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.

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.

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 ([Formula: see text]) 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 [Formula: see text] have a peripheral venous first arrival of drug-times parameter, early [Formula: see text] peaks and very slow washouts of [Formula: see text]. 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 ([Formula: see text]), and functions of time, f(t), for drug mass remaining (M), apparent volume of distribution ([Formula: see text]), as well as [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text]. The GPC models of [Formula: see text] yielded metformin [Formula: see text]-values that were 84.8% of total renal plasma flow (RPF) as estimated from meta-analysis. The GPC [Formula: see text]-values were significantly less than the corresponding NC and E2 [Formula: see text]-values of 104.7% and 123.7% of RPF, respectively. The GPC plasma/serum only model predicted 78.9% drug [Formula: see text] average urinary recovery at 72 h; similar to prior human urine drug [Formula: see text] collection results. The GPC model [Formula: see text] of [Formula: see text], [Formula: see text] and [Formula: see text], were asymptotically proportional to elapsed time, with a constant limiting [Formula: see text] ratio of M/C averaging 7.0 times, a result in keeping with prior simultaneous [Formula: see text] and urine [Formula: see text] collection studies and exhibiting a rate of apparent volume growth of [Formula: see text] that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased [Formula: see text] and [Formula: see text] 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.

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.

A simple method for determining split renal function from dynamic (99m)Tc-MAG3 scintigraphic data.

PURPOSE: Commonly used methods for determining split renal function (SRF) from dynamic scintigraphic data require extrarenal background subtraction and additional correction for intrarenal vascular activity. The use of these additional regions of interest (ROIs) can produce inaccurate results and be challenging, e.g. if the heart is out of the camera field of view. The purpose of this study was to evaluate a new method for determining SRF called the blood pool compensation (BPC) technique, which is simple to implement, does not require extrarenal background correction and intrinsically corrects for intrarenal vascular activity. METHODS: In the BPC method SRF is derived from a parametric plot of the curves generated by one blood-pool and two renal ROIs. Data from 107 patients who underwent (99m)Tc-MAG3 scintigraphy were used to determine SRF values. Values calculated using the BPC method were compared to those obtained with the integral (IN) and Patlak-Rutland (PR) techniques using Bland-Altman plotting and Passing-Bablok regression. The interobserver variability of the BPC technique was also assessed for two observers. RESULTS: The SRF values obtained with the BPC method did not differ significantly from those obtained with the PR method and showed no consistent bias, while SRF values obtained with the IN method showed significant differences with some bias in comparison to those obtained with either the PR or BPC method. No significant interobserver variability was found between two observers calculating SRF using the BPC method. CONCLUSION: The BPC method requires only three ROIs to produce reliable estimates of SRF, was simple to implement, and in this study yielded statistically equivalent results to the PR method with appreciable interobserver agreement. As such, it adds a new reliable method for quality control of monitoring relative kidney function.

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.

Development of a modified sampling and calculation method for isotope plasma clearance assessment of the glomerular filtration rate in patients with cirrhosis and ascites.

AIM: The aim of this study was to identify a practical sampling regimen and calculation method that could be used to measure the glomerular filtration rate in patients with ascites using plasma sampling. PATIENTS AND METHODS: Thirteen potential liver transplant patients with cirrhosis and ascites were injected with Cr-51 ethylenediaminetetraacetic acid, and plasma samples were obtained at up to 16 time points for each patient. Reference clearance values were calculated using the area under the plasma clearance curve, which was calculated using all the available data points. Clearance calculations were then performed using three and four data points from each patient and three different calculation methods to identify a sampling regimen and calculation method that yielded good agreement with the reference values. RESULTS: The reference clearances ranged from 6 to 80 ml/min. Sampling at 2, 4, 8 and 24 h and calculation of the area under the plasma clearance curve using a log-linear trapezoidal rule with extrapolation to zero and infinity yielded a relative root mean square difference from the reference of less than 7%. CONCLUSION: This method for measuring glomerular filtration rate in patients with cirrhosis and ascites was found to be more accurate than the slope-intercept technique and is a practical alternative to urine collection.

