2404893
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.
10114270
A single-injection method for measuring glomerular filtration rate.
A method for estimating glomerular filtration rate (GFR) has been developed that is based on an analysis of the total area under the plasma radioactivity-time curve after a single intravenous injection of [125I]iothalamate. Glomerular filtration rates obtained by this method (method A) and those obtained with two widely used single-injection techniques, the slope-intercept method (method B), and the two-compartment method (method C), were compared with GFRs obtained by standard inulin clearance techniques in 14 dogs. Method B consistently over. estimated inulin clearances more than 30%. Method C also overestimated inulin clearance considerably in dogs with an increased extracellular fluid volume, but was fairly reliable in normal dogs. Glomerular filtration rates obtained by the new method (method A) were in excellent agreement with inulin clearances in all dogs, regardless of the state of body hydration. The mean inulin clearance for all 14 experiments was 72.7+/-6.0 SE ml/min, while GFRs obtained by method A averaged 75.1+/-6.0 ml/min. The data from this study suggest that method A is a reliable means for estimating GFR that is especially useful in chronic experiments.
10185522
Indicator Transit Time Considered as a Gamma Variate
• Several theoretical formulations have recently been proposed to explain the shape of peripheral indicator dilution curves." One such mathematical approach utilizes convolution integrals,' '*• "*• °~ in which concentration of the indicator is handled as an unknown and unspecified function of time, C(t). The widespread use of this method, however, will be limited because the required mathematical manipulations, when applied to curves obtained in vivo, involve intricate and lengthy calculations. This type of analysis would be facilitated if the indicator concentration could be conveniently expressed as a specific functon of time.' If such a suitable function were available, it would also be possible to characterize more accurately normal and abnormal indicator dilution curves and perhaps to gain insight into some of the factors determining the shape of the curves. In addition, the availability of such a function would allow more efficient processing of experimental curves by high-speed computers. A number of theoretical and empirical mathematical expressions for C(t) have been suggested.' "•' These have found limited application and have not been subjected to extensive experimental verification using a large number of normal and abnormal curves. One expression for C(t), proposed by Evans in
6641116
Physiological interpretation of the skewness of indicatordilution curves; theoretical considerations and a practical application
SummaryIndicator-dilution curves can be interpreted and analysed by describing the system between injection-and sampling site with a physical model. Till now mainly compartmental and distributed models have been investigated. One feature of distributed models is the possibility to interpret skewness or asymmetry of the curve in terms of a parameter, proportional with the Peclet number, which is a measure of the relative contribution between convection and diffusion in indicator transport. In patients with and without pulmonary edema, we analyzed a number of curves obtained with an intravascular indicator (131I radioiodinated serum albumin, RISA) and a diffusing indicator (tritiated water, THO) over the pulmonary vascular bed. Edema was measured by indexed extravascular lung water and by critical pressure, defined as the difference between pulmonary capillary wedge pressure and plasma colloid osmotic pressure. The significant decrease of the symmetry of the RISA curves with increasing cardiac output we explained by an increasing labyrinth dispersion and increasing turbulence at higher flows.For normals we found all THO curves to be less skew than albumin curves. This difference diminished and even reversed when the degree of pulmonary edema increased. We suggest a hypothesis for this phenomenon by considering various mechanisms responsible for dispersion and capillary exchange of the indicator during transport from injection to sampling site. In normals the contribution of Taylor diffusion during laminar flow in parts of the circulatory system may be responsible for the greater symmetry of THO curves; with increasing pulmonary edema, transcapillary diffusion of THO causes THO curves to become more skew and even more asymmetric when compared with albumin curves.
