Unidirectional blood-to-brain and blood-to-tumour transport rate constants (K1) for 82Rb (half-life 76 s) and plasma water volume per unit mass of brain/tumour tissue (Vp) can be estimated in vivo using dynamic positron emission tomography (PET). The accuracy of these estimates depends upon the accuracy of PET measurements of regional brain/tumour radioactivity and scintillation well detector measurements of whole-blood radioactivity, which, in turn, depend upon the time course of arterial blood radioactivity. A two-compartmental model has been employed to derive estimates for K1, k2 (efflux rate constant) and Vp from 82Rb/PET data. Errors in these parameter estimates have been studied (1) qualitatively using sensitivity function analysis and (2) quantitatively using computer simulations. The effect of adding a third irreversible compartment and its unidirectional rate constant, k3, has also been investigated. The advantages and disadvantages of bolus injection vs continuous infusion protocols are discussed. Precision in estimated parameters from actual patient data is compared to that obtained from computer simulations in part II of this paper.