2014, 11(3): 427-448. doi: 10.3934/mbe.2014.11.427

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, United States

3. 

Brunel Institute of Computational Mathematics, Brunel University, Uxbridge, UB8 3PH, United Kingdom, United Kingdom, United Kingdom

4. 

Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London, United Kingdom, United Kingdom

5. 

Clinical Physics, Barts Health Trust, United Kingdom

Received  January 2013 Revised  May 2013 Published  January 2014

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. Mathematical Biosciences & Engineering, 2014, 11 (3) : 427-448. doi: 10.3934/mbe.2014.11.427
References:
[1]

M. Ainsworth, P. Monk and W. Muniz, Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation,, Journal of Scientific Computing, 27 (2006), 5.  doi: 10.1007/s10915-005-9044-x.  Google Scholar

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M. Akay, Noninvasive Detection of Coronary Artery Disease Using Advanced Signal Processing Methods,, PhD Dissertation, (1990).   Google Scholar

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M. Akay, Y. Akay, W. Welkowitz, J. Semmlow and J. Kostis, Application of adaptive filters to noninvasive acoustical detection of coronary occlusions before and after angioplasty,, IEEE Trans. on Biomed. Eng., 39 (1992), 176.  doi: 10.1109/10.121649.  Google Scholar

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H. T. Banks, A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering,, CRC Press, (2012).  doi: 10.1201/b12209.  Google Scholar

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H. T. Banks, J. H. Barnes, A. Eberhardt, H. Tran and S. Wynne, Modeling and computation of propagating waves from coronary stenoses,, Comp. and Appl. Math., 21 (2002), 767.   Google Scholar

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H. T. Banks and B. G. Fitzpatrick, Inverse problems for distributed systems: Statistical tests and ANOVA,, Proc. International Symp. on Math. Approaches to Envir. and Ecol. Problems, 81 (1989), 88.  doi: 10.1007/978-3-642-46693-9_18.  Google Scholar

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[14]

H. T. Banks, S. Hu, Z. R. Kenz, C. Kruse, S. Shaw, J. R. Whiteman, M. P. Brewin, S. E. Greenwald and M. J. Birch, Model validation for a noninvasive arterial stenosis detection problem,, CRSC-TR12-22, (2012), 12.   Google Scholar

[15]

H. T. Banks, Z. R. Kenz and W. C. Thompson, A review of selected techniques in inverse problem nonparametric probability distribution estimation,, J. of Inverse and Ill-Posed Problems, 20 (2012), 429.  doi: 10.1515/jip-2012-0037.  Google Scholar

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H. T. Banks, N. Medhin and G. Pinter, Nonlinear reptation in molecular based hysteresis models for polymers,, Quarterly of Applied Math., 62 (2004), 767.   Google Scholar

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H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue,, Multiscale Modeling and Simulation, 3 (2005), 395.  doi: 10.1137/040603693.  Google Scholar

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H. T. Banks and J. R. Samuels, Jr, Detection of cardiac occlusions using viscoelastic wave propagation,, Advances in Appl. Math. and Mech., 1 (2009), 1.   Google Scholar

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H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, CRC Press, (2009).   Google Scholar

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J. D. De Basabe, M. K. Sen and M. F. Wheeler, The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion,, Geophys J. Int., 175 (2008), 83.   Google Scholar

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A. O. Borisyuk, Noise field in the human chest due to turbulent flow in a larger blood vessel,, Flow, 61 (1999), 269.  doi: 10.1016/S0889-9746(03)00056-2.  Google Scholar

[25]

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[26]

A. O. Borisyuk, Model study of noise field in the human chest due to turbulent flow in a larger blood vessel,, J. of Fluids and Structures, 17 (2003), 1095.  doi: 10.1016/S0889-9746(03)00056-2.  Google Scholar

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M. P. Brewin, M. J. Birch and S. E. Greenwald, et al., Characterization of the uniaxial elastic properties of an agar-based tissue mimicking material,, in preparation., ().   Google Scholar

[28]

S. Catheline, J.-L. Gennisson, G. Delon, M. Fink, R. Sinkus, S. Abouelkaram and J. Culioli, Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: an inverse problem approach,, J. Acoust. Soc. Am, 116 (2004), 3734.  doi: 10.1121/1.1815075.  Google Scholar

