Korean J Transplant.  2020 Sep;34(3):167-177. 10.4285/kjt.2020.34.3.167.

Mathematical model for early functional recovery pattern of kidney transplant recipients using serum creatinine

  • 1Department of Surgery, Ajou University School of Medicine, Suwon, Korea


Commonly used equations for calculating estimated glomerular filtration rate (eGFR) are not applicable when serum creatinine (Scr) is rapidly changing like the post-transplant period. A new mathematical model applicable to the post-transplant period is required.
All 623 patients who underwent kidney transplantation from January 2008 to June 2018 at a single institute were included to validate the Scr mathematical equations, and 14,360 Scr laboratory results from the time of re-perfusion to 30 days post-transplantation were analyzed.
In the validation of model equations, linear regression analysis yielded adjusted R 2 values of 0.972 and 0.925 for equation 5 (applicable when renal function is changing) and equation 1 (applicable when renal function is unchanged), respectively. In selected cases, the population comprised individuals who presented an adjusted R 2 value >0.95 with equation 5. Linear regression analysis showed that adjusted R 2 values and Pearson's correlation coefficients for equation 5 and equation 1 were 0.994 and 0.997 (P<0.001) and 0.956 and 0.978 (P<0.001), respectively. Most of the eGFR formulas are mathematically applicable only if the creatinine input rate equals the creatinine output rate when comparing between commonly used eGFRs and creatinine clearance using the modeled equation.
The proposed equations can provide a new perspective for calculating renal function during the early phase of kidney transplantation. A study of a correlation between the equations and long-term graft outcomes is required.


Creatinine; Kidney transplantation; Recovery of function; Mathematics
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