Single voxel vascular transport functions of arteries, capillaries and veins; and the associated arterial input function in dynamic susceptibility contrast magnetic resonance brain perfusion imaging

Abstract

Purpose: The composite vascular transport function of a brain voxel consists of one convolutional component for the arteries, one for the capillaries and one for the veins in the voxel of interest. Here, the goal is to find each of these three convolutional components and the associated arterial input function.

Pharmacokinetic modelling: The single voxel vascular transport functions for arteries, capillaries and veins were all modelled as causal exponential functions. Each observed multipass tissue contrast function was as a first approximation modelled as the resulting parametric composite vascular transport function convolved with a nonparametric and voxel specific multipass arterial input function. Subsequently, the residue function was used in the true perfusion equation to optimize the three parameters of the exponential functions.

Deconvolution methods: For each voxel, the parameters of the three exponential functions were estimated by successive iterative blind deconvolutions using versions of the Lucy-Richardson algorithm. The final multipass arterial input function was then computed by nonblind deconvolution using the Lucy-Richardson algorithm and the estimated composite vascular transport function.

Results: Simulations showed that the algorithm worked. The estimated mean transit time of arteries, capillaries and veins of the simulated data agreed with the known input values. For real data, the estimated capillary mean transit times agreed with known values for this parameter. The nonparametric multipass arterial input functions were used to derive the associated map of the arrival time. The arrival time map of a healthy volunteer agreed with known arterial anatomy and physiology.

Conclusion: Clinically important new voxelwise hemodynamic information for arteries, capillaries and veins separately can be estimated using multipass tissue contrast functions and the iterative blind Lucy-Richardson deconvolution algorithm.

Keywords: Arterial input functions; Brain perfusion; DSC-MRI; Mean transit times; Vascular transport functions.