Short answers, pulled from the story.
Pharmacokinetics (PK) is the branch of pharmacology that studies how the body affects a substance after administration, tracing any chemical xenobiotic from entry to complete elimination. It is based on mathematical modeling of the relationship between drug plasma concentration and the time elapsed since administration. Pharmacokinetics is contrasted with pharmacodynamics, which studies how the drug affects the organism.
ADME stands for Absorption, Distribution, Metabolism, and Excretion, the four phases a drug passes through after entering the body. An extended version, LADME, includes Liberation as a separate first step. Metabolism and excretion are sometimes grouped together under the single term elimination.
Bioavailability is the proportion of an administered drug that reaches systemic circulation. Intravenous administration yields a bioavailability of 1 (100%), and all other routes are measured against that benchmark. A drug with a bioavailability of 0.8 administered at 100 mg delivers an effective dose of 80 mg.
Noncompartmental analysis estimates pharmacokinetic parameters directly from concentration-time data without assuming a specific biological model, making it versatile and suitable for bioequivalence studies. Compartmental analysis models the organism as a system of differential equations with interacting compartments, allowing parameters to be modified and extrapolated to new situations. The tradeoff is that compartmental models require more effort to develop and validate and still make simplifying assumptions.
Ciclosporin was nearly abandoned as an immunosuppressant after it was found to cause nephrotoxicity in a number of patients. Pharmacokinetic monitoring, which involves tracking each patient's plasma concentrations individually and adjusting the dose, made it possible to use the drug safely and has since facilitated a large number of organ transplants.
Non-linear pharmacokinetics occurs when drug handling stops scaling proportionally with dose, due to enzymatic saturation, enzyme induction or inhibition, or kidney-driven active elimination independent of plasma concentration. Fluvoxamine, fluoxetine, and phenytoin are examples of drugs that inhibit or induce their own metabolism, causing the elimination half-life to lengthen as doses increase. These non-linearities can arise at any stage of the ADME sequence.