- Open Access
Assessing the utility of an anti-malarial pharmacokinetic-pharmacodynamic model for aiding drug clinical development
© Zaloumis et al.; licensee BioMed Central Ltd. 2012
Received: 26 April 2012
Accepted: 1 August 2012
Published: 30 August 2012
Mechanistic within-host models relating blood anti-malarial drug concentrations with the parasite-time profile help in assessing dosing schedules and partner drugs for new anti-malarial treatments. A comprehensive simulation study to assess the utility of a stage-specific pharmacokinetic-pharmacodynamic (PK-PD) model for predicting within-host parasite response was performed.
Three anti-malarial combination therapies were selected: artesunate-mefloquine, dihydroartemisinin-piperaquine, and artemether-lumefantrine. The PK-PD model included parameters to represent the concentration-time profiles of both drugs, the initial parasite burden and distribution across the parasite life cycle, and the parasite multiplication factor due to asexual reproduction. The model also included the maximal killing rate of each drug, and the blood drug concentration associated with half of that killing effect (in vivo EC50), derived from the in vitro IC50, the extent of binding to 0.5% Albumax present in the in vitro testing media, and the drugs plasma protein binding and whole blood to plasma partitioning ratio. All stochastic simulations were performed using a Latin-Hypercube-Sampling approach.
The simulations demonstrated that the proportion of patients cured was highly sensitive to the in vivo EC50 and the maximal killing rate of the partner drug co-administered with the artemisinin derivative. The in vivo EC50 values that corresponded to on average 95% of patients cured were much higher than the adjusted values derived from the in vitro IC50. The proportion clinically cured was not strongly influenced by changes in the parameters defining the age distribution of the initial parasite burden (mean age of 4 to 16 hours) and the parasite multiplication factor every life cycle (ranging from 8 to 12 fold/cycle). The median parasite clearance times, however, lengthened as the standard deviation of the initial parasite burden increased (i.e. the infection became more asynchronous).
This simulation study demonstrates that the PD effect predicted from in vitro growth inhibition assays does not accord well with the PD effect of the anti-malarials observed within the patient. This simulation-based PK-PD modelling approach should not be considered as a replacement to conducting clinical trials but instead as a decision tool to improve the design of a clinical trial during drug development.
Despite significant progress in control of malaria over the last decade, it remains a major global health problem. Almost 40% of the world’s population live in malaria endemic areas, with each year about a quarter of a billion people experiencing clinical malaria and an estimated 655,000 malaria-related deaths. With no vaccine currently available, malaria control relies on preventative measures (i.e. insecticidal bed nets and indoor residual spraying) and effective treatment with artemisinin-based combination therapy (ACT). ACT involves treatment with two or more anti-malarials; a fast acting but short lived artemisinin derivative and a less effective, but of longer duration, partner drug. ACT is recommended by WHO as the first-line treatment of uncomplicated falciparum malaria, but recent reports from western Cambodia raise concerns that Plasmodium falciparum has developed reduced susceptibility to oral artesunate[3, 4]. In the context of emerging resistance to artesunate (the most widely used artemisinin derivative), it is critical that new anti-malarial treatments are developed and assessed.
Mechanistic within-host pharmacokinetic-pharmacodynamic (PK-PD) models that relate blood anti-malarial drug concentrations to the parasite-time profile have potential to aid anti-malarial drug development. Simulated parasite-time profiles for hypothetical patients can be generated from the mechanistic PK-PD model and incorporate between-patient variability in the drug concentration profiles. Comparisons of parasitological outcomes (e.g. distribution of parasite clearance times and proportion of patients cured) derived from these hypothetical individuals can then be used as a decision tool for assessing dosing schemes and potential partner drugs for new anti-malarial drugs. This simulation-based approach has been adopted previously using a within-host continuous-time PK-PD model for comparing dosing schemes of mefloquine[5, 6], artesunate, chloroquine, and the ACT, mefloquine and artesunate. More recently a parasite stage-specific discrete-time within-host PK-PD model has been developed, and a stochastic simulation-based approach implemented to compare dosing schemes for artesunate.
