Owens Corning, Science and Technology Center, Granville, Ohio, USA
Inhalation Toxicology, in press (2000)
Copyright © 2000 Taylor & Francis
A method was tested for calculating the dissolution rate constant
in the lung for a wide variety of synthetic vitreous silicate
fibers from the oxide composition in weight percent. It is based
upon expressing the logarithm of the dissolution rate as a linear
function of the composition and using a different set of coefficients
for different types of fibers. The method was applied to 29 fiber
compositions including rock and slag fibers as well as refractory
ceramic and special purpose, thin E glass fibers and borosilicate
glass fibers for which in-vivo measurements have been carried
out. These fibers had dissolution rates that ranged over a factor
of about 400, and the calculated dissolution rates agreed with
the in-vivo values typically within a factor of four. The method
presented here is similar to one developed previously for borosilicate
glass fibers that was accurate to a factor of 1.25. The present
coefficients work over a much broader range of composition than
the borosilicate ones but with less accuracy. The dissolution
rate constant of a fiber may be used to estimate whether disease
would occur in animal inhalation or intraperitoneal injection
studies of that fiber.
The main property that determines the results of animal studies
of different types of fibers, tested at the same dose of the same
length and diameter, is the dissolution rate constant of the long
fibers in the extracellular environment of the lung
(Eastes and Hadley, 1996).
This paper describes a reasonably accurate and
efficient method for computing this dissolution rate constant
directly from the oxide composition for a wide range of rock and
slag wool compositions. The compositions for which this method
works cover the range of both high alumina new rock wools and
conventional low alumina rock wool compositions, many slag wools,
as well as a variety of other synthetic vitreous silicate fiber
The dissolution rate constant has been shown to predict the decrease
in diameter of long fibers after intratracheal instillation in
(Eastes et al., 1995), and to predict the biopersistence
of long fibers after short-term inhalation in rats
(Bernstein et al., 1996;
Eastes and Hadley, 1995). Additionally, the dissolution
rate constant can be used to predict the incidence of fibrosis
and lung tumors following inhalation and tumors following intraperitoneal
injection in rats
(Eastes and Hadley, 1996). It may also be measured
accurately in many cases in vitro
(Potter and Mattson, 1991;
Mattson, 1994) and a standard protocol is available for performing these
(Bauer et al., 1997).
The dissolution rate constant kdis is an expression of
the rate at which a fiber, particularly one longer than 10 to
20 µm or too long to be effectively enveloped by alveolar
macrophages, dissolves in the mammalian lung and is eliminated
thereby. The complete disappearance of the long fiber from the
lung may take place by total dissolution and systemic removal
of the dissolution products, by breakage of the partially leached
fiber and macrophage mediated clearance of the fragments, or by
a combination of these mechanisms. The exact extent and contribution
of each of these mechanisms is not so important as the fact that
they both occur because of dissolution, which is captured in the
The next section describes the theory involved in obtaining an
expression for the dissolution rate constant of a fiber from its
composition. The following section applies the theory to a set
of fiber compositions for which reliable dissolution rates are
available from in-vivo inhalation biopersistence studies. The
final section discusses the implications of these results.
The dissolution rate of a fiber is approximated here as proportional
to its surface area. The dissolution is thus considered to be
a zero order reaction
(Scholze, 1988), in the sense that it is
independent of reactant concentrations. The dissolution rate is
proportional to the fiber surface area, which changes with time
as it dissolves, and to the dissolution rate constant kdis.
The parameter kdis in this reaction is a property of the
material making up the fiber, and does not depend on its size
or shape. Thus kdis depends on the fiber composition, conventionally
expressed as the weight percent of oxides. One may expect, therefore,
to be able to calculate kdis to a reasonable approximation
directly from the oxide composition. The kdis depends also,
but to a much lesser extent for most fibers, on the glass structure
that is affected by the fiber cooling rate and thus by the method
of fiberizing and the fiber diameter
(Potter and Mattson, 1991;
Scholze, 1988). These effects are much smaller than the influence
of composition on kdis. Often they are so small as to be
and they will not be considered
in what follows.
