Aleksandar Milovanović1*, Ognjen Matić2, Igor Saveljić1 and Velibor Isailović2
1Institute for Information Technologies, University of Kragujevac, 34000 Kragujevac, Serbia
2Faculty of Engineering, University of Kragujevac, 34000 Kragujevac, Serbia
acakg85 [at] hotmail.com
Abstract
Invasive Fractional Flow Reserve (FFR) remains the clinical gold standard for assessing the functional significance of coronary artery stenosis. However, its high cost and invasive nature have spurred the development of non-invasive alternatives. While Computational Fluid Dynamics (CFD) offers high accuracy, its clinical utility is hindered by long processing times. Analytical models have emerged as a rapid (sub-2-minute) alternative, but they often struggle with diagnostic accuracy in the "gray zone" (FFR 0.75–0.80), where clinical decision-making is most critical.
This study aims to enhance the predictive accuracy of an analytically determined FFR (aFFR) specifically within the diagnostic gray zone by refining the energy loss coefficients associated with boundary layer development and entry region effects.
We analyzed 40 patient-specific coronary artery datasets with borderline stenoses. 3D models were reconstructed from angiographic images. The total pressure drop (ΔP) was calculated as a summation of convection, contraction, diffusion, and sudden expansion losses. To optimize the model for intermediate lesions, we replaced fixed empirical constants with dynamic coefficients sensitive to the transitional Reynolds numbers typical of the 0.75–0.80 FFR range. Additionally, patient-specific aortic pressure (P_a) was integrated to replace standardized population averages.
Initial results indicate that the optimized analytical model reduced the misclassification rate in the gray zone by 14% compared to standard analytical approaches. The coefficient of determination (R^2) for lesions between 0.70 and 0.85 improved from 0.67 to 0.76. The average computation time remained under 120 seconds per case on a standard workstation.
Refining analytical energy loss equations allows for a highly efficient and more reliable non-invasive assessment of intermediate stenosis. This approach bridges the gap between the speed of analytical models and the precision of CFD, providing a viable tool for real-time clinical support in the catheterization laboratory.
Keywords: Stenosis, FFR, Analytical, Gray Zone