**DOI:**10.1128/AAC.00903-07

## ABSTRACT

The selection and spread of antimalarial drug resistance pose enormous challenges to the health of people living in tropical countries. Most antimalarial drugs are slowly eliminated and so, following treatment in areas of endemicity, provide a gradient of concentrations to which newly acquired parasites are exposed. There is a variable period during which a new blood-stage infection with resistant malaria parasites can emerge from the liver and subsequently produce gametocyte densities sufficient for transmission while reinfection by sensitive parasites is still suppressed. This “window of selection” drives the spread of resistance. We have examined the factors which determine the duration of this window and, thus, the resistance selection pressure. The duration ranges from zero to several months and is dependent on the degree of parasite resistance, the slope of the concentration-effect relationship, and the elimination kinetics of the antimalarial drug. The time at which the window opens and the duration of opening are both linear functions of the terminal elimination half-life. Because of competition from sibling susceptible parasites, the greater risks of extinction with low starting numbers, and opening of the window only when blood concentrations have fallen below the MIC, the window of selection for de novo resistance is narrower than that for resistance acquired elsewhere. The windows were examined for the currently available antimalarials. Drugs with elimination half-lives of less than 1 day, such as the artemisinins and quinine, do not select for resistance during the elimination phase.

The development of antimalarial drug resistance can be divided into two discrete parts: first, the relatively rare de novo emergence event (23) and then the survival, multiplication, and subsequent spread to other humans of the resistant parasite progeny of that event (7, 8, 9, 21). Resistance can emerge de novo within an acute infection, when a spontaneously arising drug-resistant mutant malaria parasite is selected by antimalarial concentrations which are sufficient to eliminate the susceptible parasite population but which still allow the survival and subsequent multiplication of the mutant (23). As parasite numbers are highest in the acute phase of infection, this event is most likely to happen at the time of the mitotic division which preceded the peak parasite density. In a proportion of cases (determined by the multiplication rate), the mutation will have happened in an earlier division (i.e., before drug treatment) and several resistant parasites will be present. The selection of resistant parasites occurs if antimalarial concentrations eradicate the drug-sensitive parasites but do not cause extinction of the mutant subpopulation. Selection leads to spread only if the mutant resistant parasite population expands and produces gametocytes and these gametocytes are transmitted (13).

The spread of resistance also depends on this selection process; resistant parasites acquired from elsewhere (i.e., from another person carrying resistant parasites or, much more rarely, a de novo event in a mosquito) can survive and multiply in the presence of residual antimalarial drug concentrations which inhibit the multiplication of drug-sensitive parasites. Watkins and Mosobo (20) highlighted the importance of antimalarial pharmacokinetics, notably, the drug's terminal elimination half-life (*t*_{1/2}), in determining the selection pressure driving the spread of resistance. As high-grade resistance to antimalarial drugs is usually a stepwise process and rarely occurs with a single genetic event (single point mutations in cytochrome *b* conferring atovaquone resistance are the exception to this), de novo selection is more likely to occur when a large infecting parasite population is exposed to subtherapeutic concentrations of a single antimalarial drug (12, 23). The resistant parasite or parasites will survive and multiply when the concentrations of drug in the blood of the patient are below the level required to keep the multiplication rate of the resistant subpopulation of parasites below 1 or, in other words, when the concentrations are below the MIC for the resistant parasites (MIC_{R}). The resistant population will then reexpand as the drug is eliminated and concentrations fall further, eventually causing a recrudescence of the infection and, critically, producing gametocytes for transmission (1, 24). There has been considerable debate as to the relative importance of the primary infection versus exposure of newly acquired infections to residual drug levels as the source of de novo resistance to antimalarial drugs and the degree of selection provided by slowly eliminated antimalarials. Rapidly eliminated antimalarials are thought to provide little or no selection opportunity during the elimination phase.

The aim of the study described in this paper was to investigate the relationship between the pharmacokinetic characteristics of the antimalarial drugs, the resistance attributes (pharmacodynamics), and parasite multiplication rates to determine the drug-specific opportunities for the selection of resistance during the elimination phase.

