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Pharmacokinetic Modeling (describing what happens). Volume of distribution. AKA “Apparent volume of distribution” The volume of fluid that appears to contain the amount of drug in the body May not be actual physiologic space(s) Relates amount to plasma concentration

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Pharmacokinetic Modeling (describing what happens)

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Pharmacokinetic modeling describing what happens

Pharmacokinetic Modeling

(describing what happens)

Volume of distribution

Volume of distribution

  • AKA “Apparent volume of distribution”

    • The volume of fluid that appears to contain the amount of drug in the body

    • May not be actual physiologic space(s)

  • Relates amount to plasma concentration

  • The volume that must be processed by organs of elimination

Volume of distribution1

Volume of distribution

  • Equations

    • Experimentally:

      • Vz = Dose / Cp0

    • Intellectually:

      • Vz = Amount in the body / Cpt

  • Units

    • Liters or milliliters (whole animal or human beings)

    • Liters/kg or milliliters/kg (typical vet med)

Volume of distribution2

Volume of distribution

  • Give IV Bolus

  • Take samples over time

  • Cp0 is Y axis interecept

  • You know the dose

  • Vz = Dose / Cp0

Volume of distribution3

Volume of Distribution

Volume of distribution4

Volume of distribution

Much like row 4 of table

Much like row 2 or 3 of table



  • The volume of plasma water cleared of drug during a specified period of time



  • Organ clearance is:

    • Efficiency X Flow (fraction of drug removed X organ flow)

      • Clearance = Q x E

  • Total clearance is:

    • The sum of all organ clearances

      • Cl total=Cl hepatic + Cl renal + Cl pulmonary

  • Experimentally:

    • Clearance = Vz x λz



  • I know it’s weird but:

    • At a particular concentration, extracting ½ the drug from ALL the flow is the same thing as extracting ALL the drug from ½ the flow

      • (We “clearance” not “amount removed” because it works int with the samples we take and the math we can do).

So in one minute

So in one minute…

0% cleared from

0.5 ml.

200 µg/ml

(1 ml)

100 µg/ml

(1 ml)

Passes through liver in

1 minute

100 % cleared from

0.5 ml.

Clearance is 0.5 ml/min



  • Units

    • Volume / unit time (l/hr, l/min, ml/min, etc.)

      • Whole animals or human beings

    • Volume / kilogram / unit time

      • Animals

Rate constant of elimination z

Rate constant of elimination (λz)

  • The fraction of the volume of distribution cleared per unit time.

    • The slope of the natural log plot of drug concentration verus time profile.

Clearing the tank

Clearing the tank…

Clearing the tank1

Clearing the tank

Concentration vs time points represent concentrations determined for samples taken from the tank.

Elimination half life

Elimination half-life

  • The time for elimination of one half of the total amount in the body

  • Equation:

    • T1/2 = 0.693/λz (elimination rate constant)

  • Units:

    • Time (hours, minutes, seconds…)

Elimination half life1

Elimination half life

  • Utility

    • Tissue Residues

      • At 5 x T1/2 (after you stop dosing) 97% has been eliminated.

        • Make sure you use the longest half-life

        • Metabolites MAY be more important than the drug

        • Absorption may have the longest half-life.

Elimination half life2

Elimination half-life

  • Utility

    • Approach to “Steady state”

      • Drugs with long half-lifes “accumulate” during repeated administration

      • A 5 x T1/2 concentrations reach 97% of steady state

      • Digoxin – maximum effects 8 days after therapy starts

    • Need for loading dose

      • A loading dose is an initial dose given to shorten the time it takes to reach steady state (“load” the body to steady state amounts and concentrations).

Steady state

Steady state

Absorption rate constant ka

Absorption rate constant (ka)

  • Fractional rate at which drug moves from the place the dose was put INTO the circulatory system.

  • Units

    • Time (hours, minutes, seconds…)

  • Application

    • Combined with elimination rate, determines time to reach peak concentration (C max)

Fraction of dose absorbed

Fraction of dose absorbed

  • Other than IV, it is rare that the ENTIRE dose is actually absorbed

    • Oral

      • Destroyed, eliminated unchanged

    • IM

      • Hydrolyzed in tissue, bound to tissues, stuck in abscess

  • Units

    • Percentage or decimal (80% = 0.8)

Fraction of dose absorbed1

Fraction of dose absorbed

  • Bioavailability

Two oral dose forms of the same drug. F of the “open triangle” dose form is ½ the “filled triangle” dose form.

Fraction of dose aborbed

Fraction of dose aborbed

  • Bioavailability and Bioequivalence

Equal bioavailability (same F) and Bioequivalent

Equal bioavailability (same F) and not Bioequivalent

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