No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Computational Simulations of Bone Remodeling under Natural Mechanical Loading or Muscle Malfunction Using Evolutionary Structural Optimization Method
... 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. ...
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.
Osteoporosis induced bone fracture is not limited to simple damage according to its fractured region and the age of the damaged person. Therefore, there has been more necessity to understand and study the biomechanical aspects of osteoporosis, and relevant research has actively been conducted. With the development of medical imaging technology, the reconstruction of CT images into a 3D model has been made possible, and it has been conducted to analyze 3-dimensionally and inhomogeneously distributed bone mineral density according to CT values. The 3D bone strength computational analysis based on 2D bone images utilized for evaluating the new treatment using the mixture of PLGA and curcumin for rat osteoporosis model. After the treatment, bone mineral density recovered by 65% compared to the osteoporosis model, moreover, bone strength improved by 113%. This study suggested that the limitations of conventional bone monitoring method using 2D bone images can be overcome by considering 3D bone computational analysis. It is considered that introducing the newly proposed Deformation Per Volume (DPW) and Stress Per Weight (SPW) can be also used as effective parameters to more accurately predict the change in bone stiffness.
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.
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.
Background
The ovine stifle joint is an important location for investigations on the repair of articular cartilage defects in preclinical large animals. The classical medial parapatellar approach to the femoral trochlea is hazardous because of the high risk of postoperative patellar luxation. Here, we describe a low morbidity surgical exposure of the ovine trochlea without the necessity for intraoperative patellar luxation.
Methods
Bilateral surgical exposure of the femoral trochlea of the sheep stifle joint was performed using the classical medial parapatellar approach with intraoperative lateral patellar luxation and transection of the medial patellar retinaculum in 28 ovine stifle joints. A low morbidity approach was performed bilaterally in 116 joints through a mini-arthrotomy without the need to transect the medial patellar retinaculum or the oblique medial vastus muscle nor surgical patellar luxation. Postoperatively, all 72 animals were monitored to exclude patellar luxations and deep wound infections.
Results
The novel approach could be performed easily in all joints and safely exposed the distal two-thirds of the medial and lateral trochlear facet. No postoperative patellar luxations were observed compared to a postoperative patellar luxation rate of 25% experienced with the classical medial parapatellar approach and a re-luxation rate of 80% following revision surgery. No signs of lameness, wound infections, or empyema were observed for both approaches.
Conclusions
The mini-arthrotomy presented here yields good exposure of the distal ovine femoral trochlea with a lower postoperative morbidity than the classical medial parapatellar approach. It is therefore suitable to create articular cartilage defects on the femoral trochlea without the risk of postoperative patellar luxation.
The purpose of this study was to propose finite element (FE) modeling methods for predicting stress distributions on teeth and mandible under chewing action.
For FE model generation, CT images of skull were translated into 3D FE models, and static analysis was performed considering linear material behaviors and nonlinear geometrical effect. To find out proper boundary and loading conditions, parametric studies were performed with various areas and directions of restraints and loading. The loading directions are prescribed to be same as direction of masseter muscle, which was referred from anatomy chart and CT image. From the analysis, strain and stress distributions of teeth and mandible were obtained and compared with experimental data for model validation.
As a result of FE analysis, the optimized boundary condition was chosen such that 8 teeth were fixed in all directions and condyloid process was fixed in all directions except for forward and backward directions. Also, fixing a part of mandible in a lateral direction, where medial pterygoid muscle was attached, gave the more proper analytical results. Loading was prescribed in a same direction as masseter muscle. The tendency of strain distributions between the teeth predicted from the proposed model were compared with experimental results and showed good agreements.
This study proposes cost efficient FE modeling method for predicting stress distributions on teeth and mandible under chewing action. The proposed modeling method is validated with experimental data and can further be used to evaluate structural safety of dental prosthesis.
Understanding normal gait requires allowing for variations in normal patterns by the sex, age, and species in question. Therefore, the aim of this study was to evaluate kinetic and temporospatial parameters in clinically healthy sheep from three different age groups with a pressure-sensing walkway. The sheep were judged to be healthy based on the results of complete physical and orthopaedic examinations and had no history of lameness. Twenty-one clinically healthy female Santa Ines sheep were divided into three groups: G1 - seven animals, aged from 8 to 12 months and weighing 19.5-33 kg; G2 - seven individuals, aged from 2 to 4 years and weighing 26.5-42 kg; and G3 - seven sheep, aged more than 5 years and weighing 37.3-45 kg. The animals were examined from two directions: first on the left side and then on the right side of the handler. The data from the first five valid trials in each direction were collected for each sheep and analysed using the designated software. A trial was considered valid if the sheep walked within the correct velocity (1.1-1.3 m/s) and acceleration (from -0.15 to 0.15 m/s2) ranges. The peak vertical force (PVF), vertical impulse (VI), gait cycle time, stance time, swing time, stride length, and the percentage body weight distribution among the four limbs were determined.
