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Comparison of Computer Simulations of Total Lung
Deposition to Human Subject Data in Healthy Test
Subjects
R.A. Segal a b , T.B. Martonen b & C.S. Kim c
a Mathematics Department , North Carolina State University , Raleigh , North
Carolina , USA
b U.S. Environmental Protection Agency, ETD, NHEERL , Research Triangle Park , North
Carolina , USA
c U.S. Environmental Protection Agency, HSD, NHEERL , Chapel Hill , North Carolina ,
USA
Published online: 27 Dec 2011.
To cite this article: R.A. Segal , T.B. Martonen & C.S. Kim (2000) Comparison of Computer Simulations of Total Lung
Deposition to Human Subject Data in Healthy Test Subjects, Journal of the Air & Waste Management Association, 50:7,
1262-1268, DOI: 10.1080/10473289.2000.10464155
To link to this article: http://dx.doi.org/10.1080/10473289.2000.10464155
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Segal, Martonen, and Kim
TECHNICAL PAPER
ISSN 1047-3289 J. Air & Waste Manage. Assoc. 50:1262-1268
Copyright 2000 Air & Waste Management Association
Comparison of Computer Simulations of Total Lung Deposition
to Human Subject Data in Healthy Test Subjects
R.A. Segal
Mathematics Department, North Carolina State University, Raleigh, North Carolina and U.S. Environmental
Protection Agency, ETD, NHEERL, Research Triangle Park, North Carolina
T.B. Martonen
U.S. Environmental Protection Agency, ETD, NHEERL, Research Triangle Park, North Carolina
C.S. Kim
U.S. Environmental Protection Agency, HSD, NHEERL, Chapel Hill, North Carolina
ABSTRACT
assessment efforts to estimate the inhalation hazards of
airborne pollutants.
A mathematical model was used to predict the deposi-
tion fractions (DF) of PM within human lungs. Simula-
tions using this computer model were previously
validated with human subject data and were used as a
control case. Human intersubject variation was ac-
counted for by scaling the base lung morphology dimen-
sions based on measured functional residual capacity
(FRC) values. Simulations were performed for both con-
trolled breathing (tidal volumes [VT] of 500 and 1000
mL, respiratory times [T] from 2 to 8 sec) and spontane-
ous breathing conditions. Particle sizes ranged from 1 to
5 µm. The deposition predicted from the computer model
compared favorably with the experimental data. For ex-
ample, when VT = 1000 mL and T = 2 sec, the error was
1.5%. The errors were slightly higher for smaller tidal
volumes. Because the computer model is deterministic
(i.e., derived from first principles of physics), the model
can be used to predict deposition fractions for a range of
situations (i.e., for different ventilatory parameters and
particle sizes) for which data are not available. Now that
the model has been validated, it may be applied to risk
INTRODUCTION
To estimate the threat to human health presented by in-
haled PM, it is valuable to know the spatial distribution of
the inhaled particles. Therefore, an ongoing goal of our work
is to effectively model deposition, beginning with healthy
subjects, so that we can predict deposition for a large range
of particle types and ventilatory parameters. In subsequent
efforts, we shall address the effects of airway diseases (e.g.,
chronic obstructive pulmonary disease [COPD]).
Determining where airborne PM is deposited in the
lung is a complicated problem. The site of deposition is
affected by many variables. These variables include par-
ticle characteristics, ventilatory parameters, and lung mor-
phology. In this work, we improved upon our existing,
previously validated model1-3 by using a more physiologi-
cally realistic lung morphology. We then used the model
to calculate deposition patterns for particle sizes other than
those used in the reported human subject experiments.
METHODS
The primary mechanisms for particle deposition in the
lung are sedimentation, diffusion, and inertial impaction.
The mechanism by which an individual particle is depos-
ited depends on the size and velocity of the particle. In
turn, a particle’s velocity depends on ventilatory param-
eters and lung morphology.
