Mathematical models describing the pharmacometric properties of the artemisinin antimalarials have assumed a simple and direct relationship between drug exposure and malaria parasite killing. Because these drugs are eliminated very rapidly these models naturally predicted that more sustained exposure, created by slowing drug clearance, administering by constant infusion or by frequent dosing, would enhance parasite clearance, and thus improve therapeutic responses 4,19,20. This was proposed as a solution to the challenge posed by artemisinin resistant P. falciparum infections. However, clinical studies did not confirm these predictions 3 and there was no significant advantage in terms of parasite clearance or cure rate from giving the artemisinin derivatives more than once daily despite their rapid elimination. The simple models thus appear to be wrong.
Artemisinin resistance in P. falciparum is characterised by a reduced parasite clearance rate in vivo 18. This reflects reduced susceptibility of the circulating ring stage parasites to the drug 21. Artemisinin resistance in field isolates is associated with mutations in the propeller region of the Pfkelch gene on chromosome 13 (K13). This causal association has been confirmed in transfection studies, although the contribution of other genes (often described collectively as the genetic background) is substantial 22. Artemisinin resistance is thought to involve altered parasite cellular responses rather than receptor or transporter alterations, but the exact mechanism remains unclear 23. As the more mature stages of K13 mutant P. falciparum isolates remain sensitive to the artemisinin derivatives the drugs do remain efficacious in clinical practice, but they kill less parasites per asexual cycle and so the therapeutic responses are diminished. Longer exposures from longer courses over three or four asexual cycles improve therapeutic responses in artemisinin resistant infections, but giving the drugs more frequently than once daily does not 1–3.
In the present study, a new mathematical model expanding the earlier simpler models (20,21) was evaluated. This model was constructed to account for the dose-response relationship and could explain the lack of additional effect by more frequent administration. The proposed model incorporated the hypothesis that, in the presence of artemisinins, some parasites are injured, stop growing and become temporarily insensitive to the drug. These parasites can, however, recover and return to their normal, drug-sensitive state. Whether this unresponsive (“injury”) state causing a temporary arrest in development is the same or a similar process as the well described “dormancy” phenomenon has not been specified, and both processes can explain recrudescences following standard treatments is not specified 9. The model was fitted to parasite count data obtained from patients in western Cambodia (where artemisinin resistance was prevalent) and western Thailand (before the main emergence of artemisinin resistance there) 18. The model captured satisfactorily the dynamics of P. falciparum parasites in patients receiving artesunate monotherapy every 24 hours for 7 days. As reported previously 19 the major difference between parasites from Pailin, which were artemisinin resistant, and those from Wang Pha, which were sensitive, was the more than ten fold estimated reduction in ring stage killing. Trophozoite stage killing was similar and schizont killing was reduced by about 45%. Recovery rates were slightly but not significantly different between the two sites. This suggests, if this hypothesis is correct, that recovery rates from parasite injury are not greatly affected by the mechanisms involved in artemisinin resistance.
The lower predicted death rates of the asexual ring stage parasites in the artemisinin resistant infections 19 is supported by extensive experimental investigations 7–12, 21,24,25 and the strong correlation between specific ring stage in-vitro susceptibility evaluations, K13 mutations and slow parasite clearance. The unresponsive (“injury”) state postulated in this model suggested that the parasites were in a damaged state between 2 and 50 hours prior to dying. The estimated parasite recovery rate from this model was about 1 in 740–850 unresponsive parasites per 24 hours. The estimate of the recovery lag-time was 2–2.4 hours suggesting that the parasites became damaged or dormant shortly after being exposed to the drug.
This model was developed to account for the failure of frequent dosing regimens to accelerate parasite clearance or enhance cure rates in artemisinin containing antimalarial drug regimens. It did this satisfactorily but there are several limitations to this modelling exercise. Many of the pharmacodynamic parameter values in this model have not been measured directly so the system is unidentifiable. It has also simplified the complex relationship between parasite stage of development, and time and intensity of drug exposure, and assumed homogeneous parasite stage distributions and multiplication and elimination kinetics. Although the model can reproduce the observed data, this does not mean that it has explained the underlying biology (i.e. the model may not be correct). Nevertheless, it does represent a relatively simple hypothesis that is consistent with observations and is testable. But there may well be other hypotheses whose models would fit equally well with the data. We propose that, as a minimum, such models should be capable of reproducing both delayed clearance and the unchanged clearance rates under frequent dosing in order to be consistent with observed data.
In conclusion, a new within-host pharmacometric model is proposed, which supports the hypothesis that parasites enter a temporary drug refractory injury state after contact with artemisinin antimalarials, which is followed by delayed death or reactivation. The model fitted the observed sequential parasitaemia data from patients with artemisinin resistant and sensitive P. falciparum infections and confirmed the known dose-response relationship for reduced ring stage activity in artemisinin resistant infections.