## MATERIALS AND METHODS

For antimalarial resistance to spread, resistant parasites must be transmitted. If a resistant parasite occurs de novo during an acute infection, then its progeny must multiply sufficiently to generate transmissible gametocyte densities. Selection refers to the survival advantage in the presence of antimalarial drug conferred by genetic changes in the malaria parasite. We concentrate on pharmacological aspects and do not deal with other important factors determining the spread of resistance, such as fitness and recombination breakdown of multigenic resistance. Immunity, which is such an important determinant of malaria parasite population dynamics, is discussed only in relation to selection.

Sporozoite inocula are skew distributed, with median values of 6 to 10 sporozoites inoculated, but on occasions up to 100 sporozoites may be inoculated (14, 16). Each successfully infected hepatocyte produces 10^{4} to 10^{5} merozoites, each of which can invade a red blood cell (6). Thus, between 10^{4} and 10^{6} parasites emerge from the liver to start the asexual infection of red blood cells (6). If a malaria parasite infection emerges from the liver while there are concentrations of antimalarial sufficient to kill both sensitive and resistant parasites, then there can be no selection of resistance. If the infection emerges from the liver when antimalarial blood concentrations have fallen to levels which will not drive resistant parasites to extinction but will extinguish sensitive parasites, then there is the opportunity for selection. For resistant parasites acquired from elsewhere, all or many (in a multiclonal infection) of the parasites emerging from the liver will be resistant. Thus, for a drug with only blood-stage activity, the “window of selection” may open immediately after the emergence of parasites from the liver. At this stage, the antimalarial drug concentrations may temporarily inhibit parasite multiplication (i.e., exceed the MIC_{R}), but selection is possible as long as these concentrations do not drive the new resistant parasite population to extinction (Fig. 1A). The window of selection closes when antimalarial blood concentrations have fallen to levels such that the survival probabilities of resistant and sensitive parasites are equal.

In the rare event that a resistant parasite emerges de novo during intrahepatic development or in one or more of the merozoites emerging from the liver, then the dynamics are slightly different (Fig. 1B). This usually single parasite's progeny must survive (and stochastic effects mean that not all progeny would survive, even in the absence of drugs) and then outstrip the growth of approximately 10^{5} of its sensitive sibling parasites emerging from the liver to generate sufficient gametocytes for transmission. Thus, for the progeny of a single resistant mutant to survive, the parasite multiplication rate must exceed 1; that is, the drug concentrations must be less than or equal to MIC_{R} (22). So, for the progeny of a de novo resistant parasite to survive, the level of resistance needs to be higher than that for the resistant parasite acquired from elsewhere. The single or relatively few de novo resistant mutants are then in a “race” with their otherwise identical drug-sensitive siblings to attain parasite densities sufficient to be transmitted. This numerical advantage of the sensitive sibling parasites balances the “start” provided by the greater multiplication of the resistant parasites in the race to produce gametocytes and so creates a boundary condition for *t*_{1/2} relative to the degree of resistance induced, below which de novo selection during the elimination phase cannot take place (22). This boundary condition is parameterized by the slope and the right shift in the concentration-effect relationship (i.e., the degree of resistance). Asynchronous hepatic schizogony further tips the balance in favor of the majority sensitive parasites because in most cases schizonts containing the sensitive parasites will have liberated merozoites before the schizont bearing the resistant parasite ruptures.

Mathematical model.We assume that the concentration of antimalarial drug is at the maximum at time zero (*t*_{0}) and that the drug is then eliminated in a first-order process, so that
$$mathtex$$\[C(t){=}C(0){\cdot}e^{{-}kt}\]$$mathtex$$(1) where *k* is equal to ln(2)/*t*_{1/2} and is the terminal elimination rate constant, *t* is time (in days), *C*(*t*) is the concentration at time *t*, and *C*(0) is the maximum concentration (at *t*_{0}). Although many antimalarial drugs have a more complex elimination profile, selective concentrations are present mainly or only during the terminal elimination phase following correct dosing.

Therefore, we assume for simplicity that de novo selection events or infection with a resistant parasite takes place during the terminal elimination phase, although multiphasic elimination could be incorporated by using a series of exponential terms. The pharmacodynamic effects of the antimalarial drug are characterized by parasite killing, a first-order process of fractional reduction in the numbers per asexual cycle (4), which can be considered the reciprocal of parasite multiplication (22).

