The link between FFR / iFR / CFR:
blood viscosity

What place should blood viscosity occupy in coronary artery disease? A synthesis of clinical evidence, physical models, and the consequences for revascularization decisions.

Blood viscosity shapes coronary indices FFR, iFR, and CFR don't measure the same thing — and blood viscosity is one identifiable cause of their disagreement.

Viscosity explains iFR / CFR / FFR discordances

In the FiGARO study (Kovarnik et al., J Am Heart Assoc 2022)7, across 1,884 paired measurements in 1,564 patients, FFR and iFR were discordant in 20.9% of cases (cut-offs FFR ≤ 0.80 and iFR ≤ 0.89), with a majority FFR+/iFR− subtype at 14.0% and an FFR−/iFR+ subtype at 6.8%. Multivariate analysis identifies hemoglobin — a clinical proxy for blood viscosity — as an independent predictor of FFR−/iFR+ discordance, alongside smoking and chronic kidney disease.

Figure 4 of the article extends the observation to CFR: at a CFR < 2.0 cut-off, the CFR / FFR and CFR / iFR discordances are even more pronounced than the FFR / iFR discordance itself. Correlations are weak to moderate (R = 0.36 between CFR and FFR, R = 0.56 between CFR and iFR), with wide dispersion around the respective cut-offs.

Figure 4 — Correlation CFR vs FFR and CFR vs iFR (FiGARO) Two scatter plots: left CFR vs FFR (R=0.36; P<0.001), right CFR vs iFR (R=0.56; P<0.001). Dashed lines mark cut-offs FFR=0.80, iFR=0.90, and CFR=2.0. R = 0.36; P < 0.001 R = 0.56; P < 0.001 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 FFR iFR CFR CFR
Figure 4 (adapted from Kovarnik et al., FiGARO, JAHA 2022). Correlation between CFR and FFR (left panel, R = 0.36) and between CFR and iFR (right panel, R = 0.56). Dashed lines mark the decision cut-offs (FFR = 0.80, iFR = 0.9, CFR = 2.0) and delineate four quadrants per panel. In the cohort (343 lesions with a CFR measurement), a substantial fraction of points falls into the discordant quadrants. Source: Kovarnik et al., J Am Heart Assoc 2022; 11: e021490 — figure used for research purposes, under attribution.

This reading aligns with a converging body of literature. Eight studies (FiGARO7, Yamazaki, Goto, Kato, Muroya, Honda, Akdi, Ceyhun) show a single pattern: high Hb → FFR+ / iFR− (FFR false positive), low Hb → FFR− / iFR+ (FFR false negative). Statistical reanalysis of FiGARO adds that the indices' sensitivity to clinical variables (Hb, eGFR, age) is stronger among discordant cases than among concordant ones. These variables are not noise — they are the cause of the discordance.

Direct link to FFR

By construction, FFR is defined as FFR = Pd / Pa = 1 − ΔP / Pa, with ΔP = Pa − Pd the transstenotic pressure drop. Any change in ΔP mechanically translates into a change in FFR.

Analytical modeling of ΔP rests on three successive frameworks. Gould (1974)10 experimentally established the non-linear dependence of ΔP on percent stenosis and flow. Young and Tsai (1973)11 formalized this dependence by decomposing ΔP into a viscous (Poiseuille) and an inertial (turbulent) term. The overarching framework remains the incompressible Navier–Stokes equations, in which the viscous term depends directly on viscosity µ.

Two CFD studies explicitly vary µ: Sankaran 20166 (across two hematocrit values, 30% and 55%) and Gashi 2019. To our knowledge, these are the only sources that treat viscosity as a variable. At identical anatomy, simulated FFR varies by 0.04 to 0.13 depending on hematocrit — a spread that fully covers the width of the FFR gray zone (0.75–0.80) documented by Petraco5.

Conclusion: FFR is not a purely geometric index. Its value depends on viscosity by physical construction, independently of the stenosis itself.

Core formula of the revised model

Pa − Pd = ΔP = ΔPPoiseuille + ΔPturbulent
ΔPPoiseuille = 128 · µ · Ls · Q / (π · Ds4)   [unchanged]
ΔPturbulent = K₀ · Kt · ρ/(2A₀²) · (A₀/As − 1)² · Q² · √(µref/µ)   [modified]

Coefficients calibrated on Sankaran 2016: K₀ = 0.572; Kt = 1.52 (original Young-Tsai); µref = 3.5 cP. Error at the two calibration points: < 3%.