The theory of calculating fiber dissolution from composition has
been described in detail previously
(Eastes et al., 2000a). Briefly,
it consists of the observation that, by virtue of the Arrhenius
rate equation, the logarithm of kdis is approximately proportional
to a weighted sum of the oxide weight percents:
In a previous publication
(Eastes et al., 2000a), this procedure
was carried out for a large set of borosilicate glass wool fibers
with in-vitro measured kdis values. It was found that a
single set of coefficients Pi in Eq. (1) fit the measured
kdis reasonably well over a fairly wide range of compositions.
However, it would be expected that neither the previous coefficients
Pi nor any single set of coefficients would fit adequately
all of the rock and slag wool fiber compositions for at least
two reasons: First, the rock and slag compositions contain no
boron and have mostly lower silica (SiO2) concentrations
than the borosilicate glass wool fibers. These facts suggest that
the nature of the glass forming network would be different and
that at least the coefficient for silica in Eq (1) would be different.
Second, the alumina (Al2O3) concentration
in the rock and slag wools ranges from nearly 0 to 50% by weight,
with the larger concentrations represented by the newer, high-alumina
rock wool fibers, whereas the range was only 0 to 7.5% in the
borosilicate fibers. It would not be unexpected for the structure
of aluminum in the glass network to be qualitatively different
at the lower alumina concentrations than at the higher ones, leading
to different coefficients Pi for alumina at lower concentrations
than at higher weight percent. On the other hand, it might be
expected that the other components of the rock and slag fibers,
the network modifiers like CaO, MgO, and
Na2O, would act similarly in the rock and slag
fibers as they do in the borosilicates, because they tend to disrupt
the silicate network that is present in all of these silicate
If these suggestions about the effect of different components
of the rock and slag fibers on kdis are correct, then all
of the coefficients Pi in Eq. (1) except those for silica
and alumina can be taken to be the same as for the borosilicate
glass fibers. Then Eq (1) may be partitioned
If these considerations are shown to be generally correct by a
demonstration that the partial dissolution rate S is approximately
linear in the alumina/silica ratio, then it is feasible to take
the method one step further. One or more other oxides could be
split out of the sum in Eq. (2) of those oxides for which coefficients
Pi are available and fit to the measured dissolution rate.
One good candidate for such an oxide is FeO. Only a
small amount of iron oxide is present in the borosilicate glass
fibers considered previously, and much of that is in the Fe2O3
oxidation state, since these glasses are melted
under oxidizing conditions. Many rock wool compositions, on the
other hand, contain ten times as much iron oxide and much of that
is in the FeO state due to the reducing conditions
in these furnaces. Thus it is reasonable to fit FeO
for these compositions to an equation of the form
A determination of the coefficients PSiO2,
PAl3O3, and PFeO
involves fitting the measured kdis and composition data
to Eq (4). An important detail in these fits is to normalize the
composition of each fiber to 100% in all of the oxides included
in the fit
(Eastes et al., 2000a).
|7753, 7484, 7779, MMVF 10, MMVF 11||Intratracheal Instillation||Eastes et al., 1995|
|RCF 1a, Rock MMVF 21, E MMVF 32, JM475 MMVF 33, and HT MMVF 34||Short-term Inhalation||Hesterberg et al., 1998|
|SG MMVF 11, SG A, SG B, SG C, SG F, SG G, SG H, SG J X607, and SG L||Short-term Inhalation||Bernstein et al., 1996|
|JM 901 MMVF 10, CT B MMVF 11, Rock Wool MMVF 21, and Slag Wool MMVF 22||Short-term Inhalation||Musselman et al., 1994|
A number of in-vivo measurements of rock and slag wool fiber
dissolution rate constants kdis have been made on fibers
with known compositions that allow one to test the theory just
described, and these are summarized in Table 1. Two separate biopersistence
studies have been done on a conventional rock wool composition
known as MMVF 21
(Musselman et al., 1994;
Hesterberg et al., 1998),
and the in-vivo kdis has been obtained from each study
(Eastes et al., 2000b).
