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Antimicrobial Agents and Chemotherapy, December 2000, p. 3414-3424, Vol. 44, No. 12
0066-4804/00/$04.00+0
Copyright © 2000, American Society for Microbiology. All rights reserved.
Mefloquine Pharmacokinetic-Pharmacodynamic Models:
Implications for Dosing and Resistance
Julie A.
Simpson,1,2
Emmeline R.
Watkins,3
Ric N.
Price,2,4
Leon
Aarons,5
Dennis E.
Kyle,6,
and
Nicholas
J.
White1,2,*
Faculty of Tropical Medicine, Mahidol
University,1 and Department of
Immunology and Medicine, U.S. Armed Forces Research Institute of
Medical Sciences,6 Bangkok, and Shoklo
Malaria Research Unit, Mae Sod 63110, Tak Province,4
Thailand, and Centre for Tropical Medicine, Nuffield
Department of Clinical Medicine, John Radcliffe Hospital,
Headington,2 and Wellcome Trust
Centre for the Epidemiology of Infectious Diseases, University of
Oxford, Oxford,3 and School of
Pharmacy and Pharmaceutical Sciences, University of Manchester,
Manchester,5 United Kingdom
Received 11 October 1999/Returned for modification 11 April
2000/Accepted 11 September 2000
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ABSTRACT |
Antimalarial resistance develops and spreads when spontaneously
occurring mutant malaria parasites are selected by concentrations of
antimalarial drug which are sufficient to eradicate the more sensitive
parasites but not those with the resistance mutation(s). Mefloquine, a
slowly eliminated quinoline-methanol compound, is the most widely used
drug for the treatment of multidrug-resistant falciparum malaria. It
has been used at doses ranging between 15 and 25 mg of base/kg of body
weight. Resistance to mefloquine has developed rapidly on the borders
of Thailand, where the drug has been deployed since 1984. Mathematical
modeling with population pharmacokinetic and in vivo and in vitro
pharmacodynamic data from this region confirms that, early in the
evolution of resistance, conventional assessments of the therapeutic
response 
28 days after treatment underestimate considerably the level
of resistance. Longer follow-up is required. The model indicates that
initial deployment of a lower (15-mg/kg) dose of mefloquine provides a greater opportunity for the selection of resistant mutants and would be
expected to lead more rapidly to resistance than de novo use of the
higher (25-mg/kg) dose.
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INTRODUCTION |
Malaria is the most important
parasitic disease of humans. Malaria parasites infect a large
proportion of the indigenous peoples of tropical countries, and the
infection is estimated to cause between 0.5 million and 2.5 million
deaths each year, mostly in sub-Saharan Africa. This heavy death toll
is held in check by the widespread availability of cheap and effective
antimalarial drugs. The malaria parasite, however, has evolved
mechanisms of resistance to most of these available antimalarials, and
morbidity and mortality rise as efficacy falls (18).
Resistance is thought to arise from spontaneous chromosomal mutations
in malaria parasites which confer a selective survival advantage in the
presence of antimalarial drugs. Selection of resistant mutants is most
likely to occur when a large number of parasites encounter submaximal
concentrations of the antimalarial drug in blood. At these
concentrations drug-resistant parasites are more likely to have a
significant survival advantage over drug-sensitive parasites, as most
initial resistance mutations do not confer very large reductions in
susceptibility (18). De novo mutation arises rarely. These
mutants will spread only if they survive to be transmitted, and their
resistance advantage outweighs any fitness disadvantage the resistance
mutation may confer. Selection can occur with inadequate primary
treatment or when a newly acquired infection encounters residual
concentrations of antimalarials following treatment of a previous
infection. In the latter case the chance of resistance selection is
higher for antimalarial drugs with long terminal elimination
half-lives, as, by definition, these exist in the blood at
subtherapeutic concentrations longer (14). Once a resistant
mutant parasite population has been selected in an individual, the
probability and rate at which the mutants spread will depend on several
factors including the degree of reduced susceptibility, the
characteristics of the parasite population, and the pattern of drug
use. The same factors which give rise to de novo selection will also
facilitate spread, although for mutations which confer small reductions
in susceptibility, preferential survival is initially more likely when
newly acquired infections encounter residual levels in blood. Only when
considerable resistance has developed can such parasites survive the
much higher concentrations of antimalarial drugs in blood that follow
immediately after treatment is given.
Mefloquine is an antimalarial drug used for the oral treatment of
uncomplicated multidrug-resistant falciparum malaria. It has a terminal
elimination half-life of 2 to 3 weeks in patients with malaria
(16). The elimination phase of the drug is bi- or
triexponential, with a slow decline in concentrations in blood in the
terminal phase, which provides a considerable period during which blood
mefloquine concentrations are associated with intermediate (e.g., 20 to
80%) inhibitory activity against Plasmodium falciparum. Thus, as for bacteria (8), an important factor that
determines the propensity to develop resistance may be the time taken
in vivo for drug concentrations to fall between approximately 80 and
20% of the concentrations at which they exhibit maximum inhibitory effects against the prevalent parasite populations (i.e., a combination of the pharmacokinetic and pharmacodynamic properties of the drug) (18).
