Figure 3

Derivation of volumetric flow rate and the FI. Volumetric flow rate is the volume infused per unit of time; volume is the product of area multiplied by distance. The formula can be expressed as \(F = \frac{V}{t} = \frac{A \cdot d}{t}\), where \(A\) is the area, \(d\) is the distance, F is the volumetric flow rate, \(t\) is the time, and V is the volume. Area is the product of π\(\cdot\) radius²; velocity is the quotient of distance divided by the time. The formula can be further expressed as \(F = \frac{V}{t} = \frac{A \cdot d}{t} = A \cdot \overline{V} = \overline{V} \cdot \pi \cdot r^{2}\), where π is the circular constant, \(r\) is the radius, and \(\overline{V}\) is the velocity. The radius can be expressed as 100%-stenosis% measured by CTA; velocity can be expressed as PSV measured by DUS. Thus, we used the FI as to replace volumetric flow rate in measuring arterial perfusion. \(FI = PSV \cdot \left( {100\% - S_{Z1} } \right)^{2} \left( {100\% - S_{Z2} } \right)^{2} \cdots \left( {100\% - S_{Z5B} } \right)^{2}\), where \(S_{zn}\) is the stenotic percentage of the referred zone of PLA system. CTA: computed tomography angiography, DUS: dynamic duplex sonography, FI: flow index, PSV: peak systolic velocity.