Predicting fracture using 2D finite element modelling

In Silico Modeling of Stress Distribution in the Diseased Ankle Joint

Background/Objectives: Osteoarthritis is a feature of the aging process. Here, we adopted in silico 2D finite element modeling (FEM) for the simulation of diseased ankle joints. We delved into the influence of body weight intensity on the stress distribution caused by subchondral cysts imitating degenerative age-related arthritic changes. Methods: FEM was performed using virtually generated pictorial schemes of the ankle joint skeletal contour. It included a constellation of scenarios with solitary or multiple cysts, or the lack thereof, located centrally, peripherally, or both in the talus and tibia at increased fixed levels of body weight. Results: The modeling showed that the highest stress was in the presence of a solitary central cyst in the talus and two centrally located cysts in the talus and the tibia, with the averaged values of 1.81 ± 0.52 MPa and 1.92 ± 0.55 MPa, respectively; there was a significant increase compared with the 1.24 ± 0.35 MPa in the control condition without cysts. An increase in body weight consistently increased the strain on the ankle joint. In contrast, peripherally located cysts failed to affect the stress distribution significantly. Conclusions: We conclude that subchondral central cysts substantially enhance the stress exerted on the ankle joint and its vicinity with body weight dependence. FEM's ability to predict the location and magnitude of subchondral stress changes when confirmed in clinical trials might help to optimize the management of age-related degenerative joint changes.

The bone strain index predicts fragility fractures. The OFELY study

Recently, the bone strain index (BSI), a new index of bone strength based on a finite element model (FEA) from dual X-ray absorptiometry (DXA), has been developed. BSI represents the average equivalent strain inside the bone, assuming that a higher strain level (high BSI) indicates a condition of higher risk. Our study aimed to analyze the relationship between BSI and age, BMI and areal BMD in pre- and postmenopausal women and to prospectively investigate fracture prediction (Fx) by BSI in postmenopausal women. Methods. At the 14th annual follow-up of the OFELY study, BSI was measured at spine (Spine BSI) and femoral scans (Neck and Total Hip BSI), in addition to areal BMD with DXA (Hologic QDR 4500) in 846 women, mean (SD) age 60 yr (15). The FRAX® (fracture risk assessment tool) for major osteoporotic fractures (MOF) was calculated with FN areal BMD (aBMD) at baseline; incident fragility fractures were annually registered until January 2016. Results. In premenopausal women (n = 261), Neck and Total Hip BSI were slightly negatively correlated with age (Spearman r = -0.13 and -0.15 respectively, p = 0.03), whereas all BSIs were positively correlated with BMI (r = +0.20 to 0.37, p < 0.01) and negatively with BMD (r = -0.69 to -0.37, p < 0.0001). In postmenopausal women (n = 585), Neck and Total Hip BSI were positively correlated with age (Spearman r = +0.26 and +0.31 respectively, p < 0.0001), whereas Spine BSI was positively correlated with BMI (r = +0.22, p < 0.0001) and all BSIs were negatively correlated with BMD (r = -0.81 to -0.60, p < 0.0001). During a median [IQ] 9.3 [1.0] years of follow-up, 133 postmenopausal women reported an incident fragility Fx, including 80 women with a major osteoporotic Fx (MOF) and 26 women with clinical vertebral Fx (VFx). Each SD increase of BSI value was associated with a significant increase of the risk of all fragility Fx with an age-adjusted HR of 1.23 for Neck BSI (p = 0.02); 1.27 for Total Hip BSI (p = 0.004) and 1.35 for Spine BSI (p < 0.0001). After adjustment for FRAX®, the association remained statistically significant for Total Hip BSI (HR 1.24, p = 0.02 for all fragility Fx; 1.31, p = 0.01 for MOF) and Spine BSI (HR 1.33, p < 0.0001 for all fragility Fx; 1.33, p = 0.005 for MOF; 1.67, p = 0.002 for clinical VFx). In conclusion, spine and femur BSI, an FEA DXA derived index, predict incident fragility fracture in postmenopausal women, regardless of FRAX®.

