Objective: To explore the influence of the blood flow-diameter scaling laws of $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{3} $, $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{2.7} $ and $ \text{Q}\alpha \text{D}{}^{7}\!\!\diagup\!\!{}_{3}\; $ on the numerical simulation of fraction flow reserve based on CTA images and to find the optimal exponents.
Methods: 1) 26 patients with coronary artery disease were screened according to the inclusion criteria; 2) Microcirculation resistance (Rm) was calculated under the 3, 2.7 and 7/3 power of the flow-diameter scaling law, which were recorded as 3Rm, 2.7Rm and 7/3Rm, respectively; 3) 3Rm, 2.7Rm and 7/3Rm were used as exit boundary conditions to simulate FFRCT, quoted as 3FFRCT, 2.7FFRCT and 7/3FFRCT, respectively; 4) The correlation and diagnostic performance between three kinds of FFRCT and FFR were analyzed.
Results: The p-values of comparing 3Rm, 2.7Rm and 7/3Rm with FFR were 0.004, 0.005 and 0.010, respectively; the r value between 7/3FFRCT and FFR (0.96) was better than that of 3FFRCT (0.95) and 2.7FFRCT (0.95); the 95% LoA between 7/3FFRCT and FFR (-0.08~0.11) was smaller than that of 3FFRCT (-0.10~0.12) and 2.7FFRCT (-0.09~0.11); the AUC and accuracy of 7/3FFRCT [0.962 (0.805-0.999), 96.15%] were the same as those of 2.7FFRCT [0.962 (0.805-0.999), 96.15%] and better than those of 3FFRCT [0.944 (0.777-0.996), 92.3%]. The prediction threshold of 7/3FFRCT (0.791) was closer to 0.8 than that of 3FFRCT (0.816) and 2.7FFRCT (0.787).
Conclusion: The blood flow-diameter scaling law affects the FFRCT simulation by influencing the exit boundary condition Rm of the calculation. With $ Q\alpha D{}^{7}\!\!\diagup\!\!{}_{3}\; $, FFRCT had the highest diagnostic performance. The blood flow-diameter scaling law provides theoretical support for the blood flow distribution in the bifurcated vessel and improves the FFRCT model.
Keywords: 0D/3D geometric multi-scale model; FFRCT; blood flow-diameter scaling law; microcirculation resistance; numerical calculation.