This paper uses mathematical modeling based on in vivo and in vitro
data to compare the development of resistance with the de novo use of
the two most widely used antimalarial doses of mefloquine (15 and 25 mg/kg of body weight).
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MATERIALS AND METHODS |
Mathematical model.
The aim of this section is to find a
mathematical equation that describes the change in total parasite
burden with time, in the presence of drug.
For de novo selection of resistant mutants, if one malaria parasite in
every 10x malaria parasites contains a mutation
that confers a significant reduction in susceptibility to the drug
being used, then the probability that a patient harbors such a
resistant mutant is
(1/10x) · Pt, where
Pt is the number of parasites in a single
patient at time t.
To find a mathematical equation that describes the change in total
parasite burden over time in the presence of the drug,
a slightly
altered form of the mathematical model published by
Hoshen et al.
(
3) has been
used.
Pt is a balance between the average parasite
multiplication rate and the proportion of parasites that are killed and
cleared
by the antimalarial and host defenses. Thus, the change in
parasitemia
can be described as (
dP/
dt) =
a ·
P 
f(
C) ·
P f(
I) ·
P, where
a is a
parameter representing the growth rate constant of the
parasite,
f(
C) is a function, dependent on the
concentration of
the drug (
C), that represents the killing
of the parasites; and
f(
I) is a function that
represents the host's background immunity
to
malaria.
The host contribution, which reflects background immunity, contributes
relatively little to the drug effect at high concentrations
but becomes
important at low drug concentrations. It will not
be used further in
this analysis, although in areas of high stable
transmission where
partially effective or ineffective drugs are
used, it is the main
determinant of therapeutic outcome. Thus,
(
dP/
dt) =
a ·
P f(
C) ·
P.
Killing is considered a first-order process which continues unchanged
throughout the process of parasite elimination (
1).
It
should be noted that malaria is exclusively an intravascular
infection
(extravascular forms are not pathogenic) and that the
antimalarial
activity is related to the concentrations of free
(unbound)
antimalarial drug in
plasma.
Parasite killing can then be described by a sigmoid
Emax model:
where
k1 is the first order rate constant
of parasite killing,
is the slope of the concentration-effect
curve,
C is the
antimalarial drug concentration, and
C50 is the drug concentration
which kills 50%
of the parasites. The plasma antimalarial drug
concentration in vivo is
not constant; it rises as the drug is
absorbed and then declines over
time as the drug distributes throughout
the body and the drug is
eventually eliminated. In the case of
mefloquine, the elimination phase
has been shown to be biexponential
or triexponential (
16).
Assuming that the intermediate concentrations
which are selective occur
only during the terminal phase (at least
at low or intermediate levels
of resistance), a monoexponential
elimination phase corresponding to
the terminal elimination phase
of the drug was used. Therefore,
C =
C0 ·
e
k · t where
t is time (in days),
k is the terminal
elimination rate
constant of mefloquine, and
C0
is maximum concentration of mefloquine
(i.e.,
Cmax).
Pt was determined by integrating
(
dP/
dt) (see the
Appendix). The following
solution results:
where
P0 is the total parasite burden at
time zero (i.e., before administration of
mefloquine).
Parameter estimation and statistical analysis.
In nonimmune
subjects, the multiplication rate of the asexual stages of P. falciparum in the blood averages 6-fold and can reach 20-fold per
cycle (5, 6). For this simulation, a was calculated by assuming that a single asexual malaria parasite multiplies 10-fold every 2 days. This gives a growth rate constant a of 1.15 (ln 10/2). The terminal elimination rate constant
(k) of the drug was assumed to be 0.036 (per day)
(11) following administration of a treatment dose of
mefloquine. The maximum parasite killing rate resulting from mefloquine
was assumed to be 99% per cycle or 90%/day, which corresponds to a
k1 of 3.45/day. This corresponds to a
parasite reduction ratio (PRR) of 100, a relatively poor antimalarial
effect, but one that has been documented and that is associated with
mefloquine resistance (12, 18). Killing rates up to 99.9%
per cycle may occur with mefloquine. The artemisinin derivatives have
been shown to have the highest PRRs of all the antimalarial drugs:
greater than 10,000, or a reduction of 99.99% parasites per 2-day
asexual life cycle (17). As the mutational events which may
confer resistance occur randomly, resistant mutants are more likely to
occur in high-biomass infections. We have therefore chosen a worst-case
scenario of a relatively high-biomass P. falciparum
infection corresponding to a total parasite burden at time zero of
1012 parasites in an adult (which corresponds to a parasite
count of approximately 100,000/µl, or 2% parasitemia). The parameter estimates chosen and presented above do not represent an average patient but, instead, represent a patient with a relatively high level
of parasitemia from an area with existing mefloquine resistance.
