Development and extension of a bio-mathematical model in rats to describe particle specific clearance and translocation of inhaled particles and early biological responses.

A number of studies have investigated the bio kinetics of the translocation of inhaled nanoparticles in different target organs using animal experiments. These studies provide details of how nanoparticles distribute in the body after inhalation and the amount of particles in organs within the body. These data provide a means to model the inhalation and translocation of nanoparticles. A model of the compartments of the body was drawn based on biological information about the major organs and how they relate to one another. This model is quantified by a set of differentialequations ‘describing’ the passage of nanoparticles through the body and gives estimates of the mass of inhaled particles that are present in each organ. The optimal estimates of the parameters of the model were found by minimising the model MSE. The modelling and minimisation were carried out for data from a number of experiments. One provided data from an endotracheal instillation study. After carrying out the parameter optimization the results from the model gave estimates close (R2 = 0.99) to the actual amount of nano particles in the lung, brain, kidney, liver and spleen. The second paper used a different method of exposure, inhalation, and particle size, so although the same model structure was used the estimates of the unknown parameters were different, but still gave results close to the amounts measured in the study (R2 = 0.98). Injection was the exposure method of the third paper, which again resulted in different estimates of the parameters but a close fit to the data (R2 = 0.94). Plots confirmed how closely the fitted values matched the actual data. The model of compartments describes the translocation of nano particles reasonably well. The estimates of the unknown parameters, however, are dependent on the method of exposure and possibly particle size. Using new data some validation of the model was attempted. This data also enabled an extension to the model to estimate the dose-response. Further validation of each model (instillation, inhalation, injection and that including dose-response) needs to carried out in the near future using new data.