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A computer program for the simulation of fiber deposition in the human respiratory tract
Computers in Biology and Medicine 36 (2006) 1252 – 1267 www.intl.elsevierhealth.com/journals/cobm
A computer program for the simulation of fiber deposition in the human respiratory tract Robert Sturma,∗ , Werner Hofmannb a Brunnleitenweg 41, A-5061 Elsbethen, Austria b Division of Physics and Biophysics, Department of Molecular Biology, University of Salzburg, Hellbrunner Strasse 34,
A-5020 Salzburg, Austria Received 30 September 2004; accepted 25 July 2005
Abstract As inhaled fibers may lead to a variety of lung diseases, detailed information on their deposition in the human respiratory tract is an indispensable requirement in medical science. In the work presented here, a Visual Basic䉸 computer program, termed FIBROS, is described which enables the simulation of fibrous particle deposition in both the extrathoracic region and different parts of the lung itself, including the results of published numerical studies on inertial/interceptional as well as diffusional and gravitational deposition. The input window of FIBROS includes the selection of specific breathing conditions by variation of the tidal volume and breathing cycle. Furthermore, the user is able to determine fiber properties such as diameter, aspect ratio, specific weight, and fiber orientation with respect to the air stream in the upper and lower airways of the lungs. Besides the offer of various deposition formulae for each region of the respiratory tract, thereby also allowing a distinction between mouth and nose breathing, the user may select between different morphometric datasets of the lung and respective airway scaling procedures. Analysis routines of FIBROS include the estimation of regional deposition fractions, thereby distinguishing between extrathoracic, bronchial, and acinar compartments, and a calculation of generation-by-generation deposition probabilities within tubular and alveolar structures. Preliminary results presented here should demonstrate the effects on fiber deposition due to variations of the breathing behaviour and the particle properties. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fiber; Inertial impaction; Interception; Gravitational settling; Human respiratory tract; Computer program; Visual Basic䉸
∗ Corresponding author. Tel. +43 662 80445709; fax: +43 662 8044 150.
E-mail address: [email protected] (R. Sturm). 0010-4825/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2005.07.004
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1. Introduction Fibrous materials have found a wide distribution in various industrial fields due to their inexpensive production in high amounts and their partly remarkable physicochemical properties (e.g. high heat resistance). Despite these positive qualities, fibers have also been classified as a potential health hazard, when they are inhaled and deposited in the lungs. The toxicity of fibers is mainly dependent upon the site of deposition, thereby assuming alveolar deposition as more harmful than tracheobronchial deposition, because particles accumulated in this region are characterized by significantly longer residence times [1]. Toxicity of fibrous material in the bronchial region, however, is enhanced due to the preferential formation of hot spots (i.e., high particle concentrations within rather small surface areas) at the carinal sites of proximal bifurcations combined with a much smaller total surface area with respect to the alveolar compartment [2–4]. Fiber deposition in the human lungs is caused by the interrelationship of impaction, interception, sedimentation, and diffusion, whereby the first two mechanisms are most prominent in the upper conducting airways due to higher flow velocities, while sedimentation plays a leading role within the peripheral airways and alveoli. Brownian diffusion has a rather marginal meaning, because most artificial fibers have a length > 1 m and thus are only negligibly affected by the collision with air molecules. Inhalation experiments for working out the deposition behaviour of fibrous particles have been limited to airway casts and various laboratory animals until now, with partly insurmountable problems arising from the production of monodisperse fibrous aerosols [5]. Contrary to the very small source of experiments with aerosolized fibers, the number of theoretical studies dealing with various aspects of fiber transport and deposition in both human and animal lungs has continuously increased during the last decades [6–11]. Concerning the behaviour of aerosolized fibers in the tracheobronchial tree, previous models like that of Cai and Yu [6] assumed a simple flow field within the airway tubes, where deposition of fibrous particles due to inertial and interceptional forces was computed for different fiber orientations. A more complex mathematical approach considering fiber motion in a shear flow, where elongated particles undergo both rotation and translation, was introduced by Zhang et al. [9]. This numerical model is among others based on the early theoretical studies of Jeffery [12] who described the orientation changes of elongated particles in viscous flows by supposing the particle to hold a fixed position. Recently, empirical deposition equations based on cast experiments with glass fibers were outlined by Myojo and Takaya [5], exhibiting a rather good correspondence with earlier model predictions, according to which penetration of fibrous particles into the lungs negatively correlates with the fiber aspect ratio for a fiber diameter > 1 m. As many man-made fibers are flexible and thus deform under the action of forces, this specific property was additionally subject to theoretical investigations [13–15]. The studies uniformly came to the result that the behaviour of flexible fibers in a fluid flow is even more complex than that of rigid fibers, with deposition rates mainly depending upon their initial shapes, orientations, and positions within the flow fields. Regarding gravitational deposition of fibrous particles in the more peripheral airway system and alveoli, previous studies carried out by Gallily and Eisner [16] assumed a constant gradient laminar flow within distal lung structures. Based on these findings, more complex mathematical approaches were developed [7,17], at last, to enable the prediction of fiber behaviour in an arbitrary flow field. As a main result from the published models, deposition efficiency positively correlates with the inclination angle a of the respective airway and the fiber aspect ratio . Alveolar fiber deposition in rodents and humans was theoretically described by Dai and Yu [1], whose considerations were exclusively based on the concept of the aerodynamic diameter, depending upon fiber density, physical dimension, and orientation with
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respect to the air flow direction. The authors found that in humans alveolar deposition of fibrous material significantly varies with breathing conditions (i.e., resting, light or moderate workload), but, however, deposition maxima are usually recognizeable for aerodynamic diameters ranging from 2 to 3 m. Computer programs especially dealing with fiber transport and deposition in the human respiratory tract have not been described in the open literature until now. This can be mainly led back to the fact that respective computations were carried out by using well-described and validated computer codes such as LUDEP䉷 [21] and by inserting pre-defined aerodynamic diameters of the fibers into the input files. Although with this procedure reasonable data for fiber deposition in the extrathoracic and thoracic regions of the respiratory tract were produced, the high complexity of fiber transport, which was tried to be worked out in detail in the studies noted above, was not sufficiently taken into account. As another drawback, both programs calculate deposition in the upper bronchial region by using analytical deposition formulae derived from bent airways [20] and partly considering the specific geometry of single bifurcations by the introduction of correction factors. The aims of the work presented here are two-fold: Firstly, a computer program exclusively dealing with fiber transport and deposition in the human respiratory tract is subject to a detailed description. The computer code termed FIBROS was written in Visual Basic䉷 , thereby offering the scientist all the user-friendliness of a typical Windows䉷 application. Secondly, preliminary calculations carried out with the program are presented, and influences of both specified breathing parameters and fiber properties on regional as well as local fiber deposition are discussed.
2. Program description 2.1. Organization of the input window and data input FIBROS was developed to fulfill the following goals: ease of use, time efficiency, and processing of the input data with high accuracy. To accomplish these aims, FIBROS was programmed, using typical windows-based graphical user interfaces (GUIs) with a menu bar and command buttons for a user-friendly navigation. Development of the program was carried out in Visual Basic䉷 version 6, allowing a quick processing of mathematical formulae as those used in the specific case of the work presented here. FIBROS runs as a stand-alone application within later versions of the Windows䉷 operating system (i.e., version 98 or later). When starting FIBROS by double-clicking on the program icon, the program will open the “Entrance” window as it is exhibited in Fig. 1a, from which one can either obtain several informations concerning the program and fibers in general or can directly navigate to the “Data input” window (Fig. 1b). In this window, the user is able to either create a new data file or load a previously saved file (extension txt) using the file → load command in the menu bar. In general, the organization of the “Data input” window is characterized by a subdivision into four main parts, containing all the information needed for an appropriate calculation of regional and local fiber deposition. Therefore, on the upper left panel, breathing and flow conditions during respiration of the aerosol may be specified (Fig. 1b). The breathing cycle is determined by the tidal volume in cm3 , the inhalation time in seconds, and the breath-hold time in seconds. If asymmetric breathing is selected in the respective control box, which is of higher relevance in diseased lungs, the user is also asked for an exhalation time (s). The air flow profile can be assumed as either parabolic with highest flow velocities in the centre of the airways and lowest velocities at the airway
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Fig. 1. Entrance window (a) and (b) Data input window of FIBROS for the input of breathing data and particle properties as well as the selection of fiber deposition formulae, datasets of lung morphometry, and the mode of airway scaling.
walls or as uniform with a constant velocity throughout the whole cross section of each airway tube. The deposition calculation panel on the lower left part of the window (Fig. 1b) enables the scientist to select the extrathoracic path, through which particles are inhaled (“None” means that the extrathoracic region is completely excluded from the computation), and respective empirical formulae for the calculation of fiber deposition in the proximal and distal lung regions (to be discussed below). Fiber properties may be specified on the upper right panel of the “Data input” window. Besides determination of the fiber size (diameter in m, aspect ratio) and density in g/cm3 , also a detailed specification of fiber orientation with respect to the flow direction in proximal and peripheral airways is possible. The lower right panel in the window is needed for specifying the lung morphometry used for the deposition calculations. For this,
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the scientist is able to select from different morphometric datasets published in the open literature. Lung scaling may be performed according to (1) the functional residual capacity [21], (2) body length [22], and (3) pre-defined scaling factors for airway diameters and lengths. Lung scaling with constant factors again plays a major role in diseased lungs. After completion of the input data, information may be written into a txt-file using file → save command in the menu bar. Calculation is started by either pressing the “Calculate” button or clicking on the “Calculate” command in the menu bar.
