A mathematical model was developed to estimate right-to-left shunt (Fs) and the volume of distribution of 13NN in alveolar gas (VA) and shunt tissue (Vs). The data obtained from this model are complementary to, and obtained simultaneously with, pulmonary functional positron emission tomography (PET). The model describes 13NN kinetics in four compartments: central mixing volume, gas-exchanging lung, shunting compartment, and systemic recirculation. To validate the model, five normal prone (NP) and six surfactant-depleted sheep in the supine (LS) and prone (LP) positions were studied under general anesthesia. A central venous bolus of 13NN-labeled saline was injected at the onset of apnea as PET imaging and arterial 13NN sampling were initiated. The model fit the tracer kinetics well (mean r2 = 0.93). Monte Carlo simulations showed that parameters could be accurately identified in the presence of expected experimental noise. Fs derived from the model correlated well with shunt estimates derived from O2 blood concentrations and from PET images. Fs was higher for LS (54 +/- 18%) than for LP (5 +/- 4%) and NP (1 +/- 1%, P < 0.01). VA, as a fraction of PET-measured lung gas volume, was lower for LS (0.18 +/- 0.09) than for LP (0.96 +/- 0.28, P < 0.01), whereas Vs, as a fraction of PET-measured lung tissue volume, was higher for LS (0.46 +/- 0.26) than for LP (0.05 +/- 0.08, P < 0.01). The main conclusions are as follows: 1) the model accurately describes measured arterial 13NN kinetics and provides estimates of Fs, and 2) in this animal model of acute lung injury, the fraction of available gas volume participating in gas exchange is reduced in the supine position.