VERIFY analysis

The primary objective of the VERIFY study (Berry et al., JACC 2013)1 was to compare the diagnostic accuracy of iFR against FFR and to test whether iFR was independent of hyperemia. Its conclusions were:

This interpretation was partially contradicted by the DEFINE-FLAIR2 and iFR-SWEDEHEART3 outcome trials (NEJM 2017), which demonstrated the clinical non-inferiority of iFR at 12 months. However, the 5-year pooled analysis published in European Heart Journal in 20234 revealed excess mortality in the iFR arm (RR 1.34; 95% CI 1.08–1.65; p = 0.007).

Berry et al. (VERIFY, 2013) reported a 40% iFR / FFR discordance in the clinical zone, attributed to iFR's non-independence from hyperemia. The DEFINE-FLAIR and iFR-SWEDEHEART outcome trials (2017) then demonstrated the clinical non-inferiority of iFR and the proximity between iFR and CFR. FiGARO (2022) identifies hemoglobin in multivariate analysis as an independent predictor of FFR− / iFR+ discordance. Blood composition — Hb, Hct, eGFR — thus enters as an ingredient of the disagreement between the two indices, along pathways that neither the FFR ≤ 0.80 nor the iFR ≤ 0.89 threshold captures.

This suggests that a normal FFR may sometimes be artifactual. In an anemic or kidney-impaired patient, the microcirculation may not be capable of generating sufficient hyperemia. The vessel (the syringe) is failing, which prevents proper assessment of the stenosis (the pipe).

The FFR+ / iFR− pattern: hyperemia “false positives”

This is a stenosis deemed significant by FFR (FFR < 0.80) but not significant by iFR (iFR > 0.89). This profile is predicted by sex, age, and lesion location.

It corresponds to highly effective hyperemia that artificially inflates the pressure drop across a stenosis that may be less critical than it appears.

ADVISE (2012) and ADVISE in-practice (2014)

ADVISE (2012): the first large-scale validation, showing that an iFR cut-off of 0.90 was optimal for predicting FFR ≤ 0.80.

ADVISE in-practice (2014): a real-world study confirming the relationship, with an optimal iFR cut-off between 0.85 and 0.90 depending on the computation method, and classification agreement reaching 92%.

This reframing — from the iFR vs FFR debate to indices vs physiopathological reality — is consistent with:

Sensitivity of the indices to blood viscosity

Multimodal convergence

CFD, clinical literature, and statistical reanalysis all point in the same direction. The direction of the bias (Hb↑ → lower FFR) is physically predictable via the hyperemic Poiseuille term (ΔP ∝ µ·Q) and clinically observed across eight independent studies covering more than 4,000 patients.

Credible magnitude

The ΔFFR ≈ 0.05 predicted between extreme hematocrits matches exactly the width of the FFR gray zone (0.75–0.80) documented by Petraco5. This order-of-magnitude agreement between physical prediction and clinical observation is not trivial.

Consistent RCA effect

The anatomical effect of the right coronary artery (RCA × 4–5 on discordances in FiGARO) is consistent with the model: longer path → larger integrated ΔPPoiseuille → amplified sensitivity to µ. This is not an anatomical coincidence; it is a direct consequence of the physics.

Discordant / concordant asymmetry

Hb, eGFR, and age correlate significantly with the gap between indices in discordant cases, but not with the sum in concordant cases. Random noise would not produce this asymmetry — it is a measurable physiological signature.

Blood viscosity is a versatile parameter

Blood viscosity, a multiform mechanical parameter

  • It depends on Hct and plasma viscosity — and therefore on the CBC.
  • It drives flow Q and ΔP.
  • It affects WSS and appears in the Poiseuille equation.
  • It influences boundary-layer development (separation / reattachment) and vortex formation.
Dependence on blood composition

Causal leap Hb → Hct → viscosity → FFR

Clinical studies measure hemoglobin, not viscosity (except Ceyhun 2021 and Akdi 2022). In coronary patients, Hb is confounded by other variables: CKD, inflammation, malnutrition, comorbidities. Low Hb could combine a direct viscosity effect and a microvascular effect (impaired CFR). Missing critical test: a study where µ is directly measured and where microvascular function is controlled for (using IMR, for example).

