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A new formalism is presented for the destruction-replenishment perfusion quantification approach at low mechanical index. On the basis of physical considerations, best-fit methods should be applied using perfusion functions with S-shape characteristics. These functions are first described for the case of a geometry with a single flow velocity, then extended to the case of vascular beds with blood vessels having multiple flow velocity values and directions. The principles guiding the analysis are, on one hand, a linearization of video echo signals to overcome the log-compression of the imaging instrument, and, on the other hand, the spatial distribution of the transmit-receive ultrasound beam in the elevation direction. An in vitro model also is described; it was used to confirm experimentally the validity of the approach using a commercial contrast agent. The approach was implemented in the form of a computer program, taking as input a sequence of contrast-specific images, as well as parameters related to the ultrasound imaging equipment used. The generated output is either flow-parameter values computed in regions-of-interest, or parametric flow-images (e.g., mean velocity, mean transit time, mean flow, flow variance, or skewness). This approach thus establishes a base for extracting information about the morphology of vascular beds in vivo, and could allow absolute quantification provided that appropriate instrument calibration is implemented.