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OCR for page 351
PART Vl
Applications of
Mathematical Modeling
OCR for page 352
OCR for page 353
Hazard Assessment Using an Integrated
Physiologically Based Dosimetry Modeling
Appproach: Ozone
Frederick ]. Miller, John H. Overton, Jr., Elaine D. Smolko,
Richard C. Graham, and Daniel B. Menze!
INTRODUCTION
In examining the possible role of pharmacokinetics and pharmacody-
namics in risk assessment, the underlying philosophy of the legislative
mandate through which the risk assessment is applied must be kept in
mind. For example, the ability of the Food and Drug Administration to
invoke the Delaney Clause to regulate a substance is different from the
risk assessments required for the Environmental Protection Agency's Na-
tional Ambient Air Quality Standards (NAAQSs). The kind and level of
information that is available can vary greatly. Reevaluation of the NAAQSs
for ozone (03) focuses on whether or not the value of the standard should
be changed by as little as 20%, while many carcinogenic risk assessments
are trying to establish the level of risk to within one to two orders of
magnitude. In any case, the uncertainties identified in risk assessments
help to establish areas in which additional research would be useful.
The intent of this paper is to broaden the awareness that pharmacoki-
netics and mathematical dosimetry models are useful tools in risk assess-
ments of noncarcinogenic as well as carcinogenic effects. While examples
The research described in this paper has been reviewed by the Health Effects Research Lab-
oratory, U.S. Environmental Protection Agency, and approved for publication. Approval does
not signify that the contents necessarily reflect the views and policies of the Agency nor does
mention of trade names or commercial products constitute endorsement or recommendation for
use.
353
OCR for page 354
354 FREDERICK J. MILLER et al.
Of modeling applications have been predominantly related to carcinogen-
esis, health effects such as emphysema and fibrosis are not to be ignored.
This is particularly true for oxidant gases. For example, several animal
studies in different species show that long-term exposure to nitrogen diox-
ide produces emphysema (renters et al., 1973; Hyde et al., 1978; Riddick
et al., 1968), and O3 causes pulmonary fibrosis (Fujinaka et al., 19851.
Moreover, subchronic exposures at relatively low levels of these gases
have been shown to lead to cellular changes (Barry et al., 1985; Chang
et al., 1986) that are indicative of a structural remodeling of the lung.
The impetus is clear that man must be protected from such effects. But
to use the animal toxicological data more quantitatively in setting appro-
priate NAAQSs for these gases, extrapolation modeling is required.
In this volume the need to incorporate pharmacodynamics in the mod-
eling process has been discussed. Thus far, most risk assessments have
assumed a priori that an equivalency of response exists between animals
and man. As one proceeds from the molecular level or biochemical event
toward injury at the tissue or organ level, that assumption becomes less
tenable because of possible species differences in repair processes, levels
of antioxidant enzymes, etc. The dose, if it is sufficiently high, can produce
damage anywhere from the molecular to the organ level. On the other
hand, various host defense systems can interact, and if the damage is not
sufficiently severe, they can yield recovery. If the delivered dose over-
whelms these defense systems, various disease states can result. Defense
systems might conceivably play a role in the etiology of lung disease. All
of this is a dynamic situation.
Figure 1 (based on Figure 1-1 of NRC, 1983) summarizes an overview
of the research, risk assessment, and risk management processes and their
interrelationships that lead to the recommendation of a NAAQS. This
paper focuses on the phases of the processes outlined by the dashed
rectangle. Here, the area of pharmacokinetics offers great potential for
improved risk assessments, particularly when these assessments are re-
quired to be more quantitative in nature. The development of dosimetry
models that can provide a description of the uptake and distribution of
chemical compounds throughout the body and the availability of toxico-
logical data that can be used to establish dose-response relationships are
integral to these efforts. The incorporation of laboratory and field obser-
vations of adverse health effects, hazard information, and extrapolation
methods to yield dose-response assessments is critical to the risk assess-
ment process. The combining of these phases can be facilitated by the
integrated physiologically based dosimetry modeling approach, illustrated
schematically in Figure 2.