In Silico Finite Element Modeling of Stress Distribution in Osteosynthesis after Pertrochanteric Fractures

A stabilization method of pertrochanteric femur fractures is a contentious issue. Here, we assess the feasibility of rapid in silico 2D finite element modeling (FEM) to predict the distribution of stresses arising during the two most often used stabilization methods: gamma nail fixation (GNF) and dynamic hip screw (DHS). The modeling was based on standard pre-surgery radiographs of hip joints of 15 patients with pertrochanteric fractures of type A1, A2, and A3 according to the AO/OTA classification. The FEM showed that the stresses were similar for both GNF and DHS, with the medians ranging between 53-60 MPa and consistently lower for A1 than A3 fractures. Stresses also appeared in the fixation materials being about two-fold higher for GNF. Given similar bone stresses caused by both GNF and DHS but shorter surgery time, less extensive dissection, and faster patient mobilization, we submit that the GNF stabilization appears to be the most optimal system for pertrochanteric fractures. In silico FEM appears a viable perioperative method that helps predict the distribution of compressive stresses after osteosynthesis of pertrochanteric fractures. The promptness of modeling fits well into the rigid time framework of hip fracture surgery and may help optimize the fixation procedure for the best outcome. The study extends the use of FEM in complex orthopedic management. However, further datasets are required to firmly position the FEM in the treatment of pertrochanteric fractures.

Beyond Bone Mineral Density: A New Dual X-Ray Absorptiometry Index of Bone Strength to Predict Fragility Fractures, the Bone Strain Index

For a proper assessment of osteoporotic fragility fracture prediction, all aspects regarding bone mineral density, bone texture, geometry and information about strength are necessary, particularly in endocrinological and rheumatological diseases, where bone quality impairment is relevant. Data regarding bone quantity (density) and, partially, bone quality (structure and geometry) are obtained by the gold standard method of dual X-ray absorptiometry (DXA). Data about bone strength are not yet readily available. To evaluate bone resistance to strain, a new DXA-derived index based on the Finite Element Analysis (FEA) of a greyscale of density distribution measured on spine and femoral scan, namely Bone Strain Index (BSI), has recently been developed. Bone Strain Index includes local information on density distribution, bone geometry and loadings and it differs from bone mineral density (BMD) and other variables of bone quality like trabecular bone score (TBS), which are all based on the quantification of bone mass and distribution averaged over the scanned region. This state of the art review illustrates the methodology of BSI calculation, the findings of its in reproducibility and the preliminary data about its capability to predict fragility fracture and to monitor the follow up of the pharmacological treatment for osteoporosis.

A new finite element based parameter to predict bone fracture

Dual Energy X-Ray Absorptiometry (DXA) is currently the most widely adopted non-invasive clinical technique to assess bone mineral density and bone mineral content in human research and represents the primary tool for the diagnosis of osteoporosis. DXA measures areal bone mineral density, BMD, which does not account for the three-dimensional structure of the vertebrae and for the distribution of bone mass. The result is that longitudinal DXA can only predict about 70% of vertebral fractures. This study proposes a complementary tool, based on Finite Element (FE) models, to improve the DXA accuracy. Bone is simulated as elastic and inhomogeneous material, with stiffness distribution derived from DXA greyscale images of density. The numerical procedure simulates a compressive load on each vertebra to evaluate the local minimum principal strain values. From these values, both the local average and the maximum strains are computed over the cross sections and along the height of the analysed bone region, to provide a parameter, named Strain Index of Bone (SIB), which could be considered as a bone fragility index. The procedure is initially validated on 33 cylindrical trabecular bone samples obtained from porcine lumbar vertebrae, experimentally tested under static compressive loading. Comparing the experimental mechanical parameters with the SIB, we could find a higher correlation of the ultimate stress, σULT, with the SIB values (R2adj = 0.63) than that observed with the conventional DXA-based clinical parameters, i.e. Bone Mineral Density, BMD (R2adj = 0.34) and Trabecular Bone Score, TBS (R2adj = -0.03). The paper finally presents a few case studies of numerical simulations carried out on human lumbar vertebrae. If our results are confirmed in prospective studies, SIB could be used-together with BMD and TBS-to improve the fracture risk assessment and support the clinical decision to assume specific drugs for metabolic bone diseases.

