Tikhonov adaptively regularized gamma variate fitting to assess plasma clearance of inert renal markers

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

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.

A series acceleration algorithm for the gamma-Pareto (type I) convolution and related functions of interest for pharmacokinetics

Abstract

The gamma-Pareto type I convolution (GPC type I) distribution, which has a power function tail, was recently shown to describe the disposition kinetics of metformin in dogs precisely and better than sums of exponentials. However, this had very long run times and lost precision for its functional values at long times following intravenous injection. An accelerated algorithm and its computer code is now presented comprising two separate routines for short and long times and which, when applied to the dog data, completes in approximately 3 min per case. The new algorithm is a more practical research tool. Potential pharmacokinetic applications are discussed.

Graphic abstract

Supplementary Information

The online version contains supplementary material available at 10.1007/s10928-021-09779-4.

Comparison of the gamma-Pareto convolution with conventional methods of characterising metformin pharmacokinetics in dogs

A model was developed for long term metformin tissue retention based upon temporally inclusive models of serum/plasma concentration (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C) having power function tails called the gamma-Pareto type I convolution (GPC) model and was contrasted with biexponential (E2) and noncompartmental (NC) metformin models. GPC models of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C have a peripheral venous first arrival of drug-times parameter, early \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C peaks and very slow washouts of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C. The GPC, E2 and NC models were applied to a total of 148 serum samples drawn from 20 min to 72 h following bolus intravenous metformin in seven healthy mongrel dogs. The GPC model was used to calculate area under the curve (AUC), clearance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL), and functions of time, f(t), for drug mass remaining (M), apparent volume of distribution (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{d}$$\end{document}Vd), as well as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}\ f(t)$$\end{document}t1/2f(t) for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{d}$$\end{document}Vd. The GPC models of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C yielded metformin \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values that were 84.8% of total renal plasma flow (RPF) as estimated from meta-analysis. The GPC \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values were significantly less than the corresponding NC and E2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ CL $$\end{document}CL-values of 104.7% and 123.7% of RPF, respectively. The GPC plasma/serum only model predicted 78.9% drug \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M average urinary recovery at 72 h; similar to prior human urine drug \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M collection results. The GPC model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd, were asymptotically proportional to elapsed time, with a constant limiting \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 ratio of M/C averaging 7.0 times, a result in keeping with prior simultaneous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C $$\end{document}C and urine \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ M $$\end{document}M collection studies and exhibiting a rate of apparent volume growth of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_d$$\end{document}Vd and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_{1/2}$$\end{document}t1/2 with elapsing time, effects that have been observed experimentally during same-dose multidosing. The GPC heavy-tailed models explained multiple documented phenomena that were unexplained with lighter-tailed models.

Tikhonov gamma variate adaptive regularization applied to technetium Tc 99m diethylenetriamine pentaacetic acid plasma clearance, compared with three other methods, for measuring glomerular filtration rate in cats

OBJECTIVE

To evaluate agreement of 4 methods (Tikhonov gamma variate adaptive regularization of plasma concentration-time curve fitting applied to technetium Tc 99m diethylenetriamine pentaacetic acid [^99mTc-DTPA] plasma clearance [Tk-GV], plasma clearance of exogenous creatinine [CrCL], Gates gamma camera-based measurement method with ^99mTc-DTPA renal clearance and dynamic scintigraphy [GTS], and iohexol renal clearance assessed with dynamic CT with Patlak plotting [CT-Pp]) for measuring glomerular filtration rates (GFR) in healthy cats.

ANIMALS

7 healthy, laboratory-raised cats.

PROCEDURES

Each method for measuring GFR was performed twice in 7 cats at 24-day intervals. The Wilcoxon signed-rank sum test was used to compare the results obtained from the 14 studies for each method. Results from the 4 methods were assessed for agreement and correlation.

RESULTS

The median GFR values were 2.75, 2.83, 3.14, and 4.26 mL/min/kg, for Tk-GV, CT-Pp, plasma CrCL, and GTS, respectively. Analysis with Wilcoxon signed-rank sum tests identified significant pairwise differences between results obtained with the Tk-GV versus the plasma CrCL method, the Tk-GV versus the GTS method, and the plasma CrCL versus the GTS method. The least variable method was Tk-GV, with an SD of 1.27 (mL/min/kg).