The major components of the approach are the critical toxicity reference
(CTR) system (Smolko et al., in press) and the physiologically based
OCR for page 355
Establishing Dose-Response Relationships 355
RESEARCH
RISK ASSESSMENT
RISK MANAGEMENT
l
Laboratory and field
observations of
adverse health effects
and exposures to
particular agents
Information on
extrapolation methods
for high to low dose
and animal to human
Haza rd
Identifi. ation
Dose-Response
Assessment
Field measurements,
esti mated expose res,
characterization of
populations
_ _
_ J
Exposu re
Assessment _
Risk
Characterization \
+
\
Development of
regulatory options
Evaluation of
public health,
economic, social,
political
consequences of
regulatory
options
T
| Agency l
decisions and
actions
FIGURE 1 Major elements of risk assessment and risk management. The phases of the process
that can be addressed by using an integrated physiologically based dosimetry modeling approach
are contained within the dashed rectangle. Overall figure schematic is based on Figure 1-1 of
NRC (1983).
dosimetry (PBD) model. The CTR system is comprised of four elements:
(1) searching the literature for references reporting toxicity data relevant
to the toxicant being studied; (2) abstracting information from the selected
references in a form appropriate for both quantitative and descriptive
extraction; (3) constructing a data base that consists of bibliographic and
abstracted information; and (4) compiling concentration-response data by
a series of searches of the developed data base. The primary factors
considered in developing PBD models are mammalian physiological pro-
cesses, anatomical characteristics, physicochemical properties of the gas
and of relevant biochemical constituents, and mass transport processes.
PBD model predictions of dose, appropriate for species with the specific
characteristics described in the literature, are combined with the concen-
OCR for page 356
356 FREDERICK J. MILLER et al.
ll
L _ _ _ _ _ _ _
Critical Toxicity Reference
(CTR) System
Search Literature
Abstract Information
Construct Data Base
Compile Concentration-
Response Data
Exposure Concentration
Time of Exposure
-
parameters specific to 9 iven I
animal, weight, and sex
Data Base
animal, for
weight, ~ anatomical, physiological,
sex biochemical, and physical
parameters
1 1
LO Physiolog ical Iy-Based Dosi metry
(PBD) Model
T
predicted dose
response
| Dose-Response Relationship |
Species Sensitivity
Host Defense
Repair Processes
Genetics
Identifv Research Gaps
. _ .. .., .. _ .
and
Design Experiments
| Estimate Hu j an Toxicity
~ r
| Risk Characterization 1
FIGURE 2 A schematic of the elements of an integrated physiologically based dosimetry
modeling approach to estimating human toxicity that leads to one of the components of risk
characterization. The procedure diagrammed in the dashed rectangle is the proposed approach
for implementing the dashed rectangle process shown in Figure 1.
tration-response data that have been collated by species and endpoint. The
resulting dose-response relationships can use various expressions of dose
to obtain the most appropriate quantitative representation of toxicological
effects.
The analyses can incorporate species sensitivity information for con-
sideration of such factors as host defense, repair processes, and genetics.
One outcome of this approach is an estimation of human toxicity that can
be used as input into the risk assessment and risk management processes.
OCR for page 357
Establishing Dose-Response Relationships 357
A second outcome is information to aid in the identification of data gaps
and design of experiments. This latter outcome is particularly important
because it can eventually yield new data that will be used in the iterative
application of the integrated PBD model approach which will strengthen
the overall risk assessment and risk management processes.
The remaining sections of this paper illustrate the integrated PBD mod-
eling approach (Figure 2) by applying data from the CTR system and
predictions from a PBD model for O3 to construct dose-response rela-
tionships. This will be done first by discussing the formulation, as well
as sample simulation results, of a PBD model that predicts the uptake and
distribution of absorbed O3 in the lungs of mammals. Although the focus
will be on 03, the intent is primarily to illustrate the methodology and to
provide an understanding of various aspects of delivered dose. The meth-
ods discussed will be particularly important when some of these procedures
are extended to volatile organic compounds, for which first-pass metabolic
effects in the lung are a concern. Also, a brief discussion is provided of
a data base management system, CTR, that has been developed to store
and retrieve quantitative data in a manner useful for mathematical dosi-
metry models. An application to ozone toxicological data is presented to
illustrate the methodology of using mathematical dosimetry models to
examine quantitative dose-response relationships.
