Preprint for publication: Transport and Deposition of Inhaled Fibres in a Realistic Female Airway Model: A Combined Experimental and Numerical Study

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Highligh s
T anspo and Deposi ion o Inhaled Fibe s in a Realis ic Female Ai way Model: A
Combined Expe imen al and Nume ical S udy
F an iˇsek P inz, Jana K´ansk´a, Jakub Elcne , Ondˇ ej H´ajek, Ad ian Kumme l¨ande , Ma hias J.
K ause, Mi osla J´ıcha, F an iˇsek L´ızal
•ELER coupled wi h LBM was success ully applied in a ealis ic emale ai way model
•Nume ical esul s sligh ly o e es ima ed deposi ion, mainly in bi u ca ions
•Time-dependen deposi ion analysis p o ides insigh s o op imizing ae osol deli e y
•Limi a ions o echniques o modeling ibe s in complex lows we e iden i ied
•O ien a ion-dependen calcula ion is c ucial o accu a e deposi ion p edic ion
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T anspo and Deposi ion o Inhaled Fibe s in a Realis ic Female Ai way
Model: A Combined Expe imen al and Nume ical S udy
F an iˇsek P inza,∗, Jana K´ansk´aa, Jakub Elcne a, Ondˇ ej H´ajeka, Ad ian Kumme l¨ande b,
Ma hias J. K auseb, Mi osla J´ıchaa, F an iˇsek L´ızala
aB no Uni e si y o Technology, Technicka 2896, B no, 616 69, Czech Republic
bKa ls uhe Ins i u e o Technology, Kaise s aße 12, Ka ls uhe, 76131, Ge many
Abs ac
This s udy p esen s a combined expe imen al and nume ical in es iga ion o ibe anspo and
deposi ion in a ealis ic model o he emale espi a o y ac , ex ending o he se en h gene a ion
o b anching. Nume ical simula ions we e pe o med using he Eule -Lag ange Eule -Ro a ion
(ELER) me hod, an e icien al e na i e o con en ional Fini e Volume Me hods ha bene i s om
explici o mula ion and as scalabili y, enabling as pa alleliza ion on high-pe o mance clus e s.
The ELER me hod was coupled wi h he La ice Bol zmann Me hod (LBM) o simula e ibe
dynamics unde a ealis ic inspi a o y low p o ile. Expe imen al alida ion was conduc ed using
an iden ical physical ai way eplica. The esul s demons a ed good ag eemen be ween simula ions
and expe imen s in he uppe ai ways and achea, wi h some disc epancies in he bi u ca ions,
likely owing o he challenges o modeling complex u bulen low wi h ELER. This me hod is mo e
accu a e han co esponding e ec i e diame e simula ions. Deposi ion pa e ns we e analyzed as
a unc ion o ibe dimensions, e ealing highe accu acy o he ELER me hod o smalle pa icles
and con i ming he endency o highe aspec a io ibe s o pene a e deepe in o he lungs.
The o ien a ion-dependen deposi ion mechanism was deployed, unde sco ing he impo ance o
sol ing he ac ual o ien a ions o he ibe s. While ad ancing ou unde s anding o ibe anspo
in emale ai ways, he indings also e eal limi a ions in cu en nume ical echniques, pa icula ly
in bi u ca ions. This s udy emphasizes he dis inc beha io o ib ous e sus sphe ical pa icles,
wi h ibe s exhibi ing a g ea e p opensi y o each deepe lung egions, which has signi ican
implica ions o inhala ion oxicology and d ug deli e y.
Keywo ds: ibe anspo , deposi ion, in i o, in silico, emale ai way geome y, La ice
Bol zmann Me hod, Eule -Lag ange Eule -Ro a ion
1. In oduc ion
The s udy o pa icle anspo and deposi ion wi hin he human espi a o y sys em is essen ial
o unde s anding a ious physiological and pa hological p ocesses as well as o de eloping e ec i e
d ug deli e y s a egies. While conside able esea ch has ocused on male ai way models, he e is a
g owing ecogni ion o he need o in es iga e emale-speci ic ai way geome ies due o signi ican
∗Co esponding au ho
Email add ess: [email p o ec ed] (F an iˇsek P inz)
P ep in submi ed o Compu e s in Biology and Medicine May 13, 2025
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ana omical and physiological di e ences be ween sexes [1, 2, 3]. Females exhibi smalle ai way di-
ame e s, pa icula ly in he pha ynx and elopha ynx [4], di e ences in lung olume and b ea hing
pa e ns [5], and ho monal in luences ha can a ec ai way esponsi eness [6]. These di e ences
can in luence ai low pa e ns, pa icle deposi ion, and ul ima ely, he e icacy and sa e y o inhaled
he apies [7]. To add ess his gap in ou unde s anding o emale-speci ic ae osol deposi ion, ou
s udy u ilizes a ealis ic emale ai way model supplemen ed wi h idal olume and a b ea hing
pa e n ypical o emales.
Fib ous pa icle anspo has signi ican implica ions in bo h sa e y and enginee ing appli-
ca ions. Va ious man-made ibe s a e c ucial componen s o composi e ma e ials and il a ion
sys ems used ac oss many indus ies, such as ca bon ibe s in ae ospace composi es and glass ibe s
in ai il a ion sys ems. Al hough exposu e o oxic ibe s such as asbes os is a se e e heal h
haza d, biodeg adable ibe s o e unique possibili ies o a ge ed d ug deli e y [8].
Nume ical simula ion o he anspo o non-sphe ical pa icles is mo e complex han o sphe -
ical pa icles due o he nonsymme ic shape, and hence expe imen al s udies in i o a e indis-
pensable. Howe e , only a ew expe imen al s udies ocusing on he deposi ion o ibe s in human
ai ways ha e been conduc ed. Ma ijnissen e al. [9] and Myojo and Takaya [10] used simpli ied
models o a bi u ca ion o deposi ion expe imen s. The la e expe imen ally examined he depo-
si ion o ibe s in Weibel’s [11] idealized geome y up o he ou h gene a ion o ai way b anching,
e en wi h cyclic b ea hing. Su and Cheng [12] conduc ed expe imen al in es iga ions on he de-
posi ion o ca bon ibe s wi h leng hs anging om 10 o 150 µm, using a ealis ic ai way model
ex ending beyond he ou h gene a ion. A a low a e o 15 l min−1, he majo i y o ibe s we e de-
posi ed in he uppe espi a o y ac , comp ising he o al ca i y, pha ynx, and la ynx, whe eas 63
% passed h ough he eplica wi hou deposi ion. A highe low a es, 43.5 l min−1and 60 l min−1,
he deposi ion a e inc eased, wi h he ibe s p ima ily deposi ed in he o opha ynx and la ynx.
The deposi ion e iciency in he o al ca i y was signi ican ly lowe han ha in he nasal ca i y.
These indings ag ee wi h he esul s o a la e simula ion s udy by Feng e al. [13].
Subsequen ly, Su and Cheng [14] demons a ed ha ine ial impac ion was he dominan de-
posi ion mechanism in he o al ca i y. Fu he mo e, Zhou e al. [15] pe o med expe imen s using
wo lung models: one wi h he o al ca i y hal open and he o he ully open, whe e he deg ee
o opening in luenced he angle o a achmen o he o opha ynx. Su and Cheng [16] conduc ed
expe imen s using h ee ypes o ma e ials, namely glass, TiO2, and ca bon ibe s, a h ee dis inc
inhala ion low a es. In con as o hei p e ious s udies ocused on ca bon pa icles, he ibe s
exhibi ed minimal deposi ion wi hin he model, i espec i e o hei leng h o inhala ion low a e.
The au ho s a ibu ed hese esul s o he ela i ely low momen um o he ligh weigh ibe s,
which enabled hem o mo e e ec i ely ollow ai low dynamics in he ai ways. They indica ed
ha hese ibe s do no demons a e a signi ican deposi ion wi hin he ai ways up o he hi d
gene a ion o b anching, he eby acili a ing hei pene a ion deepe in o he lungs. In con as ,
ibe s wi h g ea e momen um we e obse ed o deposi in he o al ca i y, allowing o po en ial
emo al h ough swallowing.
