Model validation for a noninvasive arterial stenosis detection problem

H. Thomas Banks; Shuhua Hu; Zackary R. Kenz; Carola Kruse; Simon Shaw; John Whiteman; Mark P. Brewin; Stephen E. Greenwald; Malcolm J. Birch

doi:10.3934/mbe.2014.11.427

Article Contents

2014, Volume 11, Issue 3: 427-448. Doi: 10.3934/mbe.2014.11.427

This issue Previous Article Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology Next Article The global stability of an SIRS model with infection age

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: January 2013

Revised: May 2013

Published: December 2013

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Abstract

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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Mathematics Subject Classification: 62F12, 62F40, 65M32, 74D05.

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