In this paper, the above stage-specific model was extended to account for the action of two or more anti-malarial treatments, and the anti-malarial pharmacodynamic parameters were determined by extrapolating from in vitro data. Using a Latin-Hypercube-Sampling approach, the sensitivity of the PK-PD model to particular parameters was assessed, by comparing, across different sets of parameter values, the parasitological outcomes derived from simulated parasite-time profiles of hypothetical patients.
Within-host pharmacokinetic-pharmacodynamic model
The within-host PK-PD model is based on that described in Saralamba et al., which is a discrete-time model that incorporates the age distribution of the parasite population within the malaria patient. This model determines how the distribution of the parasite age changes post treatment as a consequence of the concentration of the anti-malarial drug. The general form of the discrete-time model (see Saralamba et al. supplemental information for more detail) and PK-PD parameter values used to simulate individual parasitaemia-time profiles in the presence of anti-malarial combination therapies is described below.
Prior to drug administration, the initial parasite load of each patient (P0i) is distributed among the 48 hourly age intervals of the P. falciparum life cycle according to a Gaussian distribution with a mean age of μ hours and a standard deviation of σ hours (see Additional file1).
In (1) and (2), is the kill rate constant for the combination therapy of the parasites aged a hours at hourly time point t, and in (2), PMF is the parasite multiplication factor that represents the number of merozoites released per schizont at the end of the 48 hour life cycle that successfully reinvade red blood cells.
where, for j = 1, 2, denotes one of the drugs comprising a combination therapy. The kill rate constant in (3) assumes that the effects of and on the parasite population in vivo are independent of one another.
where is the plasma drug concentration at time t for patient i, γ is the slope of the concentration-effect relationship, is the blood drug concentration in vivo that gives 50% parasite killing and kmax is the maximal killing rate of each drug (which was assumed to be constant across the parasite ages ‘a’ where the drug is known to have an effect).
The drug concentration-time curve for each drug assumes the form of a structural PK model, for example a one- or two- compartment PK model with first-order absorption and elimination from the central body compartment.
The model was implemented using R. Parasite counts at several different time points and in the presence of anti-malarial combination therapies were simulated from this discrete-time model for hypothetical malaria patients. The summary measures that were derived from each simulated parasite count-time curve were: (i) the hypothetical patient was clinically cured (defined as the parasite count falling below 2.5 × 108 parasites (i.e. 50 parasites per μL) and not reappearing above 2.5 × 108 parasites by day 63 of follow-up); and (ii) the parasite clearance time (PCT) (hours), defined as the time for the circulating parasite count (parasites aged approximately 1 to 26 hours) to decrease below 2.5 × 108 parasites. Circulating parasite counts were calculated from the total parasite counts following Saralamba et al., where sequestration was estimated to start at a parasite age of 11 hours and the number of parasites older than 11 hours circulating in the blood was assumed to decrease exponentially.
The anti-malarial combination therapies selected for this simulation study were three artemisinin-based combination therapies: artesunate-mefloquine, dihydroartemisinin-piperaquine, and artemether-lumefantrine. Studies of in vitro interactions between the pharmacodynamic effects of the drugs have shown no interaction between dihydroartemisinin and piperaquine, and a small amount of synergy between artesunate and mefloquine, and between artemether and lumefantrine. Thus, the assumption of independent pharmacodynamic effects of each drug in the combination therapies selected for this simulation study seems reasonable, especially considering the short amount of time (approximately six hours for dihydroartemisinin and twelve hours for artemether) that the drug concentrations of the artemisinin derivatives are present in the blood.
In order to assess the utility of the PK-PD model for determining patient outcomes (described above) the sensitivity of the model to parameter values was explored. This was implemented using Latin-Hypercube-Sampling (LHS). LHS is a method which is used to randomly sample over large parameter spaces in an evenly distributed manner.
