One Compartment Model Lecture

Introduction

• One Compartment Model: Definition
  • Drug enters blood → distributed to liver (metabolized by first-pass effect) → unchanged/metabolized drug back to systemic circulation.
  • Drug distributes to organs (heart, lungs, CNS) based on lipophilicity and volume of distribution.
  • Drug eventually excreted via kidneys in urine.
• Instantaneous Distribution
  • Assumes rapid drug distribution to all organs, forming a single compartment for kinetics analysis.
  • Key Focus: Drug distribution and elimination from a single compartment.

Compartment Modeling

• Concept: Hypothetical model simplifying drug distribution into compartments.
• One Compartment Model: Considers all organs as a single unit; immediate and uniform drug distribution; elimination from the central compartment.
• Key Parameters:
  • X₀: Initial dose of drug.
  • XC: Amount of drug in the single compartment.
  • Elimination: Follows first-order kinetics, represented by elimination rate constant (k).

Routes of Administration

• Types: IV bolus, IV infusion, extravascular.
• IV Bolus Administration
  • Single dose, instant entry to system, follows first-order kinetics.
  • Equation:
    • Amount: X = X₀ * e^(-kt)
    • Concentration: C = C₀ * e^(-kt)
  • Example Calculation:
    • Given: 500 mg IV bolus, find concentration after 4 hours.
    • Formula: C = 20 * e^(-0.57*4)
    • Result: C = 2 µg/ml
• Other Calculations
  • Half-life (t₀.₅): t₀.₅ = 0.693 / k
  • Volume of Distribution (Vd): Vd = X₀ / C₀
  • Dosage Interval: Ensure plasma concentration stays above a minimum (e.g., 1 µg/ml).

Example Problem 1

• Data: 500 mg dose, first-order kinetics (C = 20 * e^(-0.57t)).
• Tasks: Calculate concentration after 4 hours.

• Solution:

  • Given: C₀ = 20 µg/ml, k = 0.57 hr⁻¹
  • Formula: C = C₀ * e^(-kt)
  • Calculation: C₀ = 20 µg/ml, k = 0.57 hr⁻¹, t = 4 hrs
  • Result: C₄ = 20 * e^(-0.57*4) = 2 µg/ml

Example Problem 2

• Data: Calculate half-life, Vd, and next dose interval.
• Solution:
  • Half-life (t₀.₅): t₀.₅ = 0.693 / 0.57 = 1.22 hr
  • Vd:
    • Convert units: C₀ = 20 µg/ml = 20 mg/L
    • Volume: Vd = 500 mg / 20 mg/L = 25 L
  • Next Dose Timing: Maintain concentration above 1 µg/ml.
    • Formula: t = 2.303/k * log(C₀/C)
    • Calculation: t = 2.303/0.57 * log(20/1) = 5.26 hrs

IV Infusion Model

• Constant Rate Infusion: Maintaining steady-state concentration.
• Equation: Change in drug levels dX/dt = Q - kX
  • Integrated: C = Css * (1 - e^(-kt))
  • Steady-State Concentration (Css): Css = Q / Cl
  • Infusion Rate (Q): Q = Css * Cl

Example Problem 3

• Data: Given steady-state concentration (Css = 0.1 µg/ml), calculate the rate of infusion (Q) and loading dose (X₀) for a 12-hour half-life.
• Solution:
  • Rate of Infusion (Q):
    • Q = Css * Cl
    • Cl = k * Vd = (0.693/12) * 20 = 1.16 mg/hr
  • Loading Dose (X₀):
    • Loading Dose (X₀) = Css * Vd
    • X₀ = 0.1 µg/ml * 20 L = 2 mg*

Conclusion

• Key Takeaways: One compartment model simplifies pharmacokinetics by assuming rapid and uniform drug distribution.
• Next Steps: Practice with different administration routes and models to understand kinetics.
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