An alternative viewpoint of the similarities and differences of SVD and FT deconvolution algorithms used for quantitative MR perfusion studies.

Quantitative cerebral blood flow (CBF) values can be determined from residue function estimates obtained from magnetic resonance dynamic susceptibility contrast (DSC) perfusion studies using a variety of deconvolution approaches. However, there are significant differences between the CBF estimates obtained, differences that are not simply due to minor details of the implementation of the algorithms. The standard singular value decomposition (sSVD) shows a variation of CBF values with arterial-tissue delay (ATD) not present with the Fourier transform deconvolution algorithm. Fourier transform deconvolution and the newly suggested delay-invariant SVD algorithm implementations provide CBF estimates whose accuracy changes with tissue mean transit times (MTTs). Techniques combining sSVD with deliberate ATD manipulation have been proposed to compensate for this inaccuracy. Other studies indicate that CBF changes related to slice position in a multislice study, and other experimental factors, can be reduced using interpolative deconvolution algorithms. In this review, we use both time-domain and frequency-domain analysis to show the underlying theoretical relationships between these many approaches to obtain "the best" CBF estimate. This model allows us to better understand the similarities and differences, advantages and disadvantages between these variants of the deconvolution algorithms used in DSC perfusion studies.