Mass Balance

April 4, 2017 Pharmacokinetics No comments ,

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.

Creatinine Clearance Estimation – Non-Steady State

Using non-steady-state serum creatinine values to estimate creatinine clearance is difficult, and a number of approaches have been proposed. The author use Equation 1 below to estimate creatinine clearance when steady-state conditions have not been achieved.

ClCr (mL/min) = { (Production of Creatinine in mg/day) – [(SCr 2 – SCr 1)(V Cr) / t]*(10 dL/L)} * [(1000 mL/L) / (1440 min/day)] / [(SCr 2)(10 dL/L)] [Equation 1]

The daily production of creatinine in milligram is calculated by multiplying the daily production value in mg/kg/day from Table 5 by the patient’s weight in kg. The serum creatinine values in Equation 1 are expressed in units of mg/dL; t is the number (or fraction) of days between the first serum creatinine measurement (SCr1) and the second (SCr2). The volume of distribution of creatinine (Vcr) is calculated by multiplying the patient’s weight in kg times 0.65 L/kg. Equation 1 (or 79) is essentially a modification of the mass balance equation (we will discuss it in another thread later).

where the daily production of creatinine in milligram has replaced the infusion rate of the drug and the second serum creatinine value replaced C ave. The second serum creatinine is used primarily because Equation 1 is most commonly applied when creatinine clearance is decreasing (serum creatinine rising), and using the higher of the two serum creatinine values results in a lower, more conservative estimate of renal function. Some have suggested that the iterative search process, as represented by the combination of Equation 28 and 37 (won’t be discussed here; if needed, please contact Tom for detail), be used:

where C2 represents SCr2, and C represents SCr1. (S)(F)(Dose/tau) represents the daily production of creatinine, and t represents the time interval between the first and second serum creatinine concentrations. Cl represents the creatinine clearance with the corresponding elimination rate constant K being Cl/V or the creatinine clearance divided by the creatinine volume of distribution. As discussed previously, the solution would require an iterative search, and the inherent errors in the calculation process probably do not warrant this type of calculation.

Although Equation 1 (or Equation 79) can be used to estimate a patient’s creatinine clearance when a patient’s serum creatinine is rising or falling, there are potential problems associated with this and all other approaches using non-steady-state serum creatinine values. First, a rising  serum creatinine concentration may represent a continually declining renal function. To help compensate for the latter possibility, the second creatinine (SCr2) rather than the average is used in the denominator of Equation 1/79. Furthermore, there are non-renal routes of creatinine elimination that become significant in patients with significantly diminished renal function. Because as much as 30% of a patient’s daily creatinine excretion is the result of dietary intake, the ability to predict a patient’s daily creatinine production in the clinical setting is limited. One should also consider the potential errors in estimating creatinine production for the critical ill patient, the errors in serum creatinine measurements, and the uncertainty in the volume of distribution estimate for creatinine. Estimating creatinine clearance in a patient with a rising or falling serum creatinine should be viewed as a best guess under difficult conditions, and ongoing reassessment of the patient’s renal function is warranted.