Protocol for constructing subject-specific biomechanical models of knee joint

A robust protocol for building subject-specific biomechanical models of the human knee joint is proposed which uses magnetic resonance imaging, motion analysis and force platform data in conjunction with detailed 3D finite element models. The proposed protocol can be used for determining stress and strain distributions and contact kinetics in different knee elements at different body postures during various physical activities. Several examples are provided to highlight the capabilities and potential applications of the proposed protocol. This includes preliminary results on the role of body weight on the stresses and strains induced in the knee articular cartilages and meniscus during single-leg stance and calculations of the induced stresses and ligament forces during the gait cycle.     

Comparison between mechanical stress and bone mineral density in the femur after total hip arthroplasty by using subject-specific finite element analyses

The mechanism underling bone mineral density (BMD) loss that occurs in the femur after total hip arthroplasty (THA) remains unknown. We compared the equivalent stress and strain energy density (SED) to BMD in the femur after THA using subject-specific finite element analyses. Twenty-four patients who had undergone primary cementless THA were analysed. BMD was measured using dual-energy X-ray absorptiometry (DEXA) at 1 week and 3, 6 and 12 months after THA. Seven regions of interest (ROIs) were defined in accordance with Gruen's system (ROIs 1–7). Computed tomography images of the femurs were acquired pre- and postoperatively, and the images were converted into three-dimensional finite element (FE) models. Equivalent stress and SED were analysed and compared with DEXA data. BMD was maintained 1 year after THA in ROIs 3, 4, 5 and 6, whereas BMD decreased in ROIs 1, 2 and 7. FE analysis revealed that equivalent stress in ROIs 3, 4, 5 and 6 was much higher than that in ROIs 1, 2 and 7. A significant correlation was observed between the rate of changes in BMD and equivalent stress. Reduction of equivalent stress may contribute to decrease in BMD in the femur after THA.     

Prognosis of implant longevity in terms of annual bone loss: a methodological finite element study

Dental implant failure is mainly the consequence of bone loss at peri-implant area. It usually begins in crestal bone. Due to this gradual loss, implants cannot withstand functional force without bone overload, which promotes complementary loss. As a result, implant lifetime is significantly decreased. To estimate implant success prognosis, taking into account 0.2 mm annual bone loss for successful implantation, ultimate occlusal forces for the range of commercial cylindrical implants were determined and changes of the force value for each implant due to gradual bone loss were studied. For this purpose, finite element method was applied and von Mises stresses in implant–bone interface under 118.2 N functional occlusal load were calculated. Geometrical models of mandible segment, which corresponded to Type II bone (Lekholm & Zarb classification), were generated from computed tomography images. The models were analyzed both for completely and partially osseointegrated implants (bone loss simulation). The ultimate value of occlusal load, which generated 100 MPa von Mises stresses in the critical point of adjacent bone, was calculated for each implant. To estimate longevity of implants, ultimate occlusal loads were correlated with an experimentally measured 275 N occlusal load (Mericske-Stern & Zarb). These findings generally provide prediction of dental implants success.     

Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models

The goal of this study was to predict the structural response of the femoral shaft under dynamic loading conditions using subject-specific finite element (SS-FE) models and to evaluate the prediction accuracy of the models in relation to the model complexity. In total, SS-FE models of 31 femur specimens were developed. Using those models, dynamic three-point bending and combined loading tests (bending with four different levels of axial compression) of bare femurs were simulated, and the prediction capabilities of five different levels of model complexity were evaluated based on the impact force time histories: baseline, mass-based scaled, structure-based scaled, geometric SS-FE, and heterogenized SS-FE models. Among the five levels of model complexity, the geometric SS-FE and the heterogenized SS-FE models showed statistically significant improvement on response prediction capability compared to the other model formulations whereas the difference between two SS-FE models was negligible. This result indicated the geometric SS-FE models, containing detailed geometric information from CT images with homogeneous linear isotropic elastic material properties, would be an optimal model complexity for prediction of structural response of the femoral shafts under the dynamic loading conditions. The average and the standard deviation of the RMS errors of the geometric SS-FE models for all the 31 cases was 0.46 kN and 0.66 kN, respectively. This study highlights the contribution of geometric variability on the structural response variation of the femoral shafts subjected to dynamic loading condition and the potential of geometric SS-FE models to capture the structural response variation of the femoral shafts.     

