Lecture on Compartmental Models and Mass Balance Equations

Introduction

• Focus on compartmental models using mass balance equations.
• Discuss different types of models: PK models and compartmental models.
• Key topics: mass balance issues and equations.

Pharmacokinetics Overview

• AGME (Absorption, Distribution, Metabolism, Excretion) in pharmacokinetics.
• Drug distribution to sites of action and potential for off-target effects (toxicity).

Types of Compartmental Models

• Typical Compartmental Models
• PBPK (Physiologically Based Pharmacokinetic) Models
  • Focus on compact models in this lecture.
• Models are data-driven; number of compartments depends on data.
• Compartment doesn't necessarily correspond to specific organs.

Characteristics of Compartmental Models

• Advantages
  • Easy to implement, do not require prior information.
  • Can focus on specific processes, useful for parameter values.
  • Useful for simulations.
• Disadvantages
  • Data-driven, may result in inaccurate models if data is poor.
  • Cannot always extrapolate models to different populations.

One Compartment Model

• Concept of a system (tank) representing the human body.
• Goal: determine the volume of the system using mass balance.
• Steady State: uniform concentration throughout the system.
• Bolus dose method: using a known amount to measure concentration and calculate volume.
• Assumptions: well-stirred system, chemical cannot leave.

Drug Elimination and Clearance

• Elimination of drug from system (metabolism, excretion).
• Clearance: Volume cleared per unit time.
• Volume of Distribution (Vd): Dose divided by concentration at time zero.
• Use area under the curve (AUC) to calculate clearance.

Rate Equations

• Describe drug movement in body using rate equations.
• Input Types: Bolus, zero-order (constant rate), first-order (proportional rate).
• Output Types: First-order elimination primarily discussed.
• Differences between zero-order and first-order processes.

Multi-Compartment Models

• Two-compartment systems with drug movement between compartments.
• Parameters: k12 (transfer from compartment 1 to 2), k21 (transfer from 2 to 1).
• Use of macro and micro parameters to describe system.
• Writing ordinary differential equations (ODEs) to describe drug movement.

Infusion and Mixed Processes

• Drug administered by constant rate infusion, different from bolus.
• Infusion described by ODEs for input and elimination phases.
• Zero Order vs First Order: Describing both absorption and elimination.

Mammillary Compartment Model

• Common model with a central compartment and peripheral compartments.
• Describes drug distribution and elimination.

Summary

• Compartmental models facilitate understanding of drug kinetics.
• Mass balance equations, rate equations, and ODEs are key components.
• Models implemented in software like MATLAB for analysis and simulations.