Mathematical relationships between bone density and mechanical properties: a literature review

Modal analysis for the assessment of cementless hip stem primary stability in preoperative THA planning

This numerical vibration finite element (FE) study introduces resonance three-dimensional planning (RP3D) to assess preoperatively the primary stability of a cementless stem for total hip arthroplasty. Based on a patient's CT-scan and a numerical model of a stem, RP3D aims at providing mechanical criteria indicative of the achievable primary stability. We investigate variations of the modal response of the stem to changes of area and apparent stiffness of the bone-implant interface. The model is computationally cheap as it does not include a mesh of the bone. The apparent stiffness of the bone is modeled by springs attached to the nodes of the stem's mesh. We investigate an extended range of stiffness values while, in future works, patient's specific Hounsfield values could be used to define stiffness. We report modal frequencies, shapes, and a ratio of elastic potential energies (rEPE) that quantifies the proximal motion that should be minimum for a stable stem. The modal response exhibits a clear transition between loose and tight contact as area and stiffness of the interface increase. rEPE thresholds that could potentially discriminate preoperatively between stable and unstable stems are given for a Symbios SPS^® size C stem.

Machine learning techniques for the optimization of joint replacements: Application to a short-stem hip implant

Today, different implant designs exist in the market; however, there is not a clear understanding of which are the best implant design parameters to achieve mechanical optimal conditions. Therefore, the aim of this project was to investigate if the geometry of a commercial short stem hip prosthesis can be further optimized to reduce stress shielding effects and achieve better short-stemmed implant performance. To reach this aim, the potential of machine learning techniques combined with parametric Finite Element analysis was used. The selected implant geometrical parameters were: total stem length (L), thickness in the lateral (R1) and medial (R2) and the distance between the implant neck and the central stem surface (D). The results show that the total stem length was not the only parameter playing a role in stress shielding. An optimized implant should aim for a decreased stem length and a reduced length of the surface in contact with the bone. The two radiuses that characterize the stem width at the distal cross-section in contact with the bone were less influential in the reduction of stress shielding compared with the other two parameters; but they also play a role where thinner stems present better results.

Elastic Properties of Chimpanzee Craniofacial Cortical Bone

Relatively few assessments of cranial biomechanics formally take into account variation in the material properties of cranial cortical bone. Our aim was to characterize the elastic properties of chimpanzee craniofacial cortical bone and compare these to the elastic properties of dentate human craniofacial cortical bone. From seven cranial regions, 27 cylindrical samples were harvested from each of five chimpanzee crania. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived using modified equations of Hooke's law in a Mathcad program. Consistent orientations among individuals were observed in the zygomatic arch and alveolus. The density of cortical bone showed significant regional variation (P < 0.001). The elastic moduli demonstrated significant differences between sites, and a distinct pattern where E₃  > E₂  > E₁ . Shear moduli were significantly different among regions (P < 0.001). The pattern by which chimpanzee cranial cortical bone varies in elastic properties resembled that seen in humans, perhaps suggesting that the elastic properties of craniofacial bone in fossil hominins can be estimated with at least some degree of confidence. Anat Rec, 299:1718-1733, 2016. © 2016 Wiley Periodicals, Inc.

In Vivo Assessment of Elasticity of Child Rib Cortical Bone Using Quantitative Computed Tomography

Elasticity of the child rib cortical bone is poorly known due to the difficulties in obtaining specimens to perform conventional tests. It was shown on the femoral cortical bone that elasticity is strongly correlated with density for both children and adults through a unique relationship. Thus, it is assumed that the relationships between the elasticity and density of adult rib cortical bones could be expanded to include that of children. This study estimated in vivo the elasticity of the child rib cortical bone using quantitative computed tomography (QCT). Twenty-eight children (from 1 to 18 y.o.) were considered. Calibrated QCT images were prescribed for various thoracic pathologies. The Hounsfield units were converted to bone mineral density (BMD). A relationship between the BMD and the elasticity of the rib cortical bone was applied to estimate the elasticity of children's ribs in vivo. The estimated elasticity increases with growth (7.1 ± 2.5 GPa at 1 y.o. up to 11.6 ± 1.9 GPa at 18 y.o.). This data is in agreement with the few previous values obtained using direct measurements. This methodology paves the way for in vivo assessment of the elasticity of the child cortical bone based on calibrated QCT images.

