Ravindra Duddu

A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment

We present a two‐dimensional biofilm growth model in a continuum framework using an Eulerian description. A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method is used to simulate the growth of the biofilm. The model considers fluid flow around the biofilm surface, the advection–diffusion and reaction of substrate, variable biomass volume fraction and erosion due to the interfacial shear stress at the biofilm–fluid interface. The key assumptions of the model and the governing equations of transport, biofilm kinetics and biofilm mechanics are presented. Our 2D biofilm growth results are in good agreement with those obtained by Picioreanu et al. (Biotechnol Bioeng 69(5):504–515, 2000). Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated biofilm results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached. Biotechnol. Bioeng. 2009;103: 92–104.

Diffusional evolution of precipitates in elastic media using the extended finite element and the level set methods

A sharp-interface numerical formulation using an Eulerian description aimed at modeling diffusional evolution of precipitates produced by phase transformations in elastic media, is presented. The extended finite element method (XFEM) is used to solve the field equations and the level set method is used to evolve the precipitate-matrix interface. This new formulation is capable of handling microstructures with arbitrarily shaped particles and capturing their topological transitions without needing the mesh to conform with the precipitate-matrix interface. The XFEM makes it possible to model the precipitate and the matrix to be both elastically anisotropic and inhomogeneous with ease. The interface evolution velocity is evaluated using a domain integral scheme 1] that is consistent with the sharp interface. Numerical examples modeling two distinct phases of particle evolution, growth (dendritic evolution) and equilibration (Ostwald ripening) are presented. To overcome the issue of grid anisotropy in growth simulations, a random grid rotation scheme is implemented in conjunction with a bicubic spline interpolation scheme. Growing shapes are dendritic while equilibrium shapes are squarish and in this respect our simulation results are in agreement with those presented in the literature 2-4].

An Extended Finite Element Model of Crevice and Pitting Corrosion

A sharp interface model formulation is developed for simulating the electrochemical environment in crevices/pits due to galvanic corrosion in aqueous media. The concentration of ionic species and the electrical potential in the crevice is established using the non-dimensionalized Nernst-Planck equations along with the assumption of local electro-neutrality. The crevice/pit interface fluxes are defined in terms of the cathodic and anodic current densities using Butler-Volmer kinetics. The extended finite element method is used to discretize the governing equations and the level set function to describe the interface morphology independent of the underlying finite element mesh. The advantage of this formulation is that it eliminates the need for cumbersome mesh generation and remeshing when the interface morphology changes. Numerical investigations of steady-state intergranular crevice corrosion in idealized Al-Mg alloy microstructures in two-dimensions are conducted to establish the viability of the formulation. Simulation results predict large pH and chloride concentration within the crevice environment, which leads us to the conclusion that chemical reactions and precipitation play a prominent role during crevice corrosion.Copyright

Feasibility of non-linear beamforming ultrasound methods to characterize and size kidney stones

Purpose Ultrasound methods for kidney stone imaging suffer from poor sensitivity and size overestimation. The study objective was to demonstrate feasibility of non-linear ultrasound beamforming methods for stone imaging, including plane wave synthetic focusing (PWSF), short-lag spatial coherence (SLSC) imaging, mid-lag spatial coherence (MLSC) imaging with incoherent compounding, and aperture domain model image reconstruction (ADMIRE). Materials and methods The ultrasound techniques were evaluated in an in vitro kidney stone model and in a pilot study of 5 human stone formers (n = 6 stones). Stone contrast, contrast-to-noise ratio (CNR), sizing, posterior shadow contrast, and shadow width sizing were compared among the different techniques and to B-mode. CT imaging within 60 days was considered the gold standard stone size. Paired t-tests using Bonferroni correction were performed to evaluate comparing each technique with B-mode. Results Mean CT measured stone size was 6.0mm (range 2.9–12.2mm) with mean skin-to-stone distance 10.2cm (range 5.4–16.3cm). Compared to B-mode, stone contrast was best with ADMIRE (mean +12.2dB), while SLSC and MLSC showed statistically improved CNR. Sizing was best with ADMIRE (mean +1.3mm error), however this was not significantly improved over B-mode (+2.4mm). PWSF performed similarly to B-mode for stone contrast, CNR, SNR, and stone sizing. In the in vitro model, the shadow contrast was highest with ADMIRE (mean 10.5 dB vs 3.1 dB with B-mode). Shadow sizing was best with SLSC (mean error +0.9mm ± 2.9), however the difference compared to B-mode was not significant. Conclusions The detection and sizing of stones are feasible with advanced beamforming methods with ultrasound. ADMIRE, SLSC, and MLSC hold promise for improving stone detection, shadow contrast, and sizing.

Non-linear beamforming approaches for sizing and detecting large calcifications

Standard B-mode imaging has poor sensitivity and specificity for detecting kidney stones and consistently overestimates stone size. Because of this, the acoustic shadow produced by the stone and twinkling artifacts seen with color Doppler have been used as substitutes for conventional imaging for stone sizing and detection. However, often neither a shadow nor a color Doppler artifact are present. In this study, the use of several non-linear beamforming strategies was investigated in conjunction with plane wave synthetic focusing (PWSF). These include aperture domain model image reconstruction (ADMIRE), short-lag spatial coherence (SLSC), and a new mid-lag spatial coherence (MLSC) method designed specifically for kidney stone detection but not sizing. Evaluations of all four methods were performed in vitro and ex vivo. For the in vitro evaluation, various sized kidney stones (n=8 with width 9.88±5.96mm) were placed on top of a gelatin phantom doped with graphite, which served as a platform and provided a diffuse scattering background for comparisons. The stones were imaged at a depth of 4 cm and 8 cm. An ex vivo evaluation was also performed where several stones were implanted into pig kidneys. The pig kidneys were immersed in water for imaging. The in vitro sizing errors for all stones at both depths for PWSF, ADMIRE, SLSC, and MLSC were 0.89±0.74mm, 0.57±0.69mm, 0.96±1.31mm, and −0.92±3.12mm, respectively. For sizing, ADMIRE performs best in vitro, but in the ex vivo study delineation of the border was unclear. For detection, the custom MLSC method was able to achieve excellent discrimination between the stones and the diffuse scattering media with a constant threshold across all sets.

Partial Contact of a Smooth Elastic Wavy Strip Pressed Between Two Flat Surfaces

The contact of a smooth elastic wavy strip pressed between two surfaces is solved by considering a curved beam in contact with a rigid half-space. In assuming so, the Michell Fourier series expansion for elastic bodies is shown to satisfy the resulting mixed boundary value problem. When the contact region is small compared to the radius of curvature of the beam, semi-analytical solutions are obtained by exploiting dual series equation techniques. The relation between the level of loading and the extent of contact, as well as stress on the surface and in the beam, are found. Various boundary conditions on the ends, which arise as lower order terms in the Michell solution, are considered. This semi-analytical solution may prove useful in analyzing the contact of a corrugated seal.Copyright