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Understanding Pharmacokinetics: Mathematical Descriptions of Drug Processes

This article delves into the intricate biologic processes influencing and influenced by drugs, utilizing mathematical expressions to describe temporal changes in drug concentration. It explores constraints related to ADME processes, optimal dosage regimes, and the necessity for improved kinetic structures. Compartment models, linear and non-linear pharmacokinetics, as well as factors affecting the apparent volume of distribution and drug clearance are elaborated upon. Detailed insights into bioavailability and its measurement in drugs through plasma concentration vs. time plots are also provided.

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Understanding Pharmacokinetics: Mathematical Descriptions of Drug Processes

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  1. Pharmacokinetics Mathematic descript. of A) Biolog. processes affecting drugs B) Biolog. processes affected by drugs drugs • Mathematical expressions to describe temporal changes in drug conc. • Determine constrains related to ADME processes Optimal dossage regime (how much drug, how often etc.) Bad kinetics -- Need for improved structure

  2. Compartment models Two compartment model One compartment modell The whole body = central compartment Drug rapidly distributed thru out the body Central compartment (plasma etc) Peripher compartment (certain tissue, organs etc)

  3. Linear Pharmacokinetics • 1. order process; Rate (biotransformation) Size of Dose • Drug transported by passive diffusion • Drug conc in organ  Size of Dose • t 1/2 elimination, elimination rate const independent of Dose • Biotransformation: • transformation of drugs between “compartments” • absorbtion • elimination • Non-Linear Pharmacokinetics • 0. order kinetics • Rate of biotransformation independent of Dose • Carrier-Protein with a given max capasity involved in biotransform. (Michaelis-Menten) • More complicated situations: • Reabsorb. of drug in kidney • Metabolites inhib. their own formation (neg. feed back)

  4. The appearant volume of distribution (V) • Normally characteristic of drug (not biolog. systhem) • Influenced by certain diseases (changes in blood compossition, tot. body fluid, tussue permeability) • Independent of drug conc. (lineær pharmacokinetics) V: <10 L - >100 L

  5. Clearance (Cl) • Function of blood flow • Function of an organs capasity to metabol. / excrete • Hypothetic vol. of distribution from which the drug is removed / time

  6. Bioavailability Rate and extent to which the drug reach general circulation • Comparison of plasma conc vs time plots • Different drug • Same drug, different formulation • Drug with and witout food etc.

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