Multiscale Simulation of Gas

donutsclubMechanics

Oct 24, 2013 (4 years and 17 days ago)

84 views

1

Multiscale Simulation of Gas
Flow in Subject
-
Specific Models
of the Human Lung

Ching
-
Long Lin
1
, Merryn H. Tawhai
2
, Geoffrey
McLennan
1

& Eric A. Hoffman
1


1
The University of Iowa, Iowa City, Iowa, USA

2
University of Auckland, Auckland, NZ




3
rd

MSM Consortium Meeting @ SIAM Conference on the Life Science


August 4
-
7, 2008, Montreal, Quebec, Canada

Outline


Current status of multiscale breathing lung
model by 3D
-
1D coupled data
-
driven approach


Some applications based upon 3D models
alone

2

3

Concept of Multiscale 3D
-
1D Coupling

1D Poiseuelle

3D Navier
-
Stokes


1D model
: entire conducting airways,
but less accurate flow solutions


3D model
: limited number of airways,
but more accurate flow solutions


Coupled 1D + 3D model
: benefits of
each approach


Model Progression

4

2004

2005

2006
-
2007

2006

11Gen

10M Elm


16
-
28Gen


2007
-
present

Gambit (manual)

Automation

3D
-
1D

5

Ultimate Goal

Establish a data
-
driven
1
, multiscale
2
, high
-
fidelity
parallel computational fluid
-
structure interaction
framework
3

to study the structure
-
function
relationship
4

in subject
-
specific human lungs.


Imaging (Drs. Hoffman &
vanBeek
, Iowa)


Geometric modeling (Dr.
Tawhai
, Auckland, NZ)


Fluid mechanics & Computing (Dr. Lin, Iowa)


Physiology & medicine (Drs. Hoffman, McLennan
&
vanBeek
, Iowa)

Iowa Comprehensive Lung Imaging
Center (I
-
CLIC): Director Dr. Hoffman

6

Multi
-
Detector row CT (MDCT) &

Micro CT scanner

Image Analysis
via

Pulmonary Workstation
©

7

3D airway & vessel trees

Regional air volume for BC

3D
-
1D mesh

Mesh Generation:
3D
-
1D/3D
-
3D
Coupling

8

3D
-
3D mesh by
gen.

&
path

Tawhai et al.,
ABME
, 28:793
-
802, 2000.

Tawhai et al.,
JAP
, 97:2310
-
2321,2004.

Lin et al.
,
IEEE EMB
, 2008.

3D
-
3D mesh by
lobe

R
ight
L
ower
L
obe

16
Gen airways

18M tetrahedral elem.

256 partitions (METIS)

9

Computational Methodologies


3D Characteristic
-
Galerkin FEM fractional 4
-
step
method for variable
-
property Navier
-
Stokes equations
1
.


Large
-
eddy Simulation (LES) and Direct Numerical
Simulation (DNS) for turbulent and transitional flow.


Level
-
set method for immiscible two fluids to simulate
two
-
phase flow phenomena in the lungs.


Species equations for miscible two fluids.


Arbitrary Lagrangian Eulerian (ALE) method for moving
boundaries & fluid
-
structure interaction (FSI)
2
.


Equation of motion for aerosol particle transport.


MPI
-
based Parallel Computing.

1
Lin, Lee, Lee & Weber,
Int. J. Numer. Methods in Fluids
, 49(5): 521
-
547, 2005.

2
Xia & Lin,
Computers & Structures
, 86: 684
-
701, 2008.

10

Validation & Verification

TeraGrid Computing


Lin et al.,
IJNMF
, 49, 2005.


Lin et al.,
RPNB
, 157, 2007.


Lee et al.,
APS
-
DFD
, 2005


Lee et al.,
JOT
, 1, 2007.


Lee et al.,
JHE
, in press, 2008.

