Reference standard analysis of multiple new and old plasma clearance models and renal clearance with special attention to measurement of reduced glomerular filtration rate

Abstract

Nine models were evaluated as candidate glomerular filtration rate (GFR) reference standards in three datasets using [⁵¹Cr(EDTA)]^– or [¹⁶⁹Yb(DTPA)]²⁻ anions in 98 studies. Noncompartmental methods formed an upper limit for estimating mass excreted and voluntary urine collection formed a lower limit. For current models and methods, reduced GFR in adults resulted in inflated clearance estimates. Two different logarithmic models with exponential tails were created and may have underestimated reduced clearance. The logarithmic formulae can be used with only two plasma samples, and fit 13 multiple time-samples from 5 min to 24 h with an 8% standard deviation of residuals compared to 20% error for monoexponentials. For shorter times (4 or 5 h) the fit errors decreased but the ratio of errors remained at circa 2.5 times lesser for the logarithmic versus monoexponential models. Adaptively regularised gamma variate, Tk-GV, models that are well documented, but not in common use, were largely contained within the reference extreme values, were unbiased for different levels of clearance and were the only models to be uncorrelated to volume of distribution from mean residence time divided by weight. Using Tk-GV as a candidate reference standard, potentially better methods for routine clinical usage were discussed. Prospective clinical testing, and metabolic scaling of decreased renal function is advised for potential changes to patient triage.

Keywords:

• Glomerular filtration rate
• radiopharmaceuticals
• injections, intravenous
• plasma
• urine sample collection
• reference standards

Acknowledgements

The editors and reviewers, especially unnamed Reviewer 1, are thanked for the extensive improvements made during the preparation of this paper. Prof. Geoffrey T. Tucker of the University of Sheffield, Sheffield, UK is thanked for his suggestions concerning this manuscript. Maria T. Burniston and coauthors in the UK [20] are thanked for graciously providing Dataset 1. Prof. Jens H. Henriksen of the University of Copenhagen, Denmark is thanked for providing Dataset 2. Prof. Charles D. Russell of the University of Alabama at Birmingham is thanked for providing Dataset 3. Surajith N. Wanasundara is thanked for his help with computer implementation of an earlier version of the Tk-GV processing program.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The two new formulas, LCE and ln-coth, are from a more general model $\mathit{C}\left(\mathit{t}\right)=\mathit{c}\hspace{0.17em}\text{ln}\hspace{0.17em}(\frac{\mathit{\alpha }}{{\mathit{e}}^{\beta \hspace{0.17em}\mathit{ }\mathit{t}}-1}+1).$ Setting α = 1 yields $-\mathit{c}\hspace{0.17em}\text{ln}\hspace{0.17em}(1-{\mathit{e}}^{-\beta \hspace{0.17em} \mathit{t}}),$ which is the LCE function, and for α = 2, the general model reduces to $\mathit{c}\hspace{0.17em}\text{ln}\left[\text{coth}\left(\frac{\mathit{\beta }\hspace{0.17em}\mathit{t}}{2}\right)\right],$ the ln-coth model.

2 where GV is a gamma variate; $\mathit{C}\left(\mathit{t}\right)=\mathit{c}\hspace{0.17em}{\mathit{t}}^{\alpha -1}{\mathit{e}}^{-\beta \hspace{0.17em}\mathrm{ }\mathit{t}},$ and the Tk-GV algorithm minimises the relative error of β.

3 The subcutaneous route may have been chosen in an attempt to mimic constant infusion.

4 13.014 ml is the straight average of five average residual bladder urine volumes from men and women after voiding in various positions.

5 For plasma models, V is volume of drug distribution, not to be confused with the Volume of urine (also V) of a renal model.

6 Battistini et al. used oral dosing of bromide, which is not as defensible as long term constant infusion, e.g., see Schwartz et al. [47], such that although their average of obese and normal V/W values are the same, both values may be underestimations.

7 Note that the equations in Table 4 can be solved for $\mathit{x}={\mathit{m}}^{*}\mathit{y}+{\mathit{b}}^{*},$ where ${\mathit{m}}^{*}=1/\mathit{m}$ and ${\mathit{b}}^{*}=-\mathit{b}/\mathit{m},$ only because the regressions are Passing-Bablok type. In general, least squares in y does not agree in that fashion with least squares in x.

8 The asymptotes are $\mathrm{c}\hspace{0.17em}\text{ln}\hspace{0.17em}\left(\frac{\sqrt{\pi }}{2\hspace{0.17em}\mathit{\beta }\hspace{0.17em}\mathit{t}}\right)$ and $-\mathrm{c}\hspace{0.17em}\text{ln}\hspace{0.17em}(1-\frac{e^{-{(\mathit{\beta }\hspace{0.17em}\mathrm{\hspace{0.17em}}\mathit{t})}^2}}{\sqrt{\pi }\mathit{\beta }\hspace{0.17em}\mathit{t}})$.