see also:

• pharmacology main index
• absorption of drugs
• distribution of drugs - volume of distribution, etc
• metabolism of drugs
• excretion of drugs
• prescribing drugs in patients with liver impairment
• Wikipedia rate equations for chemical reactions

• rate of reaction is independent of the concentration of the reactant(s)
• dX/dt = K
• eg. saturated enzyme/transport system;infusion;
• half life = [X]₀/(2K)

• rate of reaction is proportional to the concentration of only one reactant
• dX/dt = K[X]
• half life = ln(2)/K

• rate of reaction is proportional to the concentrations of one second-order reactant, or two first-order reactants.
• dX/dt = k[X]², or
• dX/dt = k[X][Y]

• where, v = reaction rate; V = max. reaction rate;
• v = V/(1 + Km/s)
  • Km = Michaelis-Menten complex dissociation constant;
  • s = substrate concentration;
  • NB. if s » Km, v → V, thus enzyme system saturated & zero order kinetics;
  • eg. Km [ethanol] = 80mg/l (0.008 %) for oxidation to aldehyde is saturated at usual intakes which result in concentrations ~800mg/l (0.08 %), thus zero order elimination is a constant of about 7g/hr=V;
  • In addition, Km = substrate concentration that results in half maximal rate

• volume of fluid cleared of drug per unit time
  • = rate of elimination / plasma concentration
  • = (urine output x urine concentration) / plasma concentration
  • = blood flow to organ x extraction ratio
  • = (blood flow x (arterial concentration - venous concentration)) / arterial concentration
• if 1st order kinetics, then:
  • = dose / area under curve (AUC) = Vmax / (Km + plasma concentration)
• NB. is constant if 1st order kinetics but varies if zero order kinetics.
• NB. plasma clearance may be » blood flow if RBC concentration » plasma concentration eg. labetalol

• see prescribing drugs in patients with liver impairment

• if 1st order then:
  • saturable, capacity-limited, concentration dependent, non-linear Michaelis-Menten elimination;
  • rate of elimination = clearance x concentration
    • = ( Vmax x concentration) / (Km + concentration) = Vmax / (Km/concentration + 1)
    • ie. Km = concentration at which rate is half maximal
    • if concentration » Km then becomes “pseudo-zero order” as elimination is almost independent of concentration. eg. ethanol, phenytoin, aspirin concentration fluctuates widely depending on dose

• time required to eliminate 50% of drug
• single compartment approximation:
  • half-life = 0.693 x Vd / clearance
  • NB. ln2 = 0.693
  • eg. digoxin in pt with CRF:
    • renal clearance is decreased but this is offset by reduced Vd due to:
      • decreased renal/skeletal muscle mass → decreased tissue binding
      • ⇒ only mild increase in half-life.
• steady state (ss) with intermittent dosing is achieved after ~ 5 half-lives
• if concentration » EC50 then duration of effect may last many half-lives as concentration trough may still be near EC50 eg. enalapril once daily (T1/2 = 3hrs); propranolol;
• Accumulation factor = 1 / (1- fraction remaining)
  • if a drug is given every half-life:
    • accumulation factor = 2
    • ⇒ steady state concentration - peak = 2 x 1st dose concentration peak

• if time to reach SS is appreciable (ie. long half-life) then a loading dose may be given to rapidly raise the concentration to a desired level:
  • loading dose = Vd x concentration target
  • ensure rate of administration < distribution rate otherwise rapid IV → toxicity
• eg. lignocaine
• eg. theophylline: 35L x 10mg/L = 350mg

• dosing rate (ss) = rate elimination (ss) = clearance x concentration target
• maintenance dose = dosing rate x dose interval
• eg. theophylline:
  • IV infusion: dosing rate = 2.8L/hr x 10mg/L = 28mg/hr
  • Oral maintenance dose if bd = 28mg/hr x 12hr / 0.96 (bioavailability) = 350mg

• effect vs dose or concentration
• ED50 = dose at which effect is 50% of that drug's maximal effect
• EC50 - as for ED50 but drug concentration not dose
• Effect on curve of adding an irreversible non-competitive antagonist:
  • initially only shifts curve to the right until spare receptors depleted
    • ie. same effect as adding a competitive antagonist
  • then lowers maximal effect for drug

• % pts responding vs dose
• measures:
  • potential variability in responsiveness
  • potency
  • selectivity
• 4 main mechanisms contribute to variability of response:
  • i) altered [drug] that reaches receptor
    • age, sex, weight, disease, altered elimination
  • ii) altered [endogenous receptor ligand]
    • eg. b blockers have less effect on resting HR in marathon runners as basal sympathetic activity is lower
  • iii) altered no. or function of receptors more receptors in thyrotoxicosis; less if down-regulation;
  • iv) altered secondary messenger responsiveness & interacting organ systems compensatory mechanisms, etc
• ED50 = median effective dose = dose at which 50% pts exhibit specified effect
• TD50 = median toxic dose
• therapeutic index = TD50/ED50

• the concentration (EC50) or dose (ED50) required to produce 50% of that drug's maximal effect.
• Thus, a drug may have a higher potency but still have a lower maximal effect (the maximal efficacy) than another drug, indeed the less potent drug may have a greater effect even at the same dose !