How to select the elastic modulus for cancellous bone in patient-specific continuum models of the spine

Investigation on primary stability of dental implants through considering peri-implant bone damage, caused by small and large deformations: A validated non-linear micro finite element study

Primary stability of a dental implant is defined as its ability to resist the applied load without showing excessive damage in peri-implant bone, which is a prerequisite for secondary stability, and consequently for implantation success. The main goal of this study was to develop a validated micro-finite element (μFE) approach to assess the primary stability of dental implants in terms of stiffness, stiffness reduction, and irreversible displacement of the bone-implant system, subjected to an increasing step-wise quasi-static compressive loading-unloading test. The μFE models were generated based on the μCT images of bone, taken from extracted bovine tibia trabecular bone samples after drilling and implantation. A tissue constitutive model was considered for trabecular bone by describing elasto-plasticity with a modified von Mises yield criterion and element deletion technique to account for trabecular bone damage behavior. Then, the obtained force-displacement curves from the simulation were compared with the in-vitro mechanical test curves to evaluate the validity of the model. The results showed that the proposed μFE model could be properly predict the bone-implant system mechanical response in terms of irreversible displacement (R2 = 0.99), stiffness (R2 = 0.77), and stiffness reduction (R2 = 0.72) of the bone-implant construct for all the applied displacements without a significant difference from the unit slope and zero intercept of the QQ-plot (p-value<0.05). Moreover, a qualitative agreement was seen between the peri-implant bone damage predicted by the μFE model and the observed from μCT images. The adopted methodology used in this study can predict the mechanical failure response of the bone-implant system, which can be employed as a representative tool to study the effects of various dental implant design parameters on the primary stability with the ultimate goal of optimizing dental implants design.

Effects of Internal Fluid Pressure on Stresses in Subchondral Bone Cysts of the Medial Femoral Condyle

The etiology of subchondral bone cysts (SBCs) is not fully understood. Mechanical trauma and fluid pressure are two mechanisms believed to cause their formation and growth. The equine stifle joint provides a natural animal model for studying SBCs. Computed tomography images of an extended yearling cadaveric stifle joint were segmented using ScanIP to isolate bones and relevant soft tissues. Three model geometries were created to simulate cyst sizes of approximately 0.03 cm³ (C1), 0.5 cm³ (C2), and 1 cm³ (C3). A uniform pressure resulting in 3000 N force was applied at the proximal end of the femur. Two types of simulations, filled-cyst and empty-cysts with uniform pressure loads, were used to simulate fluid pressurization. Our models suggest that shear stresses are likely the cause of failure for the subchondral bone and not pressurized fluid from the joint. Bone stresses did not begin to increase until cyst pressures were greater than 3 MPa. For all cyst sizes, fluid pressure must rise above what is likely to occur in vivo in order to increase bone shear stress, shown to be most critical. Synovial fluid pressure acts upon a porous trabecular bone network, soft tissue, and marrow, so the continuum nature of our model likely overestimates the predicted effects of fluid pressures.

A novel in silico method to quantify primary stability of screws in trabecular bone

Insufficient primary stability of screws in bone leads to screw loosening and failure. Unlike conventional continuum finite-element models, micro-CT based finite-element analysis (micro-FE) is capable of capturing the patient-specific bone micro-architecture, providing accurate estimates of bone stiffness. However, such in silico models for screws in bone highly overestimate the apparent stiffness. We hypothesized that a more accurate prediction of primary implant stability of screws in bone is possible by considering insertion-related bone damage. We assessed two different screw types and loading scenarios in 20 trabecular bone specimens extracted from 12 cadaveric human femoral heads (N = 5 for each case). In the micro-FE model, we predicted specimen-specific Young's moduli of the peri-implant bone damage region based on morphometric parameters such that the apparent stiffness of each in silico model matched the experimentally measured stiffness of the corresponding in vitro specimen as closely as possible. The standard micro-FE models assuming perfectly intact peri-implant bone overestimated the stiffness by over 330%. The consideration of insertion related damaged peri-implant bone corrected the mean absolute percentage error down to 11.4% for both loading scenarios and screw types. Cross-validation revealed a mean absolute percentage error of 14.2%. We present the validation of a novel micro-FE modeling technique to quantify the apparent stiffness of screws in trabecular bone. While the standard micro-FE model overestimated the bone-implant stiffness, the consideration of insertion-related bone damage was crucial for an accurate stiffness prediction. This approach provides an important step toward more accurate specimen-specific micro-FE models. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2415-2424, 2017.

