Effects of stenosis on coronary flow

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Principles of basic fluid dynamics

According to accepted laws of fluid dynamics applied to laminar, steady flow in an in vitro system of rigid tubes, the energy or pressure loss due to constriction of a tube is caused primarily by (a) viscous friction between layers of fluid in the stenotic segment according to the Hagen-Poisuelle Law and (b) flow separation or vortex formation (eddying or swirling) at the downstream end of the stenosis. The pressure loss, AP, is related to the flow velocity, V, through a stenotic tube according to a general equation, which may be written in simplified form as ΔP = FV + SV2 . F is the coefficient of pressure loss due to viscous friction and is dependent on relative percent narrowing, absolute diameter, and length of the stenosis. S is the coefficient of pressure loss due to flow separation and is dependent on relative percent stenosis and exit or divergence angle of the stenosis. V is the first power of instantaneous, mean cross-sectional flow velocity, and V2 is the second power of velocity. An additional term may be added in order to account for inertial losses associated with pulsatile flow. However, the inertial effects are small for stenoses above 50% diameter narrowing and can be omitted as applied to the coronary circulation. The fluid dynamic equations can be written as follows in terms of coronary flow velocity or volume flow:

ΔP=8πμLAsAnAsV+ρk2(AnAs−1)2V2          Velocity equation

ΔP=8πμLAs1AsQ+ρk2(1As−1As)2Q2          Flow equationwhere ΔP is pressure loss across the stenosis, μ is absolute blood viscosity, L is stenosis. . .



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