This paper models the behavior of the longitudinal relaxation rate of the protons of tissue water R(1) (R(1) = 1/T(1) ), measured in a Look-Locker experiment at 7 Tesla after administration of a paramagnetic contrast agent (CA). It solves the Bloch-McConnell equations for the longitudinal magnetization of the protons of water in a three-site two-exchange (3S2X) model with boundary conditions appropriate to repeated sampling of magnetization. The extent to which equilibrium intercompartmental water exchange kinetics affect monoexponential estimates of R(1) after administration of a CA in dynamic contrast enhanced experiment is described. The relation between R(1) and tissue CA concentration was calculated for CA restricted to the intravascular, or to the intravascular and extracellular compartments, by varying model parameters to mimic experimental data acquired in a rat model of cerebral tumor. The model described a nearly linear relationship between R(1) and tissue concentration of CA, but demonstrated that the apparent longitudinal relaxivity of CA depends upon tissue type. The practical consequence of this finding is that the extended Patlak plot linearizes the ΔR(1) data in tissue with leaky microvessels, accurately determines the influx rate of the CA across these microvessels, but underestimates the volume of intravascular blood water.
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