@article{brewin_birch_mehta_reeves_shaw_kruse_whiteman_hu_kenz_banks_et al._2015, title={Characterisation of Elastic and Acoustic Properties of an Agar-Based Tissue Mimicking Material}, volume={43}, ISSN={["1573-9686"]}, DOI={10.1007/s10439-015-1294-7}, abstractNote={As a first step towards an acoustic localisation device for coronary stenosis to provide a non-invasive means of diagnosing arterial disease, measurements are reported for an agar-based tissue mimicking material (TMM) of the shear wave propagation velocity, attenuation and viscoelastic constants, together with one dimensional quasi-static elastic moduli and Poisson’s ratio. Phase velocity and attenuation coefficients, determined by generating and detecting shear waves piezo-electrically in the range 300 Hz–2 kHz, were 3.2–7.5 ms−1 and 320 dBm−1. Quasi-static Young’s modulus, shear modulus and Poisson’s ratio, obtained by compressive or shear loading of cylindrical specimens were 150–160 kPa; 54–56 kPa and 0.37–0.44. The dynamic Young’s and shear moduli, derived from fitting viscoelastic internal variables by an iterative statistical inverse solver to freely oscillating specimens were 230 and 33 kPa and the corresponding relaxation times, 0.046 and 0.036 s. The results were self-consistent, repeatable and provide baseline data required for the computational modelling of wave propagation in a phantom.}, number={10}, journal={ANNALS OF BIOMEDICAL ENGINEERING}, author={Brewin, M. P. and Birch, M. J. and Mehta, D. J. and Reeves, J. W. and Shaw, S. and Kruse, C. and Whiteman, J. R. and Hu, S. and Kenz, Z. R. and Banks, H. T. and et al.}, year={2015}, month={Oct}, pages={2587–2596} }
 @inproceedings{banks_catenacci_hu_kenz_2014, title={Decomposition of permittivity contributions from reflectance using mechanism models}, booktitle={2014 american control conference (acc)}, author={Banks, H. T. and Catenacci, J. and Hu, S. H. and Kenz, Z. R.}, year={2014}, pages={367–372} }
 @article{banks_birch_brewin_greenwald_hu_kenz_kruse_maischak_shaw_whiteman_2014, title={High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling}, volume={98}, ISSN={["1097-0207"]}, DOI={10.1002/nme.4631}, abstractNote={We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space‐time coupling matrices are diagonalizable over C for r ⩽100, and this means that the time‐coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG‐in‐time methodology, for the first time, to second‐order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high‐order (up to degree 7) temporal and spatio‐temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}, number={2}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Banks, H. T. and Birch, Malcolm J. and Brewin, Mark P. and Greenwald, Stephen E. and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Maischak, Matthias and Shaw, Simon and Whiteman, John R.}, year={2014}, month={Apr}, pages={131–156} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2014, title={MODEL VALIDATION FOR A NONINVASIVE ARTERIAL STENOSIS DETECTION PROBLEM}, volume={11}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2014.11.427}, abstractNote={A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.}, number={3}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. Thomas and Hu, Shuhua and Kenz, Zackary R. and Kruse, Carola and Shaw, Simon and Whiteman, John and Brewin, Mark P. and Greenwald, Stephen E. and Birch, Malcolm J.}, year={2014}, month={Jun}, pages={427–448} }
 @article{banks_hu_kenz_kruse_shaw_whiteman_brewin_greenwald_birch_2013, title={Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology}, volume={21}, number={1}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Hu, S. H. and Kenz, Z. R. and Kruse, C. and Shaw, S. and Whiteman, J. R. and Brewin, M. P. and Greenwald, S. E. and Birch, M. J.}, year={2013}, pages={25–57} }
 @article{banks_kenz_thompson_2012, title={A review of selected techniques in inverse problem nonparametric probability distribution estimation}, volume={20}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Kenz, Z. R. and Thompson, W. C.}, year={2012}, pages={429–460} }
 @misc{banks_hu_kenz_2011, title={A Brief Review of Elasticity and Viscoelasticity for Solids}, volume={3}, ISSN={["2075-1354"]}, DOI={10.4208/aamm.10-m1030}, abstractNote={There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain pro- posed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a com- putational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.}, number={1}, journal={ADVANCES IN APPLIED MATHEMATICS AND MECHANICS}, author={Banks, Harvey Thomas and Hu, Shuhua and Kenz, Zackary R.}, year={2011}, month={Feb}, pages={1–51} }