For the parameter
C0 the value of 1,200 ng/ml
was chosen and was derived from population pharmacokinetic modeling of
data
for 24 patients treated with a single mefloquine dose of 25 mg/kg
as monotherapy (
11). The parameter estimates and their
respective
variances from the derived population pharmacokinetic model
(Table
1) were also used to simulate
1,000 pharmacokinetic profiles.
The distribution of the intersubject
variability of the pharmacokinetic
parameters was lognormal, while the
residual error was normally
distributed (Table
1). The intersubject
variability values for
the different pharmacokinetic parameters were
assumed to be independent
of each other. The 1,000 simulations were
performed with the computing
package QBASIC. These simulated profiles
were used to obtain estimates
of the lowest and highest mefloquine
concentrations that would
be achieved in a population.
We assumed that one schizont releases 10 potentially viable merozoites
(approximately half of the average total number released),
which means
that the MIC at which the net parasite multiplication
rate is unity
corresponds approximately to the 90% effective concentration
(EC
90).
Now, if the MIC is the concentration at which the total parasite burden
is not changing (i.e., a transient steady state),
then
(
dP/
dt) =
a ·
P f (MIC) ·
P = 0. Substituting for
f(MIC),
Assuming that the MIC is approximately equal to
EC
90,
The EC
90 in vivo is unknown, but it must be related
to the EC
90 in vitro. However, because in vitro
susceptibility assessments
are conducted in the absence of plasma (to
which mefloquine is
reported to bind avidly), platelets, and white
cells, the two
are not equivalent. Unfortunately, because mefloquine
also binds
to laboratory ware, notably plastic, precise estimates of
plasma
protein binding are not available. Thus, EC
90 (in
vivo) is equal
to
m · EC
90 (in vitro), where
m is an unknown parameter. For this
paper
m was
given the value of 10. This value was chosen
empirically.
The EC
90 (in vitro) was derived from modeling of in vitro
concentration-effect curves, where the effect measure is inhibition
of
parasite uptake of [
3H]hypoxanthine. It was assumed that
the slope (
) of the concentration-effect
curve in vivo is the same
as that observed in
vitro.
For the parameters
and EC
90, population estimates were
derived from nonlinear mixed-effect modeling of in vitro
concentration-effect
curves for mefloquine (
7). Nonlinear
mixed-effects models produce
parameter estimates for the complete drug
population and posterior
estimates for each infecting
isolate.
The data set contained a total of 415 in vitro concentration-effect
curves for
P. falciparum isolates collected by three
different
laboratories based in
Thailand.
For in vitro susceptibility testing, all laboratories used a
semiautomated dose-response assay as described by Desjardins
et al.
(
2) and Webster et al. (
15) and used the same
beta
counter. Growth of synchronous parasite isolates or cultures was
estimated by using parasite uptake of a radioactive DNA precursor,
[
3H]hypoxanthine, as a measure. The percent growth at
different
mefloquine concentrations was calculated as the proportion of
the counts in the drug-free wells. Background counts (unparasitized,
drug-free wells) were subtracted from all
counts.
The U.S. Armed Forces Research Institute of Medical Sciences, Bangkok,
Thailand, measured 345 curves. The samples used in
the dose-response
assays were collected in field trials conducted
throughout Thailand
between 1990 and
1994.
The Wellcome Unit, Bangkok, measured 44 dose-response curves. The
samples were collected during 1997 and 1998 from the Hospital
for
Tropical Diseases, Bangkok, and on the western border of
Thailand.
The Shoklo Malaria Research Unit measured 26 dose-response curves.
These were collected from refugee camps situated along
the western
border of Thailand. The mefloquine sensitivities of
the 415 isolates
cover a wide range, from fully sensitive to highly
resistant, which
allow estimates of the best and worst possible
scenarios for
and
EC
90.
The pharmacodynamic model fitted was the following sigmoid inhibitory
effect model:
This is a reparameterized version of the standard sigmoid
inhibitory effect model, where EC
50 equals
EC
90/9
1/
.
E represents the
proportion of uptake of [
3H]hypoxanthine in the
nucleoprotein of the parasites in drug-free
control wells corresponding
to unrestrained growth in vitro. The
maximum effect occurs when there
is no uptake of [
3H]hypoxanthine (no growth).
E0 represents the minimum percent
growth,
Emax is the maximum percent growth,
EC
90 is the concentration
of mefloquine required to inhibit
90% of the control parasites'
hypoxanthine uptake, and
is the
slope of the curve. It should
be noted that the exact relationship
between inhibition of hypoxanthine
uptake and growth inhibition has not
been
characterized.
Interstrain variabilities in
Emax,
E0,
, and EC
90 were modeled with
multiplicative error models. Multiplicative error models
ensure that
the individual strain parameters (e.g.,
Emax,i)
are greater than zero and
that their distributions are skewed
to the right. The models are as
follows:
The interstrain variability (
) values for the four parameters
listed above were assumed to be independent of each
other.