Bˇelka e al. [17] expe imen ally in es iga ed he deposi ion o glass ibe s in a espi a o y ac
eplica ex ending om he o al ca i y o he 7 h bi u ca ion. The ibe deposi ion wi hin he model
was minimal, wi h deposi ion ac ions o 0.7 % a a s eady low a e o 15 l min−1, 1.9 % a 30
l min−1, and 4.6% a 60 l min−1. Highe deposi ion occu ed in he o al ca i y and mo e complex
segmen s.
Lizal e al. [18] conduc ed one o he a e expe imen al s udies ocusing on he isualiza ion o
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ibe mo emen in he simpli ied model o he espi a o y ac . They p oduced a high-speed came a
eco ding o ibe s a speci ic eco ding ames in a s aigh ube and ups eam and downs eam
o he bi u ca ion o se e al low a es. A obus s a is ical e alua ion showed wo dominan
o ien a ions, pa allel and pe pendicula o he s eamlines, and a signi ican ly highe p obabili y
o lips downs eam o he bi u ca ion han hose in he s aigh ube.
In addi ion o expe imen al s udies, se e al esea che s ha e s udied ibe anspo and de-
posi ion employing compu a ional luid and pa icle dynamics (CFPD) simula ions in silico. The
a ailable simula ion app oaches we e summa ized by Feng and Kleins eue [19]. A popula choice
is he one-way coupling simpli ied Eule - Lag angian app oach. He e, he ibe s a e ea ed as
dilu e, and o a ional mo emen is neglec ed. The p ima y in luence on he ajec o y comes om
he compu a ion o he shape ac o CDwhe e ei he empi ical co ela ions (e.g., Lasso and Wei-
dman [20], Haide and Le enspiel (H-L) [21], T an-Cong (T-C) [22]), o heo e ical o mula ions
(S obe [23]) a e used. In ha ong [24] compa ed he H-L and T-C models in simula ing he nasal
ca i y a a a he low low a e o 7.5 l min−1and showed good ag eemen o pa icles smalle han
100 µm. This s udy was ex ended by Fa kas e al. [25] o a ealis ic male model using he same
ai way eplica as ha used by Belka e al. [17] o h ee s a iona y low a es. Chen e al. [26]
in es iga ed a single idealized bi u ca ion unde s eady lamina low condi ions. They showed ha
g a i y a ec s he deposi ion cha ac e is ics. O ien a ions o deposi ed ibe s we e ob ained om
mic og aphs. The p e alen o ien a ion was pa allel wi h de ia ions mainly in he bi u ca ions
emphasizing he e ec o in e cep ion. Suppo ing nume ical simula ions used equi alen sphe e
app oaches.
Wi h he inc ease in compu a ional powe in ecen decades, me hods ha accoun o o a ional
mo ion ha e been used acco dingly. Tian e al. [27] p esen ed he Eule -Lag ange Eule -Ro a ion
(ELER) app oach and alida ed i by means o he deposi ion ac ion in a s aigh ube o low
Reynolds numbe s. In a ollow-up s udy, his eam [28] nume ically in es iga ed ca bon ibe s in
he ange o aspec a io 1 < β < 80 on a mo e ex ensi e idealized model, om he achea o he
hi d bi u ca ion, and showed di e en o a ional beha io s when passing he bi u ca ions. Shanley
e al. [29] deployed ELER in a ealis ic nasal ai way model unde s eady lamina condi ions and
p oposed wo empi ical models o p essu e d op and deposi ion e iciency.
Shacha -Be man e al. [8] in es iga ed he o al b ea hing maneu e mimicking he D y Powde
Inhale (DPI) p o ile wi h a peak low a e o 90 l min−1 o an a e age adul in a semi- ealis ic
model up o he 9 h gene a ion o b anching, and ideal ibe dimensions o medical ea men
we e sugges ed. Li e al. made signi ican con ibu ions o he ELER modeling o non-sphe ical
pa icles in he espi a o y ac . In hei ini ial s udy [30], hey simula ed ibe anspo in a
ealis ic nasal ca i y, demons a ing complex ansla ional and o a ional beha io . While he ibe s
we e gene ally aligned wi h s eamlines, occasional quick lips we e obse ed. Sub le de ia ions in
ajec o y and o a ion can signi ican ly impac deposi ion pa e ns, highligh ing he impo ance o
accu a e in e cep ion modeling. In a ollow-up s udy, Li e al. [31] in es iga ed he e ec s o shea -
induced li o ces on non-sphe ical pa icles in a ci cula duc . This o ce caused a la e al d i ,
po en ially domina ing he deposi ion o ces and emphasizing he impo ance o i s conside a ion.
In hei mos ecen s udy, Li e al. [32] nume ically in es iga ed ibe anspo and deposi ion in
an ex ended human ai way model up o he 15 h gene a ion, which is a a e scope o such s udies.
The e alua ion o he deposi ion o h ee di e en aspec a ios con i med he signi icance o bo h
he aspec a io and ae odynamic diame e in in luencing he deposi ion cu es.
Kiasadegh e al. [33] compa ed s eady and cyclic egimes in a ealis ic model o a 24-yea -
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old emale ai ways down o he achea. They emphasized he impo ance o ansien simula ion,
showing signi ican di e ences in deposi ion ac ions and pene a ion dep h compa ed wi h s eady-
s a e simula ions, especially o ibe s heading deepe in o he lungs. In ha s udy, a sinusoidal
inspi a ion p o ile was p esc ibed. Ta akol e al. [34] in es iga ed ibe deposi ion in nasal ca i ies
using he ELER me hod coupled wi h Reynolds A e aged Na ie -S okes simula ions, inco po a ing
andom walk models o accoun o u bulen luc ua ions unde s eady low condi ions. In a
consecu i e s udy, Abolhassan ash e al. [35] deployed o ce o mula ions o non-c eeping low
condi ions, de i ed by Zas awny e al. [36] and Ouchene e al. [37], and compa ed hem wi h
con en ional c eeping low o mula ions wi hin he ELER amewo k o simula ions in a emale
nasal passage unde s eady condi ions. G ea e di e ences be ween he non-c eeping and c eeping
o mula ions we e obse ed o low a es abo e 20 l min−1and wi h inc easing ibe aspec a io.
Fu he mo e, a comp ehensi e compa ison o di e en andom walk models used in conjunc ion
wi h RANS simula ions was conduc ed by Mo akham e al. [38]. Finally, ecen p og ess in he
compu a ional modeling o ibe anspo was summa ized by Tian and Ahmadi [39].
Mos o he a o emen ioned s udies ha e been ei he expe imen al o nume ical. In con as , ou
combined expe imen al and compu a ional esea ch no only allows o a compa ison o he o al
deposi ion in each segmen o he ai ways bu also enables a b oade analysis depending on he ibe
dimensions. The u iliza ion o emale ealis ic geome y wi h a ealis ic inspi a ion cycle enables
ocusing on he di e ences compa ed o male geome y, which has been commonly s udied in he
pas . Building upon he p e ious s udies o Henn e al. [40] and P inz e al. [41], his s udy ex ends
he applica ion o he La ice Bol zmann Me hod (LBM) beyond sphe ical pa icles. Speci ically,
he ELER app oach is employed as he pa icle acking algo i hm and coupled wi h he LBM
o simula e he anspo and deposi ion o ib ous pa icles. This no el combina ion allows o a
mo e accu a e ep esen a ion o ibe dynamics compa ed wi h simpli ied models, pa icula ly in
complex low egimes ound in bi u ca ions. Speci ically, we aim o answe he ollowing esea ch
ques ions:
Wha is he dis ibu ion o deposi ed inhaled ibe s wi hin a ious segmen s o he emale
espi a o y ac ? Wha is he in luence o ibe dimensions (leng h and diame e ) on he deposi ion
pa e ns? How do he expe imen al esul s compa e o he nume ical simula ions using he LBM-
ELER app oach, and wha a e he po en ial sou ces o disc epancies? How does pa icle elease
ime du ing he inspi a ion cycle a ec he deposi ion ac ion and loca ion?