LOWER RESPIRATORY TRACT MATHEMATICAL DOSIMETRY
MODELI NG
In the papers presented in this volume, much attention is placed on the
use of physiologically based pharmacokinetic models to provide a de-
scription of dose distribution following inhalation of a chemical com-
pound. To date, these models predict average levels of the chemical
throughout an entire organ (or body compartment). As illustrated below,
however, additional complexities are involved when the distribution of
inhaled gases is evaluated within the lower respiratory tract (LRT), where
dose in various lung regions can vary greatly and consequently have
different health effect outcomes.
Mode! Conceptualization
The major factors affecting the regional uptake of O3 are morphology
of the respiratory tract, the route of breathing, the depth and rate of
breathing, gaseous physiocochemical properties, the physical processes
governing gas transport, and the physiocochemical properties of the trach-
eobronchial (TB) liquid lining and of the air-blood barrier in the pulmonary
OCR for page 358
35~3 FREDERICK J. MILLER et al.
region. All these factors interact in a complex way to determine dose and
must be considered in developing a simulation model.
The mathematical model formulation will focus on the lower respiratory
tract for several reasons. Upper respiratory tract removal of inhaled gases
and particles is amenable to experimental determination of deposition
(Corn et al., 1976; Miller et al., 1979; Yokoyama, 1968; Yokoyama and
Frank, 19721. The morphology of the upper respiratory tract is quite
complex, difficult to measure, and variable between species (Schreider,
1986; Schreider and Raabe, 1981), so mathematical descriptions are dif-
ficult to obtain. Further, airflow patterns are also complex (Patra et al.,
1986), so proper treatment of gas transport processes is not apparent.
Experimental values for upper respiratory tract uptake of the inhaled gas,
however, can provide appropriate boundary conditions for mathematically
modeling delivered doses to LRT regions.
Aspects of LRT structure and their relationship to model compartments
are illustrated in Figure 3. Briefly, anatomical descriptions of the lung are
needed such as those available for man (e.g., Weibel, 1963; Yeh and
Schum, 1980) and for various animals (e.g., Kliment, 1973; Schreider
and Hutchens, 1980; Yeh et al. 19791. The top portion of Figure 3 shows
Weibel's (1963) representation of the TB and pulmonary regions of the
human lung. For mathematical modeling purposes, we conceptualize this
representation into a series of right circular cylinders; and information is
needed on the lengths, diameters, and radii of the TB airways. In the
pulmonary region, data on the structure of the pulmonary ducts and sacs
and on the number of alveoli, their surface areas, and volumes are nec-
essary to apply the model description of gas transport processes.
In the TB or conducting airways, a mucociliary layer protects the un-
derlying ciliated, goblet, brush, and basal cells, etc., from direct insult
by the inhaled gas. As can be seen in Figure 3, this layer consists of an
epiphase and a hypophase. Lacking definitive data on the thickness and
chemical composition of these phases in various portions of the TB region,
the current model formulation combines them into one compartment. For
ambient exposures to the highly reactive gases, such as 03, penetration
to the bloodstream in the TB region can be ignored (see Miller et al.,
1985, for details). Thus, in the TB region, model compartments correspond
to the air, liquid lining layer, and underlying tissue. For highly soluble
and nonreactive gases, however, a blood compartment and a description
of the fate of the gas in other organs and compartments of the body
probably would be needed.
In the pulmonary region, the epithelium is chiefly comprised of type I
and type II cells over which a very thin layer of a surfactant fluid can be
found. Underlying the epithelium are the interstitium and the endothelial
cells of the capillary network. Because the alveoli are arranged back to
OCR for page 359
Establishing Dose-Response Relationships 359
-
TB
~ 14131 2
T BL BR
B
L
~ "
PU LM ONARY
t22|21|20|19|18|17
AS AD RBL
~ W~ s~
~ W/~:
O
TRA-
CHEA
l-
,
a
. .
b ~ ,~ c
rat I · _
1
.
