Compartment Models

Compartment Model Basics - Drug's Imaginary Homes

• Theoretical pharmacokinetic spaces, not literal anatomical regions, where a drug is assumed to distribute uniformly.
• Purpose: Simplify complex ADME processes to mathematically predict drug concentration ($C_p$) over time and optimize dosing regimens.
• Key Assumptions:
  • Body acts as a system of one or more interconnected compartments.
  • Drug distribution within any compartment is instantaneous and homogenous (well-stirred).
  • Drug transfer between compartments and elimination from the body typically follow first-order kinetics (rate proportional to drug amount).
• Central Compartment ($V_c$): Includes plasma, extracellular fluid, and highly perfused tissues (e.g., heart, lungs, liver, kidneys); rapid drug equilibration.
• Peripheral Compartment(s) ($V_p$): Includes less perfused tissues (e.g., muscle, fat, bone); slower drug equilibration.

⭐ The number of exponential phases in the plasma drug concentration-time curve after an IV bolus dose determines the number of compartments in the model (e.g., two phases suggest a two-compartment model).

One-Compartment Model - The Simple Story

• Body treated as a single, uniform compartment where drug distributes instantaneously and homogeneously.

• Elimination typically follows first-order kinetics; rate of elimination is proportional to the drug amount.

• Assumptions:

  • Rapid mixing of drug throughout the compartment.
  • Linear pharmacokinetics (processes are not saturated).

• Key Parameters:

  • Volume of Distribution ($V_d$): Apparent volume into which drug distributes.
    • $V_d = ext{Dose (IV bolus)} / C_0$ (where $C_0$ is initial plasma concentration)
  • Elimination Rate Constant ($k_e$ or $k$): Fraction of drug eliminated per unit time.
  • Half-life ($t_{1/2}$): Time for drug concentration to reduce by 50%.
    • $t_{1/2} = 0.693 / k_e$
  • Clearance (CL): Volume of plasma cleared of drug per unit time.
    • $CL = k_e imes V_d$

• Graphical Representation:

  • A semi-log plot (log plasma concentration vs. time) yields a straight line after IV bolus.

• Clinical Relevance:

  • Simplifies dose calculations for drugs that rapidly distribute (e.g., some aminoglycosides after IV administration).

⭐ Following an IV bolus, drug concentration ($C_p$) declines monoexponentially: $C_p(t) = C_0 imes e^{-k_e imes t}$. The slope of the natural log plasma concentration versus time plot is $-k_e$. For log base 10, slope is $-k_e / 2.303$.

Two-Compartment Model - The Complex Tale

• Drug initially in Central Compartment (blood, highly perfused organs like heart, lungs, kidneys, brain), then distributes to Peripheral Compartment (less perfused tissues, e.g., muscle, fat).
• Plasma concentration ($C_p$) shows biexponential decline: 📌 Two compartments, two phases.
  • $\alpha$-phase (Distribution): Rapid $C_p$ fall; drug central $\rightarrow$ peripheral.
  • $\beta$-phase (Elimination): Slower $C_p$ fall; drug eliminated from central compartment post-distribution equilibrium. $\beta < \alpha$.
• Equation: $C_p(t) = A \cdot e^{-\alpha t} + B \cdot e^{-\beta t}$.
• Key Volumes of Distribution:
  • $V_c$: Central compartment volume; for initial concentration after IV bolus.
  • $V_{dss}$: Volume of distribution at steady state ($V_c + V_p$); reflects total drug after distribution.
  • $V_{d\beta}$: Volume of distribution during $\beta$-phase; used for clearance: $CL = V_{d\beta} \cdot \beta$.
• Rate Constants: $k_{12}$ (central $\rightarrow$ peripheral), $k_{21}$ (peripheral $\rightarrow$ central), $k_{10}$ (elimination from central).
• Clinical Significance:
  • Explains drug effect termination by redistribution (e.g., Thiopental: rapid IV anesthetic onset, short action due to redistribution to fat/muscle).
  • Crucial for dosing drugs with slow tissue equilibration or narrow therapeutic index (e.g., Digoxin, Vancomycin).
  • Loading dose often targets $V_c$; maintenance dose considers total clearance and $V_{dss}$ or $V_{d\beta}$.
• Examples: Lidocaine, Vancomycin, Digoxin, Diazepam.

⭐ For drugs exhibiting two-compartment kinetics, the terminal elimination half-life ($t_{1/2\beta} = 0.693/\beta$) is longer than the distribution half-life ($t_{1/2\alpha} = 0.693/\alpha$) and is the primary determinant of dosing intervals once distribution is complete.

High‑Yield Points - ⚡ Biggest Takeaways

• One-compartment model: Body as a single, uniform unit; drug distribution is instantaneous.
• Two-compartment model: Central (blood, highly perfused) & peripheral (tissues) compartments.
• Vd (Volume of Distribution): Relates drug amount in body to its plasma concentration.
• Kel (Elimination Rate Constant): Fraction of drug eliminated per unit time.
• t½ (Half-life): Time for drug concentration to decrease by 50%; inversely related to Kel.
• Loading Dose: Achieves target plasma concentration rapidly, especially for large Vd.
• Maintenance Dose: Maintains steady-state concentration within therapeutic range.