Our computer program4 calculates particle deposition
in each generation and organizes the data by deposition
mechanism. The parameters that must be specified for
the code are particle characteristics (i.e., hydroscopic
IMPLICATIONS
This work describes a mathematical computer model that
can be used to predict particle deposition fractions in
human lungs. Used in conjunction with measurement data
on PM contained in an ambient air sample, this model
can be employed to estimate human exposures for do-
simetry analyses by an inhalation toxicologist. The com-
puter model therefore provides an important link between
air pollution data and the potential threat to the health of
a population.
1262 Journal of the Air & Waste Management Association
Volume 50 July 2000

Segal, Martonen, and Kim
Table 1.Breathing parameters for test subjects in spontaneous breathing experiments.
nature, shape, density [ρ], and geometric diameter [Dg]),
ventilatory parameters (i.e., tidal volume, time of inhala-
tion, time of pause, and time of expiration), morphology
(i.e., a file consisting of a morphological definition by
lengths and volumes of generations), and simulation pa-
rameters (i.e., mouth or nose breathing). Because we were
simulating human subject experiments, the parameters
were defined based on the experiments conducted.
Subject
VT (mL)
Q (mL/sec)
1
488
195
545
656
306
491
293
478
620
341
386
383
150
270
325
124
318
169
182
348
175
275
2
3
4
5
6
Human Subject Experiments
7
Our experimental data came from two sources. The ex-
periments were headed by Bennett5 and Kim.6-7 The de-
tails can be found in the literature, but a short summary
is given below.
8
9
10
11
Bennett used 2-µm monodisperse carnauba wax par-
ticles with salt nuclei. These particles were generated us-
ing a condensation aerosol generator. Each subject was
instructed to mouth breath at a normal sedentary rate,
and this breathing pattern was recorded for use by that
subject in the experiments. The breathing parameters for
the spontaneous breathing simulations ranged from tidal
volume (VT) = 195 to 656 mL and flow volume (Q) = 124
to 383 mL/sec (see Table 1).
Table 2. List of controlled breathing experiments performed.
Dg (µm)
VT (mL)
Q (mL/sec)
1, 3, 5
500
150
250
500
Kim’s experiments also used monodisperse particles.
The particles were di-2-ethylhexyl sebacate oil aerosols
generated by an evaporation-condensation aerosol gen-
erator in 1-, 3- and 5-µm sizes. The test subjects were in-
structed to mouth breath in a controlled, predefined
manner. The breathing conditions were defined by flow
volume and flow rate. For our simulations, the breathing
parameters ranged from VT = 500 and Q = 150 mL/sec to
VT = 1000 and Q = 500 mL/sec (see Table 2).
1, 3, 5
2
1,000
500
1,000
spontaneous breathing
overcomes this by having the lung separated into two dis-
tinct lobes.
We also took into account each individual subject’s
lung volume. The functional residual capacity (FRC) mea-
surement defines the amount of air left in the lung after
the subject exhales. We added this value to half of the
tidal volume to get the average lung size during a breath-
ing cycle. Our base model uses the length and diameter
measurements from the Weibel lung,14 which Martonen15
determined to be preferable to other lung models for con-
ducting computer simulations. However, these dimensions
define a lung with a volume of 4800 mL. Since the sub-
jects we were simulating had FRC values ranging from
1850 to 6820 mL, we wanted to take into account indi-
vidual variation. To do this, we modified the airway di-
ameters (and hence the airway volumes) by a uniform
scaling factor, based on the research of Hughes, Hoppin,
and Mead,16 who determined that airway diameters scale
proportionally to the cube root of the lung volume.
Other groups, such as the International Commission
on Radiological Protection (ICRP) and the National Coun-
cil on Radiation Protection (NCRP), have developed lung
deposition models. It is beyond the scope of this paper to
compare our model with the other inhaled particle depo-
sition models, but references are included for the reader’s
Computer Model
The computer code contains additional options that do
not depend on the nature of the human subject experi-
ments. We have control over the air velocity profile used
in the simulations, and we can use either a fully devel-
oped parabolic profile or a uniform (or plug) profile. The
actual profile lies somewhere between these two curves.8
Determining the actual velocity profile requires signifi-
cant computation time,9 so it is necessary to use an ap-
proximation. If we calculate the deposition fractions twice,
once with each profile, we get an envelope that contains
the actual value.
