Characteristic size research of human nasal cavity and the respiratory airflow CFD analysis

doi:10.4236/jbm.2013.12006

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Journal of Biosciences and Medicines, 2013, 1, 23-27 JBM

http://dx.doi.org/10.4236/jbm.2013.12006 Published Online October 2013 (http://www.scirp.org/journal/jbm/)

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Characteristic size research of human nasal cavity and the

respirato ry airflow CFD analysis*

Jun Zhang

Advanced Technology of Transportation Vehicle Key Laboratory of Liaoning Province, Dalian Jiaotong University, Dalian, China

Email: [email protected]

Received 2013

ABSTRACT

To study the airflow distribution in human nasal cav-

ity during respiration and the characteristic parame-

ters for nasal structure, thirty three-dimensional,

anatomically accurate representations of adult nasal

cavity models were reconstructed based on processed

tomography images collected from normal people.

The airflow fields in nasal cavities were simulated

using the fluid dynamics with the finite element soft-

ware ANSYS. The results showed that the difference

of human nasal cavity structure led to varying airflow

distribution in the nasal cavities and the main airflow

passed through the common nasal meatus. The nasal

resistance in the regions of nasal valve and nasal ves-

tibule accounted for more than a half of overall resis-

tance. The characteristic model of nasal cavity was

extracted based on the characteristic points and di-

mensions deducted from the original models. It

showed that either the geometric structure or the air-

flow field of the two kinds of model was similar. The

characteristic dimensions were the characteristic pa-

rameters of nasal cavity that properly represented the

original model in research for nasal cavity.

Keywords: Nasal Cavity; Characteristic Dimension;

Three-Dimensional Reconstruction ; Numerical

Simula tion of Flow Field; Computational Fluid

Dyn a mic ; Finite Element Method

1. INTRODUCTION

Nose is the first barrier of defense to outer invasions in

the human respiratory system that is protective for life

long. It provides functions of filtering, warming, and

moistening inhaled air and protects the delicate structure

of the lower respiratory system. With the current devel-

opment of research towards the pathogenic mechanism

and the application of iatrical apparatus such as endos-

copes, it has been demonstrated that certain nasal diseas-

es are closely related to the abnormal structure of nasal

cavity [1]. Some researchers have investigated the air-

flow characters in nasal cavity to try to find the corre la-

tion between the nasal structure and the nasal disease [2].

The method of numerical simulation for airflow is help-

ful to this investigation. By simulating the structure and

function of the nasal cavity with three-dimensional re-

construction theory with a computer, we can profoundly

explore the outbreak, treatment and prevention of nasal

diseases. Keyhani [3] constructed a finite element mesh

of the human nasal cavity from the CAT scans. In his

work, the steady-state N avier-Stokes and continuity equ-

ations were solved numerically to determine the laminar

airflow patterns in the nasal cavity at quiet breathing

flow rates. The numerical results were validated by com-

parison with detailed experimental measurements from

Hahn’s [4] study. Martonen [5] et al. constructed a three-

dimensional computational model of the human upper-

respiratory tract that featured both sides of nasal cavity.

The model included airways of the head and the throat

based on a cast of a medical school teaching model. The

results showed the airflow patterns in different flow rate

values and the velocity profiles during inhalation and

exhalation. Subramaniam [6] et al. represented a three-

dimensional, computational model of an adult human’s

nasal cavity and nasopharynx, and solved the Navier-

Stokes and continuity equations for airflow using the

finite-element method under conditions of steady-state

inspiratory. The model was developed from magnetic

resonance imaging scans of a person’s nose. The nasal

cavity model was divided into several regions and the

flow apportionment among different regions of the nose

was detailed. Kim [7] investigated airflows in normal

and abnormal nasal cavities and surgically created mod-

els experimentally by Particle Image Velocimetry (PIV).

