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Title: Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology
Authors: Banks, HT
Hu, S
Kenz, ZR
Kruse, C
Shaw, S
Whiteman, JR
Brewin, MP
Greenwald, SE
Birch, MJ
Keywords: Viscoelastic model;Sensitivity analysis;Inverse problem;Asymptotic theory;Bootstrapping;Model selection
Issue Date: 2013
Publisher: Walter de Gruyter GmbH
Citation: Journal of Inverse and III-posed Problems, 21(1), 25 – 57, 2013
Abstract: Non-invasive detection, localization and characterization of an arterial stenosis (a blockage or partial blockage in the artery) continues to be an important problem in medicine. Partial blockage stenoses are known to generate disturbances in blood flow which generate shear waves in the chest cavity. We examine a one-dimensional viscoelastic model that incorporates Kelvin–Voigt damping and internal variables, and develop a proof-of-concept methodology using simulated data. We first develop an estimation procedure for the material parameters. We use this procedure to determine confidence intervals for the estimated parameters, which indicates the efficacy of finding parameter estimates in practice. Confidence intervals are computed using asymptotic error theory as well as bootstrapping. We then develop a model comparison test to be used in determining if a particular data set came from a low input amplitude or a high input amplitude; this we anticipate will aid in determining when stenosis is present. These two thrusts together will serve as the methodological basis for our continuing analysis using experimental data currently being collected.
Description: This is the post-print version of the final published paper that is available from the link below. Copyright @ 2013 Walter de Gruyter GmbH.
ISSN: 0928-0219
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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