# Bi: Explain the concept of pharmacokinetic modelling of single and multiple compartment models

**PK compartment**= mathematical concept describing a space in the body the drug is occupying – it does**not**correspond to anatomy/volume- Compartment models work by dividing the body into a number of hypothetical compartments
*NB: these are all mathematical concepts, there is no anatomical equivalent*- They are used to help us understand the ∆ plasma [ ] of a drug over time

## One Compartment Model

- Assumes body is one homogenous unit
- Drug is given & achieves instant distribution throughout body & equilibrates instantly b/w tissues

*INPUT (dose) → [DRUG IN BODY] → OUTPUT (elimination)*

- Drug is then eliminated in a [ ] dependent manner
*(exponentially)*

Graphically displays as a linear model

## Two Compartment Model

- Central compartment = plasma
- Peripheral compartment = tissues
- Drug enters
**K**central compartment_{01} - Drug eliminated
**K**central compartment_{10} - From central compartment drug redistributes to peripheral compartment
**K**_{12} - Drug cannot be eliminated from peripheral compartment, must return to central compartment
**K**_{21} - When drug administered to central compartment there is a
**rapid**decline in [ ] due to**K**_{12} **K**continues until equilibrium b/w both compartments_{12}- Then drug is eliminated
**K**_{10} - As that happens drug will move
**K**down its [ ] gradient to then be eliminated_{21}**K**_{10}

logCp vs time is used to distinguish from 1 compartment model

- α = initial rapid decline, distribution from Central → Peripheral compartment
- β = elimination from central compartment
- ∴t ½ α = distribution half life
- ∴t ½ β = elimination half life

### Propofol & 2 Compartment Model

- After initial induction dose 1.5 – 2.5mg/kg, there is rapid LOC → drug taken up by lipophilic CNS tissues
- The PPF distributes to peripheral tissues, Ph 1 at constant
**rate α** - If another dose isn’t given, patient will wake up
- If a continuous infusion is given, the peripheral compartment will become saturated with PPF

## Multicompartment Model

- Drug distributes >1 compartment
- logCp vs time shows >1 expotential
- Drug administered
- Rapid distribution phase
- Second slower distribution phase
- Elimination phase