The authors developed a transmission-dispersion model to estimate dispersion in blood sampling systems and to calculate dispersion-free input functions needed for kinetic analysis. Transport of molecules through catheters was considered in two parts: a central part with convective transmission of molecules and a stagnant layer that molecules may enter and leave. The authors measured dispersion caused by automatic and manual blood sampling using three PET tracers that distribute differently in blood (C15O, H2(15)O, and 11C-methylglucose). For manual sampling, dispersion was negligible. For the automated sampling procedure, characteristic parameters were calibrated for each tracer, and subsequently used in calculating dispersion-free input functions following real bolus injections. This led to shapes of dispersion-free input functions C(i)(t) that had sharper peaks than the measured C(o)(t), and the authors quantified the effect of correcting for dispersion before kinetic modeling. The transmission-dispersion model quantitatively takes apart effects of transmission and dispersion, it has transparent noise properties associated with each component, and it does not require deconvolution to calculate dispersion-free input functions. Once characteristic parameters are estimated, input functions can be corrected before applying kinetic models. This allows bias-free estimation of kinetic parameters such as blood flow.