2.2. Calculation of fiber deposition When entering the respiratory tract, high fractions of fibers are already deposited in the extrathoracic region acting as a highly efficient filter system. Forces affecting fibrous particles in the head region are impaction, interception, and, to a lower extent, diffusion. Deposition efficiencies due to nasal and oral impaction are derived from the following equations [23,24]: Nasal: Dn,imp = Oral: Dm,imp Dm,imp
1.257
(105 + 1.257 )
0.609 (inhalation and exhalation)
=0 for 3000 = − 1.117 + 0.324 log for > 3000 (inhalation) =0 (exhalation),
(1)
(2)
2 Q with d denoting the aerodynamic diameter of the fiber (m) and Q the flow rate (cm 3 /s). where =dae ae The aerodynamic diameter dae is subject to a continuous change due to the rotation of the fiber in the shear flow. According to Dai and Yu [1], a time-averaged aerodynamic diameter, where the fiber is assumed to spend equal amounts of time in all orientations, can be written as follows:
dae =
1 3 (b
+ 2b⊥ )
2
d . 0 v
(3)
In Eq. (3), b and b⊥ denote the normalized mobilities of the fiber moving parallel and perpendicular to the flow direction, whereas dv , , and 0 are the equivalent volume diameter, particle density, and density of the fluid, respectively. For a fiber with a pre-defined aspect ratio , b , and b⊥ are given as 31/3 [((22 − 1)/( 2 − 1)) ln( + 2 − 1) − ]c b = , 4(2 − 1)
(4)
31/3 [((22 − 3)/( 2 − 1)) ln( + 2 − 1) + ]c⊥ b⊥ = 8(2 − 1)
(5)
with c and c⊥ being the slip correction factors for a fiber moving parallel and perpendicular to the flow direction [1].
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In the nasal pathway, deposition by interception yields Dn,int =
0.921[1 − (1 − 24lf )7 ] 0.921
for lf < 0.035 cm, for lf = 0.035 cm (inhalation and exhalation),
(6)
where lf is the fiber length in cm [25]. Concerning the oral pathway, fiber deposition due to interception is generally considered to be negligible due to the high difference in size between the mouth cavity and fiber length. Nasal and oral fiber deposition caused by Brownian diffusion is expressed by the following equations [26]: Nasal: Oral:
Dn,diff = 1 − exp(−9.0D 1/2 Q1/8 ) (inhalation), Dn,diff = 1 − exp(−10.55D 1/2 Q1/8 ) (exhalation). Dm,diff = 1 − exp(−7.24D 1/2 Q1/8 ) (inhalation), Dm,diff = 1 − exp(−5.98D 1/2 Q1/8 ) (exhalation)
(7) (8)
with Q being the flow rate in cm3 /s and D the diffusion coefficient (cm2 /s) which for randomly oriented fibers is given by kT 1 2 D= b + b⊥ (9) 3dv 3 3 In Eq. (9), k denotes the Boltzmann constant, T the air temperature in K, and the dynamic viscosity of air. Regarding fiber deposition in the thoracic region of the respiratory tract, FIBROS includes various empirical approaches for inertial impaction and interception as well as for gravitational settling, while Brownian diffusion, being of significantly lower importance, is computed according to a widely applied standard formula [18]. Inertial and interceptional deposition of fibers according to the calculation procedure outlined by Cai and Yu [6] will be, for the sake of brevity, not fully described in the work presented here, but, with few words, the algorithm provided by the authors is mainly based on the concept of the stop distance and interception distance of a anisometric particle in the cross-section of the daughter tube, finally serving for the calculation of deposition efficiencies in the whole bifurcation. Respective formulae are based on the equivalent diameters of fibrous particles introduced by Oseen [27] and are dependent upon the bifurcation angle, the diameter ratio between daughter and parent tube of the bifurcation, the Stokes number, and the fiber length. By developing a numerical model, Zhang et al. [9] could describe inertial and interceptional fiber deposition in the upper airways of the tracheobronchial tree by a relationship between the deposition efficiency and the Stokes number, which is subject to only slight variations for different flow types (expressed by the Reynolds number) and bifurcation angles. According to the authors, Stokes number (St) may be derived from the equation St =
2V f dev
18D
,
(10)
with dev = df 1/3 (df = fiber diameter), f being the fiber density, V the mean velocity of the flow in the parent airway, and D the parent airway diameter. The relationship between the deposition efficiency
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Table 1 Coefficients used for the calculation of deposition efficiencies in the tracheobronchial tree according to the algorithms outlined by Zhang et al. [9], Myojo and Takaya [5], and Asgharian and Anjilvel [17]
Zhang et al. [9]: Dimp,int = a exp[− exp(b − c St)] Coefficients a 0.8882 Myojo and Takaya [5]: an = x1 I 2 + x2 I + x3 Coefficients x1 a0 −103658 −100875 a1 a2 −32909 −4450.2 a3 −203.4 a4 Asgharian and Anjilvel [17]: f (, ) = −0.774 5n=0 an n Coefficients n=0 1 2 3 4 5
b 1.6529
c 4.7769
x2 1837.2 1792.7 562.95 67.601 2.5374
x3 1.6762 −0.9073 −1.0819 −0.0819 0.0026
0 < 31/32 −0.844 14.400 −22.409 16.586 −5.669 −0.726
an 31/32 203.750 −64.856
Dimp,int and St is best expressed by a Gompertz function of the following general form: Dimp,int = a exp[− exp(b − cSt)]
(11)
Values for the coefficients a, b, and c are summarized in Table 1, assuming a mean Reynolds number of 500 and an average bifurcation angle of 90◦ . A similar approach of inertial and interceptional fiber deposition as that noted above was also introduced by Myojo and Takaya [5]. In their work, Stokes number for randomly oriented fibers yields St =
f df2 V sin
16R[0.385/(ln(2lf /df ) + 0.5) + 1.230/(ln(2lf /df ) − 0.5)]
(12)
with denoting the angle between the initial and final direction of the air stream and R the airway radius. Specific consideration of interceptional deposition is given by introducing a interception parameter I of the following form: lf (13) 2R For a pre-defined interception parameter, Myojo and Takaya [5] expressed the dependence between Dimp,int and St by the polynomial equation I=
Dimp,int = exp{a0 + a1 (ln St) + a2 (ln St)2 + a3 (ln St)3 + a4 (ln St)4 },
(14)
where a0 –a4 may be described as second-order polynomial functions with I as the independent variable (Table 1).
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Gravitational settling of fibers in the more peripheral airways is computed according to the concept outlined by Asgharian and Anjilvel [17], where motion of anisometric particles in an arbitrary flow field was simulated numerically and sedimentation was expressed by the dimensionless parameter 1 as follows: 1 =
f gd 2f C
(15)
18V
In Eq. (15), C denotes the fluid correction factor and g the gravitational constant. In the deeper lung, 1 is assumed to take values much smaller than 1. Additionally, a linear relationship between deposition efficiency and 1 may be observed, which one can write as
Dsed = f (, ) 1
(16)
Asgharian and Anjilvel fitted the function f (, ) by a polynomial of degree 5, thereby obtaining the following expression: f (, ) = −0.774
5
an n .
