Background
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[
1]. 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[
2], 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[
7], chloroquine[
8], and the ACT, mefloquine and artesunate[
9]. 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[
10].
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[
11], 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.
Methods
Within-host pharmacokinetic-pharmacodynamic model
The within-host PK-PD model is based on that described in Saralamba
et al.[
10], 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.[
10] 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 (P
0i) 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 file
1).
The expected number of parasites in patient
i (
) aged ‘
a’ hours (where 1 ≤
a ≤ 48) at hourly time point
t after drug administration, is expressed by the following difference equations,
(1)
and
(2)
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.
The kill rate constant for a particular combination therapy was calculated as follows:
(3)
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.
The relationship between the kill rate constant for each drug and the drug concentration is given by:
(4)
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.
Simulation study
The model was implemented using R[
12]. 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 × 10
8 parasites (i.e. 50 parasites per μL) and not reappearing above 2.5 × 10
8 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 × 10
8 parasites. Circulating parasite counts were calculated from the total parasite counts following Saralamba
et al.[
10], 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[
13], and a small amount of synergy between artesunate and mefloquine[
14], and between artemether and lumefantrine[
15]. 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.
Pharmacokinetic-pharmacodynamic parameters
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[
11].
Before carrying out the LHS sampling, pharmacokinetic profiles of each anti-malarial drug for the three artemisinin-based combination therapies were simulated for 100 hypothetical patients. The dosing regimen used was the regimen recommended by the WHO ([
2]; see Table
1) and the PK profiles were simulated using parameter values and between-subject variability obtained from the literature (see Table
2 and Additional file
2)[
16‐
19].
Table 1
Dosing regimen for each artemisinin-based combination therapy (ACT)
ARS-MQ | ARS 4.0 mg/kg and MQ 8.3 mg/kg at 0, 24, 48 h |
ART-LF | ART 80.0 mg/kg and LF 480.0 mg/kg at 0, 8, 24, 36, 48, 60 h |
DHA-PQ | DHA 4.0 mg/kg and PQ 18.0 mg/kg at 0, 24, 48 h |
Table 2
Population pharmacokinetic parameter values (BSV%)
†
for each drug
ka (/h) | 19.7d | 0.37 | 0.17 | 7d | 0.717 |
(26.5%) | (63%) | (52%) | (26%) | (168%) |
CL/F (L/h) | 24.2e | 180 | 7.04 | 0.8e | 66 |
(22.4%) | (50%) | (16%) | (33%) | (42%) |
V/F (L) | 0.83f | 217 | - | 10.2f | - |
(50%) | (30–50%) | (51%) |
Vc/F (L) | - | - | 103 | - | 8660 |
(30–50%) | (101%) |
Q/F (L/h) | - | - | 4.08 | - | 131 |
(30–50%) | (85%) |
Vp/F (L) | - | - | 272 | - | 24000 |
| | | (30–50%) | | (50%) |
The PD parameters were varied across the LHS experiment to capture both biological and empirical uncertainty. The definition of each PD parameter and the statistical distribution selected for each PD parameter are given in Table
3 and Table
4, respectively. For the parameters that are drug independent, the distributions for the parameters which determine how the parasites are distributed across the 48 hours of the parasite life cycle (
μ and
σ) were sourced from PK-PD modelling of uncomplicated falciparum malaria patients[
10] and the distribution for the parasite multiplication factor (PMF) was obtained from modelling of data collected from syphilis patients treated with an induced malaria infection[
20,
21].
