Multi Exponential Pharmacokinetics Flashcards

1. Introduction to Multi Exponential Pharmacokinetics

• Today's lecture focuses on multi exponential pharmacokinetics (PK) and the transition from mono exponential PK.

• Lecture Objectives:

  • Understand multi exponential PK and its role in pharmacokinetics.

  • Differentiate between mono exponential and multi exponential models.

  • Understand the mathematical basis of multi exponential PK.

  • Apply multi exponential PK models to calculate pharmacokinetic parameters.

  • Use case studies to enhance understanding.

2. Pharmacokinetic Models

2.1 One Compartment Model

• The simplest model, assumes:

  • Instantaneous distribution of drug following administration (IV bolus).

  • Elimination occurs solely from the central compartment (blood).

2.2 Two Compartment Model

2.2.1 Structure

• Divides the body into two compartments:

  • Central Compartment: Blood, plasma, and highly perfused tissues (liver, kidney).

  • Peripheral Compartment: Low perfused tissues (bone, fat).

2.2.2 Dynamics

• Drug enters the central compartment and achieves dynamic equilibrium with the peripheral compartment governed by rate constants.

• Elimination occurs from the central compartment, with distribution and redistribution between compartments.

2.3 Advanced Models

• Models can be expanded to three compartments and beyond to account for more complex drug behavior.

3. Importance of the Two Compartment Model

• Useful for drugs that localize in specific tissues, such as:

  • Statins: Inhibit reductase action in the liver.

  • Digoxin: Distributes into cardiac tissue for effect.

  • Thyroxine and Diazepam: Exhibit high affinity to tissue proteins.

4. Concentration-Time Profile in Two Compartment Model

4.1 Biphasic Behavior

• Initial distribution phase followed by an elimination phase.

• Plotting concentration vs. time shows:

  • Rapid decline during distribution phase.

  • Slower decline during terminal elimination phase.

4.2 Phase Analysis

• The distribution phase (alpha) involves both elimination and redistribution, while the terminal phase (beta) reflects true elimination.

• K12: Distribution rate from central to peripheral compartment.

• K21: Redistribution rate from peripheral to central compartment.

5. Assumptions of the Two Compartment Model

• Body divided into compartments representing physiological spaces.

• First order kinetics where elimination is proportional to drug concentration.

• Homogeneity assumed within compartments, with drug evenly distributed.

• Monitoring of drug concentration occurs in blood (central compartment).

6. Comparing Models: Mono Exponential vs. Multi Exponential

6.1 Mono Exponential Model

• Characterized by instantaneous distribution and elimination.

• Exhibits simple exponential decay without biphasic patterns.

• Example: Gentamicin - exhibits rapid elimination due to hydrophilic nature and limited tissue distribution.

6.2 Multi Exponential Model

• Allows for delayed distribution and compartmental behaviors.

• Characterized by drug concentrations reflecting both distribution and elimination rates, leading to bi exponential decay.

7. Key Parameters in Two Compartment Model

7.1 Rate Constants

• KEL (K10): Elimination rate constant.

• K12: First order distribution from the central to the peripheral compartment.

• K21: First order redistribution from the peripheral to the central compartment.

7.2 Volume of Distribution

• Involves distinct calculations for central and peripheral compartments, varying between:

  • Volume of distribution immediately after administration.

  • Volume of distribution during terminal phase.

  • Volume of distribution at steady state.

7.3 Half Life

• Defined as the time taken for drug concentration to decrease by 50%:

  • Alpha phase: 0.693/alpha

  • Beta phase: 0.693/beta (true biological half life).

  • Importance of half life varies between compartment models due to redistribution effects.

8. Practical Application and Case Study: Digoxin

• Example demonstrates two compartment model:

  • Time vs. concentration plots show initial rapid decline followed by slower terminal decline.

  • Effect observed relates strongly to plasma concentration dynamics, particularly the anti-clockwise hysteresis seen with digoxin.

9. Mathematical Analysis of Two Compartment Pharmacokinetics

9.1 Bi Exponential Equation

• Concentration at time (t) = A * e^(alpha * t) + B * e^(beta * t)

  • A & B: Empirical coefficients calculated from data.

  • Alpha and Beta: Define slopes of distribution and elimination.

9.2 Method of Residuals

• Allows separation of elimination from distribution phase to accurately determine rate constants.

  • Involves plotting residuals and extracting slope information to define parameters.

10. Conclusion and Summary

• Multi exponential models provide a more accurate representation of drug distribution and elimination than mono exponential models.

• Understanding the compartmental analysis is crucial for calculating pharmacokinetic parameters and applying them in clinical scenarios.