A model-based approach for estimation of changes in lumbar segmental kinematics associated with alterations in trunk muscle forces

The kinematics information from imaging, if combined with optimization-based biomechanical models, may provide a unique platform for personalized assessment of trunk muscle forces (TMFs). Such a method, however, is feasible only if differences in lumbar spine kinematics due to differences in TMFs can be captured by the current imaging techniques. A finite element model of the spine within an optimization procedure was used to estimate segmental kinematics of lumbar spine associated with five different sets of TMFs. Each set of TMFs was associated with a hypothetical trunk neuromuscular strategy that optimized one aspect of lower back biomechanics. For each set of TMFs, the segmental kinematics of lumbar spine was estimated for a single static trunk flexed posture involving, respectively, 40° and 10° of thoracic and pelvic rotations. Minimum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 0° to 0.7° and 0 mm to 0.04 mm, respectively. Maximum changes in the angular and translational deformations of a motion segment with alterations in TMFs ranged from 2.4° to 7.6° and 0.11 mm to 0.39 mm, respectively. The differences in kinematics of lumbar segments between each combination of two sets of TMFs in 97% of cases for angular deformation and 55% of cases for translational deformation were within the reported accuracy of current imaging techniques. Therefore, it might be possible to use image-based kinematics of lumbar segments along with computational modeling for personalized assessment of TMFs.

An in silico parametric model of vertebrae trabecular bone based on density and microstructural parameters to assess risk of fracture in osteoporosis

Osteoporosis is a progressive bone disease characterized by deterioration in the quantity and quality of bone, leading to inferior mechanical properties and an increased risk of fracture. Current assessment of osteoporosis is typically based on bone densitometry tools such as Quantitative Computed Tomography (QCT) and Dual Energy X-ray absorptiometry (DEXA). These assessment modalities mainly rely on estimating the bone mineral density (BMD). Hence present densitometry tools describe only the deterioration of the quantity of bone associated with the disease and not the affected morphology or microstructural changes, resulting in potential incomplete assessment, many undetected patients, and unexplained fractures. In this study, an in-silico parametric model of vertebral trabecular bone incorporating both material and microstructural parameters was developed towards the accurate assessment of osteoporosis and the consequent risk of bone fracture. The model confirms that the mechanical properties such as strength and stiffness of vertebral trabecular tissue are highly influenced by material properties as well as morphology characteristics such as connectivity, which reflects the quality of connected inter-trabecular parts. The FE cellular solid model presented here provides a holistic approach that incorporates both material and microstructural elements associated with the degenerative process, and hence has the potential to provide clinical practitioners and researchers with more accurate assessment method for the degenerative changes leading to inferior mechanical properties and increased fracture risk associated with age and/or disease such as Osteoporosis.

Noninvasive prediction of vertebral body compressive strength using nonlinear finite element method and an image based technique

Noninvasive prediction of vertebral body strength under compressive loading condition is a valuable tool for the assessment of clinical fractures. This paper presents an effective specimen-specific approach for noninvasive prediction of human vertebral strength using a nonlinear finite element (FE) model and an image based parameter based on the quantitative computed tomography (QCT). Nine thoracolumbar vertebrae excised from three cadavers with an average age of 42 years old were used as the samples. The samples were scanned using the QCT. Then, a segmentation technique was performed on each QCT sectional image. The segmented images were then converted into three-dimensional FE models for linear and nonlinear analyses. A new material model was implemented in our nonlinear model being more compatible with real mechanical behavior of trabecular bone. A new image based MOS (Mechanic of Solids) parameter named minimum sectional strength ((sigma(u)A)(min)) was used for the ultimate compressive strength prediction. Subsequently, the samples were destructively tested under uniaxial compression and their experimental ultimate compressive strengths were obtained. Results indicated that our new implemented FE model can predict ultimate compressive strength of human vertebra with a correlation coefficient (R(2)=0.94) better than usual linear and nonlinear FE models (R(2)=0.83 and 0.85 respectively). The image based parameter introduced in this study ((sigma(u)A)(min)) was also correlated well with the experimental results (R(2)=0.86). Although nonlinear FE method with new implemented material model predicts compressive strength better than the (sigma(u)A)(min), this parameter is clinically more feasible due to its simplicity and lower computational costs. This can make future applications of the (sigma(u)A)(min) more justified for human vertebral body compressive strength prediction.

Material Property Sensitivity Analysis on Resonant Frequency Characteristics of the Human Spine

The aim of this study is to investigate the effect of material property changes in the spinal components on the resonant frequency characteristics of the human spine. Several investigations have reported the material property sensitivity of human spine under static loading conditions, but less research has been devoted to the material property sensitivity of spinal biomechanical characteristics under a vibration environment. A detailed three-dimensional finite element model of the human spine, T12– pelvis, was built and used to predict the influence of material property variation on the resonant frequencies of the human spine. The simulation results reveal that material properties of spinal components have obvious influences on the dynamic characteristics of the spine. The annulus ground substance is the dominant component affecting the vertical resonant frequencies of the spine. The percentage change of the resonant frequency relative to the basic condition was more than 20% if Young’s modulus of disc annulus is less than 1.5 MPa. The vertical resonant frequency may also decrease if Poisson’s ratio of nucleus pulposus of intervertebral disc decreases.