Improving the Hip Fracture Risk Prediction Through 2D Finite Element Models From DXA Images: Validation Against 3D Models

Osteoporotic fracture incidence represents a major social and economic concern in the modern society, where the progressive graying of the population involves an highly increased fracture occurrence. Although the gold standard to diagnose osteoporosis is represented by the T-score measurement, estimated from the Bone Mineral Density (BMD) using Dual-energy X-ray Absorptiometry (DXA), the identification of the subjects at high risk of fracture still remains an issue. From this perspective, the purpose of this work is to investigate the role that DXA-based two-dimensional patient-specific finite element (FE) models of the proximal femur, in combination with T-score, could play in enhancing the risk of fracture estimation. With this aim, 2D FE models were built from DXA images of the 28 post-menopausal female subjects involved. A sideways fall condition was reproduced and a Risk of Fracture (RF^) was computed on the basis of principal strains criteria. The identified RF^ was then compared to that derived from the CT-based models developed in a previous study. The 2D and 3D RF^ turned out to be significantly correlated (Spearman's ρ = 0.66, p < 0.001), highlighting the same patients as those at higher risk. Moreover, the 2D RF^ resulted significantly correlated with the T-score (Spearman's ρ = −0.69, p < 0.001), and managed to better differentiate osteopenic patients, drawing the attention to some of them. The Hip Structural Analysis (HSA) variables explaining the majority of the variance of the 2D and 3D fracture risk were the same as well, i.e., neck-shaft angle and narrow neck buckling ratio. In conclusion, DXA-based FE models, developable from currently available clinical data, appear promising in supporting and integrating the present diagnostic procedure.

Fracture Risk Indices From DXA-Based Finite Element Analysis Predict Incident Fractures Independently From FRAX: The Manitoba BMD Registry

OBJECTIVE

Finite element analysis (FEA) is a computational method to predict the behavior of materials under applied loading. We developed a software tool that automatically performs FEA on dual-energy X-ray absorptiometry hip scans to generate site-specific fracture risk indices (FRIs) that reflect the likelihood of hip fracture from a sideways fall. This longitudinal study examined associations between FRIs and incident fractures.

METHODS

Using the Manitoba Bone Mineral Density (BMD) Registry, femoral neck (FN), intertrochanter (IT), and subtrochanter (ST) FRIs were automatically derived from 13,978 anonymized dual-energy X-ray absorptiometry scans (Prodigy, GE Healthcare) in women and men aged 50 yr or older (mean age 65 yr). Baseline covariates and incident fractures were assessed from population-based data. We compared c-statistics for FRIs vs FN BMD alone and fracture risk assessment (FRAX) probability computed with BMD. Cox regression was used to estimate hazard ratios and 95% confidence intervals (95% CIs) for incident hip, major osteoporotic fracture (MOF) and non-hip MOF adjusted for relevant covariates including age, sex, FN BMD, FRAX probability, FRAX risk factors, and hip axis length (HAL).