We made two main modifications to our existing
morphology model for this study. We used a more physi-
ologically realistic lung model that was also customized
to each individual test subject. The more physiologically
realistic lung model, developed by Martonen et al.,10,11 is
an improvement over the previous model.12,13 The old
model allowed the two lobes of the lung to grow in such
a way that they overlapped each other. The new model
Volume 50 July 2000
Journal of the Air & Waste Management Association 1263

Segal, Martonen, and Kim
edification. Details regarding the ICRP model can be found
in the literature.17,18 Further information pertaining to the
NCRP model is also available.19,20
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
a
data
RESULTS
plug
Total aerosol deposition fractions for the parameters de-
scribed above have been calculated and recorded in Fig-
ures 1–6. The graphs compare total lung deposition
fraction (DF) values calculated by the computer code with
the experimental DF data. We plotted simulation results
for runs made with parabolic and plug (i.e., uniform) ve-
locity profiles. Each figure contains the experimental data
points as well as the computer-generated points for each
individual subject. In most cases, we had additional FRC
measurements for test subjects who did not participate in
these deposition experiments; this allowed us to run ex-
tra computer simulations, so that we had more theoreti-
cal data points than experimental data points. As seen in
the graphs, the theoretical predictions of the code com-
pare very well to the outcomes of the laboratory experi-
ments. For comparison, we also plotted the DF value for
the unmodified morphology. The solid line indicates the
DF for a plug flow simulation, and the dashed line indi-
cates the DF for a parabolic velocity profile simulation.
Figure 7 shows computer-calculated deposition of
submicron particles. Here, VT = 500 mL and Q = 250 mL/
sec. The lung morphologies were based on the human
subjects from the controlled breathing experiments.
parabolic
2000
3000
4000
FRC (ml)
5000
5000
5000
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
b
data
plug
parabolic
2000
3000
4000
FRC (ml)
DISCUSSION
Several conclusions can be drawn from the results pre-
sented above. When the controlled breathing experi-
ments are examined as a group, we see that the deposition
increased as the particle size increased from 1 to 3 to
5 µm. This trend was the same for each of the five breath-
ing conditions. These figures also demonstrate the value
of customizing the lung morphology for each subject.
Qualitatively, the DF values varied as the FRC changed.
This is what we would expect, since deposition fractions
depend on airway diameters, which depend on lung size.
Quantitatively, we saw a decrease in percent error when
we compared predicted values to experimental values.
For example, when VT = 1000 mL and Q = 500 mL, the
average deposition fraction for 3-µm particles was 0.61
according to the experimental data. Our average pre-
dicted value was 0.54 with morphology modifications
and 0.53 without the modifications. The percent error
dropped from 13.1 to 11.5% when the lung morphol-
ogy was individualized. Similar results were seen in most
of the simulations.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
c
data
plug
parabolic
2000
3000
4000
FRC (ml)
Figure 1. Particle deposition fractions for flow conditions with VT =
500 mL and Q = 150 mL/sec. Figures 1a, 1b, and 1c contain data for
1-, 3- and 5-µm particles, respectively. The solid and dashed lines
indicate the DF in the unmodified morphology, using the plug flow and
parabolic velocity profiles, respectively.
