Arterial spin labeling (ASL) is a method of using MRI to image cerebral perfusion. For the measurement to be calibrated, a model is required describing the kinetics of the flow of the inverted blood from the labeling region to the imaging region. It is common to assume plug-flow, but alternatives such as a Gaussian distribution of arrival times have also been suggested. In this study a physiologically based model for dispersion is developed and compared to existing models when fit to experimental data. The model is based on the assumption of parabolic flow in the major arteries, and also allows inclusion of cardiac pulsatility. It was found that fitting using the proposed model leads to higher perfusion estimates, with the difference becoming more pronounced in regions where the dispersion is greater. This suggests that current models may underestimate perfusion in these areas. However, fitting using the proposed model also leads to high uncertainties in parameter estimates due to non-orthogonality of the parameters. Effects due to pulsatility are expected to be observable, but when no cardiacgating is used the mean curve over several cardiac cycles is predicted to closely match the curve which assumes constant flow.