Pharmacokinetic curve fitting when the experimental error of the concentration-time data is represented by a relative...

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...

A drug’s dosage and pharmacokinetic properties determine how quickly it acts, how intense its effects are, and how long it lasts. Higher doses increase drug concentration at receptor sites, producing a hyperbolic curve when pharmacologic response is plotted against drug dose. Converting this scale to a log-linear format results in a sigmoidal curve, better representing dose–response relationships.For drugs following a one-compartment model, the pharmacologic response is directly proportional to...

The empirical approach to drug therapy optimization relies on correlating pharmacological response with administered dosage. Such an approach can be costly, time-consuming, and often yields poor correlation due to variables like formulation factors and drug elimination characteristics. A more precise approach correlates response with plasma drug concentration or the amount of drug in the body, rather than dosage. This is achieved through pharmacokinetic-pharmacodynamic (PK/PD) modeling, which...

The Emax drug-concentration effect model is central to pharmacodynamics in drug discovery and development. This model is predicated on the receptor occupancy theory, which posits that the effect of a drug is directly related to the number of receptors occupied by the drug and the resultant complex formation.The model describes the reversible interaction between a drug (C) and a receptor (R) to form a drug-receptor complex (RC). The kinetics of this interaction are quantified by an equation that...

The linear concentration–effect model, underpinned by the principle that pharmacological effect (E) is directly proportional to plasma drug concentration (C), emerges as a pivotal simplification of the Emax model for conditions where C is significantly less than EC50. This model portrays a linear trajectory of the concentration–effect relationship when drug levels are markedly below the EC50 threshold.Despite its inherent assumption of continuous effect augmentation with increasing drug...

The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (Emax), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (Emax) or the effect at zero drug concentration, limiting its...