PMCOL 306 - Lecture 4

Drug Distribution - Terminology

• Cp: Plasma concentration of a drug.

• D or D0: Dose of drug administered.

• AVD or Vd: Apparent volume of distribution.

• ka: First-order rate constant of absorption.

Drug Distribution - Rate Constants

• ke: First-order rate constant of excretion.

• km: First-order rate constant of metabolism.

• k or kel: Elimination rate constant, equal to km + ke.

• K10: Elimination from the central compartment.

Drug Distribution - Compartment Rate Constants

• K12: Rate constant for distribution from the central compartment to the peripheral compartment.

• K21: Rate constant for distribution from the peripheral compartment to the central compartment.

• The two rate constants are not equal.

• t1/2: Drug half-life.

Pharmacokinetic Models - One-Compartment Model

• The simplest model involves a rapid intravenous injection of the entire dose, called an IV bolus.

• Drug moves very quickly between the blood (central) and tissue (peripheral) compartments.

• Distribution is complete by the time the first plasma sample is taken.

• A plot of the natural log of plasma concentration against time is linear.

Pharmacokinetic Models - Two-Compartment Model

• Drug moves more slowly between the central and tissue compartments.

• Distribution is incomplete by the time the first plasma sample is taken.

• A plot of log drug concentration against time is not linear, with an initial steep portion followed by a shallower portion.

• The central compartment exchanges drug with the peripheral compartment through K12 and K21, while K10 represents elimination from the central compartment.

Apparent Volume of Distribution

• The theoretical volume that would contain the total amount of drug in the body at a concentration equal to the measured plasma concentration.

• AVD = D / C, where D is the amount of drug in the body and C is the plasma concentration.

• Expressed in litres.

• It is a major pharmacokinetic property and determinant of drug half-life and dosing frequency.

Apparent Volume of Distribution - Measurement Timing

• AVD depends on when plasma concentration is measured.

• Different distribution phases produce different apparent volumes of distribution.

• Vc represents the central compartment volume immediately following an IV bolus.

• Vss represents the apparent volume of distribution at steady state.

Apparent Volume of Distribution - Vc

• Vc is the volume of the central compartment immediately following an intravenous bolus dose.

• It is often represented as V or Vd.

• It is widely used to calculate loading doses when steady state needs to be reached quickly.

• Vc = Dose / C0.

Apparent Volume of Distribution - Vss

• Vss is the volume of distribution at steady state.

• It represents the apparent distribution volume associated with the steady-state dosing paradigm under which most drugs are developed.

• Vss is the preferred measure when comparing Vd between patient groups.

• It is independent of elimination processes.

Apparent Volume of Distribution - Vbeta

• Vbeta is derived from the terminal elimination-phase half-life.

• It is not often used because it is difficult to measure.

• It is affected by changes in drug clearance.

• It represents the apparent volume of distribution associated with the terminal beta phase.

Apparent Volume of Distribution - Pharmacokinetic Parameters

• AUC: Area under the concentration-time curve.

• AUMC: Area under the moment curve, or distribution equilibrium curve.

• MRT: Mean residence time, the average time a drug molecule stays in the body; derived for drugs administered intravenously.

• CL: Clearance rate.

Apparent Volume of Distribution - Vc Equation

• Vc = Dose / C0.

• C0 is the plasma concentration immediately following an IV bolus.

• This equation is used to calculate the apparent volume of the central compartment.

• Memorize this equation.

Apparent Volume of Distribution - Total Body Water

• Vc indicates the degree of drug distribution in body water.

• Total body water is approximately 0.6 L/kg in men and 0.5 L/kg in women.

• If a drug is evenly distributed throughout the body, its calculated Vc will approximate total body water.

• The human body is approximately 50 to 70 percent water.

Apparent Volume of Distribution - Total Body Water Examples

• For a 70 kg man, total body water is approximately 42 L.

• For a 60 kg woman, total body water is approximately 30 L.

• A drug evenly distributed throughout body water will have an apparent volume of distribution near the corresponding total body water value.

