Multi-frequency shear modulus measurements discriminate tumorous from healthy tissues.

As far as their mechanical properties are concerned, cancerous lesions can be confused with healthy surrounding tissues in elastography protocols if only the magnitude of moduli is considered. We show that the frequency dependence of the tissue's mechanical properties allows for discriminating the tumor from other tissues, obtaining a good contrast even when healthy and tumor tissues have shear moduli of comparable magnitude. We measured the shear modulus G*(ω) of xenograft subcutaneous tumors developed in mice using breast human cancer cells, compared with that of fat, skin and muscle harvested from the same mice. As the absolute shear modulus |G*(ω)| of tumors increases by 42% (from 5.2 to 7.4 kPa) between 0.25 and 63 Hz, it varies over the same frequency range by 77% (from 0.53 to 0.94 kPa) for the fat, by 103% (from 3.4 to 6.9 kPa) for the skin and by 120% (from 4.4 to 9.7 kPa) for the muscle. These measurements fit well to the fractional model G*(ω)=K(iω)n, yielding a coefficient K and a power-law exponent n for each sample. Tumor, skin and muscle have comparable K parameter values, that of fat being significantly lower; the p-values given by a Mann-Whitney test are above 0.14 when comparing tumor, skin and muscle between themselves, but below 0.001 when comparing fat with tumor, skin or muscle. With regards the n parameter, tumor and fat are comparable, with p-values above 0.43, whereas tumor differs from both skin and muscle, with p-values below 0.001. Tumor tissues thus significantly differs from fat, skin and muscle on account of either the K or the n parameter, i.e. of either the magnitude or the frequency-dependence of the shear modulus.

A credible homogenized finite element model to predict radius fracture in the case of a forward fall.

Fragility fractures that occur after a fall from a standing height or less are almost always due to osteoporosis, which remains underdiagnosed and untreated. Patient-specific finite element (FE) models have been introduced to predict bone strength and strain. This approach, based on structure mechanics, is derived from Quantitative Computed Tomography (QCT), and element mechanical properties are computed from bone mineral densities. In this study, we developed a credible finite element model of the radius to discriminate low-trauma-fractured radii from non-fractured radii obtained experimentally. Thirty cadaveric radii were impacted with the same loading condition at 2 m/s, and experimental surface strain was retrieved by stereo-correlation in addition to failure loads in fracture cases. Finite element models of the distal radius were created from clinical computed tomography. Different density-elasticity relationships and failure criteria were tested. The strongest agreement (simulations-experiments) for average strain showed a Spearman's rank correlation (ρ) between 0.75 and 0.82, p < 0.0001, with a root mean square error between 0.14 and 0.19%. The experimental mean strain was 0.55%. Predicted failure load error (23%) was minimized for derived Pistoia's failure criterion. Numerical failure demonstrated area under the receiver operating characteristic (ROC) curves of 0.76 when classifying radius fractures with an accuracy of 82%. These results suggest that a credible FE modelling method in a large region of interest (distal radius) is a suitable technique to predict radius fractures after a forward fall.

Influence of loading conditions in finite element analysis assessed by HR-pQCT on ex vivo fracture prediction.

Many fractures occur in individuals with normal areal Bone Mineral Density (aBMD) measured by Dual X-ray Absorptiometry (DXA). High Resolution peripheral Quantitative Computed Tomography (HR-pQCT) allows for non-invasive evaluation of bone stiffness and strength through micro finite element (µFE) analysis at the tibia and radius. These µFE outcomes are strongly associated with fragility fractures but do not provide clear enhancement compared with DXA measurements. The objective of this study was to establish whether a change in loading conditions in standard µFE analysis assessed by HR-pQCT enhance the discrimination of low-trauma fractured radii (n = 11) from non-fractured radii (n = 16) obtained experimentally throughout a mechanical test reproducing a forward fall. Micro finite element models were created using HR-pQCT images, and linear analyses were performed using four different types of loading conditions (axial, non-axial with two orientations and torsion). No significant differences were found between the failure load assessed with the axial and non-axial models. The different loading conditions tested presented the same area under the receiver operating characteristic (ROC) curves of 0.79 when classifying radius fractures with an accuracy of 81.5%. In comparison, the area under the curve (AUC) is 0.77 from DXA-derived ultra-distal aBMD of the forearm with an accuracy of 85.2%. These results suggest that the restricted HR-pQCT scanned region seems not sensitive to loading conditions for the prediction of radius fracture risk based on ex vivo experiments (n = 27).