These in-vivo kdis values agree
well with each other and with the in-vitro measured values. These
in-vivo kdis values also agree well with that for a similar
composition, SG L (Bernstein et al., 1996). A slag wool denoted
MMVF 22 was also tested for biopersistence
(Musselman et al., 1994).
A biopersistence study of two low alumina rock wool compositions
with high dissolution rates has also been reported
(Bernstein et al., 1996).
An extreme example of a high alumina fiber, a refractory
ceramic fiber denoted RCF 1a, was also the subject of a biopersistence
(Hesterberg et al., 1998). Finally, a series of high alumina
rock wool compositions were tested in biopersistence studies
(Hesterberg et al., 1998;
Eastes et al., 2000b).
The in-vivo dissolution rate constant kdis has been calculated
(Eastes et al., 2000b) from the long fiber retention data for
each of these fibers studied in vivo. For those fibers containing
less than about 10% by weight of alumina, and for the refractory
ceramic fiber, the in-vivo kdis agreed reasonably well
with the value measured in vitro. But for the high alumina rock
wool compositions containing more than about 10% alumina, it was
not possible to measure the dissolution rate in-vitro
(Eastes et al., 2000b).
The in-vivo kdis will be used consistently
in what follows.
The data on each fiber available are summarized in Tables 2 and 3. The fiber compositions that are generally classified as slag or rock wool fibers, both the conventional low alumina and the newer high alumina rock wools, are summarized in Table 2. Table 3 shows the same information for all of the other fiber types, most of which are glass wools, but it also includes refractory ceramic fibers and thin, special purpose E glass fibers. In each table, the fibers are grouped according to the published biopersistence study. Since the composition of each fiber has been previously published as noted in Table 1, it will not be repeated here, but rather the partial dissolution rate S from Eq (3) is given along with the Al2O3/SiO2 ratio and the in-vivo kdis. However, the complete set of fiber compositions and in-vivo dissolution rates used in this paper are available separately as a tab delimited text file by clicking here.
|Rock MMVF 21||20||1.022||0.281||-0.0477|
|HT MMVF 34||346||1.068||0.600||-0.0232|
|Rock Wool MMVF 21||25||1.042||0.281||-0.0459|
|Slag Wool MMVF 22||171||1.563||0.276||-0.0868|
|E MMVF 32||11||1.028||0.256||-0.0480|
|JM475 MMVF 33||17||2.549||0.102||-0.0286|
|SG MMVF 11||138||1.512||0.061||-0.0191|
|SG J X607||222||1.718||0.021||-0.0333|
|JM 901 MMVF 10||36||1.419||0.091||-0.0449|
|CT B MMVF 11||133||1.245||0.061||-0.0193|
The partial dissolution rate S is plotted for each fiber as
a function of the Al2O3/SiO2
ratio in Figure 1. It may be seen from Figure 1 that the
partial dissolution rate S is indeed approximately linear in
the alumina/silica ratio as suggested by Eq (3) and that there
are two distinct regions of linearity, one corresponding to low
alumina, and the other to high alumina. Straight lines were fit
in the sense of minimum to the data in each region.
The R2 statistics were 0.969 and 0.957 for the left and
right hand lines in Figure 1, respectively.
Figure 1. Partial dissolution rate S derived from in-vivo
kdis for the available fibers as a function of the alumina/silica
ratio. The vertical bars represent the geometric standard deviation
of S derived from that of the in-vivo kdis.
The fiber compositions and in-vivo dissolution rate data shown
in Figure 1 were then fit to Eq (4), which includes FeO
in the fit. The fit was done twice, once with the low alumina
compositions having alumina/silica ratios below 0.30 on the left
side of Figure 1, and again with the high alumina compositions
with alumina/silica above 0.25. Several compositions where the
lines cross in Figure 1 were included in both the low and high
alumina fits, as they appear to fit in either category. Two separate
sets of coefficients Pi for SiO2,
Al2O3, and FeO were determined, one for
the low alumina and one for the high alumina regions. These coefficients
are summarized in Table 4 along with the coefficients for the
other oxides, which are the same as for the borosilicate fibers
by this theory. For comparison, that set of borosilicate coefficients
is also shown in Table 4.
