A new approach to modeling the signal observed in arterial spin labeling (ASL) experiments during changing perfusion conditions is presented in this article. The new model uses numerical methods to extend first-order kinetic principles to include the changes in arrival time of the arterial tag that occur during neuronal activation. Estimation of the perfusion function from the ASL signal using this model is also demonstrated. The estimation algorithm uses a roughness penalty as well as prior information. The approach is demonstrated in numerical simulations and human experiments. The approach presented here is particularly suitable for fast ASL acquisition schemes, such as turbo continuous ASL (Turbo-CASL), which allows subtraction pairs to be acquired in less than 3 s but is sensitive to arrival time changes. This modeling approach can also be extended to other acquisition schemes. Magn Reson Med, 2005. © 2005 Wiley-Liss, Inc.