Biomechanical implications of cortical elastic properties of the macaque mandible

Knowledge of the variation in the elastic properties of mandibular cortical bone is essential for modeling bone function. Our aim was to characterize the elastic properties of rhesus macaque mandibular cortical bone and compare these to the elastic properties from mandibles of dentate humans and baboons. Thirty cylindrical samples were harvested from each of six adult female rhesus monkey mandibles. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived from ultrasound velocity measurements. Further velocity measurements with longitudinal and transverse ultrasonic transducers along with measurements of bone density were used to compute three-dimensional cortical elastic properties using equations based on Hooke's law. Results showed regional variations in the elastic properties of macaque mandibular cortical bone that have both similarities and differences with that of humans and baboons. So far, the biological and structural basis of these differences is poorly understood.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

INTRODUCTION

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R²=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.

METHODS

Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R² and RMSE%.

RESULTS

The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%.

CONCLUSIONS

Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

Biomechanical study on surgical fixation methods for minimally invasive treatment of hallux valgus

Hallux valgus (HV) was one of the most frequent female foot deformities. The aim of this study was to evaluate mechanical responses and stabilities of the Kirschner, bandage and fiberglass fixations after the distal metatarsal osteotomy in HV treatment. Surface traction of different forefoot regions in bandage fixation and the biomechanical behavior of fiberglass bandage material were measured by a pressure sensor device and a mechanical testing, respectively. A three-dimensional foot finite element (FE) model was developed to simulate the three fixation methods (Kirschner, bandage and fiberglass fixations) in weight bearing. The model included 28 bones, sesamoids, ligaments, plantar fascia, cartilages and soft tissue. The peak Von Mises stress (MS) and compression stress (CS) of the distal fragment were predicted from the three fixation methods: Kirschner fixation (MS=6.71MPa, CS=1.232MPa); Bandage fixation (MS=14.90MPa, CS=9.642MPa); Fiberglass fixation (MS=15.83MPa, CS=19.70MPa). Compared with the Kirschner and bandage fixation, the fiberglass fixation reduced the relative movement of osteotomy fragments and obtained the maximum CS. We concluded that fiberglass fixation in HV treatment was helpful to the bone healing of distal fragment. The findings were expected to guide further therapeutic planning of HV patient.

MicroCT-based finite element models as a tool for virtual testing of cortical bone

The aim of this study was to assess a virtual biomechanics testing approach purely based on microcomputed tomography (microCT or µCT) data, providing non-invasive methods for determining the stiffness and strength of cortical bone. Mouse femurs were µCT scanned prior to three-point-bend tests. Then microCT-based finite element models were generated with spatial variation in bone elastoplastic properties and subject-specific femur geometries. Empirical relationships of density versus Young's moduli and yield stress were used in assigning elastoplastic properties to each voxel. The microCT-based finite element modeling (µFEM) results were employed to investigate the model's accuracy through comparison with experimental tests. The correspondence of elastic stiffness and strength from the µFE analyses and tests was good. The interpretation of the derived data showed a 6.1%, 1.4%, 1.5%, and 1.6% difference between the experimental test result and µFEM output on global stiffness, nominal Young's modulus, nominal yield stress, and yield force, respectively. We conclude that virtual testing outputs could be used to predict global elastic-plastic properties and may reduce the cost, time, and number of test specimens in performing physical experiments.

Biomaterials and Tissue Biomechanics: A Match Made in Heaven?

Biomaterials and tissue biomechanics have been traditionally separate areas of research with relatively little overlap in terms of methodological approaches. Recent advances in both fields on the one hand and developments in fabrication techniques and design approaches on the other have prepared the ground for joint research efforts by both communities. Additive manufacturing and rational design are examples of the revolutionary fabrication techniques and design methodologies that could facilitate more intimate collaboration between biomaterial scientists and biomechanists. This editorial article highlights the various ways in which the research on tissue biomechanics and biomaterials are related to each other and could benefit from each other’s results and methodologies.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Cyclic and Load to Failure Properties of All-Suture Anchors in Synthetic Acetabular and Glenoid Cancellous Bone

PURPOSE

To evaluate the cyclic displacement, maximum load to failure, and failure mode of multiple all-suture anchors (ASAs) in 2 different densities of sawbones cancellous bone substitute.

