TY - JOUR

T1 - [Creatinine] can change in an unexpected direction due to the volume change rate that interacts with kinetic GFR

T2 - Potentially positive paradox

AU - Chen, Sheldon

AU - Chiaramonte, Robert

N1 - Funding Information:
The graphs were created at desmos.com/calculator. The authors thank Amy Wang for technical assistance with the graphs.
Publisher Copyright:
© 2022 The Authors. Physiological Reports published by Wiley Periodicals LLC on behalf of The Physiological Society and the American Physiological Society.

PY - 2022/2

Y1 - 2022/2

N2 - [Creatinine] was proved to change in the opposite direction of the kinetic GFR (GFRK), but does the [creatinine] also change in the opposite direction of the volume rate? If volume is administered and the [creatinine] actually goes up, then the two changes move in the same direction and their ratio is positive, paradoxically. The equation that describes [creatinine] as a function of time was differentiated with respect to the volume rate. This partial first derivative has a global maximum that can be positive under definable conditions. Knowing what makes the maximum positive informs when the derivative will be positive over some continuous domain of volume rate inputs. The first derivative versus volume rate curve has a maximum and a minimum point depending on the GFRK. If GFRK is below a calculable value, then the curve's minimum vanishes, letting it descend to (Formula presented.) and not allowing the derivative to ever be positive. If GFRK lies between a lower and a higher calculable value, then the curve's maximum vanishes, letting the derivative diverge to (Formula presented.), though the clinical scenario is unrealistic. If GFRK is above the higher calculable value, then the curve's absolute maximum can become positive by decreasing the creatinine generation rate or increasing the initial [creatinine]. The derivative is potentially positive under these clinically realizable circumstances. The combination of parameters above can align in septic patients (low creatinine generation rate) with kidney failure (high initial [creatinine]) who are put on continuous dialysis (high GFRK). If a first derivative is positive, removing more volume can improve the [creatinine] and, dismayingly, giving more volume can worsen the [creatinine]. This paradox is explained by a covert interplay between the ambient [creatinine] and GFRK that excretes creatinine faster than its volume of distribution declines.

AB - [Creatinine] was proved to change in the opposite direction of the kinetic GFR (GFRK), but does the [creatinine] also change in the opposite direction of the volume rate? If volume is administered and the [creatinine] actually goes up, then the two changes move in the same direction and their ratio is positive, paradoxically. The equation that describes [creatinine] as a function of time was differentiated with respect to the volume rate. This partial first derivative has a global maximum that can be positive under definable conditions. Knowing what makes the maximum positive informs when the derivative will be positive over some continuous domain of volume rate inputs. The first derivative versus volume rate curve has a maximum and a minimum point depending on the GFRK. If GFRK is below a calculable value, then the curve's minimum vanishes, letting it descend to (Formula presented.) and not allowing the derivative to ever be positive. If GFRK lies between a lower and a higher calculable value, then the curve's maximum vanishes, letting the derivative diverge to (Formula presented.), though the clinical scenario is unrealistic. If GFRK is above the higher calculable value, then the curve's absolute maximum can become positive by decreasing the creatinine generation rate or increasing the initial [creatinine]. The derivative is potentially positive under these clinically realizable circumstances. The combination of parameters above can align in septic patients (low creatinine generation rate) with kidney failure (high initial [creatinine]) who are put on continuous dialysis (high GFRK). If a first derivative is positive, removing more volume can improve the [creatinine] and, dismayingly, giving more volume can worsen the [creatinine]. This paradox is explained by a covert interplay between the ambient [creatinine] and GFRK that excretes creatinine faster than its volume of distribution declines.

KW - CRRT

KW - creatinine clearance

KW - derivative

KW - differential equation

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U2 - 10.14814/phy2.15172

DO - 10.14814/phy2.15172

M3 - Article

C2 - 35195956

AN - SCOPUS:85125137414

VL - 10

JO - Physiological Reports

JF - Physiological Reports

SN - 2051-817X

IS - 3

M1 - e15172

ER -