The range of multiplication causing parasite expansion has a lower bound of just over 1 and an upper bound provided by the mean number of viable merozoites per the number of schizonts (approximately 34). The failure of merozoites to invade reduces this value, but cases of highly efficient multiplication have been documented (parasite multiplication rate [PMR] > 20). In these examples, when there is no drug effect, the PMR is assumed for simplicity to equal 10, which corresponds approximately to the values obtained in early studies with volunteers (5, 18). Although at higher densities parasite expansion slows and eventually stabilizes, the data from studies with volunteers indicate exponential growth in the density range examined here.

The maximum effect of the drug is a PMR of 10^{−3}. This corresponds to parasite killing of sensitive parasites by drugs such as quinine, chloroquine, and mefloquine (22). Parasite killing is synonymous with a reduction in parasite numbers in the blood and is a first-order process (4).

The relationship between parasite killing and drug concentration *C* (concentration-effect or dose-response relationship) can be described by a sigmoid maximum-effect (*E*_{max}) model:
$$mathtex$$\[f(C){=}{-}\mathrm{k}_{1}{\cdot}C^{n}/(C^{n}{+}\mathrm{EC}_{50}^{n})\]$$mathtex$$(2) where *k*_{1} is the first-order rate constant for maximum parasite killing, in this case, ln(10^{−3})/2; *n* is the slope of the linear portion of the concentration-effect curve; *C* is the antimalarial drug concentration, and EC_{50} (or IC_{50}) is the drug concentration which produces 50% of the parasite killing achieved at *E*_{max}.

Furthermore, we assume for simplicity that the shape of the concentration-effect relationship is the same for the susceptible and the resistant populations (i.e., *n* and *E*_{max} are the same) but that the curve is shifted in parallel to the right for the resistant population and the degree of shift is reflected by the ratio of the respective EC_{50}s:
$$mathtex$$\[p{=}\mathrm{EC}_{50}\mathrm{for\ resistant\ parasites}/\mathrm{EC}_{50}\mathrm{for\ sensitive\ parasites}.\]$$mathtex$$(3)

Although a parallel shift is examined initially for the purposes of illustration, more complex changes in the shape of the concentration-effect relationship with resistance could be incorporated.

The mathematical relationship between the total parasite burden and time, in the presence of drug, was described by Simpson et al. (17):
$$mathtex$$\[P(t){=}P(0){\cdot}e^{k_{2}t}{\cdot}\ \left(\frac{\mathrm{EC}_{50}^{n}{+}C(0)^{n}e^{{-}nkt}}{\mathrm{EC}_{50}^{n}{+}C(0)^{n}}\right)^{{-}k_{1}/(kn)}\]$$mathtex$$(4) where *P*(*t*) is total number of parasites in the blood or the total parasite biomass at time *t* >0; *P*(0) is the total number of parasites at *t*_{0}; *k*_{2} is equal to ln(10)/2, which is the first-order rate constant of parasite multiplication rate (per day); and *C*(0), EC_{50}, *k*, *k*_{1}, and *n* are as defined above.

In studying the effects of treatment on the acute infection, the parasite biomass usually exceeds 10^{8} parasites in an adult (and is correspondingly less in a child). This is the lowest value for the pyrogenic density and, thus, is a threshold at which the patient feels ill and seeks treatment (11). In intermittent presumptive treatment, the parasite biomass is generally lower, as the drug recipients are usually well (25).

In studying selection after resolution of the acute infection when reinfections emerge from the liver in the presence of residual drug levels, lower numbers of parasites (10^{4} to 10^{5}) are present (6).

So, if *C*(0) is reached at *t*_{0} and the blood-stage infection with *P _{s}*(

*t*

_{1}) sensitive parasites and

*P*(

_{r}*t*

_{1}) resistant parasites starts later, i.e., at time

*t*>

_{1}*t*

_{0}, then at time

*t*>

*t*

_{0}>0, we will have

*P*(

_{s}*t*) sensitive parasites and

*P*(

_{r}*t*) resistant parasites, as follows: $$mathtex$$\[P_{s}(t){=}P_{s}(t_{1}){\cdot}e^{k_{2}(t\ {-}\ t_{1})}{\cdot}\ \left(\frac{1{+}a^{n}e^{{-}nkt}}{1{+}a^{n}}\right)^{{-}k_{1}/(kn)}\]$$mathtex$$(5) $$mathtex$$\[P_{r}(t){=}P_{r}(t_{1}){\cdot}e^{k_{2}(t\ {-}\ t_{1})}{\cdot}\ \left(\frac{p^{n}{+}a^{n}e^{{-}nkt}}{p^{n}{+}a^{n}}\right)^{{-}k_{1}/(kn)}\]$$mathtex$$(6) where

*a*is the ratio between

*C*(0) and the EC

_{50}of the drug-sensitive parasite and

*p*,

*k*,

*k*

_{1},

*k*

_{2}, and

*n*are as defined above.