METHODS

Anchors tested included the Suturefix Ultra 1.7 mm, JuggerKnot 1.45 mm (No. 1 and No. 2 MaxBraid) and 2.9 mm, Y-Knot Flex 1.3 mm and 1.8 mm, Iconix 1, 2, 25, and 3, Q-Fix 1.8 mm, and Bioraptor 2.3 PK. The Bioraptor served as a non-all-suture-based control. Seven to eleven anchors were tested in both 20 and 30 pounds per cubic foot (pcf) test blocks that were chosen to simulate glenoid and acetabular cancellous bone, respectively. After a 40 N deployment force, anchors were cyclically loaded at 0.5 Hz from 10 to 50 N and then 10 to 100 N for 200 cycles each. Surviving specimens were pulled to failure at 10 mm/s. Displacement, stiffness, maximum load, and failure mode were recorded. Welch t-tests and Welch analysis of variance with Games-Howell post hoc tests were used for statistical analysis.

RESULTS

In higher density blocks, 11 of 12 anchors had significantly (P < .05) higher maximum loads to failure, and 8 anchors showed significantly lower post-cyclic displacement. The Q-Fix 1.8 displayed the lowest post-cyclic displacement in both densities (0.1 ± 0.2 mm, mean ± standard deviation, in both densities). All other groups exhibited at least 2.8 mm and 0.6 mm post-cyclic displacement in 20 and 30 pcf, respectively. The Bioraptor did not survive cyclic testing in 20 pcf and had 0.6 ± 0.3 mm post-cyclic displacement in 30 pcf.

CONCLUSIONS

ASAs show better fixation in higher density synthetic bone. The cyclic displacement and maximum load of ASAs vary widely depending on anchor design and bone density. Most anchors fail by suture anchor pullout. In general, the Bioraptor 2.3 PK outperformed ASAs in higher density test blocks with mixed results in lower density test blocks.

CLINICAL RELEVANCE

ASAs show mixed results compared with a traditional suture anchor. They perform better in higher density bone substitute.

Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135-147, 2006. doi: 10.1080/10255840600751473 ) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.

Localized tissue mineralization regulated by bone remodelling: A computational approach

Bone is a living tissue whose main mechanical function is to provide stiffness, strength and protection to the body. Both stiffness and strength depend on the mineralization of the organic matrix, which is constantly being remodelled by the coordinated action of the bone multicellular units (BMUs). Due to the dynamics of both remodelling and mineralization, each sample of bone is composed of structural units (osteons in cortical and packets in cancellous bone) created at different times, therefore presenting different levels of mineral content. In this work, a computational model is used to understand the feedback between the remodelling and the mineralization processes under different load conditions and bone porosities. This model considers that osteoclasts primarily resorb those parts of bone closer to the surface, which are younger and less mineralized than older inner ones. Under equilibrium loads, results show that bone volumes with both the highest and the lowest levels of porosity (cancellous and cortical respectively) tend to develop higher levels of mineral content compared to volumes with intermediate porosity, thus presenting higher material densities. In good agreement with recent experimental measurements, a boomerang-like pattern emerges when plotting apparent density at the tissue level versus material density at the bone material level. Overload and disuse states are studied too, resulting in a translation of the apparent-material density curve. Numerical results are discussed pointing to potential clinical applications.

On the Two-Dimensional Simplification of Three-Dimensional Cementless Hip Stem Numerical Models

Three-dimensional (3D) finite element (FE) models are commonly used to analyze the mechanical behavior of the bone under different conditions (i.e., before and after arthroplasty). They can provide detailed information but they are numerically expensive and this limits their use in cases where large or numerous simulations are required. On the other hand, 2D models show less computational cost, but the precision of results depends on the approach used for the simplification. Two main questions arise: Are the 3D results adequately represented by a 2D section of the model? Which approach should be used to build a 2D model that provides reliable results compared to the 3D model? In this paper, we first evaluate if the stem symmetry plane used for generating the 2D models of bone-implant systems adequately represents the results of the full 3D model for stair climbing activity. Then, we explore three different approaches that have been used in the past for creating 2D models: (1) without side-plate (WOSP), (2) with variable thickness side-plate and constant cortical thickness (SPCT), and (3) with variable thickness side-plate and variable cortical thickness (SPVT). From the different approaches investigated, a 2D model including a side-plate best represents the results obtained with the full 3D model with much less computational cost. The side-plate needs to have variable thickness, while the cortical bone thickness can be kept constant.