A C
A`'
_ ,,
A
d AIR
TISSUE\
a ~ r ~ /
~ TISSUE ~ ;/
l
l
LIQUID
LINING,
l
l
AIR ,
, _____________________ ________
~ ,
______________
A,.
AIR
_ _ _' . HY~
An-- ' "'AS'
UQUlD
uea~c
Use.
LIQUID LINING
FIGURE 3 The relationships between morphologies and their model representations. Panel a
is a schematic of the branching airways of the TB and pulmonary region of man (based on
Weibel, 1963). The generations are labeled from the right, beginning with the trachea. BR, BL,
and TBL indicate bronchi, bronchioles, and terminal bronchioles, respectively; the respiratory
bronchioles, alveolar ducts, and alveolar sacs are indicated by RBL, AD, and AS, respectively.
Below the TB portion of the lung schematic are three cylindrical figures that indicate the model
representation of the airways. Panel c shows a diagram of the structure of the liquid lining and
tissue of the TB region (diagram based on Jeffrey and Reid, 1979). The different cells represented
are basal (BC), ciliated (CC), brush (BrC), goblet (GC), and conciliated serous (NCC). Panel
e illustrates the model representation of TB liquid lining and tissue compartments. Panel b is an
electron micrograph of the interalveolar septa (based on Gehr et al., 1978). The air spaces (A),
capillaries (C), type I cells and their nuclei (EP1 and NEP1), endothelial cells and their nuclei
(EN and NEN), and interstitial space (IN) are indicated. Panel d illustrates the model represen-
tation of the liquid lining, tissue, and capillaries of the pulmonary region.
OCR for page 360
360 FREDERICK J. MILLER et al.
back, with capillaries between them, the model formulation for the air,
liquid lining, tissue, and blood compartments is assumed to be symmetrical
(Figure 31.
A one-dimensional equation of mass transport is used to describe the
dynamics of the cross-sectional average concentration. Experimental ev-
idence for this approach is discussed by Overton (19871. The processes
of axial convection and axial dispersion, the loss of O3 to the liquid lining,
and lung expansion and contraction are taken into account. Lung expansion
and contraction during the breathing cycle become important when pol-
lutant uptake for minute ventilations corresponding to heavy exertion is
modeled. When mass transfer in the liquid lining, tissue, and blood com-
partments is modeled, the transport of ozone is related to molecular dif-
fusion and chemical reaction terms. The reader is referred to Figure 2 of
Overton et al. (J. H. Overton, R. C. Graham, and F. J. Miller, this volume)
for explicit forms of the partial differential equations used in the model.
For a detailed discussion of the model formulation and assumptions, as
well as the basis for these assumptions, see Miller et al. (1985) and Overton
et al. (19871. Note that when other gases are modeled, modifications of
the expression for loss of the gas to airway walls may be necessary. In
addition, high solubility or nonreactivity may necessitate changes in some
aspects of treating gas transport in the airways.
The information required to model adequately transport in the mucus
or surfactant lining liquid, tissue, and blood compartments includes quan-
titative biochemical data on the constituents as well as on the chemical
reactions of O3 with these constituents. Currently, a pseudo-first-order
reaction scheme is assumed when ozone uptake is modeled (see Miller et
al., 19851. Estimates of liquid lining, tissue, and blood compartment
thickness are also required. At present, this is an area in which most of
the available information is from animal studies. Data for man are very
limited, and assumptions about the distribution of compartment thickness
must be made. Compartmental diffusion coefficients and partitition coef-
ficients, such as those used in physiologically based pharmacokinetic
models, are also needed. Much of the above topic is discussed in detail
elsewhere (Miller et al., 1985; Overton et al., 19871.
Examples of O3 Dosimetry Modeling Results
Utilizing the model formulation concepts discussed above, Miller et al.