The emainde o his pape is o ganized as ollows. Sec ion 2 desc ibes he expe imen al
se up and nume ical me hods employed, including he LBM-ELER app oach and geome y used.
Sec ion 3 p esen s he esul s o bo h he expe imen al and nume ical in es iga ions, ollowed by
a discussion compa ing he wo app oaches and analyzing he in luence o ibe dimensions and
elease ime. Sec ion 4 discusses he limi a ions o he cu en s udy. Sec ion 5 summa izes he
key indings and concludes he s udy.
2. Me hods
2.1. Expe imen al se up
This sec ion desc ibes he expe imen al se up used o in es iga e he deposi ion o glass ibe s
in a ealis ic emale ai way model. The scheme o he expe imen al se up is shown in Figu e 1 and
desc ibed in de ail below.
Polydispe se glass ibe s wi h diame e s anging om 1 o 10 µm and leng hs anging om 5 o
100 µm we e used in he expe imen s. The samples we e ob ained by c ushing glass wool (Supa il
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Ou pu low
S13 o S22
Ai in ake
and exhaus
To b ea hing
simula o
B ea hing
simula o
LLL
LUL
RLL
RML
RUL
10 Ou pu
il e s
S18
S15
S14
S13
S17
S19
S20
S16
S21
S22
Hoppe
Fluidized-bed
ype dispe se
Cha ge
equilib a o
Ro ame e
Ai
Glass beads
o e low
Figu e 1: Schema ic o he expe imen al se up used o in es iga e ibe deposi ion in a ealis ic emale ai way model.
Lo , Knau Insula ion GmbH) in a c ushe . The ibe s we e mixed wi h glass beads (Ballo ini
Impac Beads, Po e Indus ies Inc.) and sie ed o imp o e he ensuing deagglome a ion and
dispe sion o ibe s wi hin he ai way eplica. The mix u e consis ed o 2% ibe s and 98% beads.
The p epa ed mix u e o glass ibe s and beads was in oduced in o he expe imen al se up using
a hoppe , as shown in Figu e 1. F om he hoppe , he mix u e lowed in o a o a y eede , which
deli e ed i o a luidized-bed dispe se . Wi hin he dispe se , he ibe s and beads we e sepa a ed,
and he ae osolized ibe s we e hen anspo ed o a cha ge equilib a o (NEKR-10, Ecke and
Ziegle CESIO) o neu alize hei elec os a ic cha ges. The neu alized ibe s we e subsequen ly
con eyed o he ai way eplica h ough a ube connec ed o he ai in ake and exhaus sys em o
he labo a o y. This connec ion ensu ed a con olled en i onmen and p e en ed he leakage o
ibe s in o he labo a o y.
A ealis ic eplica o he emale ai way, used he e o he i s ime, was employed in his s udy.
I was de i ed by applying a uni o m linea scaling ac o o 0.88 o a p e iously alida ed male
ai way model [42, 17]. This ac o was de e mined h ough a compa a i e analysis o key ana omical
dimensions epo ed in he li e a u e o ep esen a i e adul male and emale espi a o y ac s
[43, 44, 45]. Speci ically, me ics such as acheal leng h and mean luminal c oss-sec ional a ea
se ed as p ima y pa ame e s conside ed in de i ing his a e age scaling ac o o ep esen o e all
size di e ences be ween he sexes. The eplica spans om he o al ca i y o he se en h gene a ion
o he lung bi u ca ion, and he emainde o he lung is eplaced by ou pu il e s. The model was
capable o simula ing b ea hing pa e ns using an o iginal b ea hing simula o , which ep oduced
he speci ic pa e ns o he i e lung lobes: he igh uppe lobe (RUL), igh middle lobe (RML),
igh lowe lobe (RLL), le uppe lobe (LUL), and le lowe lobe (LLL). A model o he geome y
wi h i s segmen a ion is depic ed in Figu e 2. To enhance pa icle adhesion and be e simula e
he apping e ec o he mucus laye ound in i o, he inne su aces o he ai way eplica we e
coa ed wi h a hin laye o silicone oil p io o each expe imen al un. This su ace ea men is a
common p ac ice in simila in i o deposi ion s udies [16, 17].
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0
1
2
3
45
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
RUL
RML
RLL
LUL
LLL
G0-1
G1
G1-2
G2-3
G3-7
ou le s
G3-4
Figu e 2: Segmen a ion o he ealis ic emale ai way geome y wi h co esponding segmen numbe s. Each colo
ep esen s a di e en ai way gene a ion, as indica ed in he legend.
To he bes o ou knowledge, expe imen al da a on ibe deposi ion du ing ealis ic emale
inspi a ion a e no a ailable in he li e a u e; he e o e, we conduc ed expe imen s o ill his
gap. The ealis ic b ea hing p o iles used in his s udy (see Figu e 3) we e de i ed om he da a
p esen ed in he Annals o he ICRP [46]. Speci ically, we scaled down he alues epo ed in [46]
by a ac o o 0.8, based on a compa ison o he idal olumes o he male and emale geome ies
in [46] and he ealis ic male ai way model om which he cu en emale geome y was de i ed
[17]. The dis ibu ion o low a es among he lung lobes was adap ed om Jahani e al. [47], who
analyzed ou -dimensional compu ed omog aphy da a o six b ea hing cycles a e aged o e one
minu e om heal hy olun ee s (50% women).
The ai way eplica was hen exposed o ae osolized ibe s. A e exposu e, wo ypes o samples
we e collec ed: a) samples om he ou pu il e s, which cap u ed he ibe s ha passed h ough
he en i e eplica, and b) samples ob ained om each indi idual segmen o he eplica. To collec
he ibe s deposi ed wi hin he eplica, i was i s disassembled. Each segmen was hen placed in
a beake and imme sed in isop opanol. The beake was placed in an ul asonic ba h o dislodge any
ibe s adhe ing o he segmen walls. This p ocess c ea ed a suspension o ibe s in isop opanol.
To analyze he ibe s, he suspension was il e ed h ough ni ocellulose memb ane il e s using
a acuum il a ion pump. The il e s we e hen d ied and made anspa en by placing hem on
a glass slide using an ace one apo ize (QuickFix, EMS, USA). Samples om he ou pu il e s
we e made anspa en in he same manne . Each sample was hen manually e alua ed unde a
phase-con as mic oscope (Nikon Eclipse E200, Nikon, Tokyo, Japan) using a 40x objec i e and
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0 0.5 1 1.5
0
2
4
6
8
Time (s)
Flow a e (l min−1)
RUL
RML
RLL
LUL
LLL
Figu e 3: Flow a e p o iles o each lung lobe du ing he inspi a ion cycle [46, 47].
Wal on-Becke g a icule (c . ep esen a i e sample Figu e A.22 in Appendix). Fibe coun ing was
pe o med acco ding o a me hod based on he WHO guidelines [48]. To ensu e a ep esen a i e
coun , 20 andomly selec ed a eas we e analyzed o each sample. Because o he polydispe si y o
he ibe s, he diame e and leng h o each ibe we e measu ed and eco ded o u he analysis.
2.2. Nume ical simula ion se up
This sec ion ou lines he nume ical me hods used o simula e he anspo and deposi ion
o ibe s wi hin he emale ai way model. Pa icle anspo and deposi ion we e nume ically
simula ed using Compu a ional Fluid and Pa icle Dynamics (CFPD). The solu ion was di ided
in o wo pa s – he luid low solu ion and pa icle mo ion solu ion – coupled wi h he eloci y
ield da a, as desc ibed below. The simula ion is conside ed as one-way coupling, and he disc e e
phase ep esen ed by he pa icles is dilu e wi h a e y low olume ac ion (app oxima ely 10−8)
and hence does no a ec he low ield.