Also shown in Table 4 are two statistics of the correlation between
the calculated kdis and the in-vivo measured values upon
which these coefficients were based. The R2 statistic,
which is a measure of the correlation between the calculated and
the measured values, may be interpreted as the fraction of the
variation in the measured data that is explained by the calculated
values. The geometric standard error GSE of the fit to the in-vivo
kdis is also given. It may be interpreted as follows: Approximately
two-thirds of the calculated kdis values fall within the
in-vivo measured value divided by the GSE and the measured value
times the GSE. The geometric standard error is the appropriate
statistic here rather than the standard error, since the logarithm
of kdis was the quantity subjected to a linear fit in Eq
The coefficients in Table 4, when used in Eq (1), provide an estimate
of the dissolution rate kdis for a fiber of known composition.
This calculation is carried out by first normalizing the oxide
composition to 100% in all of the oxides that have coefficients
in Table 4. Then, each oxide weight percent is multiplied by the
corresponding coefficient from Table 4 and these are summed. This
sum is the logarithm to the base 10 of the dissolution rate, the
antilogarithm of which yields the dissolution rate constant in
A computer program that runs in a web page is available to perform
this calculation conveniently.
The program may be started by clicking here.
In practice, it is not necessary
to determine beforehand whether a given composition is a low or
high alumina composition to know which of the two sets of coefficients
in Table 4 apply. One simply calculates kdis by both sets
of coefficients, which corresponds to evaluating S on both the
solid line and on the dashed line in Figure 1. It is apparent
from Figure 1 that the larger value of S and therefore the larger
value of kdis so obtained is the correct estimate, because
the larger value of S is the one upon which the measured data
The computer program just mentioned
makes use of these facts to provide an estimate of the dissolution rate
of a wide variety of different compositions, using the best set of
coefficients for each composition given.
The results of applying Eq (1) with the coefficients in
Table 4 and the considerations just described to the data of Tables
3 and 4 are summarized in Figure 2 by plotting the in-vivo measured
kdis against the calculated value for each fiber. The straight
line in Figure 2 is the line on which all of the data would fall
if there were perfect agreement of the calculated with the in-vivo
|Oxide||Low Alumina||High Alumina||Borosilicate|
|SiO2||-0.01711 ± 0.00062||-0.07423 ± 0.00034||-0.01198 ± 0.00285|
|Al2O3||-0.12091 ± 0.00262||0.10454 ± 0.00088||-0.21410 ± 0.01102|
|CaO||0.10806 ± 0.01119||0.10806 ± 0.01119||0.10806 ± 0.01119|
|MgO||0.13761 ± 0.01262||0.13761 ± 0.01262||0.13761 ± 0.01262|
|Na2O||0.09386 ± 0.00867||0.09386 ± 0.00867||0.09386 ± 0.00867|
|B2O3||0.14669 ± 0.00908||0.14669 ± 0.00908||0.14669 ± 0.00908|
|BaO||0.06921 ± 0.03095||0.06921 ± 0.03095||0.06921 ± 0.03095|
|F||0.11867 ± 0.06134||0.11867 ± 0.06134||0.11867 ± 0.06134|
|FeO||0.05154 ± 0.00303||-0.01724 ± 0.00244||-|
Figure 2. Comparison of the dissolution rate constant calculated
from the composition with the in-vivo measured value for the data
used to determine three of the coefficients. The rock and slag
wool compositions from Table 2 are denoted with
the other compositions from Table 3 are shown with a small
The vertical error bars denote the geometric standard deviation
of the in-vivo measured kdis.
The work described here began as an attempt to extend to rock
and slag wool fibers the ability to estimate the dissolution rate
constant from composition in the same way as had been done earlier
for borosilicate glass fibers
(Eastes et al., 2000a). To accomplish
this goal, it was necessary to use different equations for the
high alumina fiber compositions than for the low alumina fibers.