[29]

S. Catheline, L. Sandrin, J.-L. Gennisson, M. Tanter and M. Fink, Ultrasound-based noninvasive shear elasticity probe for soft tissues,, IEEE Ultrasonics Symposium, 2 (2000), 1799.  doi: 10.1109/ULTSYM.2000.921672.  Google Scholar

[30]

S. Chen, M. Fatemi and J. Greenleaf, Quantifying elasticity and viscosity from measurement of shear wave speed dispersion,, J. Acoust. Soc. Am., 115 (2004), 2781.  doi: 10.1121/1.1739480.  Google Scholar

[31]

S. Chen, M. Urban, C. Pislaru, R. Kinnick, Y. Zheng, A. Yao and J. Greenleaf, Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity,, IEEE Trans. on Ultrason., 56 (2009), 55.   Google Scholar

[32]

T. Cheng, Diastolic murmur caused by coronary artery stenosis,, Ann. Int. Med, 72 (1970).  doi: 10.7326/0003-4819-72-4-543.  Google Scholar

[33]

T. Deffieux, G. Montaldo and M. Tanter, Shear wave spectroscopy for in vivo quantification of human soft tissues visco-elasticity,, IEEE Trans. on Medical Imag., 28 (2009), 313.  doi: 10.1109/TMI.2008.925077.  Google Scholar

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show all references

References:
[1]

M. Ainsworth, P. Monk and W. Muniz, Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation,, Journal of Scientific Computing, 27 (2006), 5.  doi: 10.1007/s10915-005-9044-x.  Google Scholar

[2]

M. Akay, Noninvasive Detection of Coronary Artery Disease Using Advanced Signal Processing Methods,, PhD Dissertation, (1990).   Google Scholar

[3]

M. Akay, Y. Akay, W. Welkowitz, J. Semmlow and J. Kostis, Application of adaptive filters to noninvasive acoustical detection of coronary occlusions before and after angioplasty,, IEEE Trans. on Biomed. Eng., 39 (1992), 176.  doi: 10.1109/10.121649.  Google Scholar

[4]

M. Akay, Y. Akay, W. Welkowitz, J. Semmlow and J. Kostis, Noninvasive detection of coronary artery disease using neural networks,, Proc. IEEE Eng. in Med. & Biol. Soc., (1991), 1434.  doi: 10.1109/IEMBS.1991.684531.  Google Scholar

[5]

M. Akay, M. Bauer, J. Semmlow, W. Welkowitz and J. Kostis, Analysis of diastolic heart sounds before and after angioplasty,, Proc. IEEE Eng. in Med. & Biol. Soc., (1988), 257.  doi: 10.1109/IEMBS.1988.94505.  Google Scholar

[6]

M. Akay, W. Welkowitz, J. Semmlow and J. Kostis, Application of the ARMA method to acoustic detection of coronary artery disease,, Med. & Biol. Eng. & Comput., 29 (1991), 365.  doi: 10.1007/BF02441656.  Google Scholar

[7]

H. T. Banks, A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering,, CRC Press, (2012).  doi: 10.1201/b12209.  Google Scholar

[8]

H. T. Banks, J. H. Barnes, A. Eberhardt, H. Tran and S. Wynne, Modeling and computation of propagating waves from coronary stenoses,, Comp. and Appl. Math., 21 (2002), 767.   Google Scholar

[9]

H. T. Banks and K. Bihari, Modelling and estimating uncertainty in parameter estimation,, Inverse Problems, 17 (2001), 95.  doi: 10.1088/0266-5611/17/1/308.  Google Scholar

[10]

H. T. Banks and B. G. Fitzpatrick, Inverse problems for distributed systems: Statistical tests and ANOVA,, Proc. International Symp. on Math. Approaches to Envir. and Ecol. Problems, 81 (1989), 88.  doi: 10.1007/978-3-642-46693-9_18.  Google Scholar

[11]

H. T. Banks, K. Holm and D. Robbins, Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. Bootstrapping,, Math. and Comp. Modelling, 52 (2010), 09.  doi: 10.1016/j.mcm.2010.06.026.  Google Scholar

[12]

