1. Pharmacokinetics Introduction
Describes quantitatively the rates of the steps of drug disposition (i.e.- absorption, distribution, elimination)
encompasses ADME plus clearance
clearance: the removal of a drug in units of volume/time
quantitative data important to detail fate of the drug, but also to be able to predict doses, routes, etc.
allows individual adjustment based on individual pharmacokinetic assessment

2. Pharmacokinetics
Relation of dose, plasma drug concentration, and effect
a specific dose of a drug should produce a specific effect:
Dosage  Conc. in plasma water  Conc. At site of action  Intensity of effect
Intensity of effect related to drug conc. at receptor sites
Duration of action related to how long drug conc. at receptor site remains high enough to provide response
Conc. at receptor sites changes as drug enters, distributes, and is eliminated

3. Pharmacokinetics Difficulty in Quantitation
Due to the difficulty of properly modeling so many processes occurring simultaneously
Often make certain assumptions which do not greatly affect the data such as:
Intensity of effect is correlated to the concentration of free drug in plasma
not always true – may be very difficult with irreversibly acting drugs, drugs which develop tolerances, or drugs which act synergistically

4. Pharmacokinetics Modeling
Used whenever the fate of a drug is described either qualitatively or quantitatively.
Mathematical model encompassing known factors about drug (such as distribution, etc) hypothesized first, then proven (or modified) by real-life observation.
One-compartment model easiest to use, and many drugs follow this scheme.
Assumes a single compartment which is in equilibrium which accounts for drug in plasma, and various tissues.
Two (or more) compartment models more difficult to model.
Seen when drug moves into tissues and is handled at different rates than central plasma compartment.

5. Drug Fate in Body

6. One Compartment Model

7. One Compartment Model Mathematics
Assuming first-order disposition (rate at any time is proportional to concentration of the drug)
Therefore, after IV administration, plasma concentration (Cp) decreases at a rate proportional at all times (t) to the concentration at that time:
-dCp/dt = kCp (where k = rate constant)
solving, Cp = C0 e-kt (where C0 is the initial concentration, e is the natural log base, and Cp is the concentration in plasma at any time t).
OR, log Cp = logC0 – kt/2.303

8. One Compartment Model

9. One Compartment Model Mathematics
From the dose given, the volume of distribution can also be calculated:
Vd = D0/C0
The elimination half-life would then be:
t1/2 = 0.693/k ( = ln 2)

10. Two Compartment Model
Involves both distributive and elimination phases normally.
Log plot does not give a single straight line, but instead shows two phases.
So now have a central compartment (ex.- plasma), and another compartment (ex.- tissue).
Can be described mathematically by two differential equations.

11. Two Compartment Model

12. Two Compartment Model

13. Absorption and Elimination

14. Absorption Curve

15. Absorption and Elimination

16. Rates of Processes
Have been assuming first-order rate kinetics so far.
This is usually ok, but what happens if a process (ex.- elimination) is dependant on a carrier or enzyme that may become saturated?
Rate now no longer dependant on concentration, but instead becomes constant, at least until concentration falls below saturation.
This is termed zero-order kinetics, where the rate is independent of the concentration.

17. Rates of Processes

18. Repeated Drug Administration

19. Bioavailability Definitions: Mathematics
Bioavailability – percentage of a drug or drug product that enters the general systemic circulation.
Includes not only amount entering body, but also rate of entry
Bioequivalence – comparable bioavailability between drugs.
Therapeutic equivalence – comparable clinical effectiveness and safety between similar drugs.
Mathematics
Bioavailability = F = AUC (oral) / AUC (IV)

20. Bioavailability

21. Volume of Distribution
Vd = D/C0
D = amount of Drug in the body
C0 = initial plasma concentration
The volume of distribution, Vd, is the apparent or “virtual” volume into which a drug distributes.

22. Volume of Distribution
Can Vd be larger than the total plasma volume in the body?
heparin = 5 liters (plasma only)
chlordiazepoxide = 28 liters (extracellular water)
imipramine = 1600 liters (highly lipid soluble)
Note: knowledge of the Vd is also important in estimating the loading dose.

