Evaluation of the effect of arterial input function on cerebral blood flow in MR perfusion imaging

Cerebral blood flow (CBF) calculation in perfusion weighted imaging starts with the selection of arterial input function (AIF). CBF indicates the initial value of the tissue residue function found by deconvolving the tissue perfusion curve with the AIF. Conventional approach of CBF calculation by deconvolution is singular value decomposition (SVD) method. This technique is not successful if the problem is ill-posed, which is the case when the singular values of the solution decrease rapidly. The ill-posed nature of the problem is generally resolved through the model independent method based on Tikhonov regularization. In this method, optimum value of the regularization parameter is selected either according to the L-curve criterion, LCC, or by the generalized cross validation method, GCV. In this study, besides Tikhonov regularization, a more deterministic method, state space model fitting was employed as an alternative approach and CBF values were found in well agreement with those found by Tikhonov regularization. AIF is delayed and dispersed during the transition from the major artery to the small arterial branches feeding the tissue. Since delay compensation is possible by time shifting, we focused on dispersion in this study. To be able to analyze the effects of dispersion on CBF computation, time curves of AIF and the tissue response were simulated. Different levels of dispersion were produced resulting in AIFs that simulate the transition from arteries to arterial branches at distant locations of the brain. The results of the simulation studies indicate that, if ignored, dispersion might result in underestimated CBF.