Therefore, four parameters can be used to characterize the pharmacokinetic/pharmacodynamic properties of the antimalarial drug: (i) *t*_{1/2}, which is related to *k* by the equation *k* = ln(2)/*t*_{1/2}; (ii) *a*, the ratio of *C*(0) and EC_{50}; (iii) *n*, which we have assumed is the same in vitro as in vivo (15), even if there is a shift in the concentration-effect curve; and (iv) *p*, the ratio of EC_{50}s for resistant and sensitive parasites.

Resistant infection characteristics.Two scenarios were examined. In the first scenario, resistance arises as a new event among the newly acquired parasite population. In the second scenario, resistant parasites are acquired from elsewhere.

(i) Scenario A.Scenario A is a de novo genetic event conferring antimalarial resistance (Fig. 1B). We assume that one resistant parasite occurs de novo at *t*_{0} during the infection with sensitive parasites in the presence of residual antimalarial drug.

*PM*(*t*_{1}) is the probability that a resistant parasite will occur in an individual at *t*_{1}. The de novo mutation event probability depends on the total number of parasites in the body at *t*_{0}, *P*(*t*_{0}) and mutation rate 10^{x}, where *x* is <0 (23), i.e., *PM*(*t*_{1}) = *P*(*t*_{1})·10^{x}.

*PI*(*t*_{1}) is the probability of developing an infection with a resistant parasite, with *PI*(*t*_{1}) = *PM*(*t*_{1})·*PS*(*t*_{1}), where *PS*(*t*_{1}) is the probability that the resistant mutant survives.

We assume that the resistant parasite infection cannot be transmitted until the resistant parasite subpopulation makes up ≥10% of the overall parasite population and there are about 10^{8} parasites in total, that is, when the resistant population can produce enough gametocytes to have a reasonable chance of transmitting (i.e., 10^{8}/10 = 10^{7}) (1, 6, 11).

(ii) Scenario B.Scenario B is infection with a resistant parasite (Fig. 1A). We assume that following antimalarial treatment, the patient acquires a new resistant malaria parasite infection from elsewhere and at *t*_{1} approximately 10^{5} resistant parasites emerge from the liver. We assume that the resistant infection reaches transmissible densities when the population in the blood reaches 10^{7} parasites in total, that is, when enough gametocytes of the resistant population could be produced to be ingested in a normal 2- to 3-μl mosquito blood meal and form a zygote in the anopheline mosquito vector (6). This is a rather generous threshold; it assumes the complete conversion of asexual to sexual stages. The transmission potential of *Plasmodium falciparum* is low at these densities and increases until gametocyte densities reach 10^{3}/μl (1, 11), whereas *Plasmodium vivax* is more efficiently transmitted at low densities.

We call the time interval when the drug concentrations allow the drug-resistant infection but not the drug-sensitive infection to develop a window of selection.

Window of selection. (i) Scenario A: de novo genetic event conferring antimalarial drug resistance.The opening point of the window of selection is defined as the first *t*_{1} when the resistant parasite can survive; that is, when the PMR for resistant parasites is unity (or *dP*/*dt* = 0) and afterwards grows steadily to reach at least 10% of the subsequent total parasite burden (Fig. 1B). The threshold of 10% is an arbitrary point in a continuous distribution describing the relationship between the proportion of resistant asexual parasites, the resulting generation of gametocytes bearing the resistance genetic mutations or gene duplications, and the consequent probability of transmission.

The closing point of the window of selection is defined as the time after which the concentration of the drug is so low that there is no selective pressure for resistance. In other words, the difference in PMR for sensitive and resistant parasites is such that the resistant parasite numbers selected earlier will not reach 10% of the total parasite burden.