Apparent Volume of Distribution - Vc Below 3 L

• A Vc below 3 L indicates that the drug is mainly confined to plasma.

• Such a drug has limited distribution outside the bloodstream.

• Heparin is an example.

Apparent Volume of Distribution - Vc Around 17 L

• A Vc around 17 L indicates distribution mainly into extracellular water.

• The drug is relatively hydrophilic and does not readily cross biological membranes into intracellular space.

• Mannitol is an example.

Apparent Volume of Distribution - Vc Around 40 L

• A Vc around 40 L indicates distribution throughout total body water.

• The drug is sufficiently lipophilic to partition into cells but sufficiently hydrophilic to remain soluble in aqueous spaces.

• Ethanol is an example.

Apparent Volume of Distribution - Vc Above 40 L

• A Vc above 40 L can indicate that tissue binding exceeds plasma protein binding.

• A large volume of distribution means that substantial drug has partitioned into tissues outside the plasma.

• Chloroquine and propofol are examples.

• Propofol has an AVD of approximately 560 L.

Apparent Volume of Distribution - Membrane Permeability

• If a drug cannot cross membranes, its Vc cannot exceed the extracellular space.

• Such a drug remains outside cells.

• Its distribution is therefore restricted by membrane permeability.

Apparent Volume of Distribution - Plasma vs. Tissue Binding

• If plasma binding is stronger than tissue binding, Vc will generally be below 40 L.

• More drug remains in the circulation rather than penetrating into tissue.

• If tissue binding exceeds plasma protein binding, Vc can be greater than 40 L.

Apparent Volume of Distribution - Body Water

• A 100 mg dose is administered to a 100 kg woman with an estimated total body water of 50 L.

• Plasma drug concentration is 2 micrograms/mL.

• Vc = 100 / 2 = 50 L.

• This suggests distribution throughout total body water.

Apparent Volume of Distribution - Confined to Plasma

• A 100 mg dose is administered intravenously.

• Plasma drug concentration is 33.3 micrograms/mL.

• Vc = 100 / 33.3 = approximately 3 L.

• This suggests that the drug is confined mainly to plasma.

Apparent Volume of Distribution - Body Water Calculation

• A 100 mg dose is administered to a 100 kg woman with an estimated total body water of 50 L.

• Plasma drug concentration is 0.5 micrograms/mL.

• Vc = 100 / 0.5 = 200 L.

• This exceeds total body water, suggesting that substantial drug is stored in another compartment, such as fat.

Apparent Volume of Distribution - Kidney and Liver Dysfunction

• Drugs strongly bound to plasma constituents, such as phenytoin and diazepam, can have increased AVD when plasma protein binding is reduced in liver or kidney disease.

• Reduced AVD is a general phenomenon associated with renal failure.

• Pronounced changes are most likely for drugs eliminated through renal excretion, such as digoxin.

Apparent Volume of Distribution - Dehydration

• Dehydration decreases body water.

• Decreased body water can decrease AVD.

Apparent Volume of Distribution - Age

• With age, body fat generally increases while total body water decreases.

• Increased fat can increase the volume of distribution of highly lipophilic drugs.

• Diazepam and chlordiazepoxide are examples.

• Increased distribution into fat may meaningfully increase elimination half-life.

Apparent Volume of Distribution - Obesity

• Lipophilicity is a principal correlate of in-vivo AVD and the increased AVD of drugs in obese patients.

• Increased AVD can prolong drug half-life.

• Prolonged half-life can delay drug accumulation and washout during and after chronic dosing.

• The magnitude depends on the degree of obesity and the lipid solubility of the drug.

Apparent Volume of Distribution - Summary

• AVD is the theoretical volume required to dilute the total administered drug to the measured plasma concentration.

• It does not represent the actual volume of the body or its fluid compartments.

• Highly tissue-bound drugs have low plasma concentrations and high AVD.

• Drugs that remain mainly in circulation have higher plasma concentrations and low AVD.

