On the assumption of conventional FFR: A modified formulation

The standard estimation of fractional flow reserve (FFR) assumes negligible pressure losses in non-stenotic regions of a stenotic coronary artery, attributing all losses solely to the stenotic lesion. Particularly in tortuous non-stenotic regions, the pressure losses may not be negligible. To investigate the impact of this assumption, numerical simulations of the unsteady, three-dimensional incompressible Navier-Stokes equations are performed for thirteen idealized patient-specific coronary arteries. The results indicate that the total pressure drop in tortuous non-stenotic regions scales with the volume flow rate as Q^1.42. Based on this relationship, a modified FFR formula is theoretically derived, resulting in a nonlinear algebraic equation for FFR. This modified formula yields systematically higher FFR values than those of the conventional definition, with relative differences increasing from 0.66% to 16.26% as the flow rate increases. Furthermore, the proposed formulation eliminates the need to specify arbitrary proximal and distal measurement locations, enabling a more robust assessment of pressure losses in stenotic coronary arteries using non-invasive, simulation-based approaches.