## 3.1 Deposition measurements and comparison to models and lung variables

One of the purposes of the current study is to prove, or disprove, our earlier finding of significantly higher measured DF compared to those modelled using whole lung models [1, 2]. Such differences are important to investigate since, according to the experimental data, they would result in underestimations of the modelled deposited particle doses.

In the earlier study, the DF was measured using a set-up with a polydisperse aerosol. Using a polydisperse aerosol is an efficient way to measure DF over a range of particle sizes in parallel. However, the main drawback is that errors might be introduced by slight shifts in particle size in-between the sizing of the inhaled and exhaled aerosol. The three whole lung models used were also included in the current study (ICRP, NCRP and MPPD-Y&S), also using *T**bc*, *V**T* and FRC measured for each subject as input variables.

The here reported average DFmeas (0.60 ± 0.12) is somewhat lower, but close to that reported for 2.3 µm particles in the earlier study for adults (0.63 ± 0.11) [1]. The groups of participants were different in the two studies and the measurements were performed under spontaneous breathing. Thus, the relatively small difference in averages between the two studies may be due to a combination of different breathing variables (*V**T* = 0.94 L vs 0.75 L, and *T**bc* = 0.11 min− 1 vs 0.10 min− 1), lung function, and systematic experimental errors. *V**T* was highest in the present study, which would result in higher DFs [2], if all other lung properties were the same (opposite to the observation). On the other hand, the average FRC was higher in the current study than in the study from 2017 (3.9 L compared to 3.4 L), and FRC is known to correlate negatively with DF, which would result in lower DFs in the current study (in accordance with the observation). Nevertheless, all models predicted a lower DF than that measured, confirming the main observations made in the study by Rissler et al. [2].

Some of the reported DF from the 1980s [9, 20] was lower than those presented here. However, those DF measurements were performed for a small group of male subjects with typically larger lungs than the subjects in this study, possibly explaining parts of the deviation. Also, aerosol instrumentation has been improved over time. The somewhat later study by Bennett and co-authors [30], also reported relatively low DF for 2 µm particles (~ 0.30). Later experimental studies report higher DF for coarse particles than those reported by both Heyder and co-authors and Bennett and co-authors, as for example the study by Kim co-authors [17] showing just somewhat lower DF than here found. In an older study by Giacomelli-Maltoni and co-authors [14] similar average DF as in this, and in our previous study [1, 2], was reported. The large variation in experimental studies points towards that the experimental methods have limitations. There is no standard methodology for measurement of the respiratory tract deposition fraction (DF) of inhaled particles and many studies have overlooked critical methodological aspects that may have biased data [6]. In the current study, the system was optimized to minimize any foreseen experimental sources of errors.

The MPPD model, implemented using the recently developed PNNL lung model, was the model that best described the measured DF, both with respect to predicted average DF and with the highest correlation coefficients between predicted and measured DF for individual subjects. For the individuals with the lowest DF (~ 0.4), the predicted DF was very close to that measured, while for subjects with higher DF, the model showed lower DF. However, even though the MPPD-PNNL was the model best describing the measured DF for coarse particles, we have earlier shown that MPPD-Y&S well described the measured DF for submicron particles in the size range from 10 nm to 500 nm [1]. Since the DF predicted using the MPPD-PNNL model in the submicron range is higher than that predicted using the MPPD-Y&S (see Figure A1, Additional file 4) one could expect the MPPD-PNNL model to predict DF higher than those measured in the previous study of Rissler and co-authors.

Another observation made is that the individual variation predicted by all models was smaller than the individual variation found in the measurements. It is well established that the variation in DF to a large extent is driven by *V**T* and *T**bc* [17, 31], as also confirmed in our study (see Table 2). However, the lung properties will also result in individual variations, but this is scarcely studied. In earlier studies by Heyder and co-authors [20, 32] it was suggested that the volume of the breath that reaches the peripheral lung and the residence time of the air in the peripheral lung are two important variables explaining the variation in DF. This was in line with the observation made in our earlier study, where it was shown that, apart from breathing pattern, anatomic dead space and R5 (output from oscillometry) could better describe the individual variation than FRC [2]. The observed correlation with anatomic dead space is in line with the suggestion of Heyder and co-authors since the fraction of the *V**T* reaching the peripheral lung is proportional to anatomic dead space.

In both the semi-empirical regional compartment models (e.g. ICRP and NCRP) and the multiple path model (MPPD), FRC is the lung property that is used to scale lung size. From the correlation analysis we see that including the FRC of each subject does improve the correlation between modelled and measured DF. However, there is still variations in DF that are not explained by neither breathing pattern nor FRC. As stated already in the study by Heyder et al. [20], and confirmed by results from the models applied in the current study (see Table 3), 2 µm sized particles are mainly deposited in the peripheral lung by sedimentation (at relaxed breathing at rest).

The rationale behind including the new AiDA technique as a lung function test in the current study is that *r*AiDA is a lung function variable that could provide a measure of airspaces in the acinar region of the lungs, and thus should correlate with the lung deposition of the 2 µm particles (mainly deposited in the peripheral lung). From the correlation analysis we see that *r*AiDA,1/2 correlate with DFmeas, and in fact has the strongest correlation, also when including *V**T* and *T**bc* as variables in the multiple regression analysis. This fact indicates that *r*AiDA,1/2 is indeed measuring the distances in the peripheral lung and that *r*AiDA,1/2 could provide crucial information needed to explain the individual variation in the deposited fraction of the inhaled particles.

