Image-based blood flow estimation using a semi-analytical solution to the advection–diffusion equation in cylindrical domains. (10th October 2021) - Bakker, L.M.M.L.; Xiao, N.; van de Ven, A.A.F.; Schaap, M.; van de Vosse, F.N.; Taylor, C.A.
Abstract: Abstract : We propose a semi-analytical solution for the advection–diffusion equation in cylindrical domains, with an aim towards extracting blood flow rates from contrast variations in a coronary computed tomography angiography image. The solution proposed in this work, in contrast with existing methods, which only consider advection, incorporates both radial velocity variation and diffusion. By means of a Galerkin approach using Bessel functions, a solution for a three-dimensional concentration field at a single time point is obtained after a Laplace transformation. This semi-analytical solution forms the basis for a novel advection–diffusion flow estimation (ADFE) method. The ADFE is derived, validated through numerical spectral-element method computations, and shown to exhibit improved accuracy against the state-of-the-art method for image-based blood flow extraction.