Spread of viscosities and stenosis geometries

Calibration on only two points

The model is calibrated on two Sankaran 2016 points (Hct 30% and 55%) with a single geometry (D = 3.5 mm, %D = 60%, Ls = 7.5 mm). The √(µref/µ) factor may mask other dependencies (length, shape, Reynolds). True uncertainty on ΔFFR could be 0.02–0.10 depending on generalization. The model diverges for %D > 80% (Lyras 2021).

Choice of viscosity model

Choice of the formula µ(Hct) = µp / (1 − Hct)2.5

This is the Brinkman 1952 equation12, retained by Sankaran 2016. It diverges at Hct = 100% (non-physical) and ignores the non-Newtonian behavior of blood. Other models (Quemada, Cho-Kensey, Krieger-Dougherty with φmax = 0.6) yield different values at extreme Hct. ΔFFR = 0.05 depends on this choice; another non-Newtonian model would give 0.03 to 0.08.

Viscosity acts on ΔP and Q more than on FFR

FFR is a ratio, not a ΔP

The model predicts ΔP. Clinical FFR is FFR = (Pa − ΔP) / Pa. If Pa also varies under adenosine (and it does), the µ effect is partially absorbed by the denominator. FFR sensitivity to µ may be smaller than the sensitivity of isolated ΔP.

Viscosity (or Hct) absent from any stratification

No stratification in historical trials

The data collected to validate FFR over twenty-five years ago do not answer this question. No post-hoc analysis stratified on hematocrit (Hct) has been published for the FAME (I & II) or DEFER trials. Existing secondary analyses have focused on the prognostic value of intermediate lesions, without exploring the impact of hematocrit. Within the normal range, FFR / resting-index concordance remains high (≈ 81% in Muroya 202019, R² = 0.50); when discordance occurs, however, even moderate anemia (Hb ≈ 11 g/dL) is an independent determinant in multivariate analysis (OR = 0.24; p = 0.005). The effect at very low Hct (severe anemia) or very high Hct (polycythemia) has not been specifically quantified in the clinical literature.

FFR rests on a model that, in clinical practice, can be affected by extracardiac conditions. Its imperfect correlation with real-world outcomes has not been fully explored in these subpopulations, which fuels the debate over its ability to predict functional benefit across all patient subgroups.

Proposal for integrating blood viscosity

Patient stratification

The FFR, CFR, and iFR thresholds were identified pooling all patients, even though viscosity is a non-negligible source of variability for these indices.

Systematic CBC before FFR / iFR

A systematic complete blood count (CBC) before FFR / iFR could improve interpretation of gray-zone values.

Structural bias in FFR-CT algorithms

FFR-CT algorithms, which use a fixed viscosity (µ = 3.5 cP), are structurally biased at hematocrit extremes.

Prospective validation of a corrected index

Prospective validation of a viscosity-corrected index (combined FFR + Hct + MACE outcomes) is the next critical step.

If viscosity explains a substantial fraction of FFR / iFR / CFR discordances, a prospective protocol with direct measurement of µ should reveal a signal in the gray zone.

