||We present a method for absolutely quantifying pharmacokinetic parameters in dynamic contrast-enhanced (DCE)-MRI. This method, known as alternating mini-mization with model (AMM), involves jointly estimating the arterial input function (AIF) and pharmacokinetic parameters from a characteristic set of measured tissue concentration curves. By blindly estimating the AIF, problems associated with AIF measurement in pharmacokinetic modeling, such as signal saturation, flow and partial volume eff ects, and small arterial lumens can be ignored. The blind estimation method described here introduces a novel functional form for the AIF, which serves to simplify the estimation process and reduce the deleterious e ffects of noise on the deconvolution process. Computer simulations were undertaken to assess the performance of the estimation process as a function of the input tissue curves. A con fidence metric for the estimation quality, based on a linear combination of the SNR and diversity of the input curves, is presented. This con fidence metric is then used to allow for localizing the region from which input curves are drawn. Local blood supply to any particular region can then be blindly estimated, along with some measure of con fidence for that estimation. Methods for evaluating the utility of the blind estimation algorithm on clinical data are presented, along with preliminary results on quantifying tissue parameters in soft-tissue sarcomas. The AMM method is applied to in vivo data from both cardiac perfusion and breast cancer scans. The cardiac scans were conducted using a dual-bolus protocol, which provides a measure of truth for the AIF. Twenty data sets were processed with this method, and pharmacokinetic parameter values derived from the blind AIF were compared with those derived from the dual-bolus measured AIF. For seventeen of the twenty datasets there were no statistically signifi cant differences in Ktrans estimates. The cardiac AMM method presented here provides a way to quantify perfusion of myocardial tissue with a single injection of contrast agent and without a special pulse sequence. The resulting parameters are similar to those given by the dual bolus method. The breast cancer scans were processed with the AMM method and the results were compared to an analysis done with the semiquantitative DCE-MRI scans. The e ffects of the temporal sampling rate of the data on the AMM method are examined. The ability of the AMM-derived parameters to distinguish benign and malignant tumors is compared to more conventional methods.