# Inhalation Induced Stresses and Flow Characteristics in Human Airways through Fluid-Structure Interaction Analysis

Authors: Kittisak Koombua; Ramana M. Pidaparti
Journal: Modelling and Simulation in Engineering
 (2008)

---

## Abstract

Better understanding of stresses and flow characteristics in the human airways is very important for many clinical applications such as aerosol drug therapy, inhalation toxicology, and airway remodeling process. The bifurcation geometry of airway generations 3 to 5 based on the ICRP tracheobronchial model was chosen to analyze the flow characteristics and stresses during inhalation. A computational model was developed to investigate the airway tissue flexibility effect on stresses and flow characteristics in the airways. The finite-element method with the fluid-structure interaction analysis was employed to investigate the transient responses of the flow characteristics and stresses in the airways during inhalation. The simulation results showed that tissue flexibility affected the maximum airflow velocity, airway pressure, and wall shear stress about 2%, 7%, and 6%, respectively. The simulation results also showed that the differences between the orthotropic and isotropic material models on the airway stresses were in the ranges of 25–52%. The results from the present study suggest that it is very important to incorporate the orthotropic tissue properties into a computational model for studying flow characteristics and stresses in the airways.


---

## Body

## 1. Introduction

Flow characteristics in the human
respiratory airways are very important for studying particle transportation in
many applications ranging from aerosol drug therapy to inhalation toxicology as
well as gas exchange in the airways. A better understanding of the stresses and
strains and theirs influences on our airways is also important, since the airwaysare shaped by the
complex mechanical environment even in the uterus. This complex mechanical
environment continues to influence and alter the mature airways in healthy and
diseased people [1]. Many in vivo and in vitro
models have been developed to study the effect of the mechanical stresses on
the airways. The results from these models showed that the high peak airway
pressure caused airway distention and an increase in the level of an inflammatory
mediator, cytokine [2, 3]. In addition, high airway
pressure can contribute to an increase in the thickness of the airway epithelial
layer [4, 5]. Since it is very difficult
to experimentally measure the flow characteristics (airflow velocity, airway
pressure, and wall shear stress (WSS)) and airway stresses in the real
environment, the computational model can provide useful information about flow
characteristics and stresses in the airways.Many
researchers have developed computational models to investigate airflow and
particle deposition in the airways [6–12], including
the effect of airway diseases, such as tumors [6–10], asthma [11], stenosis [13], and chronic obstructive pulmonary disease (COPD) [12, 14]. The effects of carinal shape [15] and cartilage rings [16] were also studied. However,
these models were developed assuming that the airways were rigid and could not
be deformed or distended by fluid force from the airflow. In general, the
airways are flexible and are composed of many soft tissues. They can also be
distended by airflow during inhalation [17]. The literature review
indicates that there is no computational model that considers the effect of
airway tissue flexibility on the flow and tissue characteristics.In
the present study, a fluid-structure interaction (FSI) analysis along with the
finite-element method was employed to investigate the flow characteristics and stress
distributions in the airways during inhalation. Both orthotropic and isotropic material
models were used to represent airway flexibility to study stress distributions in
the airways. The results between the fluid analysis and FSI analysis are also
compared.


## 2. Materials and Methods

The transient interactions between airflow and airways during inhalation
were investigated solving two coupled sets of the governing equations with
associated boundary conditions. The governing equations for airflow and airways
are briefly described below.


### 2.1. Governing Equations for Airflow

The
governing equations for transient airflow are Navier-Stokes equations on a
moving mesh with the assumption of incompressible flow. These equations govern
the principles of mass and momentum conservation and are described below using
Einstein’s repeated index convention [18].Conservation of
mass(1)ρgg∂∂t(g)+ρg∂∂xj(uj−∂xj∂t)=0. Conservation of
momentum (2)ρgg∂∂t(gui)+ρg∂∂xj[(uj−∂xj∂t)ui]=−∂p∂xi+μ∂2ui∂xj2. In these
equations, xi represents the moving mesh location, g is the metric tensor determinate of the
transformation, that is, the local computational control-volume size, ρg is fluid density, p is fluid pressure, μ is fluid viscosity, and u is fluid velocity.


### 2.2. Governing Equations for Airways

The
governing equations for movement of the airways during inhalation are the
time-dependent structural equations and are described below using Einstein’s
repeated index convention [19].Equation of
motion(3)∂σij∂xj+Fi=ρ∂2ui∂t2. Constitutive
relations (4)σij=Cijklεkl. In the equation
above, σ is the stress in each direction, F is the body force, ρ is density, and u is the displacement, C is the elasticity tensor, and ε is the strain in each direction.