Handling limited datasets with neural networks in medical applications: A small-data approach

MOTIVATION

Single-centre studies in medical domain are often characterised by limited samples due to the complexity and high costs of patient data collection. Machine learning methods for regression modelling of small datasets (less than 10 observations per predictor variable) remain scarce. Our work bridges this gap by developing a novel framework for application of artificial neural networks (NNs) for regression tasks involving small medical datasets.

METHODS

In order to address the sporadic fluctuations and validation issues that appear in regression NNs trained on small datasets, the method of multiple runs and surrogate data analysis were proposed in this work. The approach was compared to the state-of-the-art ensemble NNs; the effect of dataset size on NN performance was also investigated.

RESULTS

The proposed framework was applied for the prediction of compressive strength (CS) of femoral trabecular bone in patients suffering from severe osteoarthritis. The NN model was able to estimate the CS of osteoarthritic trabecular bone from its structural and biological properties with a standard error of 0.85MPa. When evaluated on independent test samples, the NN achieved accuracy of 98.3%, outperforming an ensemble NN model by 11%. We reproduce this result on CS data of another porous solid (concrete) and demonstrate that the proposed framework allows for an NN modelled with as few as 56 samples to generalise on 300 independent test samples with 86.5% accuracy, which is comparable to the performance of an NN developed with 18 times larger dataset (1030 samples).

CONCLUSION

The significance of this work is two-fold: the practical application allows for non-destructive prediction of bone fracture risk, while the novel methodology extends beyond the task considered in this study and provides a general framework for application of regression NNs to medical problems characterised by limited dataset sizes.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone

BACKGROUND

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface.

METHODS

Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness.

FINDINGS

Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm³ density.

INTERPRETATION

In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.

The effect of oligo(trimethylene carbonate) addition on the stiffness of acrylic bone cement

With the increasing elderly population an increase in the number of bony fractures associated to age-related diseases such as osteoporosis also follows. The relatively high stiffness of the acrylic bone cements used in these patients has been suggested to give raise to a suboptimal load distribution surrounding the cement in vivo, and hence contribute to clinical complications, such as additional fractures. The aim of this study was to develop a low-modulus bone cement, based on currently used, commercially available poly(methyl methacrylate) (PMMA) cements for vertebroplasty. To this end, acrylate end-functionalized oligo(trimethylene carbonate) (oTMC) was incorporated into the cements, and the resulting compressive mechanical properties were evaluated, as well as the cytotoxic and handling properties of selected formulations. Sixteen wt%oTMC was needed in the vertebroplastic cement Osteopal V to achieve an elastic modulus of 1063 MPa (SD 74), which gave a corresponding compressive strength of 46.1 MPa (SD 1.9). Cement extracts taken at 1 and 12 hours gave a reduced MG-63 cell viability in most cases, while extracts taken at 24 hours had no significant effect on cell behavior. The modification also gave an increase in setting time, from 14.7 min (SD 1.7) to 18.0 min (SD 0.9), and a decrease in maximum polymerization temperature, from 41.5°C (SD 3.4) to 30.7°C (SD 1.4). While further evaluation of other relevant properties, such as injectability and in vivo biocompatibility, remains to be done, the results presented herein are promising in terms of approaching clinically applicable bone cements with a lower stiffness.

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

BACKGROUND

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

RESULTS

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

CONCLUSIONS

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

A Computational Efficient Method to Assess the Sensitivity of Finite-Element Models: An Illustration With the Hemipelvis

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

Parallel deformation of heterogeneous ChainMail models: Application to interactive deformation of large medical volumes

In this work we present a new solution for correctly handling heterogeneous materials in ChainMail models, which are widely used in medical applications. Our core method relies on two main components: (1) a novel timestamp-based propagation scheme that tracks the propagation speed of a deformation through the model and allows to correct ambiguous configurations, and (2) a novel relaxation stage that performs an energy minimization process taking into account the heterogeneity of the model. In addition, our approach extends the SP-ChainMail algorithm by supporting interactive topology changes and handling multiple concurrent deformations, increasing its range of applicability. Finally, we present an improved blocking scheme that efficiently handles the sparse computation, greatly increasing the performance of our algorithm. Our proposed solution has been applied to interactive deformation of large medical datasets. The simulation model is directly generated from the input dataset and a user defined material transfer function, while the visualization of the deformations is performed by rendering the resampled deformed model using direct volume rendering techniques. In our results, we show that our parallel pipeline is capable of interactively deforming models with several million elements. A comparison is finally discussed, analyzing the properties of our approach with respect to previous work. The results show that our algorithm correctly handles very large heterogeneous ChainMail models in an interactive manner, increasing the applicability of the ChainMail approach for more demanding scenarios both in response time and material modeling.

