Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery

The planning of refractive surgical interventions is a challenging task. Numerical modeling has been proposed as a solution to support surgical intervention and predict the visual acuity, but validation on patient specific intervention is missing. The purpose of this study was to validate the numerical predictions of the post-operative corneal topography induced by the incisions required for cataract surgery. The corneal topography of 13 patients was assessed preoperatively and postoperatively (1-day and 30-day follow-up) with a Pentacam tomography device. The preoperatively acquired geometric corneal topography – anterior, posterior and pachymetry data – was used to build patient-specific finite element models. For each patient, the effects of the cataract incisions were simulated numerically and the resulting corneal surfaces were compared to the clinical postoperative measurements at one day and at 30-days follow up. Results showed that the model was able to reproduce experimental measurements with an error on the surgically induced sphere of 0.38D one day postoperatively and 0.19D 30 days postoperatively. The standard deviation of the surgically induced cylinder was 0.54D at the first postoperative day and 0.38D 30 days postoperatively. The prediction errors in surface elevation and curvature were below the topography measurement device accuracy of ±5μm and ±0.25D after the 30-day follow-up. The results showed that finite element simulations of corneal biomechanics are able to predict post cataract surgery within topography measurement device accuracy. We can conclude that the numerical simulation can become a valuable tool to plan corneal incisions in cataract surgery and other ophthalmosurgical procedures in order to optimize patients' refractive outcome and visual function.

An experimentally validated finite element method for augmented vertebral bodies

Background Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies. Methods Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments. Findings The finite element models were able to predict apparent stiffness (R2 > 0.86) and apparent strength (R2 > 0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R2 > 0.48) and qualitative agreement with the experiments. Interpretation The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

Early changes in biochemical markers of bone formation during teriparatide therapy correlate with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis

Summary Changes of the bone formation marker PINP correlated positively with improvements in vertebral strength in men with glucocorticoid-induced osteoporosis (GIO) who received 18-month treatment with teriparatide, but not with risedronate. These results support the use of PINP as a surrogate marker of bone strength in GIO patients treated with teriparatide. Introduction To investigate the correlations between biochemical markers of bone turnover and vertebral strength estimated by finite element analysis (FEA) in men with GIO. Methods A total of 92 men with GIO were included in an 18-month, randomized, open-label trial of teriparatide (20 μg/day, n = 45) and risedronate (35 mg/week, n = 47). High-resolution quantitative computed tomography images of the 12th thoracic vertebra obtained at baseline, 6 and 18 months were converted into digital nonlinear FE models and subjected to anterior bending, axial compression and torsion. Stiffness and strength were computed for each model and loading mode. Serum biochemical markers of bone formation (amino-terminal-propeptide of type I collagen [PINP]) and bone resorption (type I collagen cross-linked C-telopeptide degradation fragments [CTx]) were measured at baseline, 3 months, 6 months and 18 months. A mixed-model of repeated measures analysed changes from baseline and between-group differences. Spearman correlations assessed the relationship between changes from baseline of bone markers with FEA variables. Results PINP and CTx levels increased in the teriparatide group and decreased in the risedronate group. FEA-derived parameters increased in both groups, but were significantly higher at 18 months in the teriparatide group. Significant positive correlations were found between changes from baseline of PINP at 3, 6 and 18 months with changes in FE strength in the teriparatide-treated group, but not in the risedronate group. Conclusions Positive correlations between changes in a biochemical marker of bone formation and improvement of biomechanical properties support the use of PINP as a surrogate marker of bone strength in teriparatide-treated GIO patients.

Finite element based estimation of contact areas and pressures of the human scaphoid in various functional positions of the hand

The scaphoid is the most frequently fractured carpal bone. When investigating fixation stability, which may influence healing, knowledge of forces and moments acting on the scaphoid is essential. The aim of this study was to evaluate cartilage contact forces acting on the intact scaphoid in various functional wrist positions using finite element modeling. A novel methodology was utilized as an attempt to overcome some limitations of earlier studies, namely, relatively coarse imaging resolution to assess geometry, assumption of idealized cartilage thicknesses and neglected cartilage pre-stresses in the unloaded joint. Carpal bone positions and articular cartilage geometry were obtained independently by means of high resolution CT imaging and incorporated into finite element (FE) models of the human wrist in eight functional positions. Displacement driven FE analyses were used to resolve inter-penetration of cartilage layers, and provided contact areas, forces and pressure distribution for the scaphoid bone. The results were in the range reported by previous studies. Novel findings of this study were: (i) cartilage thickness was found to be heterogeneous for each bone and vary considerably between carpal bones; (ii) this heterogeneity largely influenced the FE results and (iii) the forces acting on the scaphoid in the unloaded wrist were found to be significant. As major limitations, accuracy of the method was found to be relatively low, and the results could not be compared to independent experiments. The obtained results will be used in a following study to evaluate existing and recently developed screws used to fix scaphoid fractures.