2. LES of Pulmonary airflow


m6G

(medium
-
grid 6
-
G airway):
622K nodes, 3.2M elements.


c11G

(coarse
-
grid 11
-
G airway):
1.6M nodes, 6.7M elements.

m6G

c11G

1. LES of Turbulent channel flow

Re

= 12,700
(
Re


is 590)

Mesh=65x65x33; Dimension=4x2x2


Multiscale Simulation

11

Large airways

3D
CT

images

6
-
9G

Lung Parenchyma

CT

images


VF/CT
-
based 1D

centerline model


3D CT
-
derived upper & intra
-
thoracic
airways


turbulent/transitional

flow.


1D

centerline anatomic
-
based airways


provide a
link

between 3D airways
and lung parenchyma.


Image
-
based

BC for 1D terminal
bronchioles



use CT numbers
between volume scans to determine
air content at a local level.


Rigid

and
compliant

airway walls


Image Registration

fluid
-
structure
decoupled/coupled interaction

Subject
-
specific CT
-
based Airway Model

12


65 volumes


0.9M nodes


4.6M elements


128 paritions


TeraGrid

Upper Airways

Intra
-
thoracic

Central Airways

Trachea

LMB

RMB

BronInt

3 BCs


3D
-
1D
multiscale


Uniform velocity


Uniform pressure

3D
-
1D Coupled Simulation: Rigid Wall

Peak Inspiration
:

Mean U=1.24m/s

Re=1,363

13

Animation

Pressure Distribution

14

B

D

C

E

F, end of core

A, Mouth

Mouth cavity

Larynx

C

B

D

E

F, End of laryngeal jet

A, Mouth piece

Mouth cavity

Larynx

Trachea

Energy Budget

15

Upper airways

No upper airways


Pressure
-
Flow Relationship:

16

Large Airways

, where
k
=1 (laminar), 2 (turbulent), & 1.5 (1
-
D model)


Pressure
-
Flow Relationship:

17

Small Airways

Inspiration

Expiration

L
eft
L
ower
L
obe

Slope 2

Slope 2

Effect of BC on Regional Ventilation

18

Uniform Velocity

Uniform Pressure

3D
-
1D coupled

Pressure contours at peak inspiration

Vertical Distribution of Peripheral
Pressure & Regional Ventilation

19

Pressure

Flow

Lobar Flow Partition & Resistance

20

Resistance of each lobe

Flow rate of each lobe

1, LUL; 2, LLL; 3, RUL; 4, RML; 5, RLL

3D
-
1D

3D
-
1D

21

CFD & Bio
-
informatics from Lung Atlas


Use

1D centerlines and
branch points

to represent
individual branches.


Centerlines and associated
airway structures are
labeled
;
volume

and
surface

area

of
each segment are determined.


Length, diameter, branching
angle

and

rotation angle

of
each segment are calculated.


Statistical analysis of
branching pattern

due to
gender, age, and air pollution.

Image Registration for Lung Motion

22

Christensen, G. and H. Johnson. Consistent image registration.

IEEE Transactions on Medical Imaging, 20(5):568
-
582, 2001.

23

3D
-
1D Breathing Lung


IR
-
derived moving mesh


between TLC and FRC.


3D
-
1D coupled simulation


with a TV of 500 ml.


0
-
16 Gen


17.3M points


81.5M elements


512 partitions


24

3D
-
3D

16G High
-
Performance

Computing



Applications (AP)


Turbulent laryngeal jet


Inter
-
subject variabilities


Intra
-
subject variabilities


S
evere
A
sthma
R
esearch
P
rogram (SARP)


Inert gas washin and washout


Particle transport and deposition


Compliant airways: fluid
-
structure interaction


Acinar flow: mixing deep in the lung


Inter
-
species variabilities


25

26

AP1: Turbulent Laryngeal Jet

Case 1

Case 2

Mean speed: 2m/s

Re=1,700

T
urbulent

K
inetic

E
nergy

Lin, Tawhai, McLennan & Hoffman,
Respiratory Physiol. & Neurobiol.
,157:295
-
309, 2007.