Comparison of specimen-specific vertebral body finite element models with experimental digital image correlation measurements

The purpose of this study was to load cadaveric vertebral bodies (n=6) in compression and compare the response, measured with digital image correlation (DIC) on the cortex, with the predicted response from specimen-specific vertebral finite element (FE) models. Five modulus-density relationships were evaluated, and for the strongest modulus-density relationship, the correlation between the DIC and FE displacements had R² values from 0.75 to 0.93. The stiffnesses derived from the DIC measurements were strongly predicted by the FE stiffnesses (R²=0.90). DIC provides full-field measurements of surface displacement, eliminating the influence of system compliance, for validation of specimen-specific models.

Numerical simulation of mechanically stimulated bone remodelling

The numerical simulation of bone remodelling provides a great opportunity to improve the choice of therapy in particular for complex bone defects. Despite this fact, its use in clinical practice is not yet expedient because of several unresolved problems. In this paper a new bone remodelling algorithm based on standard computer tomography datasets and finite element analysis is introduced.

Trabecular architecture in the thumb of Pan and Homo: implications for investigating hand use, loading, and hand preference in the fossil record

OBJECTIVES

Humans display an 85-95% cross-cultural right-hand bias in skilled tasks, which is considered a derived behavior because such a high frequency is not reported in wild non-human primates. Handedness is generally considered to be an evolutionary byproduct of selection for manual dexterity and augmented visuo-cognitive capabilities within the context of complex stone tool manufacture/use. Testing this hypothesis requires an understanding of when appreciable levels of right dominant behavior entered the fossil record. Because bone remodels in vivo, skeletal asymmetries are thought to reflect greater mechanical loading on the dominant side, but incomplete preservation of external morphology and ambiguities about past loading environments complicate interpretations. We test if internal trabecular bone is capable of providing additional information by analyzing the thumb of Homo sapiens and Pan.

MATERIALS AND METHODS

We assess trabecular structure at the distal head and proximal base of paired (left/right) first metacarpals using micro-CT scans of Homo sapiens (n = 14) and Pan (n = 9). Throughout each epiphysis we quantify average and local bone volume fraction (BV/TV), degree of anisotropy (DA), and elastic modulus (E) to address bone volume patterning and directional asymmetry.

RESULTS

We find a right directional asymmetry in H. sapiens consistent with population-level handedness, but also report a left directional asymmetry in Pan that may be the result of postural and/or locomotor loading.

CONCLUSION

We conclude that trabecular bone is capable of detecting right/left directional asymmetry, but suggest coupling studies of internal structure with analyses of other skeletal elements and cortical bone prior to applications in the fossil record.

Estimation of conditions evoking fracture in finger bones under pinch loading based on finite element analysis

A finger finite element (FE) model was created from CT images of a Japanese male in order to obtain a shape-biofidelic model. Material properties and articulation characteristics of the model were taken from the literature. To predict bone fracture and realistically represent the fracture pattern under various loading conditions, the ESI-Wilkins-Kamoulakos rupture model in PAM-CRASH (ESI Group S.A., Paris, France) was utilized in this study with parameter values of the rupture model determined by compression testing and simulation of porcine fibula. A finger pinch simulation was then conducted to validate the finger FE model. The force-displacement curve and fracture load from the pinch simulation was compared to the result of finger pinch test using cadavers. Simulation results are coincident with the test result, indicating that the finger FE model can be used in an analysis of finger bone fracture during pinch accident. With this model, several pinch simulations were conducted with different pinching object's stiffness and pinching energy. Conditions for evoking finger bone fracture under pinch loading were then estimated based on these results. This study offers a novel method to predict possible hazards of manufactured goods during the design process, thus finger injury due to pinch loading can be avoided.

