Modeling kinetics of infused ¹³NN-saline in acute lung injury

A mathematical model was developed to estimate right-to-left shunt (F _s) and the volume of distribution of ¹³NN in alveolar gas (V_A) and shunt tissue (V_s). 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. F_s derived from the model correlated well with shunt estimates derived from O₂ blood concentrations and from PET images. F_s was higher for LS (54 18%) than for LP (5 ± 4%) and NP (1 ± 1%, P < 0.01). V_A, 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 V_s, 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 F_s, 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.