Skip to main content
SpringerLink
Log in

Early detection of carotid stenosis using sensitivity analysis and parameter estimation

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In this research work, a mathematical framework is presented to detect a mild carotid stenosis (55%) using proximal flow measurements. For this purpose, an already developed 0D model of carotid arteries is considered and stenosis near bifurcation is estimated (detected) using parameter estimation procedure, whereas the data are collected using Doppler ultrasound. The work is useful in detecting vessel abnormalities (stenosis) using flow measurements at proximal sites of the carotid stenosis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. World Health Organization, Cardiovascular Diseases (CVDs), The United Nations (2015), http://www.who.int/mediacentre/factsheets/fs317/en/. Accessed 11 May 2015

  2. S.S. Virani et al., Heart disease and stroke statistics-2020 update: a report from the American Heart Association. Circulation 141(9), e139–e596 (2020)

    Article  Google Scholar 

  3. R.E. Klabunde, Cardiovascular Physiology Concepts (Lippincott Williams and Wilkins/Wolters Kluwer, Philadelphia, 2012)

    Google Scholar 

  4. A. Saxena, E.Y.K. Ng, S.T. Lim, Imaging modalities to diagnose carotid artery stenosis: progress and prospect. Biomed. Eng. Online 18, 66 (2019)

    Article  Google Scholar 

  5. A.S. Khan, A. Shahzad, M. Zubair, A. Alvi, R. Gul, Personalized 0D models of normal and stenosed carotid arteries. Comput. Methods Programs Biomed. 200, 105888 (2021)

    Article  Google Scholar 

  6. A. Parton, V. McGilligan, M. O’Kane, F.R. Baldrick, S. Watterson, Computational modelling of atherosclerosis. Brief. Bioinform. 17(4), 562–575 (2016)

  7. A. Quarteroni, A. Manzoni, C. Vergara, The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications. Acta Numer. 26, 365–590 (2017)

    Article  MathSciNet  Google Scholar 

  8. L. Formaggia, A. Veneziani, Reduced and multiscale models for the human cardiovascular system. Lecture notes VKI, Lecture Series 07, Brussels (2003)

  9. K. Laganàa, R. Balossinoa, F. Migliavaccaa, G. Pennatia, E.L. Boveb, M.R. de Levalc, G. Dubinid, Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation. J. Biomech. 38, 1129–1141 (2005)

    Article  Google Scholar 

  10. W. Kinsner, Y. Yan, A model of the carotid vascular system with stenosis at the carotid bifurcation. Math. Comput. Model. 14, 582–585 (1990)

    Article  Google Scholar 

  11. N. El Khatib, O. Kafi, A. Sequeira, S. Simakov, Yu. Vassilevski, V. Volpert, Mathematical modelling of atherosclerosis. Math. Model. Nat. Phenom. 14, 603 (2019)

    Article  MathSciNet  Google Scholar 

  12. R. Gul, S. Shahzadi, Beat-to-beat sensitivity analysis of human systemic circulation coupled with the left ventricle model of the heart: a simulation-based study. Eur. Phys. J. Plus 134, 314 (2019)

    Article  Google Scholar 

  13. Z. Duanmu, M. Yin, X. Fan, X. Yang, X. Luo, A patient-specific lumped-parameter model of coronary circulation. Sci. Rep. 8, 874 (2018)

    Article  ADS  Google Scholar 

  14. R. Gul, A. Shahzad, M. Zubair, Application of 0D model of blood flow to study the vessel abnormalities in the human systemic circulation: an in-silico study. Int. J. Biomath. 11(8), 1850106 (2018)

    Article  MathSciNet  Google Scholar 

  15. R. Gul, C. Schuette, S. Bernhard, Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries. Appl. Math. Model. 40, 7724–7738 (2016)

    Article  MathSciNet  Google Scholar 

  16. R. Gul, S. Bernhard, Parametric uncertainty and global sensitivity analysis in a model of the carotid bifurcation: identification and ranking of most sensitive model parameters. Math. Biosci. 269, 104–116 (2015)

    Article  MathSciNet  Google Scholar 

  17. R. Gul, Mathematical modeling and sensitivity analysis of a lumped-parameter model of the human cardiovascular system. PhD thesis, Freie Universitat, Berlin, Germany (2016)

  18. D.A. Johnson, W.C. Rose, J.W. Edwards, U.P. Naik, A.N. Besis, Application of 1D blood flow models of the human arterial network to differential pressure predictions. J. Biomech. 44, 869–876 (2011)

    Article  Google Scholar 

  19. R. Gul, N. Shaheen, A. Shahzad, Personalized mathematical model of human arm arteries with inflow boundary condition. Eur. Phys. J. Plus 135, 10 (2020)