The influence of the modulus-density relationship and the material mapping method on the simulated mechanical response of the proximal femur in side-ways fall loading configuration

Contributing to slow advance of finite element (FE) simulations for hip fracture risk prediction, into clinical practice, could be a lack of consensus in the biomechanics community on how to map properties to the models. Thus, the aim of the present study was first, to systematically quantify the influence of the modulus-density relationship (E-ρ) and the material mapping method (MMM) on the predicted mechanical response of the proximal femur in a side-ways fall (SWF) loading configuration and second, to perform a model-to-model comparison of the predicted mechanical response within the femoral neck for all the specimens tested in the present study, using three different modelling techniques that have yielded good validation outcome in terms of surface strain prediction and whole bone response according to the literature. We found the outcome to be highly dependent on both the E-ρ relationship and the MMM. In addition, we found that the three modelling techniques that have resulted in good validation outcome in the literature yielded different principal strain prediction both on the surface as well as internally in the femoral neck region of the specimens modelled in the present study. We conclude that there exists a need to carry out a more comprehensive validation study for the SWF loading mode to identify which combination of MMMs and E-ρ relationship leads to the best match for whole bone and local mechanical response. The MMMs tested in the present study have been made publicly available at https://simtk.org/home/mitk-gem.

Individual and combined effects of OA-related subchondral bone alterations on proximal tibial surface stiffness: a parametric finite element modeling study

The role of subchondral bone in OA pathogenesis is unclear. While some OA-related changes to morphology and material properties in different bone regions have been described, the effect of these alterations on subchondral bone surface stiffness has not been investigated. The objectives of this study were to characterize the individual (Objective 1) and combined (Objective 2) effects of OA-related morphological and mechanical alterations to subchondral and epiphyseal bone on surface stiffness of the proximal tibia. We developed and validated a parametric FE model of the proximal tibia using quantitative CT images of 10 fresh-frozen cadaveric specimens and in situ macro-indentation testing. Using this validated FE model, we estimated the individual and combined roles of OA-related alterations in subchondral cortical thickness and elastic modulus, and subchondral trabecular and epiphyseal trabecular elastic moduli on local surface stiffness. A 20% increase in subchondral cortical or subchondral trabecular elastic moduli resulted in little change in stiffness (1% increase). A 20% reduction in epiphyseal trabecular elastic modulus, however, resulted in an 11% reduction in stiffness. Our parametric analysis suggests that subchondral bone stiffness is affected primarily by epiphyseal trabecular bone elastic modulus rather than subchondral cortical and trabecular morphology or mechanical properties. Our results suggest that observed OA-related alterations to epiphyseal trabecular bone (e.g., lower mineralization, bone volume fraction, density and elastic modulus) may contribute to OA proximal tibiae being less stiff than normal.

Remodeling of the Mandibular Bone Induced by Overdentures Supported by Different Numbers of Implants

The objective of this study was to investigate the process of mandibular bone remodeling induced by implant-supported overdentures. computed tomography (CT) images were collected from edentulous patients to reconstruct the geometry of the mandibular bone and overdentures supported by implants. Based on the theory of strain energy density (SED), bone remodeling models were established using the user material subroutine (UMAT) in abaqus. The stress distribution in the mandible and bone density change was investigated to determine the effect of implant number on the remodeling of the mandibular bone. The results indicated that the areas where high Mises stress values were observed were mainly situated around the implants. The stress was concentrated in the distal neck region of the distal-most implants. With an increased number of implants, the biting force applied on the dentures was almost all taken up by implants. The stress and bone density in peri-implant bone increased. When the stress reached the threshold of remodeling, the bone density began to decrease. In the posterior mandible area, the stress was well distributed but increased with decreased implant numbers. Changes in bone density were not observed in this area. The computational results were consistent with the clinical data. The results demonstrate that the risk of bone resorption around the distal-most implants increases with increased numbers of implants and that the occlusal force applied to overdentures should be adjusted to be distributed more in the distal areas of the mandible.

Uncertainty quantification for personalized analyses of human proximal femurs

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (ϵ1 and ϵ3) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coefficients of variation of ≈40%. Between 60 and 80% of the variance in ϵ1 and ϵ3 are attributable to the uncertainty in the E-ρ relationship, while ≈10% are caused by the load magnitude and 5-30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (pf<0.001). In summary, uncertainty quantification with PC has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs.

