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2010 CSSR 2010 Initial Submission

The Effect of Mild Stenosis to Flow in Trachea

K. Osman, W.M.Basri, N.H. Johari*, M.Rafiq

Faculty of Mechanical EngineeringUniversiti Teknologi Malaysia,81300 Skudai, Johor, Malaysia

*Faculty of Mechanical EngineeringUniversiti Malaysia Pahang,

26600 Pekan, Pahang, Malaysia

Tel: (6019) 9111787

E-mail: [email protected]

Abstract — Flow in the trachea is essential to be properly

understood since it is the inlet to the lungs. Disturbance to

this flow will disrupt the inlet conditions to both bronchi. In

this study, disturbance of flow due to mild stenosis is

investigated via numerical models. The effect of various

stenosis sizes, at the middle of the trachea, to the flow

pattern is studied and analyzed. 3D simplified trachea

models were used and different flow conditions were

applied. The results show two stages of pressure drop

behavior appear as the size of the stenosis reaches fifty

percent of the airway size. The inlet condition to the bronchi

is also significantly disturbed as the stenosis reaches fiftypercent.

Keywords—CFD; Trachea Stenosis; Pressure; Velocity

I. I NTRODUCTION

The tracheobronchial tree in human lung has gainedattraction as a subject of research either from medical-

based researchers or their non-medical counterpart. This breathing organ used to be a biological vent or tube tomove the airflow and particles to the lower human airwayswhen the diaphragm is expended. For the flow insidetrachea, it is essential to be properly understood since it isthe primary inlet to the lungs. Any disturbance to this flow

will disrupt and alter the inlet boundary conditions to bothmain bronchi.

Tracheal stenosis is one of the respiratory diseases thatobstruct the flow from moving deep down into the lung.The progressive increment of tracheal stenosis sizes

before clinically impairment always experienced by patient and when the constriction reaches certain values,the pressure drop becomes critical and symptoms rapidlyhappen [1]. Thus, investigation on airflow in trachealstenosis is widely open to be understood.

The trachea consists of cartilaginous and membranoustube. The shape is quite cylinder and being flattened

posterior with most common shape of elliptical, circular,D-shaped, C-shaped, U-shaped and triangular [2]. It

measures about 9-12cm in length and about 2-2.5cm indiameters from side to side. Beneath the basementmembrane there is a distinct layer of longitudinal elastic

fibers with a small amount of intervening alveolar tissue.The submucous layer is composed of a loose mesh-workof connective tissue, containing large blood vessels,nerves, and mucous glands; the ducts of the latter piercethe overlying layers and open on the surface. Thedescription of complex anatomy of trachea gave limitedaccess of usage in modeling the realistic tracheobronchialfor research purpose. Due to the fact that human lung hasan extremely complex asymmetric and irregular shapevarying substantially per individual, [3] the investigationsof airflow and particles inside human lung were proceed

with idealized simplified model. For this study, theidealized model with simplify of shape and smooth walls

based on Schlesinger and Lippman model (1972) [4] wereused because this model is described as asymmetric andsubsequent bifurcation with opening angles most likelycadavers. The stenosis shape was also most easily appliedto the Schlesinger and Lippman model because it can bemodified and modeled according to the medical diseasetrachea.

Parallel with the advancing of computing technology,numerical method of Computational Fluid Dynamics(CFD) has been an eminent choice of method to studyflow in human airways. There have been many numericalstudies involving idealized smooth wall models in

determining the airflow and particle deposition analysis.[5- 9]. However, studies on diseases tracheal have receivedrelatively small numbers of researchers. Mark et al. (2006)[1] has focused on the effect of stenosis at trachea on howstenosis affects pressure drops. Farkas et al. (2007) [10]has studied on simulation of the effect of localobstructions and blockage on airflow and aerosoldeposition in central human airways.

For this paper, the objective was to determine the effectof tracheal stenosis to the flow pattern, with different sizesof stenosis and types of breathing. The pressure andvelocity distribution inside trachea and main bronchi wereobserved clearly and finally the models will provide aquick result of how severe the breathing difficulty due to

this stenosis effect.

