Deposition of Inhaled Particle in the Human Lung for Different Age Groups

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1 Deposition of Inhaled Particle in the Human Lung for Different Age Groups Xilong Guo 1, Qihong Deng 1* 1 Central South University (CSU), Changsha, China * Corresponding qhdeng@csu.edu.cn, qhdeng@gmail.com. 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

2 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

3 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 (V T ) and function f(t). Hence, lung volume is considered to vary as 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 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 x v t 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 where L i, L s, and L d 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 (1) (2) (3) (4)

4 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 adult Height (m) FRC (ml) V T (ml) T (s) 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 D R (z), L R (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 (FRC R ) (Segal et al. 2002; Martin and Finlay 2006; Pichelin et al. 2012). The method is used as follows 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 where V A (z),v A and V AR (z), V AR 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 (6) (7)

5 (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.

6 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. 5 REFERENCES Becquemin M.H., Yu C.P. et al Total deposition of inhaled particles related to age: comparison with age-dependent model calculations. Radiation Protection Dosimetry, 38: Coates A.L Guiding aerosol deposition in the lung. New England Journal of Medicine, 358: Dunnill M.S Postnatal growth of the lung. Thorax, 17: Hofmann W., Martonen T.B. and Graham R.C Predicted deposition of nonhygroscopic aerosols in the human lung as a function of subject age. Journal of Aerosol Medicine, 2: ICRP Human respiratory tract model for radiological protection. Ann. ICRP,24:1-3. Isaacs K.K., Rosati J.A. and Martonen T.B Mechanisms of particle deposition, in Aerosol Handbook: Measurement, Dosimetry, and Health Effects, L.S. Ruzer and N.H. Harley, eds., CRC Press, Boca Raton, FL, pp Jonathan M.S., Francesca D., et al Fine particulate air pollution and mortality in 20 U.S. cities. New England Journal of Medicine, 343: Katsouyanni K, Touloumi G., et al Short-term effects of ambient sulphur dioxide and particulate matter on mortality in 12 European cities: results from times series data from the APHEA project: Air Pollution and Health: a European Approach. BMJ 314: Kim C.S. and Hu S.C Regional deposition of inhaled particles in human lungs: comparison between men and women. Journal of Applied Physiology, 84: Martin A.R. and Finlay W.H A general, algebraic equation for predicting total respiratory tract deposition of micrometer-sized aerosol particles in humans. Journal of Aerosol Science, 38: Nemmar A., Hoet P.H.M. et al Passage of Inhaled Particles Into the Blood Circulation in Humans. American Heart Association, 105: Pichelin M., Caillibotte G. et al Categorization of lung morphology based on FRC and height: computer simulations of aerosol deposition. Aerosol Science and Technology, 46: Segal R.A., Martonen T.B. et al Computer simulations of particle deposition in the lungs of chronic obstructive pulmonary disease patients. Inhalation Toxicology, 14: Taulbee D.B. and Yu C.P A theory of aerosol deposition in the human respiratory tract. Journal of Applied Physiology, 38: William S.B Occupational respiratory diseases. New England Journal of Medicine, 342: