Principles of Drug Accumulation (4)

One-Compartment Open Model (Review)

• IV bolus

  • Absorption: instantaneous, complete

• One compartment

  • Distribution: instantaneous, complete

  • Compartment is homogeneous

• Elimination

  • Combination of metabolism + excretion

  • Only way drug leaves

 

What units is found in each section?

a. IV bolus

b. One compartment

c. Elimination

a. D (dose)

b. Vd = Volume of distribution

c.

• Ke = Elimination rate constant

• t½ (t 1/2) = Half-life

• Cl = Clearance

Why Single Dose Is Not Enough?

Clinically, patients usually need multiple doses

Multiple doses →

drug accumulation

Accumulation depends on:

• Rate of input (Ri)

• Rate of elimination (Re)

• Dosing frequency

Rate of Drug Input (Ri)

a. controlled?

b. average rate or Ri =

c. units…

a. controlled by use

a. Ri = Dose ÷ τ (ON FORMULA SHEET)

c. mass per time (mg/hr)

Rate of Drug Elimination (Re)

a. controlled?

b. Re =

c. units

d. key concept?

a. Not controlled by us

b. Re = C(t) × Cl

• Depends on:

  • Drug concentration at that moment

  • Clearance

c. mass per time (mg/hr)

d.

• High concentration → high elimination rate

• Low concentration → low elimination rate

Are Re and Cl the same?

• no

  • Re (mg/hr)

  • Cl (L/hr)

How to find Re by graphing?

• take concentration (y) and time (x) graph

• find slope, which is the Re

Comparing Ri and Re

• Ri > Re → concentration increases

• Ri < Re → concentration decreases

• Ri = Re → steady state (goal)

Steady State

Definition

• Average rate of drug input = average rate of drug elimination

• Concentrations become stable and bounded

• Peaks and troughs still occur, but within a fixed range

Time to reach steady state =

 5 × half-life

Tell me the 3 variables we talk about in this lecture?

Dosing Interval (τ)

Dose Number (n)

Time (t)

Dosing Interval (τ)

• Time between doses

• Assumed fixed and constant

• Always a whole number in this class

• Example:

  • TID → τ = 8 hours

Dose Number (n)

• Represents most recent dose given

• Does NOT increase until the next dose is administered

• Integer (whole number only)

Time (t)

• Time since the most recent dose

• t cannot exceed τ

  • Once next dose is given → t resets

How do we evaluate multiple doses?

• principle of superposition

• drug accumulation factor

Principle of Superposition

• Each dose contributes independently

• Total concentration = sum of contributions from all doses still present

Principle of Superposition

how does the body handle every dose?

• The body handles every dose the same way

 Principle of Superposition

what happens to residual drug from earlier dose?

 adds to newer doses

What’s a Multiple Dosing Function?

Accumulation Factor

Accumulation Factor is the…

• Mathematical shortcut for accumulation

Accumulation Factor depends on…

• Elimination rate constant

• Dosing interval (τ)

• Dose number (n)

What leads to more accumulation before the next dose?

• Shorter τ

• Longer half-life

a. When does dose number count?

b. What does dose number not count?

a. early on, as drug is still building up/before steady state

b. at steady state

Why is steady state important?

• Fewer variables

• Simpler math

• Predictable concentrations

Drug accumulates when…

input exceeds elimination

Accumulation continues until:

• Ri = Re

  • That point is steady state

Time to reach steady state depends only on…

half-life