Slope-only glomerular filtration rate and single-sample glomerular filtration rate as measurements of the ratio of glomerular filtration rate to extracellular fluid volume

Aims: The Jacobsson single-sample equation for measuring glomerular filtration rate (GFR) after bolus injection is based on two factors of questionable theoretical validity for correcting the single-compartment assumption. The aims were to redevelop a more transparent equation, show its fundamental similarity with 'slope-only' GFR and compare it with the original equation and with slope-only GFR. Methodology: The modified Jacobsson equation is k = (1/t).ln[V(t)/V(0)], where k is the rate constant of the terminal exponential and V(0) and V(t) are distribution volumes at times 0 and t. V(0) exceeds extracellular fluid volume (ECV): that is k' = (1/t).ln[V(t)/ECV], where k' > k. Moreover, [GFR/ECV] > k (= k + [15.4.k2]). The ratio k/k' was determined in 476 patients to calculate single-sample k (3 or 4 h post-injection). Slope-only and single-sample GFR/ECV were measured using Cr-51-EDTA in 105 further studies, multiplied by ECV (estimated from weight), scaled to 1.73 m2 and compared with GFR/1.73 m2 from the original Jacobsson equation against reference multi-sample GFR/1.73 m2 simultaneously and independently measured with iohexol. Results: The relation between k and k' was linear. k/k' was 0.827 at 3 h and 0.864 at 4 h. There was no difference in bias or precision between the original Jacobsson and modified equations. In both, precision was better than slope-only GFR/BSA. When GFR remained scaled to ECV, slope-only GFR showed marginally better precision against reference GFR/ECV. Conclusions: Single-sample and slope-only techniques give GFR as k. Although the theory of the modified Jacobsson equation is more transparent than the original equation, it gives the same result. It is, however, easier to use.