### 2.3. Computational Method

The
effect of fluid pressure on a structure is significant, especially if the
structure is flexible such as human airways. The finite-element software ANSYS [20] was employed to solve this fluid-structure
interaction problem. The
solution to the fluid-structure interaction problem can be obtained by solving the
governing equations for airflow and airways consecutively. At each time step, the
algorithm begins by solving the airflow
equations to obtain fluid pressure. Airway equations are then solved for the displacement using the fluid
pressure as an external force. The airflow equations are then solved again to
obtain the fluid pressure after the airway displacement changes the fluid
boundaries. This loop continues until both fluid pressure and airway
displacement converge for each time period (see Figure 1).Figure 1
A diagram of fluid-structure-interaction algorithm.


### 2.4. Computational Domains

This
study focused mainly on airway generations 3 to 5 for two reasons. First, these
airway generations have less cartilage plates and no rings when they are compared
to the proximal generations; therefore the airways can be assumed to be smooth [21]. Second, the diameters of
these airways do not change as a function of a lung volume but depend on a
transmural pressure across the airways [17]. The geometric dimensions of
airway generations 3 to 5 (see Figure 2) used in this study were based on the
ICRP [22] tracheobronchial geometry,
and airway thickness for each generation was based on measurements by Habib et al. [23]. The branching angle of the
bifurcation was 70° based on the morphological data of Horsfield and Cumming [24]. The corresponding geometric
diameter, length, and thickness of the bifurcation are given in
Table 1. The
surface geometry of the model was constructed based on the physiologically
realistic bifurcation (PRB) model suggested by Heistracher and Hofmann
[25]. This double bifurcation
geometry was previously implemented in a study by Longest and Vinchurkar [26], which evaluated the effect of transitional and turbulent flow on particle deposition in rigid airways.Table 1
Parameters for airway generations 3 to 5 based on ICRP [22] tracheobronchial geometry, and measurements by Habib et al. [23].
GenerationDiameter (cm)Length (cm)Thickness (cm)30.561.100.05340.450.920.04150.360.770.024Figure 2
Geometric representations of the airway generations
3 to 5 based on ICRP [22] tracheobronchial geometry and measurements by Habib et al. [23]. These bifurcations were used as a computational domain for
this study.


### 2.5. Computational Models and Boundary Conditions

The
computational domains of the bifurcation were created in ANSYS [20]. Due to symmetry, only one
half of the domains was constructed. The solid domain was the airways with finite
thickness, and the fluid domain was the internal volume of air in the airways.
Solid elements, BRICK45 [20], were used to represent the
solid domain, and fluid elements, FLUID142 [20], were used to represent the
fluid domain. A structural hexahedral mesh was employed to provide a high-quality
airflow solution, as suggested by Longest and Vinchurkar [27] and Vinchurkar and Longest [28]. A mesh-independence study
was performed on both solid and fluid domains to confirm that a fine enough
element had been used to represent the solid and fluid domains. Changes in
maximum pressure and velocity were used as convergence criteria for the fluid
domain, and changes in maximum displacement and von Mises stress were used as
convergence criteria for the solid domain. A converged model was obtained when
changes in those criteria were less than 4%. Having performed the
mesh-independence study, the airflow velocity from the finite-element model in
the airway generation 4 was then compared with the experiment by Zhao and
Lieber [29]. Good agreement was obtained
between the simulation and experimental results [30]. Figure 3 shows the converged
mesh that was further used for the analysis of predicting stress distributions.Figure 3
The mesh-converged finite-element model of the airway generations 3 to 5 and the boundary
conditions for this study.The
inlet boundary condition of the fluid domain was a waveform during normal
inhalation [31]. The corresponding pressure
was applied at the outlet of the fluid domain [32] (see Figure 4). Properties of
air were assumed to be those at 27°C. The airways were assumed to be of a
homogeneous material with a density of 1365.6 kg/m3 [33], a Young’s modulus of
elasticity in longitudinal direction of 130.89 kPa [34], a Young’s modulus of
elasticity in circumferential direction of 74.07 kPa [35], and Poisson’s ratio of 0.45 [35]. A zero-displacement boundary
condition was applied at the airways on both inlet and outlet of the solid
domain to represent a tethering of the airways from other tissues and organs [36]. A no-slip boundary condition
was defined at the fluid-structure interface (see Figure 3).(a) Flow waveform during the normal inhalation at the trachea and (b) the
corresponding airway pressure at the airway generation 5.
(a)(b)