2010 International Conference on Science and Social Research (CSSR 2010), December 5 - 7, 2010, Kuala Lumpur, Malaysia

978-1-4244-8986-2/10/$26.00 ©2010 IEEE 367

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II. METHODOLOGY

A. Airway Model

The geometry of the models used for this study is

based on human airway casts by Schlesinger and

Lippmann [4] study. This geometry was obtained from

the autopsy specimens of the human trachea and lungs

with no gross abnormalities. The cylinder shaped with

uniformed in diameter of trachea and main bronchi wasused because of the inconsistent shape of trachea and

main bronchi of an actual human airway. Asymmetric

shape between left and right bronchi begins at bifurcation

region. Detailed dimensions of the model are shown

Table 1. Referring to Figure 1, noted that ‘left’ and ‘right’

refer to the anatomical orientation of the human body andthe location of the stenosis. This location of stenosis is

located at the middle of trachea region and it is parallel

with the proposal of stenosis location by L.Freitag (2007)

[11] as one of the regular locations of central tracheal

stenosis.

Table I: Dimensions used for the model based on

Schlesinger and Lippman geometry.

Diametera

(cm)

Length

(cm)

Angleb

(degree)

Trachea 2.17 9.2

Right

bronchi

1.7 4.2 15

Left bronchi

1.26 5.3 30

a These values represent the mean of transverse diameters

at the midpoint of each branch b These values represent the angle of branching between

the indicated branch and its parent branch

The Schlesinger model was then modified withdifferent sizes of mild stenosis (10% up to 50% out oforiginal trachea diameter). The mild stenosis was chosenin this study for the purpose of early warning detection ondisturbed flow inside the trachea patient. According toM.Brouns (2006) [1], patients of stenosis always referredfor treatment typically are asymptomatic until criticalnarrowing of the airways occurs. Thus, the mild stenosis iscompleted the objective of flow parameters analysis inorder to provide early warning detection. Shape of thestenosis is developed with semi-circle shaped and placedat around the location. This shaped is based on a simpletypes of stenosis, quite similar with tapered transition andscar stricture [11].

B. Boundary Conditions

The velocity inlet was used and applied at the inflow boundary at trachea. It was assumed that the volumedistal to the respiratory bronchioles was the same throughthe lung and the change in volume was the same at any

location. The temperature effect was assumed isothermal;steady state condition with the used of constant Re.Incompressible flow is assumed as this flow has lowMarch number. Also, no-slip boundary condition was

assumed [12] and the airways walls were assumed to be arigid body.

Fig. 1: A reconstructed model of normal trachea andmain bronchi with the indication of stenosis location

Fig.2: Size of stenosis growth by diameter percentages at predefined location of stenosis. Narrowing of diametersizes is made from 10 up to 50%

For a human breathing system, the frequency of breathing differs based on the types of activity whichsimultaneously resulting different values of Re. For thisstudy, there are three types of breathing condition whichare simulated based on different range of Re. These three

breathing conditions are resting, moderate and extreme.Zheng Li et al. (2007) [13] had studied the human airwayflow of resting condition with Re of 1201. For moderate

breathing condition, Luo et al. (2004) [5] had made astudy by using the value of 3012 for Re that imposed this

condition of moderate. This study also used the velocityinlet from Calay et al (2002) [14] for extreme breathing

Stenosislocation

LeftRight

50%

40%

30%

20%

10%

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condition with 4.66x104 of Re. The extreme breathing

condition occurred when heavy exercise activity took place. From those three previous studies, Re for eachcondition was collected and used in defining the

boundary conditions of this study. The air physical properties and boundary condition parameters used forthis study are summarized in following Table 2 and Table

3 respectively.Table II: Physical properties of airflow

Operating pressure (kPa) 101

Physical properties,

Density ρ (kg/m3)

Viscosity μ (kg/ms-1

)

1.19

1.82 x 10-5

Table III: Summarized boundary condition parameters for

each condition of breathing

Parameters Resting

(Zheng Li

et al.)

Moderate

(Luo et al.)

Extreme

(Calay et

al.)