(17)
n=0
The respective values of an are listed in Table 1. In the program, an alternative method for the computation of fiber sedimentation is offered based on the concept of the aerodynamic diameter presented in Eq. (3) [1], for which deposition efficiency is estimated according to the formula [20] 4gC f dae L cos
Dsed = 1 − exp (18) 36RV with L denoting the airway length and the gravity angle of the bifurcation. Eqs. (10)–(18) are only valid for the computation of particle deposition following inhalation. For both breath-hold and exhalation fiber depositions due to impaction have been reduced by constant factors [4], while sedimentation and diffusion have been calculated with the same formulae as used for inspiration. As exhibited in Fig. 1b, the program allows the definition of fiber orientation for both the proximal and distal airways of the lungs. Orientations, however, are expressed by respective formulae for the Stokes number in the case of inertial impaction/interception and for the aerodynamic diameter in the case of sedimentation. For instance, assumption of random orientation in the upper airways and parallel orientation in the lower airways would be calculated by using the Stokes numbers noted above and by modifying the aerodynamic diameter of Eq. (3), deleting the variable b⊥ . By selecting a specific morphometric dataset of the lungs, all the computations described in this sections are applied to mean values of generation-specific airway diameters, lengths, and branching angles provided by this dataset. Besides morphometric parameters, also the path lengths of inhaled particles are varied stochastically, leading to typical deposition patterns with one or more maxima. 2.3. Program output In the “Results” window, the user is able to view the output data generated by the program in a numerical as well as a graphical form (Fig. 2). The window is subdivided into two main blocks: within the left block, all information specified in the “Data input” window (Fig. 1b) are summarized and listed by the
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Fig. 2. Results windows of FIBROS. (a) Regional deposition results; (b) airway generation-specific deposition results.
four main categories, according to which the input window is organized (see above). The remaining part of the “Results” window contains a panel exhibiting the computation results numerically and graphically. The panel itself is subdivided into two forms, to which one can navigate by clicking on the respective tabs on the top (Fig. 2). The form reached by activating the left tab includes regional deposition data for the fiber properties, breathing conditions, and deposition models specified in the input window. In a bar chart, regional deposition (%) is assigned to the three main compartments of the respiratory tract: (1) the extrathoracic region, (2) the air conducting zone (bronchial region), and (3) the respiratory zone (acinar region). For more detailed information, the acinar region is additionally subdivided into the ductal and alveolar compartments, and all tubular components of the lungs (i.e., bronchial and ductal part) are also summarized in a specific category (“tubular”, Fig. 2a). Numerical results are listed on the bottom
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of the form. By clicking on the right tab of the panel, one can reach the form with airway generationspecific output data (Fig. 2b). In the respective deposition-by-generation graph, tubular and alveolar fiber deposition (%) in the single airway generations of the lungs is plotted, giving an estimate of how deep the particles have penetrated into the respiratory system. Numerical results are again listed on the bottom of the form. The windows with all the input and output data can be easily printed by using the file → print command in the menu bar.
3. Preliminary results and their interpretation Preliminary results of fiber deposition computations carried out with FIBROS are shown in Figs. 2–6. Following the setup exhibited in Fig. 1b, respective output data for particle deposition on a regional and local level are summarized in Fig. 2. As clearly recognizeable from panel (a) of Fig. 2, under the given breathing conditions fibers with a diameter of 3 m and an aspect ratio of 20 are mainly captured in the extrathoracic region (∼ 65%), therefore, only a small fraction of particles being allowed to enter the tracheobronchial tree of the lungs. Within the lungs, deposition takes mainly place in the air conducting zone (21.2%), while the respiratory zone is reached by the remaining 13.8% of particles. The fraction of fibers leaving the respiratory tract after exhalation is negligible for the particle shape defined in the setup, i.e., the total deposition efficiency amounts to 100%. Concerning the more local level of fiber deposition, which is expressed by the deposition-by-generation plot in Fig. 2b, tubular deposition is characterized by two maxima, one in generation 0 (trachea) and one in generation 11 (∼ terminal bronchiole) (note: deposition was normalized to the fraction of particles entering the trachea). Alveolar deposition, on the other hand, starts by definition in airway generation 12 and reaches its maximum in generation 15. The results exhibited in Fig. 2b clearly reflect the importance of impactional and interceptional forces in the upper bronchial airways, while in the peripheral part of the lungs, deposition maxima are mainly generated by gravitational settling of the particles. Comparison between fibrous and spherical particles (both with a diameter of 3 m), for which respective deposition computations were carried out using the computer code provided by Koblinger and Hofmann [18], show several significant differences (Fig. 3): (1) Extrathoracic deposition fractions of spherical particles are significantly lower than those of fibers (21 vs. 65%), causing higher deposition in the lungs themselves (∼ 46%) (2) Contrary to fibrous particles, 3 m spheres are characterized by a high fraction leaving the respiratory tract upon exhalation (33%). (3) Deposition of spherical particles in the upper airways of the tracheobronchial tree is remarkably lower than that of fibers, indicating the negligible effect of interception in this case and, not less important, the influence of random fiber orientation on deposition. (4) Deposition in the lung periphery is higher for spheres than for fibers, which can be simply explained by the limited fraction of fibers entering this region due to the high filter efficiency in the preceeding compartments of the lung. In Fig. 4, the various deposition models provided by FIBROS and described in detail in the last section are subject to a comparison, using the breathing conditions and particle properties exhibited in Fig. 1b. Regarding the three models used for the estimation of impaction and interception (Fig. 4a), differences among the output results are very high. While with the approaches of Myojo and Takaya [5] and Cai and Yu [6] deposition maxima in the upper bronchi are strongly emphasized, with the approach of Zhang et al. [9] this maximum is significantly lower and shifted toward the trachea. In the intermediated zone of the tracheobronchial tree, deposition nearly drops to zero in the case of the Cai and Yu model, leading also to an extraordinary emphasis of sedimentation in the lung periphery (note: gravitational settling was
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Fig. 3. Comparison between the deposition of fibers and spheres in the human respiratory tract; (a) regional deposition; (b) deposition by airway generation. Input data are those exhibited in Fig. 1b. Spherical particles have a diameter of 3 m and a density of 2.5 g/cm3 .
uniformly calculated according to the approach of Asgharian and Anjilvel [17]). These effects are clearly weakened when using the other two models. Differences between the two sedimentation models provided by the program are not so high as those between the impaction/interception models (Fig. 4b). In contrast to the model of Asgharian and Anjilvel [17], with the model of Dai and Yu [1] the deposition peak in the trachea disappears at the cost of an enhanced deposition fraction in the remaining parts of the lungs. The effect of flow rate on fiber deposition is illustrated in Fig. 5. Calculations were carried out with the setup exhibited in Fig. 1b, thereby decreasing inhalation time in a stepwise fashion from 4 s (flow rate: 250 cm3 /s) to 1 s (flow rate: 1000 cm3 /s). Similar to spherical particles, an increase of the flow rate in this way causes (1) a partly dramatic increase of impaction and interception in the upper airways and, to a comparable extent, (2) a continuous decrease of gravitational settling in the intermediate and peripheral lung regions. This is mainly due to the fact that all forces controlling particle deposition depend upon
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Fig. 4. Deposition-by-generation plots using the different deposition models for inertial impaction/interception and sedimentation provided by the program; (a) variation of the inertial impaction/interception models (sedimentation according to Asgharian and Anjilvel [17]); (b) variation of the sedimentation models (inertial impaction/interception according to Zhang et al. [9]). Breathing conditions and fiber properties are defined in Fig. 1b.
flow velocity, i.e., impaction and interception correlate positively with the velocity of the air stream, while sedimentation is marked by a negative correlation as expressed in Eq. (15). Detailed comparison between fiber deposition computed for a flow rate of 250 cm3 /s and that estimated for a flow rate of 1000 cm3 /s also indicates a shift of the deposition maxima. While the first maximum is shifted to higher airway generations with increasing flow rate, the second one shows an opposite behaviour. Fig. 6 illustrates the effect of increasing fiber aspect ratio on bronchial and alveolar deposition. While on panel a of Fig. 6 an increase of the aspect ratio has been expressed by a continuous enhancement of the fiber length (constant diameter: 3 m), on panel b, aspect ratio has been increased by a stepwise reduction of the fiber diameter (constant length: 30 m). Concerning the scenario with variable fiber length, main differences in deposition can be recognized for the first 5 airway generations, where deposition of 90 m
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Fig. 5. Fiber deposition (diameter: 3 m, aspect ratio: 20, density: 2.5 g/cm3 ) under different breathing conditions. Deposition formulae selected in Fig. 1b have been used for the calculations.
long fibers is partly double as high as that of 15 m long particles. Deposition due to sedimentation is only insignificantly increased with fiber length (by about 1%). The deposition enhancement in the upper bronchi may be regarded as a result of increased interception, which correlates positively with fiber length, and of the random fiber orientation in this compartment. Continuous increase of the fiber diameter causes a similar effect as that noted above, i.e., particles with a diameter of 6 m deposit more effectively in the upper bronchi and less effectively in the peripheral airways, while fibers with 1 m diameter show a contrary behaviour. Instead of interception, inertial impaction may be evaluated as the dominant deposition force in this case.
