TY - JOUR
T1 - Estimating Creatinine Clearance in the Nonsteady State
T2 - The Determination and Role of the True Average Creatinine Concentration
AU - Chen, Sheldon
AU - Chiaramonte, Robert
N1 - Publisher Copyright:
© 2019 The Authors
PY - 2019/7/1
Y1 - 2019/7/1
N2 - 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.
AB - 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.
KW - Kinetic GFR
KW - Newton's method
KW - acute kidney injury
KW - calculus
KW - creatinine clearance
KW - differential equation
KW - mass balance
UR - http://www.scopus.com/inward/record.url?scp=85070215643&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85070215643&partnerID=8YFLogxK
U2 - 10.1016/j.xkme.2019.06.002
DO - 10.1016/j.xkme.2019.06.002
M3 - Review article
C2 - 32734201
AN - SCOPUS:85070215643
SN - 2590-0595
VL - 1
SP - 207
EP - 216
JO - Kidney Medicine
JF - Kidney Medicine
IS - 4
ER -