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

The Tk-GV model fits Gamma Variates (GV) to data by Tikhonov regularization (Tk) with shrinkage constant, λ, chosen to minimize the relative error in plasma clearance, CL (ml/min). Using (169)Yb-DTPA and (99m)Tc-DTPA (n = 46, 8-9 samples, 5-240 min) bolus-dilution curves, results were obtained for fit methods: (1) Ordinary Least Squares (OLS) one and two exponential term (E1 and E2), (2) OLS-GV and (3) Tk-GV. Four tests examined the fit results for: (1) physicality of ranges of model parameters, (2) effects on parameter values when different data subsets are fit, (3) characterization of residuals, and (4) extrapolative error and agreement with published correction factors. Test 1 showed physical Tk-GV results, where OLS-GV fits sometimes-produced nonphysical CL. Test 2 showed the Tk-GV model produced good results with 4 or more samples drawn between 10 and 240 min. Test 3 showed that E1 and E2 failed goodness-of-fit testing whereas GV fits for t > 20 min were acceptably good. Test 4 showed CL(Tk-GV) clearance values agreed with published CL corrections with the general result that CL(E1) > CL(E2) > CL(Tk-GV) and finally that CL(Tk-GV) were considerably more robust, precise and accurate than CL(E2), and should replace the use of CL(E2) for these renal markers.

An improved method for determining renal sufficiency using volume of distribution and weight from bolus 99mTc-DTPA, two blood sample, paediatric data.

OBJECTIVES: To find an improved method of determining renal sufficiency by exploring power functions for estimating normal value, E(arg), single compartment glomerular filtration rate (G1), rate constant (gamma) and renal sufficiency index, RSI = gamma/E(gamma) = G1/E(G1), using compartment volume (V), patient mass ( W), patient age (A), patient height (H), and sex (S). To present the best estimator of normal, E(G1) = f(V, W). METHODS: One hundred and thirty 99mTc-diethylenetriaminepentaacetic acid (99mTc-DTPA) combined imaging and G1 studies in 97 children were screened by findings and history to obtain 44 normal studies of patients 1.46-18.5 years of age with blood samples at 109 (90-214) and 152 (120-246) min. Normal studies were used to generate predictive formulae. RESULTS: For power functions, [equation: see text] the statistically acceptable formulae in descending order of adjusted R2 were f(V, W), f(V,A), f(V,H), f(V), f(W,A,H), f( W), f(H) and f(A). Relationships of the body surface area type, f(W, H, S) and f(W, H), were statistically unwarranted. Kleiber's law, E(G1) proportional to W(3/4), with E(G1) = 6.9190W(0.7618) found here, allowed confirmation of GFRinulin approximately 0.87G1. The best estimator is f(V, W) = 10.998V(0.64717 W(0.20185), and may relate to a volumetric measure of body habitus. To verify methods, Monte Carlo simulation of the glomerular filtration rate (GFR) and f(V, W) was performed and yielded less than 5% precision error, 98% of the time. Normal RSI from f(V, W) had the smallest standard deviation, 11.3%, no regression bias over a six-fold range on a Bland-Altman ratio plot, p = 0.4, and good agreement with clinical classification at 95% specificity (RSI > 0.8589, Cohen's Kappa 0.70+/-0.062 (mean+/-bootstrap standard error). CONCLUSIONS: The best RSI from f(V, W) is RSI = 90.927gammaV(0.35283)W(-0.20185) and should detect mildly (14.1%) reduced renal sufficiency.

Improved lesion detection from spatially adaptive, minimally complex, Pixon reconstruction of planar scintigraphic images.

Pixon noise reduction was applied to 18 planar images, six each from 99mTc-methylene diphosphonate (99mTc-MDP), 67Ga citrate (67Ga), and (123)I-metaiodobenzylguanidine ((123)I-MIBG) studies. Pixon processing increased patient signal-to-noise ratio, 6.8-11.8 fold. Three specialists preferred processed images 44 of 54 times with good agreement (87%). Most (9/10, p<0.02) of the null and negative preferences were from (123)I-MIBG studies. Inter-rater association was shown for 1-4 scale rated artifact p<0.1, noise p<0.01 and lesion detection p<0.05. Pixon images had superior lesion detection ability, p<0.02, and noise levels, p<0.02 and no statistically significant change in artifacts.