What are the Main Concentration-time Relationships? - Mathematical Relationship of Vd, Cl and t¡
It is important to remember that the elimination rate constant (and therefore the half-life) of a drug is not an independent variable but is dependent on two other indices of drug disposition - the drug's clearance (Cl) and its apparent volume of distribution (Vd). These parameters are mathematically related by the following equations:
and t½ = 0.693/k
... t½ = 0.693.Vd/Cl
Half-life is directly proportional to Vd and inversely proportional to Cl. This is best illustrated by a graph showing how the three indices are related (Fig 11). This shows that drugs with high volumes of distribution and low clearance values have half-lives that are too long for practical use.
It is interesting to compare warfarin and nortriptyline, two drugs with similar half-lives for very different reasons. Whereas warfarin has a small volume of distribution and a low clearance, nortriptyline has a large volume of distribution and high clearance. On the other hand, consider gentamicin and chloroquine, two drugs with similar clearance values, have a 1000-fold difference in half-life owing to vast differences in their volumes of distribution, whereas dutasteride and propranolol, two drugs with similar volumes of distribution, have more than a 100-fold difference in half-life owing to vast differences in their clearance values.
