# True Fractional Flow Reserve of Left Main Coronary Artery Stenosis in the Presence of Downstream Coronary Stenoses

## Author + information

- Published online August 17, 2015.

## Author Information

- Naritatsu Saito, MD
^{∗}(naritatu{at}kuhp.kyoto-u.ac.jp)

- ↵∗Department of Cardiovascular Medicine, Graduate School of Medicine, Kyoto University, 54 Shogoin Kawahara-cho, Sakyo-ku, Kyoto 606-8507, Japan

With great interest I read the recent paper by Fearon et al. (1) in which they assessed the impact of downstream left anterior descending (LAD) or left circumflex (LCX) coronary stenosis on the assessment of fractional flow reserve (FFR) of an left main coronary artery (LMCA) stenosis. They concluded that if the apparent FFR of the LMCA (FFR_{app}) is >0.85, the true FFR of the LMCA (FFR_{true}) is always >0.80. If FFR_{app} is between 0.81 and 0.85 and the epicardial FFR (FFR_{epi}) is ≦0.45, then FFR_{true} is ≦0.80 in some cases.

However, these conclusions are not surprising. These conclusions can be proven mathematically. Bruyne et al. (2) previously described theoretical equations that calculate the true FFR of individual stenosis in a tandem lesion. Based on their study, an equation that calculates FFR_{true} in a bifurcation lesion can be derived. When the downstream stenosis is located in the LAD, and *n* is defined as the ratio of microcirculatory resistances of the LCX to the LAD, FFR_{true} is calculated as per the following Equation 1._{true} with respect to FFR_{epi} is calculated as follows:_{true} monotonically increases when FFR_{epi} is larger. Similarly, the partial differentiation of FFR_{true} with respect to FFR_{app} and *n* are calculated as follows:

The inequalities in Equations 2, 3, and 4 suggest that FFR_{true} increases with FFR_{epi} and FFR_{app}, but that it decreases with an increase in *n*. *n* is the ratio of microcirculatory resistances of the LCX to the LAD, which is usually considered approximately 2. Thus, FFR_{true} > 080 is always true when FFR_{app} is >0.85, FFR_{epi} is >0.45, and *n* = 2. Similarly, Equation 1 suggests that when FFR_{app} is between 0.81 and 0.85 and the epicardial FFR (FFR_{epi}) is ≦0.45, then FFR_{true} can be either larger or smaller than 0.80. These calculations are completely in accordance with the study results of Fearon et al. (1). Their study was well designed and the results were reasonable, but it lacked the understandings of the background mechanism. Another important limitation of their study is that they only assessed the LMCA plus 1 downstream stenosis and lacked the assessment of the LMCA plus 2 downstream stenoses both in the LAD and LCX, which is also frequently encountered in clinical practice. In the case of the LMCA plus 2 downstream stenoses, FFR_{true} is calculated as per Equation 5 when the epicardial FFR of the LAD and LCX are defined as FFR_{LAD} and FFR_{LCX}.

## Footnotes

Please note: Dr. Saito has reported that he has no relationships relevant to the contents of this paper to disclose.

- 2015 American College of Cardiology Foundation

## References

- ↵
- Fearon W.F.,
- Yong A.S.,
- Lenders G.,
- et al.

- ↵
- De Bruyne B.,
- Pijls N.H.,
- Heyndrickx G.R.,
- Hodeige D.,
- Kirkeeide R.,
- Gould K.L.