RESULTS

During mean follow-up of 6 yr, there were 268 subjects with incident hip fractures, 1003 with incident MOF, and 787 with incident non-hip MOF. All FRIs gave significant stratification for hip fracture (c-statistics FN-FRI: 0.76, 95% CI 0.73-0.79, IT-FRI 0.74, 0.71-0.77; ST-FRI 0.72, 0.69-0.75). FRIs continued to predict hip fracture risk even after adjustment for age and sex (hazard ratio per standard deviation FN-FRI 1.89, 95% CI 1.66-2.16); age, sex, and BMD (1.26, 1.07-1.48); FRAX probability (1.30, 1.11-1.52); FRAX probability with HAL (1.26, 1.05-1.51); and individual FRAX risk factors (1.32, 1.09-1.59). FRIs also predicted MOF and non-hip MOF, but the prediction was not as strong as for hip fracture.

SUMMARY

Automatically-derived FN, IT, and ST FRIs are associated with incident hip fracture independent of multiple covariates, including FN BMD, FRAX probability and risk factors, and HAL.

Osteoporotic hip fracture prediction: is T-score based criterion enough? A Hip Structural Analysis based model

At present, the current gold-standard for osteoporosis diagnosis is based on bone mineral density measurement, which, however, has been demonstrated to poorly estimate fracture risk. Further parameters in the hands of the clinicians are represented by the Hip Structural Analysis (HSA) variables, which include geometric information of the proximal femur cross-section. The purpose of this study was to investigate the suitability of HSA parameters as additional hip fracture risk predictors. With this aim, twenty-eight three-dimensional patient-specific models of the proximal femur were built from CT images and a sideways fall condition was reproduced by finite element analyses. A tensile or compressive predominance based on minimum and maximum principal strains was determined at each volume element and a Risk Factor (RF) was calculated. The power of HSA variables combinations to predict the maximum superficial RF values was assessed by multivariate linear regression analysis. The optimal regression model, identified through the Akaike information criterion, only comprises two variables, the buckling ratio and the neck-shaft angle. In order to validate the study, the model was tested on two additional patients who suffered a hip fracture after a fall. The results classified the patients in the high risk level, confirming the prediction power of the adopted model.

Prediction of femoral strength using 3D finite element models reconstructed from DXA images: validation against experiments

Computed tomography (CT)-based finite element (FE) models may improve the current osteoporosis diagnostics and prediction of fracture risk by providing an estimate for femoral strength. However, the need for a CT scan, as opposed to the conventional use of dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnostics, is considered a major obstacle. The 3D shape and bone mineral density (BMD) distribution of a femur can be reconstructed using a statistical shape and appearance model (SSAM) and the DXA image of the femur. Then, the reconstructed shape and BMD could be used to build FE models to predict bone strength. Since high accuracy is needed in all steps of the analysis, this study aimed at evaluating the ability of a 3D FE model built from one 2D DXA image to predict the strains and fracture load of human femora. Three cadaver femora were retrieved, for which experimental measurements from ex vivo mechanical tests were available. FE models were built using the SSAM-based reconstructions: using only the SSAM-reconstructed shape, only the SSAM-reconstructed BMD distribution, and the full SSAM-based reconstruction (including both shape and BMD distribution). When compared with experimental data, the SSAM-based models predicted accurately principal strains (coefficient of determination >0.83, normalized root-mean-square error <16%) and femoral strength (standard error of the estimate 1215 N). These results were only slightly inferior to those obtained with CT-based FE models, but with the considerable advantage of the models being built from DXA images. In summary, the results support the feasibility of SSAM-based models as a practical tool to introduce FE-based bone strength estimation in the current fracture risk diagnostics.

