Time-Efficient Fourier Domain Evaluation of Pharmacokinetic Model in Dynamic Contrast-Enhanced Magnetic Resonance Imaging

摘要

Dynamic contrast-enhanced magnetic resonance imaging obtains information about tissue perfusion and permeability.Following the administration of a contrast agent,concentration-time curves measured in each voxel are fitted by a pharmacokinetic model formulated as a time-domain convolution of an arterial input function(AIF)and an impulse residue function(IRF).Since the measurement window contains hundreds of time samples,the discrete convolution is demanding,even when it is performed via discrete Fourier transform(DFT).Additionally,its discretization causes convergence complications in the curve fitting and it is not applicable to functions without a closed-form expression in the time domain,e.g.tissue homogeneity model IRF.Both issues can be solved by formulating the functions in a closed form in the Fourier domain.In the Fourier domain,the model transforms to multiplication of IRF and AIF,followed by the inverse DFT.To avoid time-domain aliasing,the number of samples in the Fourier domain must be higher than the sum of supports of the functions in the time domain.If the functions are slowly decaying exponentials,the support is theoretically infinite,which dramatically reduces the computational performance.In this contribution,we propose a modification of IRF in the Fourier domain to consider the measurement window.Our solution reduces the required number of samples to three times the measurement window compared to dozens needed without the modification and reduces the number of DFTs.This provides faster evaluation of the pharmacokinetic model and its derivatives for each voxel in each iteration of the curve fitting.