(2B) Compartmental Systems to Evaluate Drug Distribution

WHAT HAPPENS AFTER IV BOLUS?

tep 1: Concentration vs Time

• Looks like normal decline (similar to 1-compartment at first)

Step 2: ln(C) vs Time → IMPORTANT

• Now reveals TWO PHASES ✅⭐

This equation used for…

For:

• Single IV bolus

• 2-compartment drug

WHAT MICRO CONSTANTS REPRESENT

• These are TRUE rate constants

• Govern:

  • Distribution

  • Elimination

• NOT just math — real physiology

k20 ≈ negligible

why?

Drug eliminated mainly from central (live + kidney)

Major metabolism/excretion happens there

WHAT IF k20 NOT NEGLIGIBLE?

• You CANNOT use k10

• You USE β instead ✅⭐

• β is:

  • An approximation of elimination

• If complex elimination:

• If simple (central only):

• If complex elimination:

  • Use β (approximation)

• If simple (central only):

  • Use k10 (true)

What phrases means to use 2-compartment model?

• “bi-exponential decline”

• “two-phase elimination”

JUST READ:

EXAM FOCUS ON CALCULATIONS

• Homework → calculate all micro constants

• EXAM → ONLY k10 ✅⭐

• Will NOT ask:

  • k12

  • k21

• Assume k20 is negligible

• “What is best elimination rate constant?

k10

k10 vs β

k10:

• TRUE elimination constant

• Used for:

  • Half-life

  • Clearance

β:

• Approximation

• Used when:

  • Peripheral elimination exists

👉 RULE:

• Use k10 if possible

• Otherwise → β

VOLUMES IN 2-COMPARTMENT

1. Central Volume (Vd,c)

• Initial distribution space

• Governs initial concentration

👉 Similar to:

• Dose / C₀

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2. Peripheral Volume (Vd,p)

• Drug storage space

• Affects later concentrations

3. Steady State Volume

4. Extrapolated Volume

STEADY STATE VOLUME of Distribution

• Represents:

Entire system volume

STEADY STATE VOLUME of Distribution

• Occurs when:

Distribution equilibrium reached

DISTRIBUTION STEADY STATE is NOT the same as…

normal steady state

DISTRIBUTION STEADY STATE

Definition:

Rate (central → peripheral) = Rate (peripheral → central)

Concentrations NOT equal
👉 Movement rates ARE equal

Extrapolated Volume Of Distribution

Define

The volume of the system at the elimination phase

CONCEPT: DISTRIBUTION PHASE VS ELIMINATION PHASE

a. early

b. later

c. graph

a. Drug moves:

• Central → Peripheral

b. Drug moves BOTH ways

• Reaches equilibrium

c. Graph:

• Two parallel lines in elimination phase

If k12 > k21:

If k21 > k12:

If k12 > k21:

• Drug prefers peripheral

• Larger peripheral volume

If k21 > k12:

• Drug prefers central

DISTRIBUTION HALF-LIFE based on…

α

Time to reach distribution equilibrium:

≈ 5 half-lives

JUST LOOK:

WHY USE STEADY STATE VOLUME?

• Drug distributes beyond central

• Need full-body representation

JUST LOOK:

EXAM FOCUS ON CALCULATIONS

• Homework → calculate all micro constants

• EXAM → ONLY k10 ✅⭐

• Will NOT ask:

  • k12

  • k21

TWO TYPES OF DISTRIBUTION

Fast Distribution

• Drug moves into:

  • Tissue compartment

    • Fat (adipose)

    • Organs

2. Slow Distribution

• Drug moves into:

  • Deep tissue compartment

    • Bone

    • Ligaments

    • Connective tissue

    • Hair

• These have low blood flow → drug stays longer

How fast drug goes to tissue compartment

• Tissue compartment = like oil/fat

• Drug goes there relatively quickly

• Deep tissue = very slow entry

Distribution processes can be:

• Simultaneous

• OR Sequential

HOW TO DIFFERENTIATE between Simultaneous OR Sequential?

• Requires:

  • Statistics

  • Specialized software

👉 Not determined manually

3-COMPARTMENT MODEL

Central((blood, highly vascularized) + Tissue + Deep tissue

JUST LOOK

RATE CONSTANTS IN 3-COMPARTMENT

• 6 distribution rate constants

• 3 elimination rate constants

What drug follows 3-compartment model?

• Fentanyl

• But:

  • Many clinicians simplify:

    • Use 2-compartment instead

3-compartment is what type of decline?

tri-exponential drug decline

3 compartment model MACRO CONSTANTS?

3-compartment:

• A, α → fast distribution

• B, β → slow distribution

• C, γ → elimination ✅⭐

2-compartment:

• A, α → distribution

• B, β → elimination

How graph of 3-model compartment

NUMBER OF RATE CONSTANTS for EACH TYPE OF COMPARTMENTS

• 1-compartment → 1 rate constant

• 2-compartment → 4 rate constants

• 3-compartment →

  • 6 distribution

  • 3 elimination

  • Total = 9

Pattern:

• rate constants = (compartments)²

More compartments =

• very complex math

• Clinicians often:

  • Simplify models

Assume elimination…

• only from central

• Ignore:

  • k20, k30

TERMINAL ELIMINATION HALF-LIFE

• Comes from simplified model

• Focuses only on:

  • Elimination phase (later)

Stuff happens early → we ignore it”

• NOT from time of dosing

• Ignores early distribution

MULTIPLE HALF-LIVES

• Regular half-life

• Terminal half-life

If professor says:
👉 “terminal elimination half-life”

→ Means: what model

2 or 3 compartment model

INFUSION IN 2-COMPARTMENT

• Equation is:

Very complex (“nasty”)

He said:

• NOT doing math on this ❌

Even if drug is 2-compartment:

• Clinicians often use:

• 1-compartment approximation

👉 Because:

• Focus = steady state