Volume of distribution (Vd)
The first volume of distribution to discuss is after an IV bolus, as it is referred to most commonly. Vd = Dose administered / initial drug concentration.
With Vd = Dose/Initial_Concentration, the Dose units must be the same as the numerator in the concentration. so that they cancel. The units of Vd will be the same as the units in the denominator of the Initial_Concentration variable.
The more hydrophobic a drug is the higher the Vd will be. The lower limit is generally around 3 L. The upper limit can be as high as 10s of thousands of L for hydrophobic small molecules.
An important note is that Vd generally changes in time. It generally increases in time logarithmically (or linearly and then reaches an asymptote).
A non-invasive approach:
Volume of distribution at the terminal phase (Vd_beta=Varea)
To calculate the volume of distribution in the terminal phase, use the following:
Vd_terminal_phase = Vd_beta = Dose * bioavailability / beta / AUC = Clearance / beta; clearance is in units of volume per time.
bioavailability is the fraction of the drug that can be absorbed. beta is the concentration that is extrapolated to the y-axis from the terminal phase (to identify the terminal phase, you will want to see a plot of concentration versus time for the drug. Usually you will see a distribution phase (the first downward slope), and a terminal phase (the 2nd downward slope of the plot). If you draw a line extending the terminal phase to the y-axis, you can determine the concentration at time 0. That is what beta is.
AUC is area under the curve and will have units of concentration*time.
Volume of distribution at steady-state (Vss)
The Vss can be calculated by dividing the amount of drug given by the steady state concentration (Css). Vss = Dose/Css.
Also,
Typically…
V1 <= Vss <= Vd_beta
If distribution is instantaneous…
All of the mentioned volumes of distributions are equal.
When clearance approaches 0…
Vd_beta approaches Vss.
What affects the rates of distribution
Blood flow, physicochemical properties of the drug, binding/binding kinetics