1. Par$cle
Deposi$on
in
Human
Lungs
due
to
Varying
Cross-­‐Sec$onal
Ellip$city
of
the
Le>
and
Right
Main
Bronchi
Introduc$on
The
authors
would
like
to
thank
Dr.
Jeff
Feinstein
for
providing
the
CT
image
dataset.
Results
Methods
Conclusions
Steven
C.
Roth,
Jessica
Oakes,
PhD,
Shawn
C.
Shadden,
PhD
Mechanical
Engineering,
UC
Berkeley
Email:
shadden@berkeley.edu;
Web:
shaddenlab.berkeley.edu
American
Physical
Society
68th
Annual
Division
of
Fluid
Dynamics
MeeCng
Boston,
MA|
Nov
22-­‐24,
2015
[1]
Fox
et
al+
Lazy
Dog
Weekly,
2014;
Biomechanical
Engineering
Computational
Laboratory
Image-­‐Based
Airway
Geometry
and
Mesh:
• Medical
CT
image
dataset
were
converted
into
a
3D
model
with
the
open
source
soUware
SimVascular
(hXp://simvascular.github.io/).
• Primary
bronchi
cross-­‐sec]ons
were
modified
to
three
various
major/minor
diameter
ra]os
of
the
airway
while
preserving
cross-­‐sec]onal
area.
• Geometries
were
meshed
with
unstructured
tetrahedral
elements
with
MeshSim.
• Boundary
layer
meshing
was
applied
at
the
wall
where
velocity
gradients
are
high.
Flow
and
ParCcle
Transport
SimulaCons:
• Assuming
incompressible
and
Newtonian
fluid,
the
fluid
velocity
and
pressure
were
calculated
by
solving
the
Navier-­‐Stokes
equa]ons:
with
a
stabilized
Finite
Element
solver.2
• Constant
flow
rate
(0.25
L/s)
was
prescribed
at
the
trachea
and
resistances
were
applied
at
the
outlet
faces
by
assuming
the
resistance
(R)
is
propor]onal
to
the
lobe
volume
and
the
cross-­‐sec]onal
area
frac]on:
• The
resistances
were
iterated
on
un]l
the
desired
flow
division
was
achieved:3
• Assuming
spherical,
and
non-­‐interac]ng,
par]cles
were
tracked
by
solving
a
reduced
form
of
the
Maxey-­‐Riley
equa]on:
• Flow
field
and
par]cle
deposi]on
sites
were
independent
of
the
mesh
and
par]cle
integra]on
parameters.
MoCvaCon:
• The
extent
of
par]cle
deposi]on
in
the
human
lungs
due
to
varying
lungs
geometries
has
yet
to
be
extensively
studied.1
• Complex
flow
structures
arise
due
to
varia]ons
in
lung
geometries
which
may
affect
par]cle
deposi]on.
Study
Overview:
• 3D
airway
geometries
were
studied
with
various
degrees
of
primary
bronchi
ellip]city.
• Airflow
and
par]cle
deposi]on
sites
were
determined
numerically.
Fig.
1:
Velocity
Magnitude
for
the
3
Airway
Geometries
Fig.
2:
Pressure
in
2:1
Geometry
• Velocity
magnitudes
are
higher
in
the
higher
ra]o
models.
The
secondary-­‐flow
velocity
magnitudes
are
the
highest
in
the
1.5:1
model.
• Fig.
2
shows
large
pressure
drop
across
the
lower
conduc]ng
airways.
• Par]cle
deposi]on
maps
(Fig.
3)
for
all
three
models
are
similar
to
each
other
and
thus
there
was
negligible
effect
of
the
cross-­‐sec]onal
ra]os
on
total
deposi]on
(Fig.
4).
• Dean-­‐like
flow
structures
occurred
in
the
main
bronchi
of
all
models.
Recircula]on
zones
were
enhanced
in
the
models
with
the
smaller
ellip]city
ra]os.
• Varying
main
bronchi
ellip]city
did
not
influence
the
total
par]cle
deposi]on
in
the
airways.
Future
ConsideraCons:
• To
fully
understand
the
effect
of
the
main
bronchi
ellip]city
on
par]cle
deposi]on,
unsteady
flow
and
resistance-­‐compliance
boundary
condi]ons
should
be
considered.
[1]
Snyder,
B.,
and
D.
E.
Olson.
"Flow
development
in
a
model
airway
bronchus."Journal
of
Fluid
Mechanics
207
(1989):
379-­‐392.
[2]
Taylor,
C.,
Hughes,
T.,
and
Zarins,
C.
“Finite
element
modeling
of
blood
flow
in
arteries.”
Computer
Methods
in
Applied
Mechanics
and
Engineering.
(1998):
155-­‐196.
[3]
Horsfield,
Keith,
et
al.
"Models
of
the
human
bronchial
tree."
Journal
of
applied
physiology
31.2
(1971):
207-­‐217.
Qin (mm3
/s) RT (g/mm4 ·s) VF(RU) VF(RM) VF(RL) VF(LU) VF(LL)
2.5 · 105
1.96 · 10−4
0.21 0.09 0.25 0.20 0.25
Table
1:
Simula$on
Parameters3
2:1 1:1
g/mm-s2
Particle Diameter ( µm)
1 3 5 7 9
PercentDeposited
0
10
20
30
40
1:1
1.5:1
2:1
Fig.
3:
Par$cle
Deposi$on
Map
(7
microns)
Fig.
4:
Total
Percent
Deposi$on
in
Airways