(ii) Scenario B: infection with a resistant parasite from elsewhere.The opening point of the window of selection is defined as the first *t*_{1} when the drug effect in subsequent cycles does not kill all the resistant parasites in the body and so the resistant parasite population can survive and later expand after *t*_{1}.

The closing point of the window of selection is the time at which there is no preferential survival of the resistant parasites.

These points were estimated for a number of different pharmacokinetic parameters in a simulation study.

Simulation study.In the simulation study, the important variables affecting the probability of resistance selection in newly emergent infections arising after an antimalarial treatment were varied. Table 1 lists the values of the parameters (*a*, *n*, *t*_{1/2}, *p*) which were investigated. (See Table 4 for the pharmacological characteristics of current antimalarial drugs for comparison.) The objective was to characterize the conditions required for potential preferential transmission of resistant parasites (i.e., selection of resistance). For each set of pharmacokinetic parameters, emerging resistant and sensitive parasite populations were simulated starting at *t*_{0} (when the drug is at the maximum concentration) and then at 1-h intervals up to the closing point of the selection window.

For each given set of values of *a*, *n*, *t*_{1/2}, and *p* and *t*_{1}, the expanding populations of resistant and sensitive parasites (or resistant parasites only) were simulated by using equations 1 and 2 until it was clear whether or not the resistant population could survive and attain the required proportion for transmission (at least 10% of the total infecting parasite population) when the total parasite burden reached 10^{8}. The maximum value of *t*_{1} for which the resistant population could still reach the required size was taken as the closing point for the selection window.

Linear regression was used to characterize the relationship between the drug *t*_{1/2} and the opening and the closing points for the window of selection.

The minimum antimalarial drug *t*_{1/2} for which a selection window exists was estimated as the *t*_{1/2} for which the opening and the closing times were the same, in other words, when regression lines fitted to the opening points and the closing points cross. If this point corresponded to a negative value, then the minimum *t*_{1/2} was estimated as the value for which the closing point's regression line crosses the *x* axis. In order to obtain the precise estimates, the regression lines were fitted to the opening and closing times only for *t*_{1/2}s less than 4 days, as a very slight curvature was observed for some combinations of parameters: for *p* = 4, *a* = 5, and *n* = 5 and for *p* = 4, *a* = 5, and *n* = 10.

As antimalarial drugs show stage specificity in their action (19) and infections may be synchronous, the minimum *t*_{1/2} for which the selection window is at least 12 h or 24 h wide was estimated.

Sensitivity analysis.Sensitivity analysis was performed for the number of sensitive parasites emerging from the liver, the parasite multiplication rate, and the maximum drug effect. All simulations for the window of selection for scenario A and *p* equal to 2 were repeated for (i) 10^{6} and 10^{7} sensitive parasites emerging from the liver at *t*_{1}, (ii) parasite multiplication rates of 2 and 5, and (iii) maximum parasite killing rates (*k*_{1} values) of log(0.01)/2 and log(0.1)/2.

All simulations were run in the Java program, and the results were analyzed by using Stata (release 9.0, 2005) statistical software (Stata Corp., College Station, TX).

## RESULTS

Two scenarios were examined: scenario A, in which resistance arose in a newly acquired infection, and scenario B, in which a resistant infection was acquired from elsewhere.

Scenario A: de novo genetic event conferring antimalarial drug resistance.The calculated windows of selection with different values for the various parameters are shown in Fig. 2. Importantly a window of selection does not exist for all drug *t*_{1/2}s. Rapidly eliminated drugs provided no selective pressure in many circumstances. High initial drug concentrations (*a* = 100), high levels of resistance, and a steep dose-response relationship lowered the *t*_{1/2} limit for “no selection.” Table 2 gives the shortest drug *t*_{1/}_{2}s for which the window of selection existed. Table 3 provides the shortest *t*_{1/2}s for which the selection window was at least 12 h and 24 h wide (i.e., a quarter or a half of the single asexual cycle). In the examples given, there was no selection provided by *t*_{1/2}s of less than 2 days. Except for extreme levels of resistance, there was no selection with *t*_{1/2}s of less than 1 day; and for very rapidly eliminated drugs, such as the artemisinin derivatives (*t*_{1/2}s, ≤1 h), there was no window under any condition.