### 2.6. Methods of Analysis

Airflow
velocity, airway pressure, and airway stresses were calculated in this study. Stresses
in the airways during inhalation are from fluid shear force and airway
pressure. Fluid shear force during inhalation creates wall shear stress (WSS)
at the surface of the airways. WSS is the tangential stress at a wall due to
fluid viscosity and is related to a transverse velocity gradient [37]. In contrast, airway pressure
acting in the normal direction to the airways creates stresses across thickness
of the airways. Stresses from the airway pressure are normal and shear stress
distributions in all directions. In this study, stress distributions in the
airways were analyzed employing the longitudinal and von Mises stresses. The
von Mises stress is an average stress in all directions and is associated with
distorting the shape of material. Any material will yield if the von Mises
stress is greater than its yield strength [38].Effects
of airway tissue flexibility on airflow velocity, airway pressure, and WSS in
the bifurcation were analyzed assuming the airways to be rigid or flexible. For
the rigid model, analysis was performed only on the fluid domain. The
bifurcation in this case acts like a rigid tube that cannot be deformed by
fluid forces from the airflow; therefore, there is no stress in the airways.
For the flexible model, analysis was performed on both fluid and solid domains.
The bifurcation in this case acts like a flexible tube that can be deformed by
fluid forces from the airflow. Therefore, stresses in the airways are
considered in this analysis. The FSI analysis [20] was implemented for the
flexible model.To
investigate the effect of tissue flexibility on stress distributions in the
airways, simulations were performed using orthotropic and isotropic material
models. For the orthotropic material model, the properties of the airways
described in Section2.5 were used. In contrast to the orthotropic material
model, the Young’s modulus of elasticity of 130.89 kPa [34] and Poisson’s ratio of 0.45 [35] was used for the isotropic material model.


## 2.1. Governing Equations for Airflow

The
governing equations for transient airflow are Navier-Stokes equations on a
moving mesh with the assumption of incompressible flow. These equations govern
the principles of mass and momentum conservation and are described below using
Einstein’s repeated index convention [18].Conservation of
mass(1)ρgg∂∂t(g)+ρg∂∂xj(uj−∂xj∂t)=0. Conservation of
momentum (2)ρgg∂∂t(gui)+ρg∂∂xj[(uj−∂xj∂t)ui]=−∂p∂xi+μ∂2ui∂xj2. In these
equations, xi represents the moving mesh location, g is the metric tensor determinate of the
transformation, that is, the local computational control-volume size, ρg is fluid density, p is fluid pressure, μ is fluid viscosity, and u is fluid velocity.


## 2.2. Governing Equations for Airways

The
governing equations for movement of the airways during inhalation are the
time-dependent structural equations and are described below using Einstein’s
repeated index convention [19].Equation of
motion(3)∂σij∂xj+Fi=ρ∂2ui∂t2. Constitutive
relations (4)σij=Cijklεkl. In the equation
above, σ is the stress in each direction, F is the body force, ρ is density, and u is the displacement, C is the elasticity tensor, and ε is the strain in each direction.


## 2.3. Computational Method

The
effect of fluid pressure on a structure is significant, especially if the
structure is flexible such as human airways. The finite-element software ANSYS [20] was employed to solve this fluid-structure
interaction problem. The
solution to the fluid-structure interaction problem can be obtained by solving the
governing equations for airflow and airways consecutively. At each time step, the
algorithm begins by solving the airflow
equations to obtain fluid pressure. Airway equations are then solved for the displacement using the fluid
pressure as an external force. The airflow equations are then solved again to
obtain the fluid pressure after the airway displacement changes the fluid
boundaries. This loop continues until both fluid pressure and airway
displacement converge for each time period (see Figure 1).Figure 1
A diagram of fluid-structure-interaction algorithm.


