1. Pharmacokinetic Modeling (describing what happens)

2. 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
Clinical pharmacokinetics is based on plasma concentrations. Put (any) amount of drug in the body. If most of the drug finds its way to tissues, the plasma concentration will be low(er) which makes the volume look large. If very little of the drug gets to the tissues, the plasma concentration will be high(er) which makes the volume look small.
REALLY, we’re talking about the ratio of plasma to tissue at equilibrium. If the equilibrium is TISSUE > Plasma then the volume is high. If the equilibrium is Plasma > Tissue, the volume is low.
It is important to remember that the organs of elimination process body water (the volume of distribution). Large volumes take longer to process than do small ones.

3. 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)
Experimentally, we know the dose, we can determine the plasma concentrations and we can extrapolate to “time zero” (the time of injection).
We CAN calculate the amount in the body at any point in time following a dose but this is rarely done. It is enough for us to know the concentration in the body at any point in time.
When you look up volumes of distribution for human beings, you will find volumes for the “whole patient.” This assumes that all people are the same size! In veterinary medicine, we determine a volume of distribution for (say) dogs. THEN we need to work with the values in everything from Chihuahuas to Great Danes. Also, we dose all our patients in mg/kg (not total mg like people). It only makes sense to factor in body weight.

4. Volume of distribution
Give IV Bolus
Take samples over time
Cp0 is Y axis interecept
You know the dose
Vz = Dose / Cp0
This is how you determine the volume of distribution.

5. Volume of Distribution
Scenario
Physiologic Space Vz
Plasma water only
Blood volume = 7% of body weight
Plasma water = 55% of blood volume
liters/kg
ECF only
plasma water is ECF
ECF = 25% of body weight
0.25 liters/kg
ECF and ICF only
[ECF] = [ICF]
ICF = 40% of body weight
0.65 liters/kg
ICF concentration = 3 x ECF
ECF volume + 3 x (actual) ICF volume
1.45 liters/kg
All of these are based on the concentration you can determine in plasma or serum which represents (very directly) the ECF concentration.
Based on serum / plasma concentrations

6. Volume of distribution
Scenario
Physiologic Space Vz
Drug distributed only to plasma water Blood volume = 7% of body weight liters/kg
Plasma water = 55% of blood volume
Drug distributed evenly in ECF only Extracellular fluid volume = 25% of body weight 0.25 liters/kg
Drug distributed evenly ECF +ICF only Intracellular fluid volume = 40% of body weight 0.65 liters/kg
Drug distributed evenly in ECF Extracellular fluid volume + 3x ICF volume 1.45 liters/kg
and concentrated 3x in ICF
Much like row 4 of table
Much like row 2 or 3 of table

7. Clearance
The volume of plasma water cleared of drug during a specified period of time
The cirulatory system brings fluid (the volume of distribution) TO the organs of elimination.
The efficiency of the organs of elimination determines what fraction of the drug molecules (the concentration) get removed as the fluid passes through.
Organ blood flow determines how much fluid gets “cleared” per minute.

8. Clearance Organ clearance is: Total clearance is: Experimentally:
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
Q is blood flow to the organ.
E is extraction efficiency of the organ.
Cl total is total clearance
Cl hepatic is liver clearance
Cl pulmonary is lung clearance.

9. Clearance 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 with the samples we can take and the math we can do).

10. Passes through liver in
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

11. Clearance Units Volume / unit time (l/hr, l/min, ml/min, etc.)
Whole animals or human beings
Volume / kilogram / unit time
Animals

12. 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.

13. Clearing the tank…

14. Clearing the tank
30 min 96.6 µg/ml
1 hour 93.3
2 hours 87.1
4 hours 75.8
8 hours 57.4
12 hours 43.5
24 hours 19.0
Concentration vs time points represent concentrations determined for samples taken from the tank.

15. 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…)
It’s also the time for the plasma concentration to drop by ½ (but you knew that since the amount in the body is proportional to the plasma concentration).

16. 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.
Longest half-life? Clinically the half-life of gentamicin is about an hour. If I dose every 8 hours, every dose is ALMOST completely gone before I give the next one. HOWEVER, a LITTLE bit of gentamicin binds very tightly to kidney tissues. The half-life of this VERY LITTLE BIT of gentamicin is measured in days. This little bit of gentamicin doesn’t affect therapy for (say) pneumonia, but it does cause residues of gentamicin to persist in the kidneys.
The time it takes to eliminate an injected dose of procaine penicillin G is controlled by the long absorption half-life NOT the elimination half-life.

17. 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).
The question one might ask about digoxin is: How long, from the time I start my patient on digoxin, should I wait until I’m sure the concentrations have stopped rising (and I can stop worrying about whether toxicity will appear).
Loading doses take the form of: “Give two tablets once, then one tablet each day for…”

18. Steady state
The fact that concentrations are continuing to rise for the first 6 doses is referred to as accumulation. Accumulation may or may not occur.
For the last 4 doses, the peak and trough concentrations (and the shape of each little triangle) are VERY similar. The regimen is said to be “at steady state.”
IF accumulation does not occur, then a dose regimen will be at steady state by the end of the first dose interval.

19. 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)
Ka is very much like λz. This is because (in general) a constant fraction of a dose is absorbed during any given time period.

20. 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)

21. 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.

22. Fraction of dose absorbed
Bioavailability and Bioequivalence
Bioequivalence means that the activity (performance) of the two dose forms is the same. In the figure on the right, the two drugs have the same “area under the curve” and (therefore) the same F – really! However, because the peak concentration of one is SO much lower than the peak concentration of the other, the two dose forms are not likely to produce the same activity, duration of activity, or toxicity profile.
Equal bioavailability (same F) and Bioequivalent
Equal bioavailability (same F) and not Bioequivalent