Cardiovascular Engineering and Technology

, Volume 9, Issue 4, pp 597–622 | Cite as

Uncertainty Quantification and Sensitivity Analysis for Computational FFR Estimation in Stable Coronary Artery Disease

  • Fredrik E. Fossan
  • Jacob Sturdy
  • Lucas O. Müller
  • Andreas Strand
  • Anders T. Bråten
  • Arve Jørgensen
  • Rune Wiseth
  • Leif R. Hellevik



The main objectives of this study are to validate a reduced-order model for the estimation of the fractional flow reserve (FFR) index based on blood flow simulations that incorporate clinical imaging and patient-specific characteristics, and to assess the uncertainty of FFR predictions with respect to input data on a per patient basis.


We consider 13 patients with symptoms of stable coronary artery disease for which 24 invasive FFR measurements are available. We perform an extensive sensitivity analysis on the parameters related to the construction of a reduced-order (hybrid 1D–0D) model for FFR predictions. Next we define an optimal setting by comparing reduced-order model predictions with solutions based on the 3D incompressible Navier–Stokes equations. Finally, we characterize prediction uncertainty with respect to input data and identify the most influential inputs by means of sensitivity analysis.


Agreement between FFR computed by the reduced-order model and by the full 3D model was satisfactory, with a bias (\(\text{FFR} _{{\text {3D}}}- \text{FFR} _{{\text {1D}}{-}{\text {0D}}}\)) of \(-\,0.03\,(\pm\, 0.03)\) at the 24 measured locations. Moreover, the uncertainty related to the factor by which peripheral resistance is reduced from baseline to hyperemic conditions proved to be the most influential parameter for FFR predictions, whereas uncertainty in stenosis geometry had greater effect in cases with low FFR.


Model errors related to solving a simplified reduced-order model rather than a full 3D problem were small compared with uncertainty related to input data. Improved measurement of coronary blood flow has the potential to reduce uncertainty in computational FFR predictions significantly.


Computational FFR Uncertainty quantification Model complexity Total uncertainty 



This work was partially supported by NTNU Health (Strategic Research Area at the Norwegian University of Science and Technology) and by The Liaison Committee for Education, Research and Innovation in Central Norway. Computational resources in Norwegian HPC Infrastructure were granted by the Norwegian Research Council by Project Nr. NN9545K. LRH was partly funded by a Peder Sather Grant: Mainstreaming Sensitivity Analysis And Uncertainty Auditing.

Conflict of interest

There are no conflicts of interest.

Ethical Approval

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.

Informed Consent

Informed consent was obtained from all individual participants included in the study.