(1985) examined the uptake of O3 in the LRT of man and performed
various sensitivity analyses to illustrate the importance of LRT secretions
on delivered dose. Their work shows that the net amount of O3 removed
in the trachea can be several orders of magnitude different from the amount
of O3 that penetrates to the underlying tissue. Proceeding distally from
OCR for page 361
Establishing Dose-Response Relationships 361
the trachea, this difference diminishes mainly because of the decline in
the thickness of the liquid lining. Furthermore, because the gas-exchange
region is lined with a very thin fluid that does not contain many constituents
that react with 03, the net amount of O3 removed and the tissue dose of
O3 are essentially the same. According to Miller et al. (1985), the net O3
dose curves are much less dependent on the thickness of the TB liquid
lining than are the O3 tissue dose curves.
Another example of sensitivity analysis demonstrating the importance
of model parameters is concerned with the values of the liquid lining rate
constants. Simulations show that the effect of increased chemical reactivity
in the TB liquid lining is to increase the net airway doses in the TB region
and to decrease the tissue dose throughout the LRT. Furthermore, tissue
dose is found to be much more sensitive to the TB liquid lining reactions
than is the net dose. For example, the tracheal tissue dose is predicted to
decrease by about 3 orders of magnitude, and the tracheal net dose is
predicted to increase by about 1 order of magnitude because of a rate
constant change from 0 to twice the reference value. However, pulmonary
net and tissue dose values are predicted to change by less than a factor
of 2 as a result of the same change in the TB liquid lining rate constant.
By contrast, changes in the pulmonary liquid lining rate constant lead to
simulation results for LRT net and tissue doses that are essentially un-
changed from those obtained with the reference values. These types of
analyses show that to determine dose-effect relationships for various cell
types or components (e.g., cilia) in the conducting airways, better quan-
titative data than are presently available on TB liquid lining rate constants
and thickness are desirable. On the other hand, the lower sensitivity of
predicted pulmonary doses to parameter uncertainties gives a greater con-
fidence in making interspecies comparisons of dose-effect relationships in
this region compared with making such comparisons in the TB region.
An example of interspecies dosimetric comparisons is illustrated in
Figure 4, in which the solid and dashed lines are O3 dosimetry simulation
data for the rats and man, respectively. Predictions for the rat lung use
the Yeh et al. (1979) anatomical model in which the morphometric data
are represented in a generational-type model analogous to the Weibel
(1963, generational morphometric data for the human lung. Both the net
and tissue doses of O3 are shown for these species. Dose is expressed in
Figure 4 as micrograms of O3 per square centimeter of airway surface
area per minute, standardized to a tracheal O3 value of 1 ~g/m3. In the
mathematical dosimetry model the processes are linear. Thus, dose is
proportional to the tracheal concentration. For example, for a tracheal
concentration of 1,000 ~g/m3, the predicted airway doses are 1,000 times
the plotted values; for a tracheal concentration of 1 ppm, multiply the
plotted values by 1,960 (~g/m3 per ppm).
OCR for page 418
4 ~ ~ PAU ~ F. MORR ISON ET AL.
except for a decade difference in ordinate scale. The first curve (a) also
scales with dose by the appropriate factor of 5. This scalability arises, in
spite of the presence of nonlinearities in the complete scheme, because
over 95% of the volume of MTX distribution is composed of non-transport-
saturating, rapidly equilibrating compartments, principally the kidney,
liver, plasma, skin, and extracellular volume of the muscle. In addition,
the small compartments that do exhibit nonlinear distribution, the intra-
cellular spaces of the gut, spleen, and bone marrow, do not rapidly trans-
port drug into their cells. Hence, several plasma half-lives in the rat (tin
= 0.3 h) can pass after administration of drug in the therapeutic dose
range before plasma levels fall to the point where return of the small
amount of drug in these deep nonlinear compartments could influence
plasma kinetics.