2.2.1. Fluid phase
Fluid low modeling is based on he La ice Bol zmann Me hod (LBM), a mesoscopic nume ical
app oach o anspo p oblems based on a disc e iza ion o he Bol zmann equa ion [49]. Due o
i s algo i hmic s uc u e, he LBM is uniquely sui ed o highly pa allel execu ion on s a e-o - he-
a high-pe o mance compu e s [50]. Speci ically, i is an e icien al e na i e [51] o con en ional
ini e- olume me hods, p o iding 32- old pe o mance imp o emen s compa ed o OpenFOAM
when ixing he nume ical e o in a ai compa ison o an indus ial e e ence case.
In LBM, he spa ial simula ion domain is disc e ized by a egula la ice on which popula ions
(x, 
ξ, ), desc ibing he s a e o he sys em1, p opaga e along disc e e eloci ies ci ollowing a so
1 (x, 
ξ, ) explici ly desc ibes he p obabili y o he o al mass o pa icles in posi ion x wi h mic oscopic eloci y

ξin ime .
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called collision s ep ha elaxes he pe -cell popula ions owa ds hei mac oscopic equilib ium
dis ibu ion:
i(x +ci∆ , + ∆ ) = 1−∆
τ i(x, ) + ∆
τ (eq)
i(x, ),∀i∈ ⟨0,18⟩.(1)
He e, cideno es he disc e e eloci y s emming om he eloci y se D3Q19, (eq)
iis he equilib ium
dis ibu ion unc ion and τ he elaxa ion ime in he Bha naga -G oss-K ook (BGK) collision
ope a o esol ing he pa icle in e ac ions. This equa ion can be di ided in o wo s eps, collision
and s eaming.
coll
i(x, ):= 1−∆
τ i(x, ) + ∆
τ (eq)
i(x, ),(2)
s
i(x +ci∆ , + ∆ ):= coll
i(x, ).(3)
Mac oscopic quan i ies a e compu ed using disc e e eloci y momen s
ρ(x, ) = X
i
i, u(x, ) = 1
ρX
i
i
ξi, p(x, ) = ρ
c2
s
,(4)
whe e ρdeno es he densi y o he luid, u deno es he mac oscopic eloci y, pdeno es he p essu e,
and csdeno es he speed o sound. The Chapman-Enskog expansion [52] can be used o demon-
s a e he con e gence o his me hod o solu ions o he incomp essible Na ie -S okes equa ions,
jus i ying i s use in he p esen applica ion.
To model u bulen phenomena, a La ge Eddy Simula ion (LES) wi h he Smago insky subg id-
scale (SGS) model [53] was enabled ( u he implemen a ion de ails a e p o ided in [41]). The
Smago insky cons an was assigned he common alue o 0.1. LES p o ides he ime- a ying la ge-
scale u bulen eloci y ields, which can cap u e he majo i y (e.g., >80%) o he u bulen kine ic
ene gy in well- esol ed simula ions [54]. The in luence o smalle subg id eddies on pa icle dispe -
sion is commonly accoun ed o in Reynolds-A e aged Na ie -S okes (RANS) simula ions h ough
models such as andom walk app oaches [55]. Fo LES, while SGS u bulen dispe sion e ec s
can be modeled, hei impac on he deposi ion o mic ome e -sized pa icles has been epo ed as
ela i ely small in ce ain con ex s (e.g., [56, 57]. Consequen ly, explici modeling o SGS pa icle
u bulen dispe sion has o en no been included in LES s udies o ai low and deposi ion in he
espi a o y ac ([58]). Suppo ing his app oach, Koullapis e al. [59] demons a ed in a bench-
ma k compa ison ha LES models wi hou explici SGS u bulen dispe sion o pa icles achie ed
easonable accu acy agains expe imen al da a o egional deposi ion in human ai ways. Based
on hese conside a ions om he li e a u e and he common p ac ice in he ield, explici modeling
o SGS u bulen dispe sion e ec s on pa icle ajec o ies was no included in he p esen s udy,
hough i emains an impo an a ea o u u e esea ch.
A p essu e bounda y condi ion, as p oposed by Sko dos [60], was imposed a he mou h inle . A
he ou le s, uni o m eloci y bounda y condi ions, as p oposed by Sko dos [60], we e p esc ibed,
wi h ime-dependen eloci ies calcula ed om a ealis ic inspi a ion p o ile (Figu e 3) and he
co esponding idal olume dis ibu ions. Veloci ies we e implemen ed using a linea in e pola ion
scheme. Two consecu i e inhala ions we e simula ed wi h a educed hold-up ime o 0.25 s be ween
hem. Each lung lobe in ou model con ains wo unnels, which a e connec ed o he espec i e
lobe pis ons o he b ea hing simula o . The low a e dis ibu ion be ween he unnels in he
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Collision
s ep
S eaming
s ep
Bounda y
ea men
New ime
s ep
Momen
upda e
Flow ield da a
pos p ocessing
Flow
ini ialisa ion
Da a
s o age
Compu e
pa icle
o ques
Compu e
pa icle
o ces
Deposi ion
ea men
Pa icle da a
pos p ocessing
Fibe
ini ialisa ion
Upda e
angula
eloci y
LBM ELER
eloci y ans e
no da a ans e
Repea un il e mina ion c i e ia a e ul illed
Upda e
o ien a ion
Upda e
posi ion
Figu e 6: Schema ic o he nume ical se up. A e he ini ializa ion s ep, each i e a ion in ol es one LBM cycle
and one ELER cycle. A e compu ing he low eloci ies (u) in he LBM cycle, hese alues a e ans e ed o he
ELER algo i hm. Due o he one-way coupling, no da a a e ans e ed back om he ELER algo i hm o he LBM
sol e . In p inciple, di e en numbe s o LBM o ELER cycles can be pe o med wi hin each i e a ion (e.g., inne
i e a ions), as indica ed by he do ed a ows. The simula ion e mina es when he speci ied c i e ia (e.g., simula ion
ime o numbe o i e a ions) a e me , and he da a a e hen pos -p ocessed.
p opo ional o he ac ual low a e a ha ime (see Figu e 3), e lec ing he ac ha a highe
low a e ca ies mo e pa icles in o he ai way.
The nume ical simula ions we e pe o med using he open-sou ce C++ lib a y OpenLB [70,
71, 72]. This so wa e enables lexible and pe o man simula ions using he LBM, bene i ing om
e icien pa alleliza ion and scalabili y o bo h CPUs and GPUs on high-pe o mance compu e s.
The sui abili y o OpenLB o his ype o applica ion was demons a ed in a p e ious pape by
he au ho s [41], which esul ed in high pe o mance and accu acy. To simula e ibe anspo
and deposi ion, OpenLB was ex ended using an in eg a ed in-house code ha implemen ed he
ELER model. The simula ions we e pe o med on he Ka olina supe compu e pe ascale sys em
a he IT4Inno a ion Na ional Compu ing Cen e in Czechia using 1024 CPU co es dis ibu ed
ac oss mul iple nodes, le e aging he high memo y capaci y and in e connec bandwid h o he
HPC sys em.
Fo compa ison wi h expe imen al esul s, he ollowing s a is ical quan i ies we e e alua ed:
Deposi ion ac ion
DF = Ns
N o
,(33)
whe e Nsis he numbe o pa icles deposi ed in a gi en segmen , and N o is he o al numbe o
pa icles en e ing he geome y.
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The deposi ion e iciency DE desc ibes he e iciency o a segmen in cap u ing he pa icles.
DE = Ns
Ns,in
,(34)
whe e Ns,in is he numbe o pa icles en e ing he segmen .
Volume equi alen diame e
deq =3
6V
π,(35)
is de ined as he diame e o he sphe ical pa icle ha ing he same olume as he ibe .
Ae odynamic diame e
dae =deq ρp
ρ0χR
(36)
is de ined as he diame e o a sphe e wi h uni densi y (ρ0) ha se les wi h he same e minal
eloci y as he ibe . χRdeno es he dynamic shape ac o o a andom o ien a ion.