4. Summary and conclusions The main objective of the work presented here was the detailed description of a computer program termed FIBROS which enables e.g. the medical scientist to estimate fiber deposition in the human respiratory tract after specification of breathing conditions, deposition models, fiber properties, and the morphometric lung model. Besides regional (i.e. extrathoracic, bronchial, alveolar) deposition fractions, FIBROS additionally allows the creation of deposition-by-airway generation plots, describing fiber deposition on a more local level. According to preliminary results derived from the program, under normal breathing conditions with an inhalative flow rate of 500 cm3 /s, most of the inhaled fibers are already deposited in the extrathoracic region, while in the lungs usually two deposition maxima can be recognized: one in the upper tracheobronchial tree (generation 0–5) and one in the more peripheral part of the lungs (generation 10–15). The first maximum is caused by impactional and interceptional forces affecting fibrous particles mainly in those parts of the tracheobronchial tree, where flow velocities are high (> 50 cm/s), whereas the second maximum may be regarded as the result of gravitational settling, which becomes most prominent in a slow flow regime (< 1 cm/s). Deviation from the standard breathing conditions influences fiber deposition more or less significantly, whereby in this study highest modifications of the deposition pattern
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Fig. 6. Effect of the aspect ratio on fiber deposition using the setup exhibited in Fig. 1b; (a) fibers with constant diameter (3 m) and variable length; (b) Fibers with constant length (30 m) and variable diameter. Deposition formulae selected in Fig. 1b have been used for the calculations (a.r. = aspect ratio).
could be observed for a flow rate 1000 cm3 /s, corresponding with an intermediate work load. For these specific type of breathing, the filter efficieny of the upper bronchi becomes remarkable enhanced, and, as a consequence of that, alveolar fiber deposition is clearly decreased. A similar effect on deposition as by increasing the flow rate is noticeable for an modified aspect ratio (i.e., length per diameter) of the fibers. The higher either fiber length or fiber diameter get, the more effectively respective particles are already deposited in the trachea and the following airway generations due to the continuously enhanced influence of either interceptional or impactional forces. From the results presented in this study, it may be concluded that fiber deposition in the human respiratory tract is characterized by several specificities with respect to spherical particles. The computer program described here considers these specific properties to a certain degree, therefore representing an alternative to available transport and deposition codes being solely based on the aerodynamic
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diameter concept. FIBROS might find enhanced usage not only in medical science for the modelling of particle-lung interactions, but also for the simulation of the effect of dust exposures in different working environments. References [1] Y.T. Dai, C.P. Yu, Alveolar deposition of fibers in rodents and humans, J. Aerosol Med. 11 (1998) 247–258. [2] I. Balàshàzy, T.B. Martonen, W. Hofmann, Fiber deposition in airway bifurcations, J. Aerosol Med. 3 (1990) 243–260. [3] I. Balásházy, W. Hofmann, Particle deposition in airway bifurcations: I. inspiratory flow, J. Aerosol Sci. 24 (1993) 745–772. [4] I. Balásházy, W. Hofmann, Particle deposition in airway bifurcations: II. expiratory flow, J. Aerosol Sci. 24 (1993) 773–786. [5] T. Myojo, M. Takaya, Estimation of fibrous aerosol deposition in upper bronchi based on experimental data with model bifurcation, Ind. Health 39 (2001) 141–149. [6] F.S. Cai, C.P. Yu, Inertial and interceptional deposition of spherical particles and fibers in a bifurcating airway, J. Aerosol Sci. 19 (1988) 679–688. [7] Y.K. Chen, C.P. Yu, Sedimentation of fibers from laminar flows in a horizontal circular duct, Aerosol Sci. Technol. 14 (1991) 343–347. [8] L. Gradon, D. Orlicki, Deposition of inhaled aerosol particles in a generation of the tracheobronchial tree, J. Aerosol Sci. 21 (1990) 3–19. [9] L. Zhang, B. Asgharian, S. Anjilvel, Inertial and interceptional deposition of fibers in a bifurcating airway, J. Aerosol Med. 9 (1996) 419–430. [10] C.P. Yu, B. Asgharian, K.E. Pinkerton, Intrapulmonary deposition and retention modeling of chrysotile asbestos fibers in rats, J. Aerosol Sci. 22 (1991) 757–763. [11] J.Y. Ding, C.P. Yu, L. Zhang, Y.K. Chen, Deposition modeling of fibrous particles in rats: Comparison with available experimental data, Aerosol Sci. Technol. 26 (1997) 403–414. [12] G.B. Jeffrey, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Sci. Lond. A 102 (1922) 161–179. [13] L. Gradon, A. Podgorski, Flexible fibrous particle behaviour in the carrier gas flow around cylindrical obstacle, Chem. Eng. Sci. 45 (1990) 3435–3441. [14] A. Podgorski, L. Gradon, Grzybowski, Theoretical study on deposition of flexible and stiff fibrous aerosol particles in a cylindrical collector, Chem. Eng. Sci. 58 (1995) 109–121. [15] M. Shams, G. Ahmadi, H. Rahimzadeh, Transport and deposition of flexible fibers in turbulent duct flows, J. Aerosol Sci. 32 (2001) 525–547. [16] I. Gallily, A.D. Eisner, On the orderly nature of the motion of nonspherical aerosol particles, J. Colloid Int. Sci. 68 (1979) 320–337. [17] B. Asgharian, S. Anjilvel, Movement and deposition of fibers in an airway with steady viscous flow, Aerosol Sci. Technol. 22 (1995) 261–270. [18] L. Koblinger, W. Hofmann, Monte Carlo modeling of aerosol deposition in human lungs Part I: simulation of particle transport in a stochastic lung structure, J. Aerosol Sci. 21 (1990) 661–674. [20] H. Yeh, G.M. Schum, Models of human lung airways and their application to inhaled particle deposition, Bull Math. Biol. 42 (1980) 461–480. [21] International Commission on Radiological Protection (ICRP), Human Respiratory Tract Model for Radiological Protection, Publication 66. Ann. ICRP, Pergamon Press, Oxford, 1994, p. 456. [22] R.F. Phalen, M.J. Oldman, C.B. Beaucage, T.T. Crocker, J.D. Mortensen, Postnatal enlargement of human tracheobronchial airways and implications for particle deposition, Anat. Rec. 212 (1985) 368–380. [23] L. Zhang, C.P. Yu, Empirical equations for nasal deposition of inhaled particles in small laboratory animals and humans, Aerosol Sci. Technol. 19 (1993) 51–56. [24] C.P. Yu, C.K. Diu, T.T. Soong, Statistical analysis of aerosol deposition in nose and mouth, Am. Ind. Hyg. Assoc. J. 42 (1981) 726–733. [25] B. Asgharian, C.P. Yu, Deposition of inhaled fibrous particles in the human lung, J. Aerosol Med. 1 (1988) 37–50.
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[26] Y.S. Cheng, Y.F. Su, H.C. Yeh, Deposition of thoron progeny in human head airways, Aerosol Sci. Technol. 18 (1993) 359–375. [27] C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Leipzig, 1927 p. 18. Robert Sturm attended the University of Salzburg, Austria, receiving M.Sc. degrees in earth sciences and biology and his Ph.D. degree in Biophysics. He has held different positions as research assistant at the University of Salzburg and presently is employed as a scientific co-worker within a research project of the European Communities (BIODOS). Werner Hofmann attended the University of Vienna, Austria, where he received his Ph.D. degree in Nuclear Physics. He has held different positions at the University of Salzburg, presently heading the Institute of Physics and Biophysics, and visiting professor positions at the University of Lincoln, NE, Duke University, NC, both in the USA, and the Nova Gorica Polytechnic, Slovenia. For about 25 years, he has been involved in theoretical research on the dosimetry of inhaled particles in the human respiratory tract. The work reported here was part of the Institutes commitment to research projects supported by the European Communities.
