Chen Sheldon, Chiaramonte Robert
Section of Nephrology, MD Anderson Cancer Center, Houston, TX.
State University of New York Downstate Medical Center, Brooklyn, NY.
Kidney Med. 2019 Jul 9;1(4):207-216. doi: 10.1016/j.xkme.2019.06.002. eCollection 2019 Jul-Aug.
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.
肌酐清除率是肾脏病学实践的一项基本原则。然而，由于肌酐清除率公式的分母中仅包含单一的肌酐浓度，所得值似乎仅适用于稳态。基本清除率公式在非稳态下是否有效，它能否概括动态肾小球滤过率（GFR）方程？在动态状态下，非线性肌酐轨迹可简化为一个“真正的平均值”，该值可通过微积分从基于质量平衡原理的微分方程中得出。利用微积分基本定理，我们明确证明了真正的平均值是用于除法运算的正确肌酐值，即便该数学模型考虑了诸如容量变化和其他影响肌酐动力学的因素等临床复杂性。两个测量肌酐值之间肌酐随时间变化函数的真正平均值可通过定积分得出。为了使用真正的平均值来计算动态GFR，展示了两种技术，一种是图形法，另一种是数值法。我们将这一概念应用于一例需要透析的急性肾损伤患者的临床病例；尽管血液透析对血清肌酐浓度有影响，但动态GFR能够追踪潜在的肾功能，并提供有关肾功能恢复的关键信息。最后，使先前关于肌酐每日最大增加值的概念在临床上更具客观性。因此，当使用真正的平均肌酐值时，清除率范式也适用于非稳态，为从现实生活中急性肾损伤和肾脏恢复过程中出现的血清肌酐趋势推断动态GFR提供了一种根本有效的策略。
