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A new signal model and processing method for quantitative ultrasound perfusion analysis is presented, called bolus-and-burst. The method has the potential to provide absolute values of blood flow, blood volume, and mean transit time. Furthermore, it provides an estimate of the local arterial input function which characterizes the arterial tree, allowing accurate estimation of the bolus arrival time. The method combines two approaches to ultrasound perfusion analysis: bolus-tracking and burst-replenishment. A pharmacokinetic model based on the concept of arterial input functions and tissue residue functions is used to model both the bolus and replenishment parts of the recording. The pharmacokinetic model is fitted to the data using blind deconvolution. A preliminary assessment of the new perfusion-analysis method is presented on clinical recordings.