The residual intrastrain error was modeled by using an additive error
model since the error between the observed and predicted
values was
observed to be constant:
Eij = Epij + 
ij.
Emax,i,
E0,i,
i,
and EC
90,i are the pharmacodynamic parameters
for the isolate, and,
Emax,
E0,
, and EC
90 are the population
means.
iEmax,
iE0,
i, and
iEC90 are random effects with
zero mean and variances
2Emax,
2E0,
2,
and
2EC90, respectively. They represent
the interisolate variability
for each of the parameters. The magnitude
of this variability
is expressed as a coefficient of variation.
Eij is the
jth measure
of effect for
the
ith strain, and
Epij is the
jth predicted measure
of effect for the
ith
strain.
ij is the residual intrasubject
error
term and is assumed to be randomly and normally distributed
with a mean
of zero and a variance of
2. The nonlinear mixed effects
procedure (NLME) procedure (
7)
of the SPLUS data program
(SPLUS 4.5 for Windows; Mathsoft, Inc.)
was used to calculate estimates
of the population pharmacodynamic
parameters
(
Emax,
E0,
,
EC
90) and their respective interstrain
variances
(
Emax,
E0,
,
EC90). The program also provides estimates of the
residual random
intrastrain error (
) and the variances of the
interstrain error
terms
(
2Emax,
2E0,
2 ,
2EC90). The goodness of fit of each
model (e.g., models with different
numbers of random effects)
was determined by the change in the
objective function (minus twice the
log likelihood of the data).
A significant drop in the objective
function (with use of the
2 distribution) determined the
model that best described the data.
The goodness of fit of each model
was also determined by the precision
of the parameter estimates and the
examination of the scatter
plot of residuals versus the predicted
measure of
effect.
| |
RESULTS |
In vitro concentration-effect curves.
Data collected from
three different laboratories in Thailand were modeled to estimate
parameters that describe the in vitro concentration-effect
relationships for mefloquine. The model that gave the best fit to the
three different sources of data was the inhibitory sigmoid
Emax effect model with
Emax, EC90, and fitted as random
effects. Fitting of E0 as a random effect did
not significantly reduce the objective function. The mean population
pharmacodynamic parameters of the final model for the isolates from the
three laboratories were similar (Table
2). These data were then combined, and
the sigmoid Emax model was fitted to all 415 isolates (Table 2). The population estimate of EC90
(population estimate, 50.4 ng/ml) had a 95% prediction interval (PI)
from 213 ng/ml down to 12 ng/ml. The population estimate of the slope
of the concentration-effect curve was 2.50, with a 95% PI of 1.22 to
5.13. The observed and population predicted effect measures (percent
uptake of [3H]hypoxanthine) versus mefloquine
concentrations for the three laboratories are shown in Fig. 1a, b, and
c.
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TABLE 2.
Population pharmacodynamic parameters derived from
nonlinear mixed-effects modeling of the in vitro mefloquine
susceptibility data
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FIG. 1.
Percent uptake of [3H]hypoxanthine
compared to that in drug-free control wells for various mefloquine
concentrations. The solid line shows the fit of the data and represents
the predicted concentration-time profile for the population mean. The
outer, dashed lines represent the 90% prediction intervals. The three
panels show the fits for the following data sets: U.S. Armed Forces
Research Institute of Medical Sciences (a), Wellcome Unit, Bangkok (b),
and the Shoklo Malaria Research Unit (c).
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Pharmacokinetics of mefloquine.
The terminal elimination rate
constant is dose independent, and so the time over which the infecting
parasite population is exposed to intermediate (20 to 80%) inhibitory
concentrations is unrelated to the dose. In the case of mefloquine this
is approximately 11 days (Fig. 2). An
important factor driving the selection of resistance, however, is the
number of parasites (Pt) exposed to these drug
levels which give submaximal effects. The concentration range in whole
blood that gave intermediate levels of growth inhibition was chosen as
400 to 600 ng/ml. As the precise relationship between in vivo and in
vitro concentration-effect relations is not known, this range cannot be
defined precisely. This range was chosen because in 1990, when
mefloquine resistance was first detected in Thailand, the mean (95%
CI) concentration in serum at the time of first recrudescence was 638 ng/ml (546 to 730 ng/ml) (9). This represented a
concentration capable of sustaining growth in the parasites infecting
29% of patients. We chose a slightly lower concentration range to
reflect an earlier stage of resistance. These parasites exposed to
"selective" levels of mefloquine in blood are derived from two
sources: (i) those remaining from the initial infection, which, in
turn, depends on the starting biomass and susceptibility, and (ii) the
frequency with which newly acquired infections would emerge during this
period.
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FIG. 2.
Simulated pharmacokinetic profiles for the two standard
mefloquine doses, 15 and 25 mg/kg, obtained with the parameter
estimates given in Table 1.
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Predicting therapeutic outcomes.