Biomechanical behaviour of cancellous bone on patellofemoral arthroplasty with Journey prosthesis: a finite element study

Isolated patellofemoral (PF) arthritis of the knee is a common cause of anterior knee pain and disability. Patellofemoral arthroplasty (PFA) is a bone conserving solution for patients with PF degeneration. Failure mechanisms of PFA include growing tibiofemoral arthritis and loosening of components. The implant loosening can be associated with bone resorption or fatigue-failure of bone by overload. This research work aims at determining the structural effects of the implantation of PF prosthesis Journey PFJ (Smith & Nephew, Inc., Memphis, TN, USA) on femoral cancellous bone. For this purpose, the finite element method is considered to perform computational simulations for different conditions, such as well-fixed and loosening scenarios. From the global results obtained, in the well-fixed scenario, a decrease in strain on cancellous bone was noticed, which can be related to bone resorption. In the loosening scenario, when the cement layer becomes inefficient, a significant increase in cancellous bone strain was observed, which can be associated with bone fatigue-failure.These strain changes suggest a weakness of the femur after PFA.     

Predicting the permeability of trabecular bone by micro-computed tomography and finite element modeling

The intrinsic permeability of bone plays an important role in the transport of nutrients and minerals within the tissue, and affects the mechanical stimuli that are related to the fate of the stem cells. The objective of this study was to establish a method to assess trabecular bone permeability using experimental and finite element (FE) modeling approaches based on micro computed tomography (µCT) images. Human cadaveric tibia cube specimens (N=23) were scanned with µCT. The permeability was measured experimentally using a custom-developed constant-head permeameter, and computationally by a poroelastic formulation to simulate the fluid flow within the discretized bone matrix and pore phase. The average of the experimentally measured permeability was 4.84×10⁻¹⁰ m² with a standard deviation of 3.70×10⁻¹⁰ m². A regression model of the µCT determined that the maximum bone area to total area ratio (maxBA/TA) for all slices that are perpendicular to the direction of fluid flow explained 84% of the variability of the natural logarithm of the experimentally measured permeability. The 2D measure of maxBA/TA performed better than 3D measures in general, although some parameters were reasonably well associated with permeability such as bone volume ratio (BV/TV, r=−0.71), the bone surface/bone volume (BS/BV, r=0.73), and the trabecular thickness (TbTh, r=−0.71). The correlation between the permeability predicted with FE models and experimentally measured permeability was reasonable (r=0.69), but the FE approach did not accurately represent the wide variability of permeability measured experimentally. The results of this study suggest that the changes in the trabecular bone microarchitecture have an exponential relationship with permeability, and the use of µCT-based 2D measurement of maxBA/TA performs well at predicting permeability, thus providing a convenient approach to measure this important aspect affecting biomechanical functions in the tissue.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

Objective: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA).

Materials and methods: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed.

Results: Proper displacement results and strain–stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found.

Conclusion: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Hexahedral meshing of subject-specific anatomic structures using mapped building blocks

To extend the use of computational techniques like finite element analysis to clinical settings, it would be beneficial to have the ability to generate a unique model for every subject quickly and efficiently. This work is an extension of two previously developed mapped meshing tools that utilised force and displacement control to map a template mesh to a subject-specific surface. The objective of this study was to map a template block structure, common to multiblock meshing techniques, to a subject-specific surface. The rationale is that the blocks are considerably less refined and may be readily edited after mapping, thereby yielding a mesh of high quality in less time than mapping the mesh itself. In this paper, the versatility and robustness of the method was verified by processing four data-sets. The method was found to be robust enough to cope with the variability of bony surface size, spatial position and geometry, producing building block structures (BBSs) that generated meshes comparable to those produced using BBSs that were created manually.     

Achilles tendon stress is more sensitive to subject-specific geometry than subject-specific material properties: A finite element analysis

This study used subject-specific measures of three-dimensional (3D) free Achilles tendon geometry in conjunction with a finite element method to investigate the effect of variation in subject-specific geometry and subject-specific material properties on tendon stress during submaximal isometric loading. Achilles tendons of eight participants (Aged 25–35 years) were scanned with freehand 3D ultrasound at rest and during a 70% maximum voluntary isometric contraction. Ultrasound images were segmented, volume rendered and transformed into subject-specific 3D finite element meshes. The mean (±SD) lengths, volumes and cross-sectional areas of the tendons at rest were 62 ± 13 mm, 3617 ± 984 mm³ and 58 ± 11 mm² respectively. The measured tendon strain at 70% MVIC was 5.9 ± 1.3%. Subject-specific material properties were obtained using an optimisation approach that minimised the difference between measured and modelled longitudinal free tendon strain. Generic geometry was represented by the average mesh and generic material properties were taken from the literature. Local stresses were subsequently computed for combinations of subject-specific and generic geometry and material properties. For a given geometry, changing from generic to subject-specific material properties had little effect on the stress distribution in the tendon. In contrast, changing from generic to subject-specific geometry had a 26-fold greater effect on tendon stress distribution. Overall, these findings indicate that the stress distribution experienced by the living free Achilles tendon of a young and healthy population during voluntary loading are more sensitive to variation in tendon geometry than variation in tendon material properties.     

