Inhibition of Absorption
When a drug and herbal preparation are administered concomitantly, inhibition of absorption is a possible scenario. As discussed previously, the absorption process is complex; however, we normally model it with only two pharmacokinetics parameters (F and ka). Modeling the inhibition of absorption is very similar to modeling enhancements. If the amount of drug absorbed is reduced (either due to increased pre-systemic metabolism or lack of absorption from the gut lumen), it can be modeled as a reduction in F as shown below:
where Fherb is the bioavailability in the presence of the herb, and F1 is the reduction in bioavailability due to the presence of the herb. The value for Fherb must be between 0 and 1, and the value of F1 must always be less than or equal to F, the bioavailability of the drug in the absence of the herb.
If the herbal preparation slows the rate of drug absorption, then a change in the absorption rate constant, ka, can be modeled, as shown in eqn (5.31). As noted, to model changes in the absorption rate constant, several concentration measurements are needed between the time of dose administration and the tmax. The herbal preparation may cause a reduction in both the extent of absorption (F) and the rate of drug absorption (ka), in which case you would include both eqn (5.31) and (5.32) in the pharmacokinetic model for the drug.
Modeling of Pharmacodynamic Interactions
If two compounds act on the same receptor, or if they act on the same component of the pharmacodynamics cascade, they have the potential to elicit a pharmacodynamic interaction, whether additive or synergistic, or antagonistic. Modifications to the Hill equation have been used alongside response surface methodology to mathematically describe these interactions. For example, if a drug D and a partial receptor agonist A interact, the overall effect can be described as
where [A] is the concentration of the agonist, IC50 is the concentration of the agonist at 50% inhibition, and Imax is the maximum inhibitory effect.