## 2.4. Computational Domains

This
study focused mainly on airway generations 3 to 5 for two reasons. First, these
airway generations have less cartilage plates and no rings when they are compared
to the proximal generations; therefore the airways can be assumed to be smooth [21]. Second, the diameters of
these airways do not change as a function of a lung volume but depend on a
transmural pressure across the airways [17]. The geometric dimensions of
airway generations 3 to 5 (see Figure 2) used in this study were based on the
ICRP [22] tracheobronchial geometry,
and airway thickness for each generation was based on measurements by Habib et al. [23]. The branching angle of the
bifurcation was 70° based on the morphological data of Horsfield and Cumming [24]. The corresponding geometric
diameter, length, and thickness of the bifurcation are given in
Table 1. The
surface geometry of the model was constructed based on the physiologically
realistic bifurcation (PRB) model suggested by Heistracher and Hofmann
[25]. This double bifurcation
geometry was previously implemented in a study by Longest and Vinchurkar [26], which evaluated the effect of transitional and turbulent flow on particle deposition in rigid airways.Table 1
Parameters for airway generations 3 to 5 based on ICRP [22] tracheobronchial geometry, and measurements by Habib et al. [23].
GenerationDiameter (cm)Length (cm)Thickness (cm)30.561.100.05340.450.920.04150.360.770.024Figure 2
Geometric representations of the airway generations
3 to 5 based on ICRP [22] tracheobronchial geometry and measurements by Habib et al. [23]. These bifurcations were used as a computational domain for
this study.


## 2.5. Computational Models and Boundary Conditions

The
computational domains of the bifurcation were created in ANSYS [20]. Due to symmetry, only one
half of the domains was constructed. The solid domain was the airways with finite
thickness, and the fluid domain was the internal volume of air in the airways.
Solid elements, BRICK45 [20], were used to represent the
solid domain, and fluid elements, FLUID142 [20], were used to represent the
fluid domain. A structural hexahedral mesh was employed to provide a high-quality
airflow solution, as suggested by Longest and Vinchurkar [27] and Vinchurkar and Longest [28]. A mesh-independence study
was performed on both solid and fluid domains to confirm that a fine enough
element had been used to represent the solid and fluid domains. Changes in
maximum pressure and velocity were used as convergence criteria for the fluid
domain, and changes in maximum displacement and von Mises stress were used as
convergence criteria for the solid domain. A converged model was obtained when
changes in those criteria were less than 4%. Having performed the
mesh-independence study, the airflow velocity from the finite-element model in
the airway generation 4 was then compared with the experiment by Zhao and
Lieber [29]. Good agreement was obtained
between the simulation and experimental results [30]. Figure 3 shows the converged
mesh that was further used for the analysis of predicting stress distributions.Figure 3
The mesh-converged finite-element model of the airway generations 3 to 5 and the boundary
conditions for this study.The
inlet boundary condition of the fluid domain was a waveform during normal
inhalation [31]. The corresponding pressure
was applied at the outlet of the fluid domain [32] (see Figure 4). Properties of
air were assumed to be those at 27°C. The airways were assumed to be of a
homogeneous material with a density of 1365.6 kg/m3 [33], a Young’s modulus of
elasticity in longitudinal direction of 130.89 kPa [34], a Young’s modulus of
elasticity in circumferential direction of 74.07 kPa [35], and Poisson’s ratio of 0.45 [35]. A zero-displacement boundary
condition was applied at the airways on both inlet and outlet of the solid
domain to represent a tethering of the airways from other tissues and organs [36]. A no-slip boundary condition
was defined at the fluid-structure interface (see Figure 3).(a) Flow waveform during the normal inhalation at the trachea and (b) the
corresponding airway pressure at the airway generation 5.
(a)(b)


## 2.6. Methods of Analysis

Airflow
velocity, airway pressure, and airway stresses were calculated in this study. Stresses
in the airways during inhalation are from fluid shear force and airway
pressure. Fluid shear force during inhalation creates wall shear stress (WSS)
at the surface of the airways. WSS is the tangential stress at a wall due to
fluid viscosity and is related to a transverse velocity gradient [37]. In contrast, airway pressure
acting in the normal direction to the airways creates stresses across thickness
of the airways. Stresses from the airway pressure are normal and shear stress
distributions in all directions. In this study, stress distributions in the
airways were analyzed employing the longitudinal and von Mises stresses. The
von Mises stress is an average stress in all directions and is associated with
distorting the shape of material. Any material will yield if the von Mises
stress is greater than its yield strength [38].Effects
of airway tissue flexibility on airflow velocity, airway pressure, and WSS in
the bifurcation were analyzed assuming the airways to be rigid or flexible. For
the rigid model, analysis was performed only on the fluid domain. The
bifurcation in this case acts like a rigid tube that cannot be deformed by
fluid forces from the airflow; therefore, there is no stress in the airways.
For the flexible model, analysis was performed on both fluid and solid domains.
The bifurcation in this case acts like a flexible tube that can be deformed by
fluid forces from the airflow. Therefore, stresses in the airways are
considered in this analysis. The FSI analysis [20] was implemented for the
flexible model.To
investigate the effect of tissue flexibility on stress distributions in the
airways, simulations were performed using orthotropic and isotropic material
models. For the orthotropic material model, the properties of the airways
described in Section2.5 were used. In contrast to the orthotropic material
model, the Young’s modulus of elasticity of 130.89 kPa [34] and Poisson’s ratio of 0.45 [35] was used for the isotropic material model.


