Modeling physiological processes using tracer kinetic methods implies knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We wish to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anaesthetized pigs following inhalation of intravascular [¹⁵O]-carbon monoxide (CO) or injections of diffusible 3-O-[¹¹C]methylglucose (MG). The parameters of the impulse response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time T and standard deviation of transit times . The results include estimates of mean transit times from the aorta to the portal vein in pigs: T = 0.35 ± 0.05 min for CO and T = 1.7 ± 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggest that the proposed model can be adapted for use in humans.