General Principles of Pharmacology: Pharmacokinetics

Bioavailability
- Definition: fraction of unchanged drug that reaches systemic circulation following administration (by any Route of Administration)
- Examples:
  - IV administration: bioavailability = 1
  - Other routes of administration = < 1
- Major factors that reduce bioavailability to less than 100%:
  - Incomplete absorption
  - First-pass effect (liver metabolizes drug before drug reaches systemic circulation)
- Extent of Absorption:
  - Incomplete absorption following oral drug administration is common:
  - For example, only 70% of a digoxin dose reaches systemic circulation. Factors:
    - Poor GI tract absorption
    - Digoxin metabolism by gastrointestinal flora
  - Very hydrophilic drugs may not be well absorbed as they cannot easily cross cell membrane lipid component
  - Excessively lipid-soluble (hydrophobic) drugs may not be soluble enough to cross a water layer near the cell membrane.
- First-pass Elimination:
  - Transport sequence:
    1. Across the gut wall into the portal circulation
    2. Portal blood transports of the drug to the liver
    3. The drug may then reach the systemic circulation
    4. Bioavailability may be affected by steps 1-3
  - Drug metabolism may occur in the intestinal wall or in the blood
  - Drug metabolism (potentially extensive) may occur in liver
  - Liver may excrete drug into the bile
  - Overall process that contributes to bioavailability reduction is the first-pass lost or elimination
  - Magnitude of first pass hepatic effect: Extraction ratio (ER)
    - ER = CL liver / Q ; where Q is hepatic blood flow (usually about 90 L per hour)
    - Systemic drug bioavailability (F) may be determined from the extent of absorption (f) and the extraction ratio (ER):
      - F = f x (1 -ER)
- Absorption rate:
  - Rate of absorption:dependent on site of administration and drug formulation
  - Zero order: drug absorption rate is independent of amount remaining in the gut
  - First order: drug absorption rate is proportional to the drug concentration dissolved in the gastrointestinal tract
- Extraction Ratios, Routes of Administration, and the First-Pass Effect
  - Some drugs that exhibit high extraction by the liver are given orally.
    - Some examples:
      - Desipramine (Norpramin)
      - Imipramine (Tofranil),
      - Meperidine (Demerol)
      - Propranolol (Inderal)
      - Amitriptyline (Elavil, Endep)
      - Isoniazid (INH).
  - Some drugs which have relatively low bioavailability are not given orally because of concern of metabolite toxicity -- lidocaine (Xylocaine) is an example (CNS toxicity, convulsions)
  - High extraction ratio drugs show interpatient bioavailability variation because all of sensitivity to:
    - Hepatic function
    - Blood flow
    - Hepatic disease (intrahepatic or extrahepatic circulatory shunting)
  - Drugs (some examples) poorly extracted by the liver:
    - Phenytoin (Dilantin)
    - Diazepam (Valium)
    - Digitoxin (Crystodigin)
    - Chlorpropamide (Diabinese)
    - Theophylline
    - Tolbutamide (Orinase)
    - Warfarin (Coumadin)
  - Avoiding the first-pass effect:
    - Sublingual (e.g. nitroglycerin) administration provides drugs direct access to systemic circulation
    - Transdermal
    - Use of suppositories in the lower rectum )if suppositories move upward, absorption may occur through the superior hemorrhoidal veins, which lead to the liver)
    - Inhalation: first-pass pulmonary loss by excretion or metabolism may occur.

Holford, N. H.G. and Benet, L.Z. Pharmacokinetics and Pharmacodynamics: Dose Selection and the Time Course of Drug Action, in Basic and Clinical Pharmacology, (Katzung, B. G., ed) Appleton-Lange, 1998, pp 34-49.

Benet, Leslie Z, Kroetz, Deanna L. and Sheiner, Lewis B The Dynamics of Drug Absorption, Distribution and Elimination. In, Goodman and Gillman's The Pharmacologial Basis of Therapeutics,(Hardman, J.G, Limbird, L.E, Molinoff, P.B., Ruddon, R.W, and Gilman, A.G.,eds) TheMcGraw-Hill Companies, Inc.,1996, pp. 3