Figure
3 shows the model simulations of the
total parasite numbers versus time for the two commonly used mefloquine
doses of 15 and 25 mg/kg, based on the parameter estimates in Table 3. The estimate for
C50 is derived from the population estimates of
EC90 and . Both EC90 and are the
population estimates from nonlinear mixed-effects modeling of the in
vitro data for isolates from Thailand.
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FIG. 3.
Total malaria parasite burden versus time for the two
standard mefloquine doses, 15 and 25 mg/kg, based on the PK/PD
parameter estimate in Table 3. The initial parasite burden corresponds
to a parasite count of approximately 100,000/µl, or 2% parasitemia,
in an adult with falciparum malaria.
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TABLE 3.
Parameter estimates derived from population
pharmacokinetic (C0 and k) and
pharmacodynamic ( and C50) modeling and a
previously published article (a and
k1)a
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With the lower dose there are more parasites at all times (including
during the period of intermediate or selective mefloquine
concentrations) compared to the number of parasites with the higher
dose of 25 mg/kg. If the parasite populations are all more drug
sensitive than those given in the example, then the differential
advantage of the higher dose is smaller. Thus, as resistant mutants
are
selected, the differential advantage increases, accelerating
the
apparent emergence of resistance. Furthermore, it is apparent
that with
the starting parameters chosen for the model in this
case (which
represented a worse-case scenario and which were consistent
with a
significant level of resistance), the patient will not
be cured with a
dose of 15 mg/kg for any total parasite burden
on admission since a
nonimmune person is cured of malaria only
if the total parasite burden
falls below one parasite. The same
patient would be cured with a dose
of 25 mg/kg if the total burden
on admission did not exceed
10
9 parasites. With lower levels of mefloquine resistance
(or greater
background immunity), an increasing proportion of patients
treated
with 15 mg/kg would be
cured.
Other factors besides the dosage can affect the maximum concentration
achieved. Acute malaria may affect absorption of drugs
because of
reduced food intake, vomiting, reduced gastric motility
and visceral
blood flow and change the apparent volume of distribution.
Figure
4 depicts the parasite-time profiles for
the population
mean
Cmax following the
administration of 25 mg of mefloquine
per kg (defined as
C0 in our paper) and for the minimum and maximum
Cmax values for the 1,000 simulated
pharmacokinetic profiles.
With a dose of 25 mg/kg the mean
Cmax was 1,200 ng/ml, with a
range from 400 to
7,440 ng/ml. With the starting parameters of
the model, the absolute
minimum
Cmax required to cure an adult
patient
with an admission parasitemia of 2% is 1,400 ng/ml. Nonlinear
mixed-effects modeling of the 1,000 simulated pharmacokinetic
profiles
produced parameter and variance estimates similar to
those used in the
original simulation of the 1,000 profiles (Table
1).
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FIG. 4.
Relationship between parasite clearance over time and
maximum mefloquine concentration (C0) in blood.
In this example, P0 is 1012,
a is 1.15/day, k is 0.036/day,
k1 is 3.45/day, is 2.5, and
C50 is 665.4 ng/ml.
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The effects of varying the values of the parameters
, MIC in vivo,
and
m on the parasite number-versus-time profiles are
shown
in Fig.
5,
6, and
7.
The flatter the slope of the concentration-effect
curve, the more
likely the patient will suffer a subsequent recrudescence
of the
infection (Fig.
5). For the lower limit (
= 1.22) and
the
population mean estimate (
= 2.50), the parasites never cleared
and their numbers started to rise again about 3 weeks following
treatment. Patients will start to fail treatment with mefloquine
if the
slope of the concentration-effect curve drops below 3.5.
Increases in
the in vivo MIC will also increase the risk of treatment
failure (Fig.
6). For example, if the in vivo MIC is 120 ng/ml,
all the parasites are
cleared from the body in less than 2 weeks.
If the MIC in vivo
increases to 2,126 ng/ml (the upper limit of
the 95% PI of the
population estimate), then the level of parasitemia
will continue to
rise following treatment (
R3 resistance).
If
the MIC in vivo is fivefold the EC
90 in vitro
(i.e.,
m = 5), then
all the parasites are cleared from
the body at 2 weeks (Fig.
7).
However, if the MIC in vivo is at least
20 times larger than the
EC
90 in vitro (i.e.,
m = 20), the level of parasitemia keeps rising
following treatment. For
m equal to 10 and 15, the parasites
never
clear and their numbers start to rise again at about 3 and 2 weeks,
respectively.
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FIG. 5.
Relationship between parasite clearance over time and
the slope of the concentration-effect curve (). In this example,
P0 is 1012, a is
1.15/day, k is 0.036/day, C0 is 1,200 ng/ml, k1 is 3.45/day, and
C50 is 665.4 ng/ml.
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FIG. 6.
Relationship between parasite clearance over time and
the MIC in vivo. In this example, P0 is
1012, a is 1.15/day, k is 0.036/day,
C0 is 1,200 ng/ml, k1 is
3.45/day, and is 2.5.
