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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 3: 427-448. doi: 10.3934/mbe.2014.11.427
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Model validation for a noninvasive arterial stenosis detection problem

  • 1.
    Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212
  • 2.
    Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212
  • 3.
    Brunel Institute of Computational Mathematics, Brunel University, Uxbridge, UB8 3PH
  • 4.
    Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London
  • 5.
    Clinical Physics, Barts Health Trust
  • Received: 01 January 2013 Accepted: 29 June 2018 Published: 01 January 2014

  • MSC : 62F12, 62F40, 65M32, 74D05.

  • 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.

    Citation: H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Carola Kruse, Simon Shaw, John Whiteman, Mark P. Brewin, Stephen E. Greenwald, Malcolm J. Birch. Model validation for a noninvasive arterial stenosis detection problem[J]. Mathematical Biosciences and Engineering, 2014, 11(3): 427-448. doi: 10.3934/mbe.2014.11.427

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  • 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.


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