Input-adaptive linear mixed-effects model for estimating alveolar lung-deposited surface area (LDSA) using multipollutant datasets

Lung-deposited surface area (LDSA) has been considered to be a better metric to explain nanoparticle toxicity instead of the commonly used particulate mass concentration. LDSA concentrations can be obtained either by direct measurements or by calculation based on the empirical lung deposition model and measurements of particle size distribution. However, the LDSA or size distribution measurements are neither compulsory nor regulated by the government. As a result, LDSA data are often scarce spatially and temporally. In light of this, we developed a novel statistical model, named the input-adaptive mixed-effects (IAME) model, to estimate LDSA based on other already existing measurements of air pollutant variables and meteorological conditions. During the measurement period in 2017-2018, we retrieved LDSA data measured by Pegasor AQ Urban and other variables at a street canyon (SC, average LDSA Combining double low line 19.7 ± 11.3 μm2 cm-3) site and an urban background (UB, average LDSA Combining double low line 11.2 ± 7.1 μm2 cm-3) site in Helsinki, Finland. For the continuous estimation of LDSA, the IAME model was automatised to select the best combination of input variables, including a maximum of three fixed effect variables and three time indictors as random effect variables. Altogether, 696 submodels were generated and ranked by the coefficient of determination (R2), mean absolute error (MAE) and centred root-mean-square difference (cRMSD) in order. At the SC site, the LDSA concentrations were best estimated by mass concentration of particle of diameters smaller than 2.5 μm (PM2.5), total particle number concentration (PNC) and black carbon (BC), all of which are closely connected with the vehicular emissions. At the UB site, the LDSA concentrations were found to be correlated with PM2.5, BC and carbon monoxide (CO). The accuracy of the overall model was better at the SC site (R2Combining double low line0.80, MAE Combining double low line 3.7 μm2 cm-3) than at the UB site (R2Combining double low line0.77, MAE Combining double low line 2.3 μm2 cm-3), plausibly because the LDSA source was more tightly controlled by the close-by vehicular emission source. The results also demonstrated that the additional adjustment by taking random effects into account improved the sensitivity and the accuracy of the fixed effect model. Due to its adaptive input selection and inclusion of random effects, IAME could fill up missing data or even serve as a network of virtual sensors to complement the measurements at reference stations.