A computer program for the simulation of fiber deposition in the human respiratory tract Robert Sturma,∗ , Werner Hofmannb a Brunnleitenweg 41, A-5061 Elsbethen, Austria b Division of Physics and Biophysics, Department of Molecular Biology, University of Salzburg, Hellbrunner Strasse 34,
A-5020 Salzburg, Austria Received 30 September 2004; accepted 25 July 2005
Abstract As inhaled fibers may lead to a variety of lung diseases, detailed information on their deposition in the human respiratory tract is an indispensable requirement in medical science. In the work presented here, a Visual Basic䉸 computer program, termed FIBROS, is described which enables the simulation of fibrous particle deposition in both the extrathoracic region and different parts of the lung itself, including the results of published numerical studies on inertial/interceptional as well as diffusional and gravitational deposition. The input window of FIBROS includes the selection of specific breathing conditions by variation of the tidal volume and breathing cycle. Furthermore, the user is able to determine fiber properties such as diameter, aspect ratio, specific weight, and fiber orientation with respect to the air stream in the upper and lower airways of the lungs. Besides the offer of various deposition formulae for each region of the respiratory tract, thereby also allowing a distinction between mouth and nose breathing, the user may select between different morphometric datasets of the lung and respective airway scaling procedures. Analysis routines of FIBROS include the estimation of regional deposition fractions, thereby distinguishing between extrathoracic, bronchial, and acinar compartments, and a calculation of generation-by-generation deposition probabilities within tubular and alveolar structures. Preliminary results presented here should demonstrate the effects on fiber deposition due to variations of the breathing behaviour and the particle properties. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fiber; Inertial impaction; Interception; Gravitational settling; Human respiratory tract; Computer program; Visual Basic䉸
∗ Corresponding author. Tel. +43 662 80445709; fax: +43 662 8044 150.
E-mail address: [email protected] (R. Sturm). 0010-4825/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compbiomed.2005.07.004
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1. Introduction Fibrous materials have found a wide distribution in various industrial fields due to their inexpensive production in high amounts and their partly remarkable physicochemical properties (e.g. high heat resistance). Despite these positive qualities, fibers have also been classified as a potential health hazard, when they are inhaled and deposited in the lungs. The toxicity of fibers is mainly dependent upon the site of deposition, thereby assuming alveolar deposition as more harmful than tracheobronchial deposition, because particles accumulated in this region are characterized by significantly longer residence times [1]. Toxicity of fibrous material in the bronchial region, however, is enhanced due to the preferential formation of hot spots (i.e., high particle concentrations within rather small surface areas) at the carinal sites of proximal bifurcations combined with a much smaller total surface area with respect to the alveolar compartment [2–4]. Fiber deposition in the human lungs is caused by the interrelationship of impaction, interception, sedimentation, and diffusion, whereby the first two mechanisms are most prominent in the upper conducting airways due to higher flow velocities, while sedimentation plays a leading role within the peripheral airways and alveoli. Brownian diffusion has a rather marginal meaning, because most artificial fibers have a length > 1 m and thus are only negligibly affected by the collision with air molecules. Inhalation experiments for working out the deposition behaviour of fibrous particles have been limited to airway casts and various laboratory animals until now, with partly insurmountable problems arising from the production of monodisperse fibrous aerosols [5]. Contrary to the very small source of experiments with aerosolized fibers, the number of theoretical studies dealing with various aspects of fiber transport and deposition in both human and animal lungs has continuously increased during the last decades [6–11]. Concerning the behaviour of aerosolized fibers in the tracheobronchial tree, previous models like that of Cai and Yu [6] assumed a simple flow field within the airway tubes, where deposition of fibrous particles due to inertial and interceptional forces was computed for different fiber orientations. A more complex mathematical approach considering fiber motion in a shear flow, where elongated particles undergo both rotation and translation, was introduced by Zhang et al. [9]. This numerical model is among others based on the early theoretical studies of Jeffery [12] who described the orientation changes of elongated particles in viscous flows by supposing the particle to hold a fixed position. Recently, empirical deposition equations based on cast experiments with glass fibers were outlined by Myojo and Takaya [5], exhibiting a rather good correspondence with earlier model predictions, according to which penetration of fibrous particles into the lungs negatively correlates with the fiber aspect ratio for a fiber diameter > 1 m. As many man-made fibers are flexible and thus deform under the action of forces, this specific property was additionally subject to theoretical investigations [13–15]. The studies uniformly came to the result that the behaviour of flexible fibers in a fluid flow is even more complex than that of rigid fibers, with deposition rates mainly depending upon their initial shapes, orientations, and positions within the flow fields. Regarding gravitational deposition of fibrous particles in the more peripheral airway system and alveoli, previous studies carried out by Gallily and Eisner [16] assumed a constant gradient laminar flow within distal lung structures. Based on these findings, more complex mathematical approaches were developed [7,17], at last, to enable the prediction of fiber behaviour in an arbitrary flow field. As a main result from the published models, deposition efficiency positively correlates with the inclination angle a of the respective airway and the fiber aspect ratio . Alveolar fiber deposition in rodents and humans was theoretically described by Dai and Yu [1], whose considerations were exclusively based on the concept of the aerodynamic diameter, depending upon fiber density, physical dimension, and orientation with
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respect to the air flow direction. The authors found that in humans alveolar deposition of fibrous material significantly varies with breathing conditions (i.e., resting, light or moderate workload), but, however, deposition maxima are usually recognizeable for aerodynamic diameters ranging from 2 to 3 m. Computer programs especially dealing with fiber transport and deposition in the human respiratory tract have not been described in the open literature until now. This can be mainly led back to the fact that respective computations were carried out by using well-described and validated computer codes such as LUDEP䉷 [21] and by inserting pre-defined aerodynamic diameters of the fibers into the input files. Although with this procedure reasonable data for fiber deposition in the extrathoracic and thoracic regions of the respiratory tract were produced, the high complexity of fiber transport, which was tried to be worked out in detail in the studies noted above, was not sufficiently taken into account. As another drawback, both programs calculate deposition in the upper bronchial region by using analytical deposition formulae derived from bent airways [20] and partly considering the specific geometry of single bifurcations by the introduction of correction factors. The aims of the work presented here are two-fold: Firstly, a computer program exclusively dealing with fiber transport and deposition in the human respiratory tract is subject to a detailed description. The computer code termed FIBROS was written in Visual Basic䉷 , thereby offering the scientist all the user-friendliness of a typical Windows䉷 application. Secondly, preliminary calculations carried out with the program are presented, and influences of both specified breathing parameters and fiber properties on regional as well as local fiber deposition are discussed.
2. Program description 2.1. Organization of the input window and data input FIBROS was developed to fulfill the following goals: ease of use, time efficiency, and processing of the input data with high accuracy. To accomplish these aims, FIBROS was programmed, using typical windows-based graphical user interfaces (GUIs) with a menu bar and command buttons for a user-friendly navigation. Development of the program was carried out in Visual Basic䉷 version 6, allowing a quick processing of mathematical formulae as those used in the specific case of the work presented here. FIBROS runs as a stand-alone application within later versions of the Windows䉷 operating system (i.e., version 98 or later). When starting FIBROS by double-clicking on the program icon, the program will open the “Entrance” window as it is exhibited in Fig. 1a, from which one can either obtain several informations concerning the program and fibers in general or can directly navigate to the “Data input” window (Fig. 1b). In this window, the user is able to either create a new data file or load a previously saved file (extension txt) using the file → load command in the menu bar. In general, the organization of the “Data input” window is characterized by a subdivision into four main parts, containing all the information needed for an appropriate calculation of regional and local fiber deposition. Therefore, on the upper left panel, breathing and flow conditions during respiration of the aerosol may be specified (Fig. 1b). The breathing cycle is determined by the tidal volume in cm3 , the inhalation time in seconds, and the breath-hold time in seconds. If asymmetric breathing is selected in the respective control box, which is of higher relevance in diseased lungs, the user is also asked for an exhalation time (s). The air flow profile can be assumed as either parabolic with highest flow velocities in the centre of the airways and lowest velocities at the airway
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Fig. 1. Entrance window (a) and (b) Data input window of FIBROS for the input of breathing data and particle properties as well as the selection of fiber deposition formulae, datasets of lung morphometry, and the mode of airway scaling.
walls or as uniform with a constant velocity throughout the whole cross section of each airway tube. The deposition calculation panel on the lower left part of the window (Fig. 1b) enables the scientist to select the extrathoracic path, through which particles are inhaled (“None” means that the extrathoracic region is completely excluded from the computation), and respective empirical formulae for the calculation of fiber deposition in the proximal and distal lung regions (to be discussed below). Fiber properties may be specified on the upper right panel of the “Data input” window. Besides determination of the fiber size (diameter in m, aspect ratio) and density in g/cm3 , also a detailed specification of fiber orientation with respect to the flow direction in proximal and peripheral airways is possible. The lower right panel in the window is needed for specifying the lung morphometry used for the deposition calculations. For this,
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the scientist is able to select from different morphometric datasets published in the open literature. Lung scaling may be performed according to (1) the functional residual capacity [21], (2) body length [22], and (3) pre-defined scaling factors for airway diameters and lengths. Lung scaling with constant factors again plays a major role in diseased lungs. After completion of the input data, information may be written into a txt-file using file → save command in the menu bar. Calculation is started by either pressing the “Calculate” button or clicking on the “Calculate” command in the menu bar.
