Myocardial fractional flow reserve (FFR), an important index of coronary stenosis, is measured by a pressure sensor guidewire. The determination of FFR, only based on the dimensions (lumen diameters and length) of stenosis and hyperaemic coronary flow with no other ad hoc parameters, is currently not possible. We propose an analytical model derived from conservation of energy, which considers various energy losses along the length of a stenosis, i.e. convective and diffusive energy losses as well as energy loss due to sudden constriction and expansion in lumen area.
In vitro
(constrictions were created in isolated arteries using symmetric and asymmetric tubes as well as an inflatable occluder cuff) and
in vivo
(constrictions were induced in coronary arteries of eight swine by an occluder cuff) experiments were used to validate the proposed analytical model. The proposed model agreed well with the experimental measurements. A least-squares fit showed a linear relation as (Δ
p
or FFR)
experiment
=
a
(Δ
p
or FFR)
theory
+
b
, where
a
and
b
were 1.08 and −1.15 mmHg (
r
2
= 0.99) for
in vitro
Δ
p
, 0.96 and 1.79 mmHg (
r
2
= 0.75) for
in vivo
Δ
p
, and 0.85 and 0.1 (
r
2
= 0.7) for FFR. Flow pulsatility and stenosis shape (e.g. eccentricity, exit angle divergence, etc.) had a negligible effect on myocardial FFR, while the entrance effect in a coronary stenosis was found to contribute significantly to the pressure drop. We present a physics-based experimentally validated analytical model of coronary stenosis, which allows prediction of FFR based on stenosis dimensions and hyperaemic coronary flow with no empirical parameters.
A validated predictive model of coronary fractional flow reserve