The average distributions of airflow in normal and ab-

normal nasal were obtained. In the case of simulation of

surgical operations, velocity distribution in coronal sec-

tion changed locally. Reimersdahl [8] and Hörschler [9]

presented the results of numerical simulation of the air-

flow in a model of the human nasal cavity which showed

*Project of Liaoning Province Education Department, LS2010030.

J. Zhang / Journal of Biosciences and Medicines 1 (2013) 23-27

a good agreement with the experimental findings. Till

now, little potent principle for describing the nasal cavi-

ties with characteristic parameters of nasal structure has

been put forward.

It is essential to build various numerical models to in-

vestigate airflow characters in different nasal structure

considering the individual difference of human nasal

cavity. In this paper, thirty finite element models of nasal

cavity of healthy volunteers were reconstructed. The

simulation results showed the distribution of airflow and

the relationship between the airflow distribution and the

nasal cavity structure. One of these models was com-

pared with its characteristic model in geometrical struc-

ture and airflow field to evaluate the feasibility of the

method for extracting characteristic dimensions of hu-

man nasal cavities.

2. METHODS

2.1. Reconstruction of Models

Thirty volunteers (18 males and 12 females aging from

25 to 55 years, median 30 years, Han nationality) from

Northeast China were randomly selected. They did not

have histories of nasal diseases or any other abnormity in

the nasal passages. Each volunteer was fully examined

by nasal anterior rhinoscopy and endoscopy which al-

lowed researchers to qualitatively designate his or her

septum as having no deviation. The nasal models were

developed from CT scans operated in the Second Affi-

liated Hospital of Dalian Medical University. The coron-

al images of nasal cavity at intervals of 3 mms wer e used

to complete the reconstruction since the coronal view

could best illustrate nasal structure. With the assistance

of a radiologist and a surgeon expertised at nasal CT

scans and anatomy, the interface between the nasal mu-

cosa and air in the nasal cavity was delineated from each

coronal image which would be linked together to form a

three-dimensional model. The models were constructed

and meshed automatically by the finite element software

of ANSYS after necessary artifact correction was carried

out.

The horizontal, sagittal and top views of a meshed

nasal model example are shown in Fi g u re 1 . The models

at the air outlet were lengthened artificially so that air-

flow could extend thoroughly there.

2.2. Numerical Simulation

The governing equations for the airflow through the up-

per airway are the conservation of mass (continuity) and

the Navier-Stokes equations, expressed as:

xyz

∂

∂∂

++=

∂∂∂

(1)

Figure 1. Three-dimensional reconstruction

model of the nasal cavity.

xxxx

x y zxx

x y zyy

zzzz

x y zzz

uuuup

uuufu

txyz x

uy uyuyp

uuu fu

txyz y

uuuu p

uuufu

txyz z

∂∂∂∂∂

+++=−+ +∇

∂∂∂∂∂

∂

∂∂∂ ∂

+++=−+ +∇

∂∂∂∂ ∂

∂∂∂∂∂

+++=−++∇

∂∂∂∂∂

(2)

where

are the velocity component in the

Cartesian coordinates and p stands for the pressure. P is

the mass density of air and υ is its dynamic viscous coef-

ficient.

The nostril (Section Ω1 of Figure 1) directly opened

to the atmosphere with pressure boundary condition PΩ1

= 101,325 Pa. The interior wall (Section Ω of Figure 1)

of the nasal cavity was simplified as a rigid surface since

the deformation is minor and consequently weakly af-

fects the airflow field. The non-slip boundary condition,

uΩ = 0, was assigned to the inner wall. The regular in-

spiratory capacity for a relaxed, steady inhalation/exha-

lation is between 400mls and 600 mls per period [10]

with an inspiratory rate of 15 - 25 breath/minutes [11]

based on medical observations. The upper limit value of

600 mls was adopted in this paper. It was assumed that

the breathing period (the cycle of an inhalation and an

exhalation) is 3 seconds, and airflow velocity varies li-

nearly with time at the exit section, as shown in Figure 2.