Variabilities in µQCT-based FEA of a tumoral bone mice model.

A finite element analysis based on Micro-Quantitative Computed Tomography (µQCT) is a method with high potential to improve fracture risk prediction. However, the segmentation process and model generation are generally not automatized in their entirety. Even with a rigorous protocol, the operator might add uncertainties during the creation of the model. The aim of this study was to evaluate a µQCT-based model of mice tumoral and sham tibias in terms of the variabilities induced by the operator and sensitivity to operator-dependent variables (such as model orientation or length). Two different operators generated finite element (FE) models from µCT images of 8 female Balb/c nude mice tibias aged 10 weeks old with bone tumors induced in the right tibia and with sham injection in the left. From these models, predicted failure load was determined for two different boundary conditions: fixed support and spherical joints. The difference between the predicted and experimental failure load of both operators was large (-122% to 93%). The difference in the predicted failure load between operators was less for the spherical joints boundary conditions (9.8%) than for the fixed support (58.3%), p < 0.001, whereas varying the orientation of bone tibia caused more variability for the fixed support boundary condition (44.7%) than for the spherical joints (9.1%), p < 0.002. Varying tibia length had no significant effect, regardless of boundary conditions (<4%). When using the same mesh and same orientation, the difference between operators is non-significant (<6%) for each model. This study showed that the operator influences the failure load assessed by a µQCT-based finite element model of the tumoral and sham mice tibias. The results suggest that automation is needed for better reproducibility.

Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study.

Several studies showed the ability of the cortex of long bones such as the radius and tibia to guide mechanical waves. Such experimental evidence has given rise to the emergence of a category of quantitative ultrasound techniques, referred to as the axial transmission, specifically developed to measure the propagation of ultrasound guided waves in the cortical shell along the axis of long bones. An ultrasound axial transmission technique, with an automated approach to quantify cortical thickness and porosity is described. The guided modes propagating in the cortex are recorded with a 1-MHz custom made linear transducer array. Measurement of the dispersion curves is achieved using a two-dimensional spatio-temporal Fourier transform combined with singular value decomposition. Automatic parameters identification is obtained through the solution of an inverse problem in which the dispersion curves are predicted with a two-dimensional transverse isotropic free plate model. Thirty-one radii and fifteen tibiae harvested from human cadavers underwent axial transmission measurements. Estimates of cortical thickness and porosity were obtained on 40 samples out of 46. The reproducibility, given by the root mean square error of the standard deviation of estimates, was 0.11 mm for thickness and 1.9% for porosity. To assess accuracy, site-matched micro-computed tomography images of the bone specimens imaged at 9 µm voxel size served as the gold standard. Agreement between micro-computed tomography and axial transmission for quantification of thickness and porosity at the radius and tibia ranged from R2=0.63 for porosity (root mean square error RMSE=1.8%) to 0.89 for thickness (RMSE=0.3 mm). Despite an overall good agreement for porosity, the method performs less well for porosities lower than 10%. The heterogeneity and general complexity of cortical bone structure, which are not fully accounted for by our model, are suspected to weaken the model approximation. This study presents the first validation study for assessing cortical thickness and porosity using the axial transmission technique. The automatic signal processing minimizes operator-dependent errors for parameters determination. Recovering the waveguide characteristics, that is to say cortical thickness and porosity, could provide reliable information about skeletal status and future fracture risk.

An ex vivo experiment to reproduce a forward fall leading to fractured and non-fractured radii.

