One-compartment models are widely used to quantify hemodynamic parameters such as perfusion, blood volume and mean transit time. These parameters are routinely used for clinical diagnosis and monitoring of disease development and are thus of high relevance. However, it is known that common estimation techniques are discretization dependent and values can be erroneous. In this paper we present a new model that enables systematic quantification of discretization errors. Specifically, we introduce a continuous flow model for tracer propagation within the capillary tissue, used to evaluate state-of-the-art one-compartment models. We demonstrate that one-compartment models are capable of recovering perfusion accurately when applied to only one compartment, i.e. the whole region of interest. However, substantial overestimation of perfusion occurs when applied to fractions of a compartment. We further provide values of the estimated overestimation for various discretization levels, and also show that overestimation can be observed in real-life applications. Common practice of using compartment models for fractions of tissue violates model assumptions and careful interpretation is needed when using the computed values for diagnosis and treatment planning.