CONCLUSIONS AND CLINICAL RELEVANCE

Findings indicated that Tk-GV yielded GFR measurements comparable with those obtained with CT-Pp, plasma CrCL, and GTS; however, the Tk-GV method yielded the tightest range of results among the methods evaluated.

A gamma-distribution convolution model of 99mTc-MIBI thyroid time-activity curves

BACKGROUND

The convolution approach to thyroid time-activity curve (TAC) data fitting with a gamma distribution convolution (GDC) TAC model following bolus intravenous injection is presented and applied to 99mTc-MIBI data. The GDC model is a convolution of two gamma distribution functions that simultaneously models the distribution and washout kinetics of the radiotracer. The GDC model was fitted to thyroid region of interest (ROI) TAC data from 1 min per frame 99mTc-MIBI image series for 90 min; GDC models were generated for three patients having left and right thyroid lobe and total thyroid ROIs, and were contrasted with washout-only models, i.e., less complete models. GDC model accuracy was tested using 10 Monte Carlo simulations for each clinical ROI.

RESULTS

The nine clinical GDC models, obtained from least counting error of counting, exhibited corrected (for 6 parameters) fit errors ranging from 0.998% to 1.82%. The range of all thyroid mean residence times (MRTs) was 212 to 699 min, which from noise injected simulations of each case had an average coefficient of variation of 0.7% and a not statistically significant accuracy error of 0.5% (p = 0.5, 2-sample paired t test). The slowest MRT value (699 min) was from a single thyroid lobe with a tissue diagnosed parathyroid adenoma also seen on scanning as retained marker. The two total thyroid ROIs without substantial pathology had MRT values of 278 and 350 min overlapping a published 99mTc-MIBI thyroid MRT value. One combined value and four unrelated washout-only models were tested and exhibited R-squared values for MRT with the GDC, i.e., a more complete concentration model, ranging from 0.0183 to 0.9395.

CONCLUSIONS

The GDC models had a small enough TAC noise-image misregistration (0.8%) that they have a plausible use as simulations of thyroid activity for querying performance of other models such as washout models, for altered ROI size, noise, administered dose, and image framing rates. Indeed, of the four washout-only models tested, no single model approached the apparent accuracy of the GDC model using only 90 min of data. Ninety minutes is a long gamma-camera acquisition time for a patient, but a short a time for most kinetic models. Consequently, the results should be regarded as preliminary.

Time Varying Apparent Volume of Distribution and Drug Half-Lives Following Intravenous Bolus Injections

We present a model that generalizes the apparent volume of distribution and half-life as functions of time following intravenous bolus injection. This generalized model defines a time varying apparent volume of drug distribution. The half-lives of drug remaining in the body vary in time and become longer as time elapses, eventually converging to the terminal half-life. Two example fit models were substituted into the general model: biexponential models from the least relative concentration error, and gamma variate models using adaptive regularization for least relative error of clearance. Using adult population parameters from 41 studies of the renal glomerular filtration marker ¹⁶⁹Yb-DTPA, simulations of extracellular fluid volumes of 5, 10, 15 and 20 litres and plasma clearances of 40 and 100 ml/min were obtained. Of these models, the adaptively obtained gamma variate models had longer times to 95% of terminal volume and longer half-lives.