Dosing regimen for each artemisinin-based combination therapy (ACT)
Dosing regimen (WHO)
ARS 4.0 mg/kg and MQ 8.3 mg/kg at 0, 24, 48 h
ART 80.0 mg/kg and LF 480.0 mg/kg at 0, 8, 24, 36, 48, 60 h
DHA 4.0 mg/kg and PQ 18.0 mg/kg at 0, 24, 48 h
Population pharmacokinetic parameter values (BSV%) † for each drug
Parameter definitions for the within-host pharmacokinetic-pharmacodynamic model
Mean of the age distribution of the initial parasite burden
Standard deviation of the age distribution of the initial parasite burden
Parasite multiplication factor (/48 h cycle)
Maximal killing rate of the drug / h
Slope of in vivo concentration-effect curve
In vivo concentration when killing rate is 50% of the maximum
Statistical distributions selected for each pharmacodynamic parameter
μ IPL a
σ IPL a
TRI(8, 12, 10)
TRI(0.26, 0.47, 0.37)c
PRR = 105.28; KZ = 38
TRI(0.12, 0.33, 0.22)c
PRR = 102.9; KZ = 38
TRI(0.18, 0.54, 0.36)c
PRR = 103; KZ = 22
TRI(0.11, 0.46, 0.28)c
PRR = 102.25; KZ = 22
TRI(0.33, 0.65, 0.49)c
PRR = 104.6; KZ = 24
lnN (0.81, 0.58)
lnN (0.97, 0.54)
lnN (1.35, 0.66)
a = (adjusted)(ng/mL)b,d; b = 0.5×Cmax (ng/mL)b,d
The maximal killing rate (kmax) of the drug was assumed to follow a triangular distribution. The middle values were taken from published clinical data[3, 22, 23]. Piperaquine was the only drug with no clinical studies of it administered as a monotherapy and the mode was set to a value equal to that derived from in vitro experiments. The minimum and maximum values of the triangular distribution for each anti-malarial correspond to a 50-fold decrease and 50-fold increase in the number of parasites killed every 48 hours. Artesunate, dihydroartemisnin and artemether were assumed to kill parasites aged 6 to 44 hours; mefloquine 18 to 40 hours; piperaquine (assumed similar to chloroquine) 12 to 36 hours; and lumefantrine (assumed similar to mefloquine) 18 to 40 hours.
The slope of the concentration-effect curve (i.e. in vivo γ) was assumed to have the same statistical distribution (i.e. Log-normal) and parameter values (mean and standard deviation on loge scale) as the in vitro γ which was derived from modelling of in vitro concentration-effect curves measured from a large number of parasite isolates.
The distribution of the EC50 for each anti-malarial drug is unknown, therefore, the conservative continuous-uniform distribution was chosen with the minimum value set to the adjusted in vitro IC50 and the maximum value equal to half of the maximum concentration of the population mean PK profile.
Five thousand parameter sets were selected from the above statistical distributions using LHS. For each parameter set, simulated parasite count versus time profiles for the 100 hypothetical patients (with the PK profiles determined above) were derived for each artemisinin-based combination therapy. The initial parasite burden for each of the 100 hypothetical patients was randomly selected from a log-normal distribution with a geometric mean of 1.14 × 1011 (i.e. parasitaemia of 22746 parasites per μL) and a standard deviation on the log-scale of 1.13. The initial parasite burdens for the 100 patients did not vary with LHS parameter set or with the artemisinin combination therapy used in the simulation.
Determination of the in vitro IC50 and slope (γ) of concentration-effect relationship
Parameter values derived from in vitro experiments
IC50 measured concentration(nM)†
Molecular weight (g/mol)
Binding to media of in vitro experiment (0.5% Albumax) (% bound)
Human plasma protein binding (% bound)
Human whole blood to plasma ratio
IC50 (adjusted) concentration (ng/mL)†
γ (Slope of concentration-effect curve)
SD of γ on log-scale
The in vitro free drug IC50 was calculated from the measured in vitro IC50 (uncorrected for binding) by multiplying by the unbound fraction in the in vitro testing media. This value was then converted to an adjusted in vitro IC50 in whole blood (to represent concentrations comparable to an in vivo situation) by first dividing by the free fraction in plasma and then multiplying by the whole blood to plasma ratio (see Table 5).