The form of these two equations is the same, but the coefficients
are different. Once this division was made, it was found that
a much wider variety of fiber compositions, including refractory
ceramic fibers and special purpose thin E glass fibers, for example,
could be estimated just as well as the rock and slag wool fibers
by the same equations. Even borosilicate glass fibers were estimated
fairly accurately by the low alumina equation and are included
in the results in Figures 1 and 2. Thus the low alumina and the
high alumina equation coefficients listed in Table 4 represent
a "universal" method for estimating the dissolution
rate of a wide variety of commercial and experimental vitreous
silicate glass fibers. The low alumina equations work fairly well
for the borosilicate glass fibers too, but the borosilicate coefficients
provide a much more accurate estimate for those fibers that fall
into that class of compositions. For fibers that are not borosilicates,
one falls back upon the low or high alumina coefficients, which
cover a much wider range of compositions, but with less confidence
in the accuracy of the estimate.
As shown in Table 4, all three sets of coefficients have large
and similar values of R2, all over 0.95. This fact means
that over 95% of the variation in the in-vivo kdis was
explained by the calculated values. The real differences among
these sets of coefficients is revealed by the geometric standard
error of the fit, GSE, which is much smaller for the borosilicate
coefficients than for the other two sets. If the composition is
a borosilicate, then one can use these coefficients with the expectation
that the calculated value will be within the GSE factor of 1.25
of the actual value about two-thirds of the time. On the other
hand, the other two equations are accurate only to a factor of
about four in the same sense.
This large difference in the accuracy of the equations comes about
because the borosilicate equation was developed over a relatively
small range of composition using much more measured data. The
low and high alumina coefficients were based on in-vivo data alone
on a much smaller set of compositions that at the same time covered
a much wider range of composition. The tradeoff between accuracy
and composition range covered is a general feature of this sort
of dissolution rate model. It is likely that equations could be
developed for rock and slag wool that could be just as accurate
as the borosilicate equations, if the composition range were just
as restricted and the data were available.
Another difference between the borosilicate equation and the other
two is that the borosilicate coefficients were developed from
in-vitro measured kdis, whereas the low and high alumina
coefficients were developed exclusively from in-vivo dissolution
rates. In nearly all cases, the in-vitro dissolution rates for
the low alumina compositions agreed well with in-vivo values
(Eastes et al., 2000b),
but not for some high alumina fibers. Also, the
borosilicate in-vitro kdis measurements agreed well with
the in-vivo values that were available. Therefore, the kdis
estimates provided by the coefficients in Table 4 may be
considered to be estimates of the dissolution rates in vivo, which
do in fact agree with the in-vitro kdis for all except
the high alumina rock wool compositions.
Figure 2 summarizes the quality of the estimate of dissolution
rate provided by the low and high alumina equations by comparing
the calculations with the values measured in vivo. It is seen
first of all that the calculated values for rock and slag wool
compositions are not consistently better or worse than those for
borosilicate and other compositions, which underscores the "universal"
nature of these equations. However, the quality of the calculated
values appears to fall into two distinct regions: Below about
1000 ng/cm2/hr, the calculated kdis
agrees reasonably well with the in-vivo value with two notable
exceptions; Above 1000, the calculated kdis is typically
significantly higher than the in-vivo value.
The two notable exceptions to the reasonable agreement between
the calculated and the in-vivo kdis below 1000
ng/cm2/hr in Figure 2 are the fiber 7779 with a calculated
kdis of 20 but in-vivo kdis of 3 and JM 901 MMVF
10 with calculated kdis 346 but in vivo kdis 36.
In view of the large uncertainty in the in-vivo kdis for
7779, it is not clear that the discrepancy is statistically unexpected.
However, the JM 901 MMVF 10 point is an obvious anomaly, differing
by almost a factor of ten. It is interesting that the MMVF 10
composition was measured twice in vivo, once by inhalation biopersistence,
and again from intratracheal diameter change, and both appear
in Figure 2. This latter in-vivo kdis was 201, which agrees
with the calculated value within the average error of the calculation.
