Scanner influence on the mechanical response of QCT-based finite element analysis of long bones

Method for computer tomography voxel-based finite element analysis and validation with digital image correlation system

Understanding the mechanical behavior of heterogeneous materials is becoming increasingly crucial across various fields, including aerospace engineering, composite materials development, geology, and biomechanics. While substantial literature exists on this topic, conventional methods often rely on commercial software packages. This study presents a framework for computed tomography (CT) scan-based finite element (FE) analysis of such materials using open-source software in most of the workflow. Our work focuses on three key aspects:1.Mesh generation that incorporates spatially varying mechanical properties and well-defined boundary conditions.2.Validation of the FE results through comparison with digital image correlation (DIC) system measurements.3.Open-source software utilization throughout the entire process, making it more accessible and cost-effective.This work aims to demonstrate the effectiveness of this framework for analyzing heterogeneous materials in various fields, offering a more accessible and affordable approach.

Feasibility study of femur bone with continuum model

It is known that the geometric structures of bones are very complex. This has made researchers unable to model them with the continuum approach and suffice to model them with simulation or experimental tests. Undoubtedly, provide a simple and accurate continuum model for studying bones is always desirable. In this article, as the first serious endeavour, a suggested beam model is investigated to see whether it is suitable for modelling femur bones or not. If this model gives an acceptable answer, it can be a link to the continuum theories for beams. In other words, the approximated beam model can be formulated with continuum approach to study femur bone. For feasibility study of the approximated model for femur bones, both static and dynamic analysis of them are investigated and compared. It is found that in most cases for vibration analysis, the suggested model has acceptable results but in static analysis, the mean difference between the results is about 16%. This research is hoped to be the first serious step in this category.

On the influence of computed tomography's slice thickness on computer tomography based finite element analyses results

BACKGROUND

Patient-specific autonomous finite element analyses of femurs, based on clinical computed tomography scans may be used to monitor the progression of bone-related diseases. Some CT scan protocols provide lower resolution (slice thickness of 3 mm) that affects the accuracy. To investigate the impact of low-resolution scans on the CT-based finite element analyses results, identical CT raw data were reconstructed twice to generate a 1 mm ("gold standard") and a 3 mm slice thickness scans.

METHODS

CT-based finite element analyses of twenty-four femurs (twelve patients) under stance and sideways fall loads were performed based on 1 and 3 mm slice thickness scans. Bone volume, load direction, and strains were extracted at different locations along the femurs and differences were evaluated.

FINDINGS

Average differences in bone volume were 1.0 ± 1.5%. The largest average difference in strains in stance position was in the neck region (11.0 ± 13.4%), whereas in other regions these were much smaller. For sidewise fall loading, the average differences were at most 9.2 ± 16.0%.

INTERPRETATION

Whole-body low dose CT scans (3 mm-slice thickness) are suboptimal for monitoring strain changes in patient's femurs but may allow longitudinal studies if larger than 5% in all areas and larger than 12% in the upper neck. CT-based finite element analyses with slice thickness of 3 mm may be used in clinical practice for patients with smoldering myeloma to associate changes in strains with progression to active myeloma if above ∼10%.

Predicting fracture in the proximal humerus using phase field models

Proximal humerus impacted fractures are of clinical concern in the elderly population. Prediction of such fractures by CT-based finite element methods encounters several major obstacles such as heterogeneous mechanical properties and fracture due to compressive strains. We herein propose to investigate a variation of the phase field method (PFM) embedded into the finite cell method (FCM) to simulate impacted humeral fractures in fresh frozen human humeri. The force-strain response, failure loads and the fracture path are compared to experimental observations for validation purposes. The PFM (by means of the regularization parameter ℓ₀) is first calibrated by one experiment and thereafter used for the prediction of the mechanical response of two other human fresh frozen humeri. All humeri are fractured at the surgical neck and strains are monitored by Digital Image Correlation (DIC). Experimental strains in the elastic regime are reproduced with good agreement (R²=0.726), similarly to the validated finite element method (Dahan et al., 2022). The failure pattern and fracture evolution at the surgical neck predicted by the PFM mimic extremely well the experimental observations for all three humeri. The maximum relative error in the computed failure loads is 3.8%. To the best of our knowledge this is the first method that can predict well the experimental compressive failure pattern as well as the force-strain relationship in proximal humerus fractures.

Can neck fractures in proximal humeri be predicted by CT-based FEA?

BACKGROUND

Proximal humeri fractures at anatomical and surgical neck (∼5% and ∼50% incidence respectively) are frequent in elderly population. Yet, neither in-vitro experiments nor CT-based finite element analyses (CTFEA) have investigated these in depth. Herein we enhance (Dahan et al., 2019) (addressing anatomical neck fractures) by more experiments and specimens, accounting for surgical neck fractures and explore CTFEA's prediction of humeri mechanical response and yield force.

METHODS

Four fresh frozen human humeri were tested in a new experimental configuration inducing surgical neck fractures. Digital image correlation (DIC) provided strains and displacements on humeri surfaces and used to validate CTFEA predictions. CTFEA were enhanced herein to improve the accuracy at the proximal neck: A cortical bone mapping (CBM) algorithm was implemented to overcome insufficient scanning resolution, and a new trabecular material mapping was investigated.

