The mass balance technique has been suggested as a more direct alternative to the iterative approach. The mass balance technique is relatively simple and can be best visualized by examining the relationship between the rate of drug administration and the rate of drug elimination. At steady state, the rate of drug elimination (RE) is equal to the rate of administration (RA) and the change in the amount of the drug in the body with time is zero.
RA – RE = Change in the Amount of Drug in the Body with Time = 0
Under non-steady-state conditions, however, there will be a change in the amount of drug in the body with time. This change can be estimated by multiplying the difference in the plasma concentration (deltaC) by the volume of distribution and divided by the time interval between the two drug concentrations.
By substituting the appropriate values in the left equation, an estimate of clearance can be derived as follows:
RA – RE = (deltaC)(V) / t
(S)(F)(Dose/tau) – RE = (C2 – C1)(V) / t
(S)(F)(Dose/tau) – (C2 – C1)(V) / t = RE
(S)(F)(Dose/tau) – (C2 – C1)(V) / t = (Cl)(C ave)
Note that the average plasma concentration (C ave) is generally assumed to be the average of C1 and C2.
While this C ave is not the steady-state average, it is assumed to be the average concentration that results in the elimination of drug as the concentration proceeds toward steady state. Equation 65 is an accurate method for estimating clearance if the following conditions are met:
1.t, or time between C1 and C2, should be equal to at least one but no longer than two of the revised drug half-lives. This rule helps to ensure that the time interval is not so short as to be unable to detect any change in concentration and yet not so long that the second concentration (C2) is at steady state.
2.The plasma concentration values should be reasonably close to one another. If the drug concentrations are increasing, C2 should be less than two times C1; if the plasma concentrations are dealing, C2 should be more than one-half of C1 (i.e., 0.5 < C2/C1 < 2.0). This rule limits the change in concentration so that the assumed value for V will not be a major determinant for the value of Cl calculated from Equation 65.
3.The rate of drug administration [(S)(F)(Dose/tau)] should be regular and consistent. This rule helps to ensure a reasonably smooth progression from C1 to C2 such that the value of C ave [(C1 + C2)/2] is approximately equal to the true average drug concentration between C1 and C2.
The mass balance approach is a useful technique if the above conditions are met. It is relatively simple and allows for the calculation of clearance under non-steady-state conditions by a direct solution process. There are certain situations in which the above conditions are not met but the mass balance technique still works relatively well. For example, if the time interval between C1 and C2 is substantially greater than two half-lives but the value of C2 is very close to C1, then Equation 65 approximates Equation 15 because the average plasma concentration approximates the average steady-state value.
The mass balance approach is most commonly applicable for drugs that are given as a continuous IV infusion, as a sustained-release product, or at a dosing interval that is much less than the half-life.