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 predictive mechanical model for evaluating vertebral fracture probability in lumbar spine under different osteoporotic drug therapies

Osteoporotic vertebral fractures represent a major cause of disability, loss of quality of life and even mortality among the elderly population. Decisions on drug therapy are based on the assessment of risk factors for fracture from bone mineral density (BMD) measurements. A previously developed model, based on the Damage and Fracture Mechanics, was applied for the evaluation of the mechanical magnitudes involved in the fracture process from clinical BMD measurements. BMD evolution in untreated patients and in patients with seven different treatments was analyzed from clinical studies in order to compare the variation in the risk of fracture. The predictive model was applied in a finite element simulation of the whole lumbar spine, obtaining detailed maps of damage and fracture probability, identifying high-risk local zones at vertebral body. For every vertebra, strontium ranelate exhibits the highest decrease, whereas minimum decrease is achieved with oral ibandronate. All the treatments manifest similar trends for every vertebra. Conversely, for the natural BMD evolution, as bone stiffness decreases, the mechanical damage and fracture probability show a significant increase (as it occurs in the natural history of BMD). Vertebral walls and external areas of vertebral end plates are the zones at greatest risk, in coincidence with the typical locations of osteoporotic fractures, characterized by a vertebral crushing due to the collapse of vertebral walls. This methodology could be applied for an individual patient, in order to obtain the trends corresponding to different treatments, in identifying at-risk individuals in early stages of osteoporosis and might be helpful for treatment decisions.

3D Finite Element Technology and Its use in Craniofacial Injuries

Quite a bit of interest and evolution has happened in the field of research in the recent times toward analyzing and understanding of trauma and injuries especially that on the human skull and related organs. With the development of faster and latest computers, high fidelity human models have been created to understand the biomechanics of these structures to trauma. In the present article a broad methodology of the fundamentals of model creation and analysis and fracture mechanics has been presented. In particular this paper highlights the methodology of 3D simulation of craniofacial region and an insight to the role of FEA (Finite Element Analysis) in craniofacial trauma. The paper also explains the various steps in computational simulation of the craniofacial skeleton.

How to cite this article

Shobha ES, Raghuveer HP, Nagesh S, Rayapati DK, Prashanth NT, Rangan V. 3D Finite Element Technology and Its use in Craniofacial Injuries. World J Dent 2014;5(4):223-228.

How accurately can we predict the fracture load of the proximal femur using finite element models?

BACKGROUND

Current clinical methods for fracture prediction rely on two-dimensional imaging methods such as dual-energy X-ray absorptiometry and have limited predictive value. Several researchers have tried to integrate three-dimensional imaging techniques with the finite element (FE) method to improve the accuracy of fracture predictions. Before FE models could be used in clinical settings, a thorough validation of their accuracy is required. In this paper, we try to evaluate the current state of accuracy of subject-specific FE models that are used for prediction of the fracture load of proximal femora.

METHODS

All the studies that have used FE for prediction of fracture load and have compared the predicted fracture load with experimentally measured fracture loads in vitro are identified through a systematic search of the literature. A quantitative analysis of the results of those studies has been carried out to determine the absolute prediction error, percentage error, and linear correlations between predicted and measured fracture loads.

FINDINGS

The reported coefficients of determination (R(2)) vary between 0.773 and 0.96 while the percentage error in prediction of fracture load varies between 5 and 46% with most studies reporting percentage errors between 10 and 20%.

INTERPRETATION

We conclude that FE models, which are currently used only experimentally, are in general more accurate than clinically used fracture risk assessment techniques. However, the accuracy of FE models depends on the details of their modeling methodologies. Therefore, modeling procedures need to be optimized and standardized before FE could be used in clinical settings.

Precision study of DXA-based patient-specific finite element modeling for assessing hip fracture risk

Finite element (FE) modeling based on a patient's hip dual energy X-ray absorptiometry (DXA) image is a promising tool for more accurately assessing hip fracture risk, as it is able to comprehensively consider effects from all the mechanical parameters affecting hip fracture. However, a number of factors influence the precision (also known as repeatability or reproducibility) of a DXA-based FE procedure, for example, subject positioning in DXA scanning. As a procedure is required to have adequately high precision in clinical application, we investigated the effects of the involved factors on the precision of a DXA-based patient-specific FE procedure developed by the authors, to provide insight into how the precision of the procedure can be improved so that it can meet the clinical standards. Fracture risk indices corresponding to initial and repeat DXA scans acquired in 30 typical clinical subjects were computed and compared to assess short term repeatability of the procedure. It was found that inconsistent positioning followed by manual segmentation of the projected femur contour induced significant variability in the predicted fracture risk indices. This research suggests that, to apply the DXA-based FE procedure in clinical assessment, it will be necessary to pay more strict attention to subject positioning in DXA scanning.