Re 1.201x103

3.012x103

4.66x104

Inlet diameter

(m)

0.0217 0.0217 0.0217

Inlet velocity

(m/s)

0.85 2.03 32.84

Inspiratory

rate (l/min)

18.77≈19 45 726

Pressure

outlet (Pa)

101325 101325 101325

III. RESULTS

Simulations were made on the airway models withstenosis constriction and the results of these simulationswere analyzed in pressure and velocity drivenrespectively.

A. Pressure Distribution

The effect of growth stenosis varies the pressuredistribution inside the airway model. In Fig. 3, pressuredistribution over the cross section along the airway modelis plotted as a function of length for flow of restingcondition. The effect of the constriction which is locatedat L/Lo=63.0+1.0 is observed to be in same pattern ofcurve but varied in magnitude and it shows significantchanges in pressure distribution in the respiratory system.

From Fig 3, pressure begins to drop as flow passesthrough the stenosis constriction area. At 10% of stenosisconstriction, pressure distribution shows a very smallchange as it passes through the constriction area. As sizeof stenosis constriction increases to 20%, pressure starts todrop after passing through stenosis constriction. Thisevent of pressure drop is repeated at 30% where at 30%the pressure drop records even larger difference of

pressure from its previous sizes. As stenosis constriction isincreased in size, the pressure drop as flow passes throughthe stenosis constriction also increases in magnitude.Therefore, as observed from this study on restingcondition with stenosis constriction from 10 to 50% ofconstricted size, the highest pressure drop is observed at

the downstream of 50% which it produces the higher pressure gradient.

Fig. 3: Pressure distribution across the airway model ofresting condition (Re=1.201x10

3)

The same pattern of curve was obtained as referred toFig. 4 and Fig. 5 which is also the plot of pressuredistribution along the airway model as a function of lengthfor moderate and extreme breathing conditionrespectively. Note that by comparing Fig. 3 with Fig. 4and Fig. 5, the obtained range of maximum and minimumof P/Po is different. Moderate breathing condition is largerin range than the resting condition. This shows thatmoderate condition experiences more pressure drop asflow passes through the stenosis constriction, compared toresting condition. Meanwhile, extreme condition has evenlarger range than the moderate and resting condition. Thesame event of pressure drop can be interpreted from Fig. 5of extreme condition when comparison with resting andmoderate condition is made where extreme condition hasmore pressure drop than resting and moderate condition.

Fig. 4: Pressure distribution across the airway model ofmoderate condition (Re=3.012x10

3)

As flow passes through the constriction area, pressure isreduced which then resulting the pressure that enters themain bronchi. The pressure at a location just before theinlet of main bronchi was then plotted in Fig. 6 and Fig. 7where for each size is compared with 10% of stenosisconstriction. The losses of pressure as the stenosis weremade increased show that the ratio of pressure drop at theinlet of bronchi was also increased. The same pattern was

obtained as referred to Fig. 7 for moderate and extremecondition.

0.999910

0.999920

0.999930

0.999940

0.999950

0.999960

0.999970

0.999980

0.999990

1.000000

1.000010

0 20 40 60 80 100 120 140 160 180 200

P / P o

L/Lo

Pressure Along the Model of Resting Condition With Stenosis

Constriction

10%

20%

30%

40%

50%

0.999500

0.999600

0.999700

0.999800

0.999900

1.000000

1.000100

0 20 40 60 80 100 120 140 160 180 200

P / P o

L/Lo

Pressure Along the Model of Moderate Condition With Stenosis

Constriction

10%

20%

30%

40%

50%

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Fig. 5: Pressure distribution across the airway model ofextreme condition (Re=4.66x10

4)

Fig. 6: Pressure at a location just before the inlet of main bronchi for each size, compared with pressure inlet atmain bronchi of 10% (▲resting and ■ moderatecondition)

Fig. 7: Pressure at a location just before the inlet of main bronchi for each size, compared with pressure inlet atmain bronchi of 10% (■ moderate condition and ♦ extreme condition)