On the other hand, if one is interested in assessing the drug delivery
to the gut, spleen, and bone marrow, then nonlinear pharmacokinetics
prevents dose scaling from applying. These organs exhibit two strong
nonlinearities in the first few hours after drug administration: saturable
uptake of MTX from plasma, and strong binding of MTX (and its poly-
glutamates) to the target enzyme dihydrofolate reductase. This is exhibited
in Figure 3, in which total MTX concentrations in rat bone marrow (ex-
tracellular MTX + intracellular MTX) are plotted as a function of time
for four doses (Dedrick et al., 19731. The bar denotes the concentration
of reductase in this tissue. Note that plasma-to-marrow concentration ratios
are not constant over the 140 min shown here, and thus that marrow
concentration does not scale with dose. The total marrow concentration
shown in Figure 3 does scale with dose at short times, but this only reflects
the rapid equilibrium attained between plasma and extracellular space (the
dominant transport before cell uptake becomes significant). Note also that
the marrow curves of the two lower dose levels are flat at long times and
lie below the reductase content bar, thereby reflecting strong nonlinear
enzyme binding of the drug that enters the cells in the first few minutes
of exposure. Because the tight binding prevents drug efflux from occur-
ring, the mass of enzyme-bound drug reflects the cumulative result of
transport into the cell. At 0.05 and 0.25 mg/kg, this mass scales with
dose (0.02 versus 0.10 ~g/ml) and thus transport is linear. However,
attempts at using linear transport to extrapolate from 0.25 to 2.5 mg/kg
fail, an observation that is consistent with plasma levels at the higher dose
exceeding a Michaelis transport constant of about 1 ~M, a value char-
acteristic of the range found in a variety of cell lines (Goldman, 1969,
1971; Schilsky et al., 19811. Figure 4 shows the magnitude of this saturable
transport effect by dose level as the difference between the dashed and
solid lines. The solid line shows rat marrow concentrations when saturation
OCR for page 419
Methotrexate: Pharmacokinetics and Toxicity 4~9
t00
10
or
1.0
At
lo
he
o
-
\ 2 S mg~g
_
_
~ _
-
-
_
-
-
-
-
-
-
-
-
\L- ~ §
0.1
0.25
0.05
GO' 20
40 60 80
TIME, min
100 120 140
FIGURE 4 Companson of model simulation of linear and saturable transport in bone marrow
at several doses. The dashed lines represent the model simulations for linear transport to the
intracellular compartment of bone malTow. The solid lines represent model simulations with
saturable transport. SOURCE: Dedrick et al. (1973).
is operative, while the dashed line, providing a poor fit to the data (not
shown), shows the result when linear transport is assumed.
Hence, it can be concluded that, for sufficiently short times (e.g.,
<4 h in the rat), many organ regions are dose scalable, while others, for
example, the gut, marrow, and spleen, are not.
OCR for page 420
420 PAUL F. MORRISON ET AL.
DOSE SCHEDULING
We next turn our attention to the rather dramatic effects that dose
scheduling has on toxic response and to the formal connection between
MIX pharmacokinetics and toxic response. Up to this point, the discussion
has mainly involved distributional events that occur after bolus dosage.
We will now see that the time of inhibition of dihydrofolate reductase is
the primary correlate with toxicity.
Table 2 shows acute toxic response in terms of the lethal dose for 50%
of mice (LDso) exposed to a variety of drug schedules (Zaharko, 19751.
The first entry is for a bolus dose of 350 mg/kg, while the next entries
correspond to divided doses of decreasing total dose, and the final entry
corresponds to a 96-h infusion of a 3-mg/kg total dose. These results
immediately show that response does not directly correlate with total dose.
Decreasing dose by more than a factor of 100 led to an increase, rather
than a substantial decrease, in toxicity. Furthermore, the area under the
plasma concentration-time curve, a frequently used metric, does not cor-
relate with toxic response. This can be seen in Figure 5 (Zaharko, 19751.
The steep curve shows the MIX plasma concentration following the 350-
mg/kg bolus dose, while the flat curve shows the concentration following
the 3-mg/kg 96-h infusion. The area under the bolus curve is about 2
orders of magnitude greater than that under the infusion curve, yet toxic
response is greater with infusion.