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FIG. 7.
Relationship between parasite clearance over time and
m (scalar value relating EC90 in vitro to MIC in
vivo). In this example, P0 is 1012,
a is 1.15/day, k is 0.036/day,
C0 is 1,200 ng/ml, k1 is
3.45/day, is 2.5, and EC90 in vitro is 50.43 ng/ml.
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Ratio of Cmax to MIC in vivo.
The
ratio of the Cmax to the MIC, a widely used
parameter in anti-infective drug pharmacodynamic modeling, is probably
an important determinant of outcome in the case of antimalarial
treatment with mefloquine.
The function
Pt can be rewritten as
where
R is equal to
C0/MIC.
R will decrease with increasing resistance in areas where
the treatment dose is fixed, and
R will remain constant if
the treatment dose is increased commensurate
with the increase in
resistance.
Figure
8 shows the in vivo parasite
number-time profiles for
R equal to 1, 1.5, 2, and 3. If the
Cmax is three times greater
than the MIC, the
patient will be cured of malaria (all the asexual-stage
parasites will
be cleared from the body within 3 weeks). The infection
will recrudesce
if the
Cmax achieved is only twofold the in vivo
MIC.
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FIG. 8.
Relationship between parasite clearance over time and
the ratio of maximum mefloquine C0 to MIC (R).
In this example, P0 is 1012,
a is 1.15/day, k is 0.036/day,
k1 is 3.45/day, and is 2.5.
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We can define
RC as the minimum value of
R at which the patient will still be cured of malaria.
Rc occurs when the minimum
value of
Pt is less than or equal to 1. To find the
minimum value
of
Pt, the derivative
(
dP/
dt) is set equal to zero and the equation
is
solved for
t. This gives the time when the minimum
parasitemia
(
tmin) occurs:
tmin = log
e(
R1/k).
Substitution of
tmin into
Pt gives the following equation:
The above equation cannot be solved analytically; therefore,
RC is derived
numerically.
Figure
9 plots
RC
over the full range of possible parasite burdens.
View larger version (8K):
[in this window]
[in a new window]
|
FIG. 9.
Relationship between the minimum value of
C0 to MIC ratio (RC)
required to clear all parasites and the total body parasite burden on
admission. In this example, a is 1.15/day, k is
0.036/day, k1 is 3.45/day, and is 2.5.
|
|
Benefit of a mefloquine dose of 25 mg/kg over a dose of 15 mg/kg.
As stated earlier, for patients with comparable infections,
the total parasite burden exposed to submaximally effective blood concentrations is greater for those patients receiving 15 mg/kg than
for those patients receiving the larger dose of 25 mg/kg.
If we assume that when the whole-blood mefloquine concentration falls
below 600 ng/ml the patient is exposed to drug levels
which give
submaximal effects (i.e., 600 ng/ml represents the
minimal
parasiticidal concentration), then blood mefloquine levels
fall below
the minimal parasiticidal concentration on day 6 for
those patients
receiving 15 mg/kg and on day 20 for those receiving
25 mg/kg. On these
days the total parasite burden predicted for
patients receiving 15 mg
of mefloquine per kg in the earlier example
was 4.87 × 10
10 parasites, and for those receiving 25 mg/kg it was
only 1,152
parasites; this equates to a 4.23 × 10
7-fold difference. If the selective range is lower, all
the parasites
will have been eliminated by mefloquine before
concentrations
decline to the selective range if 25 mg/kg is given
initially.
Time to recrudescence.
The interval between administration of
mefloquine antimalarial treatment and recrudescence of the patient's
infection depends on the killing rate of the drug and the level of
resistance of the parasites. Figure 10
is a three-dimensional plot illustrating the relationship between three
parameters: the time of recrudescence, k1, and
the in vivo MIC. To create Fig. 10, parasite number-versus-time curves
were simulated for patients receiving the high dose of mefloquine (25 mg/kg). The pharmacokinetic parameters used were the mean parameter
estimates from the population pharmacokinetic modeling of mefloquine
monotherapy conducted in northwestern Thailand: Cmax = 1,200 ng/ml and k = 0.036 /day (11). Those curves in which the level of
parasitemia fell below the level of detection (defined as 50 parasites/µl, or 5 × 108 parasites in the body)
before day 7 were selected. If k was 1.2 and the MIC was
360 ng/ml, the parasitemia does not clear by day 7 (R2 or R3 resistance).
The time of recrudescence is the time at which the parasites can be
detected again microscopically. As k1 increases,
that is, the drug has a higher PRR or greater parasiticidal activity,
cure rates will increase, but for those few failures which do occur,
the interval from treatment to recrudescence occurs later. With higher
levels of resistance (i.e., a high MIC), the patients' infections will
recrudesce earlier. The time to recrudescence was normally distributed
with a mean ± standard deviation of 42 ± 11 days, with a
range from 20 up to 64 days. Table 4
presents the distribution of times to recrudescence for different
levels of resistance (i.e., various MICs in vivo).
