on the femoral cortex. At the midstance phase of gait, principal cortical bone strains were rotated up to 29 degrees relative to the long axis of the femur, suggesting torsional loads on the femur. These data in combination provide valuable insights on the loading parameters of the canine hip which can be used in future applications of the canine as a model for evaluating mechanically based phenomena such as bone ingrowth and remodeling or hip prostheses.
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Muscle forces and bending moments were calculated with a two-dimensional non-linear force and moment analysis (according to the Finite Element Method) during the foot-lowering phase, stance phase and stem phase in the hind legs of sheep. During the foot-lowering phase, the largest production of force is detectable in the m. biceps femoris and the highest bending moment in the proximal third of the metatarsal bone. The lowest influence of force resulted during the stance phase. During the stance phase, high forces are detectable only in the patellar ligament and middle-high forces in the m. flexor digitalis profundus. In contrast, bending forces are almost equal in strength in the metatarsus and tibia. The strongest forces are detectable in the m. quadriceps femoris and extreme demands of the patellar ligament as well as of the flexors in the proximal ankle joint during the stem phase.
Article
Hip fracture is an important cause of morbidity and mortality among the elderly. Current methods of assessing a patient's risk of hip fracture involve local estimates of bone density (densitometry), and are limited by their inability to account for the complex structural features of the femur. In an effort to improve clinical and research tools for assessing hip fracture risk, this study investigated whether automatically generated, computed tomographic (CT) scan-based finite element (FE) models can be used to estimate femoral fracture load in vitro. Eighteen pairs of femora were examined under two loading conditions one similar to loading during the stance phase of gait, and one simulating impact from a fall. The femora were then mechanically tested to failure and regression analyses between measured fracture load and FE-predicted fracture load were performed. For comparison, densitometry measures were also examined. Significant relationships were found between measured fracture load and FE-predicted fracture load (r = 0.87, stance; r = 0.95, fall; r = 0.97, stance and fall data pooled) and between measured fracture load and densitometry data (r = 0.78, stance; r = 0.91, fall). These results indicate that this sophisticated technique, which is still early in its development, can achieve precision comparable to that of densitometry and can predict femoral fracture load to within -40% to +60% with 95% confidence. Therefore, clinical use of this approach, which would require additional X-ray exposure and expenditure for a CT scan, is not justified at this point. Even so, the potential advantages of this CT/FE technique support further research in this area.
Article
Computed tomography-based finite element analysis represents a powerful research tool for investigating the mechanics of skeletal fractures. To provide evidence that this technique can be used to predict failure loads and fracture patterns for bone structures, we compared the observed and predicted failure behaviors of 18 midsagittal sections, 10 mm thick, cut from human vertebral bodies. The specimens were scanned by computed tomography, and finite element models were generated with use of empirically determined density-property relations to assign element-specific material properties. The specimens were loaded to failure in uniaxial compression, and the models were analyzed under matching conditions. The models provided predictions of yield load that were strongly correlated with experimentally measured values (r2 > 0.86) and were typically within 25% of measured values. Predicted stiffness values were moderately correlated with measured values, but large absolute differences existed between them. Comparisons between regions of observed fracture and of high predicted strain indicated that strain was an accurate indicator of the pattern of local fracture in more than two-thirds of the bone specimens. In addition, strain contour plots provided better indicators of local fracture than did stress plots in these heterogeneous bone structures. We conclude that computed tomography-based finite element analysis can be used successfully to predict both global and local failure behavior of simplified skeletal structures.
Article
Whole bone bending tests are commonly used in mechanical evaluation of long bones. Reliable information about the midshaft can only be obtained if the bending moment is uniformly distributed along the shaft, and if the distribution of the bending stress is not adversely influenced by rigid clamping of the bone ends. A testing device was developed to determine bending stiffness of long bones in 24 directions, perpendicular to the bone axis. For optimal distribution of bending moment and stress, four-point bending was performed, and bone ends were simply supported, not rigidly clamped. The method was validated by repeated testing of a stainless steel rod, and a sheep femur. Left-right ratios were assessed twice in 2 groups of 5 sheep: one control group, and one group in which the left femur was stabilized with a stainless steel interlocking nail for 2.5 yr, after a midshaft osteotomy. Test results obtained with the steel rod reproducibly were close to predicted values. Measurements with the sheep femurs were reproducible and precise for 3 of the 4 parameters of the bending test. Stiffness parameters were significantly higher in the operated sheep than in the control group. We conclude that the method described here provides accurate and reproducible information, which is representative for the long bone shaft.