To further investigate this, we looked at the correlation between lung function variables and the difference in modelled and measured DF (DFdiff defined as DFmod - DFmeas). This step was performed to see if any measure of the lung properties could explain the remaining variability after accounting for FRC and breathing variables in the models. As expected, FRC (and thus VC) correlated with DF for the models that did not include FRC for scaling the lungs. Even though *V**T* and *T**bc* were used as input to the models, DFdiff correlated negatively with *T**bc* and *V**T* for ICRP and MPPD-PNNL. This could indicate that the models overestimate the effect of *T**bc* and *V**T*. The strongest correlation with DFdiff was found to be that with *r*AiDA,1/2, which is a measure of the radius of airspaces in primarily the acini at normal breathing.

Multivariate linear regression models were applied to explain DFdiff for the models where FRC was varied for each individual (group A), and those where FRC was fixed (group B). In the analysis we only included the variables that were significantly correlated to DFdiff for any of the models in each group (p < 0.05), which for group A were VC, FEV1, *r*AiDA,1/2, *T*bc, and *V*T and for group B were FRC, R5, *R*0 and *r*AiDA,1/2. As can be seen from the results (given in Table A4 and A5 in Additional file 2), *r*AiDA,1/2 can significantly explain the difference between the measured and modelled DF, further supporting that *r*AiDA,1/2 is a measure of the lung properties that explains much of the individual variation.

Often lung deposition of inhaled drugs is estimated using whole lung models. However, such models do not differentiate between healthy and diseased lungs. We here show that the individual variation in DF is explained by the structure of the peripheral lung through measurement of *r*AiDA,1/2 in healthy subjects. Lung diseases and age cause a change in distal airspace size [33], an effect that has been shown to be measurable with AiDA [34, 35]. Using *r*AiDA and/or *r*AiDA,1/2 in models used for particle deposition modelling could presumably improve.

## 3.2 AiDA at half inflation

In this study, the *r*AiDA was for the first time measured at half inflation as this would provide peripheral airspace dimensions closer to those at normal relaxed breathing. Based on the breathing pattern logged before and during the inhalation manoeuvre in the AiDA instrument, we see that the lung inflation at half VC is very close to FRC. This could be the reason that *r**AiDA,1/2* (at half inflation) has a stronger correlation with DF than *r**AiDA* (at full inflation).

In accordance with the hypothesis, the measured *r*AiDA,1/2 was typically lower than *r*AiDA (280 ± 36 µm compared to 261 ± 36 µm), with a ratio of 1.11. Assuming a symmetric expansion of the lung, the ratio was predicted to 1.09, based on RV and the volumes inhaled during the AiDA measurement (Eq. 3). Despite small difference in airspace dimensions at full and half inflation, the AiDA values are in agreement with the prediction on a group level. This observation strengthens the hypothesis that *r*AiDA is indeed a measure of the average radius of the airspaces in the acinar region of the lungs [35].

It is not yet fully concluded what *R*0 is a measure of, but one hypothesis is that it reflects geometric properties, such as heterogeneity, of small conducting airways. The average *R**0* measured at half inflation was significantly lower than that measured at full inflation, which agrees with earlier observations [36]. The observed decrease in *R*0 can be explained by less deposition in the conducting airways at a shorter and shallower breathing cycle. However, *R*0 measured at full inflation has earlier been shown to correlate with measures of lung heterogeneity [35, 37]. The decreased *R**0* at the smaller inhaled volume with particles could also be due to a larger influence of entrainment and mixing with particle free air from the residual volume (the relative volume of air with particles is smaller at half inflation compared to the particle free air in the residual volume), which would strengthen the hypothesis that *R**0* is a measure of lung heterogeneity.

## 3.4 Estimation and discussion of experimental errors

The set-up was built according to the criteria given and discussed by Löndahl and co-authors [6]. The experimental set-up to measure the DF was carefully designed to minimize any foreseen systematic or randomized errors (optimizing precision and accuracy in the measurement). Furthermore, the system was designed to minimise particle losses and the flow lines from the inhalation and exhalation tank were made symmetric to have as similar losses as possible. The dead space volume of the mouthpiece was minimized and further corrected for (minimized to reduce the correction and potential errors) as described by Equations 1 and 2. In the earlier set-up only one APS was used. The major reason for this was that we avoid any error due to instrumental differences. However, when having only one instrument, alternating between sampling from the inhalation and exhalation tank, any drift in particle concentration over time can introduce a substantial error in the determined DF. Therefore, two APSs were used in the current experimental set-up.

The estimated errors are shown as error bars in Fig. 2. The error is estimated considering several factors, added assuming that they are uncorrelated. The factors included in the error propagation are gradients in the particle concentration, variations in APS counting efficiency, uncertainty in the loss calibration curve, non-isokinetic sampling efficiency, and factors related to uncertainties in breathing variables, including breathing frequency determined by the algorithm, tidal volume measured by the pneumotachograph, and effects of the periodization. The error in tidal volume and breathing frequency was translated to an error in DF according to their respective effect on DF as predicted by the model described in the study by Kim and Hu [17]. The largest errors were introduced by uncertainty in the determination of instrumental particle losses and gradients in particle concentration, due to the time it takes for the aerosol to pass from the inhalation sampling point to the point of the sampling from the exhalation tank (residence time in the lungs and in the system was not considered in the data analysis).