Eight healthy male, Vietnamese subjects were administered 1 × 250, 2 ×250 and 4 ×250 mg artemisinin capsules in a cross-over design with randomized sequence with a 7-day washout period between administrations. The inter-individual variability in artemisinin pharmacokinetics was large with parameter coefficients of variation (CV) typically between 50 -70%. The parameter with the smallest variability was the elimination half-life (CV : 30 -40%). Analysis of variance indicated also a large intra-subject variability (CV 524%) for the dose-normalized area under the plasma concentration-time curve (AUC/dose). The pharmacokinetic results suggested artemisinin to be subject to high pre-systemic extraction. Artemisinin half-life could not predict the extent of in vivo exposure to the drug, there being no correlation between half-life and oral clearance. Artemisinin oral plasma clearance was about 400 L h − 1 exhibiting a slight decrease with dose, although the effect was weak. Thus results from studies using different artemisinin doses may, within the studied dose range, be compared without the complication of disproportionate changes in drug exposure with varying dose levels. Half-lives appeared to increase with dose. An observed period effect in the analysis of variance was tentatively associated with time-dependency in artemisinin pharmacokinetics. There was a high correlation between artemisinin plasma concentrations determined at various time-points after drug administration and the AUCs after the 500 and 1000 mg doses, but less so after the 250 mg dose. This may show a tentative approach to assess the systemic exposure of the patients to artemisinin from the determination of artemisinin plasma concentrations in one or two plasma samples only. Artemisinin was well tolerated with no apparent dose or time dependent effects on blood pressure, heart rate or body temperature.

In this paper, we present a new iteration method for solving monotone equilibrium problems. This new method is based on the ergodic iteration method Ronald and Bruck in (J Math Anal Appl 61:159-164, 1977) and the auxiliary problem principle Noor in (J Optim Theory Appl 122:371-386, 2004), but it includes the usage of symmetric and positive definite matrices. The proposed algorithm is very simple. Moreover, it simplifies the assumptions necessary in order to converge to the solution. Specifically, whereas previous methods require strong monotonicity and Lipschitz-type continuous conditions, our proposed method only requires weak monotonicity conditions. Applications to the generalized variational inequality problem and some numerical results are reported.

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