2.2. Calculation of fiber deposition When entering the respiratory tract, high fractions of fibers are already deposited in the extrathoracic region acting as a highly efficient filter system. Forces affecting fibrous particles in the head region are impaction, interception, and, to a lower extent, diffusion. Deposition efficiencies due to nasal and oral impaction are derived from the following equations [23,24]: Nasal: Dn,imp = Oral: Dm,imp Dm,imp
1.257
(105 + 1.257 )
0.609 (inhalation and exhalation)
=0 for 3000 = − 1.117 + 0.324 log for > 3000 (inhalation) =0 (exhalation),
(1)
(2)
2 Q with d denoting the aerodynamic diameter of the fiber (m) and Q the flow rate (cm 3 /s). where =dae ae The aerodynamic diameter dae is subject to a continuous change due to the rotation of the fiber in the shear flow. According to Dai and Yu [1], a time-averaged aerodynamic diameter, where the fiber is assumed to spend equal amounts of time in all orientations, can be written as follows:
dae =
1 3 (b
+ 2b⊥ )
2
d . 0 v
(3)
In Eq. (3), b and b⊥ denote the normalized mobilities of the fiber moving parallel and perpendicular to the flow direction, whereas dv , , and 0 are the equivalent volume diameter, particle density, and density of the fluid, respectively. For a fiber with a pre-defined aspect ratio , b , and b⊥ are given as 31/3 [((22 − 1)/( 2 − 1)) ln( + 2 − 1) − ]c b = , 4(2 − 1)
(4)
31/3 [((22 − 3)/( 2 − 1)) ln( + 2 − 1) + ]c⊥ b⊥ = 8(2 − 1)
(5)
with c and c⊥ being the slip correction factors for a fiber moving parallel and perpendicular to the flow direction [1].
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In the nasal pathway, deposition by interception yields Dn,int =
0.921[1 − (1 − 24lf )7 ] 0.921
for lf < 0.035 cm, for lf = 0.035 cm (inhalation and exhalation),
(6)
where lf is the fiber length in cm [25]. Concerning the oral pathway, fiber deposition due to interception is generally considered to be negligible due to the high difference in size between the mouth cavity and fiber length. Nasal and oral fiber deposition caused by Brownian diffusion is expressed by the following equations [26]: Nasal: Oral:
Dn,diff = 1 − exp(−9.0D 1/2 Q1/8 ) (inhalation), Dn,diff = 1 − exp(−10.55D 1/2 Q1/8 ) (exhalation). Dm,diff = 1 − exp(−7.24D 1/2 Q1/8 ) (inhalation), Dm,diff = 1 − exp(−5.98D 1/2 Q1/8 ) (exhalation)
(7) (8)
with Q being the flow rate in cm3 /s and D the diffusion coefficient (cm2 /s) which for randomly oriented fibers is given by kT 1 2 D= b + b⊥ (9) 3dv 3 3 In Eq. (9), k denotes the Boltzmann constant, T the air temperature in K, and the dynamic viscosity of air. Regarding fiber deposition in the thoracic region of the respiratory tract, FIBROS includes various empirical approaches for inertial impaction and interception as well as for gravitational settling, while Brownian diffusion, being of significantly lower importance, is computed according to a widely applied standard formula [18]. Inertial and interceptional deposition of fibers according to the calculation procedure outlined by Cai and Yu [6] will be, for the sake of brevity, not fully described in the work presented here, but, with few words, the algorithm provided by the authors is mainly based on the concept of the stop distance and interception distance of a anisometric particle in the cross-section of the daughter tube, finally serving for the calculation of deposition efficiencies in the whole bifurcation. Respective formulae are based on the equivalent diameters of fibrous particles introduced by Oseen [27] and are dependent upon the bifurcation angle, the diameter ratio between daughter and parent tube of the bifurcation, the Stokes number, and the fiber length. By developing a numerical model, Zhang et al. [9] could describe inertial and interceptional fiber deposition in the upper airways of the tracheobronchial tree by a relationship between the deposition efficiency and the Stokes number, which is subject to only slight variations for different flow types (expressed by the Reynolds number) and bifurcation angles. According to the authors, Stokes number (St) may be derived from the equation St =
2V f dev
18D
,
(10)
with dev = df 1/3 (df = fiber diameter), f being the fiber density, V the mean velocity of the flow in the parent airway, and D the parent airway diameter. The relationship between the deposition efficiency
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Table 1 Coefficients used for the calculation of deposition efficiencies in the tracheobronchial tree according to the algorithms outlined by Zhang et al. [9], Myojo and Takaya [5], and Asgharian and Anjilvel [17]
Zhang et al. [9]: Dimp,int = a exp[− exp(b − c St)] Coefficients a 0.8882 Myojo and Takaya [5]: an = x1 I 2 + x2 I + x3 Coefficients x1 a0 −103658 −100875 a1 a2 −32909 −4450.2 a3 −203.4 a4 Asgharian and Anjilvel [17]: f (, ) = −0.774 5n=0 an n Coefficients n=0 1 2 3 4 5
b 1.6529
c 4.7769
x2 1837.2 1792.7 562.95 67.601 2.5374
x3 1.6762 −0.9073 −1.0819 −0.0819 0.0026
0 < 31/32 −0.844 14.400 −22.409 16.586 −5.669 −0.726
an 31/32 203.750 −64.856
Dimp,int and St is best expressed by a Gompertz function of the following general form: Dimp,int = a exp[− exp(b − cSt)]
(11)
Values for the coefficients a, b, and c are summarized in Table 1, assuming a mean Reynolds number of 500 and an average bifurcation angle of 90◦ . A similar approach of inertial and interceptional fiber deposition as that noted above was also introduced by Myojo and Takaya [5]. In their work, Stokes number for randomly oriented fibers yields St =
f df2 V sin
16R[0.385/(ln(2lf /df ) + 0.5) + 1.230/(ln(2lf /df ) − 0.5)]
(12)
with denoting the angle between the initial and final direction of the air stream and R the airway radius. Specific consideration of interceptional deposition is given by introducing a interception parameter I of the following form: lf (13) 2R For a pre-defined interception parameter, Myojo and Takaya [5] expressed the dependence between Dimp,int and St by the polynomial equation I=
Dimp,int = exp{a0 + a1 (ln St) + a2 (ln St)2 + a3 (ln St)3 + a4 (ln St)4 },
(14)
where a0 –a4 may be described as second-order polynomial functions with I as the independent variable (Table 1).
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Gravitational settling of fibers in the more peripheral airways is computed according to the concept outlined by Asgharian and Anjilvel [17], where motion of anisometric particles in an arbitrary flow field was simulated numerically and sedimentation was expressed by the dimensionless parameter 1 as follows: 1 =
f gd 2f C
(15)
18V
In Eq. (15), C denotes the fluid correction factor and g the gravitational constant. In the deeper lung, 1 is assumed to take values much smaller than 1. Additionally, a linear relationship between deposition efficiency and 1 may be observed, which one can write as
Dsed = f (, ) 1
(16)
Asgharian and Anjilvel fitted the function f (, ) by a polynomial of degree 5, thereby obtaining the following expression: f (, ) = −0.774
5
an n .