No significant differences were observed, in either the forelimbs or the hind limbs, between the left and right sides or between the two directions for any of the variables. No significant temporospatial differences were found among the groups. Significant PVF (%BW) differences were observed in the forelimbs (G1>G3) and hind limbs (G1>G3), and significant VI differences were observed in the forelimbs (G1>G3).
Young healthy sheep differ from older sheep in the vertical forces they create when walking at the same velocity on a pressure-sensing walkway.
Effective fixation of fracture requires careful selection of a suitable implant to provide stability and durability. Implant with a feature of locking plate (LP) has been used widely for treating distal fractures in femur because of its favourable clinical outcome, but its potential in fixing proximal fractures in the subtrochancteric region has yet to be explored. Therefore, this comparative study was undertaken to demonstrate the merits of the LP implant in treating the subtrochancteric fracture by comparing its performance limits against those obtained with the more traditional implants; angle blade plate (ABP) and dynamic condylar screw plate (DCSP).
Nine standard composite femurs were acquired, divided into three groups and fixed with LP (n = 3), ABP (n = 3) and DCSP (n = 3). The fracture was modeled by a 20 mm gap created at the subtrochanteric region to experimentally study the biomechanical response of each implant under both static and dynamic axial loading paradigms. To confirm the experimental findings and to understand the critical interactions at the boundaries, the synthetic femur/implant systems were numerically analyzed by constructing hierarchical finite element models with nonlinear hyperelastic properties. The predictions from the analyses were then compared against the experimental measurements to demonstrate the validity of each numeric model, and to characterize the internal load distribution in the femur and load bearing properties of each implant.
The average measurements indicated that the constructs with ABP, DCPS and LP respectively had overall stiffness values of 70.9, 110.2 and 131.4 N/mm, and exhibited reversible deformations of 12.4, 4.9 and 4.1 mm when the applied dynamic load was 400 N and plastic deformations of 11.3, 2.4 and 1.4 mm when the load was 1000 N. The corresponding peak cyclic loads to failure were 1100, 1167 and 1600 N. The errors between the displacements measured experimentally or predicted by the nonlinear hierarchical hyperelastic model were less than 18 %. In the implanted femur heads, the principal stresses were spatially heterogeneous for ABP and DCSP but more homogenous for LP, meaning LP had lower stress concentrations.
When fixed with the LP implant, the synthetic femur model of the subtrochancteric fracture consistently exceeds in the key biomechanical measures of stability and durability. These capabilities suggest increased resistance to fatigue and failure, which are highly desirable features expected of functional implants and hence make the LP implant potentially a viable alternative to the conventional ABP or DCSP in the treatment of subtrochancteric femur fractures for the betterment of clinical outcome.
This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.
Bone modeling and remodeling is an optimization process where no agreement has been reached regarding a unified theory or model. We measured 384 pieces of bone in vivo by 64-slice CT and discovered that the bone's center of mass approximately superposes its centroid of shape. This phenomenon indicates that the optimization process of non-homogeneous materials such as bone follows the same law of superposition of center of mass and centroid of shape as that of homogeneous materials. Based upon this principle, an index revealing the relationship between the center of mass and centroid of shape of the compact bone is proposed. Another index revealing the relationship between tissue density and distribution radius is followed. Applying these indexes to evaluate the strength of bone, we have some new findings.
The use of artificial endoprostheses has become a routine procedure for knee and hip joints while ankle arthritis has traditionally been treated by means of arthrodesis. Due to its advantages, the implantation of endoprostheses is constantly increasing. While finite element analyses (FEA) of strain-adaptive bone remodelling have been carried out for the hip joint in previous studies, to our knowledge there are no investigations that have considered remodelling processes of the ankle joint. In order to evaluate and optimise new generation implants of the ankle joint, as well as to gain additional knowledge regarding the biomechanics, strain-adaptive bone remodelling has been calculated separately for the tibia and the talus after providing them with an implant.
FE models of the bone-implant assembly for both the tibia and the talus have been developed. Bone characteristics such as the density distribution have been applied corresponding to CT scans. A force of 5,200 N, which corresponds to the compression force during normal walking of a person with a weight of 100 kg according to Stauffer et al., has been used in the simulation. The bone adaptation law, previously developed by our research team, has been used for the calculation of the remodelling processes.
