Mathematical Processes in Pharmacokinetics

• AUC: the total amount of drug that has entered the general circulation.
• Slope: allows rates of change to be calculated.
• F: the extent of absorption - biolavailability.
• F = AUC oral / AUC IV
• F = (AUC oral / AUC IV) X (dose IV / dose oral)
• A two component model is biphasic. The initial slope determines the distribution, the second slope determines the elimination.
• A one component model is monophasic and is based upon the assumption that the drug distributes to tissues very rapidly. Only elimination is occurring.
• Rate of distribution (alpha): the initial rate of decrease in plasma concentrations after a dose.
• Cp: the change in the concentration of drug in the plasma.
• V: apparent volume of distribution - the dose divided by the plasma concentration of the drug after it has been distributed.
• The gradient of the blue line is the rate of distribution. This is characteristic for a drug that depends on the rate of uptake by tissues.

  
• C0: the plasma concentration after the drug has been fully distributed and can be calculated from the intercept of the extrapolated line.

  
• V = dose / C0

  (For a one compartment model administered by IV)
• For a two-compartment model, at t = 0 little or no distribution will have occurred. Plasma concentration should only be used if distribution is instantaneous.

  
• V = dose / y-intercept

  (for a two compartment model administered by IV)
• V is:

  • Dependent on the physiochemical properties of the drug
  • An indication of extent of tissue uptake
  • Independent of dose
  • Non-physiological dilution factor
  • Can be presented as L or L/kg
  • Allow for calculation of the dose necessary to give a particular plasma concentration
• Rate of elimination: represented as k/min, where k is the terminal rate of decrease in plasma concentrations after either an oral or IV dose. It is characteristic for a drug.
• k = CL / V
• Plasma clearance (CL): the volume of plasma cleared of drug per minute or hour e.g., ml/min or L/h. Is specific for a drug. Will be similar to the blood flow for the organ via which it is eliminated.
• CL plasma = CL metabolic + CL renal
• CL = (dose X F) / AUC
• t1/2 = 0.693 / k
• Drugs that affect the activity of the liver can change the metabolic clearance - inducers will increase the CL metabolic.
• Chronic administration is continuous IV infusion. This maintains a constant concentration at the site of action with a persistent therapeutic effect.

  
• It takes 5 times the elimination half-life to reach steady state (Css).
• Css = rate of infusion / CL
• Css= (dose X F) / (dose interval X CL)
• Multiple dosing is used to maintain a constant concentration in the blood, by repeated oral dosing.

  
• Shorter intervals between doses produce higher Css. For drugs with long half-lives, the delay in time to steady-state concentrations may be inacceptable. The delay can be avoided by giving a large first dose (loading dose) which has the effect of topping up the apparent volume of distribution.

  
• Loading dose = Css X V

  (for IV administration)
• Loading dose = (Css X V) / F

  (for oral administration)