Estimates of drug binding to the in vitro testing media (i.e. 0.5% Albumax in RPMI) and human plasma were determined using ultracentrifugation. Briefly, blank Albumax media and plasma were each spiked with compound and divided into six aliquots; three aliquots were subjected to ultracentrifugation (Beckman Optima XL-100K Ultracentrifuge, Rotor type 42.2 Ti; 223,000 x g) for 4.2 hours at 37°C to pellet the proteins whereas the remaining three aliquots served as controls and were incubated at 37°C for the same time period but without centrifugation. Controls were also stored at −20°C to confirm sample stability over the centrifugation period. Aliquots of the supernatants from the ultracentrifuged samples were first diluted 1:1 in acetonitrile, assayed by LC-MS and the responses compared to a calibration curve prepared in 50% aqueous acetonitrile to determine the unbound (i.e. free) concentration. Control concentrations in each matrix were determined using LC-MS by first precipitating the proteins with acetonitrile (3:1 acetonitrile: matrix) and then comparing the responses to a calibration curve from a blank matrix prepared using the same protein precipitation procedure. The free fraction in each matrix was then determined from the ratio of the average unbound (e.g. free) concentration to the average total concentration in each matrix.
The whole blood to plasma partitioning ratio (B/P) was determined by spiking aliquots of whole blood or plasma maintained at 37°C with compound, incubating for 2 min, and then centrifuging the whole blood sample to obtain the plasma fraction. Both the plasma fraction of whole blood and the plasma control were assayed for compound by LC-MS as described above. The blood to plasma ratio was calculated from the ratio of the concentration in the plasma control (used as a surrogate for the total whole blood concentration since whole blood assays were not available for each compound) to that in the plasma fraction of whole blood. The two-minute time point was used to avoid confounding issues due to potential blood instability; rapid equilibration between plasma and erythrocytes was assumed.
Sensitivity of pharmacokinetic-pharmacodynamic (PK-PD) model to parameter values
Figure 1 (left panel) shows that the proportion clinically cured (for ease of exposition referred to subsequently as proportion cured) after treatment with artemether-lumefantrine was sensitive to changes in the standard deviation of the age distribution of the initial parasite burden, and that it tended to decrease as the standard deviation of the age distribution (i.e.σ) increases (i.e. as the infection becomes more asynchronous). The proportion cured after treatment with artemisinin-lumefantrine was not strongly influenced by changes in the mean of the age distribution of the initial parasite burden (i.e. μ) and the PMF. The proportion cured for the remaining artemisinin combination therapies was not very sensitive to changes in the parameters defining the age distribution of the initial parasite burden (i.e. μ and σ) and the PMF.
The PCTs for all three artemisinin combination therapies were sensitive to changes in the mean and standard deviation of the age distribution of the initial parasite burden (see Figure 1, right panel). The PRCCs plotted in the right panel of Figure 1 show that the PCTs for all three artemisinin combination therapies tended to lengthen as the standard deviation of the age distribution increased (or the infection became more asynchronous) and tended to shorten as the mean of the age distribution increased.
Tornado plots of the PRCCs between the model outputs and the drug dependent parameters (EC50, kmax and γ) for each artemisinin combination therapy are also provided in Additional file3.
Comparing alternative dosing regimens
The utility of the mechanistic within host PK-PD model as a decision tool for comparing dosing regimens was investigated for different dosing schemes for each of the partner drugs, mefloquine (WHO recommended dosing of 8.3 mg/kg at 0, 24 and 48 hours versus dosing of 15 mg/kg at 48 hours) and piperaquine (WHO recommended dosing of 18 mg/kg at 0, 24 and 48 hours versus 36 mg/kg at 0, 24 and 48 hours), administered with the artemisinin derivatives, artesunate and dihydroartemisinin respectively. Since the proportion of patients cured was highly dependent on the EC50 value of the partner drug (a parameter for which we don’t know the value), different dosing schemes were compared for the 25th, 50th and 75th percentile values of the 5000 parameter values selected using LHS. All other parameters were fixed at their mean/mode value given in Table 4.