A total bone mass loss of 2% in the tibia and 13% in the talus was calculated. The greater decline of density in the talus is due to its smaller size compared to the relatively large implant dimensions causing remodelling processes in the whole bone tissue. In the tibia, bone remodelling processes are only calculated in areas adjacent to the implant. Thus, a smaller bone mass loss than in the talus can be expected. There is a high agreement between the simulation results in the distal tibia and the literature regarding.
In this study, strain-adaptive bone remodelling processes are simulated using the FE method. The results contribute to a better understanding of the biomechanical behaviour of the ankle joint and hence are useful for the optimisation of the implant geometry in the future.
The formation of a fracture callus in vivo tends to form in a structurally efficient manner distributing tissues where mechanical stimulus persists. Therefore, it is proposed that the formation of a fracture callus can be modelled in silico by way of an optimisation algorithm. This was tested by generating a finite element model of a transversal bone fracture embedded in a large tissue domain which was subjected to axial, bending and torsional loads. It was found that the relative fragment motion induced a compressive strain field in the early callus tissue which could be utilised to simulate the formation of external callus structures through an iterative optimisation process of tissue maintenance and removal. The phenomenological results showed a high level of congruence with in vivo healing patterns found in the literature. Consequently, the proposed strategy shows potential as a means of predicting spatial bone healing phenomena for pre-clinical testing.
Recent advancements in magnetic resonance imaging (MRI) have enabled clinical imaging of human cortical bone, providing a potentially powerful new means for assessing bone health with molecular-scale sensitivities unavailable to conventional X-ray-based diagnostics. To this end, (1)H nuclear magnetic resonance (NMR) and high-resolution X-ray signals from human cortical bone samples were correlated with mechanical properties of bone. Results showed that (1)H NMR signals were better predictors of yield stress, peak stress, and pre-yield toughness than were the X-ray derived signals. These (1)H NMR signals can, in principle, be extracted from clinical MRI, thus offering the potential for improved clinical assessment of fracture risk.
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.
An alternative solution to conventional stump-socket prosthetic limb attachment is offered by direct skeletal fixation. This study aimed to assess two percutaneous trans-femoral implants, the OPRA system (Integrum AB, Göteborg, Sweden), and the ISP Endo/Exo prosthesis (ESKA Implants AG, Lübeck, Germany) on bone failure and stem-bone interface mechanics both early post-operative (before bony ingrowth) and after full bone ingrowth. Moreover, mechanical consequences of implantation of those implants in terms of changed loading pattern within the bone and potential consequences on long-term bone remodeling were studied using finite-element models that represent the intact femur and implants fitted in amputated femora. Two experimentally measured loads from the normal walking cycle were applied. The analyses revealed that implantation of percutaneous prostheses had considerable effects on stress and strain energy density levels in bone. This was not only caused by the implant itself, but also by changed loading conditions in the amputated leg. The ISP design promoted slightly more physiological strain energy distribution (favoring long-term bone maintenance), but the OPRA design generated lower bone stresses (reducing bone fracture risk). The safety factor against mechanical failure of the two percutaneous designs was relatively low, which could be improved by design optimization of the implants.
Bone is a dynamic tissue that is constantly renewed. The cell populations that participate in this process--the osteoblasts and osteoclasts--are derived from different progenitor pools that are under distinct molecular control mechanisms. Together, these cells form temporary anatomical structures, called basic multicellular units, that execute bone remodeling. A number of stimuli affect bone turnover, including hormones, cytokines, and mechanical stimuli. All of these factors affect the amount and quality of the tissue produced. Mechanical loading is a particularly potent stimulus for bone cells, which improves bone strength and inhibits bone loss with age. Like other materials, bone accumulates damage from loading, but, unlike engineering materials, bone is capable of self-repair. The molecular mechanisms by which bone adapts to loading and repairs damage are starting to become clear. Many of these processes have implications for bone health, disease, and the feasibility of living in weightless environments (e.g., spaceflight).
The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young's modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500 N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.
The material composition and structural design of bone determine its strength. Structure determines loads that can be tolerated but loads also determine structure. Bone modifies its material composition and structure to accommodate loads by adaptive modeling and remodeling. Adaptation is successful during growth but not aging because accumulating insults, including a reduction in the volume of bone formed in the basic multicellular unit (BMU), increased resorption in the BMU, increased remodeling rate in midlife in women and in some men because of sex hormone deficiency, and in both sexes in old age as a consequence of secondary hyperparathyroidism and reduced periosteal bone formation, all of which compromises the material composition of bone and its structure. An understanding of the mechanisms of adaptation and failed adaptation provides rational approaches to interventions that can prevent or restore bone fragility.
