The Fractional Flow Reserve (FFR) is a simple relationship of the local pressure (Pd) after an atherosclerotic plate in the coronal arteries divided with the pressure at the aortic root (Pa). Cardiologist suggest that a value FFR

Pa FFR= RS Pa Pa Pd Analytically, there are some equations obtained from the Poiseuille Law to obtain the loss of pressure inside pipes with a geometrically ideal stenosis. A cylindrical stenosis will have a cone entrance (a), a straight cylindrical stenosis (b) and a conic expansion (c). b AP = + . total friction-cone + AP friction-stenosis inertia-cone AP friction-cone 128 LI: AD I. (D/D.)-1 3(1-B AP friction-stenosis 128 L. AD . inertia-cone = 0.5p [(+)*-(+) ] (A =stenosis area, A;=internal area of the artery) Determine the FFR for a coronal artery with the next characteristics: . . Internal diameter Di= 3 mm = 0.003 m Stenosis diameter Ds= 1.5 mm = 0.0015 m Blood's density = 1060 kg/m3 Blood's viscosity = 0.0036 N s/m2 Internal flow (Q) = 1.66x10^-6 m3/s LC= Length of the input cone = 4 mm = 0.004 m LS= Length of the stenosis cylinder = 4 mm = 0.004 m Pa= Aortic Pressure = 100 mm Hg = 13332.2 Pa