FIG. 1.

LCFR methodology and validation with in silico phantoms. (a) Methodology of localized convolutional function regression (LCFR), wherein spatiotemporal contrast agent concentration data are convolved with a smooth basis-function and its derivatives, divided into 3 × 3 × 3 (x, y, z) windows. The coefficients of the factored transport PDE are then solved for using linear regression. (b) Validation of LCFR coefficient $\overrightarrow{{\xi }_u}$ on a divergent flow field (initial condition, white) with spatially invariant diffusion and the true direction and magnitude of velocity denoted in red bars. (c) Validation of LCFR on a Poiseuille shear flow field with spatially invariant diffusion (initial condition, white) and the true direction and magnitude of velocity denoted in red bars.