Pharmacokinetics Elimination Models

Elimination from Initial Concentration

• The elimination rate of a substance from a compartment is proportional to the amount of the substance present.
• Half-life (t½) is the time it takes for the concentration of a substance in a compartment to decrease by 50%.
• Mean residence time is the average time a particle spends in a compartment and is related to the half-life.

Non-Steady-State PK Model

• This model describes the concentration of a substance in a compartment over time, considering both elimination and continuous input.
• The model incorporates the initial concentration (C(0)), average daily dose (ADD), elimination constant (k), and volume of distribution (V).

Modeling Elimination

• Two-compartment model: The substance is distributed between two compartments, each with its own elimination rate.
• Second-order elimination: The elimination rate is not constant, but instead depends on the concentration of the substance.
• Effective half-life (keff): The slower elimination mechanism in a multi-compartment model controls the overall elimination rate.

Multiple Compartment Model

• Clearance-volume based models: These models use the apparent volume of distribution (Vd) to determine the dose within an organism.
• Physiologically based pharmacokinetics (PBPK): This model incorporates physiological and anatomical features to describe the kinetics of a substance.

Bioaccumulation

• Bioaccumulation is the net concentration of a substance within an organism after uptake, biotransformation, and elimination.
• Bioconcentration factor (BCF): This is the ratio of the concentration of a substance in a tissue to the concentration in water.
• Bioaccumulation factor (BAF): This is the ratio of the concentration of a substance in an organism to its concentration in the environment.
• Bioaccumulation factor from sediment (BSAF): This is the ratio of the concentration of a substance in an organism to its concentration in sediment.

Interactions with Organism Surface

• Before uptake, a substance can interact with the organism's surface, influencing its bioavailability.

Adsorption

• Adsorption is the process of a substance attaching to a surface.
• Freundlich and Langmuir Isotherm Equations: These equations model the adsorption of substances onto surfaces, considering factors like concentration and saturation.

Adsorption Isotherms

• Freundlich Equation: This equation describes the concentration of a substance adsorbed on a surface based on the concentration in solution.
• Langmuir Equation: This equation describes adsorption on planar surfaces with a fixed number of identical sites, considering factors like bonding strength and maximum adsorption.

Across the Cell Membrane

• Diffusion: This is the movement of a substance down its concentration gradient.
• Active transport: This is the movement of a substance against its concentration gradient, requiring energy.
• Facilitated diffusion: This is the movement of a substance down its concentration gradient through a carrier protein, without energy.
• Endocytosis: This is the process of bringing a substance into the cell by engulfing it in a membrane- bound vesicle.

Reaction Order - Kinetics of Uptake & Elimination

• Zero-order reaction: The rate of elimination is constant regardless of the concentration.
• First-order reaction: The rate of elimination is proportional to the concentration.
• Michaelis-Menten Kinetics: This describes enzyme-mediated processes with a threshold concentration, exhibiting zero-order kinetics above and first-order kinetics below the threshold.

Biotransformation

• Biotransformation is the process of changing a substance within the body to facilitate elimination.
• Detoxification: This process transforms substances into less toxic or more hydrophilic forms for easier elimination.
• Activation: This process transforms substances into more toxic forms.

Mechanisms of Biotransformation & Detoxification

• Metals and Metalloids: These can undergo biomethylation, biomineralization, or binding to metallothioneins.
• Organic compounds: These can be eliminated rapidly or undergo Phase I and Phase II metabolism to become more hydrophilic.

Elimination Mechanisms

• Depuration: The release of a contaminant into the environment.
• Clearance: The rate of contaminant movement between compartments.
• Growth dilution: As organisms grow, the concentration of a contaminant decreases due to dilution.

Plants and Animals

• Plants: They eliminate contaminants through leaf dropping, leaching, evaporation, root exudation, and herbivore grazing.
• Animals: They eliminate contaminants through gills, exhalation, bile secretion, intestinal mucosa, molting, kidney excretion, and egg deposition.

Modeling Elimination

• First-order kinetics: The most common model for elimination.
• Zero-order kinetics: Less common than first-order kinetics.
• Saturation kinetics: Also less common, occur at high contaminant concentrations when elimination pathways become saturated.
• Compartment models: These model the movement of a contaminant between different body compartments.

Pharmacokinetic Models

• Pharmacokinetic (PK) models: These models evaluate the internal dose of a compound.
• Simple models: One-compartment, first-order models.
• Complex models: Multi-compartment, physiologically-based pharmacokinetic models.

Bioconcentration Factor

• This is the concentration of a substance in an organism or sediment compared to its concentration in water.

Persistency of Chemicals in Soil

• Chemicals are classified based on their persistence in soil, with categories including persistent, moderately persistent, and non-persistent.

Why Concentrations are Higher in Predators

• Predators accumulate more contaminants due to their larger size and higher trophic level, leading to a dilution effect in prey.
• Biomagnification: This occurs when the concentration of a substance increases as it moves up the food chain.

Trophic Transfer

• Twin-tracer technique: This technique uses radioisotopes to measure the assimilation efficiency of a contaminant.
  • Trophic position: This refers to an organism's position in the food chain, often determined using stable nitrogen isotope analysis.

Quantifying Bioaccumulation from Food

• Assimilation from food: This evaluates the transfer of a contaminant between trophic levels.
• Assimilation efficiency: This quantifies the bioavailability of a contaminant from food.

Explore the principles of drug elimination from initial concentration in pharmacokinetics. This quiz covers half-life, mean residence time, and both one and two-compartment models. Test your understanding of non-steady-state pharmacokinetic models and key concepts in drug concentration over time.