View larger version (26K):
[in this window]
[in a new window]
|
FIG. 10.
Time to recrudescence following treatment with
mefloquine at 25 mg/kg as a function of MIC in vivo and killing rates
(k1). The z axis is the time to
recrudescence, the y axis is the killing rate of mefloquine
(k1), and the x axis is the MIC in
vivo. The pharmacokinetic parameters used in the simulation were the
population mean values as described previously from studies in
northwestern Thailand (11). Nonraised rectangles represent
two possible scenarios: either the patient is cured or at day 7 the
parasites are still detectable. This illustrates that for relatively
drug-sensitive parasites (MIC, < 500 ng/ml) the infections are all
cured with high killing rates and that with low killing rates
recrudescences occur long after the conventional follow-up period of 28 days. Conversely, with highly resistant parasites, long follow-up
(i.e., >42 days) is not necessary.
|
|
| |
DISCUSSION |
The development of resistance to antimalarial drugs is a major
threat to the health of people living in tropical countries. The speed
at which resistance develops is affected considerably by the pattern of
antimalarial drug use. Uncontrolled self-medication with inadequate
treatment courses provides a particularly potent selection pressure to
the development of resistance as it exposes a large number of parasites
to partially effective antimalarial drug concentrations. In this study
the effects of two different systematic antimalarial treatment
strategies are examined by using mefloquine as an example. This is a
particularly relevant example, as resistance to mefloquine has
developed rapidly on the eastern and western borders of Thailand and
the adjacent areas and is now emerging separately in Vietnam. This
could have been delayed or perhaps prevented. When new drugs are
introduced, dose-ranging studies are performed to determine the optimum
dose and treatment schedule on the basis of the therapeutic ratio. For
most anti-infective drugs, with the notable exception of
antituberculous and antiretroviral drugs, the prevention of resistance
is usually not considered in this assessment. This conventional
therapeutic appraisal usually leads to the conclusion that the smallest
dose that gives an "acceptable" cure rate should be deployed
initially. For slowly eliminated antimalarial drugs, such as
mefloquine, this will lead more rapidly to resistance than if a higher
dose were deployed de novo. There are two reasons for this. First, the
lower dose chosen initially, which for mefloquine was 15 mg of base/kg,
provides a greater opportunity for the de novo selection of genetic
mutants, such as those containing increased numbers of copies of the
pfmdr 1 gene, with significantly reduced susceptibility
(10). This is because there is a greater probability of
failing to achieve concentrations which would kill a mutant parasite
and its progeny. Second, once these mutants have arisen and have been
transmitted, provided they are highly mefloquine resistant (see below),
they will be more likely to survive low-dose treatment in subsequent
hosts. This increased survival probability results in an increase in the proportion of resistant mutant parasites. Thus, resistance is
selected more efficiently by the general use of a lower dose (15 mg/kg)
than a higher dose (25 mg/kg). It should be noted that we simulated the
situation in an area of low transmission where background immunity is
low or absent (such as much of Southeast Asia and South America). In
areas of high stable transmission, host immunity may be sufficient to
clear infections with resistant parasites. In addition, a significant
proportion of infections are transmitted from individuals who do not
receive antimalarials. These two factors reduce the selection of
resistant mutants and retard the evolution of drug resistance.
In the pharmacokinetic-pharmacodynamic models presented here, we have
assumed dose linearity for mefloquine, but recent studies indicate that
acute malaria reduces oral mefloquine bioavailability (11).
If the higher dose of mefloquine is split (15 mg/kg and then 10 mg/kg),
the second part of the dose is associated with a disproportionate
increase in the blood drug level and a 50% increase in the area under
the concentration-time curve. Thus, the 66% higher dose has greater
bioavailability and would be even less likely to select for resistance.
The relationship between EC90 (in vivo) and
EC90 (in vitro) for mefloquine is unknown. The in vivo
concentration-effect curve is shifted to the right of the in vitro
concentration-effect curve because of binding to proteins and other
factors. Plasma or whole blood drug levels measured in vivo include
free (unbound) drug and protein-bound drug. Only the drug that is not
bound in plasma is capable of crossing membranes and killing the
malaria parasites. The correlation between in vitro and in vivo
susceptibility is often poor. In vitro attempts to assess mefloquine
plasma protein binding are also confounded by its tendency to stick to
plastics and other laboratory ware. The level of protein binding is
generally considered to be very high, approximately 98%
(4). Concentrations in plasma are slightly lower than
whole-blood mefloquine concentrations; the mean (95% confidence
interval) ratio of the concentration in whole blood to the
concentration in plasma for this population was 1.15 (1.03 to 1.29)
(13). The EC90 (in vitro) was derived from
modeling of in vitro concentration-effect curves in which the effect
measure is inhibition of parasite uptake of
[3H]hypoxanthine. This inhibition of purine uptake is a
measure that correlates with growth inhibition of multiplication, but it does not equate with it.