Finite element analyses of human vertebral bodies embedded in polymethylmethalcrylate or loaded via the hyperelastic intervertebral disc models provide equivalent predictions of experimental strength

Quantitative computer tomography (QCT)-based finite element (FE) models of vertebral body provide better prediction of vertebral strength than dual energy X-ray absorptiometry. However, most models were validated against compression of vertebral bodies with endplates embedded in polymethylmethalcrylate (PMMA). Yet, loading being as important as bone density, the absence of intervertebral disc (IVD) affects the strength. Accordingly, the aim was to assess the strength predictions of the classic FE models (vertebral body embedded) against the in vitro and in silico strengths of vertebral bodies loaded via IVDs. High resolution peripheral QCT (HR-pQCT) were performed on 13 segments (T11/T12/L1). T11 and L1 were augmented with PMMA and the samples were tested under a 4° wedge compression until failure of T12. Specimen-specific model was generated for each T12 from the HR-pQCT data. Two FE sets were created: FE-PMMA refers to the classical vertebral body embedded model under axial compression; FE-IVD to their loading via hyperelastic IVD model under the wedge compression as conducted experimentally. Results showed that FE-PMMA models overestimated the experimental strength and their strength prediction was satisfactory considering the different experimental set-up. On the other hand, the FE-IVD models did not prove significantly better (Exp/FE-PMMA: R²=0.68; Exp/FE-IVD: R²=0.71, p=0.84). In conclusion, FE-PMMA correlates well with in vitro strength of human vertebral bodies loaded via real IVDs and FE-IVD with hyperelastic IVDs do not significantly improve this correlation. Therefore, it seems not worth adding the IVDs to vertebral body models until fully validated patient-specific IVD models become available.

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.

Preliminary Study on Finite Element Simulation for Optimizing Acetabulum Reorientation after Periacetabular Osteotomy

Periacetabular osteotomy (PAO) is an effective approach for surgical treatment of hip dysplasia. The aim of PAO is to increase acetabular coverage of the femoral head and to reduce contact pressures by reorienting the acetabulum fragment after PAO. The success of PAO significantly depends on the surgeon’s experience. Previously, we have developed a computer-assisted planning and navigation system for PAO, which allows for not only quantifying the 3D hip morphology for a computer-assisted diagnosis of hip dysplasia but also a virtual PAO surgical planning and simulation. In this paper, based on this previously developed PAO planning and navigation system, we developed a 3D finite element (FE) model to investigate the optimal acetabulum reorientation after PAO. Our experimental results showed that an optimal position of the acetabulum can be achieved that maximizes contact area and at the same time minimizes peak contact pressure in pelvic and femoral cartilages. In conclusion, our computer-assisted planning and navigation system with FE modeling can be a promising tool to determine the optimal PAO planning strategy.

Comparison of proximal femur and vertebral body strength improvements in the FREEDOM trial using an alternative finite element methodology

Denosumab reduced the incidence of new fractures in postmenopausal women with osteoporosis by 68% at the spine and 40% at the hip over 36 months compared with placebo in the FREEDOM study. This efficacy was supported by improvements from baseline in vertebral (18.2%) strength in axial compression and femoral (8.6%) strength in sideways fall configuration at 36 months, estimated in Newtons by an established voxel-based finite element (FE) methodology. Since FE analyses rely on the choice of meshes, material properties, and boundary conditions, the aim of this study was to independently confirm and compare the effects of denosumab on vertebral and femoral strength during the FREEDOM trial using an alternative smooth FE methodology. Unlike the previous FE study, effects on femoral strength in physiological stance configuration were also examined. QCT data for the proximal femur and two lumbar vertebrae were analyzed by smooth FE methodology at baseline, 12, 24, and 36 months for 51 treated (denosumab) and 47 control (placebo) subjects. QCT images were segmented and converted into smooth FE models to compute bone strength. L1 and L2 vertebral bodies were virtually loaded in axial compression and the proximal femora in both fall and stance configurations. Denosumab increased vertebral body strength by 10.8%, 14.0%, and 17.4% from baseline at 12, 24, and 36 months, respectively (p < 0.0001). Denosumab also increased femoral strength in the fall configuration by 4.3%, 5.1%, and 7.2% from baseline at 12, 24, and 36 months, respectively (p < 0.0001). Similar improvements were observed in the stance configuration with increases of 4.2%, 5.2%, and 5.2% from baseline (p ≤ 0.0007). Differences between the increasing strengths with denosumab and the decreasing strengths with placebo were significant starting at 12 months (vertebral and femoral fall) or 24 months (femoral stance). Using an alternative smooth FE methodology, we confirmed the significant improvements in vertebral body and proximal femur strength previously observed with denosumab. Estimated increases in strength with denosumab and decreases with placebo were highly consistent between both FE techniques.

