Quantification of cerebral blood flow (CBF) and the tissue residue function (R) using bolus-tracking MRI requires deconvolution of the arterial input function (AIF). Currently, the most commonly used deconvolution method is singular value decomposition (SVD), which has been shown to produce accurate estimations of CBF. However, this method introduces unwanted oscillations in the time course of R, and there are situations in which the actual shape is of interest (e.g., in calculating flow heterogeneity and assessing bolus dispersion). In such cases, the conventional SVD method may no longer be suitable, and an alternative approach may be required. This work describes the implementation of Tikhonov regularization with the L-curve criterion to quantify CBF and obtain a better characterization of R. The methodology is tested on simulated and patient data, and the results are compared to those found using the conventional SVD approach. Although both methods produce similar CBF values, the deconvolved R shape obtained using SVD is dominated by oscillations and fails to characterize the shape in the presence of dispersion. On the other hand, the use of the proposed regularization method improves the char- Key words: perfusion; dynamic susceptibility contrast MRI; deconvolution; singular value decomposition; arterial input function Bolus-tracking MRI, also known as dynamic susceptibility contrast MRI, is becoming a well-established technique for measuring cerebral blood flow (CBF) (1). The most important clinical application by far is in the investigation of cerebral ischemia. Although some limitations have been reported (2,3), this technique is playing an increasingly important role in the diagnosis, assessment, and management of acute stroke patients (4 -7).The fundamental equation for CBF quantification is (8):where C(t) is the tissue concentration time curve, C a (t) is the arterial input function (AIF; i.e., the concentration of contrast entering the tissue of interest at time t), R(t) is the tissue residue function (i.e., the fraction of contrast agent concentration at time t for the case of an ideal instantaneous bolus injected at t ϭ 0), and the symbol V indicates the convolution operation (1). Bolus-tracking MRI relies on the deconvolution of the AIF to obtain the product function CBF ⅐ R(t), and the calculation of CBF from the initial (or maximum) value of this function (8). Currently, the most common deconvolution method is singular value decomposition (SVD), which has been shown to produce fairly accurate estimations of CBF (8). However, this method introduces unwanted oscillations 1 in the shape of R(t) (9,10), and there are situations in which the actual shape of R(t)-not just its initial value-is of interest. For example, the determination of flow heterogeneity and oxygen delivery relies on characterization of the whole residue function (11). In addition, the presence of bolus dispersion has been shown to be a significant source of error in CBF quantification (11,12), and accurate determination of the sha...