A parametric model of the brain vascular system for estimation of the arterial input function (AIF) at the tissue level

In this paper, we introduce a novel model of the brain vascular system, which is developed based on laws of fluid dynamics and vascular morphology. This model is used to address dispersion and delay of the arterial input function (AIF) at different levels of the vascular structure and to estimate the local AIF in DCE images. We developed a method based on the simplex algorithm and Akaike information criterion to estimate the likelihood of the contrast agent concentration signal sampled in DCE images belonging to different layers of the vascular tree or being a combination of different signal levels from different nodes of this structure. To evaluate this method, we tested the method on simulated local AIF signals at different levels of this structure. Even down to a signal to noise ratio of 5.5 our method was able to accurately detect the branching level of the simulated signals. When two signals with the same power level were combined, our method was able to separate the base signals of the composite AIF at the 50% threshold. We applied this method to dynamic contrast enhanced computed tomography (DCE‐CT) data, and using the parameters estimated by our method we created an arrival time map of the brain. Our model corrected AIF can be used for solving the pharmacokinetic equations for more accurate estimation of vascular permeability parameters in DCE imaging studies. We present a model of the cerebral vascular system based on vascular morphology and laws of fluid dynamics, to be used for estimating the local arterial input function in DSC and DCE MRI and DCE‐CT studies. Using this local arterial input function can reduce errors in estimation of permeability and perfusion parameters in these studies. The model was tested on DCE‐CT images by creating an arrival time map using the model parameters, which matched the expected values in the brain.