The proportion cured for 100 hypothetical patients with varying PK profiles for the two dosing schemes of mefloquine was 100% when the EC50 value of mefloquine was 287 ng/ml, however, under-dosing patients with only 15 mg/kg of mefloquine resulted in only 50% of the patients being cured if the EC50 is 554 ng/ml and 20% if the EC50 was 821 ng/ml. For the standard recommended mefloquine dose of 8.3 mg/kg at 0, 24 and 48 hours, approximately 95% and 80% would be expected to be cured at the respective EC50 values of 554 and 821 ng/ml (Figure8A).
Doubling the recommended WHO dose of piperaquine given each day over 3 days results in a higher proportion of patients cured at the EC50 values of 53 and 74 ng/ml for piperaquine (Figure8B).
The parasitological outcomes simulated in this paper were proportion of patients cured and parasite clearance times, for three different artemisinin-based combination therapies currently recommended by the WHO as the first line treatment for uncomplicated falciparum malaria. This simulation study was comprehensive, randomly drawing from each distribution of the six key pharmacodynamic parameters using Latin-Hypercube-Sampling (LHS), and included between-patient variability in the pharmacokinetic profiles of each anti-malarial drug. The proportion of hypothetical patients cured was observed to be highly correlated to the in vivo EC50 and the killing rate (kmax) of the partner drug co-administered with the artemisinin derivative. However, in vivo EC50 values that corresponded to on average 95% of patients cured (a value observed in most clinical efficacy studies of these regimens) were much higher than the values we derived from in vitro data (i.e. adjusted in vitro IC50), even though the difference in protein binding in vitro and in vivo were taken into account in the model. In vitro experiments typically assess the pharmacodynamic effect of an anti-malarial drug by measuring inhibition of parasite growth in rising concentration of free drug for the length of one parasite life cycle (i.e. 48 hours). The duration of the in vitro assay is usually 48 to 72 hours and although this permits a reproducible estimate of parasite drug susceptibility, it may be too short for this estimate to reflect accurately clinical correlates. This may explain in part why in vitro measures accord so poorly with the observed pharmacodynamic effect in vivo.
There was evidence that the proportion cured decreased if asynchronous infections were treated with artemether-lumefantrine, but the synchronicity of the infection did not strongly influence the proportion cured following treatment with either artesunate-mefloquine or dihydroartemisinin-piperaquine. The PCT for all three artemisinin combination therapies tended to lengthen as the infection became more asynchronous and to shorten as the mean age of the initial parasite burden increased. The finding that asynchronous infections take longer to clear is plausible because it is more likely that there will be parasites outside the killing zone (i.e. early rings and schizonts) during the times when the patient is only exposed to the partner drug (e.g. approximately 7 to 24 hours for mefloquine or piperaquine). The distributions of PCTs in Additional files4B, Additional file5B and Additional file6B are bimodal because the hypothetical patients do not receive a single dose of the artemisinin derivative but are given multiple doses at 24 and 48 hrs (and also 8, 36 and 60 hours for artemether).