Some Pharmacokinetic Equations
Elimination Rate Constant k_el = k_m+ k_ex where k_el = drug elimination rate constant k_m = elimination rate constant due to metabolism k_ex = elimination rate constant due to excretion Half-Life t_1/2 = ln 2 /k_el = 0.693/k_el where t_1/2 is the elimination half-life (units=time) Amount of Drug in Body X_b = V_d · C X_b: amount of drug in the body (units, e.g. mg) V_d: apparent volume of distribution (units, e.g. mL) C: plasma drug concentration (units, e.g. mg/mL) Volume of Distribution Calculation (one compartment, i.v. infusion) V_d = D_iv / C_o V_d: apparent volume of distribution (units, e.g. ml/kg) D_iv: i.v dose (units, e.g. mg/kg) C_o: plasma drug concentration (units, e.g. mg/ml) Clearance CL = rate of elimination/C rate of elimination = CL· C CL = Vd x k_el where V_d = volume of distribution and k_el is the elimination rate constant CL = Vd · (0.693/t_1/2) where 0.693 = ln 2 and t_1/2 is the drug elimination half-life note that plasma clearance CL_p include renal (CL_r) and metabolic (CL_m) components Renal Clearance CL_r = (U · C_ur) / C_p ; where U is urine flow (ml/min); C_ur is urinary drug concentration and C_p is plasma drug concentration. Steady-State Drug Plasma Concentration (C_ss) The calculation required to determine being steady-state drug plasma concentration illustrates the sensitivity of the plasma concentration to number of factors, in this case for a drug taken orally. First look at the overall form of the equation: Equation 1: C_ss= 1/(k_eV_d) (FD)/T The drug elimination rate constant,k_e is related to the drug half-life ( t_1/2 = 0.693/k_e) and thus can be calculated from knowledge of the drug half-life. The plasma steady-state drug levels also dependent on the dose, D, as well as a fraction of the drug that's actually absorbed following ingestion (F). "T" is the dosing interval, so the once-a-day dosing would be 1 day or to keep the units consistent, 24 hours. The steady-state level will also be dependent on the apparent volume of distribution (V_d) Now let's take an example using the drug phenytoin (Dilantin) which is used to manage epilepsy. The once-a-day dose is 200 mg. The drug half-life is 15 hours For the once-a-day dose, the dosing interval (T) is 24 hours [to keep the units the same as the drug half-life will use "hours"] Let's say that about 60% of the ingested does is in fact absorbed, giving us a value of 0.6 for "F" in equation 1 above. The volume of distribution for phenytoin (Dilantin) is 40,000 mls (40 liters) k_e = 0.693/15 hours = 0.0462/hr Let's now compute the results: Equation 1: C_ss= 1/(k_eV_d) * (FD)/T or C_ss= 1/(0.0462/hour40000 ml) * 0.6 (200 mg)/24 hours or Css = 0.0027 mg/ml or 2.7 ug/ml Time to Steady-State Let's consider the above problem from a little different point of view, that is, How long would it take to reach 50% of the C_ss (no bolus). Consider the dose is 300 mg/24h (dosing interval is 24 h or T; dose is 300 mg) but for convenience we'll represent it as 12.5 mg/hr, such that T is now 1 hr. The equation is: f = 1 - e ^-ke^TN or 0.5 = 1 - e ^-ke^TNwhere k_e is the elimination half-time of 0.0462/hr, T = 1 and N is the number of doses needed to reach 50% of C_ss. Rearranging, 0.5 = e ^{-0.0462/hr * 1 hr * N} --(note time (hour) units cancel) so taking antilogs, -0.693 = -0.0462 * N or N = -0.693/-0.0462 = 15 15 doses at an interval of 1 hour/dose gives the time to 50% of C_ss equal to 15 hours--a predictable time since drugs reach 50% of their steady-state value in 1 half-life Constant Infusion Dosing Next, let's consider the case by which drugs are administered by constant infusion. The infusion rate is Q or in this example, 150 ug/min and for simplicity, the drug is again phenytoin with a k_e of 0.0462/hr; t_1/2 of 15 hrs and a V_d of 40000 mls C_ss = Q/(k_eV_d ) or 150 ug/min / (0.0462/60min 40000 ml) = 4.87 ug/ml; [note that we have been careful to use the same units for k_e and Q, i.e. 0.0462/hr = 0.0462/60 min] Holford, N. H.G. and Benet, L.Z. Pharmacokinetics and Pharmacodynamics: Dose Selection and the Time Course of Drug Action, in Basic and Clinical Pharmacology, (Katzung, B. G., ed) Appleton-Lange, 1998, pp 34-49. Benet, Leslie Z, Kroetz, Deanna L. and Sheiner, Lewis B The Dynamics of Drug Absorption, Distribution and Elimination. In, Goodman and Gillman's The Pharmacologial Basis of Therapeutics,(Hardman, J.G, Limbird, L.E, Molinoff, P.B., Ruddon, R.W, and Gilman, A.G.,eds) TheMcGraw-Hill Companies, Inc.,1996, pp. 3-27 Pazdernik, T.L. General Principles of Pharmacology, in ACE the Boards, (Katzung, B. G., Gordon, M.A, and Pazdernik, T.L) Mosby, 1996, pp 22-28 Edward J. Flynn, Ph.D. Professor of Pharmacology, New Jersey School of Medicine and Dentistry, personal communication, 1980, 1999.

**References**
Stoelting, R.K., "Pharmacokinetics and Pharmacodynamics of Injected and Inhaled Drugs", in Pharmacology and Physiology in Anesthetic Practice, Lippincott-Raven Publishers, 1999, 1-17. Dolin, S. J. "Drugs and pharmacology" in Total Intravenous Anesthesia, pp. 13-35 (Nicholas L. Padfield, ed), Butterworth Heinemann, Oxford, 2000