Estimating Creatinine Clearance in the Nonsteady State: The Determination and Role of the True Average Creatinine Concentration

Abstract

Creatinine clearance is a tenet of nephrology practice. However, with just a single creatinine concentration included in the denominator of the creatinine clearance equation, the resulting value seems to apply only in the steady state. Does the basic clearance formula work in the nonsteady state, and can it recapitulate the kinetic glomerular filtration rate (GFR) equation? In the kinetic state, a nonlinear creatinine trajectory is reducible into a "true average" value that can be found using calculus, proceeding from a differential equation based on the mass balance principle. Using the fundamental theorem of calculus, we prove definitively that the true average is the correct creatinine to divide by, even as the mathematical model accommodates clinical complexities such as volume change and other factors that affect creatinine kinetics. The true average of a creatinine versus time function between 2 measured creatinine values is found by a definite integral. To use the true average to compute kinetic GFR, 2 techniques are demonstrated, a graphical one and a numerical one. We apply this concept to a clinical case of an individual with acute kidney injury requiring dialysis; despite the effects of hemodialysis on serum creatinine concentration, kinetic GFR was able to track the underlying kidney function and provided critical information regarding kidney function recovery. Finally, a prior concept of the maximum increase in creatinine per day is made more clinically objective. Thus, the clearance paradigm applies to the nonsteady state as well when the true average creatinine is used, providing a fundamentally valid strategy to deduce kinetic GFRs from serum creatinine trends occurring in real-life acute kidney injury and kidney recovery.

Using Kinetic eGFR for Drug Dosing in AKI: Concordance between Kinetic eGFR, Cockroft-Gault Estimated Creatinine Clearance, and MDRD eGFR for Drug Dosing Categories in a Pilot Study Cohort

“…(1) The original algebraic equation which uses the mean of the 2 Cr values has been used. The later calculus version uses the true average value of Cr based on a differential equation and as such is likely to be more accurate [11,12]. (2) The V d used in this study was fixed for each patient derived from baseline data and may not accurately reflect the changes in V d over the 48-h period.…”

In creatinine kinetics, the glomerular filtration rate always moves the serum creatinine in the opposite direction

“…The creatinine serves mostly as a surrogate to calculate the GFR. The [creatinine] is relatable to the GFR by a differential equation (Chen, 2018a;Chen & Chiaramonte, 2019). The rate of change in the creatinine amount is a function of the rate of creatinine coming in minus the rate of creatinine going out of its volume of distribution, which is total body water (TBW) (Chow, 1985;Edwards, 1959;Jones & Burnett, 1974;Pickering et al, 2013).…”

“…where [Cr] 0 is the initial serum [creatinine] for each clinical time interval (Chen, 2018a;Chen & Chiaramonte, 2019). That is to say, the serum [creatinine] at a given time is equal to the initial [creatinine] plus a time-evolved portion of the spread between the initial [creatinine] and the [creatinine] reached at a new steady state if the kinetic GFR and volume change rate remained at those levels.…”

“…is a decidedly qualitative art. Creatinine slope analysis became more quantitative when the science of creatinine kinetics was applied, a technique that has been called the kinetic glomerular filtration rate (GFR) (Chen, 2013(Chen, , 2018a(Chen, , 2018bChen & Chiaramonte, 2019). Now, the creatinine trajectory with all its slopes can be decoded into a kinetic GFR format that shows how the kidney function is evolving.…”

[Creatinine] can change in an unexpected direction due to the volume change rate that interacts with kinetic GFR: Potentially positive paradox

“…The differential equation that underpins the kinetic GFR states that the rate of change in the creatinine mass is equal to the creatinine input rate minus the creatinine output rate (Chen, 2018a , 2018b ; Chen & Chiaramonte, 2019 ). Further, the creatinine mass at any given time is the current [creatinine] times the volume of distribution, typically taken to be total body water (TBW) (Bjornsson, 1979 ; Chow, 1985 ; Edwards, 1959 ; Jones & Burnett, 1974 ; Pickering et al, 2013 ).…”