Definition 3: IC50.

The IC₅₀ is defined as the theoretical concentration of drug at which the parasite reduction ratio is L_min/2 over the course of one life cycle. This is the concentration causing half the maximal growth per asexual cycle (e.g., 5-fold growth per cycle if the maximum average growth rate was 10-fold/cycle).

The four parameters (θ_PD = {L_max, L_min, k, ρ_1/2}) uniquely define the pharmacodynamic properties of the drug. A commonly used mathematical formula for this sigmoid relationship is given by the logistic function. For example, the 48-h parasite reduction ratio as a function of the logarithm of the drug concentration ρ can be written as

We note that the slope of this sigmoid curve at the midpoint is given by k/4. Empirical data, both in vivo and in vitro, can usually give a robust characterization of the central aspect of this curve, i.e., around the ρ_1/2 and concentrations at which the effect is close to L_max (maximal effect) (20). However, the relationship between in vitro and in vivo measures has not been well characterized, and direct measurement in vivo is very difficult (5). The MIC is determined by the parameters {L_max, L_min, k, ρ_1/2}, but small errors in k will have a large impact on the estimation of ρ_MIC. This can be observed by the relationship:

where ρ_MIC is the logarithmic concentration of drug which gives a PRR of 1 and ρ_1/2 is also on a logarithmic scale.

In the following we assume that L_min is known: this is the reciprocal of the normal parasite growth rate with negligible drug concentrations. In the estimation algorithm we set L_min = 0.1 (e.g., parasite growth rate of 10-fold per 48-h cycle). This value is independent of the drug studied.

We also assume that the L_max is known for chloroquine and is 10³.