Table 3
Parameter definitions for the within-host pharmacokinetic-pharmacodynamic model
μ
IPL
| Mean of the age distribution of the initial parasite burden |
σ
IPL
| Standard deviation of the age distribution of the initial parasite burden |
PMF
| Parasite multiplication factor (/48 h cycle) |
k
max
| Maximal killing rate of the drug / h |
γ
| Slope of in vivo concentration-effect curve |
EC
50
| In vivo concentration when killing rate is 50% of the maximum |
Table 4
Statistical distributions selected for each pharmacodynamic parameter
μ
IPL
a
| DU(4, 16) | | |
σ
IPL
a
| DU(2, 8) | | |
PMF
a
| TRI(8, 12, 10) | | |
k
max
| ARS/DHA | TRI(0.26, 0.47, 0.37)c | PRR = 105.28; KZ = 38 |
ART | TRI(0.12, 0.33, 0.22)c | PRR = 102.9; KZ = 38 |
LF | TRI(0.18, 0.54, 0.36)c | PRR = 103; KZ = 22 |
MQ | TRI(0.11, 0.46, 0.28)c | PRR = 102.25; KZ = 22 |
PQ | TRI(0.33, 0.65, 0.49)c | PRR = 104.6; KZ = 24 |
γ
| ARS/DHA | lnN(1.31, 0.65) | |
| ART | lnN(1.53, 0.31) | |
| LF | lnN (0.81, 0.58) | |
| MQ | lnN (0.97, 0.54) | |
| PQ | lnN (1.35, 0.66) | |
EC50 (ng/mL) | ARS/DHA | U(1.44, 532.05) | a = (adjusted)(ng/mL)b,d; b = 0.5×Cmax (ng/mL)b,d |
| ART | U(4.38, 46.20) | |
| LF | U(1.75, 2331.60) | |
| MQ | U(20.48, 1087.22) | |
| PQ | U(11.56, 94.19) | |
The maximal killing rate (k
max) 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[
24]. 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[
25].
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
Estimates of the
in vitro IC50 (not corrected for binding) and
γ for artesunate, dihydroartemisinin, mefloquine, piperaquine, and lumefantrine (refer to Table
5), were determined from statistical modelling of individual isolate effect versus drug concentration curves. The fresh
P. falciparum parasite isolates were obtained from blood samples of 487 patients attending outpatient clinics in Papua, Indonesia between 2004 and 2010[
26]. The
in vitro drug susceptibility was determined using the World Health Organization guidelines for schizont maturation tests. The
in vitro data for artemether were measured at the Swiss Tropical and Public Health Institute (Switzerland; Basel) against asynchronous intraerythrocytic forms of the
P. falciparum strain NF54 (obtained from MR4) using the [3H]-hypoxanthine incorporation assay[
27].
Table 5
Parameter values derived from
in vitro
experiments
IC50 measured concentration(nM)† | 1.39 | - | 13.42 | 9.34 | 17.67 |
Molecular weight (g/mol) | 384.4 | - | 528.9 | 378.3 | 535.5 |
IC50 concentration(ng/mL) | 0.53 | 2.64 | 7.1 | 3.53 | 9.46 |
Binding to media of in vitro experiment (0.5% Albumax) (% bound) | 82.8 | 82.8 | 99.6 | 85 | 98.1 |
Human plasma protein binding (% bound) | 93 | 91.7 | 98.7 | 95.6 | 98.6 |
Human whole blood to plasma ratio | 1.1 | 0.8 | 0.8 | 1.7 | 0.9 |
Scalar (adjusted) | 2.7 | 1.66 | 0.25 | 5.8 | 1.22 |
IC50 (adjusted) concentration (ng/mL)† | 1.44 | 4.38 | 1.75 | 20.48 | 11.56 |
γ (Slope of concentration-effect curve) | 3.72 | 4.61 | 2.24 | 2.63 | 3.48 |
SD of γ on log-scale | 0.65 | 0.31 | 0.58 | 0.54 | 0.66 |
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.
Discussion
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 files
4B, Additional file
5B and Additional file
6B 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[
9]. 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 (k
max) 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.[
10]. 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, k
max values for the artemisinin derivatives were randomly selected from a Parasite Reduction Ratio at 48 hours (PRR
48) ranging from 5 × 10
4.28 to 5 × 10
6.28 with a mode value of 10
5.28[
3] parasites reduced every 48 hours. In the observations by Saralamba
et al.[
10], 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 (~10
0.42) 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.
Acknowledgements
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.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
JAS developed the idea for a simulation study with AH, SC, RP, JM, JG-B, JMcC and SZ making contributions to the concept and design of the study. SC, AH and RP were involved in the acquisition of data required to obtain estimates of (or ranges for) the model parameters. SZ wrote the R code to run the simulation-based decision tool with contributions from JMcC, KS and KJ. JAS and SZ wrote the first draft of the paper and together with AH, SC, RP, JM, JG-B, JMcC, KJ and KS contributed to the interpretation of the simulated output. All authors reviewed the paper and approved the final version.