Inhomogeneity of tissue-level strain distributions in individual trabeculae: Mathematical model studies of normal and osteoporosis cases

Little is known about the distributions of mechanical strains and stresses in individual trabeculae of cancellous bone, despite evidence that tissue-level strains affect the metabolism of bone. Recently, micro-finite element (micro-FE) studies have provided the first insights into the mechanical conditions in trabeculae, and suggested that osteoporotic cancellous bone experience higher and substantially less-uniform strains with respect to healthy cancellous bone. We may therefore ask whether the inhomogeneity of bone tissue strains is predominantly a consequence of micro-architectural differences between trabeculae, or is it mostly caused by the curvatures of each individual trabecula. Accordingly, the objectives of the present study were to determine the contribution of the shape of a trabecula to the intra-trabecula strain inhomogeneity, and to determine potential differences in intra-trabecula strain inhomogeneities between normal and thinner, osteoporotic-like trabeculae. We employed our previously reported generic single-trabecula model, which is a mathematical representation of the shape of a trabecula based on statistical analyses of mammalian trabecular dimensions. The single-trabecula model was loaded axially and in bending, and strain distributions were calculated for individual trabeculae as well as for "populations" of trabeculae, formed by assigning different trabecular thickness values in the trabecular model, in order to represent the distributions of trabecular shapes in normal and osteoporotic bones. We found that when subjected to equivalent loads, thinner, osteoporotic-like individual trabeculae and populations of thin trabeculae developed substantially greater strain inhomogeneities compared with normal trabeculae. We conclude that the intra-trabecula strain inhomogeneities are likely to be an important factor contributing to the overall increased strain inhomogeneity in osteoporotic cancellous bone, as previously observed in micro-FE studies.

Parametric equations to represent the profile of the human intervertebral disc in the transverse plane

Computational and finite element models of the spine are used to investigate spine and disc mechanics. Subject specific data for the transverse profile of the disc could improve the geometric accuracy of these models. The current study aimed to develop a mathematical algorithm to describe the profile of the disc components, using subject-specific data points. Using data points measured from pictures of human intervertebral discs sectioned in the transverse plane, parametric formulae were derived that mapped the outer profile of the anulus and nucleus. The computed anulus and nucleus profile were a similar shape to the discs from which they were derived. The computed total disc area was similar to the experimental data. The nucleus:disc area ratios were sensitive to the data points defined for each disc. The developed formulae can be easily implemented to provide patient specific data for the disc profile in computational models of the spine.

A method for patient-specific evaluation of vertebral cancellous bone strength: in vitro validation

BACKGROUND

In the context of osteoporosis, important determinants of the fracture risk are the apparent strength and stiffness of cancellous bone, as well as its brittleness and energy absorption capacity. Standard medical imaging, however, cannot measure these mechanical properties directly. Consequently, an estimation of the risk for fracture is made by correlating relative density or mineral density at a skeletal site with statistics of fracture occurrence, which provides limited and partial indications on fracture risks. A better method for evaluating the patient-specific mechanical properties of cancellous bone is therefore required.

METHODS

In order to asses the mechanical properties of vertebral cancellous bone, we developed a finite element parametric model of lattice trabecular architecture that, in the future, will be suitable for use with bone imaging modalities. The model inputs are apparent morphological parameters (trabecular thickness and trabecular separation) and the bone mineral density. We conducted uniaxial compression tests on 36 canine vertebral cancellous bone specimens (C7 and L1) to validate model predictions of strength and stiffness in vitro.

FINDINGS

Predictions of strength and stiffness matched the experimental results within relative absolute errors of 17.7% and 12.8%, respectively (average of differences between model-predicted and measured values, divided by the average of measured values). We also employed the model for evaluation of strength and stiffness of human L1 and L5 vertebrae and found mean strength of 1.67 MPa (confidence interval 0.42 MPa) and mean elastic modulus of 190 MPa (confidence interval 50 MPa), which are well within the range of previously reported apparent strength and stiffness properties.

INTERPRETATION

The present model can be used to improve medical imaging-based evaluation of the spine in osteoporotic individuals by providing more specific information on the individual bone's susceptibility to fracture once clinical bone scans will be able to provide more reliable measures of trabecular thickness and separation.