Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four 2 cows were obtained following rapid injection of para-aminohippuric acid (PAH) plus glucose 3 into the external iliac artery. For the measurement of extracellular volume and kinetics of 4 nutrient uptake from indicator dilution curves, several models of solute dispersion and 5 disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary 6 assume negligible washout of solutes from the extracellular space and do not describe entire 7 dilution curves. The Goresky models include a distribution of capillary transit times to generate 8 whole system outflow profiles but require two indicators to parametize extracellular behavior. A 9 compartmental capillary, convolution integration model is proposed that uses one indicator to 10 account for the extracellular behavior of the nutrient following a paired indicator/nutrient 11 injection. Using an iterative approach to least squares, unique solutions for non-exchanging 12 vessel transit time ^- µ and its variance were obtained from all 33 PAH curves. The average of 13 heterogeneous vascular transit times was approximated as 2 = 8.5 s. The remainder of indicator 14 dispersion was considered to be due to washout from a well-mixed compartment representing 15 extracellular space which had an estimated volume of 5.5 L or 24% of mammary gland weight. 16 More than 99% of the variation in the timecourse of venous PAH concentration following rapid 17 injection into the arterial supply of the mammary glands was explained in an unbiased manner by 18 partitioning the organ into a heterogeneous non-exchanging vessel subsystem and a well-mixed 19 compartmental capillary subsystem.