From Fig. 3, 4 and 5, graphs of correlation were madefor those three conditions. The differences between

maximum and minimum of P/Po for each size of stenosisconstriction were calculated and plotted in Fig. 8 forresting, Fig. 9 for moderate and Fig. 10 for extreme

condition. Referring to these figures, two trends of curvewere identified which it is denoted by the linear fittingequations for each line. From 10 to 30% of stenosisconstriction for all three conditions, it is put in a group sothat it fits the equation of linear fitting. The same goes tostenosis from 40 to 50%. Slope for each line is calculatedso that the risk of pressure drop can be determined

approximately as the stenosis constriction increases. Bycomparing the slopes between those three conditions, it isobtained that resting condition produces the lowest slopesfor both lines (10 to 30% and 40 to 50%). For moderatecondition, the acquired slopes are higher than slopes forresting condition. This shows that the risk of pressure dropincreases as Re increases. The pattern of the slope is theninfluenced by the size of stenosis constriction. Extremecondition (with the highest in Re than resting andmoderate condition) generates the highest slopes,compared to resting and moderate.

Fig. 8:Range of (P/Po) between maximum and minimumfor each stenosis constriction size of resting condition

Fig. 9:Range of (P/Po) between maximum and minimumfor each stenosis constriction size of moderate condition

By comparing the slope of 10 to 30% and 40 to 50%,the severity of pressure drop for each condition can besummarized as in Fig. 11. As observed from Fig. 11, theseverity of pressure drop for extreme condition shows thehighest in risk whereas the slope of 40 to 50% hasapproximately 12 times higher of pressure drop than the

slope of 10 to 30%. More reduction in pressure due tostenosis constriction means that the difficulty of breathingis getting harder to perform.

0.840000

0.860000

0.880000

0.900000

0.920000

0.940000

0.960000

0.980000

1.000000

1.020000

0 20 40 60 80 100 120 140 160 180 200

P / P o

L/Lo

Pressure Along the Model of Extreme Condition With Stenosis

Constriction

10%

20%

30%

40%

50%

3.49E-04

2.69E-03 2.69E-03

6.92E-03

0.00E+00

1.84E-03

3.57E-03

7.81E-03

2.12E-02

0.00

0.01

0.01

0.02

0.02

0.03

0 10 20 30 40 5 0

D i f f e r e n c e o f P r e s s u r e a t B r o n c h i I n l e t P e r c e n t a g e ( % )

Stenosis Size (%)

Comparison of Pressure at the Inlet of Bronchi for Each Size with 10% of

Stenosis Constriction (Resting and Moderate Condition)

Resting

Moderate

1 .8 4E-0 3 3.5 7E-0 3 7.81E-03 2.12E-020.00E+00

2.65E-01

6.07E-01

1.82E+00

5.62E+00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 10 20 30 40 50

D i f f e r e n c e o f P r e s s u r e a t B r o n c h i I n l e t P e r c e n t a g e ( % )

StenosisSize (%)

Comparison of Pressure at the Inlet of Bronchi for Each Size with 10% of

Stenosis Constriction (Moderate and Extreme Condition)

Moderate

Extreme

0.00000

0.00001

0.00002

0.00003

0.00004

0.00005

0.00006

0.00007

0.00008

0.00009

0.00010

0 10 20 30 40 50

∆ ( P / P o )

Stenosis Constriction (%)

Correlation of∆(P/Po) Over Stenosis Constriction for Resting Condition

y=0.5470e-06x+0.7518e-06 y=0.0050e-03x-0.1625e-03

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

0.00040

0.00045

0.00050

0 10 20 30 40 50

∆ ( P / P o )

StenosisConstriction (%)

Correlation of∆(P/Po) Over Stenosis Constriction for Moderate

Condition

y=0.2985e-05x-0.9325e-05 y=0.0269e-03x-0.8911e-03

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Fig. 10: Range of (P/Po) between maximum andminimum for each stenosis constriction size of extreme

condition

Fig. 11: Severity of pressure drop analyzed from slopes of10 to 30% and 40 to 50%

B. Velocity Profile

Fig. 12, 13 and 14 demonstrate the velocity distribution

along the airway model. Basically, the results of velocity

distribution are conversed with the results of pressure

distribution. Again, the effect of stenosis growth variesthe velocity distribution inside the airway model. As flow

passes through the constricted area, velocity increases

dramatically. This event of increasing velocity when flow

passes through constricted area of stenosis is agreed with

the flow through orifice concept. Then, as flow travelsafter stenosis through the remaining part of trachea,velocity starts to reduce with slightly small in magnitude.