H. T. Banks, S. Hu and Z. R. Kenz, A brief review of elasticity and viscoelasticity for solids,, Adv. in Applied Math. and Mech., 3 (2011), 1.   Google Scholar

[13]

H. T. Banks, S. Hu, Z. R. Kenz, C. Kruse, S. Shaw, J. R. Whiteman, M. P. Brewin, S. E. Greenwald and M. J. Birch, Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology,, J. Inverse and Ill-Posed Problems, 21 (2012), 12.  doi: 10.1515/jip-2012-0081.  Google Scholar

[14]

H. T. Banks, S. Hu, Z. R. Kenz, C. Kruse, S. Shaw, J. R. Whiteman, M. P. Brewin, S. E. Greenwald and M. J. Birch, Model validation for a noninvasive arterial stenosis detection problem,, CRSC-TR12-22, (2012), 12.   Google Scholar

[15]

H. T. Banks, Z. R. Kenz and W. C. Thompson, A review of selected techniques in inverse problem nonparametric probability distribution estimation,, J. of Inverse and Ill-Posed Problems, 20 (2012), 429.  doi: 10.1515/jip-2012-0037.  Google Scholar

[16]

H. T. Banks, Z. R. Kenz and W. C. Thompson, An extension of RSS-based model comparison tests for weighted least squares,, CRSC-TR12-18, 79 (2012), 12.   Google Scholar

[17]

H. T. Banks and N. Luke, Modeling of propagating shear waves in biotissue employing an internal variable approach to dissipation,, Communication in Computational Physics, 3 (2008), 603.   Google Scholar

[18]

H. T. Banks, N. Medhin and G. Pinter, Multiscale considerations in modeling of nonlinear elastomers,, Inter. J. for Comp. Methods in Eng. Science and Mechanics, 8 (2007), 53.  doi: 10.1080/15502280601149346.  Google Scholar

[19]

H. T. Banks, N. Medhin and G. Pinter, Nonlinear reptation in molecular based hysteresis models for polymers,, Quarterly of Applied Math., 62 (2004), 767.   Google Scholar

[20]

H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue,, Multiscale Modeling and Simulation, 3 (2005), 395.  doi: 10.1137/040603693.  Google Scholar

[21]

H. T. Banks and J. R. Samuels, Jr, Detection of cardiac occlusions using viscoelastic wave propagation,, Advances in Appl. Math. and Mech., 1 (2009), 1.   Google Scholar

[22]

H. T. Banks and H. T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes,, CRC Press, (2009).   Google Scholar

[23]

J. D. De Basabe, M. K. Sen and M. F. Wheeler, The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion,, Geophys J. Int., 175 (2008), 83.   Google Scholar

[24]

A. O. Borisyuk, Noise field in the human chest due to turbulent flow in a larger blood vessel,, Flow, 61 (1999), 269.  doi: 10.1016/S0889-9746(03)00056-2.  Google Scholar

[25]

A. O. Borisyuk, Experimental study of voise produced by steady flow through a simulated vascular stenosis,, J. of Sound and Vibration, 256 (2002), 475.   Google Scholar

[26]

A. O. Borisyuk, Model study of noise field in the human chest due to turbulent flow in a larger blood vessel,, J. of Fluids and Structures, 17 (2003), 1095.  doi: 10.1016/S0889-9746(03)00056-2.  Google Scholar

[27]

M. P. Brewin, M. J. Birch and S. E. Greenwald, et al., Characterization of the uniaxial elastic properties of an agar-based tissue mimicking material,, in preparation., ().   Google Scholar

[28]

S. Catheline, J.-L. Gennisson, G. Delon, M. Fink, R. Sinkus, S. Abouelkaram and J. Culioli, Measurement of viscoelastic properties of homogeneous soft solid using transient elastography: an inverse problem approach,, J. Acoust. Soc. Am, 116 (2004), 3734.  doi: 10.1121/1.1815075.  Google Scholar

[29]

S. Catheline, L. Sandrin, J.-L. Gennisson, M. Tanter and M. Fink, Ultrasound-based noninvasive shear elasticity probe for soft tissues,, IEEE Ultrasonics Symposium, 2 (2000), 1799.  doi: 10.1109/ULTSYM.2000.921672.  Google Scholar

[30]

