VM 8314
Pharmacokinetic Modeling
(describing what happens)
Dr. Jeff Wilcke

VM 8314
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
Dr. Jeff Wilcke

VM 8314
 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)
Dr. Jeff Wilcke

VM 8314
1) Give IV Bolus
2) Take samples over time
3) Cp0 is Y axis interecept
4) You know the dose
Vz = Dose / Cp0
Dr. Jeff Wilcke

VM 8314
Scenario
Drug distributed only to plasma water
Physiologic Space
Blood volume = 7% of body weight
Plasma water = 55% of blood volume
Vz
0.0385 liters/kg
Drug distributed evenly in ECF only
Drug distributed evenly ECF and
ICF only.
Extracellular fluid volume = 25% of body weight
Intracellular fluid volume = 40% of body weight
ICF concentration = 3 x’s ECF Extracellular fluid volume + 3x intracellular fluid volume
0.25 liters/kg
0.65 liters/kg
1.45 liters/kg
Dr. Jeff Wilcke

VM 8314
Much like row 2 or 3 of table
Much like row 4 of table
Dr. Jeff Wilcke

VM 8314
 The volume of plasma water cleared of drug during a specified period of time
Dr. Jeff Wilcke

VM 8314
 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 = V z x λ z
Dr. Jeff Wilcke

VM 8314
 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).
Dr. Jeff Wilcke

VM 8314
0% cleared from
0.5 ml.
200 µg/ml
(1 ml) Passes through liver in
1 minute
100 % cleared from
0.5 ml.
100 µg/ml
(1 ml)
Clearance is 0.5 ml/min
Dr. Jeff Wilcke

VM 8314
 Units
 Volume / unit time (l/hr, l/min, ml/min, etc.)
 Whole animals or human beings
 Volume / kilogram / unit time
 Animals
Dr. Jeff Wilcke

VM 8314
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.
Dr. Jeff Wilcke

VM 8314
Dr. Jeff Wilcke

VM 8314
Concentration vs time points represent concentrations determined for samples taken from the tank.
Dr. Jeff Wilcke

VM 8314
 The time for elimination of one half of the total amount in the body
 Equation:
 T
1/2
= 0.693/λz (elimination rate constant)
 Units:
 Time (hours, minutes, seconds…)
Dr. Jeff Wilcke

VM 8314
 Utility
 Tissue Residues
 At 5 x T
1/2 eliminated.
(after you stop dosing) 97% has been
 Make sure you use the longest half-life
 Metabolites MAY be more important than the drug
 Absorption may have the longest half-life.
Dr. Jeff Wilcke

VM 8314
 Utility
 Approach to “Steady state”
 Drugs with long half-lifes “accumulate” during repeated administration
 A 5 x T
1/2 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).
Dr. Jeff Wilcke

VM 8314
Dr. Jeff Wilcke

VM 8314
 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
)
Dr. Jeff Wilcke

VM 8314
 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)
Dr. Jeff Wilcke

VM 8314
 Bioavailability
60
Two oral dose forms of the same drug. F of the
“open triangle” dose form is ½ the
“filled triangle” dose form.
50
40
30
20
10
0
0 1 2 3 4
Hours
5 6 7 8
Dr. Jeff Wilcke

VM 8314
 Bioavailability and Bioequivalence
Equal bioavailability (same F) and Bioequivalent
Equal bioavailability (same F) and not Bioequivalent
Dr. Jeff Wilcke