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Mathematical Biosciences and Engineering (MBE)
 

Model validation for a noninvasive arterial stenosis detection problem

Pages: 427 - 448, Volume 11, Issue 3, June 2014      doi:10.3934/mbe.2014.11.427

 
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H. Thomas Banks - Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, United States (email)
Shuhua Hu - Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, United States (email)
Zackary R. Kenz - Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, United States (email)
Carola Kruse - Brunel Institute of Computational Mathematics, Brunel University, Uxbridge, UB8 3PH, United Kingdom (email)
Simon Shaw - Brunel Institute of Computational Mathematics, Brunel University, Uxbridge, UB8 3PH, United Kingdom (email)
John Whiteman - Brunel Institute of Computational Mathematics, Brunel University, Uxbridge, UB8 3PH, United Kingdom (email)
Mark P. Brewin - Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, United Kingdom (email)
Stephen E. Greenwald - Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, United Kingdom (email)
Malcolm J. Birch - Clinical Physics, Barts Health Trust, United Kingdom (email)

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.

Keywords:  Viscoelastic model, sensitivity analysis, inverse problem, asymptotic theory.
Mathematics Subject Classification:  62F12, 62F40, 65M32, 74D05.

Received: January 2013;      Accepted: May 2013;      Available Online: January 2014.

 References