The proportion cured following treatment with artesunate-mefloquine was highly correlated to the in vivo EC50 value of mefloquine. This is not surprising given the brief time the parasite is exposed to dihydroartemisinin concentrations (approximately 6 hours following each dose of artesunate) compared to mefloquine which remains in the body, on average, for 40 days. This finding concurs with observations from deterministic simulated individual patient parasite versus time profiles using a continuous-time PK-PD model. The association between the proportion cured and the in vivo EC50 values of piperaquine and lumefantrine was even stronger than that observed for mefloquine. Both piperaquine and lumefantrine have an enormous volume of distribution and an elimination profile that comprises a steep short distribution phase followed by a slow elimination phase from day 5–7 onwards[19, 30]. However, lumefantrine has a much lower volume of distribution compared with piperaquine and this explains why higher values of in vivo EC50 for lumefantrine are required before the simulated observations predict, on average, 10-20% cured. PCTs did not increase when the maximal killing rate (kmax) of artesunate/dihydroartemisinin decreased, although this was observed for the ring stage parasites in the discrete-time PK-PD model reported by Saralamba et al.. These conflicting findings are likely to arise for a number of reasons. First, in this paper it was assumed that the maximal killing rate of the artemisinin derivatives was constant across the killing zone (i.e. the age range of parasites for which the drug kills) since stage-specific killing rates for each anti-malarial was not known. Second, kmax values for the artemisinin derivatives were randomly selected from a Parasite Reduction Ratio at 48 hours (PRR48) ranging from 5 × 104.28 to 5 × 106.28 with a mode value of 105.28 parasites reduced every 48 hours. In the observations by Saralamba et al., the maximal killing rate of artesunate observed for the ring stages with delayed PCTs was a mean of 62% /cycle corresponding to a much lower PRR (~100.42) than our minimal value. Third, in this study the partner drugs were administered at the same times as the doses of the artemisinin derivatives and therefore contributed to the parasite clearance times whereas in Saralamba et al. only artesunate was administered in the first 48 hours of treatment.
This simulation study has a number of strengths which includes: the method of LHS for randomly selecting 5000 sets of the pharmacodynamic parameter values combined with simulations of 100 pharmacokinetic profiles for each anti-malarial to capture between-patient variability in drug exposure. Moreover our comparison of alternative dosing regimens highlight the utility of PK-PD models to compare dosing schemes and have the capacity to examine the association between a range of PK parameters (e.g. time above therapeutic concentration, maximum concentration or area under the concentration-time profile) and parasitological outcome. The limitations of this study were: the within-host PK-PD model assumes that the background immunity of the hypothetical patients was low or absent; no pharmacodynamic synergism between the two anti-malarials of each combination therapy evaluated was assumed; and the a priori assumption that the maximal killing rate of the artemisinin derivatives and the partner drugs remained constant across the different ages of the parasite within the defined killing zone (e.g. 6 to 44 hours for artesunate). Furthermore, the median PCTs were approximately 24 hours whereas in many clinical studies approximately 48 hours is often observed. This difference may be due to one or a combination of factors including: an assumption that there was no synergy between the drugs; the maximal killing rate of the partner drug, piperaquine, was taken from an in vitro experiment and thus may be higher than observed in vivo; and the number of circulating parasites was calculated in time steps of one hour post initial treatment for determining PCT whereas in clinical efficacy studies this is often determined from blood smears collected only every 24 hours.
In conclusion, this simulation study demonstrates the utility of using mechanistic within-patient PK-PD models for comparing parasitological outcomes of different dosing schemes of anti-malarial treatments and different anti-malarial combination therapies. The findings of this study suggest that the parasitological outcomes be compared for a number of scenarios of the pharmacodynamic parameter values, especially the unknown in vivo EC50 value. These simulation studies should not be used as a replacement to conducting the clinical efficacy trials but instead used to assist in determining the best dosing schemes and potential partner drugs to be considered for new anti-malarial treatments. This simulation-based approach has the potential to reduce the number of clinical efficacy trials carried out in the Phase II and Phase III stages of drug development, which will reduce the cost of drug development, speed up the process of drug registration, and could help identify non-ethical trials of malaria patients.
We thank Dr Sergio Whittlin of the Swiss Tropical and Public Health Institute, Basel, Switzerland for providing the in vitro data for the anti-malarial, artemether. The work was supported by Medicines for Malaria Venture, and the National Health and Medical Research Centre of Australia (NHMRC) Centre of Research Excellence 1035261. James McCaw is supported by an Australian Research Council Future Fellowship 1101002580.
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