68052714
Bolus injections of measured amounts of radioactivity
Many time-based radionuclide techniques, such as glomerular filtration rate measurement (GFR), require prompt intravenous delivery of and accurately measured tracer bolus with minimal residual tracer retention at the injection site. The quality assurance aspects of two antecubital vein, quantitative injection techniques were investigated. A flush bolus technique using a tuberculin syringe piggybacked onto a 10-ml saline flush was compared to a single blood pressure cuff injection technique. Scintillation camera data for each technique were compared for bolus duration in the abdominal aorta and for residual activity at the injection site at 5 min. Bolus times were measured as the FWHM of the gamma variate fit to the abdominal aortic regional time-activity curves. Relatively little focal activity was seen in the antecubital injection site following the flush bolus: marked residual activity was seen following the blood pressure cuff injections. The injection site/arm background ratios averaged 1.3 for the flush bolus and 30.1 for the cuff technique. Although both methods allowed accurate in vitro determination of administered radioactivity, only the tuberculin syringe flush bolus technique was acceptable for time-based quantitation because of its superior in vivo characteristics.
22538903
Indicator-dilution dispersion models and cardiac output computing methods.
The general theory of indicator-dilution methods provides a basis for computing improved cardiac output estimates. Interpretation is via indicator-dispersion modeling with Brownian motion of drifting particles. Detected curves indicate the distribution of passage times from the injection site: the local density random walk (LDRW) function of a Wiener process. Fitting the LDRW to 70 dye curves by nonlinear regression for examples, I show how all possible undistorted curves can, in principle, be simulated. I show via semilogarithmic plots that conventional exponential decay constructs systematically underestimate cardiac output by up to 8%. To help reconcile the predictions of LDRW-fitted dilution curves and contemporary practice, I show how curve-shape asymmetry (skewness) dramatically affects the enclosed areas. Mean transit times may overestimate blood volumes by 15-100% in very skewed thermodilution curves if the dispersion effects are overlooked. Triangle constructions, which accounted for hundreds of experimental findings, also have theoretical explanations. Curve-fitting methods reduce the extrapolation biases inherent in many computers and in any respiration-induced artifacts. Compatibility of cardiac output predictions from various dilution methods and modules becomes feasible.
34143107
A fractal approach for evaluation of pulmonary circulation in man at rest and during exercise.
Changes in pulmonary circulation caused by muscular exercise and body position are usual in daily life. By using first-pass radiocardiography and fractal analysis, pulmonary circulation in man was evaluated at rest and during muscular exercise. At rest, pulmonary circulation was heterogeneous as described by the relative dispersion (which is the coefficient of variation, i.e. the standard deviation of the pulmonary transit times divided by the mean transit time; RD = 0.51 +/- 0.06) and fractal in nature. During exercise, pulmonary circulation became more homogeneous (RD = 0.35 +/- 0.04; P < 0.001). The calculated fractal dimension decreases from 1.09 at rest to 1.06 during exercise. The model identifies a cubic-law response for circulation heterogeneity and a quarter-power law for resistance during muscular exercise.
20200546
Negative power functions of time in pharmacokinetics and their implications
When a clearance curve in pharmacokinetic studies- and in tracer kinetics in general — is well fitted by a sum of negative exponentials of time, in very many cases the data would also be well fitted over much or all of the same period by a function of time consisting mainly of a negative power or by a gamma function. There are also instances where two such power functions can be observed in the same clearance curve. Examples are given from numerous reanalyses of published results. These facts have not been explained, except as being fortuitous, by any existing theory or model based on two or more homogeneous compartments. Theoretical and practical implications are outlined and some general recipes are put forward with a view to replacing multicompartmental analysis.
20931091
A Fractal Approach to Heterogeneous Drug Distribution: Calcium Pharmacokinetics
AbstractPurpose. To point out the importance of heterogeneity in drug distribution processes and develop a noncompartmental approach for the description of the distribution of drug in the body.
Methods. A dichotomous branching network of vessels for the arterial tree connected to a similar venous network was used to describe the heterogeneity of blood flow in the successive generations of the networks. The relevant kinetics of drug distribution in the well perfused and the deep tissues was considered to take place under well stirred (homogeneous) and understirred (heterogeneous) conditions, respectively.
