Mathematical Modeling to Predict the Responses to Poorly Soluble Particles in Rat Lungs

Abstract

Rat inhalation experiments with titanium dioxide (TiO₂) and barium sulfate (BaSO₄), at concentrations calculated to produce similar volumetric lung burden for both dusts, showed overload with TIO₂ but not for BaSO₄ “Overload,” occurring in rats exposed to “low-toxicity” dusts at high concentrations, is characterized by a rapid deterioration in clearance and onset of inflammation. Impairment of alveolar macrophage (AM) mediated clearance, dust translocation to the lymph nodes, and neutrophil (PMN) recruitment for both dusts were better predicted by the lung burden expressed as surface area rather than mass or volume. A mathematical model describing the translocation (in terms of particulate mass) of inhaled particles in various physiologically based pulmonary compartments was used to calculate pulmonary clearance when effective and also when impairment by overload leads to increased dust translocation to the lymph nodes. Our objectives were: (I) to modify this model to include the influence of particle surface area on clearance and interstitialization; (2) to extend the model to describe the PMN recruitment; and (3) to use the model to estimate the highest exposure level such that overload would be avoided in a chronic inhalation experiment with rats. In extrapolating down to no-overload concentrations, due account was taken of the observed interanimal variation (assuming this variation was mainly due to differences in inhaled dose). For TiO₂ and BaSO₄, with the given size distributions, the predicted concentrations at which 95% of the animals were expected to avoid overload were 3 mg m⁻³ and 7.5 mg m⁻³, respectively. The general quantitative relationships on the role of particle surface area and on the estimation of the no-overload level have important implications for setting standards for poorly soluble particles.