## 3. Results and Discussion

The distributions of airflow
velocity, airway pressure, WSS, longitudinal stress, and von Mises stress for
the flexible model were evaluated only with orthotropic material model as the
distributions for both flexible and rigid models are similar. The effect of
tissue flexibility on airflow velocity, airway pressure, and WSS and the effect
of material models on longitudinal and von Mises stresses are also discussed.


### 3.1. Airflow Velocity

The distributions of airflow
velocity in the airways during the peak airflow are shown in Figure5. The
maximum airflow velocity during the peak airflow was 3.692 m/s. High airflow
velocity spread throughout G3. Airflow velocity in the medial side of G4 was
higher than that in the lateral side of G4 because the secondary flow after the
bifurcation moved air toward the medial side of G4. Airflow velocity in both G3
and G4 was symmetric; however velocity profiles in G5 were not symmetric.
Airflow velocity in branch G5M was higher than that in branch G5L because of the
high airflow velocity in the medial side of G4.Figure 5
A distribution of the airflow velocity in the airway generations 3 to 5 for the
orthotropic flexible model during the peak inhalation.


### 3.2. Airway Pressure and von Mises Stress

The distributions of airway pressure
and von Mises stress in the airways during the peak airflow are shown in Figure6. The maximum airway pressure during the peak airflow was −3.209 Pa. High airway
pressure was observed at the beginning of G3 and the bifurcations. The pressure
at the first bifurcation between G3 and G4 was about two times higher than that
at the second bifurcation between G4 and G5 since the airflow that impinged the
first bifurcation had more momentum (higher velocity) than the air that
impinged the second bifurcation. The von Mises stress in the airways, which resulted
from the airway pressure, was observed to be high at the beginning of G3 and
the bifurcations. The von Mises stresses in branch G5M were higher than those
in branch G5L. The maximum von Mises stress during the peak airflow was 1142 Pa.Figure 6
A distribution of the airway pressure and von Mises stress in the airway
generations 3 to 5 for the orthotropic flexible model during the peak
inhalation.


### 3.3. Wall Shear Stress (WSS)  and Longitudinal Stress

The distributions of wall shear
stress (WSS) at the airways and longitudinal stress in the airways during the
peak airflow are shown in Figure7. The maximum WSS, 0.4185 Pa, occurred at the
bifurcations since the velocity gradient is highest at those locations. WSS in
the medial side of G4 was higher than that in the lateral side of G4, and WSS
in G5M was higher than that in G5L. When the locations of the high WSS are
compared with the particle deposition locations from the previous study by
Longest and Vinchurkar [26], we can see that the
particles deposit in the high WSS locations (see Figure 8). The longitudinal stress
in the airways, which resulted from the airway pressure, was observed to be
high where WSS was observed to be high. The maximum longitudinal stress during
the peak airflow was −1497 Pa.
The negative value of the longitudinal stress indicates that the length of the
airways decreased during the peak airflow.Figure 7
A distribution of the wall shear stress (WSS) and longitudinal stress in the
airway generations 3 to 5 for the orthotropic flexible model during the peak
inhalation.Figure 8
A distribution of wall shear stress (WSS) and locations of particle deposition in
the airway generations 3 to 5 from the previous study by Longest and Vinchurkar
[26].


### 3.4. Tissue Flexibility Effect

Figure9 shows the effect of tissue
flexibility on the airflow velocity, airway pressure, and WSS during inhalation.
As can be seen from this figure, tissue flexibility affected each flow
characteristic to a different degree. Airway pressure and WSS were
significantly affected by tissue flexibility. The maximum differences between
the flexible and rigid models were 2%, 7%, and 6%, for airflow velocity, airway
pressure, and WSS, respectively. The airflow velocity from the flexible model
was higher than that from the rigid model for the first 0.9 seconds since the
airways contracted due to the negative pressure inside the airways. However,
the airflow velocity from the flexible model was lower than that from the rigid
model for the last 0.9 seconds since the airways expanded due to the positive
pressure inside the airways. The airway pressure from the flexible model was
lower than that from the rigid model throughout the inhalation process. The
movement of the airway tissue decreased the airway pressure, and the maximum
differences between the flexible and rigid models were highest at the peak
airflow. The increase in airway pressure associated with the rigid wall
suggests that people with stiff airways, for example, elderly people [39] or asthma patients [40] can experience high airway
pressure during normal inhalation. Tissue flexibility decreased WSS for the
first 0.9 seconds; however, it increased WSS for the last 0.9 seconds. The
effects of tissue flexibility on WSS from this study were similar to results
from the previous studies in the abdominal aortic aneurysm (AAA) by Leung et al. [41] and Torii et al. [42] as well as Scotti and Finol [43]. Their results showed that
tissue flexibility can increase or decrease WSS, and the influence on WSS is
highly depended on AAA geometry.Figure 9
The tissue flexibility effect on airflow velocity, airway pressure, and wall shear
stress (WSS) during the inhalation.


### 3.5. Material Model Effect

Figure10 shows the effect of the
material models on the longitudinal and von Mises stresses. The longitudinal
stress from the orthotropic material model was lower than that from the isotropic
material model for entire inhalation since the isotropic material model was
stiffer than the orthotropic material model. The differences between both
material models for the longitudinal stress are in the ranges of 22–52%. The differences
between both material models were observed to be lowest near the peak airflow. The
von Mises stress from the orthotropic material model was higher than that from
the isotropic material model for the first 0.9 seconds; however, the von Mises
stress from the orthotropic material model was lower than that from the
isotropic material model for the last 0.9 seconds. The differences between both
material models for the von Mises stress are in the ranges of 25–28%. The maximum
difference was observed near the peak airflow.Figure 10
The material model effect on longitudinal and von Mises stresses during the
inhalation.


## 3.1. Airflow Velocity

The distributions of airflow
velocity in the airways during the peak airflow are shown in Figure5. The
maximum airflow velocity during the peak airflow was 3.692 m/s. High airflow
velocity spread throughout G3. Airflow velocity in the medial side of G4 was
higher than that in the lateral side of G4 because the secondary flow after the
bifurcation moved air toward the medial side of G4. Airflow velocity in both G3
and G4 was symmetric; however velocity profiles in G5 were not symmetric.
Airflow velocity in branch G5M was higher than that in branch G5L because of the
high airflow velocity in the medial side of G4.Figure 5
A distribution of the airflow velocity in the airway generations 3 to 5 for the
orthotropic flexible model during the peak inhalation.


## 3.2. Airway Pressure and von Mises Stress

The distributions of airway pressure
and von Mises stress in the airways during the peak airflow are shown in Figure6. The maximum airway pressure during the peak airflow was −3.209 Pa. High airway
pressure was observed at the beginning of G3 and the bifurcations. The pressure
at the first bifurcation between G3 and G4 was about two times higher than that
at the second bifurcation between G4 and G5 since the airflow that impinged the
first bifurcation had more momentum (higher velocity) than the air that
impinged the second bifurcation. The von Mises stress in the airways, which resulted
from the airway pressure, was observed to be high at the beginning of G3 and
the bifurcations. The von Mises stresses in branch G5M were higher than those
in branch G5L. The maximum von Mises stress during the peak airflow was 1142 Pa.Figure 6
A distribution of the airway pressure and von Mises stress in the airway
generations 3 to 5 for the orthotropic flexible model during the peak
inhalation.


## 3.3. Wall Shear Stress (WSS)  and Longitudinal Stress

The distributions of wall shear
stress (WSS) at the airways and longitudinal stress in the airways during the
peak airflow are shown in Figure7. The maximum WSS, 0.4185 Pa, occurred at the
bifurcations since the velocity gradient is highest at those locations. WSS in
the medial side of G4 was higher than that in the lateral side of G4, and WSS
in G5M was higher than that in G5L. When the locations of the high WSS are
compared with the particle deposition locations from the previous study by
Longest and Vinchurkar [26], we can see that the
particles deposit in the high WSS locations (see Figure 8). The longitudinal stress
in the airways, which resulted from the airway pressure, was observed to be
high where WSS was observed to be high. The maximum longitudinal stress during
the peak airflow was −1497 Pa.
The negative value of the longitudinal stress indicates that the length of the
airways decreased during the peak airflow.Figure 7
A distribution of the wall shear stress (WSS) and longitudinal stress in the
airway generations 3 to 5 for the orthotropic flexible model during the peak
inhalation.Figure 8
A distribution of wall shear stress (WSS) and locations of particle deposition in
the airway generations 3 to 5 from the previous study by Longest and Vinchurkar
[26].


## 3.4. Tissue Flexibility Effect

Figure9 shows the effect of tissue
flexibility on the airflow velocity, airway pressure, and WSS during inhalation.
As can be seen from this figure, tissue flexibility affected each flow
characteristic to a different degree. Airway pressure and WSS were
significantly affected by tissue flexibility. The maximum differences between
the flexible and rigid models were 2%, 7%, and 6%, for airflow velocity, airway
pressure, and WSS, respectively. The airflow velocity from the flexible model
was higher than that from the rigid model for the first 0.9 seconds since the
airways contracted due to the negative pressure inside the airways. However,
the airflow velocity from the flexible model was lower than that from the rigid
model for the last 0.9 seconds since the airways expanded due to the positive
pressure inside the airways. The airway pressure from the flexible model was
lower than that from the rigid model throughout the inhalation process. The
movement of the airway tissue decreased the airway pressure, and the maximum
differences between the flexible and rigid models were highest at the peak
airflow. The increase in airway pressure associated with the rigid wall
suggests that people with stiff airways, for example, elderly people [39] or asthma patients [40] can experience high airway
pressure during normal inhalation. Tissue flexibility decreased WSS for the
first 0.9 seconds; however, it increased WSS for the last 0.9 seconds. The
effects of tissue flexibility on WSS from this study were similar to results
from the previous studies in the abdominal aortic aneurysm (AAA) by Leung et al. [41] and Torii et al. [42] as well as Scotti and Finol [43]. Their results showed that
tissue flexibility can increase or decrease WSS, and the influence on WSS is
highly depended on AAA geometry.Figure 9
The tissue flexibility effect on airflow velocity, airway pressure, and wall shear
stress (WSS) during the inhalation.


## 3.5. Material Model Effect

Figure10 shows the effect of the
material models on the longitudinal and von Mises stresses. The longitudinal
stress from the orthotropic material model was lower than that from the isotropic
material model for entire inhalation since the isotropic material model was
stiffer than the orthotropic material model. The differences between both
material models for the longitudinal stress are in the ranges of 22–52%. The differences
between both material models were observed to be lowest near the peak airflow. The
von Mises stress from the orthotropic material model was higher than that from
the isotropic material model for the first 0.9 seconds; however, the von Mises
stress from the orthotropic material model was lower than that from the
isotropic material model for the last 0.9 seconds. The differences between both
material models for the von Mises stress are in the ranges of 25–28%. The maximum
difference was observed near the peak airflow.Figure 10
The material model effect on longitudinal and von Mises stresses during the
inhalation.


## 4. Limitations

In
this study, the airway geometry was based on an idealized ICRP [22] symmetric model. However, a study
by Horsfield et al. [44] showed that airway diameters
and branching airways were asymmetric. In addition, material properties of the
airways in the present study were assumed to be linear. Studies by Ito et al. [45] and Smith et al. [46] showed that the airways exhibited
viscoelastic properties and nonlinear dynamic behaviors. Further study is needed
to investigate the effect of the airway diameters, branching angles, and airway
properties on flow characteristics and stresses in the airways.


## 5. Conclusions

The
airflow velocity, airway pressure, WSS, and stresses within the airway
generations 3 to 5 were analyzed in this study using the finite-element method
with the FSI algorithm. The analysis was performed to investigate the effects
of tissue flexibility and the material model on flow characteristics and stresses
in the airways during inhalation. The simulation results showed that tissue
flexibility decreased the airway pressure and altered airflow velocity and WSS.
The simulation results also showed that the material model of the airways
significantly affected stresses in the airways. The results from this study highlight
the importance of incorporating tissue flexibility along with orthotropic properties
into a computational model that is developed to study flow characteristics and
stresses in the airways.



---

*Source: 358748-2008-08-04.xml*