(17)
n=0
The respective values of an are listed in Table 1. In the program, an alternative method for the computation of fiber sedimentation is offered based on the concept of the aerodynamic diameter presented in Eq. (3) [1], for which deposition efficiency is estimated according to the formula [20] 4gC f dae L cos
Dsed = 1 − exp (18) 36RV with L denoting the airway length and the gravity angle of the bifurcation. Eqs. (10)–(18) are only valid for the computation of particle deposition following inhalation. For both breath-hold and exhalation fiber depositions due to impaction have been reduced by constant factors [4], while sedimentation and diffusion have been calculated with the same formulae as used for inspiration. As exhibited in Fig. 1b, the program allows the definition of fiber orientation for both the proximal and distal airways of the lungs. Orientations, however, are expressed by respective formulae for the Stokes number in the case of inertial impaction/interception and for the aerodynamic diameter in the case of sedimentation. For instance, assumption of random orientation in the upper airways and parallel orientation in the lower airways would be calculated by using the Stokes numbers noted above and by modifying the aerodynamic diameter of Eq. (3), deleting the variable b⊥ . By selecting a specific morphometric dataset of the lungs, all the computations described in this sections are applied to mean values of generation-specific airway diameters, lengths, and branching angles provided by this dataset. Besides morphometric parameters, also the path lengths of inhaled particles are varied stochastically, leading to typical deposition patterns with one or more maxima. 2.3. Program output In the “Results” window, the user is able to view the output data generated by the program in a numerical as well as a graphical form (Fig. 2). The window is subdivided into two main blocks: within the left block, all information specified in the “Data input” window (Fig. 1b) are summarized and listed by the
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Fig. 2. Results windows of FIBROS. (a) Regional deposition results; (b) airway generation-specific deposition results.
four main categories, according to which the input window is organized (see above). The remaining part of the “Results” window contains a panel exhibiting the computation results numerically and graphically. The panel itself is subdivided into two forms, to which one can navigate by clicking on the respective tabs on the top (Fig. 2). The form reached by activating the left tab includes regional deposition data for the fiber properties, breathing conditions, and deposition models specified in the input window. In a bar chart, regional deposition (%) is assigned to the three main compartments of the respiratory tract: (1) the extrathoracic region, (2) the air conducting zone (bronchial region), and (3) the respiratory zone (acinar region). For more detailed information, the acinar region is additionally subdivided into the ductal and alveolar compartments, and all tubular components of the lungs (i.e., bronchial and ductal part) are also summarized in a specific category (“tubular”, Fig. 2a). Numerical results are listed on the bottom
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of the form. By clicking on the right tab of the panel, one can reach the form with airway generationspecific output data (Fig. 2b). In the respective deposition-by-generation graph, tubular and alveolar fiber deposition (%) in the single airway generations of the lungs is plotted, giving an estimate of how deep the particles have penetrated into the respiratory system. Numerical results are again listed on the bottom of the form. The windows with all the input and output data can be easily printed by using the file → print command in the menu bar.
3. Preliminary results and their interpretation Preliminary results of fiber deposition computations carried out with FIBROS are shown in Figs. 2–6. Following the setup exhibited in Fig. 1b, respective output data for particle deposition on a regional and local level are summarized in Fig. 2. As clearly recognizeable from panel (a) of Fig. 2, under the given breathing conditions fibers with a diameter of 3 m and an aspect ratio of 20 are mainly captured in the extrathoracic region (∼ 65%), therefore, only a small fraction of particles being allowed to enter the tracheobronchial tree of the lungs. Within the lungs, deposition takes mainly place in the air conducting zone (21.2%), while the respiratory zone is reached by the remaining 13.8% of particles. The fraction of fibers leaving the respiratory tract after exhalation is negligible for the particle shape defined in the setup, i.e., the total deposition efficiency amounts to 100%. Concerning the more local level of fiber deposition, which is expressed by the deposition-by-generation plot in Fig. 2b, tubular deposition is characterized by two maxima, one in generation 0 (trachea) and one in generation 11 (∼ terminal bronchiole) (note: deposition was normalized to the fraction of particles entering the trachea). Alveolar deposition, on the other hand, starts by definition in airway generation 12 and reaches its maximum in generation 15. The results exhibited in Fig. 2b clearly reflect the importance of impactional and interceptional forces in the upper bronchial airways, while in the peripheral part of the lungs, deposition maxima are mainly generated by gravitational settling of the particles. Comparison between fibrous and spherical particles (both with a diameter of 3 m), for which respective deposition computations were carried out using the computer code provided by Koblinger and Hofmann [18], show several significant differences (Fig. 3): (1) Extrathoracic deposition fractions of spherical particles are significantly lower than those of fibers (21 vs. 65%), causing higher deposition in the lungs themselves (∼ 46%) (2) Contrary to fibrous particles, 3 m spheres are characterized by a high fraction leaving the respiratory tract upon exhalation (33%). (3) Deposition of spherical particles in the upper airways of the tracheobronchial tree is remarkably lower than that of fibers, indicating the negligible effect of interception in this case and, not less important, the influence of random fiber orientation on deposition. (4) Deposition in the lung periphery is higher for spheres than for fibers, which can be simply explained by the limited fraction of fibers entering this region due to the high filter efficiency in the preceeding compartments of the lung. In Fig. 4, the various deposition models provided by FIBROS and described in detail in the last section are subject to a comparison, using the breathing conditions and particle properties exhibited in Fig. 1b. Regarding the three models used for the estimation of impaction and interception (Fig. 4a), differences among the output results are very high. While with the approaches of Myojo and Takaya [5] and Cai and Yu [6] deposition maxima in the upper bronchi are strongly emphasized, with the approach of Zhang et al. [9] this maximum is significantly lower and shifted toward the trachea. In the intermediated zone of the tracheobronchial tree, deposition nearly drops to zero in the case of the Cai and Yu model, leading also to an extraordinary emphasis of sedimentation in the lung periphery (note: gravitational settling was
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Fig. 3. Comparison between the deposition of fibers and spheres in the human respiratory tract; (a) regional deposition; (b) deposition by airway generation. Input data are those exhibited in Fig. 1b. Spherical particles have a diameter of 3 m and a density of 2.5 g/cm3 .
uniformly calculated according to the approach of Asgharian and Anjilvel [17]). These effects are clearly weakened when using the other two models. Differences between the two sedimentation models provided by the program are not so high as those between the impaction/interception models (Fig. 4b). In contrast to the model of Asgharian and Anjilvel [17], with the model of Dai and Yu [1] the deposition peak in the trachea disappears at the cost of an enhanced deposition fraction in the remaining parts of the lungs. The effect of flow rate on fiber deposition is illustrated in Fig. 5. Calculations were carried out with the setup exhibited in Fig. 1b, thereby decreasing inhalation time in a stepwise fashion from 4 s (flow rate: 250 cm3 /s) to 1 s (flow rate: 1000 cm3 /s). Similar to spherical particles, an increase of the flow rate in this way causes (1) a partly dramatic increase of impaction and interception in the upper airways and, to a comparable extent, (2) a continuous decrease of gravitational settling in the intermediate and peripheral lung regions. This is mainly due to the fact that all forces controlling particle deposition depend upon
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Fig. 4. Deposition-by-generation plots using the different deposition models for inertial impaction/interception and sedimentation provided by the program; (a) variation of the inertial impaction/interception models (sedimentation according to Asgharian and Anjilvel [17]); (b) variation of the sedimentation models (inertial impaction/interception according to Zhang et al. [9]). Breathing conditions and fiber properties are defined in Fig. 1b.
flow velocity, i.e., impaction and interception correlate positively with the velocity of the air stream, while sedimentation is marked by a negative correlation as expressed in Eq. (15). Detailed comparison between fiber deposition computed for a flow rate of 250 cm3 /s and that estimated for a flow rate of 1000 cm3 /s also indicates a shift of the deposition maxima. While the first maximum is shifted to higher airway generations with increasing flow rate, the second one shows an opposite behaviour. Fig. 6 illustrates the effect of increasing fiber aspect ratio on bronchial and alveolar deposition. While on panel a of Fig. 6 an increase of the aspect ratio has been expressed by a continuous enhancement of the fiber length (constant diameter: 3 m), on panel b, aspect ratio has been increased by a stepwise reduction of the fiber diameter (constant length: 30 m). Concerning the scenario with variable fiber length, main differences in deposition can be recognized for the first 5 airway generations, where deposition of 90 m
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Fig. 5. Fiber deposition (diameter: 3 m, aspect ratio: 20, density: 2.5 g/cm3 ) under different breathing conditions. Deposition formulae selected in Fig. 1b have been used for the calculations.
long fibers is partly double as high as that of 15 m long particles. Deposition due to sedimentation is only insignificantly increased with fiber length (by about 1%). The deposition enhancement in the upper bronchi may be regarded as a result of increased interception, which correlates positively with fiber length, and of the random fiber orientation in this compartment. Continuous increase of the fiber diameter causes a similar effect as that noted above, i.e., particles with a diameter of 6 m deposit more effectively in the upper bronchi and less effectively in the peripheral airways, while fibers with 1 m diameter show a contrary behaviour. Instead of interception, inertial impaction may be evaluated as the dominant deposition force in this case.