The S okes numbe , gi en by
S k = ρ0d2
aeu0
18µD0
,(37)
is an impo an dimensionless pa ame e o e alua ing he a e o he ine ial impac ion. I is
pa icula ly use ul o compa ing da a ac oss di e en low a es and geome ies because i accoun s
o he combined e ec s o pa icle ine ia, luid iscosi y, and cha ac e is ic leng h scales. In his
equa ion, u0 ep esen s he cha ac e is ic eloci y o he low, and D0 ep esen s he cha ac e is ic
dimension o he geome y.
2.3. Nume ical e i ica ion
Ve i ica ion o he ELER me hod implemen a ion wi hin he LBM amewo k was pe o med
using a benchma k case o lamina ai low h ough a ci cula ube. This benchma k, o en wi h
small a ia ions, has been used o e i ica ion in se e al s udies [27, 13, 73, 74, 75]. In his pape ,
he speci ic se up i s desc ibed by Tian e al. [27] was simula ed, and da a om Feng e al. [13]
we e also used o compa ison. This in ol ed simula ing lamina low h ough a ho izon al pipe
wi h a diame e o 4.2 mm and a co esponding Reynolds numbe o Re = 169. A sphe oidal
pa icle wi h a mino axis o 0.5 µm and an aspec a io o 14 was injec ed a a posi ion 0.45
mm abo e he bo om edge o he pipe, wi h an ini ial pe pendicula o ien a ion. The pa icle
ajec o y was hen acked o 0.2 s (see Figu e 7).
To compa e he esul s o ou simula ion wi h hose o Tian e al. [27] and Feng e al. [13],
he di ec ional cosines be ween he ibe symme y axis and he coo dina e axes we e e alua ed.
The ime e olu ion o hese quan i ies o e 0.2 s o he simula ion is shown in Figu es 8(a) and
8(b). As can be seen, he ibe quickly il s om i s ini ial pe pendicula o ien a ion o a posi ion
pa allel o he low. A e each pe iod o 0.055 s, i unde goes a 180-deg ee lip.
The sedimen a ion eloci y, shown in Figu e 8(c), was also compa ed. G a i y ac s on he ibe ,
causing i o mo e in he nega i e y di ec ion. The sedimen a ion eloci y inc eases om ze o o a
e minal eloci y, a which poin he g a i a ional o ce is balanced by d ag o ce. When he ibe
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0.45 mm
x
y
z
g
u
Figu e 7: Ini ial condi ion o he ibe in he nume ical e i ica ion case, showing i s posi ion and o ien a ion ela i e
o he ai low in he ho izon al pipe.
0 0.05 0.1 0.15 0.2
−1
−0.5
0
0.5
1
Time (s)
cos x(-)
Tian
Feng
ELER
(a)
0 0.05 0.1 0.15 0.2
−1
−0.5
0
0.5
1
Time (s)
cos y(-)
Tian
Feng
ELER
(b)
0 0.05 0.1 0.15 0.2
−3
−2
−1
0·10−4
Time (s)
y(m s−1)
Tian
Feng
ELER
(c)
Figu e 8: Compa ison o he ime e olu ion o (a) he di ec ional cosine be ween he symme y axis o a ibe and
he x-axis (cos x), (b) he di ec ional cosine be ween he symme y axis o a ibe and he y-axis (cos y), and (c) he
sedimen a ion eloci y ( y) ob ained in his s udy wi h he esul s epo ed by Tian e al. [27]. and Feng e al. [13].
lips om a pa allel o a pe pendicula o ien a ion, i s c oss-sec ional a ea dec eases, leading o a
educ ion in he d ag o ce and sudden accele a ion.
To demons a e a mo e obus compa ison, he ajec o y o he pa icle in he mo ing xy
plane was plo ed and compa ed (see Figu e 9). The pa icle is d i en p edominan ly in he luid
di ec ion, while g a i y go e ns a slow downwa d shi .
In all cases, he close ag eemen be ween ou esul s and hose o Tian e al. and Feng e al.
demons a es he co ec ness o ou implemen a ion o he ELER me hod. The disc epancies may
be a ibu ed o di e ences in nume ical se up - he case depends on he iscosi y and densi y o
he luid which a e no s a ed in any o he a o emen ioned s udies. Fu he mo e, as p e iously
epo ed by Cui e al. [74], he equency o lips depends on he Re, which sligh ly a ies be ween
he s udies. Di e en nume ical disc e iza ion schemes o disc epancies in he li o ce o mula ions
can also con ibu e o a ia ions [13].
2.4. G id independence s udy
To assess he alidi y o he nume ical simula ions and ensu e ha he esul s we e no signi i-
can ly in luenced by g id esolu ion, a g id-independence s udy was conduc ed. The g id size was
ini ially chosen based on a p e ious s udy [41], which used he same escaled ealis ic geome y.
To e alua e g id independence, line p obes we e placed downs eam o he i s bi u ca ion nea
he ca ina, wi h wo p obes in he an e io di ec ion and wo in he supe io di ec ion (see Figu e
11(a)). This a ea is cha ac e ized by u bulen low condi ions, making i sui able o assessing he
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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
4
4.1
4.2
4.3
4.4
4.5·10−4
x(m)
y(m)
Tian
Feng
ELER
Figu e 9: Compa ison o he ibe s cen oid ajec o y wi h he esul s epo ed by Tian e al. [27] and Feng e al.
[13].
Figu e 10: De ail o he compu a ional g id o he igh uppe lobe (RUL)
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Table 1: P ope ies o la ices used o he g id independence s udy.
Numbe o cells Cell size Time s ep Relaxa ion ime
40 mil. 0.00018 m 3.5.10−7s 0.5005
60 mil. 0.00015 m 2.6.10−7s 0.5005
82 mil. 0.00013 m 2.0.10−7s 0.5005
impac o g id esolu ion on low ea u es. A ime pe iod o 0.1 s was simula ed wi h a cons an
low a e co esponding o he peak low a e o he inspi a o y cycle (27 l min−1). This low a e
was chosen because he nume ical e o s end o be he highes a he maximum luid eloci y. The
mean eloci y magni ude along he line p obes was used o compa ison o minimize he in luence
o local luc ua ions.
Th ee di e en g ids wi h a uni o m g id size ( o de ails, see Table 1 and Figu e 10) we e
simula ed, and he esul s a e shown in Figu e 11(b)-(e). Good ag eemen in he mean eloci y
magni ude was obse ed be ween he g ids wi h 60 million and 82 million cells. The inal simula ion
was pe o med using an in e media e g id o 60 million cells.
2.5. E ec i e diame e simula ions
The e ec i e diame e simula ions a e simpli ied Eule -Lag ange simula ions, whe e he pa -
icles a e app oxima ed by sphe es and he o a ion (Equa ion 11) is neglec ed. To es ablish an
accu a e compa ison o ELER wi h his me hod, wo addi ional simula ions wi h he mos pop-
ula empi ical models, H-L [22] and T-C [21], on he same geome y unde he same b ea hing
condi ions we e conduc ed. The hyd odynamic d ag o ce is de ined as

FD=1
2CDApρp(u − )|u − |(38)
whe e Apis he p ojec ed su ace a ea, and CDis he hyd odynamic shape ac o .
In he H-L co ela ion, he CDis de e mined as
CD=24
Rep
(1 + HaReHb
p) + HcRep
Hd+ Rep
,(39)
whe e
Rep=|u − |dp
ν(40)
is he Reynolds numbe o he pa icle. νdeno es he luid kinema ic iscosi y, and Ha,Hb,Hc
and Hda e model-speci ic pa ame e s ha depend on pa icle sphe ici y ϕ.
T-C de ines he shape ac o as ollows.
CD=24
Rep
dA
deq 1 + 0.15
√cdA
deq
Rep0.687!+
0.42 dA
deq 2
√c1 + 42500 dA
deq Rep−1.16,(41)
whe e dAis he su ace equi alen sphe e diame e , and cis he su ace sphe ici y.
