Thermalization of an anisotropic granular particle

We investigate the dynamics of a needle in a two-dimensional bath composed of thermalized point particles. Collisions between the needle and points are inelastic and characterized by a normal restitution coefficient $\alpha<1$. By using the Enskog-Boltzmann equation, we obtain analytical expressions for the translational and rotational granular temperatures of the needle and show that these are, in general, different from the bath temperature. The translational temperature always exceeds the rotational one, though the difference decreases with increasing moment of inertia. The predictions of the theory are in very good agreement with numerical simulations of the model.Comment: 7 pages, 6 Figures, submitted to PRE. Revised version (Fig1, Fig5 and Fig6 corrected + minor typos

Studies of Mass and Size Effects in Three-Dimensional Vibrofluidized Granular Mixtures

We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments performed by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature and circulation pattern are in good qualitative agreement with the experiments. We then studied the effect of varying the mass ratio and the size ratio independently while holding the other parameters constant. The mass and size ratio are shown to affect the distribution of the energy. The changes in the energy distributions affect the packing fraction and temperature of each component. The temperature of the heavier component has a non-linear dependence on the mass of the lighter component, while the temperature of the lighter component is approximately proportional to its mass. The temperature of both components is inversely dependent on the size of the smaller component.Comment: 14 Pages, 12 Figures, RevTeX

ImageParser: a tool for finite element generation from three-dimensional medical images

BACKGROUND: The finite element method (FEM) is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures) of interest (ROIs) may be irregular and fuzzy. METHODS: A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. RESULTS: The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. CONCLUSION: The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information

Diffusion of impurities in a granular gas

Diffusion of impurities in a granular gas undergoing homogeneous cooling state is studied. The results are obtained by solving the Boltzmann--Lorentz equation by means of the Chapman--Enskog method. In the first order in the density gradient of impurities, the diffusion coefficient $D$ is determined as the solution of a linear integral equation which is approximately solved by making an expansion in Sonine polynomials. In this paper, we evaluate $D$ up to the second order in the Sonine expansion and get explicit expressions for $D$ in terms of the restitution coefficients for the impurity--gas and gas--gas collisions as well as the ratios of mass and particle sizes. To check the reliability of the Sonine polynomial solution, analytical results are compared with those obtained from numerical solutions of the Boltzmann equation by means of the direct simulation Monte Carlo (DSMC) method. In the simulations, the diffusion coefficient is measured via the mean square displacement of impurities. The comparison between theory and simulation shows in general an excellent agreement, except for the cases in which the gas particles are much heavier and/or much larger than impurities. In theses cases, the second Sonine approximation to $D$ improves significantly the qualitative predictions made from the first Sonine approximation. A discussion on the convergence of the Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.

Do quantitative and qualitative shear wave elastography have a role in evaluating musculoskeletal soft tissue masses?

Objectives: To determine if quantitative and qualitative shear wave elastography have roles in evaluating musculoskeletal masses. Methods: 105 consecutive patients, prospectively referred for biopsy within a specialist sarcoma centre, underwent B-mode, quantitative (m/s) and qualitative (colour map) shear wave elastography. Reference was histology from subsequent biopsy or excision where possible. Statistical modelling was performed to test elastography data and/or B-mode imaging in predicting malignancy. Results: Of 105 masses, 39 were malignant and 6 had no histology but benign characteristics at 12 months. Radiologist agreement for B-mode and elastography was moderate to excellent Kw 0.52-0.64; PABAKw 0.85-0.90). B-Mode imaging had 78.8% specificity, 76.9% sensitivity for malignancy. Quantitatively, adjusting for age, B-mode and lesion volume there was no statistically significant association between longitudinal velocity and malignancy (OR [95% CI] 0.40[0.10, 1.60], p=0.193), but some evidence that higher transverse velocity was associated with decreased odds of malignancy (0.28[0.06, 1.28], p=0.101). Qualitatively malignant masses tended to be towards the blue spectrum (lower velocities); 39.5% (17/43) of predominantly blue masses were malignant, compared to 14.3% (1/7) of red lesions. Conclusions: Quantitatively and qualitatively there is no statistically significant association between shear wave velocity and malignancy. There is no clear additional role to B-mode imaging currently. Key Points: • Correlation between shear wave velocity and soft tissue malignancy was statistically insignificant• B-mode ultrasound is 76.9 % sensitive and 78.8 % specific• Statistical models show elastography does not significantly add to lesion assessmen

Microscale characterization of prostate biopsies tissues using optical coherence elastography and second harmonic generation imaging

© 2018 USCAP, Inc All rights reserved. Photonics, especially optical coherence elastography (OCE) and second harmonic generation (SHG) imaging are novel high-resolution imaging modalities for characterization of biological tissues. Following our preliminary experience, we hypothesized that OCE and SHG imaging would delineate the microstructure of prostate tissue and aid in distinguishing cancer from the normal benign prostatic tissue. Furthermore, these approaches may assist in characterization of the grade of cancer, as well. In this study, we confirmed a high diagnostic accuracy of OCE and SHG imaging in the detection and characterization of prostate cancer for a large set of biopsy tissues obtained from men suspected to have prostate cancer using transrectal ultrasound (TRUS). The two techniques and methods described here are complementary, one depicts the stiffness of tissues and the other illustrates the orientation of collagen structure around the cancerous lesions. The results showed that stiffness of cancer tissue was ∼57.63% higher than that of benign tissue (Young's modulus of 698.43±125.29 kPa for cancerous tissue vs 443.07±88.95 kPa for benign tissue with OCE. Using histology as a reference standard and 600 kPa as a cut-off threshold, the data analysis showed sensitivity and specificity of 89.6 and 99.8%, respectively. Corresponding positive and negative predictive values were 99.5 and 94.6%, respectively. There was a significant difference noticed in terms of Young's modulus for different Gleason scores estimated by OCE (P-value<0.05). For SHG, distinct patterns of collagen distribution were seen for different Gleason grade disease with computed quantification employing a ratio of anisotropic to isotropic (A:I ratio) and this correlated with disease aggressiveness