Forward falls represent a risk of injury for the elderly. The risk is increased in elderly persons with bone diseases, such as osteoporosis. However, half of the patients with fracture were not considered at risk based on bone density measurement (current clinical technique). We assume that loading conditions are of high importance and should be considered. Real loading conditions in a fall can reach a loading speed of 2m/s on average. The current study aimed to apply more realistic loading conditions that simulate a forward fall on the radius ex vivo. Thirty radii from elderly donors (79y.o.±12y.o., 15 males, 15 females) were loaded at 2m/s using a servo-hydraulic testing machine to mimic impact that corresponds to a fall. Among the 30 radii, 14 had a fracture after the impact, leading to two groups (fractured and non-fractured). Surfacic strain fields were measured using stereovision and allow for visualization of fracture patterns. The average maximum load was 2963±1274N. These experimental data will be useful for assessing the predictive capability of fracture risk prediction methods such as finite element models.

In Vivo Assessment of Elasticity of Child Rib Cortical Bone Using Quantitative Computed Tomography.

Elasticity of the child rib cortical bone is poorly known due to the difficulties in obtaining specimens to perform conventional tests. It was shown on the femoral cortical bone that elasticity is strongly correlated with density for both children and adults through a unique relationship. Thus, it is assumed that the relationships between the elasticity and density of adult rib cortical bones could be expanded to include that of children. This study estimated in vivo the elasticity of the child rib cortical bone using quantitative computed tomography (QCT). Twenty-eight children (from 1 to 18 y.o.) were considered. Calibrated QCT images were prescribed for various thoracic pathologies. The Hounsfield units were converted to bone mineral density (BMD). A relationship between the BMD and the elasticity of the rib cortical bone was applied to estimate the elasticity of children's ribs in vivo. The estimated elasticity increases with growth (7.1 ± 2.5 GPa at 1 y.o. up to 11.6 ± 1.9 GPa at 18 y.o.). This data is in agreement with the few previous values obtained using direct measurements. This methodology paves the way for in vivo assessment of the elasticity of the child cortical bone based on calibrated QCT images.

Abdominal wall muscle elasticity and abdomen local stiffness on healthy volunteers during various physiological activities.

The performance of hernia treatment could benefit from more extensive knowledge of the mechanical behavior of the abdominal wall in a healthy state. To supply this knowledge, the antero-lateral abdominal wall was characterized in vivo on 11 healthy volunteers during 4 activities: rest, pullback loading, abdominal breathing and the "Valsalva maneuver". The elasticity of the abdominal muscles (rectus abdominis, obliquus externus, obliquus internus and transversus abdominis) was assessed using ultrasound shear wave elastography. In addition, the abdomen was subjected to a low external load at three locations: on the midline (linea alba), on the rectus abdominis region and on lateral muscles region in order to evaluate the local stiffness of the abdomen, at rest and during "Valsalva maneuver". The results showed that the "Valsalva maneuver" leads to a statistically significant increase of the muscle shear modulus compared to the other activities. This study also showed that the local stiffness of the abdomen was related to the activity. At rest, a significant difference has been observed between the anterior (0.5N/mm) and the lateral abdomen locations (1N/mm). Then, during the Valsalva maneuver, the local stiffness values were similar for all locations (ranging from 1.6 to 2.2N/mm). This work focuses on the in vivo characterization of the mechanical response of the human abdominal wall and abdomen during several activities. In the future, this protocol could be helpful for investigation on herniated patients.

Mechanical response of human abdominal walls ex vivo: Effect of an incisional hernia and a mesh repair.