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(a)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
Rela i e leng h (-)
Mean eloci y mag. (m/s)
40 mil.
60 mil.
82 mil.
(b)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
Rela i e leng h (-)
Mean eloci y mag. (m/s)
40 mil.
60 mil.
82 mil.
(c)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
Rela i e leng h (-)
Mean eloci y mag. (m/s)
40 mil.
60 mil.
82 mil.
(d)
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
Rela i e leng h (-)
Mean eloci y mag. (m/s)
40 mil.
60 mil.
82 mil.
(e)
Figu e 11: G id independence s udy: (a) Loca ions o he line p obes used o assess g id independence, (b)-(e) mean
eloci y magni ude along he line p obes o h ee di e en g id esolu ions; (b) Le b anch, ho izon al p obe (LG1h),
(c) Le b anch, e ical p obe (LG1 ), (d) Righ b anch, ho izon al p obe (RG1h), (e) Righ b anch, e ical p obe
(RG1 ).
3. Resul s and discussion
3.1. Compa ison be ween simula ion and expe imen
Figu e 12 compa es he nume ical and expe imen al esul s o he ibe deposi ion. The sim-
ula ion da a we e analyzed a he end o he simula ion, and app oxima ely 5% o he pa icles
ha had no ye been deposi ed we e excluded om he e alua ion. In many segmen s, good
ag eemen was obse ed be ween he simula ion and he expe imen , pa icula ly in he segmen s
abo e he bi u ca ions (segmen s 1, 2, and 3) and a he unnels a he ou le s (segmen s 13o-22o).
Nume ical simula ion gene ally p edic s a sligh ly highe deposi ion ac ion in mos bi u ca ions.
This disc epancy can be a ibu ed pa ly o di e ences in he deposi ion mechanisms and su -
ace in e ac ions. In he LBM simula ions, e e y con ac be ween a pa icle and he wall esul ed
in deposi ion ( he ’pe ec sink’ assump ion). While he expe imen al eplica su ace was coa ed
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wi h silicone oil o p omo e adhesion and mimic mucus cap u e [16, 17], he simula ion’s assump-
ion o 100% cap u e upon any con ac migh s ill ep esen an uppe bound compa ed o he
in i o eali y, po en ially con ibu ing o he obse ed o e es ima ion. Fu he in es iga ion o
pa icle-wall in e ac ions unde a ying su ace condi ions is necessa y o imp o e he accu acy o
he deposi ion model. Ano he sou ce o disc epancies may s em om assump ions o linea shea
low in he o ce calcula ion. This assump ion migh esul in disc epancies in he a eas o he
bi u ca ions ([76]). In addi ion, he pe iodic o a ional mo ion o he pa icles, which is assumed
in he ELER me hod, is no consis en ly obse ed in expe imen s, as epo ed by Lizal e al. [18].
The la ges di e ences be ween he simula ion and expe imen occu ed in segmen s 5, 6, and 7,
which co esponded o he second and hi d gene a ions o b anching in he le lung. This excess
deposi ion in he simula ion is likely compensa ed o by a consequen lowe deposi ion ac ion
in he downs eam segmen s (13, 13o, 16o, 17, 17o), whe e he expe imen al esul s show highe
alues. The nume ical esul s o he igh lung we e in good ag eemen wi h he expe imen al
da a. A u he s a is ics o he expe imen al da a, speci ically on coun s and dimensions o ibe s
deposi ed in each segmen can be ound in Table A.2 in he Appendix.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 13o14o15o16o17o18o19o20o21o22o
10−3
10−2
10−1
Deposi ion ac ion by coun (-)
ELER H-L T-C EXP
Figu e 12: Compa ison o deposi ion ac ions ob ained om expe imen al measu emen s and nume ical simula ions.
To u he assess he accu acy o he nume ical simula ions, a compa ison was made be ween
he ELER me hod and wo simpli ied models based on he e ec i e diame e concep : he T-C
model [22] and H-L model [21]. These models app oxima e he ibe s as sphe es wi h equi alen
diame e s and neglec hei o a ion. Analysis o he esul s e ealed ha he ELER model p o ided
he mos accu a e p edic ions o deposi ion, wi h he bes ag eemen wi h he expe imen al da a
in 26 segmen s, compa ed o i e segmen s o he T-C model and only wo segmen s o he H-L
model. The absolu e e o s o he ELER, T-C, and H-L models we e 0.0106, 0.0120, and 0.0146,
espec i ely, con i ming he supe io accu acy o he ELER app oach. This inding is consis en
wi h H-L and T-C compa ison s udies by Fa kas [25]. Based on hese esul s, only he ELER
simula ion esul s we e conside ed in he subsequen analysis and discussion.
The deposi ion pa ame e s we e analyzed as a unc ion o ai way gene a ion o p o ide a com-
pa ison ele an o medical applica ions. Each segmen was assigned i s highes gene a ion numbe ,
as shown in Figu e 2. The deposi ion ac ion and e iciency we e hen calcula ed o he ollowing
egions: uppe ai way (UA); achea (gene a ion 0, G0); gene a ions G1, G2, and G3; and gene a-
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ions G4-G7. Gene a ions G4-G7 we e g ouped oge he because hese highe -gene a ion segmen s
a e manu ac u ed as single pieces due o hei small dimensions.
UA G0 G1 G2 G3 G4-G7
10−3
10−2
10−1
100
Deposi ion e iciency by coun (-)
ELER EXP
Figu e 13: Compa ison o deposi ion e iciencies ob ained om expe imen al measu emen s and nume ical simula-
ions, so ed by ai way gene a ion.
Figu e 13 shows he deposi ion e iciency o each gene a ion. The deposi ion e iciency gene ally
inc eased wi h inc easing gene a ion o de in bo h he simula ion and expe imen , wi h a s eepe
inc ease obse ed in he LBM esul s. Howe e , in he expe imen al esul s, G2 de ia ed om his
end, showing a dec ease in deposi ion e iciency compa ed o G1. La ge disc epancies be ween
he simula ion and expe imen we e obse ed o he highe gene a ions o b anching.
The expe imen al se up used in his s udy allowed o a unique analysis o he deposi ion da a
based on he dimensions o he cap u ed ibe s in each segmen . This ype o analysis is a e
in simila expe imen al s udies on ibe deposi ion. Figu e 14 compa es he mean alues o he
olume equi alen diame e (deq) and aspec a io (β) o he deposi ed ibe s in he uppe ai ways
and di e en gene a ions o b anching. In bo h cases, a easonable ag eemen was obse ed be ween
he simula ion and expe imen .
As expec ed, pa icles wi h highe deq we e p edominan ly deposi ed in he uppe ai ways and
he i s ew acheob onchial gene a ions because o hei highe ine ia. On he o he hand, smalle
ibe s end o pene a e deepe in o he lungs. This end was e iden in bo h he expe imen al
and nume ical esul s, al hough he expe imen al da a exhibi ed sligh ly mo e luc ua ions. The
la ges disc epancies be ween he simula ion and expe imen occu ed in G1, which could be due o
he low numbe o deposi ed and measu ed pa icles in his segmen , leading o a highe s a is ical
e o .
