A poisson process model for hip fracture risk

Advancing HR-pQCT-based homogenised FE models with smooth structured hexahedral meshes

Nonlinear homogenised finite element (hFE) models can accurately predict stiffness and strength of ultra-distal sections of the radius and tibia using in vivo HR-pQCT images. Recent findings showed good stiffness prediction at these distal sections but a limited ability to reproduce experimental strain localisation. The coarseness of voxel-based meshes reduces the computational effort at the cost of heavily simplifying the underlying geometry of the cortex, the gradient of material properties, and the resulting strain distribution. To overcome these limitations, we present a comprehensive approach to generating fully automated, smooth, and structured hexahedral meshes for HR-pQCT scans at the distal radius and tibia. This study used three datasets to validate the proposed hFE pipeline and its short-term repeatability: ex vivo 2nd generation HR-pQCT images of 21 human radii and 25 human tibiae, and 208 in vivo images from same-day repeated scans on 39 individuals. Results show high accuracy in predicting stiffness (tibia: R2=0.94, radius: R2=0.88) and yield force (tibia: R2=0.93, radius: R2=0.95). Mesh sensitivity analysis reveals stabilisation within a ± 3 % error margin. Dice similarity coefficients between mesh and scanned image were >0.98, and good element quality was achieved across the validation datasets (tibia: S-ICNavg=0.809, radius: S-ICNavg=0.764). Along with the improved volumetric representation of distal cortical and trabecular bone geometry and the good element quality, the new pipeline shows gains in computational performance: 11.70±1.49 min for triple-stack tibia images and 11.00±0.97 min for double-stack radius images, respectively. Generating structured meshes with consistent element-to-element correspondence facilitates seamless comparison between patient models or in longitudinal settings, providing an additional clinical information.

Acoustic emission applied to stochastic modeling of microdamage in compact bone

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain ( ε max ).

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

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.

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.