Reaching the bifurcation area, flow is then divided into

the division of bronchi where here it is clearly noted that

the velocity of flow (as it enters bronchi) shows a really

significant velocity reduction. Passing the main bronchiand heading to the outlets, velocity seems to fluctuate.

This event of fluctuation is maybe due to the grid of

meshing used in the simulation.

Fig. 12: Velocity distribution along the airway model forresting condition (Re=1.201x10

3)

Fig. 13: Velocity distribution along the airway model formoderate condition (Re=3.012x10

3)

Comparison is made on differences of velocitymagnitude at a location just before flow enters main

bronchi with velocity of 10% stenosis constriction.Generally from Fig. 15 and 16, the plot of velocity tendsto decrease which is meant that the velocity at the location

just before flow enters the main bronchi is higher than itsvelocity at 10% stenosis constriction for each condition.Also, it is observed that velocity at the location beforeflow enters the main bronchi is always higher than inletvelocity at trachea and the accumulating magnitude ofvelocity as it passes through stenosis constriction isinfluenced by the size of stenosis constriction. The

dramatic raise of velocity as flow passes through stenosisconstriction simultaneously reduces pressure and as pressure is reduced in the human airway, the driving forcefor respiratory system is also reduced. This results indifficulty of breathing.

0.00000

0.02000

0.04000

0.06000

0.08000

0.10000

0.12000

0.14000

0.16000

0 10 20 30 40 50

∆ ( P / P o )

Stenosis Constriction (%)

Correlation of∆(P/Po) Over Stenosis Constriction for Extreme Condition

y=0.0087x-0.3031 y=0.0007x-0.0038

1.09E-01 1.11E-01

1.24E+01

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

Resting Moderate Extreme

R i s k

o f P r e s s u r e D r o p

BreathingCondition

Comparison of Pressure Drop Between Slopes for Each Condition

(Interpreted from Fig. 8, 9 and 10)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 20 40 60 80 100 120 140 160 180 200

V / V o

L/Lo

Velocity Along the Model of Resting Condition W ith Stenosis

Constriction

10%

20%

30%

40%

50%

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 20 40 60 80 100 120 140 160 180 200

V / V o

L/Lo

Velocity Along the Model of Moderate Condition With Stenosis

Constriction

10%

20%

30%

40%

50%

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Fig. 14:Velocity distribution along the airway model forextreme condition (Re=4.66x10

4)

Fig. 15: Velocity at a location just before the inlet of main bronchi for each size, compared with velocity inlet atmain bronchi of 10% (resting and moderate condition)

Fig. 16: Velocity at a location just before the inlet of main bronchi for each size, compared with velocity inlet atmain bronchi of 10% (moderate and extreme condition)

IV. CONCLUSIONS

Firstly, this CFD method had solved a fluid dynamic inthe simplified model of human airway. The effects ofstenosis constriction at a predefined location were thenanalyzed. The size of constriction was made increased

from 10 to 50%. The results showed a series of pressuredrop as flow passes through the constriction area. As thestenosis size increased, the range of pressure drop betweenmaximum and minimum of P/Po was also increased. For10 to 50% of stenosis constriction, the severity of pressuredrop for extreme condition was approximately 12 timeshigher than resting and moderate condition. As for

velocity distribution, flow showed increment in velocitymagnitude as it passed through the constriction. Theincrement of velocity at larger size of constriction washigher than the smaller size of constriction. Also, flow asit entered the main bronchi was higher than its magnitudeat trachea inlet.

In conclusion, the size of stenosis constriction gives asignificant effect to the flow in an obstructed humanairway. Due to this constriction, the higher in magnitudeof pressure drop produces a harder condition in difficultyof breathing. The interpretation of pressure drop is agreedwith the results of velocity distribution of this study.

