On the Form of the Residue Function for Brain Tissue

Peter Gall¹, Valerij Kiselev¹

The residue function, R(t), is fundamental for description of microcirculation. To define this function is one of the aims of DSC perfusion MRI. It is found by solving an ill-posed problem, the deconvolution, for which one of approaches is to fit a model R(t) to data. Commonly, phenomenological functional shapes are used to model R(t) respecting only its most general properties. Studies based on ASL indicate insufficiency of this approach. In this work we present a derivation the residue function from the laws of laminar flow and a model for the architecture of the vascular tree.