S. Chen, M. Fatemi and J. Greenleaf, Quantifying elasticity and viscosity from measurement of shear wave speed dispersion,, J. Acoust. Soc. Am., 115 (2004), 2781.  doi: 10.1121/1.1739480.  Google Scholar

[31]

S. Chen, M. Urban, C. Pislaru, R. Kinnick, Y. Zheng, A. Yao and J. Greenleaf, Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity,, IEEE Trans. on Ultrason., 56 (2009), 55.   Google Scholar

[32]

T. Cheng, Diastolic murmur caused by coronary artery stenosis,, Ann. Int. Med, 72 (1970).  doi: 10.7326/0003-4819-72-4-543.  Google Scholar

[33]

T. Deffieux, G. Montaldo and M. Tanter, Shear wave spectroscopy for in vivo quantification of human soft tissues visco-elasticity,, IEEE Trans. on Medical Imag., 28 (2009), 313.  doi: 10.1109/TMI.2008.925077.  Google Scholar

[34]

B. El-Asir, L. Khadra, A. Al-Abbasi and M. Mohammed, Time-frequency analysis of heart sounds,, Proc. IEE TENCON, (1996), 553.  doi: 10.1109/TENCON.1996.608401.  Google Scholar

[35]

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues,, Springer-Verlag, (1993).  doi: 10.1115/1.3138285.  Google Scholar

[36]

A. Góral-Wójcicka, W. Borgieł, Z. Małota and Z. Nawrat, On the acoustic phenomena produced by turbulence in the flowing blood,, Polish J. Med. Phys. & Eng., 8 (2002), 29.   Google Scholar

[37]

A. Karpiouk, S. Alglyamov, Y. Illinskii, E. Zabolotskaya and S. Emelianov, Assessment of shear modulus of tissue using ultrasound radiation force acting on a spherical acoustic inhomogeneity,, IEEE Trans. on Ultrason., 56 (2009), 2380.  doi: 10.1109/TUFFC.2009.1326.  Google Scholar

[38]

C. Kruse, S. Shaw and J. R. Whiteman, High order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling,, in preparation., ().   Google Scholar

[39]

T. S. Lee, W. Liao and H. T. Low, Numerical simulation of turbulent flow through series stenoses,, Inter. J. for Numer. Methods in Fluids, 42 (2003), 717.  doi: 10.1002/fld.550.  Google Scholar

[40]

S. Levinson, M. Shinagawa and T. Sato, Sonoelastic determination of human skeletal muscle elasticity,, J. Biomechanics, 28 (1995), 1145.  doi: 10.1016/0021-9290(94)00173-2.  Google Scholar

[41]

S. Lundin, R. Metcalf and C. Hartley, Effects of severity and eccentricity of carotid stenosis on pulsatile blood flow,, Proc. Joint EMBS/BMES, (2003), 1311.  doi: 10.1109/IEMBS.2002.1106403.  Google Scholar

[42]

N. Luke, Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation,, PhD Dissertation, (2006).   Google Scholar

[43]

S. E. Nissen, Application of intravascular ultrasound to characterize coronary artery disease and assess the progression or regression of atherosclerosis,, Am. J. Cardiol., 89 (2002).  doi: 10.1016/S0002-9149(02)02217-8.  Google Scholar

[44]

S. E. Nissen and P. Yock, Intravascular ultrasound: Novel pathophysiological insights and current clinical applications,, Circulation, 103 (2001), 604.  doi: 10.1161/01.CIR.103.4.604.  Google Scholar

[45]

N. Owsley and A. Hull, Beamformed nearfield imaging of a simulated coronary artery containing a stenosis,, IEEE Trans. Med. Imaging, 17 (1998), 900.  doi: 10.1109/42.746623.  Google Scholar

[46]

N. Owsley, A. J. Hull, M. H. Ahmed and J. Kassal, A proof of concept experiment for the detection of occluded coronary arteries using array sensor technology,, Engr. in Medicine and Biol. Society, 1 (1995), 145.  doi: 10.1109/IEMBS.1995.575042.  Google Scholar

[47]

V. Padmanabhan and J. Semmlow, A dedicated system for acoustic detection of coronary artery disease,, Proc. Eng. in Med. & Biol. Soc., (1992), 457.  doi: 10.1109/IEMBS.1992.595658.  Google Scholar

[48]

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