The principal correlate with response is the length of time that dihy-
drofolate reductase and, consequently, DNA synthesis are strongly inhib-
ited. If inhibition of DNA synthesis is a good correlate, then one would
expect that the onset of toxicity should be observable after the same
inhibition time, regardless of dose schedule. For at least two infusion
schedules, this has been observed experimentally in mouse small intestine
(Zaharko et al., 19771. Figure 6 shows the recovery of DNA synthesis in
mice, as measured by deoxyuridine incorporation into DNA, following
an infusion of 1 fig of MTX/h for 48 h, a schedule that just barely avoids
TABLE 2 Schedule Dependence of Methotrexate Toxicity in Mice
-
Peak plasma
Individual concentration
dose (mg/kg) Schedule Total dose (mg/kg) (M) Effect
350 Single dose 350 10-3 LDso
25 Twice daily 50 lO-4 LDSo
3 Every 3 h, 5 times, rest 8 h, and then 24 1o-s >Lids
every 3 h, 3 times
0.5 Every 3 h, 20 times 10 lo-6 >LDso
0.8 ~g/h Infusion 96 h 3 10-8 >LDso
OCR for page 421
Methotrexate: Pharmacokinetics and Toxicity 421
1000
-~ 1 00
10
~ O
BY
\ O O
O \:,
.
~_~
·
o
.
-2 X 1O - 8M
0.001 . 1 . I . 1 . 1 . ~
0 20 40 60 80 100
Ti me, Or
FIGURE 5 Concentration of methotrexate in mouse plasma. Open circles, single dose of
350 mg/kg i.v.; closed circles, constant infusion of 0.8 ~g/h. SOURCE: Zaharko (1975).
lethal toxicity. If severe inhibition of greater than 90% is considered, DNA
synthesis is inhibited relative to control for 35 h. Figure 7 shows similar
data for a 10-fold higher rate of infusion (10 ~g/h) but of shorter duration
(17 h). Like the previous schedule, this one is designed to just barely
avoid lethal toxicity at the end of the infusion period (Table 2 of Zaharko
et al., 1977~. An inhibition time virtually identical to that above was
observed, a period of about 30 h.
Further indication of DNA synthesis inhibition time as an appropriate
measure of toxicity comes from observing the trend in lethality if, at a
fixed infusion rate, infusion times are lengthened. As expected, lethality
increases. For 10 fig of MTX/h, lethality jumps from 20% following a
24-h infusion to 90% following a 56-h infusion (Zaharko et al., 19771.
OCR for page 422
200
I
~ 1
o
at
I
o
L,
ILL
I foot
fir
50
|I SEM Controk
~ SEM Controk
\
422 PAUL F. MORRISON ET AL.
am_
1 , ~ ,
i
l
-
b~fus~on
_ _ _
1\
~ -1
1 1
10 20 30 40 50
~ 70 80 90
HOURS
FIGURE 6 Incorporation of 3H into DNA of small intestine following an MTX infusion of
1 ~g/h for 48 h and an injection of [3H]thymidine (dark circle) or [3H]uridine injection (open
circle). Vertical standard error bars indicate the range of the two mice used per point. At least
six controls were used for each experiment. The first 10 cm of the small intestine was used
from each mouse. SOURCE: Zaharko et al. (1977).
Lethality correlation with total dose exists for a fixed infusion rate, but
not when extended over a range of infusion rates.
To predict toxic response from a given dose and schedule, the phar-
macokinetic model of MIX must be coupled to the inhibition of DNA
OCR for page 423
Methotrexate: Pharmacokinetics and Toxicity 423
I ~ ~ ~ 1 ~
290
C)
~ 1~
on
C)
lo
he
o
0 100
at
50
_
~ SEW Control
1
/1 ~
_
\Intus~on ~ ~
- \ ~~-
_
' -
-
1
610 70 110 90
10 20 30 40 50
HOURS
FIGURE 7 Same as described in the legend to Figure 6, except that the MTX infusion was
10 ,ug/h for 17 h. Solid dots without vertical error bars are an identical experiment with MTX
(intraperitoneal dose of 25 mg/kg) given at the start of infusion; mean of two mice; the range
was not included, but it was similar to those in other experiments. SOURCE: Zaharko et al.