References

  1. Berry C, van 't Veer M, Witt N, et al. VERIFY (VERification of Instantaneous Wave-Free Ratio and Fractional Flow Reserve for the Assessment of Coronary Artery Stenosis Severity in EverydaY Practice). J Am Coll Cardiol. 2013;61:1421-1427. DOI: 10.1016/j.jacc.2012.09.065
  2. Davies JE, Sen S, Dehbi HM, et al. Use of the Instantaneous Wave-free Ratio or Fractional Flow Reserve in PCI (DEFINE-FLAIR). N Engl J Med. 2017;376:1824-1834. DOI: 10.1056/NEJMoa1700445
  3. Götberg M, Christiansen EH, Gudmundsdottir IJ, et al. Instantaneous Wave-free Ratio versus Fractional Flow Reserve to Guide PCI (iFR-SWEDEHEART). N Engl J Med. 2017;376:1813-1823. DOI: 10.1056/NEJMoa1616540
  4. Sen S, Ahmad Y, Dehbi HM, et al. Five-year major cardiovascular events are increased when coronary revascularization is guided by instantaneous wave-free ratio compared to fractional flow reserve: a pooled analysis of iFR-SWEDEHEART and DEFINE-FLAIR trials. Eur Heart J. 2023;44:4376-4384. DOI: 10.1093/eurheartj/ehad582
  5. Petraco R, Sen S, Nijjer S, et al. Fractional Flow Reserve-Guided Revascularization: Practical Implications of a Diagnostic Gray Zone and Measurement Variability on Clinical Decisions. JACC Cardiovasc Interv. 2013;6(3):222-225. DOI: 10.1016/j.jcin.2012.10.014
  6. Sankaran S, Kim HJ, Choi G, Taylor CA. Uncertainty quantification in coronary blood flow simulations: impact of geometry, boundary conditions and blood viscosity. J Biomech. 2016;49(12):2228-2235. DOI: 10.1016/j.jbiomech.2015.11.001
  7. Kovarnik T, Hitoshi M, Kral A, et al. Fractional Flow Reserve Versus Instantaneous Wave-Free Ratio in Assessment of Lesion Hemodynamic Significance and Explanation of their Discrepancies. International, Multicenter and Prospective Trial: The FiGARO Study. J Am Heart Assoc. 2022;11(9):e021490. DOI: 10.1161/JAHA.121.021490
  8. Pijls NHJ, De Bruyne B, Peels K, et al. Measurement of fractional flow reserve to assess the functional severity of coronary-artery stenoses. N Engl J Med. 1996;334:1703-1708.
  9. Tonino PAL, De Bruyne B, Pijls NHJ, et al. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention (FAME). N Engl J Med. 2009;360:213-224.
  10. Gould KL, Lipscomb K, Hamilton GW. Physiologic basis for assessing critical coronary stenosis. Instantaneous flow response and regional distribution during coronary hyperemia as measures of coronary flow reserve. Am J Cardiol. 1974;33(1):87-94.
  11. Young DF, Tsai FY. Flow characteristics in models of arterial stenoses — I. Steady flow. J Biomech. 1973;6:395-410.
  12. Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20:571.
  13. Quemada D. Rheology of concentrated disperse systems and minimum energy dissipation principle. Rheol Acta. 1977;16:82-94.
  14. Cho YI, Kensey KR. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Biorheology. 1991;28:241-262.
  15. De Simone G, Devereux RB, Chien S, et al. Relation of blood viscosity to demographic and physiologic variables and to cardiovascular risk factors in apparently normal adults. Circulation. 1990;81(1):107-117.
  16. Lyras KG, Lee J. An improved reduced-order model for pressure drop across arterial stenoses. PLoS ONE. 2021;16:e0258047.
  17. Yamazaki T, Saito Y, Kobayashi T, et al. Factors associated with discordance between fractional flow reserve and resting full-cycle ratio. J Cardiol. 2022;80(1):9-13.
  18. Goto R, Takashima H, Ohashi H, et al. Independent predictors of discordance between the resting full-cycle ratio and fractional flow reserve. Heart Vessels. 2021;36(6):790-798.
  19. Kato Y, Dohi T, Chikata Y, et al. Predictors of discordance between fractional flow reserve and resting full-cycle ratio in patients with coronary artery disease. J Cardiol. 2021;77(3):313-319.
  20. Muroya T, Kawano H, Hata S, et al. Relationship between resting full-cycle ratio and fractional flow reserve in assessments of coronary stenosis severity. Catheter Cardiovasc Interv. 2020;96(4):E432-E438. DOI: 10.1002/ccd.28835
  21. Honda T, Kawano H, Akashi R, et al. Nutrition Status May be Related to Discordance of the Resting Full-Cycle Ratio and Fractional Flow Reserve. Catheter Cardiovasc Interv. 2025;107(1):114-123.
  22. Akdi A, Yilmaz S, Kahraman F, Gedikli O. The Role of Whole Blood Viscosity Estimated by De Simone's Formula in Evaluation of Fractional Flow Reserve. Eurasian J Clin Med. 2022;10(1):18-24.
  23. Ceyhun G, et al. Whole blood viscosity in patients with FFR < 0.80. Int J Angiol. 2021;30:117-121.
  24. Lee BK, Götberg M, Fröbert O, et al. Coronary Revascularization Guided With Fractional Flow Reserve or Instantaneous Wave-Free Ratio: A 5-Year Follow-Up of the DEFINE FLAIR Randomized Clinical Trial. JAMA Cardiol. 2024.
  25. Vrints C, Andreotti F, Koskinas KC, et al. 2024 ESC Guidelines for the management of chronic coronary syndromes. Eur Heart J. 2024.

Collaborate with Hemodynes on research

Clinician, researcher, lab director, or industry partner? We're actively building our network of investigator sites and scientific partners. Let's talk about your project.

Get in touch