27

AP2: Inter
-
subject Variabilities

Choi, Lin, Tawhai & Hoffman,
APS DFD
, 2007; manuscript in review, 2008.

(A) Subject H869 (B) Subject H1016

28

AP3: Intra
-
subject Variabilities

Choi, Lin, Tawhai & Hoffman,
APS DFD
, 2007; manuscript in review, 2008.

Mean velocity contours of subject
H1016

Re @ trachea=1482, 472

Flow rate 15.2 l/min, 4.83 l/min

Effect of truncated airway


(Re=1482)

Effect of boundary condition

AP4: SARP Severe Asthma

29

Triangular cross
-
section at trachea

30

AP5a: Mixing of Xe, He & Air (Upright)




Xe WI

Xe WO

He WI

He WO

Lin and Hoffman,
SPIE Medical Imaging: Physiology, Function, and Structure from Medical
Images
, 5746: 92
-
100, 2005.

AP5b: 1D Washin and Washout

31


Governing Equation:

1D Advection
-
diffusion equation





Washin

and Washout for 50 cycles each


inspiration

-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0.0
1.0
2.0
3.0
4.0
5.0
trachea
velocity (m/s)

time (s)

expiration

Node A

Node B

Node C

Node D

0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
100
200
300
400
500
Volume fraction

time (s)

Node A
Node B
Node C
Node D
Washout

Washin

Washin and Washout curve for
Xe
-
O
2

and air breathing

Xenon
-
concentration

Case 1

Case 2

AP6: Particle Transport & Deposition

32

Particle diameter: 1
μ
m 5
μ
m


Wall shear stress

generated by airflow
in the airways is reported to
elicit
biological relevant signals

(
Sidhaye

et
al
.,
PNAS
, 2008; Button & Boucher
RPNB

2008;Tarran
et al. JBC
. 2005).


The relationship between
airway wall
stiffness

and
shear stress

via. fluid
-
structure interaction (FSI).


Wall shear stress on rigid airways can
be
10 times

stronger than on compliant
airways (3
rd
-
4
th

generation bifurcation).

33

AP7: Structure
-
Function Relation:
Compliant Airways vs Wall Shear Stress

Xia, Lin, Tawhai, Hoffman,
APS DFD
, 2007; manuscript in review, 2008.

34

AP8: Acinar Flow
-

Chaotic Mixing &


Kinematic Reversibility

Re <0.6(~18
th

generation), recirculation disappears

3 sec

A Duct & 19 Alveolar Sacs

(Tawhai & Burrowes,

Anatomical Record

2003)

Kumar, Tawhai, Hoffman & Lin,
BMES
, 2006;
APS
-
DFD
, 2007; manuscripts in review, 2008.

Re =0.52

35

AP9: Inter
-
Species Variability
-

Sheep

Pressure

Contours

Kabilan, Lin, and Hoffman,
Journal of Applied Physiology
, 102: 1469
-
1482, 2007.

Streaklines

with markers

colored by

speed


7
-
13 gen.


451 outlets


3.5 M elems

Peripheral

Core

Summary


We have established a computational framework for
pulmonary flow that is:


Multi
-
scale via 3D
-
3D and 3D
-
1D coupling,


Data
-
driven for subject
-
specific lung motion and regional
ventilation,


High
-
fidelity and parallel high
-
performance for future
peta
-
scale computing.


We have applied it to study:


Turbulent laryngeal jet,


Inter
-
subject, intra
-
subject, and inter
-
species variabilities,


Energy budget analysis,


Wall shear stress in rigid and compliant airways for
airway remodeling


And more…





36

37

Acknowledgements


E. van Beek, MD PhD, G. Xia &
H. Lee, PhD


H. Baumhauer, J. Wilson, J. Sieren, and J.
Cook
-
Granroth


J. Choi, H. Kumar, Y. Yin and A. Lambert


SARP committee



NIH NIBIB R01 EB005823


NIH BRP R01 HL064368


NIH NCRR S10 RR022421


UI Clinical & Translational Science award


NSF TeraGrid for computer time

38

Thank You!