Results. A “homogeneous model” with classical kinetics (which is mathematically equivalent with the one-compartment model) was developed for these drugs which are confined to well perfused (“well stirred”) spaces. A “heterogeneous model” was proposed for the drugs reaching understirred spaces using a decreasing with time rate coefficient (fractal kinetics) to model the diffusion of drug under heterogeneous conditions. The analysis of the model equations revealed that the homogeneous model can be considered as a special case of the heterogeneous model. Concentration-time plots of multiexponential type were generated using the heterogeneous model equation. The empirically used power functions of time for the analysis of calcium clearance curves, were found to be similar to the equation adhering to the heterogeneous model. Fittings comparable to multiexponential models were obtained when the heterogeneous model equation with only one adjustable parameter was applied to six sets of long period calcium data.
Conclusions. The heterogeneous processes of drug distribution in the body can obey the principles of fractal kinetics. Calcium clearance curves were analysed with the heterogeneous model. The validity of multicompartmental models which are based on the concept of homogeneity to describe drug distribution should be reconsidered.
5060573
The effect of improved modelling of plasma clearance in paediatric patients with expanded body spaces on estimation of the glomerular filtration rate.
The glomerular filtration rate (GFR) is used clinically to assess renal function. The most accurate estimation technique is tracer clearance where deterministic compartment pharmacokinetic models are most widely used. The aim of this study was to assess the viability of alternative pharmacokinetic models to describe tracer clearance, and in turn, measure GFR. This study was carried out on 126 clearance datasets obtained from 44 patients with large solid tumours; these were fitted to four pharmacokinetic models with superiority of model determined by Akaike Information Criteria. A fractal model was found to be superior to the best deterministic compartment model (70% of datasets, P < 0.0020) as was a gamma-distributed residence time model (93% of datasets, P < 0.0020); both models also gave greater mean weighted coefficients of determination than deterministic compartment models. These results suggest that gamma-distributed residence time and fractal models better describe tracer clearance than deterministic compartment models and therefore should allow more accurate estimation of GFR.
5975407
A direct modeling approach to the early renal vascular transit of 99mTc chelates.
Delay channel integral methods are developed and applied for analyzing human renal scintiangiographic data produced after peripheral venous injection of a 99mTc chelete. The results include information for two renal vascular compartments (C1, C2) and a residual compartment (Cr). Each vascular compartment is associated with a fraction of the total renal plasma flow (A1, A2) and a mean transit time (T1, T2). The residual compartment has the residual plasma flow fraction Ar. The results obtained in 40 normal kidneys are presented and compared theoretically to the results from other methods.
45877147
Comparison of inulin, iothalamate, and 99mTc-DTPA for measurement of glomerular filtration rate.
Clearances of inulin, 125I-iothalamate, and 99mTc-Sn-DTPA were measured simultaneously in five mongrel dogs exhibiting a wide range of glomerular filtration rates (GFR). Standard constant-infusion inulin clearance was compared to radionuclide clearances after subcutaneous injection of the emitters mixed with aqueous epinephrine. All three substances were found to have virtually identical clearances. The accuracy, accessibility, low cost, low radiation hazard, and short half-life of 99mTc-Sn-DTPA make it an excellent substance for measuring GFR. The subcutaneous technique offers an accuracy comparable to the more difficult constant-infusion method.
783670
Total body water distribution of creatinine and urea in nephrectomized dogs.
It was the purpose of this study to measure and to compare the volumes of distribution of creatinine, urea and tritiated water in nephrectomized dogs. After bilateral nephrectomy a solution contain...
45795542
Glomerular filtration rate measurement by "single-shot" injection of inulin.