  1. 1.
    Antiga, L., M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, and D. A. Steinman. An image-based modeling framework for patient-specific computational hemodynamics. Med. Biol. Eng. Comput. 46(11):1097–1112, 2008.
  2. 2.
    Blanco, P. J., C. A. Bulant, L. O. Müller, G. D. M. Talou, C. G. Bezerra, P. L. Lemos, and R. A. Feijóo. Comparison of 1D and 3D models for the estimation of fractional flow reserve. arXiv:1805.11472 [physics] (2018). ArXiv: 1805.11472.
  3. 3.
    Boileau, E., S. Pant, C. Roobottom, I. Sazonov, J. Deng, X. Xie, and P. Nithiarasu. Estimating the accuracy of a reduced-order model for the calculation of fractional flow reserve (FFR). Int. J. Numer. Methods Biomed. Eng. 34(1):e2908, 2018.
  4. 4.
    Bråten, A. T., and R. Wiseth. Diagnostic Accuracy of CT-FFR Compared to Invasive Coronary Angiography with Fractional Flow Reserve—Full Text View— (2017).
  5. 5.
    Brault, A., L. Dumas, and D. Lucor. Uncertainty quantification of inflow boundary condition and proximal arterial stiffness coupled effect on pulse wave propagation in a vascular network. 2016, arXiv preprint. arXiv:1606.06556.
  6. 6.
    Cook, C. M., R. Petraco, M. J. Shun-Shin, Y. Ahmad, S. Nijjer, R. Al-Lamee, Y. Kikuta, Y. Shiono, J. Mayet, D. P. Francis, S. Sen, and J. E. Davies. Diagnostic accuracy of computed tomography–derived fractional flow reserve: a systematic review. JAMA Cardiol. 2017.
  7. 7.
    De Bruyne, B., N. H. Pijls, B. Kalesan, E. Barbato, P. A. Tonino, Z. Piroth, N. Jagic, S. Möbius-Winkler, G. Rioufol, N. Witt, P. Kala, P. MacCarthy, T. Engström, K. G. Oldroyd, K. Mavromatis, G. Manoharan, P. Verlee, O. Frobert, N. Curzen, J. B. Johnson, P. Jüni, and W. F. Fearon. Fractional flow reserve-guided PCI versus medical therapy in stable coronary disease. N. Engl. J. Med. 367(11), 991–1001, 2012.
  8. 8.
    Dubin, J., D. C. Wallerson, R. J. Cody, and R. B. Devereux. Comparative accuracy of Doppler echocardiographic methods for clinical stroke volume determination. Am. Heart J. 120(1):116–123, 1990.
  9. 9.
    Eck, V. G., W. P. Donders, J. Sturdy, J. Feinberg, T. Delhaas, L. R. Hellevik, and W. Huberts. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int. J. Numer. Methods Biomed. Eng. 2015.
  10. 10.
    Eck, V. G., J. Sturdy, and L. R. Hellevik. Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions. J. Biomech. 2016.
  11. 11.
    Evju, Ø., and M. S. Alnæs. CBCFLOW. Bitbucket Repository. 2017.Google Scholar
  12. 12.
    Feinberg, J., and H. P. Langtangen. Chaospy: an open source tool for designing methods of uncertainty quantification. J. Comput. Sci. 11:46–57, 2015. MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fiorentini, S., L. M. Saxhaug, T. G. Bjastad, and J. Avdal: Maximum velocity estimation in coronary arteries using 3D tracking Doppler.
  14. 14.
    Gaur, S., K. A. Øvrehus, D. Dey, J. Leipsic, H. E. Bøtker, J. M. Jensen, J. Narula, A. Ahmadi, S. Achenbach, B. S. Ko, E. H. Christiansen, A. K. Kaltoft, D. S. Berman, H. Bezerra, J. F. Lassen, and B. L. Nørgaard. Coronary plaque quantification and fractional flow reserve by coronary computed tomography angiography identify ischaemia-causing lesions. Eur. Heart J. 37(15), 1220–1227, 2016.
  15. 15.
    Hannawi, B., W. W. Lam, S. Wang, and G. A. Younis. Current use of fractional flow reserve: a nationwide survey. Tex. Heart Inst. J. 41(6):579–584, 2014. Scholar
  16. 16.
    Holte, E.: Transthoracic Doppler Echocardiography for the Detection of Coronary Artery Stenoses and Microvascular Coronary Dysfunction. NTNU, 2017.
  17. 17.
    Hunyor, S. N., J. M. Flynn, and C. Cochineas. Comparison of performance of various sphygmomanometers with intra-arterial blood-pressure readings. Br. Med. J. 2(6131):159–162, 1978.
  18. 18.
    Huo, Y., and G. S. Kassab. Intraspecific scaling laws of vascular trees. J. R. Soc. Interface 9(66), 190–200, 2012. Scholar
  19. 19.
    Itu, L., P. Sharma, V. Mihalef, A. Kamen, C. Suciu, and D. Lomaniciu. A patient-specific reduced-order model for coronary circulation. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI). IEEE, 2012, pp. 832–835.
