Section of Nephrology, MD Anderson Cancer Center, Houston, TX, USA.
Internal Medicine, The State University of New York Downstate Health Sciences University, Brooklyn, NY, USA.
Physiol Rep. 2021 Aug;9(16):e14957. doi: 10.14814/phy2.14957.
When the serum [creatinine] is changing, creatinine kinetics can still gauge the kidney function, and knowing the kinetic glomerular filtration rate (GFR) helps doctors take care of patients with renal failure. We wondered how the serum [creatinine] would respond if the kinetic GFR were tweaked. In every scenario, if the kinetic GFR decreased, the [creatinine] would increase, and vice versa. This opposing relationship was hypothesized to be universal.
Serum [creatinine] and kinetic GFR, along with other parameters, are described by a differential equation. We differentiated [creatinine] with respect to kinetic GFR to test if the two variables would change oppositely of each other, throughout the gamut of all allowable clinical values. To remove the discontinuities in the derivative, limits were solved.
The derivative and its limits were comprehensively analyzed and proved to have a sign that is always negative, meaning that [creatinine] and kinetic GFR must indeed move in opposite directions. The derivative is bigger in absolute value at the higher end of the [creatinine] scale, where a small drop in the kinetic GFR can cause the [creatinine] to shoot upward, making acute kidney injury similar to chronic kidney disease in that regard.
All else being equal, a change in the kinetic GFR obligates the [creatinine] to change in the opposite direction. This does not negate the fact that an increasing [creatinine] can be compatible with a rising kinetic GFR, due to differences in how the time variable is treated.
当血清[肌酐]发生变化时，肌酐动力学仍可评估肾功能，了解动力学肾小球滤过率（GFR）有助于医生照顾肾衰竭患者。我们想知道如果调整动力学 GFR，血清[肌酐]会如何反应。在每种情况下，如果动力学 GFR 降低，[肌酐]就会增加，反之亦然。这种相反的关系被假设是普遍存在的。
血清[肌酐]和动力学 GFR 以及其他参数由微分方程描述。我们对动力学 GFR 求[肌酐]的导数，以测试在所有允许的临床值范围内，这两个变量是否会相互反向变化。为了消除导数中的不连续性，我们求解了极限。
对导数及其极限进行了全面分析，并证明其符号始终为负，这意味着[肌酐]和动力学 GFR 确实必须朝着相反的方向移动。导数在[肌酐]尺度的较高端绝对值更大，动力学 GFR 的微小下降会导致[肌酐]急剧上升，使得急性肾损伤在这方面与慢性肾病相似。
在其他条件相同的情况下，动力学 GFR 的变化必然会迫使[肌酐]朝着相反的方向变化。这并没有否定一个事实，即由于时间变量的处理方式不同，增加的[肌酐]可以与上升的动力学 GFR 兼容。