Excep o he ou le s, he simula ions gene ally p edic ed a highe mean deq and β han he
expe imen . While βinc eased wi h inc easing gene a ion downs eam o he achea in bo h he
expe imen al and nume ical esul s, deq dec eased. This obse a ion sugges s a complex in e play
be ween he o a ional mo ion o he pa icles and he endency o he ELER me hod o cap u e
pa icles in bi u ca ions. Howe e , he low in he i s ew bi u ca ions is u bulen , which makes
i challenging o simula e he o a ional mo emen s o he ibe s accu a ely. Fo pa icles wi h
high β, changes in o ien a ion can signi ican ly al e hei ajec o y (owing o he dependence
o he d ag o ce on he s eamwise c oss-sec ion, as shown in Equa ion (13)). This can lead o
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UA G0 G1 G2 G3 G4-G7 ≧G8
0.25
0.5
0.75
1·10−5
Diame e (m)
ELER deq EXP deq
4
8
12
16
Aspec a io (-)
ELER βEXP β
Figu e 14: Compa ison o he mean equi alen diame e (deq ) and mean aspec a io (β) o deposi ed ibe s o each
ai way gene a ion. The ba cha (le e ical axis) shows he mean equi alen diame e , while he symbols ( igh
e ical axis) show he mean aspec a io.
di e ences in he deposi ion pa e ns be ween he simula ion and he expe imen , pa icula ly o
la ge pa icles. This is consis en wi h he obse a ion ha he mean deq o he pa icles passing
h ough he geome y (i.e., ≥G8) was highe in he expe imen al se up. A simila beha io was
epo ed by Shacha -Be man e al. [8]. Again, a sligh de ia ion om his end was obse ed a
G1 in he expe imen , likely due o he low numbe o deposi ed ibe s and he esul ing highe
s a is ical e o .
UA G0 G1 G2 G3 G4-G7 ≧G8
10−3
10−2
10−1
100
Deposi ion ac ion by coun (-)
ELER 1 µm ELER 2 µm ELER 3 µm
EXP 1 µm EXP 2 µm EXP 3 µm
Figu e 15: Compa ison o deposi ion ac ions o ibe s so ed in o h ee size g oups based on hei diame e (dp).
A simila end can be obse ed in Figu e 15, which shows he deposi ion ac ion o he
ibe s so ed in o h ee classes acco ding o hei hickness (dp= 2b= 2c). Fo small pa icles
(dp= 1 µm and dp= 2 µm), he uppe ai way and achea showed good ag eemen be ween he
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simula ion and expe imen al esul s. Howe e , la ge disc epancies we e obse ed in gene a ions
G1, G2, and G3, wi h he di e ences inc easing wi h he pa icle hickness. This is consis en wi h
p e ious obse a ions ha o ien a ion changes ha e a mo e signi ican impac on he ajec o ies o
la ge pa icles. In gene a ions G4-G7, he di e ences be ween he simula ion and expe imen we e
smalle , which could be a ibu ed o he na owe channels in hese egions and he ansi ion
back o a lamina low egime.
In e es ingly, hese esul s di e om hose o a p e ious s udy using an LBM [41] ha sim-
ula ed sphe ical pa icles in a escaled child ai way geome y. In ha s udy, la ge disc epancies
be ween he simula ion and he expe imen we e obse ed o smalle pa icles. This highligh s
he impac o he pa icle shape on he deposi ion pa e ns and he impo ance o conside ing he
ibe o ien a ion in simula ions.
Figu e 16 compa es he deposi ion e iciency ob ained in his s udy wi h da a a ailable in he
li e a u e. To acili a e his compa ison, he pa icles we e so ed in o g oups based on hei S okes
numbe s (S k) o ensu e s a is ically ele an sample sizes o each e alua ion. The achea and
segmen s up o he ou h gene a ion o b anching we e e alua ed sepa a ely.
To he bes o ou knowledge, compa able expe imen al o simula ion da a o ibe deposi ion
in a ealis ic emale ai way geome y a e missing. The e o e, we included da a om s udies using
he male ai way geome y by Belka e al. [17] and Fa kas e al. [25]. Addi ionally, we included
expe imen al da a om Su e al. [16] and Zhou e al. [15], who used di e en ealis ic ai way
geome ies, and Myojo and Takaya [10], who used he idealized Weibel lung model A om he
hi d o ou h gene a ion o b anching.
Analysis o he da a in Figu e 16 e eals good ag eemen be ween ou esul s and he expe i-
men al da a o he achea (Figu e 16(a)). Disc epancies compa ed o he simpli ied T-C and H-L
models a e negligible in his egion, sugges ing less complex low beha io han in deepe gene a-
ions. In gene a ions 1-3 (Figu es 16(b)–(d)), ou simula ions p edic ed a sligh ly highe deposi ion
e iciency han he expe imen al da a. This di e ence may be due o he use o a ealis ic inspi a-
ion p o ile in ou simula ions, which includes a highe peak eloci y ha could inc ease deposi ion
in compa ison wi h s udies ha used cons an low a es. The di e ences be ween he ELER model
and simpli ied models become mo e p onounced in highe gene a ions, highligh ing he impo ance
o conside ing ibe o a ion in he b anching egions. I is wo h no ing ha he expe imen al da a
om Su e al. [16] ha e a highe s anda d de ia ion, which should be conside ed when compa ing
ou esul s. O e all, he ELER simula ions end o o e es ima e he ibe deposi ion compa ed
wi h ou expe imen s, which is consis en wi h p e ious indings.
In Gene a ion 4 (Figu e 16(e)), bo h ou expe imen al and nume ical esul s show highe de-
posi ion ac oss he en i e S k ange compa ed o Myojo and Takaya [10]. This disc epancy could
be a ibu ed o he use o an idealized geome y and he absence o ups eam bi u ca ions in hei
model, which does no accoun o he ull low his o y. The expe imen s o Zhou e al. [15] we e
conduc ed o highe S k alues; howe e , ex apola ing hei da a o he lowe S k ange would
s ill indica e lowe deposi ion han ha obse ed in ou s udy.
In e es ingly, he expe imen al da a om Belka e al. [17] show a lowe deposi ion e iciency
o almos all segmen s and S k numbe s compa ed o o he s udies, including he co esponding
H-L and T-C simula ions pe o med by Fa kas e al. [25]. This disc epancy could be ela ed o
di e ences in he expe imen al se up o speci ic cha ac e is ics o he ai way models used.
In summa y, he emale ai way geome y used in his s udy appea s o esul in a sligh ly highe
deposi ion a e compa ed o he male ai way geome y, wi h a shi o he cap u e-e iciency cu e
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•The ini ial posi ion and o ien a ion o he pa icles eleased in he simula ions we e andomly
gene a ed, as i is challenging o measu e hese pa ame e s expe imen ally. This unce ain y
in he ini ial condi ions could ha e a ec ed he deposi ion pa e ns and in oduced inaccu-
acies in he esul s.
•The subg id-scale u bulence luc ua ions smalle han he g id size we e no conside ed
in his s udy and can lead o small disc epancies in ajec o ies and o ien a ions, and can
in luence exac deposi ion posi ions o pa icles nea he walls, p edominan ly when eaching
he peak low a e. Modeling o he u bulence luc ua ions, using, e.g., a Gaussian andom
il e ([56]), will be in ol ed in u u e wo k in es iga ing highe low a es.
•A dilu e ai and one-way coupling model was used, assuming ha he pa icles do no in lu-
ence he ai low. This assump ion may no be alid in all egions o he ai way, pa icula ly
in he u bulen low egime nea bi u ca ions, whe e wo-way coupling migh be necessa y
o highe accu acy.
•Pa icle concen a ion was assumed o be low, and in e -pa icle collisions we e neglec ed.
Addi ionally, po en ial changes in he pa icle shape owing o collisions we e no conside ed.
•Due o he ime-consuming na u e o he expe imen s, only one epe i ion was pe o med.
Addi ional expe imen al da a would be use ul o a be e es ima ion o he unce ain ies.
•The e ec o expi a ion on pa icle deposi ion was no conside ed in his s udy. This could
be pa icula ly ele an o pa icles deposi ed owa ds he end o he inspi a ion cycle, as
hey migh be exhaled be o e ha ing a chance o deposi pe manen ly.
•Only one low a e was simula ed in his s udy. Sys ema ic explo a ion o he in luence o
a ious b ea hing pa e ns was pe o med by e.g. [80, 81], and hence simila ends in he
deposi ion cha ac e is ics can be expec ed.