Article
Testing orthopaedic implants at the proximal femur of sheep requires knowledge of the contact forces acting on this joint. Telemeterized implants were used for long-term measurements of these forces in four sheep, mostly during treadmill walking. Joint forces in the same sheep varied widely from day to day and interindividual differences were also pronounced. Forces during walking were mostly higher than in previous short-term measurements. At medium walking speed, loads in the range of 65-140% of the body weight were typical. Fast walking increased the forces by only 20%, compared to slow speed. Stomping on the ground at the beginning of the stance phase and starting to run freely led to very high forces. The highest values observed were nearly four times the body weight. As in humans, the directions of high forces varied only slightly in the frontal plane throughout the whole stance phase but much more in the transverse plane. With regard to the force magnitudes and their directions, sheep seem to be a good model for testing human implant at the proximal femur.
Article
This review discusses advances in knowledge regarding the composition and structure of bone, the modeling and remodeling of bone, the formation of bone during growth and its reconstruction in adults, and how age-related abnormalities in these processes compromise the composition and structure of bone.
Article
The detailed spatial distributions of longitudinal ultrasonic velocity in cortical bone specimens obtained from three bovine femoral diaphysis were experimentally investigated using a pulse-echo system. The relationship between velocity, density, bone mineral density (BMD) and microstructure was investigated. Velocity was found to vary as a function of the direction of propagation and the location of the measured specimens in the bone diaphysis. A significant correlation was found between density and velocity, and between density and BMD. In some parts with plexiform structure, clear variations in velocity anisotropy were found despite no significant difference in density, BMD and microstructure.
Article
The effect of weight gain in late adolescence on bone is not clear. Young women who consistently gained weight (n = 23) from 17 to 22 yr of age had increased BMD but a lack of subperiosteal expansion compared with stable weight peers (n = 48). Bone strength increased appropriately for lean mass in both groups but decreased relative to body weight in weight gainers, suggesting increased bone fragility in weight gainers. Weight gain leading to obesity often starts in adolescence, yet little is known about its effects on bone. We used longitudinal data to examine the effects of weight gain in late adolescence (from 17 to 22 yr of age) on proximal femur BMD, geometry, and estimates of bending strength. Participants were classified as either weight gainers (WG, n = 23) or stable weight (SW, n = 48) using a random coefficients model. Weight gainers had positive increases in weight (p < 0.05) at each clinic visit from age 17 onward. Proximal femur DXA scans (Hologic QDR 2000) taken annually from 17 to 22 yr of age were analyzed for areal BMD (g/cm(2)), subperiosteal width (cm), and bone cross-sectional area (CSA) at the proximal femoral shaft. Cortical thickness was measured, and section modulus (Z, cm(3)) was calculated as a measure of bone bending strength. Total body lean (g) and fat (g) mass were measured from DXA total body scans. Over ages 17-22, height remained stable in both groups. Weight remained static in the SW group but increased 14% on average in the WG group (p < 0.05). After controlling for age 17 baseline values, WG had higher BMD (+2.6%), thicker cortices (+3.6%), and greater bone CSA (+2.3%). Increased BMD did not translate to greater increases in bone bending strength (Z). The SW group achieved similar gains in Z by greater subperiosteal expansion. Bone strength index (SI = Z/height) normalized for body weight remained constant in the SW group but decreased significantly in the WG group. In contrast, SI normalized to lean mass did not change over time in either group. Other variables including physical activity, nutrition, and hormone levels (estradiol, testosterone, cortisol) did not differ significantly between groups. These data suggest that weight gain in late adolescence may inhibit the periosteal expansion known to normally occur throughout life in long bones, resulting in decreased bone strength relative to body weight.