On renal insufficiency measurement and reference standards using the logarithm of a cumulative exponential and multiple other plasma and renal clearance models

Abstract

For current models and methods, glomerular filtration rates below 20 ml/min in adults resulted in modelling concentration tails that were frequently unseen on linear-log plotting. The resulting sometimes unobservable tail was predicted using the negative logarithm of a cumulative exponential (LCE), from the latter of its two asymptotes; a logarithm for decreasing time and an exponential tail as time increases. Lambert's Omega is the scaled time at which the two asymptotes are equal. The LCE formula uses two plasma samples, minimum, and fit 13 24 h $^{51}$Cr-EDTA studies with an 8% standard deviation of residuals compared to 20% error for monoexponentials. The LCE model was unbiased for prediction of 43 5 h urinary $^{51}$Cr-EDTA activity cases whereas the mono- and bi-exponential, as well as, adaptively regularised gamma variate models were relatively overestimating. Reference standard corrections were explored. The LCE model detected two otherwise unidentified absent renal function cases (GFR < 0.01 ml/min) in a 41 case $^{169}$Yb-DTPA dataset suggesting its use for detecting anephric conditions. Prospective clinical testing, and metabolic scaling of renal insufficiency is advised for potential changes to patient triage, e.g., for conservative management, dialysis, and kidney or liver transplantation.Comment: 21 pages, 9 figures, under revie