ACKNOWLEDGMENT

Aid from Computational Fluid Mechanics Lab, UTM isvery much appreciated in the completion of this study.

R EFERENCES

[1] Mark B.M,Jayaraju, S.T. Lacor C., Mey JD,, Noppen M, Vincken,W.Verbanck, “Tracheal stenosis” A Flow Dynamics Study,Journal Applied Physiology 2006

[2] Mehta S.Myat HM, The cross sectional shape and circumferenceof the human trachea, Ann Royal College Surg Englan1984;66:356-8

[3] R.K.Freitas, W.Schroder, Numerical investigation of the three-dimensional flow in a human lung model, Journal odBiomechanics 41 (2008) 2446-2457

[4] Sclesinger RB, Lippmann M., “Particle deposition in casts of the

human upper tracheobroncial tree”. Am Ind Hyg Assoc J1972;33:237-51.

[5] Luo XY, Hinton JS, Liew TT, Tan KK. LES modeling of flow in asimple airway model. J Med Eng Phys, 2004;26:403

[6] Wang JB, Lai ACK. A new drift-flux model for particle transportand deposition in human airways. J Biomech, Eng 2006; 128:97–105.

[7] Zhang Z, Kleinstreuer C, Donohue JF, Kim CS. Comparison ofmicroand nano-size particle depositions in a human upper airwaymodel. J Aerosol Sci 2005;36:21 1–33

[8] Y.Liu, R.M.C. So, C.H. Zhang, Modeling the bifurcating flow in ahuman lung airway, Journal of Biomechanics 35 (2002) 465-473

[9] G.yu, Z.Zhang, R.Lessmann, Computer simulation of the flow fieldand particle deposition by diffusion in a 3-D human airway

bifurcation,Aerosol Science and Technology (1996), 25:3,338-352

[10] Arpad Farkas, Imre Balashazy, “Simulation of the Effect of Local

Obstructions and Blockage on Airflow and Aerosol Deposition inCentral Human Airways.” Elsevier, 2007

[11] L. Freitag, A. Ernst, M. Unger, K. Kovitz and C.H. Marquette, AProposed Classification system of central airway stenosis, EurRespir J 2007; 30::7 7 -12

[12] Yang X.L. and Liu Y., “Simulation of effect of COPD onrespiratory flow”, Tsinghua University Press & Springer-Verlag,2006.

[13] Zheng Li, Kleinstruer C. and Zhang, Z., “Simulation of airflowfields and microparticle deposition in realistic human lung airwaymodels. Part I: Airflow patterns”. Journal of Mechanics-B/Fluids,2007

[14] Calay R.K, Kurujareon J. and Holdo A.E., “Numerical simulationof respiratory flow patterns within human lung” Respiratory physiology and neurobiology, 130,201-221,2002

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 20 40 60 80 100 120 140 160 180 200

V / V o

L/Lo

Velocity Along the Model of Extreme Condition With Stenosis

Constriction

10%

20%

30%

40%

50%

-2.12E+01

-6.08E+01

-1.14E+02

-1.98E+02

0.00E+00

-2.28E+01

-6.08E+01

-1.14E+02

-1.14E+02

-250

-200

-150

-100

-50

0

0 10 20 30 40 50

D i f f e r e n c e o f V e l o c i t y a t B r o n c h i I n l e t P e r c e n t a g e ( % )

Stenosis Size (%)

Comparison of Velocity at the Inlet of Bronchi for Each Size with 10% of

Stenosis Constriction (Resting and Moderate Condition)

Resting

Moderate

0.00E+00

-2.28E+01

-6.08E+01

-1.14E+02

-1.14E+02

- 1. 73 E+ 01 - 1.7 3E+ 01

-1.11E+02

-4.51E+01

-140

-120

-100

-80

-60

-40

-20

0

0 10 20 30 40 50

D i f f e r e n c e o f V e l o c i t y a t B r o n c h i I n l e t P e r c e n t a g e ( % )

StenosisSize (%)

Comparison of Velocity at the Inlet of Bronchi for Each Size with 10% of

Stenosis Constriction (Moderate and Extreme Condition)

Moderate

Extreme

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