This is the only example known in which two in-vivo tests give
such differing results. The weight of the evidence suggests that
the larger kdis is the correct one for this fiber.
Figure 3. Predicted incidence of lung tumors and Wagner Grade 4 or higher fibrosis for chronic inhalation rat studies of 1-µm-diameter fibers as a function of the fiber dissolution rate constant. The estimated standard error associated with the predicted incidence (solid red lines) are shown as arbitrarily spaced vertical red lines.
In the high dissolution region above 1000 ng/cm2/hr,
the calculated kdis is consistently larger than
the in-vivo measured value. It was noted in a previous study
(Eastes et al., 2000b)
that the in-vitro measured kdis also appeared
to be larger than the in-vivo value, and it was postulated that
the nature of the inhalation biopersistence protocol made it difficult
to accurately determine the dissolution rate outside the range
of 3 to 300 ng/cm2/hr. Not only are such high
dissolution rates difficult to determine by inhalation biopersistence,
but also they have little significance for chronic effects in
rat inhalation studies. Figure 3
(Eastes and Hadley, 1996) shows
the incidence of lung tumors and fibrosis predicted in a state
of the art chronic rat inhalation study with fibers of different
dissolution rates. It is clear from Figure 3 that disease incidence
has dropped to background levels at dissolution rates well below
the 300 to 1000 ng/cm2/hr at which significant
discrepancies are observed between the calculated and either the
in-vitro or the in-vivo measured value.
This consideration of the agreement and especially the nature
of what lack of agreement exists between the in-vivo and the calculated
dissolution rate leads to the seemingly outrageous suggestion
that the calculated kdis is more reliable than the measured
value, at least for the sorts of fibers studied so far. This unseemly
reliability of the calculated kdis could come about because
the chemical basis of the calculation method allows it to be extended
into regions of high and low dissolution rate where the in-vivo
protocol is not as sensitive. In any case, it appears that, when
the calculated dissolution rate is very large or very small, then
the in-vivo rate is also. It is merely that the quantitative agreement
between calculated and in-vivo kdis is not as good as it
is in the 3 to 300 ng/cm2/hr region.
The fact that the absolute accuracy of the high alumina and low
alumina equations for predicting the in-vivo dissolution rate
of rock, slag, and other synthetic vitreous fibers is about a
factor of four, as indicated by the geometric standard error (Table
4), needs to be viewed in context. First of all, the range of
in-vivo dissolution rate over which this statistic was compiled
is about a factor of 400. Thus a method that places the dissolution
rate within a factor of four in a range that spans a factor of
400 may have considerable practical utility. Secondly, the in-vivo
measured dissolution rate, upon which the calculation methods
are verified, are not much more precise either, as seen from the
error bars in Figure 2. In fact, five of the 29 fibers exhibited
in Tables 2 and 3 have geometric standard deviations for the in-vivo
dissolution rate constant above two. Thus the dissolution rate
calculated simply from the composition is not a lot less variable
than the in-vivo data to which it is being compared.
The method just described provides a way to estimate the dissolution rate constant for a fairly wide range of rock and slag wool and other synthetic vitreous silicate fibers from their compositions. With a knowledge of the dissolution rate constant, one may estimate whether disease would be observed in animal inhalation or intraperitoneal studies, as has been described previously (Eastes and Hadley, 1996). The method given in this paper serves to extend to a wide variety of fiber compositions what has been published previously for borosilicate glass wool fiber types (Eastes et al., 2000a). A computer program that runs in a web page is available to perform this calculation conveniently for any composition entered into it. The program may be started by clicking here.
The ability to determine kdis simply from the composition
of a synthetic vitreous silicate fiber should be useful both to
fiber manufacturers and to researchers who are interested in changing
the dissolution rate of vitreous silicate fibers. Additionally,
it provides a tool by which interested regulatory bodies may monitor
the dissolution rate of insulation wool products simply by monitoring
their composition without expensive and time-consuming animal
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