5. Conclusion
This s udy success ully applied he LBM in conjunc ion wi h he ELER me hod o simula e
ibe anspo and deposi ion in a ealis ic emale ai way model. A unique compa ison o he
deposi ion cha ac e is ics be ween nume ical simula ions and expe imen s conduc ed on he same
ai way geome y, ex ending o he 7 h gene a ion o b anching, is p esen ed. The esul s showed
good ag eemen in he uppe ai ways and achea, bu some disc epancies we e obse ed in he
b onchial bi u ca ions, likely owing o he challenges in cap u ing complex low phenomena (such
as Dean o ices and u bulence) using he ELER me hod.
In addi ion o compa ing he ELER me hod wi h expe imen al da a, i s accu acy was also
assessed by compa ing i wi h simpli ied ibe deposi ion models ha neglec ibe o a ion (T-C
and H-L me hods). The ELER ou pe o med hese simpli ied models, demons a ing i s supe io
abili y o p edic ibe deposi ion in a ealis ic ai way geome y and emphasizing he impo ance
o o ien a ion-dependen calcula ion o ibe anspo and deposi ion.
This s udy also enabled a de ailed analysis o he deposi ion pa e ns o di e en ibe size
g oups. No ably, he ELER me hod exhibi ed be e ag eemen wi h he expe imen al da a o
smalle pa icles, indica ing a highe accu acy in p edic ing he deposi ion ac ions o hese size
anges. Fu he mo e, he esul s con i med ha ibe s wi h highe aspec a ios had a g ea e
endency o pene a e deepe in o he lungs, which is consis en wi h p e ious indings.
A compa ison o he deposi ion e iciency wi h li e a u e da a, using S k as a basis o com-
pa ison, showed good ag eemen in he achea. Howe e , disc epancies we e obse ed in he
bi u ca ions, po en ially owing o he di e ences in ai way geome ies and low egimes be ween
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he s udies. The use o a ealis ic, ansien inspi a ion p o ile in ou simula ions led o a highe
deposi ion e iciency compa ed o s udies ha employed s eady low condi ions, likely owing o he
highe peak eloci ies and esul ing highe S k numbe s in ou simula ions.
The nume ical analysis e ealed ha pa icles eleased a he beginning o he inspi a ion
cycle, when he low a es we e he highes , we e mo e likely o deposi in he uppe ai ways.
This inding highligh s he impo ance o conside ing ini ial high low a es when designing d ug
deli e y s a egies. Fo ins ance, adjus ing he elease iming o a oid his ini ial phase could
help p e en unwan ed deposi ion in he uppe ai ways. No signi ican di e ences in deposi ion
we e obse ed o pa icles eleased a e he i s hi d o he inspi a ion cycle, sugges ing ha
he ini ial high low a es had he g ea es impac on he deposi ion loca ion. Fu he mo e, only
negligible di e ences in deposi ion we e ound among he a ious b anching segmen s, indica ing a
ela i ely uni o m dis ibu ion o deposi ion h oughou he acheob onchial ee. App oxima ely
70% o he pa icles we e deposi ed du ing he i s inspi a ion cycle.
No ably, he o ien a ion-dependen deposi ion mechanism, which accoun s o he angle o he
ibe ela i e o he ai way wall, was ac i a ed in 93% o he pa icles. This emphasizes i s c ucial
ole in accu a ely p edic ing deposi ion, pa icula ly o applica ions such as locally a ge ed d ug
deli e y, in which p ecise con ol o e he deposi ion loca ion is essen ial.
Simula ing ib ous pa icles in ealis ic ai way geome ies using a ealis ic b ea hing p o ile
p o ides aluable insigh s in o op imizing he inhala ion p ocess and p edic ing ibe deposi ion
pa e ns. Howe e , he esul s also demons a ed ha cu en nume ical echniques o ibe mod-
eling, speci ically ELER, and he d ag models H-L and T-C, s ill exhibi some disc epancies com-
pa ed o he expe imen al da a, especially in he b anching egions. Fu he esea ch is needed
o imp o e hese echniques and expand hei applicabili y, ul ima ely enabling hem o eplace
o complemen expe imen al s udies in a wide ange o scena ios and con ibu ing o he ongoing
de elopmen o e ec i e medical ea men s.
This s udy also highligh s a key di e ence be ween sphe ical and ib ous pa icles: ibe s exhibi
a g ea e abili y o bypass he uppe ai ways and pene a e deepe in o he lungs. This inding has
impo an implica ions o unde s anding he po en ial heal h isks associa ed wi h inhala ion o
di e en ypes o pa icles and o de eloping a ge ed d ug deli e y s a egies ha can e ec i ely
each speci ic egions o he espi a o y sys em.
Finally, i is c ucial o conside he in luence o indi idual ai way geome ies and b ea hing
pa e ns on pa icle deposi ion. This s udy ocused on a emale ai way model, bu u u e e-
sea ch should in es iga e he di e ences in deposi ion be ween male, emale, and child ai ways
and e alua e he impac o a ious inhala ion egimes. This knowledge is essen ial o de eloping
pe sonalized inhala ion he apies ailo ed o he speci ic cha ac e is ics o indi idual pa ien s.
Acknowledgmen
This wo k was suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech Republic
h ough he e-INFRA CZ (ID: 90254), by he Czech Science Founda ion g an 22-20357S, and by
he in e nal esea ch p ojec o B no Uni e si y o Technology, eg. no. FSI-S-23-8192.
The au ho s exp ess g a i ude o Pa el F ¨oml o conduc ing a se ies o expe imen al measu e-
men s.
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Decla a ion o gene a i e AI and AI-assis ed echnologies in he w i ing p ocess
Du ing he p epa a ion o his s udy, he au ho s used Cha GPT, G amma ly, and Pape Pal
o imp o e he language and eadabili y. A e using hese ools, he au ho s e iewed and edi ed
he con en as needed and ook ull esponsibili y o he con en s o he published a icle.
Da a a ailabili y
The da a used in his a icle a e accessible in he Zenodo eposi o y unde he ollowing DOI:
10.5281/zenodo.15166271.
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Appendix A. De ail o he expe imen al se up
Figu e A.22: A ep esen a i e mic og aph showing collec ed glass ibe s on a il e memb ane
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Table A.2: Summa y s a is ics o he o al ibe coun s and hei leng h 2aand hickness dpob ained by he
expe imen al measu emen .
Segmen no. No. o pa icles Mean o dp(µm) S d. de ia ion o dp(µm) Mean o 2a(µm) S d. de ia ion o 2a(µm)
1 325264 2.0 1.3 15.8 14.5
2 96341 2.4 1.2 18.2 15.3
3 37160 1.9 1.0 20.1 15.9
4 42206 1.7 0.9 14.7 8.3
5 43583 1.9 1.1 14.8 11.5
6 42106 2.2 1.8 17.0 14.0
7 36242 1.6 0.6 13.7 9.4
8 29820 2.4 1.8 13.9 9.6
9 26608 1.4 0.6 14.3 8.3
10 20644 1.7 0.9 13.7 11.6
11 18351 1.6 0.7 21.3 18.5
12 22021 2.2 1.9 21.7 15.9
13 83954 1.9 0.7 14.3 10.3
14 30278 1.4 0.6 21.8 28.9
15 22021 1.9 1.1 15.7 12.8
16 112397 1.8 0.6 15.9 11.7
17 26608 1.9 0.8 21.2 13.7
18 53676 1.8 0.9 19.2 24.6
19 61016 1.9 0.7 21.4 24.4
20 23397 1.3 0.5 13.6 7.6
21 37160 1.5 0.8 15.1 10.6
22 38995 1.7 0.5 13.8 9.6
13o 856273 1.5 0.6 17.4 15.9
14o 585743 1.5 0.7 16.2 13.9
15o 757403 1.6 0.7 16.7 14.8
16o 1031666 1.6 0.7 17.3 15.2
17o 340679 1.5 0.6 16.5 16.9
18o 1087424 1.6 0.8 17.4 16.3
19o 837929 1.6 0.7 16.3 14.3
20o 347844 1.5 0.7 16.8 15.0
21o 847405 1.7 0.7 16.8 15.6
22o 1047117 1.6 0.7 16.1 14.9
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