Because we were not able to scale the lung to fit the
subjects in the spontaneous breathing experiments (no
FRC value was available from the literature), we found
1264 Journal of the Air & Waste Management Association
Volume 50 July 2000

Segal, Martonen, and Kim
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
a
a
b
c
data
data
plug
plug
parabolic
parabolic
2000
3000
4000
FRC (mL)
5000
2000
3000
4000
FRC (mL)
5000
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
data
data
plug
b
plug
parabolic
parabolic
2000
3000
4000
FRC (mL)
5000
2000
3000
4000
FRC (mL)
5000
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
c
data
data
plug
plug
parabolic
parabolic
2000
3000
4000
FRC (mL)
5000
2000
3000
4000
FRC (mL)
5000
Figure 3. Particle deposition fractions for flow conditions with VT =
500 mL and Q = 500 mL/sec. Figures 3a, 3b, and 3c contain data for
1-, 3- and 5-µm particles, respectively. The solid and dashed lines
indicate the DF in the unmodified morphology, using the plug flow and
parabolic velocity profiles, respectively.
Figure 2. Particle deposition fractions for flow conditions with VT =
500 mL and Q = 250 mL/sec. Figures 2a, 2b, and 2c contain data for
1-, 3- and 5-µm particles, respectively. The solid and dashed lines
indicate the DF in the unmodified morphology, using the plug flow and
parabolic velocity profiles, respectively.
Volume 50 July 2000
Journal of the Air & Waste Management Association 1265

Segal, Martonen, and Kim
1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
a
data
0.9
a
b
c
data
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
plug
plug
parabolic
parabolic
2000
3000
4000
4000
4000
5000
5000
5000
2000
3000
4000
FRC (mL)
5000
FRC (mL)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
b
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
data
plug
data
plug
parabolic
parabolic
2000
3000
4000
FRC (mL)
5000
2000
3000
FRC (mL)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
c
data
plug
data
plug
parabolic
parabolic
2000
3000
4000
FRC (mL)
5000
2000
3000
FRC (mL)
Figure 5. Particle deposition fractions for flow conditions with VT =
1000 mL and Q = 500 mL/sec. Figures 5a, 5b, and 5c contain data for
1-, 3- and 5-µm particles, respectively. The solid and dashed lines
indicate the DF in the unmodified morphology, using the plug flow and
parabolic velocity profiles, respectively.
Figure 4. Particle deposition fractions for flow conditions with VT =
1000 mL and Q = 250 mL/sec. Figures 4a, 4b, and 4c contain data for
1-, 3- and 5-µm particles, respectively. The solid and dashed lines
indicate the DF in the unmodified morphology, using the plug flow and
parabolic velocity profiles, respectively.
1266 Journal of the Air & Waste Management Association
Volume 50 July 2000

Segal, Martonen, and Kim
the deposition code to be less effective for this data set.
We still obtained reasonable agreement, but for the sub-
jects with higher tidal volumes the match is not as good.
Scaling for each individual’s lungs should reduce the er-
ror in our predictive values.
1.0000
0.9000
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
data
plug
parabolic
The DF simulations for the submicron particles pro-
vide some interesting information. The DF for the 0.01-
µm particles was very high, due to the high rate of
deposition by diffusion. It is interesting to note that while
the parabolic profile and the plug profile provide differ-
ent DFs for the other submicron particles, the difference
between the two values for the 0.01-µm particle was small,
because diffusion was very efficient for the small particles.
In the other cases, the diffusion was not as efficient, and
the difference in the velocity profile resulted in different
deposition efficiencies. Assuming uniform particle dis-
tribution in the inhaled air, particles transported in flow
with a parabolic profile are less likely to be close to the
airway wall than particles in a uniform flow field. There-
fore, particle deposition due to diffusion will be lower
100
200
300
400
500
600
700
Tidal Volume (mL)
Figure 6. Particle deposition fractions for 2-µm particles. Flow
conditions are based on the spontaneous breathing patterns used by
patients as described in Table 1.
1.0000
1.0000
a
c
parabolic
plug
0.9000
0.9000
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
parabolic
plug
2000
3000
4000
FRC (mL)
5000
2000
3000
4000
FRC (mL)
5000
1.0000
0.9000
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
1.0000
0.9000
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
b
d
parabolic
plug
parabolic
plug
2000
3000
4000
FRC (mL)
5000
2000
3000
4000
FRC (mL)
5000
Figure 7. Particle deposition fractions for flow conditions of VT = 500 mL and Q = 250 mL/sec. Figures 7a, 7b, 7c, and 7d contain data for 0.01-,
0.05-, 0.1- and 0.5-µm particles, respectively.
