Pharmacokinetics: Reaction Rates and Orders

Pharmacokinetic Models and Mathematical Fundamentals

Rate of a Chemical Reaction

• The rate of a chemical reaction is the velocity at which it occurs.
• The order of a reaction is the way in which the concentration of a drug or reactant affects the rate.

Types of Rate Processes

• Zero-order rate process: the drug concentration changes at a constant rate with respect to time.
• First-order rate process: the drug concentration changes with respect to time, equal to the product of the rate constant and the concentration of the drug.
• Pseudo-order rate process: describes a situation where one of the reactants is present in large excess or does not affect the overall reaction.

Zero-Order Reaction

• The drug concentration changes at a constant rate with respect to time: C = -K0t + C0
• Where: C = drug concentration at any time, K0 = zero-order rate constant, and C0 = drug concentration when time (t) equals zero.

First-Order Reaction

• The drug concentration changes with respect to time, equal to the product of the rate constant and the concentration of the drug: C = C0e-kt
• Where: C = drug concentration at any time, k = first-order rate constant, and C0 = drug concentration when time (t) equals zero.

Significance of Rate Constants (k)

• Characterize the change of drug concentration in a particular reference region.
• Give the speed at which a drug:
  • Enters the compartment (absorption rate constant, ka).
  • Distributes between a central and peripheral compartment (distribution rate constant).
  • Is eliminated from the systemic circulation (elimination rate constant, k).

Elimination Kinetics

• Zero-order elimination kinetics: the rate of elimination is constant and independent of the drug concentration.
• First-order elimination kinetics: the rate of elimination is proportional to the drug concentration.

Half-Life (t½)

• The time required for the concentration of a drug to decrease by one half.
• Units: time.
• Significance of Half-Life:
  • Determine the dosing interval necessary to obtain the desired Cp of the drug.
  • Predict how long it will take a drug to reach steady-state levels.
  • Predict the accumulation of a drug in the body for a specific dosing interval.

Nonlinear Pharmacokinetics

• Also known as capacity-limited, dose-dependent, or saturation pharmacokinetics.
• Do not follow first-order kinetics as the dose increases.
• Result from the saturation of an enzyme- or carrier-mediated system.

Characteristics of Nonlinear Pharmacokinetics

• The AUC is not proportional to the dose.
• The amount of drug excreted in the urine is not proportional to the dose.
• The elimination half-life may increase at higher doses.
• The ratio of metabolites formed changes with increased dose.

Michaelis-Menten Kinetics

• Describe the velocity of enzyme reactions.
• Used to describe nonlinear pharmacokinetics.

Models and Compartments

• A model is a mathematical description of a biologic system.
• A compartment is a group of tissues with similar blood flow and drug affinity.

One-Compartment Model

• The drug entering the body distributes instantly between the blood and other body fluids or tissues.
• Characteristics of Open One-Compartment Model:
  • No absorption.
  • Rapid distribution of drug between bloodstream and tissue.
  • Equilibrium is instantly obtained.
  • Fall of drug concentration depends on excretion and metabolism.

Open Two-Compartment Model

• The drug entering the body does not instantly distribute between the blood and other body fluids or tissues.
• Characteristics of Open Two-Compartment Model:
  • No absorption.
  • Slow distribution of drug between bloodstream and tissue.
  • Equilibrium is obtained some later time after administration.
  • Steep fall of first part of blood level curve due to distribution.

Bioavailability and Bioequivalence

• Bioavailability: a measurement of the rate and extent to which the active ingredient or active moiety becomes available at the site of action.
• Bioequivalence: achieved if the extent and rate of absorption are not statistically significantly different from those of the standard when administered at the same molar dose.

Parameters for Bioavailability and Bioequivalence

• Time for peak plasma concentration (tmax).
• Peak plasma concentration (Cmax).
• Area under the plasma drug concentration versus time curve (AUC).

Determining Bioavailability and Bioequivalence

• Using plasma drug concentration versus time profiles.
• Using urinary drug excretion studies.
• Using measurements of an acute pharmacological effect.
• Using clinical studies.
• Using in vitro studies.### Urinary Drug Excretion Studies
• Most accurate method of determining bioavailability if the active moiety is excreted unchanged in significant quantity in the urine
• Cumulative amount of active drug excreted in the urine (Du∞) directly related to the extent of systemic drug absorption
• Rate of drug excretion in the urine (dDu/ dt) directly related to the rate of systemic absorption
• Time for the drug to be completely excreted (t∞) corresponds to the total time for the drug to be systemically absorbed and completely excreted after administration

Measurements of Acute Pharmacologic Effects

• Onset time: time from administration to the Minimum Effective Concentration (MEC)
• Intensity: proportional to the number of receptors occupied by the drug
• Duration of action: time for which the drug concentration remains above the MEC
• Therapeutic window: drug concentration range between the MEC and Minimum Toxic Concentration (MTC)

Factors Modifying Bioavailability

• Physiologically modified bioavailability:
  • Age
  • Sex
  • Physical state of the patient
  • Time of administration
  • Stomach emptying rate
  • Type and amount of food
  • pH and enzyme variations in GIT
  • Motility of GIT
  • Blood flow
  • Liver and kidney function
  • Body weight
• Dosage form modified bioavailability:
  • Particle size
  • Polymorphic form
  • Presence of solvate or a hydrate
  • Chemical presentation of salts, ester, ether, complexes
  • pH of dosage forms and environment
  • Solubility characteristics
  • Type and amount of vehicle substances
  • Manufacturing method employed

Bioavailability vs Bioequivalence

• Bioavailability: rate and extent to which the active ingredient or active moiety is absorbed from a drug product and becomes available at the site of action
• Bioequivalence: absence of a significant difference in the rate and extent to which the active ingredient or active moiety becomes available at the site of drug action when administered at the same molar dose under similar conditions

Bioavailability and Bioequivalence Studies

• Purpose: to compare the bioavailability of the same drug from various drug products in the process of approving pharmaceutical products for marketing
• Types of studies:
  • Early and late clinical trial formulations
  • Formulations used in clinical trials and stability studies
  • Clinical trial formulations and to-be-marketed drug products
  • Product strength equivalence

Relative and Absolute Bioavailability

• Relative bioavailability: compares the bioavailability of a drug in a designated formulation with that of the same drug in a reference formulation
• Absolute bioavailability: compares the bioavailability of the active drug in the systemic circulation following extravascular administration with the bioavailability of the same drug following intravenous administration

Methods for Assessing Bioavailability and Bioequivalence

• In vivo measurement of active moiety or moieties in biological fluid (pharmacokinetic study)
• In vivo pharmacodynamic (PD) comparison
• In vivo limited clinical comparison
• In vitro comparison
• Any other approach deemed acceptable by the FDA

Biopharmaceutic Factors Influencing Bioavailability

• Biopharmaceutic factors:
  • Physicochemical properties of the drug molecule
  • Route of drug administration
  • Desired pharmacodynamic effect
  • Toxicologic properties of the drug
  • Safety of excipients
  • Effect of excipients and dosage form on drug product performance
  • Manufacturing processes
• Importance of biopharmaceutic principles in drug product design and development

This quiz covers the fundamentals of pharmacokinetic models, including the rate and order of chemical reactions, and various classes of rate processes.