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Pharmacokinetics 2

Created: 23/2/2006
a. Explain the concept of pharmacokinetic modelling of single and multiple compartment models and define: half-life, clearance, volume of distribution, bioavailability, area under the “plasma concentration-time curve”, extraction ratio.

  • The time taken for the plasma concentration of a drug to fall by 50% when first-order kinetics are observed.
  • Many drugs have an initial redistribution phase with a short half-life (t1/2a) followed by an elimination phase with a longer half-life (t1/2ß).
  • The apparent volume of plasma from which a drug is entirely removed per unit time.
  • Usually expressed in proportion to bodyweight or surface area.
Volume of distribution
  • The volume into which a drug appears to be uniformly distributed at the concentration measured in plasma.
  • Usually a steady state volume of distribution equal to the amount of drug in the body.
  • (n) divided by the plasma concentration (C).

Also equal clearance (Cl) times elimination half-life divided by ln2

  • The proportion of a dose of a specified drug preparation entering the systemic circulation after administration by a specified route
  • Usually used to mean “oral bioavailability”: the ratio of the areas under the plasma concentration-time curves of intravenous and oral administration of the same dose of a drug

Area under plasma concentration-time curve

  • The integral of plasma concentration with respect to time from the time of administration to the time of no detectable drug is equal to the amount of drug appearing in the systemic circulation. This is used in calculating bioavailability.
  • A semi-logarithmic plot gives more information about the kinetics of a drug’s distribution and elimination as first-order (exponential) curves become straight lines.
  • This allows easier calculation of distribution and elimination half-lives (proportional to gradients of lines a and ß in the graph).

Extraction ratio
  • The proportion of a drug removed from blood by a single pass through the liver.
  • Equal to 1 - bioavailability.
  • A high extraction ratio indicates perfusion-dependent hepatic metabolism. A low ratio suggests enzyme activity dependent metabolism.
b. Apply Fick’s Law to absorption of drugs by enteric, sublingual, rectal, nasal, intramuscular, subcutaneous, transmucosal and transdermal routes.

Fick’s Law
  • relates rate of diffusion (J) to permeability coefficient (P), thickness (T), area (A) and concentration gradient (C1 - C2) for a drug diffusing across a membrane.

  • permeability coefficient is related to solubility of the drug in the tissue between the site of administration and the blood draining the tissue
  • concentration gradient is maintained by a high concentration of drug at the site of administration and rapid blood flow
  • diffusion is also accelerated by a rise in temperature
c. Explain factors influencing the distribution of drugs and apply these in disease states.

Distribution occurs by several processes, the effect of each is determined by aspects of the drug involved.

Bulk flow 

  • drugs of MW < 200 flow with water through intercellular pores
Facilitated diffusion
  • some drugs bind specific membrane receptors which facilitate transport across the membrane. This mechanism displays saturability and competition.
Active transport 

  • secondary active transport of many organic molecules e.g. glucose, amino acids active uptake from gut

Determined by solubility in water 
  • hydrophilic groups 
  • molecule size 
Membrane penetration is related to lipid solubility 
  • reduced with ionization 
    • depends on pH for basic or acidic drugs 
    • other polar groups 
  • reduced with increasing size
Protein binding

  • most drugs which are protein bound, bind either albumin or a1-acid glycoprotein according to their pKa 
  • some bind specialized proteins e.g. steroid binding globulin, transcortin etc 
  • increases Vd and reduces free fraction of drug 
  • reduces renal clearance by filtration but not active secretion 
  • is a source of interactions 

  • the largest component of plasma proteins 
  • has three major binding sites 
    • warfarin, bilirubin, salicylates, phenytoin, sulfonamides 
    • benzodiazepine, NSAIDs, penicillin 
    • digoxin, verapamil, quinidine 
  • level is reduced by
    • catabolic states: burns, malignancy, renal/hepatic disease, pregnancy, old age, neonates 
A1-acid glycoprotein 
  • level increased in catabolic states: burns, renal transplant, malignancy, trauma, inflammatory diseases: RA, UC, Crohn’s, myocardial infarct 
  • level decreased in pregnancy, neonates

d. Identify the mechanisms of hepatic and non-hepatic metabolism of drugs.


Phase I 


  • mixed function oxidases (including cytochrome P450) 
  • reaction with active oxygen species derived from O2 and NADPH 
  • oxidation, dealkylation, hydroxylation, deamination, desulfuration, 
  • some reductions, dehydrogenation 
  • activity is unregulated by many drugs 
    • barbiturates, rifampicin 
  • inhibited by a few drugs 
    • cimetidine 
  • increase polarity of drugs 

Phase II 

  • conjugation with polar groups which increase renal and biliary secretion 
    • glucuronide, sulfate, acetate, amino acids

First order kinetics 

elimination is proportional to concentration, clearance is constant 

Cl = Vd • kel 
where kel is the elimination constant 

so for a single compartment, concentration falls exponentially 

Ct = C0 · e-kt

where k is the rate constant, equal to ln2 ÷ t1/2ß

In a two compartment model, with both distribution and elimination 

Ct = Ae-at + Be-ßt

where A and B are the intercepts on the log plasma concentration-time graph and a and ß are the gradients of the lines drawn to approximate the two compartments at a steady state with repeat dosing

dose rate = elimination rate

dose x bioavailability ÷ time interval = mean concentration x clearance

e. Explain the mechanics and significance of drug absorption and elimination such as first-order and zero-order kinetic processes and factors affecting renal excretion of drugs.

f. Explain and apply concepts related to infusion kinetics as well as absorption and distribution of drugs following epidural and spinal administration.

g. Calculate loading and maintenance dosage regimens.

h. Explain clinical drug monitoring with regard to peak and trough concentrations, minimum therapeutic concentration and toxicity.

Kindly provided by Dr James Mitchell from his pharmacodynamics series.

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