    Article  Google Scholar 

  20. B. Quatember, M. Mayr, Mathematical modeling and simulation in coronary blood flow, in Aspects of Mathematical Modelling Mathematics and Biosciences in Interaction. ed. by R.J. Hosking, E. Venturino (Birkhauser, Basel, 2008). https://doi.org/10.1007/978-3-7643-8591-0_9

    Chapter  MATH  Google Scholar 

  21. A.P. Avolio, Multi-branched model of the human arterial system. Med. Biol. Eng. Comput. 18, 709–718 (1980)

    Article  Google Scholar 

  22. N. Westerhof, F. Bosman, C.J. De Vries, A. Noordergraaf, Analog studies of the human systemic arterial tree. J. Biomech. 2, 121–143 (1969)

    Article  Google Scholar 

  23. L. Dumas, Inverse problems for blood flow simulation, in EngOpt 2008—International Conference on Engineering Optimization Rio de Janeiro, Brazil, 01–05 (2008)

  24. C.B. Wong, J.C. Wong, A novel method to quantify carotid artery stenosis by Doppler ultrasound: using the continuity principle. Int. J. Angiol.: Off. Publ. Int. Coll. Angiol., Inc. 19(2), 86–90 (2010)

    Article  Google Scholar 

  25. D. Netuka, T. Belsan, K. Broulikova, V. Mandys, F. Charvat, J. Malik, L. Coufalova, O. Bradac, S. Ostry, V. Benes, Detection of carotid artery stenosis using histological specimens: a comparison of CT angiography, magnetic resonance angiography, digital subtraction angiography and Doppler ultrasonography. Acta Neurochir. 158, 1505–1514 (2016)

    Article  Google Scholar 

  26. A. Saxena, E.Y.K. Ng, S.T. Lim, Imaging modalities to diagnose carotid artery stenosis: progress and prospect. Biomed. Eng. Online 18, 66 (2019)

    Article  Google Scholar 

  27. M.H.F. Poorthuis, D.R. Morris, G.J. de Borst, M.L. Bots, J.P. Greving, F.L.J. Visseren, P. Sherliker, R. Clack, R. Clarke, S. Lewington, R. Bulbulia, A. Halliday, Detection of asymptomatic carotid stenosis in patients with lower-extremity arterial disease: development and external validations of a risk score. Br. J. Surg. 108(8), 960–967 (2021)

    Article  Google Scholar 

  28. A.K. Gupta, Performance and analysis of blood flow through carotid artery. Int. J. Eng. Bus. Manag. 3(4), 1–6 (2011)

    Google Scholar 

  29. H.T. Banks, S. Hu, Z.R. Kenz, C. Kruse, S. Shaw, J. Whiteman, M.P. Brewin, S.E. Greenwald, M.J. Birch, Model validation for a non-invasive arterial stenosis detection problem. Math. Biosci. Eng. 11(3), 427–448 (2014)

    Article  MathSciNet  Google Scholar 

  30. D. Marquardt, An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11, 431–441 (1963)

    Article  MathSciNet  Google Scholar 

  31. Z. Zi, Sensitivity analysis approaches applied to systems biology models. IET Syst. Biol. 5(6), 336–346 (2011)

    Article  Google Scholar 

  32. A. Saltelli, K. Chan, E.M. Scott, Sensitivity Analysis Wiley Series in Probability and Statistics England (Wiley, Hoboken, 2000)

    Google Scholar 

  33. I. Sobol, Sensitivity estimates for nonlinear mathematical models. Matematicheskoe Modelirovanie 2, 112118 (1990, in Russian, translated in English)

  34. J. Doke, GRABIT, MATLAB Central File Exchange (2005)

Download references

Acknowledgements

The authors would like to thank Ayub Teaching Hospital (ATH) and Mufti Clinic Abbottabad, Pakistan, for providing patient data.

Funding

All measurements/data collection costs are borne by COMSATS University Islamabad, Pakistan, with Grant Number 16-04/CRGP/CUI/ATD/18/707.

Author information

Authors and Affiliations

  1. COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan

    Raheem Gul, Saba Hafeez, Shamsul Haq, Aamir Shahzad & Muhammad Zubair

Authors
  1. Raheem Gul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saba Hafeez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shamsul Haq
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aamir Shahzad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Muhammad Zubair
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raheem Gul.

Ethics declarations

Conflict of interest

All authors declare no conflict of interest.

Compliance with ethical standards

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gul, R., Hafeez, S., Haq, S. et al. Early detection of carotid stenosis using sensitivity analysis and parameter estimation. Eur. Phys. J. Plus 136, 1125 (2021). https://doi.org/10.1140/epjp/s13360-021-02122-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-02122-3

Search

Navigation