SUPPLEMENTARY INFORMATION
A Review of Hygroscopic Growth Factors of Submicron Aerosols
from Different Sources and its Implication for Calculation of
Lung Deposition Efficiency of Ambient Aerosols
Tuan V. Vu, Juana Maria Delgado-Saborit and Roy M.Harrison
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Modified Growth Factor of Particle in the Regional Lung
When a particle penetrates into the lung, its growth is not only controlled by its hygroscopic
properties but also due to its residence time. The submicron particles can growth rapidly while
larger particles may not reach their equilibrium size during the inhalation cycle.
To address the particle growth dependence of time, we used an approach provided by Ferron
(1977). The particle growth can be approximated by the following equation (ICRP, 1995):
𝐹(𝑡) =
𝐷𝑝 (𝑡)−𝐷𝑝(0)
𝐷𝑝(𝑒)−𝐷𝑝(0)
=
𝐷𝑝(0)∗[exp(−
0.6
10𝑡0.55
) −1]
𝐷𝑝(0)
(S1)
𝐷𝑝(𝑒)−𝐷𝑝(0)
Where, F(t) is fraction of equilibrium size, Dp(t) is particle size at t (s); Dp(0) is the initial dry
particle (µm), Dp(e): Equilibrium particle size (µm), and t is residence time in the lung (s).
The variation of the hygroscopic growth fraction as a function of time calculated from
different initial size of dry particles is shown in Figure S1:
Figure S1. The variation of the hygroscopic growth as function of time and size.
To estimate the growth factor in each lung region, we assumed that the residence time of
particles in the extra-thoracic (ET), tracheobronchial (TB), and alveolar (AL) regions are
0.116 s, 0.308 s and 1.32 s (respectively) during inspiration and 1.56 s, 0.356 s and 1.56 s
(respectively) during expiration with a pause time of 0.2 s (Ferron, 1977). The particle growth
factor in each region is calculated by:
𝑡2
∫ 𝐺𝑓′(𝑡) ∗ 𝑑𝑡
𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑑 𝐺𝑓 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑙𝑢𝑛𝑔 𝑟𝑒𝑔𝑖𝑜𝑛 = 𝑡1
𝑡2 − 𝑡1
Where, t1 and t2 are the time when particle comes in and out of the regional lung. For
example, t1=0 and t2=0.116 s for particles which come in and out the ET region during
inspiration.
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If we define 𝐺′𝑓(𝑡) as the growth factor of a particle at t (s) (𝐺′𝑓(𝑡) =
𝐷𝑝(𝑡)
), 𝐺𝑓(𝑚𝑎𝑥) is the
𝐷𝑝(0)
maximum growth factor of particles where particle can reach their equilibrium size
𝐷𝑝(𝑒)
( 𝐺𝑓(𝑚𝑎𝑥) = 𝐷𝑝(0), from equation S1) we have:
𝐺′𝑓(𝑡) = 𝐺𝑓(𝑚𝑎𝑥) + F(t)*( 𝐺𝑓(𝑚𝑎𝑥) − 1)
(S2)
Using Equation S2 in combination with the residence times of particles in each region, we can
calculate the growth factor of each particle in each region (at 37oC and 99.5% RH). Figure S2
shows the growth factor of hygroscopic particles from a rural environment in each region of
the lung.
Figure S2: Estimated hygroscopic growth factor of particles in different regions of the lung.
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