Mefloquine resistance that leads to treatment failure results in the
preferential transmission of mefloquine-resistant malaria parasites.
This accelerates the spread of resistant strains and may increase the
incidence of malaria. In the case of mefloquine, this could have been
delayed by deploying a higher dose initially, although this would have
had significant cost implications. The benefits derived from deployment
of a higher initial dose of mefloquine cannot necessarily be
extrapolated to other antimalarial drugs. If resistance arises through
single mutations which give very large decreases in susceptibility
(e.g., greater than fivefold), then these mutants would require an
equivalent increase in dose to ensure adequate cure rates. Atovaquone
is an example in which the initial dose may not be important in the
selection of resistance. Resistance is associated with mutants which
are up to 10,000 times less susceptible. An increase in the drug dose
will have no impact on these parasites. However, when resistance
increases in small increments, as for the arylaminoalcohol
antimalarials, and also the initial dihydrotolate reductase mutations
that confer pyrimethamine resistance, then the principles derived
here should apply. Recent studies in Africa indicate frequent
underdosing with pyrimethamine-sulfadoxine in children (F. ter Kuile,
personal communication). This, together with underdosing
through self-medication, acts as an important pressure driving
drug resistance.
The level of antimalarial drug resistance is commonly underestimated.
When in vivo drug assessments are performed, patients are usually
monitored for between 1 and 4 weeks. This is insufficient for
mefloquine. The models presented here explain that recrudescences may
occur well after 1 month following treatment. Furthermore, early in the
evolution of resistance, when there are few recrudescences, a greater
proportion of recrudescences occurs after 28 days. Thus, the degree to
which mefloquine resistance is underestimated (number of treatment
failures in 
28 days divided by total failure rate) is greater at low
levels of drug resistance. These models provide estimates of these values.
Cost is a very important factor in the determination of antimalarial
drug use. If an antimalarial drug treatment costs 60% more (as would
be the case for the high versus the low dose of mefloquine), this could
impose a significant financial burden on developing countries. However,
this must be balanced by the costs of resistance in terms of both
morbidity and perhaps mortality and also the need to fund newer and
usually more expensive alternative drugs. The data and modeling
predictions presented here provide a framework for such a
pharmacoeconomic assessment. There is increasing acceptance that
existing antimalarial drugs should be combined with an artemisinin
derivative as protection from the development of resistance
(18). The extrapolations from the models presented in this
paper still pertain to combination treatment, except that the numbers
of parasites exposed to subtherapeutic drug concentrations in a patient
population are reduced by many orders of magnitude. The differential
benefit of the higher mefloquine dose is retained, however. For the
optimum prevention of resistance, mefloquine should be deployed
initially at a dose of 25 mg/kg, not a dose of 15 mg/kg, and should be
combined with an artemisinin derivative.
| |
APPENDIX |
To find Pt integrate dP/dt:
Substitute
Thus,
(since
C is a function of time and
a,
k1,
, and
C50 are
constants).
Using the separation-of-variables method to integrate
where
| |
ACKNOWLEDGMENTS |
We thank Stephen Duffull for assistance in programming and
helpful comments, Alan Brockman for providing the in vitro data from
the Shoklo Malaria Research Unit, and the efforts of Prasit Sookto and
Theera Wimonwattrawatee in providing the in vitro drug susceptibility
data from the U.S. Armed Forces Research Institute of Medical Sciences.
We thank the dean of the Faculty of Tropical Medicine, Sornchai
Looarrsuwan for his support.
This study was part of the Wellcome-Mahidol University Oxford Tropical
Medicine Research Programme, supported by the Wellcome Trust of Great Britain.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Faculty of
Tropical Medicine, Mahidol University, 420/6 Rajvithi Rd., Bangkok
10400, Thailand. Phone: (66 2) 246 0832. Fax: (66 2) 246 7795. E-mail: fnnjw{at}diamond.mahidol.ac.th.
Present address: Division of Experimental Therapeutics, Walter Reed
Army Institute of Research Washington, DC 20307.
| |
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Antimicrobial Agents and Chemotherapy, December 2000, p. 3414-3424, Vol. 44, No. 12
0066-4804/00/$04.00+0
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Top
Abstract
Introduction
![<LIM><OP>∫</OP></LIM><FR><NU>C<SUP>&ggr;</SUP></NU><DE>C<SUP>&ggr;</SUP>+C<SUB>50</SUB><SUP>&ggr;</SUP></DE></FR> dt=<LIM><OP>∫</OP></LIM><FR><NU>(C<SUB><UP>0</UP></SUB>·e<SUP>−k · t</SUP>)<SUP>&ggr;</SUP></NU><DE>[(C<SUB>0</SUB>·e<SUP>−k · t</SUP>)<SUP>&ggr;</SUP>+C<SUB>50</SUB><SUP>&ggr;</SUP>]</DE></FR> dt](/content/vol44/issue12/fulltext/3414/img019.gif)