A biomechanical sorting of clinical risk factors affecting osteoporotic hip fracture

Osteoporotic fracture has been found associated with many clinical risk factors, and the associations have been explored dominantly by evidence-based and case-control approaches. The major challenges emerging from the studies are the large number of the risk factors, the difficulty in quantification, the incomplete list, and the interdependence of the risk factors. A biomechanical sorting of the risk factors may shed lights on resolving the above issues. Based on the definition of load-strength ratio (LSR), we first identified the four biomechanical variables determining fracture risk, i.e., the risk of fall, impact force, bone quality, and bone geometry. Then, we explored the links between the FRAX clinical risk factors and the biomechanical variables by looking for evidences in the literature. To accurately assess fracture risk, none of the four biomechanical variables can be ignored and their values must be subject-specific. A clinical risk factor contributes to osteoporotic fracture by affecting one or more of the biomechanical variables. A biomechanical variable represents the integral effect from all the clinical risk factors linked to the variable. The clinical risk factors in FRAX mostly stand for bone quality. The other three biomechanical variables are not adequately represented by the clinical risk factors. From the biomechanical viewpoint, most clinical risk factors are interdependent to each other as they affect the same biomechanical variable(s). As biomechanical variables must be expressed in numbers before their use in calculating LSR, the numerical value of a biomechanical variable can be used as a gauge of the linked clinical risk factors to measure their integral effect on fracture risk, which may be more efficient than to study each individual risk factor.

A method of determining bending properties of poultry long bones using beam analysis and micro-CT data

While conventional mechanical testing has been regarded as a gold standard for the evaluation of bone heath in numerous studies, with recent advances in medical imaging, virtual methods of biomechanics are rapidly evolving in the human literature. The objective of the current study was to evaluate the feasibility of determining the elastic and failure properties of poultry long bones using established methods of analysis from the human literature. In order to incorporate a large range of bone sizes and densities, a small number of specimens were utilized from an ongoing study of Regmi et al. (2016) that involved humeri and tibiae from 3 groups of animals (10 from each) including aviary, enriched, and conventional housing systems. Half the animals from each group were used for 'training' that involved the development of a regression equation relating bone density and geometry to bending properties from conventional mechanical tests. The remaining specimens from each group were used for 'testing' in which the mechanical properties from conventional tests were compared to those predicted by the regression equations. Based on the regression equations, the coefficients of determination for the 'test' set of data were 0.798 for bending bone stiffness and 0.901 for the yield (or failure) moment of the bones. All regression slopes and intercepts values for the tests versus predicted plots were not significantly different from 1 and 0, respectively. The study showed the feasibility of developing future methods of virtual biomechanics for the evaluation of poultry long bones. With further development, virtual biomechanics may have utility in future in vivo studies to assess laying hen bone health over time without the need to sacrifice large groups of animals at each time point.

Long-term response of femoral density to hip implant and bone fracture plate: Computational study using a mechano-biochemical model

Although bone fracture plates can provide appropriate stability at the fracture site and lead to early patient mobilization, they significantly change the loading pattern in the bone after union (Stress shielding). This phenomenon results in a bone density decrease, which may cause premature failure of the implant. This paper presents the first study that quantifies the long-term response of femoral density to hip implantation and plating (lateral and anterior plating) using a mechano-biochemical model which considers the coupling effect between mechanical loading and biochemical affinities as stimuli for bone remodeling. The results showed that the regions directly beneath the plate experienced severe bone loss (i.e. up to ∼ -70%). However, some level of bone formation was observed in the vicinity of the most proximal and distal screw holes in both lateral and anterior plated femurs (i.e. up to ∼ +110%). The bone under the plate was divided into six zones. With respect to bone remodeling response, the findings revealed that anterior plating was not superior to lateral plating since the maximum and average bone losses among the zones in the anterior plated femur (i.e. -36% and -24%, respectively) were approximately the same as their corresponding values in the lateral plated femur (i.e. -38% and -24%, respectively).

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship

BACKGROUND

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error.

METHODS

Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points).

FINDINGS

Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%.

INTERPRETATION

Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness.

Piezoelectric Sensor to Measure Soft and Hard Stiffness with High Sensitivity for Ultrasonic Transducers

During dental sinus lift surgery, it is important to monitor the thickness of the remaining maxilla to avoid perforating the sinus membrane. Therefore, a sensor should be integrated into ultrasonic dental tools to prevent undesirable damage. This paper presents a piezoelectric (PZT) sensor installed in an ultrasonic transducer to measure the stiffness of high and low materials. Four design types using three PZT ring materials and a split PZT for actuator and sensor ring materials were studied. Three sensor locations were also examined. The voltage signals of the sensor and the displacement of the actuator were analyzed to distinguish the low and high stiffness. Using sensor type T1 made of the PZT-1 material and the front location A1 provided a high sensitivity of 2.47 Vm/kN. The experimental results demonstrated that our design can measure soft and hard stiffness.