For small ratios of *C*(0)/EC_{50}, any slope of the concentration-effect curve, and a *p* value of greater than 2, the window of selection opened very early, even at *t*_{0}. There were small differences (up to 30%) between the duration of the window of selection for different pharmacodynamic parameters at the small (*p* = 2) and medium (*p* = 4) intensities of resistance. The differences were more profound only between different levels of ratios of *C*(0)/EC_{50} with the highest intensity of resistance (*p* = 6), where the window of selection width increased by up to 50% for the medium ratio of *C*(0)/EC_{50} and up to 100% for the highest ratio of *C*(0)/EC_{50}.

A linear function of the *t*_{1/2} of the drug estimated well the relationship between the opening point, the closing point, and the width of the selection window for a given resistance intensity; the slope of the concentration-effect curve, and the ratio *C*(0)/EC_{50} with positive slopes (all *R*^{2} values were >0.99 except for two cases for the opening points of *p* = 4, *a* = 5, and *n* = 5 and of *p* = 4, *a* = 5, and *n* = 10, when *R*^{2} was >0.96). As expected for comparable levels of antimalarial activity, the opening and the closing of the window occurs later for drugs with long *t*_{1/2}s than for drugs with short *t*_{1/2}s. The width of the selection window is directly proportional to the length of the terminal *t*_{1/2}. The ratios of the duration of the selection window to *t*_{1/2} were equal to median values of 1.11 (range, 1.01 to 1.3) for a value of *p* of 2, 2.10 (range, 1.66 to 2.30) for a value of *p* of 4, and 2.60 (range, 1.66 to 2.89) for a value of *p* of 6 across all values of the other parameters used in the simulation. It should be noted that drugs with very long terminal *t*_{1/2}s, such as chloroquine and piperaquine, have a multiexponential decline in plasma concentrations, and therefore, selection for higher levels of resistance may occur in the distribution phase. This effectively shortens the window of selection for increasing levels of resistance.

The slopes of the linear relationships between the opening and the closing points and the duration of the window depend on other pharmacodynamic parameters, i.e., the slope of the concentration-effect curve and the ratio *C*(0)/EC_{50}, and also on the intensity of the resistance.

For the window opening point, the slope is inversely correlated with the slope of the concentration-effect curve, is directly proportional to the *C*(0)/EC_{50} ratio, and decreases with increasing intensity of resistance.

For the window closing point, the effects of the pharmacodynamic parameters were similar, but there were no differences between different resistance intensities. Consequently, the width of the window of selection increases with increasing drug resistance, since the window opens sooner for higher levels of resistance but the closing points are the same for different intensities of resistance. The selection window for higher-intensity resistance contains the selection window for the lower-intensity resistance.

Table 4 gives the estimated selection windows for current antimalarial drugs. For drugs with short *t*_{1/2}s, artemisinin and quinine, the window of selection effectively does not exist for values of *p* of ≤20.

Sensitivity analysis.In the sensitivity analysis, the opening of the window remained the same for 10^{5}, 10^{6}, or 10^{7} parasites emerging from the liver, but the window closed earlier for the higher numbers of sensitive parasites. This resulted in differences in window durations of about 1 day for a slope of the concentration-effect curve of 3 and about 0.6 days for a slope of the concentration-effect curve of 10 for each 10-fold increase in the number of emerging parasites. Decreases in the maximum parasite killing rate increased the *t*_{1/2}s for which the selection window exists and created wider windows. The minimum *t*_{1/2} for the selection window to exist was approximately 2 days, for a parasite reduction ratio (PRR) of 1,000 [rate = log(0.001)/2] (22), approximately 4 days for a PRR of 100, and about 8 days for a PRR of 10^{2}. For longer *t*_{1/2}s, the increases in the window duration were constant between PRRs of 1,000 and 100 for each combination of parameters and varied between 2.5 and 3.5 days for different values of *n*. The window was the widest for a weak antimalarial effect (PRR = 10) and, when it existed, always opened at the time of parasite emergence from the liver. For this rate, the increase in the window duration was much steeper than it was for higher rates.

Correspondingly, the duration of the window decreased for lower parasite multiplication rates; the window opened later, but the closing times were the same for all rates. The reduction was up to 70% for a *t*_{1/2} of 5 days and up to 50% for a *t*_{1/2} of 20 days.