The design of meshes for the treatment of incisional hernias could benefit from better knowledge of the mechanical response of the abdominal wall and how this response is affected by the implant. The aim of this study was to characterise the mechanical behaviour of the human abdominal wall. Abdominal walls were tested ex vivo in three states: intact, after creation of a defect simulating an incisional hernia, and after reparation with a mesh implanted intraperitonally. For each state, the abdominal wall was subjected to air pressure loading. Local strain fields were determined using digital image correlation techniques. The strain fields on the internal and external surfaces of the abdominal wall exhibited different patterns. The strain patterns on the internal surface appeared to be related to the underlying anatomy of the abdominal wall. Higher strains were observed along the linea alba than along the perpendicular direction. Under pressure loading, the created incision increased the strain of the abdominal wall compared to the intact state in 5 cases of a total 6. In addition, the mesh repair decreased the strains of the abdominal wall compared to the incised state in 4 cases of 6. These results suggest that the intraperitoneal mesh restores at least partially the mechanical behaviour of the wall and provides quantification of the effects on the strains in various regions.

Contribution of the skin, rectus abdominis and their sheaths to the structural response of the abdominal wall ex vivo.

A better understanding of the abdominal wall biomechanics could help designing new treatments for incisional hernia. In the current study, an experimental protocol was developed to evaluate the contributions of the abdominal wall components to the structural response of the anterior part of the abdominal wall. The specimens underwent 3 dissections (removal of (1) skin and subcutaneous fat, (2) anterior rectus sheath, (3) rectus abdominis muscles). After each dissection, they were subjected to air pressure up to 3 kPa. Ultrasound images and associated elastographic maps were collected at 0, 2 and 3 kPa in the intact state and strains on the internal surface were calculated using stereo-correlation in all states. Strains on the rectus abdominis and linea alba were analyzed. After the dissection of the anterior sheath of the rectus abdominis, longitudinal strain was found significantly different on the linea alba (5% at 3 kPa) and on the rectus abdominis area (11% at 3 kPa). The current results highlight the importance of the rectus sheath in the structural response of the anterior part of the abdominal wall ex vivo. Geometrical characteristics such as thicknesses and radii of curvature and mechanical properties (shear modulus of the rectus abdominis, e.g. at 0 pressure the average value is 14 kPa) were provided in order to facilitate future modeling efforts.

Effect of two loading rates on the elasticity of the human anterior rectus sheath.

Tensile properties of connective tissues of the abdominal wall are necessary to better analyze the mechanical response of the human abdominal wall. Some tensile properties of these tissues have been reported in the past but data are still missing regarding the dependence of the elasticity on the loading rate, especially for the rectus sheath. Thus the aim of this study was to assess for the variation of human anterior rectus sheath elasticity using two loading rates. Seventeen samples of the rectus sheath were taken from three human post-mortem subjects and tested under tension at two different loading rates (0.01s(-1) and 50s(-1)). The mean value (standard deviation) of the quasi-static elasticity is 5.6 (3.2)MPa for the rectus sheath. The values at the high loading rate are 14 (8.3)MPa. The failure strength and the elasticity (at 50s(-1)) are significantly correlated (r²=0.79, p<0.01). Such a relationship opens the way to the estimation of the failure strength by a unique measurement of the elasticity. The loading rate influence was statistically significant with a linear elasticity 2.5 times greater at 50s(-1) than 0.01s(-1). Thus the loading rate influence on the mechanical properties would have to be taken into account in models considering transitory loading such as coughing and sneezing.

Mechanical response of animal abdominal walls in vitro: evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally.

Better mechanical knowledge of the abdominal wall is requested to further develop and validate numerical models. The aim of this study was to characterize the passive behaviour of the abdominal wall under three configurations: intact, after creating a defect simulating an incisional hernia, and after a repair with a mesh implanted intraperitonally. For each configuration, controlled boundary conditions were applied (air pressure and then contact loading) to the abdominal wall. 3D local strain fields were determined by digital image correlation. Local strains measured on the internal and external surfaces of the intact abdominal wall showed different patterns. The air pressure and the force applied to the abdominal wall during contact loading were measured and used to determine stiffness. The presence of a defect resulted in a significant decrease of the global stiffness compared to the intact abdominal wall (about 25%). In addition, the presence of the mesh enabled to restore the stiffness to values that were not significantly different from those of the intact wall. These results suggest that intraperitoneal mesh seems to restore the global biomechanics of the abdomen.