Apparent Volume of Distribution - Limitations

• AVD provides a reference for the expected plasma concentration for a given dose.

• It provides limited information about the specific pattern of drug distribution.

• Drugs may distribute primarily into fat, remain in extracellular fluid, or bind extensively to particular tissues.

• Each drug has its own distribution pattern.

Pharmacokinetic Constants - Models Studied

• One-compartment model with IV bolus administration.

• One-compartment model with IV infusion.

• Loading dose followed by IV infusion.

• Oral administration and the two-compartment model with IV bolus administration.

Drug Elimination Kinetics - Zero Order

• Zero-order kinetics involve elimination of a constant amount of drug per unit time.

• The amount eliminated per unit time does not depend on the drug concentration.

• Ethanol is an example of a drug that follows zero-order kinetics.

Drug Elimination Kinetics - First Order

• First-order kinetics involve elimination of a constant fraction of drug per unit time.

• The amount eliminated per unit time depends on the amount of drug present.

• First-order kinetics are the most common type in pharmacokinetics.

Drug Elimination - Logarithmic Transformation

• Drug elimination is typically a first-order process described by an exponential decay curve.

• Pharmacokinetic data can be converted into a linear relationship to make rate constants easier to calculate.

• A logarithmic concentration-time plot is linear for first-order elimination in a one-compartment model.

Logarithmic Conversion - Natural Log and Base-10 Log

• The base-10 logarithm is commonly written as log, while the natural logarithm is written as ln.

• The value of e is approximately 2.71828.

• The natural logarithm of 10 is approximately 2.303.

• Multiply ln by approximately 2.303 to convert to log; divide log by approximately 2.303 to convert to ln.

One-Compartment Model - IV Bolus

• The amount of drug in the body is not measured directly; blood samples are collected at intervals and plasma drug concentrations are analyzed.

• The relationship between drug amount and plasma concentration is DB = Vd x Cp.

• DB is the amount of drug in the body at time t.

• D0B is the amount of drug in the body at time zero, corresponding to the administered dose.

One-Compartment Model - Calculating Vd

• Sampling blood soon after administration provides a reasonable estimate of the initial plasma concentration, C0p.

• The dose and initial plasma concentration can be used to calculate Vd.

• Vd = Dose / C0p.

• Vd = D0B / C0p.

One-Compartment Model - Drug Amount Over Time

• DB = D0B x e^(-kt).

• DB is the total amount of drug in the body at time t.

• D0B is the initial amount of drug in the body.

• k is the elimination rate constant, and t is elapsed time.

One-Compartment Model - Plasma Concentration Over Time

• C = C₀ x e^(-kt).

• C is the plasma concentration at time t.

• C₀ is the initial plasma concentration.

• k is the elimination rate constant, and t is elapsed time.

One-Compartment Model - Logarithmic Equations

• log DB = (-kt / 2.3) + log D0B.

• ln DB = -kt + ln D0B.

• These equations express first-order elimination as a linear relationship after logarithmic transformation.

Drug Half-Life - Equation

• t1/2 = 0.693 / k.

• t1/2 is the time required for drug concentration to decrease to half its initial value.

• k is the elimination rate constant.

IV Bolus - Calculating Concentration

• Initial concentration C0 = 100 mg/L, k = 0.10 h^-1, and elapsed time t = 6 h.

• Use C = C0 x e^(-kt).

• The concentration after 6 hours is approximately 54.9 mg/L.

Elimination Rate Constant and Half-Life - Clinical Importance

• Help estimate the time required to reach steady state.

• Help estimate the time required to eliminate all or part of a drug from the body.

• Help estimate the amount of drug accumulated in the body and the degree of peak-trough fluctuation.

• Help determine the appropriate dosing interval.

Drug Elimination - Five Half-Lives

• Approximately five half-lives are required to reach steady state.

• Approximately five half-lives are also required to eliminate nearly all of a drug from the body.

• Five half-lives represent near-complete elimination, rather than literal removal of every drug molecule.