Bolus tracking magnetic resonance imaging (MRI) is a powerful technique for measuring perfusion, and is playing an increasing role in the investigation of acute stroke. However, limitations have been reported when assessing patients with steno-occlusive disease. The presence of a steno-occlusive disease in the artery may cause bolus dispersion, which has been shown to introduce significant errors in cerebral blood flow (CBF) quantification. Bolus dispersion is commonly described by a vascular transport function, but the function that properly characterizes the dispersion is unknown. A novel method to quantify bolus dispersion errors on perfusion measurements is presented. A realistic patient-specific model is constructed from anatomical and physiologic MR data, and the arterial blood flow pattern and the transport of the bolus of contrast agent are computed using finite element analysis. The methodology presented was used also to evaluate the accuracy of three simple vascular models. The methodology was tested on MR data from two normal subjects and two subjects with mild carotid artery stenosis. The estimated CBF errors were of the order of 15% to 20%. However, the presence of stenosis did not necessarily introduce larger dispersion (not only the geometrical model but also the particular physiologic conditions influence the degree of bolus dispersion). The method described will contribute to a better understanding of errors introduced by dispersion effects, to the assessment and validation of vascular models, and to the development of new methods for the correction of dispersion errors in CBF quantification.