23. Clearance Introduction
Quantitative measure of the removal of endogenous or exogenous substances from the body or a specific organ.
Examples include:
Hepatic biotransformation
Renal excretion
Fecal excretion
Lung exhalation
Can be mathematically modeled to help define proper dosing regimes.

24. Total Body Clearance Cltot = k Vd , where: Cltot = D / AUC
Cltot = total body clearance
k = first order elimination rate constant
Vd = apparent volume of distribution
Cltot = D / AUC
Assumes drug is completely absorbed (IV)
D = dose of drug
AUC = area under plasma conc. (y) vs time curve (x)
If not completely absorbed, Cltot = F D / AUC, where F is the fraction ‘absorbed’ (bioavailability)

25. IV AUC

26. Dosage for IV Infusion
Goal is to provide a constant plasma level while supplying drug at the same rate as elimination.
Q = k Vd Cpss , where:
Q = amount of drug supplied per unit time
k = elimination rate constant
Vd = apparent volume of distribution
Cpss = plasma concentration at steady state
Since Cltot = k Vd, then Q = Cltot Cpss

27. Loading Dose
Used to reach steady state plasma concentration (Cpss) immediately, instead of waiting the normal 5 half-lives.
L = Vd Cpss , where:
L = loading dose (amount of drug)
Vd = apparent volume of distribution
Cpss = plasma concentration desired at steady state

28. Repeated IV Dosing
Can not maintain a constant Cpss, but instead maintain an average Cpss.
Dosing interval will determine severity of fluctuation above and below average Cpss.
Cpss = (Dm / Tm) / Cl , where:
Dm = maintenance dose (amount)
Tm = maintenance dose interval
Dm = k Vd Cpss Tm (rearranging by Cl = k Vd)

29. Ideal Dosing Regimen
Determine the maintenance dose which will keep plasma level in therapeutic window:
Dm = (Cptox – Cpther) Vd
Tm = (ln Cptox – ln Cpther) / k
= (2.3 / k) log (Cptox / Cpther)
= t1/2 log (Cptox / Cpther)
To determine a loading dose:
L = Vd Cptox

30. IV AUC

31. Practical Dosing Regimen
Maintenance doses are frequently given at intervals equal to their t1/2 , but must also be given at manageable times (ex. – q4h, q6h, q12h, qd).
Mathematically, giving a dose at intervals of it’s t1/2 yields a Cpmax = 2Cpmin, which is a 100% fluctuation.
Obviously more frequent dosing would be preferred to diminish fluctuations, but may not be critical.

32. Practical Dosing Regimen
Drugs with a t1/2 less than 6 hours require a very wide therapeutic window to use them in repeated doses.
Drugs with narrow therapeutic windows should be given by continuous infusion.
To utilize repeated oral dosing, one must take bioavailability (F, the fraction entering general systemic circulation) into all calculations.

33. Clearance By Specific Organs
Clearances are additive.
Cltot = ClH + ClR + …
Amount of drug removed by an organ dependant on perfusion and extraction ratio:
E = (Ca – Cv) / Ca , where:
E = extraction ratio
Ca = concentration in arterial inflow
Cv = concentration in venous outflow

34. Clearance By Specific Organs
By taking blood flow into account,
Cltissue = Qtissue E , where Q = tissue blood flow
Then, ClH = QH (Ca – Cv) / Ca
First pass effect can also be described as:
FH = 1 – E , where:
FH = the bioavailability fraction due to first pass
First pass may be saturable, and like all liver metabolism may increase due to enzyme induction.

35. Clearance By Specific Organs
High Extraction Ratio
ClH controlled by blood flow rate
Strong first-pass effect
Plasma protein binding may facilitate clearance
Low Extraction Ratio
ClH controlled by intrinsic clearance
Biotransformation limited by diffusion
Plasma protein binding reduces clearance
Sensitive to enzyme inhibition and induction

36. Clearance By Specific Organs
For Kidneys:
Rate of renal excretion = Rate of filtration + Rate of secretion – Rate of reabsorption
ClR = (Excreted amount / Time Interval)
Plasma Concentration
For Biliary Excretion:
ClB = (Conc. in bile / Conc. In plasma) Bile flow
Bile flow normally 0.5 – 0.8 ml/min.