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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 21, Issue 1

Issues

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

H. Thomas Banks
  • Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, USA
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/ Shuhua Hu
  • Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, USA
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/ Zackary R. Kenz
  • Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, USA
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/ Carola Kruse / Simon Shaw / John R. Whiteman / Mark P. Brewin
  • Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, England
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/ Steve E. Greenwald
  • Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, England
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/ Malcolm J. Birch
Published Online: 2013-02-01 | DOI: https://doi.org/10.1515/jip-2012-0081

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.

Keywords: Viscoelastic model; sensitivity analysis; inverse problem; asymptotic theory; bootstrapping; model selection

About the article

Received: 2012-04-12

Published Online: 2013-02-01

Published in Print: 2013-02-01


Citation Information: Journal of Inverse and Ill-Posed Problems, Volume 21, Issue 1, Pages 25–57, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0081.

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[1]
M. P. Brewin, M. J. Birch, D. J. Mehta, J. W. Reeves, S. Shaw, C. Kruse, J. R. Whiteman, S. Hu, Z. R. Kenz, H. T. Banks, and S. E. Greenwald
Annals of Biomedical Engineering, 2015, Volume 43, Number 10, Page 2587
[2]
H. T. Banks, Malcolm J Birch, Mark P Brewin, Stephen E Greenwald, Shuhua Hu, Zackary R Kenz, Carola Kruse, Matthias Maischak, Simon Shaw, and John R Whiteman
International Journal for Numerical Methods in Engineering, 2014, Volume 98, Number 2, Page 131
[3]
H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Carola Kruse, Simon Shaw, John Whiteman, Mark P. Brewin, Stephen E. Greenwald, and Malcolm J. Birch
Mathematical Biosciences and Engineering, 2014, Volume 11, Number 3, Page 427
[4]
Zackary R. Kenz, H. T. Banks, and Ralph C. Smith
SIAM/ASA Journal on Uncertainty Quantification, 2013, Volume 1, Number 1, Page 348

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