Influence of anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study

Although the biomechanical behavior of the acetabular cup (AC) implant is determinant for the surgical success, it remains difficult to be assessed due to the multiscale and anisotropic nature of bone tissue. The aim of the present study was to investigate the influence of the anisotropic properties of peri-implant trabecular bone tissue on the biomechanical behavior of the AC implant at the macroscopic scale. Thirteen bovine trabecular bone samples were imaged using micro-computed tomography (μCT) with a resolution of 18 μm. The anisotropic biomechanical properties of each sample were determined at the scale of the centimeter based on a dedicated method using asymptotic homogenization. The material properties obtained with this multiscale approach were used as input data in a 3D finite element model to simulate the macroscopic mechanical behavior of the AC implant under different loading conditions. The largest stress and strain magnitudes were found around the equatorial rim and in the polar area of the AC implant. All macroscopic stiffness quantities were significantly correlated (R² > 0.85, p < 6.5 e-6) with BV/TV (bone volume/total volume). Moreover, the maximum value of the von Mises stress field was significantly correlated with BV/TV (R² > 0.61, p < 1.6 e-3) and was always found at the bone-implant interface. However, the mean value of the microscopic stress (at the scale of the trabeculae) decrease as a function of BV/TV for vertical and torsional loading and do not depend on BV/TV for horizontal loading. These results highlight the importance of the anisotropic properties of bone tissue.     

Biomechanical analysis of foot with different foot arch heights: a finite element analysis

Clinically, different foot arch heights are associated with different tissue injuries to the foot. To investigate the possible factors contributing to the difference in foot arch heights, previous studies have mostly measured foot pressure in either low-arched or high-arched feet. However, little information exists on stress variation inside the foot with different arch heights. Therefore, this study aimed to implement the finite element (FE) method to analyse the influence of different foot arches. This study established a 3D foot FE model using software ANSYS 11.0. After validating the FE model, this study created low-arched, high-arched and normal-arched foot FE models. The FE analysis found that both the stress and strain on the plantar fascia and metatarsal were higher in the high-arched foot, whereas the stress and strain on the calcaneous, navicular and cuboid were higher in low-arched foot. Additionally, forefoot pressure was increased with an increase in arch height.     

Prediction of globe rupture caused by primary blast: a finite element analysis

Although a human eye comprises less than 0.1% of the frontal body surface area, injuries to the eye are found to be disproportionally common in survivors of explosions. This study aimed to introduce a Lagrangian–Eulerian coupling model to predict globe rupture resulting from primary blast effect. A finite element model of a human eye was created using Lagrangian mesh. An explosive and its surrounding air domain were modelled using Eulerian mesh. Coupling the two models allowed simulating the blast wave generation, propagation and interaction with the eye. The results showed that the peak overpressures caused by blast wave on the corneal apex are 2080, 932.1 and 487.3 kPa for the victim distances of 0.75, 1.0 and 1.25 m, respectively. Higher stress occurred at the limbus, where the peaks for the three victim distances are 25.5, 14.1 and 6.4 MPa. The overpressure threshold of globe rupture was determined as 2000 kPa in a small-scale explosion. The findings would provide insights into the mechanism of primary blast-induced ocular injuries.     

Sensitivity of periprosthetic stress-shielding to load and the bone density-modulus relationship in subject-specific finite element models

Subject-specific finite element (FE) computer models of the proximal femur in hip replacement could potentially predict stress-shielding and subsequent bone loss in individual patients. Before such predictions can be made, it is important first to determine if between subject differences in stress-shielding are sensitive to poorly defined parameters such as the load and the bone material properties. In this study we investigate if subject-specific FE models provide consistent stress-shielding patterns in the bone, independent of the choice of the loading conditions and the bone density-modulus relationship used in the computer model. FE models of two right canine femurs with and without implants were constructed based on contiguous computed tomography (CT) scans so that subject-specific estimates of stress-shielding could be calculated. Four different loading conditions and two bone density-modulus relationships were tested. Stress-shielding was defined as the decrease of strain energy per gram bone mass in the femur with the implant in place relative to the intact femur.The analyses showed that for the four loading conditions and two bone density-modulus relationships the difference in stress-shielding between the two subjects was essentially constant (1% variation) when the same loading condition and density-modulus relationship was used for both subjects. The severity of stress-shielding within a subject was sensitive to these input parameters, varying up to 20% in specific regions with a change in loading conditions and up to 10% for a change in the assumed density-modulus relationship. We conclude that although the choice of input parameters can substantially affect stress-shielding in an individual, this choice had virtually no effect on the relative differences in femoral periprosthetic stress-shielding between individuals. Thus, while care should be taken in the interpretation of the absolute value of stress-shielding calculated with these type of models, subject-specific FE models may be useful for explaining the variation in bone adaptation responsiveness between different subjects in experimental or clinical studies.     