Gamma-variate plasma clearance versus urinary plasma clearance of 51 Cr-EDTA in patients with cirrhosis with and without fluid retention

In patients with fluid retention, the plasma clearance of ⁵¹ Cr-EDTA (Cl_exp obtained by multiexponential fit) may overestimate the glomerular filtration rate (GFR). The present study was undertaken to compare a gamma-variate plasma clearance (Cl_gv) with the urinary plasma clearance of ⁵¹ Cr-EDTA (Cl_u ) in patients with cirrhosis with and without fluid retention. A total of 81 patients with cirrhosis (22 without fluid retention, 59 with ascites) received a quantitative intravenous injection of ⁵¹ Cr-EDTA followed by plasma and quantitative urinary samples for 5 h. Cl_gv was determined from the injected dose relative to the plasma concentration-time area, obtained by a gamma-variate iterative fit. Cl_exp and Cl_u were determined by standard technique. In patients without fluid retention, Cl_gv , Cl_exp and Cl_u were closely similar. The difference between Cl_gv and Cl_u (Cl_gv - Cl_u  = ΔCl) was mean -0·6 ml min^-1  1·73 m^-2 . In patients with ascites, ΔCl was significantly higher (11·8 ml min^-1  1·73 m^-2 , P<0·0001), but this value was lower than Cl_exp - Cl_u (17·5 mL min^-1  1·73 m^-2 , P<0·01). ΔCl increased with lower values of GFR (P<0·001). In conclusion, in patients with fluid retention and ascites Cl_gv and Cl_exp overestimates GFR substantially, but the overestimation is smaller with Cl_gv . Although Cl_u may underestimate GFR slightly, patients with ascites should collect urine quantitatively to obtain a reliable measurement of GFR.

Accurate and precise plasma clearance measurement using four 99mTc-DTPA plasma samples over 4 h

OBJECTIVES

Glomerular filtration rate can be measured as the plasma clearance (CL) of a glomerular filtration rate marker despite body fluid disturbances using numerous, prolonged time samples. We desire a simplified technique without compromised accuracy and precision.

MATERIALS AND METHODS

We compared CL values derived from two plasma concentration curve area methods - (a) biexponential fitting [CL (E2)] and (b) Tikhonov adaptively regularized gamma variate fitting [CL (Tk-GV)] - for 4 versus 8 h time samplings from 412 Tc-DTPA studies in 142 patients, mostly paediatric patients, with suspected fluid disturbances.

RESULTS

CL (Tk-GV) from four samples/4 h and from nine samples/8 h, both accurately and precisely agreed with the standard, which was taken to be nine samples/8 h CL from (noncompartmental) numerical integration [CL (NI)]. The E2 method, four samples/4 h, and nine samples/8 h median CL values significantly overestimated the CL (NI) values by 4.9 and 3.8%, respectively.

CONCLUSION

Compared with the standard, CL (E2) from four samples/4 h and from nine samples/8 h proved to be the most inaccurate and imprecise method examined, and can be replaced by better methods for calculating CL. The CL (Tk-GV) can be used to reduce sampling time in half from 8 to 4 h and from nine to four samples for a precise and accurate, yet more easily tolerated and simplified test.

The early plasma concentration of 51Cr-EDTA in patients with cirrhosis and ascites: a comparison of three models

Objectives

The aim of the study was to determine which of three two-parameter fitting functions (exponential, linear-log, and negative-power function of time) most accurately models early chromium-51-EDTA (⁵¹Cr-EDTA) plasma concentration data prior to 120 min in patients with cirrhosis and ascites and understand how these fitting functions affect the calculation of the area under the plasma concentration curve (AUC).

Methods

A bolus, antecubital intravenous injection of 2.6 MBq of ⁵¹Cr-EDTA was given to 13 patients with cirrhosis and ascites. Up to 16 blood samples were drawn at time points ranging from 5 to 1440 min following injection. The concentration data prior to 120 min were used as reference data. Early time concentration values, estimated by fitting exponential, linear-log, and negative-power functions of time to the time samples at 120, 180, and 240 min, were then compared with reference data. The AUC was calculated for each patient using the exponential, Bröchner-Mortensen-corrected exponential, and linear-log functions, and these values were compared.

Results

The withheld, observed plasma concentrations were (a) most accurately estimated by linear-log functions (Wilcoxon P=0.4548), (b) significantly underestimated by exponential functions (Wilcoxon P=0.0002), and (c) significantly overestimated by negative-power functions (Wilcoxon P=0.0034). The relative errors when ranked from best to worst were those for the linear-log (12.0%, 9.0%), exponential (22.9%, 14.2%), and negative-power (31.9%, 48.4%) functions of time, respectively (median, interquartile range). For each patient, the values for AUC calculated by the exponential function differed significantly (range=3.4–15.3%, median=8.3%) from those calculated by the corrected Bröchner-Mortensen exponential, as to a lesser extent did those values calculated using linear-log functions (range=0.4–8.0%, median=3.0%).

Conclusion

In patients with cirrhosis, linear-log functions were significantly more accurate than exponential or power functions in estimating early time plasma concentrations (<120 min). However, the improved linear-log early time plasma concentration model does not provide as much correction to the total AUC as does the corrected Bröchner-Mortensen exponential method. This is likely because of the large contribution of late time data to the AUC, and future work is suggested to explore the late time fit problem.

Optimized robust plasma sampling for glomerular filtration rate studies

In the presence of abnormal fluid collection (e.g. ascites), the measurement of glomerular filtration rate (GFR) based on a small number (1-4) of plasma samples fails. This study investigated how a few samples will allow adequate characterization of plasma clearance to give a robust and accurate GFR measurement. A total of 68 nine-sample GFR tests (from 45 oncology patients) with abnormal clearance of a glomerular tracer were audited to develop a Monte Carlo model. This was used to generate 20 000 synthetic but clinically realistic clearance curves, which were sampled at the 10 time points suggested by the British Nuclear Medicine Society. All combinations comprising between four and 10 samples were then used to estimate the area under the clearance curve by nonlinear regression. The audited clinical plasma curves were all well represented pragmatically as biexponential curves. The area under the curve can be well estimated using as few as five judiciously timed samples (5, 10, 15, 90 and 180 min). Several seven-sample schedules (e.g. 5, 10, 15, 60, 90, 180 and 240 min) are tolerant to any one sample being discounted without significant loss of accuracy or precision. A research tool has been developed that can be used to estimate the accuracy and precision of any pattern of plasma sampling in the presence of 'third-space' kinetics. This could also be used clinically to estimate the accuracy and precision of GFR calculated from mistimed or incomplete sets of samples. It has been used to identify optimized plasma sampling schedules for GFR measurement.

Validation of Tikhonov adaptively regularized gamma variate fitting with 24-h plasma clearance in cirrhotic patients with ascites

Purpose

The aim was to compare late-time extrapolation of plasma clearance (CL) from Tikhonov adaptively regularized gamma variate fitting (Tk-GV) and from mono-exponential (E1) fitting.

Methods

Ten ⁵¹Cr-ethylenediaminetetraacetic acid bolus IV studies in adults—8 with ascites—assessed for liver transplantation, with 12–16 plasma samples drawn from 5-min to 24-h, were fit with Tk-GV and E1 models and CL results were compared using Passing-Bablok fitting.

Results

The 24-h CL(Tk-GV) values ranged from 11.4 to 79.7 ml/min. Linear regression of 4- versus 24-h CL(Tk-GV) yielded no significant departure from a slope of 1, whereas the 4- versus 24-h CL(E1) slope, 1.56, was significantly increased. For CL(Tk-GV-24-h) versus CL(E1-24-h), there was a biased slope and intercept (0.85, 5.97 ml/min). Moreover, the quality of fitting of 24-h data was significantly better for Tk-GV than for E1, as follows. For 10 logarithm of concentration curves, higher r values were obtained for each Tk-GV fit (median 0.998) than for its corresponding E1 fit (median 0.965), with p < 0.0001 (paired t-test of z-statistics from Fisher r-z transformations). The E1 fit quality degraded with increasing V/W [volume of distribution (l) per kg body weight, p = 0.003]. However, Tk-GV fit quality versus V/W was uncorrelated (p = 0.8).

Conclusion

CL(E1) values were dependent on sample time and the quality of fit was poor and degraded with increasing ascites, consistent with current opinion that CL(E1) is contraindicated in ascitic patients. CL(Tk-GV) was relatively more accurate and the good quality of fit was unaffected by ascites. CL(Tk-GV) was the preferred method for the accurate calculation of CL and was useful despite liver failure and ascites.