Scenario B: infection with a resistant parasite acquired from elsewhere.Figure 3 shows the window opening times for each *t*_{1/2} and for each combination of the pharmacokinetic parameters and resistance. If the resistant infection starts (i.e., if the parasite emerges from the liver) earlier than these times, the resistant infection will be killed by the antimalarial drug levels; if the resistant infection starts later than these times but before “window closure,” it will develop and will have a chance to be transmitted.

For low initial drug concentrations [*C*(0)/EC_{50} values of 3 or 5] and for short drug *t*_{1/2}s, the infection will never be eradicated so the window opens at *t*_{0}.

There is a linear relationship between the opening point and the drug *t*_{1/2} for any given resistance intensity, the slope of the concentration-effect curve, and the *C*(0)/EC_{50} ratio. This relationship always has a positive slope; i.e., opening of the widow occurs later for drugs with longer *t*_{1/2}s (Fig. 3). The slope increases with increasing antimalarial concentrations at *t*_{0}. The slope of the concentration-effect curve had relatively little effect on the opening times for the values studied. The selection window obviously opens earlier if the level of resistance is higher. The time when the window closes is proportional to the *t*_{1/2}; it increases with *a* and decreases with *n*. The resistance level does not have any effect on the time of window closure. Figure 4 compares the selection window for scenario A and the opening and closing times for scenario B on the same graph. Figure 5 shows the relationship between the widths of the windows for scenarios A and B, and Table 4 gives the selection windows for current antimalarials. Table 4 provides a representative selection of drug susceptibilities as examples. A window exists for all drugs and has a very long duration relative to the drug *t*_{1/2} if the ratios of the maximum drug concentration (*C*_{max}) to the 50% inhibitory concentration (IC_{50}) are large.

The principal conclusions from these simulation exercises are that *t*_{1/2} is the main determinant of the time of onset and the duration of the window of selection for both scenarios. *C*_{max}s do affect the duration of the window only for high levels of resistance; for lower levels of resistance, *C*_{max} changes only the time at which the window opens. Steeper slopes in the concentration-effect relationship (for which the value of *n* is higher) slightly decrease (in our study, a range from 3 to 10) the duration of the window. The level of resistance does not affect the closing time for scenario A or B but affects the opening times, so higher levels of resistance extend the duration of the window.

## DISCUSSION

The emergence and spread of chloroquine resistance and, subsequently, sulfadoxine-pyrimethamine resistance has killed millions of people over past 30 years.

With the increasing deployment of artemisinin combination treatments containing slowly eliminated partner drugs, there is concern that these valuable drugs may also be lost to resistance. The de novo emergence of resistance to antimalarial drugs resulting from genetic mutations is a rare occurrence. The genetic event is most likely to occur at the peak of infection, when parasite numbers are the greatest (23); but this is also when antimalarial drug levels are the highest, so only highly resistant parasites will survive correct dosing. Single point mutations in the gene encoding cytochrome *b*, which confers atovaquone resistance, are examples of a single step that confers high-level resistance, but for the resistance mechanisms for the other drugs, the initial genetic event usually confers low-level resistance (*P* ≤ 10) (24). However, if the patient receives inadequate or substandard treatment or malabsorbs or vomits the medication (all of which are relatively common in practice) or the patient has an unusually large volume of distribution for that particular compound, then low blood concentrations may result. These concentrations may be below the MIC for the resistant mutant and may therefore allow its growth. In order for resistant parasites then to spread, the de novo resistant parasite or parasites must multiply sufficiently to generate enough parasites to produce transmissible gametocyte densities (>5/μl of blood). The resistant mutants must also contend with immune responses, directed mainly against the variant surface antigens (mainly PfEMP1) expressed on the exterior of the infected erythrocytes. This reduces the selection probability. Stable resistance selection in a single passage has been demonstrated conclusively for pyrimethamine and atovaquone resistance in *Plasmodium falciparum* infections in humans (3). So, clearly, this specific immune response is not very efficient in reducing the selection of resistance. The relationship between the level of parasitemia, the antimalarial drug dose, and selection probability was elegantly established for pyrimethamine resistance in experimental infections with the Kampala strain of *Plasmodium falciparum* by Martin and Arnold (12). Combinations reduce the probability of de novo selection because if a parasite which is resistant to one component occurs, it should be killed by the other. Combinations therefore protect each of the partner drugs (13, 24).

