Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Assessing the Viability of Complex Electrical Impedance Tomography (EIT) with a Spatially Distributed Sensor Array for Imaging of River Bed Morphology: a Proof of Concept (Study)

This report was produced as part of a NERC funded ‘Connect A’ project to establish a new collaborative partnership between the University of Worcester (UW) and Q-par Angus Ltd. The project aim was to assess the potential of using complex Electrical Impedance Tomography (EIT) to image river bed morphology. An assessment of the viability of sensors inserted vertically into the channel margins to provide real-time or near real-time monitoring of bed morphology is reported. Funding has enabled UW to carry out a literature review of the use of EIT and existing methods used for river bed surveys, and outline the requirements of potential end-users. Q-par Angus has led technical developments and assessed the viability of EIT for this purpose. EIT is one of a suite of tomographic imaging techniques and has already been used as an imaging tool for medical analysis, industrial processing and geophysical site survey work. The method uses electrodes placed on the margins or boundary of the entity being imaged, and a current is applied to some and measured on the remaining ones. Tomographic reconstruction uses algorithms to estimate the distribution of conductivity within the object and produce an image of this distribution from impedance measurements. The advantages of the use of EIT lie with the inherent simplicity, low cost and portability of the hardware, the high speed of data acquisition for real-time or near real-time monitoring, robust sensors, and the object being monitored is done so in a non-invasive manner. The need for sophisticated image reconstruction algorithms, and providing images with adequate spatial resolution are key challenges. A literature review of the use of EIT suggests that to date, despite its many other applications, to the best of our knowledge only one study has utilised EIT for river survey work (Sambuelli et al 2002). The Sambuelli (2002) study supported the notion that EIT may provide an innovative way of describing river bed morphology in a cost effective way. However this study used an invasive sensor array, and therefore the potential for using EIT in a non-invasive way in a river environment is still to be tested. A review of existing methods to monitor river bed morphology indicates that a plethora of techniques have been applied by a range of disciplines including fluvial geomorphology, ecology and engineering. However, none provide non-invasive, low costs assessments in real-time or near real-time. Therefore, EIT has the potential to meet the requirements of end users that no existing technique can accomplish. Work led by Q-par Angus Ltd. has assessed the technical requirements of the proposed approach, including probe design and deployment, sensor array parameters, data acquisition, image reconstruction and test procedure. Consequently, the success of this collaboration, literature review, identification of the proposed approach and potential applications of this technique have encouraged the authors to seek further funding to test, develop and market this approach through the development of a new environmental sensor

Lagrangian-based Hydrodynamic Model for Traffic Data Fusion on Freeways

This paper conducts a comprehensive study of the Lagrangian-based hydrodynamic model with application to highway state estimation. Our analysis is motivated by the practical problems of freeway traffic monitoring and estimation using multi-source data measured from mobile devices and fixed sensors. We conduct rigorous mathematical analysis on the Hamilton-Jacobi representation of the Lighthill-Whitham-Richards model in the transformed coordinates, and derive explicit and closed-form solutions with piecewise affine initial, boundary, and internal conditions, based on the variational principle. A numerical study of the Mobile Century field experiment demonstrates some unique features and the effectiveness in traffic estimation of the Lagrangian-based model

Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulation

Ultrasound-modulated optical tomography is an emerging biomedical imaging modality which uses the spatially localised acoustically-driven modulation of coherent light as a probe of the structure and optical properties of biological tissues. In this work we begin by providing an overview of forward modelling methods, before deriving a linearised diffusion-style model which calculates the first-harmonic modulated flux measured on the boundary of a given domain. We derive and examine the correlation measurement density functions of the model which describe the sensitivity of the modality to perturbations in the optical parameters of interest. Finally, we employ said functions in the development of an adjoint-assisted gradient based image reconstruction method, which ameliorates the computational burden and memory requirements of a traditional Newton-based optimisation approach. We validate our work by performing reconstructions of optical absorption and scattering in two- and three-dimensions using simulated measurements with 1% proportional Gaussian noise, and demonstrate the successful recovery of the parameters to within +/-5% of their true values when the resolution of the ultrasound raster probing the domain is sufficient to delineate perturbing inclusions.Comment: 12 pages, 6 figure

Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes

We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is firstly presented in a general 4-dimensional setting and then specialized to the case of spherical symmetry within a 3+1 splitting of spacetime. As a direct application, we have constructed a one-dimensional code, EDGES, which has been used to asses the viability of these methods via a series of tests involving highly relativistic flows in strong gravity. Our results show that discontinuous Galerkin methods are able not only to handle strong relativistic shock waves but, at the same time, to attain very high orders of accuracy and exponential convergence rates in smooth regions of the flow. Given these promising prospects and their affinity with a pseudospectral solution of the Einstein equations, discontinuous Galerkin methods could represent a new paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR

A New Label-Free and Contactless Bio-Tomographic Imaging with Miniaturized Capacitively-Coupled Spectroscopy Measurements

A new bio-imaging method has been developed by introducing an experimental verification of capacitively coupled resistivity imaging in a small scale. This paper focuses on the 2D circular array imaging sensor as well as a 3D planar array imaging sensor with spectroscopic measurements in a wide range from low frequency to radiofrequency. Both these two setups are well suited for standard containers used in cell and culture biological studies, allowing for fully non-invasive testing. This is true as the capacitive based imaging sensor can extract dielectric spectroscopic images from the sample without direct contact with the medium. The paper shows the concept by deriving a wide range of spectroscopic information from biological test samples. We drive both spectra of electrical conductivity and the change rate of electrical conductivity with frequency as a piece of fundamentally important information. The high-frequency excitation allows the interrogation of critical properties that arise from the cell nucleus.</p