  20. 20.
    Johnson, N. P., D. T. Johnson, R. L. Kirkeeide, C. Berry, B. De Bruyne, W. F. Fearon, K. G. Oldroyd, N. H. J. Pijls, and K. L. Gould. Repeatability of fractional flow reserve despite variations in systemic and coronary hemodynamics. JACC Cardiovasc. Interv. 8(8):1018–1027, 2015.
  21. 21.
    Johnson, N. P., R. L. Kirkeeide, and K. L. Gould. Is discordance of coronary flow reserve and fractional flow reserve due to methodology or clinically relevant coronary pathophysiology? JACC Cardiovasc. Imaging 5(2):193–202, 2012. CrossRefGoogle Scholar
  22. 22.
    Jones, E., T. Oliphant, P. Peterson, et al. SciPy: open source scientific tools for Python (2001–).
  23. 23.
    Kenner, T.: The measurement of blood density and its meaning. Basic Res. Cardiol. 84(2):111–124, 1989.
  24. 24.
    Kim, H. J., I. E. Vignon-Clementel, J. S. Coogan, C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Patient-specific modeling of blood flow and pressure in human coronary arteries. Ann. Biomed. Eng. 38(10):3195–3209, 2010. CrossRefGoogle Scholar
  25. 25.
    Liang, F., K. Fukasaku, H. Liu, and S. Takagi. A computational model study of the influence of the anatomy of the circle of Willis on cerebral hyperperfusion following carotid artery surgery. Biomed. Eng. Online 10:84, 2011. CrossRefGoogle Scholar
  26. 26.
    Logg, A., K. A. Mardal, and G. Wells, eds. Automated Solution of Differential Equations by the Finite Element Method. Lecture Notes in Computational Science and Engineering, vol. 84. Berlin: Springer, 2012.
  27. 27.
    Mantero, S., R. Pietrabissa, and R. Fumero. The coronary bed and its role in the cardiovascular system: a review and an introductory single-branch model. J. Biomed. Eng. 14(2):109–116, 1992.
  28. 28.
    Matsuda, J., T. Murai, Y. Kanaji, E. Usui, M. Araki, T. Niida, S. Ichijyo, R. Hamaya, T. Lee, T. Yonetsu, M. Isobe, and T. Kakuta. Prevalence and clinical significance of discordant changes in fractional and coronary flow reserve after elective percutaneous coronary intervention. J. Am. Heart Assoc. 2016. Scholar
  29. 29.
    Morris, P. D., D. A. Silva Soto, J. F. Feher, D. Rafiroiu, A. Lungu, S. Varma, P. V. Lawford, D. R. Hose, and J. P. Gunn. Fast virtual fractional flow reserve based upon steady-state computational fluid dynamics analysis. JACC Basic Transl. Sci. 2(4):434–446, 2017.
  30. 30.
    Mortensen, M., and K. Valen-Sendstad. Oasis: a high-level/high-performance open source Navier–Stokes solver. Comput. Phys. Commun. 188:177–188, 2015.
  31. 31.
    Murray, C. D. The physiological principle of minimum work. Proc. Natl Acad. Sci. USA 12(3):207–214, 1926.
  32. 32.
    Otsuki, T., S. Maeda, M. Iemitsu, Y. Saito, Y. Tanimura, R. Ajisaka, and T. Miyauchi. Systemic arterial compliance, systemic vascular resistance, and effective arterial elastance during exercise in endurance-trained men. Am. J. Physiol. Regul. Integr. Comp. Physiol. 295(1):R228–R235, 2008.
  33. 33.
    Pijls, N. H., W. F. Fearon, P. A. Tonino, U. Siebert, F. Ikeno, B. Bornschein, M. van’t Veer, V. Klauss, G. Manoharan, T. Engstrøm, K. G. Oldroyd, P. N. Ver Lee, P. A. MacCarthy, and B. De Bruyne. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention in patients with multivessel coronary artery disease. J. Am. Coll. Cardiol. 56(3):177–184, 2010.
  34. 34.
    Ri, K., K. K. Kumamaru, S. Fujimoto, Y. Kawaguchi, T. Dohi, S. Yamada, K. Takamura, Y. Kogure, N. Yamada, E. Kato, R. Irie, T. Takamura, M. Suzuki, M. Hori, S. Aoki, and H. Daida. Noninvasive computed tomography-derived fractional flow reserve based on structural and fluid analysis: reproducibility of on-site determination by unexperienced observers. J. Comput. Assist. Tomogr. 1, 2017.
  35. 35.
    Robert, C. P., and G. Casella. Monte Carlo Statistical methods, 2nd edn., Softcover Reprint of the Hardcover 2, 2004 edn. Springer Texts in Statistics. New York: Springer, 2010.Google Scholar
  36. 36.
    Rogers, G., and T. Oosthuyse. A comparison of the indirect estimate of mean arterial pressure calculated by the conventional equation and calculated to compensate for a change in heart rate. Int. J. Sports Med. 21(02):90–95, 2000.
