Antoine-Augustin Parmentier: pharmacist extraordinaire

Mathematical principles play a crucial role in pharmacokinetics, providing a framework for understanding and quantifying drug distribution and elimination dynamics in the body. By utilizing mathematical expressions and units, pharmacologists can accurately characterize the behavior of drugs, optimize dosing regimens, and predict therapeutic outcomes.
One significant application of mathematics in pharmacokinetics is the characterization of drug distribution through the volume of distribution...

Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
Two primary types of compartment models are recognized: mammillary and catenary. The more...

In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
Pharmacokinetic reactions...

Pharmaceutical products contain more than just the active drug; they also contain various excipients such as binders, solubilizers, stabilizers, preservatives, and other elements. In some cases, impurities or contaminants might be present. Traditionally, quality control in pharmaceuticals has primarily focused on the analysis of the active drug, often overlooking the impact of these additional components. The recent issue with heparin contamination by over-sulfated chondroitin sulfate, a...

Clearance measures drug elimination from the central compartment, including plasma and highly perfused organs like kidneys and liver. Its calculation varies depending on pharmacokinetic models and administration routes. The one-compartment model, for instance, portrays the pharmacokinetics of polar drugs such as aminoglycoside antibiotics administered intravenously and readily excreted in urine. In this case, clearance is influenced by the terminal rate constant (λz) and the total volume of...

Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...