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient R2≥0.93. As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.

Nitinol Stent Oversizing in Patients Undergoing Popliteal Artery Revascularization: A Finite Element Study

Nitinol stent oversizing is frequently performed in peripheral arteries to ensure a desirable lumen gain. However, the clinical effect of mis-sizing remains controversial. The goal of this study was to provide a better understanding of the structural and hemodynamic effects of Nitinol stent oversizing. Five patient-specific numerical models of non-calcified popliteal arteries were developed to simulate the deployment of Nitinol stents with oversizing ratios ranging from 1.1 to 1.8. In addition to arterial biomechanics, computational fluid dynamics methods were adopted to simulate the physiological blood flow inside the stented arteries. Results showed that stent oversizing led to a limited increase in the acute lumen gain, albeit at the cost of a significant increase in arterial wall stresses. Furthermore, localized areas affected by low Wall Shear Stress increased with higher oversizing ratios. Stents were also negatively impacted by the procedure as their fatigue safety factors gradually decreased with oversizing. These adverse effects to both the artery walls and stents may create circumstances for restenosis. Although the ideal oversizing ratio is stent-specific, this study showed that Nitinol stent oversizing has a very small impact on the immediate lumen gain, which contradicts the clinical motivations of the procedure.

Differences in endplate deformation of the adjacent and augmented vertebra following cement augmentation

Vertebral cement augmentation can restore the stiffness and strength of a fractured vertebra and relieve chronic pain. Previous finite element analysis, biomechanical tests and clinical studies have indirectly associated new adjacent vertebral fractures following augmentation to altered loading. The aim of this repeated measures in situ biomechanical study was to determine the changes in the adjacent and augmented endplate deformation following cement augmentation of human cadaveric functional spine units (FSU) using micro-computed tomography (micro-CT). The surrounding soft tissue and posterior elements of 22 cadaveric human FSU were removed. FSU were assigned to two groups, control (n = 8) (loaded on day 1 and day 2) and augmented (n = 14) (loaded on day 1, augmented 20% cement fill, and loaded on day 2). The augmented group was further subdivided into a prophylactic augmentation group (n = 9), and vertebrae which spontaneously fractured during loading on day 1 (n = 5). The FSU were axially loaded (200, 1,000, 1,500-2,000 N) within a custom made radiolucent, saline filled loading device. At each loading step, FSUs were scanned using the micro-CT. Endplate heights were determined using custom software. No significant increase in endplate deformation following cement augmentation was noted for the adjacent endplate (P > 0.05). The deformation of the augmented endplate was significantly reduced following cement augmentation for both the prophylactic and fracture group (P < 0.05, P < 0.01, respectively). Endplate deformation of the controls showed no statistically significant differences between loading on day 1 and day 2. A linear relationship was noted between the applied compressive load and endplate deflection (R (2) = 0.58). Evidence of significant endplate deformation differences between unaugmented and augmented FSU, while evident for the augmented endplate, was not present for the adjacent endplate. This non-invasive micro-CT method may also be useful to investigate endplate failure, and parameters that predict vertebral failure.

The influence of yield surface shape and damage in the depth-dependent response of bone tissue to nanoindentation using spherical and Berkovich indenters

Prevention and treatment of osteoporosis rely on understanding of the micromechanical behaviour of bone and its influence on fracture toughness and cell-mediated adaptation processes. Postyield properties may be assessed by nonlinear finite element simulations of nanoindentation using elastoplastic and damage models. This computational study aims at determining the influence of yield surface shape and damage on the depth-dependent response of bone to nanoindentation using spherical and conical tips. Yield surface shape and damage were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic-to-total work ratio is well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not statistically significant (p<0.0001). For spherical tips, damage was not a significant parameter (p<0.0001). The gained knowledge can be used for developing an inverse method for identification of postelastic properties of bone from nanoindentation.