The vertical axis and the horizontal axes showed airflow

flux and time, respectively. Point a showed the peak val-

ue of airflow flux in an inspiration period; point b

showed the peak value of airflow flux in an expiration

period. At the exit section, the peak velocity was calcu-

lated through uΩ2 = Q /0.75S, where Q was the tidal vo-

lume and S was the cross sectional area of the exit. The

velocity boundary condition was given at the top cross

section of the oropharynx (Section Ω2 in Figure 1)

based on the above assumptions.

Airflow through the nasal cavity was numerically si-

mulated over the entire breathing period after the model

was meshed with tetrahedron element. The airflow was

described as a transient-state turbulence flow with gas

parameters ρ = 1.25 kg/m3, υ = 1.7894 × 10−5 N·s/m2.

J. Zhang / Journal of Biosciences and Medicines 1 (2013) 23-27

Figure 2. The change of flow rate with time in a breath-

ing period.

The standard k-ε turbulent model was adopted in AN-

SYS.

2.3. Extraction of Characteristic Dimensions

The nasal cavity was divided into six main parts: nasal

vestibule, nasal valve, common nasal meatus, middle

nasal meatus, inferior nasal meatus and nasopharynx

region, which were defined as characteristic structures of

nasal cavity. The proper cross-section of nasal cavity

could be found out where the middle and inferior turbi-

nates just appeared or disappeared (blue lines in Figure

3(B)), and the juncture (red lines in Figure 3(B)) of ad-

jacent characteristic structures were. These were charac-

teristic sections of the nasal structure where vertexes

were defined as characteristic points. The sectional shape

of nasal vestibule, nasal valve and nasopharynx were

simplified as quadrilaterals, and the width and height

were defined as their characteristic dimensions. Anatomy

of nasal meatus was much more complex than the others.

Each meatus was simplified as a corner (as shown in

Figure 3(A)). Characteristic points in nasal meatus were

extracted as shown in Figure 4 and the widths of nasal

meatus were defined as characteristic dimensions. The

characteristic nasal cavity model of a volunteer was es-

tablished in ANSYS based on the coordinate data of the

person’s characteristic points and the airflow field was

numerically simulated. The comparison of geometry be-

tween the characteristic model and original one was

shown in Figure 3.

3. RESULTS

3.1. Airflow Distribution in Nasal Cavity

The pressure and velocity at any point in the nasal cavity

could be obtained after numerical simulations for thirty

nasal models were completed. The model shown in Fig-

ure 5 was a replic a t ion of a wom a n’s nasal cavity. A slice

at a proper position was selected to display the velocity

Figure 3. Extraction of characteristic points in nasal

meatus.

Figure 4. Velocity (left), pressure (middle) and vector (right)

plot at the moment b.

Figure 5. Distribution of airflow in the nasal passages at the

moment of point “a”.

distribution (Figure 5 left), velocity vectors (Figure 5

right) and pressure drops (Figure 5 middle) which pre-

sented airflow direction in th e nasal cav ity at the moment

b when the expiratory air flow flux and the pres sure drop

were on their peak values. The highest airflow velocity

appeared in the region of nasal valve. In the region of

nasal valve and nasal vestibule, the air pressure changed

sharply. By contrast, it changed slowly in the posterior

region of nasal proper cavity and the nasopharynx. In

these thirty examples, the airflow resistance in region of

3 cm distance from nostril accounted for from 50.5% to

77.8% of overall nasal airway resistances.