Volume 50 July 2000
Journal of the Air & Waste Management Association 1267

Segal, Martonen, and Kim
when using a parabolic flow profile. We would like to
expand our analysis of submicron particle deposition to
determine whether adjusting the model lung to each in-
dividual test subject improves our prediction capabilities.
In summary, good agreement was found between
theory and experiment. These results support the use of
our computer model for studying factors affecting PM
deposition. The findings indicate that scaling the lung
based on an FRC measurement provides a basis for a more
accurate prediction of deposition.
Because the computer model is deterministic (i.e.,
derived from first principles of physics), the model can
be used to predict deposition fractions for a range of con-
ditions (i.e., different ventilatory parameters and particle
sizes) for which data is not readily available. The model
may, therefore, be extended in future efforts to simulate
effects of airway disease (e.g., COPD) in risk assessment
efforts to estimate the inhalation hazards of airborne pol-
lutants for a sensitive subpopulation.
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1. Martonen, T.B.; Katz, I.M. Pharm. Res. 1993, 10(6), 871-878.
2. Martonen, T.B.; Katz, I.M. J. Aerosol Med. 1993, 6(4), 251-274.
3. Martonen, T.B.; Katz, I.M. S.T.P. Pharm. Sci. 1994, 4(1), 11-18.
4. Martonen, T.B. Bull. Math. Bio. 1982, 44, 425-442.
5. Bennett, W.D.; Zeman, K.L.; Kim, C.S.; Mascarella, J. Inhal. Tox. 1997,
9, 1-14.
6. Kim, C.S.; Hu, S.C. J. Appl. Phys. 1998, 84, 1834-1844.
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159, A615.
8. Schroter, R.C.; Sudlow, M.F.; Respir. Phys. 1969, 7, 341-355.
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199-213.
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14. Weibel, E.R. Morphometry of the Human Lung; Academic Press Inc.:
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16. Hughes, J.M.B.; Hoppin, F.G.; Mead, J. J. Appl. Phys. 1972, 32(1), 25-35.
17. Blair, W.J. Radiat. Prot. Dosim. 1991, 38(1/3), 147-152.
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Swift, D.L.; Yeh, H.C. Radiat. Prot. Dosim. 1991, 38(1/3), 179-184.
20. Cuddihy, R.G.; Fisher, G.L.; Moss, O.R.; Phalen, R.F.; Schlessinger,
R.B.; Swift, D.L.; Yeh, H.C. Ann. Occup. Hyg. 1988, 32, 833-841.
ACKNOWLEDGMENTS
R. A. Segal’s work is funded by the North Carolina State
University (NCSU)/U.S. Environmental Protection Agency
Cooperative Training Program in Environmental Sciences
Research, Training Agreement CT826512010, NCSU.
DISCLAIMER
About the Authors
Rebecca Segal is a graduate student in the Mathematics
Department at North Carolina State University, Box 8205,
Raleigh, NC 27695. Ted Martonen is a senior research sci-
entist at the U.S. Environmental Protection Agency, ETD,
NHEERL, Mail Drop 74, Research Triangle Park, NC 27711.
Chong Kim is a senior research scientist at the U.S. Envi-
ronmental Protection Agency, HSD, NHEERL, Mail Drop
58B, Chapel Hill, NC 27599.
The information in this document has been funded wholly
(or in part) by the U.S. Environmental Protection Agency.
It has been subjected to review by the National Health
and Environmental Effects Research Laboratory and ap-
proved for publication. Approval does not signify that the
contents reflect the views of the Agency, nor does men-
tion of trade names or commercial products constitute
endorsement or recommendation for use.
1268 Journal of the Air & Waste Management Association
Volume 50 July 2000