Rapidly eliminated drugs such as the artemisinin derivatives cannot protect their partner drugs once the blood concentrations have fallen below their MICs. The artemisinin derivatives are eliminated in hours. Thus, a newly acquired infection may encounter subtherapeutic concentrations during the elimination phase of a partner drug from a previously administered treatment which is unprotected by the artemisinin derivative. In order for these parasites to survive, they must encounter concentrations of drug which fall below the MIC (23) before all of these parasites are killed. If the drug has liver-stage activity, then in order for the newly acquired parasites developing in the liver to survive, these stages must encounter sub-MICs for liver-stage activity as well. If resistant parasites are acquired from elsewhere (i.e., a large proportion or all the merozoites produced at hepatic schizogony carry resistance genes), then there is a period, determined by the elimination kinetics of the antimalarial and the relative susceptibilities of the resistant and sensitive parasites (i.e., the magnitude of the right shift in the respective concentration-effect relationships), during which resistant but not susceptible parasites may establish a transmissible infection. This window of selection has been extensively used to model the emergence and spread of resistance, particularly to sulfadoxine-pyrimethamine (7, 8, 9, 20, 21).

In this study we examined the relationship between the pharmacokinetic and pharmacodynamic properties of the antimalarial drug and the window of selection. It is clear that the window of selection is determined mainly by the *t*_{1/2} of the drug; but it is also affected by the degree of resistance, the blood concentrations of drug achieved, and to a lesser extent, the slope of the concentration-effect relationship. Resistance often confers a fitness disadvantage, which may be reflected in reduced growth rates. This would have the effect of narrowing the window of selection.

The longer the terminal *t*_{1/2} is and the flatter the concentration-effect relationship is, the wider the window of selection becomes. In most cases in which blood concentrations are initially high relative to the minimum parasiticidal concentration (atovaquone resistance is the notable exception), the window of selection opens one or more 48-h cycles after the cessation of antimalarial drug administration. Rapidly eliminated drugs (those with *t*_{1/2}s of less than 1 day) usually provide no window of selection at all. Artemisinin derivatives are eliminated so rapidly that the concentrations decline by more than 2,000-fold in 12 h, so they provide only a few hours of potentially selective concentrations and, thus, no window. Quinine can select for resistance in at most three posttreatment cycles (if a very high level of resistance were to arise). Drugs which are very slowly eliminated provide a wide window, provided that the concentrations in the terminal elimination phase are suppressive. However, as resistance increases, drugs such as chloroquine and piperaquine with prominent distribution phases and very long terminal elimination phases effectively become drugs with shorter *t*_{1/2}s and with correspondingly shorter windows of selection for progressively higher levels of resistance (24).

If a genetic event conferring resistance occurs in a newly acquired infection (de novo resistance), then it is most likely that only a single parasite (or a very few parasites) is resistant initially. This single parasite must survive, multiply, and generate gametocytes in sufficient numbers to be transmitted for resistance to spread. However, it has up to 10^{5} drug-sensitive siblings. It is therefore far behind in the “race” to attain densities sufficient for transmission in competition with its siblings. Furthermore, whereas resistant parasites acquired from elsewhere can be selected by blood concentrations exceeding the MIC, de novo resistant parasites cannot (Fig. 1). Together these factors provide a much narrower window of selection opportunity for de novo resistance (Fig. 4) compared with that for the acquisition of resistant parasites from elsewhere. Most importantly for drugs with short *t*_{1/2}s, the window is very brief or, in the case of artemisinin derivatives, nonexistent. This has very important implications; resistance to artemisinin can occur only by inadequate treatment.

## ACKNOWLEDGMENTS

We thank N. P. J. Day and P. Olliaro for advice.

This study was a part of the Mahidol Oxford Tropical Medicine Research Unit research program, funded by the Wellcome Trust of Great Britain.

## FOOTNOTES

- Received 10 July 2007.
- Returned for modification 15 September 2007.
- Accepted 15 February 2008.
↵▿ Published ahead of print on 25 February 2008.

- American Society for Microbiology