Several representative velocity distributions at the

moment were shown in Figure 6. These figures illu-

strated that airflow distribution in each model was a little

J. Zhang / Journal of Biosciences and Medicines 1 (2013) 23-27

Figure 6. Comparison of velocity (left) and pressure (right) distribution be-

tween characteristic model and origin one of nasal cavity.

different and the airflow flux on one side of the nasal

cavity was different from the other’s. The results indi-

cated that there were three airflow distribution modes in

the nasal airway:

1. The main stream passed through the common nasal

meatus and the residual part passed through the middle

and inferior nasal meatus (shown in Fig ure 6 left). In

this mode, the airflow flux through the common nasal

meatus accounted for 56.6% of overall flux. 2. The main

stream passed through the inferior nasal meatus and the

common nasal meatus (shown in Figure 5 middle). In

this mode, the airflow flux through inferior nasal meatus

and common nasal meatus accounted for 60.5% of over-

all flux. 3. The main airflow passed through the middle

nasal meatus and the common nasal meatus (shown in

Figure 5 right). In this mode, the airflow flux through

the middle nasal meatus and the common nasal meatus

accounte d for 77.0 % of o ve r all flux.

Among thirty examples, seven of them agreed with the

first mode; seven of them were categorized the second

mode. The other fourteen examples belonged to the third

mode.

3.2. Comparison of Airflow Distribution between

Characteristic Model and the Original One

By comparing the airflow distribution of velocity field

(Figure 6 left) and the pressure field (Figure 6 rig ht)

between the characteristic model and original one, it

showed that either the geometry structure or numerical

simulation was similar, and the numerical comparison

and difference was shown in Table 1.

4. DISCUSSIO N

The mechanism of airflow in human nose is important

for understanding many aspects of the biology and pa-

thology in the respiratory tract. The present investigation

showed that the airflow flux through left or right side of

nasal cavity lies on the airflow resistance or the cross-

sectional area. On each side, the airflow distribution de-

pends on the structure of airway as the main airflow

Tabl e 1. Difference of geometry dimensions and airflow cha-

racter between two models.

Original

model Characteristic

model Difference

Cross dim. 0.036 m 0.046 m 12.20%

Vertical dim. 0.084 m 0.085 m 0.59%

Longitudinal dim. 0.136 m 0.136 m 0.00%

Pressure drop 94.8 Pa 79.8 Pa 8.59%

Maximal velocity 9.279 m/s 9.260 m/s 0.10%

passed through the route with wider airway. The resis-

tance is usually lower in the wider airway like the com-

mon nasal meatus or where it intersects with the middle

nasal meatus. So long as the presentative structure di-

mensions of nasal cavity are obtained, which were ex-

pressed as characteristic points and dimensions in this

paper, the airflow distribution in the real nasal cavity

could be well described. The models under the definition

of characteristic dimension can represent not only its

original model, but also the models with approximate

characteristic dimensions. Ulyanov [12] provided two

typical nasal models of the southern type and the north-

ern type. The characters of the northern type nasalcavity

were that the inferior turbinate was large in size and the

main airflow passed through the middle passage. The

characters of southern type nasal cavity were that the

inferior turbinate was small in size and the main airflow

passed through the inferior interior passage [6]. Because

of the large inferior turbinate, the inferior nasal meatus

was narrow and the resistance in this airway was high

which led to most of airflow passing through the middle

nasal meatus. The principle for the southern type nasal

cavity was the same as the northern type. This was a

good use of characteristic dimension for identifying hu-

mans with the structure character of nasal cavity.

5. CONCLUSION

A feasible method was developed to reconstruct the nu-

merical models of nasal cavities. Through numerical

J. Zhang / Journal of Biosciences and Medicines 1 (2013) 23-27

simulation results of thirty examples, the details of air-

flow distribution in the nasal cavity were illustrated. The

results showed that the wider the meatus were, the more

airflow would pass through. The distribution of the air-

flow would be changed on two sides of the nasal cavity if

any part of nasal structure varies. The numerical model

based on characteristic dimension was then reconstructed.

It showed that either the geometric structure or the air-

flow distribution in the characteristic model was similar

to the original one. The conclusion can be made that the

characteristic model can partly replace the original one

and even the models with approximate characteristic

dimensions during the model research towards nasal cav-

ity.

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