The requirements for understanding the role played by the circle of Willis in the cerebral circulation are two-fold: 1. The basic patterns of blood flow in the circle of Willis should be studied in relation to the interindividual variation of the circle itself and 2. The interindividual variation should be investigated in a quantitative way and possible hemodynamically induced relations should be clarified. With regard to the first question an extensive study on mathematical models of the cerebral circulation was performed, revealing that flow patterns can be understood by applying the principles of the Wheatstone bridge, known from electric circuit theory. With this knowledge the question of the variability was investigated. For this purpose 19 measurements of 100 circles of Willis were obtained from human cadavers. This data set was analysed using both bivariate and multivariate statistical techniques. The result of this analysis indicated that several sources of variation are involved. The first one is the size: some people have larger vessels than others, probably depending on age sex and genetic factors. Other sources of variation appeared to be of hemodynamic origin. The clear hemodynamic relation between vessel sizes in the circle of Willis indicate that they are adapted to the amount of flow, just like vessels elsewhere in the body. For instance, the size of the posterior communicating artery reflects the relative contribution of the anterior (carotid) and posterior (vertebral) vessels to the cerebral circulation. Furthermore, a relation could be established between the variations of the major cerebral vascular territories and the circle of Willis, both during development and in adults.(ABSTRACT TRUNCATED AT 250 WORDS)