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 2.5yr, 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.
It is proposed that the external asymmetric for-mation 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 opti-misation 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 pro-posed methods show potential as a means of predicting callus formation in pre-clinical testing.
Reliability-based topology optimization (RBTO) is used to obtain an optimal topology satisfying given constraints, as well as to consider uncertainties in design variables. In this study, RBTO was applied to obtain an optimal topology for the inner reinforcement of a vehicle’s hood based on bidirectional evolutionary structural optimization (BESO). A multi-objective topology optimization technique was implemented to obtain the optimal topology for two models with different curvatures while simultaneously considering the static stiffness of bending, torsion, and natural frequency. A performance measure approach (PMA) with probabilistic constraints formulated in terms of the reliability index was employed to evaluate the probabilistic constraints. The optimal topology obtained by RBTO was evaluated and compared to that obtained by deterministic topology optimization (DTO). A more suitable topology was obtained through RBTO than DTO even though the final volume obtained by RBTO was generally slightly greater than that obtained by DTO. The multiobjective optimization technique based on BESO can be applied very effectively with topology optimization for a vehicle’s hood reinforcement.
Individual differences in bone mass distribution at the proximal femur may be determined by daily weight-bearing physical activity (PA) since bone self-adapts according to the mechanical loads that is submitted. The aim of this study was to analyse computationally the effect of different weight-bearing PA types in the adaptation of the femoral neck (FN) by analysing regional differences in bone mineral density (BMD) at the integral FN and its superior, inferior, anterior and posterior subregions. To achieve this, it was adopted a 3-D femoral finite element (FE) model coupled with a suitable bone remodeling model. Different PA types were determined based both on ordinary lifestyle and mechanically more demanding PA as low magnitude impacts (L-I), moderate-magnitude impacts from odd directions (O-I) and high-magnitude vertical impacts (H-I). It was observed that as time spent in weight-bearing PA increases, BMD augment around the integral FN, but with different bone mass gain rates between subregions depending on the magnitude and directions of the hip contact forces; H-I was the type of weight-bearing PA which structurally most favor the gain of bone mass superiorly at the FN while both the H-I and the O-I types of PA promoted the largest bone mass gain rates at the anterior and posterior subregions of the FN. Because these types of weight-bearing PA were associated with a more uniform bone mass spatial distribution at the FN, they should provide a potential basis for targeted PA-based intervention programs for improving hip strength.
There are several well-established techniques for the generation of solid-void optimal topologies such as solid isotropic
material with penalization (SIMP) method and evolutionary structural optimization (ESO) and its later version bi-directional
ESO (BESO) methods. Utilizing the material interpolation scheme, a new BESO method with a penalization parameter is developed
in this paper. A number of examples are presented to demonstrate the capabilities of the proposed method for achieving convergent
optimal solutions for structures with one or multiple materials. The results show that the optimal designs from the present
BESO method are independent on the degree of penalization. The resulted optimal topologies and values of the objective function
compare well with those of SIMP method.
A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.
The success of GA-based topology optimisation methods for continuum structures has been limited. Though a number of methods exist, the results are far from comparable to solutions from more established methods in terms of quality and fidelity. This had led many structural optimisation researchers to dismiss the GA as a viable method for topology optimisation of continuum structures. The authors believe however that the deficiencies of previous applications lie not in the GA but in the manner in which it was applied. Based on insights gained from these applications, a new GA-based method for the continuum topology optimisation problem is herein presented which yields high-fidelity solutions comparable to those produced through more well-known and established methods. The method is centred on a number of novel concepts, most notably the simultaneous use of multiple genetic algorithms, and the use of a high-level string coding based on structural response information. In this work, the basis and methodology of the multi-GA approach are explained, and key algorithms detailed. The method was also applied to a number of structural problems to show its efficacy, and the results presented and discussed.
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.
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.
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.
A special purpose gamma-ray computed tomography scanner has been developed for precise measurements of bone density in the human appendicular skeleton. Details of the scanner's hardware and of the software organization for system control and data analysis are given, together with an outline of the theoretical basis for conversion of measured linear attenuation coefficients to physical bone densities. Performance of the system was evaluated on bone-like phantoms. Clinically, a precision of +/- 0.5% is obtained for bone density determinations. This device is being used in experimental studies and clinical investigations.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.