RESULTS

The new experimental setting induced impacted surgical neck fractures in all humeri. Excellent DIC to CTFEA correlation in strains was obtained at the shaft (slope 0.984, R²=0.99) and a fair agreement (slope 0.807, R²=0.73) at the neck. CBM algorithm had worsened the correlation, whereas the new material mapping had a negligible influence. Yield loads predictions improved considerably when trabecular yielding (maximum principal strain criterion) was considered instead of surface cortical yielding.

DISCUSSION

CTFEA well predicts strains on the shaft and reasonably well on the neck. This enhances former conclusions by past studies conducted using SGs, now also evident by DIC. Yield load prediction for surgical neck fractures (involving crushing of trabecular bone) is predicted better by trabecular failure laws rather than cortex ones. Further FEA studies using trabecular orthotropic constitutive models and failure laws are warrant.

Evaluation of patient tissue selection methods for deriving equivalent density calibration for femoral bone quantitative CT analyses

Osteoporosis affects an increasing number of people every year and patient specific finite element analysis of the femur has been proposed to identify patients that could benefit from preventative treatment. The aim of this study was to demonstrate, verify, and validate an objective process for selecting tissues for use as the basis of phantomless calibration to enable patient specific finite element analysis derived hip fracture risk prediction. Retrospective reanalysis of patient computed tomography (CT) scans has the potential to yield insights into more accurate prediction of osteoporotic fracture. Bone mineral density (BMD) specific calibration scans are not typically captured during routine clinical practice. Tissue-based BMD calibration can therefore empower the retrospective study of patient CT scans captured during routine clinical practice. Together the method for selecting tissues as the basis for phantomless calibration coupled with the post-processing steps for deriving a calibration equation using the selected tissues provide an estimation of quantitative equivalent density results derived using calibration phantoms. Patient tissues from a retrospective cohort of 211 patients were evaluated. The best phantomless calibration resulted in a femoral strength (FS) [N] bias of 0.069 ± 0.07% over FS derived from inline calibration and a BMD [kg/cm³] bias of 0.038 ± 0.037% over BMD derived from inline calibration. The phantomless calibration slope for the best method presented was within the range of patient specific calibration curves available for comparison and demonstrated a small bias of 0.028 ± 0.054 HU/(mg/cm³), assuming the Mindways Model 3 BMD inline calibration phantom as the gold standard. The presented method of estimating a calibration equation from tissues showed promise for CT-based femoral fracture analyses of retrospective cohorts without readily available calibration data.

Effect of CT imaging on the accuracy of the finite element modelling in bone

The finite element (FE) analysis is a highly promising tool to simulate the behaviour of bone. Skeletal FE models in clinical routine rely on the information about the geometry and bone mineral density distribution from quantitative computed tomography (CT) imaging systems. Several parameters in CT imaging have been reported to affect the accuracy of FE models. FE models of bone are exclusively developed in vitro under scanning conditions deviating from the clinical setting, resulting in variability of FE results (< 10%). Slice thickness and field of view had little effect on FE predicted bone behaviour (≤ 4%), while the reconstruction kernels showed to have a larger effect (≤ 20%). Due to large interscanner variations (≤ 20%), the translation from an experimental model into clinical reality is a critical step. Those variations are assumed to be mostly caused by different “black box” reconstruction kernels and the varying frequency of higher density voxels, representing cortical bone. Considering the low number of studies together with the significant effect of CT imaging on the finite element model outcome leading to high variability in the predicted behaviour, we propose further systematic research and validation studies, ideally preceding multicentre and longitudinal studies.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

Finite element analyses for predicting anatomical neck fractures in the proximal humerus

BACKGROUND

Proximal humerus fractures which occur as a result of a fall on an outstretched arm are frequent among the elderly population. The necessity of stabilizing such fractures by surgical procedures is a controversial matter among surgeons. Validating a personalized FE analysis by ex-vivo experiments of humeri and mimicking such fractures by experiments is the first step along the path to determine the necessity of such surgeries.

METHODS

Four fresh frozen human humeri were loaded using a new simple experimental setting, so to fracture the humeri at the anatomical neck. Strains on humeri's surfaces predicted by the high order FE analyses (as in Dahan et al., 2016) were compared to the experimental observations to further enhance the validity of the FE analyses. A simplified yield criterion based on a linear elastic analysis and principal strains was used to predict the anatomical neck fracture as observed in the experiment.

FINDINGS

An excellent correlation between experimental measured and FE predicted strains was obtained (slope of 0.99 and R²=0.98). All humeri were fractured at the anatomical neck. The predicted yield load was within 10%-20% accuracy.

INTERPRETATION

High-order FE analyses reliably predict strains and yield loads in the humeri. Fractures induced by the experimental setting correspond to anatomical neck fractures noticed in practice and classified as AO C1.1-C1.3. Surgical neck fractures, which are most common in clinical practice, could not be realized in the proposed experiments, and a different experimental setting should be sought to obtain them ex-vivo.