Intravoxel bone micromechanics for microCT-based finite element simulations

While micro-FE simulations have become a standard tool in computational biomechanics, the choice of appropriate material properties is still a relevant topic, typically involving empirical grey value-to-elastic modulus relations. We here derive the voxel-specific volume fractions of mineral, collagen, and water, from tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor. Biol. 287: 115, 2011), and from the measured X-ray attenuation information quantified in terms of grey values. The aforementioned volume fractions enter a micromechanics representation of bone tissue, as to deliver voxel-specific stiffness tensors. In order to check the relevance of this strategy, we convert a micro Computer Tomograph of a mouse femur into a regular Finite Element mesh, apply forces related to the dead load of a standing mouse, and then compare simulation results based on voxel-specific heterogeneous elastic properties to results based on homogeneous elastic properties related to the spatial average over the solid bone matrix compartment, of the X-ray attenuation coefficients. The element-specific strain energy density illustrates that use of homogeneous elastic properties implies overestimation of the organ stiffness. Moreover, the simulation reveals large tensile normal stresses throughout the femur neck, which may explain the mouse femur neck's trabecular morphology being quite different from the human case, where the femur neck bears compressive forces and bending moments.     

Validation of an efficient method of assigning material properties in finite element analysis of pelvic bone

Bone in the pelvis is a composite material with a complex anatomical structure that is difficult to model computationally. Rather than assigning material properties to increasingly smaller elements to capture detail in three-dimensional finite element (FE) models, properties can be assigned to Gauss points within larger elements. As part of a validation process, we compared experimental and analytical results from a composite beam under four-point load to FE models with material properties assigned to refined elements and Gauss points within larger elements. Both FE models accurately predicted deformation and the analytical predictions of internal shear stress.     

Using 3D finite element models verified the importance of callus material and microstructure in biomechanics restoration during bone defect repair

Background: There is lack of further observations on the microstructure and material property of callus during bone defect healing and the relationships between callus properties and the mechanical strength. Methods: Femur bone defect model was created in rabbits and harvested CT data to reconstruct finite element models at 1 and 2 months. Three types of assumed finite element models were compared to study the callus properties, which assumed the material elastic property as heterogeneous (R-model), homogenous (H-model) or did not change from 1 to 2 months (U-model). Results: The apparent elastic moduli increased at 2 months (from 355.58 ± 132.67 to 1139.30 ± 967.43 MPa) in R-models. But there was no significant difference in apparent elastic moduli between R-models (355.58 ± 132.67 and 1139.30 ± 967.43 MPa) and H-models (344.79 ± 138.73 and 1001.52 ± 692.12 MPa) in 1 and 2 months. A significant difference of apparent elastic moduli was found between the R-model (1139.30 ± 967.43 MPa) and U-model group (207.15 ± 64.60 MPa) in 2 months. Conclusions: This study showed that the callus structure stability remodeled overtime to achieve a more effective structure, while the material quality of callus tissue is a very important factor for callus strength. At the meantime, this study showed an evidence that the material heterogeneity maybe not as important as it is in bone fracture model.     

Hip joint degeneration due to cam impingement: a finite element analysis

The goal of this study was to investigate the impact of cam impingement, a biomechanical risk factor, on hip joint degeneration and ultimately coxarthrosis. 3D finite element solid models of a healthy and a pathologic hip were developed based on clinical reports. The biphasic characteristics of cartilaginous tissues were considered to identify localised solid matrix overloading during normal walking and sitting down (SD). Localised femoral intrusion at the anterior-superior pelvic horn was revealed in the pathologic hip during SD, where the radial and meridional solid stresses in the acetabular cartilage and circumferential solid stresses within the acetabular labrum increased by 3.7, 1.5 and 2.7 times, respectively. The increased solid-on-solid stresses, reduction in fluid-load support and associated higher friction during articulation may result in joint wear and other degenerative changes in the hip.     

Finite element prediction of fatigue damage growth in cancellous bone

Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture.