Deposition of Inhaled Particle in the Human Lung for Different Age Groups
Xilong Guo1, Qihong Deng1*
1
*
Central South University (CSU), Changsha , China
Corresponding email: [email protected], [email protected].
SUMMARY: The deposition of inhaled particle in the human lung plays an important role in
the particulate toxicology and the therapeutic drugs delivered by inhalation. A dynamic
one-dimensional mathematical model, including a loss term that is due to three mechanisms:
impaction, sedimentation and diffusion, was proposed, which is able to evaluate the transport
and deposition pattern of particle. In the paper, four age groups are chosen to estimate the
relationship between particle deposition and age. The basic structure of human lung is the
revised Weibel’s A model. The diameter and length and the alveolar volume are modified by
height and functional residual capacity (FRC). For each group, the real breathing parameters
under sedentariness are used. The deposition fraction is calculated for whole lung as a
function of particle diameter. Furthermore, the deposition density is also analyzed. The results
indicate that the total deposition fraction is very close for the groups, but the deposition
density has obviously difference. And it shows that the younger, the severer.
Key words: Inhaled Particle; Trumpet Model; Lung; Deposition Fraction; Age.
1 INTRODUCTION
There are many statistic investigations showing that the concentration of particle less than 10
micron in the atmosphere is associated with rates of mortality and morbidity (Katsouyanni et
al.1997; Jonathan et al. 2000). With the level of inhaled particle increasing in the air, the
number of deaths per day, not only from respiratory diseases but also from cardiovascular
diseases, increases obviously, even though the specific data obtained in each research have
differences. Particles passing into the human lung and deposited on there can cause of many
respiratory diseases, such as tracheitis, bronchitis, bronchiolitis, asthma, chronic obstructive
pulmonary disease (COPD), lung cancer, etc.(William, 2000). Moreover, the smaller the
particles, the deeper they come into the lung. The ultrafine particles less than 0.1 micron can
deposit in the alveoli and penetrate the alveolar wall and enter into human blood circulation
causing cardiovascular diseases (Nemmar et al. 2002).On the other hand, delivering
therapeutic drugs by inhalation has the merits of no hurt, high efficient and small does which
can reduce the side effects (Coates, 2008). Therefore, studying particle deposition in human
lung is very interesting and important.
Most of the literature on modeling particle deposition is about the normal adult. There are a
few focusing on the children and teenagers (Hofmann et al. 1989; Isaacs and Martonen, 2005)
or the different group like male and female (Pichelin et al. 2012). However, the difference of
particle deposition between various age groups exists because the morphology of lung and
breathing pattern are different. And the experiments also demonstrate it (Becquemin et al.
1991; Kim and Hu, 1998). Furthermore, Children and teenagers are susceptible group which
must be considered in estimating respiration exposure to ambient particle. And they
potentially need to take therapeutic drugs by inhalation. In the paper, the one-dimensional
variable cross-section model or so-called trumpet model is used to calculate particle
deposition in the human lung for four different age groups (Taulbee and Yu, 1975). For each
group, the morphological parameters of lung are obtained based on nonmonotonous scaling
the corresponding values of the basic structure of human lung by using FRC and height. This
is our first step for studying particle deposition patterns in the human lung for different age.
2 METHOD
2.1 Physical model
The morphology of the lung used in the present work is the classical morphometric model “A”
proposed by Weibel (1963). This model is widely employed in many researches of inhaled
particle deposition in human lung because of its ease-of-use and common comparability. The
very complicated human lung is simplified an air conducting system in the form of an airway
tree. It consists of 24 generations, which branch dichotomously beginning from generation 0,
the trachea and ending to generation 23, alveolus. The airways of each generation have the
identical diameter and length. Starting from the 17th generation, the airways are attached
alveoli. However, the original dimensions given by Weibel are based on an FRC at 4800 ml
bigger than the typical FRC value of 3300 ml published in the guidelines of the International
Commission on Radiological Protection (ICRP, 1994) for a normal adult male from the
Caucasian population. So the original data is scaled by the cube root of fraction of these two
FRC values.
Fig.1 Total cross-section area, both with and without alveoli, as a function of generation
number for the basic structure of human lung.
In order to obtain particle deposition pattern in the whole lung, the geometrical model of the
lung, in this study, is described as so-called trumpet model, which is originally proposed to
study gas transport and mixing in the lung. Accordingly, the cross-sectional area of the model
increases sharply with distance from the entrance of the mouth, because it is taken as the sum
of the cross-sectional areas of all the individual airways belonging to the same generation.
And we consider the parameters of the airway are constant. In the last seven generations,
additional volume due to alveoli encircles the channel. We assume that the alveoli are
expanded and contracted uniformly during inhalation and exhalation, respectively. The total
value of the lung volume during a breathing cycle is equal to the volume of FRC (FRC) plus
the product of tidal volume (VT) and function f(t). Hence, lung volume is considered to vary as
(1)
where f (t) is a function of time that takes values between 0 and 1,i.e. 0 f (t ) 1 . This function
describes the breathing pattern during the cycle and can be specified arbitrarily. In the present
study, equal time was allocated for inhalation and exhalation with no pause in between. And
we assume the air flow rate is uniform during inspiration and expiration.
2.2 Mathematical model
In the present study we employ the following equation to describe particle concentration(c) as
a function of time (t) and position(x) along the lung path
(2)
where A is the total airway cross-section area and v is the alveolar volume per unit length of
the airway as shown in Fig.2, Q is the air flow rate, D is the diffusion coefficient, L is the
combined particle loss due to impaction, diffusion, and sedimentation deposition per unit
length of the airway per unit time. If d is the diameter of an individual airway at the number
of generation i, then A is calculated as
.
To solve Eq. (2) the airflow rate Q = Q(x, t) along the airways of the respiratory tract is
needed. It is determined by solving the equation of continuity, which is given below
Q
v
x
t
(3)
The mechanisms of particle deposition in the lung mainly include inertial impaction,
Brownian diffusion, and sedimentation. The total deposition by combined mechanisms is
supposed to be the sum of due to three independent mechanisms
(4)
where Li, Ls, and Ld are particle deposition functions due to impaction, sedimentation, and
diffusion, respectively. These can be obtained from the literature (Taulbee and Yu, 1975).
2.3 Morphology of lung and breathing pattern
For the children younger than 4 year-ages, the number of lung generation is fewer than that of
an adult (Dunnill 1962). Therefore, it is assumed that the model is suitable only for children
older than 4 years of age. In addition, the morphology of lung is no gender difference for
young children, but it is contrary for old children and adults. However, the diverse particle
deposition for age is more interesting than for gender for the moment work. So the objects of
study chosen in the paper are all for male. The information about four age groups
recommended by ICRP 1994 is shown in Table 1.
Table 1. the morphological parameters of lung and breathing pattern under sedentary
condition
Age
5
10
15
adult
Height (m)
1.1
1.38
1.69
1.76
FRC (ml)
767
1484
2677
3300
VT (ml)
213
333
533
750
T (s)
2.4
3.2
4
5
To acquire the morphological parameters for each group, the following three steps is
necessary.
First, the diameter and length of the first 9 generations is scaled as a function of the body
height (ICRP 1994):
(5)
where DR(z), LR(z) and D(z), L(z) are the diameter and length of the revised Weibel
morphology and the considered group, respectively. C(z) is a constant depending upon
generation and its value is from ICRP 1994, H is the height in meters.
Second, starting from generation 9, it is assumed that the diameter and length is proportion of
the cube root of the ratio between the group’s FRC (FRC) and the revised Weibel FRC (FRCR)
(Segal et al. 2002; Martin and Finlay 2006; Pichelin et al. 2012). The method is used as
follows
(6)
Last, the fraction of alveolar volume is assumed no change whatever the morphology. So the
distribution of the alveolar volume per generation is determined as follows
(7)
where VA(z) ,VA and VAR(z), VAR are the alveolar volume of generation z and the total alveolar
volume of the considered group and the revised Weibel morphology, respectively.
3 RESULTS
The breathing pattern considered is under sedentary condition in the simulation as shown in
Table 1. Deposition fraction and density values along airway generation are shown in Fig.2
for three particle diameters, including ultrafine, fine and coarse particles. For particle 0.1 and
1μm, deposition fraction has no obvious difference for the groups, but for 10μm, the
difference is distinct. The deposition density increases to reach the peak about generation 19th
before it drops down for ultrafine particle. But its maximal value appears in generation 3th for
fine and coarse particles. All of the three particle diameters show that children have bigger
(a)
(b)
(c)
Fig.2 Deposition fraction and density for 0.1μm (a), 1μm (b), 10μm (c) as a function of
airway generation number z for four age groups.
(a)
(b)
Fig.3 Deposition fraction (a) and deposition density (b) as a function of particle diameter for
four age groups.
deposition density than adults. This also can be observed from Fig.3. The total deposition
fraction is very close for the groups as shown in Fig.3 (a), however, the density increases with
the age for different particle diameters. The value for children 5 year-ages is approximately
twice as big as for adults. This maybe implies that the children have more damage than adults
exposing to the ambient particle.
4 CONCLUSIONS
From the results mentioned above, it is obvious that even though the total deposition fraction
has no distinct difference for different ages under the same activity, the deposition density has
rather big difference. For the children, they receive more particle dose than adults. And the
situation may be more serious because they are easier in fierce activities than adults. This is
the first step for studying particle deposition patterns in the human lung for different age. In
the further research, more realistic lung geometry and more accurate deposition function
should be used.
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