Investigation of repeatability in hip fracture risk predicted by DXA-based finite element model

DXA (dual energy X-ray absorptiometry) based finite element model is able to integrate all mechanical factors affecting hip fracture in osteoporosis patients and it is thus, in principle, more reliable than areal bone mineral density (BMD) for assessing fracture risk. However, short-term repeatability of DXA-based finite element model in predicting fracture risk has not yet been investigated and satisfactory repeatability is a prerequisite for the procedure to be applied in clinic. Therefore, in the reported research, the repeatability of a previously developed DXA-based patient-specific finite element procedure was investigated. It was found that inconsistence in positioning the patient during DXA scanning and manual segmentation of DXA image in constructing the finite element model are the two dominant factors affecting short-term repeatability of the finite element procedure. The study outcome indicated that to apply the finite element procedure in clinic, a set of more strict guidelines for positioning the patient in DXA scanning must be established and followed.

Male osteoporosis: A review

Osteoporosis in men is a heterogeneous disease that has received little attention. However, one third of worldwide hip fractures occur in the male population. This problem is more prevalent in people over 70 years of age. The etiology can be idiopathic or secondary to hypogonadism, vitamin D deficiency and inadequate calcium intake, hormonal treatments for prostate cancer, use of toxic and every disease or drug use that alters bone metabolism.Risk factors such as a previous history of fragility fracture should be assessed for the diagnosis. However, risk factors in men are very heterogeneous. There are significant differences in the pharmacological treatment of osteoporosis between men and women fundamentally due to the level of evidence in published trials supporting each treatment. New treatments will offer new therapeutic prospects. The goal of this work is a revision of the present status knowledge about male osteoporosis.

A mechanical model for predicting the probability of osteoporotic hip fractures based in DXA measurements and finite element simulation

BACKGROUND

Osteoporotic hip fractures represent major cause of disability, loss of quality of life and even mortality among the elderly population. Decisions on drug therapy are based on the assessment of risk factors for fracture, from BMD measurements. The combination of biomechanical models with clinical studies could better estimate bone strength and supporting the specialists in their decision.

METHODS

A model to assess the probability of fracture, based on the Damage and Fracture Mechanics has been developed, evaluating the mechanical magnitudes involved in the fracture process from clinical BMD measurements. The model is intended for simulating the degenerative process in the skeleton, with the consequent lost of bone mass and hence the decrease of its mechanical resistance which enables the fracture due to different traumatisms. Clinical studies were chosen, both in non-treatment conditions and receiving drug therapy, and fitted to specific patients according their actual BMD measures. The predictive model is applied in a FE simulation of the proximal femur. The fracture zone would be determined according loading scenario (sideway fall, impact, accidental loads, etc.), using the mechanical properties of bone obtained from the evolutionary model corresponding to the considered time.

RESULTS

BMD evolution in untreated patients and in those under different treatments was analyzed. Evolutionary curves of fracture probability were obtained from the evolution of mechanical damage. The evolutionary curve of the untreated group of patients presented a marked increase of the fracture probability, while the curves of patients under drug treatment showed variable decreased risks, depending on the therapy type.

CONCLUSION

The FE model allowed to obtain detailed maps of damage and fracture probability, identifying high-risk local zones at femoral neck and intertrochanteric and subtrochanteric areas, which are the typical locations of osteoporotic hip fractures.The developed model is suitable for being used in individualized cases. The model might better identify at-risk individuals in early stages of osteoporosis and might be helpful for treatment decisions.