(1977).
synthesis. In the mid-1970s, this was accomplished very simply by ob-
serving that recovery of DNA synthesis occurred when MTX plasma
concentrations, as measured by a competitive binding assay, fell below
10-8 M (Chabner and Young, 1973~. Figure 8 shows that recovery in
OCR for page 424
424 PAUL F. MORRISON ET AL.
175 ,
150
125
2 100
a
75
50
25
- Non tumor bearing
o- - -a Tumor bearing
( ) Dow
:
O 1~7
O_
_~>'
_~ ,
' 1,,,,, , O' O
10 - 8
[MTX] plasma
t
l
I P P
(350)/ ,'{50}
I ,
I , ,
I , ,
I ,'(350},/
11° /'i50} (A
I I , /
I .
l
(5)
10~9
FIGURE 8 Incorporation of [3H]ur~dine into DNA of mouse bone marrow as a percentage of
the pretreatment rate. The indicated doses are in milligrams/kilogram, administered intraper~-
toneally. SOURCE: Chabner and Young ( 1973).
bone marrow was a strong function of this pseudo-threshold following
bolus dosing from 5 to 350 mg/kg. Thus, the pharmacokinetic model
outlined earlier only needed to be solved for the length of time that the
plasma concentration remained above 10-8 M to infer toxic response. The
10-8 M value was interpreted as the free MTX concentration in equilibrium
with just sufficient free reductase (about 5% of the total) to allow re-
sumption of thymidylate synthesis.
Since the mid-1970s, the interpretation of these observations has become
much more complex. The reason for this was the discovery of significant
metabolism of MTX. When only low bolus doses were considered, cy-
totoxic concentrations of MTX did not exist for a sufficiently long period
for significant metabolism to be detected. With the introduction of high-
dose protocols, and their long infusion times, in the mid-1970s (Frei et
al., 1975; Jaffe et al., 1978), metabolism became apparent, and new assays
were developed for the detection of metabolites.
Some of these metabolic events, particularly the polyglutamation of
MTX (Balinska et al., 1982; Baugh et al., 1973; Jolivet et al., 1982;
OCR for page 425
Methotrexate: Pharmacokinetics and Toxicity 425
Momson and Allegra, 1987) were shown to create very active drug forms
that cleared from the intracellular milieu of cells at rates that were far
slower than the clearance of parent drug from the plasma. Hence, a ratio-
nale was needed to explain just why 10-8 M plasma concentrations have
been observed to correlate so well with recovery of DNA synthesis and,
more importantly, to identify the conditions under which this correlation
might break down and when another approach to bridging MTX phar-
macokinetics to toxicity would be required. Thus, there is no theoretical
reason for expecting that when the 10-8 M concentration is reached, DNA
synthesis should immediately resume under all protocols.
- A full rationale requires more research, but preliminary analysis indi-
cates that, under single-bolus conditions (as employed in Figure 8), cells
are incapable of producing truly inhibiting quantities of polyglutamates,
leaving the parent drug form alone to account for inhibition and recovery
of DNA synthesis as observed. Under long-term infusion or closely spaced
multiple bolus conditions, however, cells have much more time to produce
polyglutamates and attain inhibiting levels of these compounds. Under
these circumstances, MTX pharmacokinetic models need to be expanded
to include polyglutamation kinetics, and intracellular MTX polyglutamate
concentrations, rather than plasma concentrations of parent compound,
need to be correlated with levels of DNA synthesis.
SUMMARY
In summary, we have seen that (1) only about half of the parameters
of the (nonmetabolizing) physiological pharmacokinetic model can be
obtained from chemical invariants and interspecies scalings; (2) dose scal-
ing applies to the large-volume organ regions (e.g., kidney, liver, plasma)
for a few hours after injection, but never to the principal organs of toxicity,
the sensitive tissues of the marrow and intestinal mucosa; and (3) toxic
response is a strong function of dose scheduling, correlating neither with
total drug dose nor area under the MTX-plasma concentration curve, but
with the time that MTX (and polyglutamate) concentrations remain above
inhibiting levels of dihydrofolate reductase.
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Representative terms from entire chapter:
bone marrow
