Steady-state volume of distribution and dilution factor

In 1919 Widmark published in Sweden a paper about the elimination of ethanol and acetone from blood introducing the concept of volume of distribution. The ratio between the total amount of drug in the body (Q(t)) and its concentration in the plasma (C(t)), usually the only site accessible to sampling, shall be called 'apparent volume of distribution'. The ratio changes with time, because Q(t) depends on the elimination and C(t) depends on both elimination and distribution. Therefore the apparent volume of distribution varies between the 'initial volume' and the 'steady-state volume'. The former is defined as the ratio between the dose D given as a bolus at time t = 0 and the value of C(t) extrapolated at t-->0 ignoring the values of the concentration taken before the drug is uniformly mixed in the plasma; the initial volume is obviously equal to plasma volume. The steady-state volume is defined as the value of the ratio between Q(t) and C(t) extrapolated at t-->infinity. Now a new parameter is introduced, called 'dilution factor' and defined as the value of the ratio between the total amount of drug in the body (Q(t)) and the amount of drug in the plasma (X1(t)) extrapolated at t-->infinity. However the ratio between X1(t) and the initial volume is equal to C(t), then the dilution factor is also equal to the ratio between the steady-state volume and the initial volume.(ABSTRACT TRUNCATED AT 250 WORDS)