  37. 37.
    Sakamoto, S., S. Takahashi, A. U. Coskun, M. I. Papafaklis, A. Takahashi, S. Saito, P. H. Stone, and C. L. Feldman. Relation of distribution of coronary blood flow volume to coronary artery dominance. Am. J. Cardiol. 111(10):1420–1424, 2013.
  38. 38.
    Saltelli, A.: Making best use of model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145(2):280–297, 2002. MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Saltelli, A.: Global Sensitivity Analysis: The Primer. Chichester Wiley, 2008.
  40. 40.
    Sankaran, S., H. J. Kim, G. Choi, and C. A. Taylor. Uncertainty quantification in coronary blood flow simulations: impact of geometry, boundary conditions and blood viscosity. J. Biomech. 49(12):2540–2547, 2016.
  41. 41.
    Schroeder, W. J., and K. M. Martin. The visualization toolkit. In: Visualization Handbook. Elsevier, 2005, , pp. 593–614.
  42. 42.
    Shahzad, R., H. Kirişli, C. Metz, H. Tang, M. Schaap, L. van Vliet, W. Niessen, and T. van Walsum. Automatic segmentation, detection and quantification of coronary artery stenoses on CTA. Int. J. Cardiovasc. Imaging 29(8):1847–1859, 2013. CrossRefGoogle Scholar
  43. 43.
    Simo, J., and F. Armero. Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier–Stokes and Euler equations. Comput. Methods Appl. Mech. Eng. 111(1–2):111–154, 1994.
  44. 44.
    Smith, N., A. Pullan, and P. Hunter. An anatomically based model of transient coronary blood flow in the heart. SIAM J. Appl. Math. 62(3):990–1018, 2002.
  45. 45.
    Spaan, J. A. E.: Coronary blood flow. In: Developments in Cardiovascular Medicine, vol. 124. Dordrecht: Springer, 1991.
  46. 46.
    Antiga, L., and S. Manini. The vascular modeling toolkit website. Accessed 27 Oct 2017.
  47. 47.
    Sturdy, J., J. K. Kjernlie, H. M. Nydal, V. G. Eck, and L. R. Hellevik. Uncertainty of computational coronary stenosis assessment and model based mitigation of image resolution limitations (Forthcoming).Google Scholar
  48. 48.
    Tonino, P. A., B. De Bruyne, N. H. Pijls, U. Siebert, F. Ikeno, M. vant Veer, V. Klauss, G. Manoharan, T. Engstrøm, K. G. Oldroyd, et al. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention. N. Engl. J. Med. 360(3):213–224, 2009.
  49. 49.
    Uren, N. G., J. A. Melin, B. De Bruyne, W. Wijns, T. Baudhuin, and P. G. Camici. Relation between myocardial blood flow and the severity of coronary-artery stenosis. N. Engl. J. Med. 330(25):1782–1788, 1994. CrossRefGoogle Scholar
  50. 50.
    Wongkrajang, P., W. Chinswangwatanakul, C. Mokkhamakkun, N. Chuangsuwanich, B. Wesarachkitti, B. Thaowto, S. Laiwejpithaya, and O. Komkhum. Establishment of new complete blood count reference values for healthy Thai adults. Int. J. Lab. Hematol.
  51. 51.
    World Health Organization. Top 10 Causes of Death, 2018.
  52. 52.
    Xiao, N., J. Alastruey, and C. Alberto Figueroa. A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int. J. Numer. Methods Biomed. Eng. 30(2):204–231, 2014. MathSciNetCrossRefGoogle Scholar
  53. 53.
    Young, D. F., and F. Y. Tsai. Flow characteristics in models of arterial stenoses—I. Steady flow. J. Biomech. 6(4):395–410, 1973.
  54. 54.
    Yushkevich, P. A., J. Piven, H. C. Hazlett, R. G. Smith, S. Ho, J. C. Gee, and G. Gerig. User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. NeuroImage 31(3):1116–1128, 2006.
  55. 55.
    Zienkiewicz, O. C., R. L. Taylor, and P. Nithiarasu. The Finite Element Method for Fluid Dynamics, 7th edn. Oxford: Butterworth-Heinemann, 2014. OCLC: ocn869413341.Google Scholar

Copyright information

© Biomedical Engineering Society 2018

Authors and Affiliations

  1. 1.Department of Structural EngineeringNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Clinic of CardiologySt. Olavs HospitalTrondheimNorway
  3. 3.Department of Circulation and Medical ImagingNorwegian University of Science and TechnologyTrondheimNorway
  4. 4.Department of Radiology and Nuclear MedicineSt. Olavs HospitalTrondheimNorway

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