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

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

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 169Yb-DTPA and 99mTc-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 CLTk-GV clearance values agreed with published CL corrections with the general result that CLE1 > CLE2 > CLTk-GV and finally that CLTk-GV were considerably more robust, precise and accurate than CLE2, and should replace the use of CLE2 for these renal markers

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

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.PubMedWoSScopu

Schematic diagram showing E2 compartmental and GV variable volume models of drug distribution.

<p>The E2 model could also be drawn as a variable volume model in which case a scale factor <i>α</i>_exp = <i>V</i>_E/<i>V</i>_d(∞) < 1 would define the physical volume at time <i>t</i> to be <i>α</i>_exp<i>V</i>_d(<i>t</i>). Similarly, for the variable volume adaptively obtained GV model, one can define <i>α</i> = <i>V</i>_E/<i>V</i>_d(∞) < 1, and an expanding physical volume <i>αV</i>_<i>d</i>(<i>t</i>). Note, both <i>α</i>_exp and <i>α</i> are constants at all times for their respective models. The term <i>V</i>_<i>SS</i> can be confusing because 1) <i>V</i>_<i>SS</i> implies that <i>V</i>_E is always a steady state volume, which is not the case as the GV model <i>αV</i>_<i>d</i>(<i>t</i>) <i>< V</i>_E is concentration depleted at late time, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158798#pone.0158798.e034" target="_blank">Eq (30)</a>. 2) <i>V</i>_<i>SS</i> implies that <i>V</i>_E only exists at <i>t</i> = ∞, whereas <i>V</i>_E is defined all of the time, i.e., on <i>t</i> = [0,∞) by Eqs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158798#pone.0158798.e010" target="_blank">8</a> & <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158798#pone.0158798.e007" target="_blank">7</a>). Finally, 3) <i>V</i>_<i>SS</i> implies an expected physical volume of distribution for sums of exponential term bolus models, and the apparent volume of distribution for a constant infusion experiment, whereas <i>V</i>_E applies to more models as the expected volume of physical distribution of a drug for both the bolus and constant infusion experiments.</p

Elymus dahuricus Turcz.

原著和名: ハマムギ科名: イネ科 = Gramineae採集地: 北海道 枝幸郡 枝幸町 北見神威岬 (北海道 北見 枝幸町 神威岬)採集日: 1989/8/26採集者: 萩庭丈壽整理番号: JH038150国立科学博物館整理番号: TNS-VS-98815

Concentration versus time curve for E2 and GV models for four <i>V</i>_E values at <i>CL</i> of 100 ml/min (left panel) and 40 ml/min (right panel).

<p>Concentration versus time curve for E2 and GV models for four <i>V</i>_E values at <i>CL</i> of 100 ml/min (left panel) and 40 ml/min (right panel).</p

Time to achieve apparent volume of distribution to 95% of <i>V</i>_area after the intravenous bolus of the drug and terminal half-life of the drug from E2 and GV models.

<p>Time to achieve apparent volume of distribution to 95% of <i>V</i>_area after the intravenous bolus of the drug and terminal half-life of the drug from E2 and GV models.</p

Pharmacokinetic parameters from the weighted biexponential (E2) and the Tk-GV models.

<p>Comparable measures boxed.</p

Wilcoxon tests with median parameter comparisons.

<p>Wilcoxon tests with median parameter comparisons.</p