4. Summary and conclusions The main objective of the work presented here was the detailed description of a computer program termed FIBROS which enables e.g. the medical scientist to estimate fiber deposition in the human respiratory tract after specification of breathing conditions, deposition models, fiber properties, and the morphometric lung model. Besides regional (i.e. extrathoracic, bronchial, alveolar) deposition fractions, FIBROS additionally allows the creation of deposition-by-airway generation plots, describing fiber deposition on a more local level. According to preliminary results derived from the program, under normal breathing conditions with an inhalative flow rate of 500 cm3 /s, most of the inhaled fibers are already deposited in the extrathoracic region, while in the lungs usually two deposition maxima can be recognized: one in the upper tracheobronchial tree (generation 0–5) and one in the more peripheral part of the lungs (generation 10–15). The first maximum is caused by impactional and interceptional forces affecting fibrous particles mainly in those parts of the tracheobronchial tree, where flow velocities are high (> 50 cm/s), whereas the second maximum may be regarded as the result of gravitational settling, which becomes most prominent in a slow flow regime (< 1 cm/s). Deviation from the standard breathing conditions influences fiber deposition more or less significantly, whereby in this study highest modifications of the deposition pattern
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Fig. 6. Effect of the aspect ratio on fiber deposition using the setup exhibited in Fig. 1b; (a) fibers with constant diameter (3 m) and variable length; (b) Fibers with constant length (30 m) and variable diameter. Deposition formulae selected in Fig. 1b have been used for the calculations (a.r. = aspect ratio).
could be observed for a flow rate 1000 cm3 /s, corresponding with an intermediate work load. For these specific type of breathing, the filter efficieny of the upper bronchi becomes remarkable enhanced, and, as a consequence of that, alveolar fiber deposition is clearly decreased. A similar effect on deposition as by increasing the flow rate is noticeable for an modified aspect ratio (i.e., length per diameter) of the fibers. The higher either fiber length or fiber diameter get, the more effectively respective particles are already deposited in the trachea and the following airway generations due to the continuously enhanced influence of either interceptional or impactional forces. From the results presented in this study, it may be concluded that fiber deposition in the human respiratory tract is characterized by several specificities with respect to spherical particles. The computer program described here considers these specific properties to a certain degree, therefore representing an alternative to available transport and deposition codes being solely based on the aerodynamic
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diameter concept. FIBROS might find enhanced usage not only in medical science for the modelling of particle-lung interactions, but also for the simulation of the effect of dust exposures in different working environments. References [1] Y.T. Dai, C.P. Yu, Alveolar deposition of fibers in rodents and humans, J. Aerosol Med. 11 (1998) 247–258. [2] I. Balàshàzy, T.B. Martonen, W. Hofmann, Fiber deposition in airway bifurcations, J. Aerosol Med. 3 (1990) 243–260. [3] I. Balásházy, W. Hofmann, Particle deposition in airway bifurcations: I. inspiratory flow, J. Aerosol Sci. 24 (1993) 745–772. [4] I. Balásházy, W. Hofmann, Particle deposition in airway bifurcations: II. expiratory flow, J. Aerosol Sci. 24 (1993) 773–786. [5] T. Myojo, M. Takaya, Estimation of fibrous aerosol deposition in upper bronchi based on experimental data with model bifurcation, Ind. Health 39 (2001) 141–149. [6] F.S. Cai, C.P. Yu, Inertial and interceptional deposition of spherical particles and fibers in a bifurcating airway, J. Aerosol Sci. 19 (1988) 679–688. [7] Y.K. Chen, C.P. Yu, Sedimentation of fibers from laminar flows in a horizontal circular duct, Aerosol Sci. Technol. 14 (1991) 343–347. [8] L. Gradon, D. Orlicki, Deposition of inhaled aerosol particles in a generation of the tracheobronchial tree, J. Aerosol Sci. 21 (1990) 3–19. [9] L. Zhang, B. Asgharian, S. Anjilvel, Inertial and interceptional deposition of fibers in a bifurcating airway, J. Aerosol Med. 9 (1996) 419–430. [10] C.P. Yu, B. Asgharian, K.E. Pinkerton, Intrapulmonary deposition and retention modeling of chrysotile asbestos fibers in rats, J. Aerosol Sci. 22 (1991) 757–763. [11] J.Y. Ding, C.P. Yu, L. Zhang, Y.K. Chen, Deposition modeling of fibrous particles in rats: Comparison with available experimental data, Aerosol Sci. Technol. 26 (1997) 403–414. [12] G.B. Jeffrey, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Sci. Lond. A 102 (1922) 161–179. [13] L. Gradon, A. Podgorski, Flexible fibrous particle behaviour in the carrier gas flow around cylindrical obstacle, Chem. Eng. Sci. 45 (1990) 3435–3441. [14] A. Podgorski, L. Gradon, Grzybowski, Theoretical study on deposition of flexible and stiff fibrous aerosol particles in a cylindrical collector, Chem. Eng. Sci. 58 (1995) 109–121. [15] M. Shams, G. Ahmadi, H. Rahimzadeh, Transport and deposition of flexible fibers in turbulent duct flows, J. Aerosol Sci. 32 (2001) 525–547. [16] I. Gallily, A.D. Eisner, On the orderly nature of the motion of nonspherical aerosol particles, J. Colloid Int. Sci. 68 (1979) 320–337. [17] B. Asgharian, S. Anjilvel, Movement and deposition of fibers in an airway with steady viscous flow, Aerosol Sci. Technol. 22 (1995) 261–270. [18] L. Koblinger, W. Hofmann, Monte Carlo modeling of aerosol deposition in human lungs Part I: simulation of particle transport in a stochastic lung structure, J. Aerosol Sci. 21 (1990) 661–674. [20] H. Yeh, G.M. Schum, Models of human lung airways and their application to inhaled particle deposition, Bull Math. Biol. 42 (1980) 461–480. [21] International Commission on Radiological Protection (ICRP), Human Respiratory Tract Model for Radiological Protection, Publication 66. Ann. ICRP, Pergamon Press, Oxford, 1994, p. 456. [22] R.F. Phalen, M.J. Oldman, C.B. Beaucage, T.T. Crocker, J.D. Mortensen, Postnatal enlargement of human tracheobronchial airways and implications for particle deposition, Anat. Rec. 212 (1985) 368–380. [23] L. Zhang, C.P. Yu, Empirical equations for nasal deposition of inhaled particles in small laboratory animals and humans, Aerosol Sci. Technol. 19 (1993) 51–56. [24] C.P. Yu, C.K. Diu, T.T. Soong, Statistical analysis of aerosol deposition in nose and mouth, Am. Ind. Hyg. Assoc. J. 42 (1981) 726–733. [25] B. Asgharian, C.P. Yu, Deposition of inhaled fibrous particles in the human lung, J. Aerosol Med. 1 (1988) 37–50.
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[26] Y.S. Cheng, Y.F. Su, H.C. Yeh, Deposition of thoron progeny in human head airways, Aerosol Sci. Technol. 18 (1993) 359–375. [27] C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik, Leipzig, 1927 p. 18. Robert Sturm attended the University of Salzburg, Austria, receiving M.Sc. degrees in earth sciences and biology and his Ph.D. degree in Biophysics. He has held different positions as research assistant at the University of Salzburg and presently is employed as a scientific co-worker within a research project of the European Communities (BIODOS). Werner Hofmann attended the University of Vienna, Austria, where he received his Ph.D. degree in Nuclear Physics. He has held different positions at the University of Salzburg, presently heading the Institute of Physics and Biophysics, and visiting professor positions at the University of Lincoln, NE, Duke University, NC, both in the USA, and the Nova Gorica Polytechnic, Slovenia. For about 25 years, he has been involved in theoretical research on the dosimetry of inhaled particles in the human respiratory tract. The work reported here was part of the Institutes commitment to research projects supported by the European Communities.