In 14 ADPKD patients the total body clearance and the urinary clearance of inulin using the constant infusion method were compared with the "single-shot" technique. Triplicate measurements of both clearances by each infusion method were obtained in 12 out of 14 patients. A high correlation was found between the total body clearance and the urinary clearance for both the constant infusion method (r = 0.96) and the single injection technique (r = 0.96). The coefficient of variation for the total body clearance of inulin was significantly lower for the constant infusion method and the single injection technique (7.8% and 7.1%) than for the urinary clearance of inulin (11.3% vs. 9.7%, P < 0.05). A constant overestimation of the urinary clearance by the total body clearance was observed with both methods (constant infusion method 8.3 ml.min-1 x 1.73 m-2 and single injection technique 13.4 ml.min-1 x 1.73 m-2). No concentration-dependent clearance was present. Determination of plasma inulin, especially at low levels, showed substantial interference by glucose. We conclude that, taking into account a constant overestimate of urinary clearance by the total body clearance of inulin, the single injection total body clearance possesses the best reproducibility and shows a good agreement with the conventional urinary clearance, which can be calculated by: GFR = TBCLss-13.1 ml.min-1 x 1.73 m-2 (in the range of 28 to 124 ml.min-1 x 1.73 m-2).
22602869
Variability of glomerular filtration rate estimation using single injection methods in Type 1 diabetic patients
Aim  Single‐injection inulin clearance (SIIC) methods without urine collection have often been compared with classical constant‐infusion inulin clearance methods. Therefore, we used repeated SIIC measurements to prove the hypothesis of a possible overestimation or variability of inulin clearance in Type 1 diabetic patients.
42083467
Day-to-day variability in glomerular filtration rate in normal dogs by scintigraphic technique.
The sources of variability in variability of scintigraphic measurements of glomerular filtration rate (GFR) have not been determined. The day to day variability of GFR was studied in 18 healthy beagle dogs. The renal uptake of 99mTc-diethylenetriaminepentaacetic acid (DTPA) of each dog was measured using a scintigraphic technique three times at intervals of 5-26 days. GFR was calculated from a regression equation relating uptake to plasma clearance, derived in our laboratory. The mean GFR was 3.97 +/- 0.72 (SD) ml/min/kg with values from 2.66 to 5.67 ml/min/kg. Analysis of variance (ANOVA) using a linear mixed model showed that most variability is a result of the dogs, less because of day to day variability and very little to the measurement variability. The repeatability coefficients for the day to day variability and measurement variability were 1.06 and 0.21 ml/min/kg respectively. The day to day variability can be caused by physiological homeostatic adjustments by the kidneys needed because of fluctuations in food and fluid intake, each dog's individual capacity to adjust, and to intrinsic errors in the measurement method. These results should be considered when using the scintigraphic method for clinical evaluation and research.
10096672
Volumes of distribution and clearances of intravenously injected creatinine in the dog.
N A RECENT study it was reported by GreenI berg ef al. (I) that the volume of distribution of creatinine in the dog was of the order of 40-60% of the body weight (average 48.5 % ; range 37.9-59.7 %). This estimate was made by dividing the equilibrium concentration of exogenous creatinine in the plasma at the end of a constant infusion into the exogenous creatinine balance in the body fluids. The latter was estimated by determining creatinine excretion after discontinuing the infusion and subtracting the ‘dead space’ creatinine and basal creatinine excretion. The crea tinine space obtained was considerably lower than that previously reported for the volume of distribution of creatinine in the dog by Dominguez, Goldblatt and Pomerene (2). These authors, studying the disappearance curve of creatinine after single intravenous injection estimated the volume of distribution of creatinine to be 76% of the body weight, a value which they recognized to be greater than the body water. In their analysis of the disappearance curve of creatinine, Dominguez et ~2. originally made the basic assumption that with the passage of time creatinine became homogeneously distributed throughout its entire volume of distribution; that is to say, that the ‘tissue’ creatinine concentration became identical with the ‘plasma’ concentration after sufficient time had elapsed. That this assumption is invalid for two compartment systems with excretory and intercompartmen tal clearances can be demonstrated readily with physical models. It has also been shown (3) that after single intravenous injections of inulin in dogs
19403977
Principles of nonlinear regression modeling
SummaryFive principles govern the selection of nonlinear regression models for bacterial growth. Examples are given of the various ways in which researchers have approached the problems of nonlinear regression modeling together with some discussion of linear modeling.
15297310
Simulated annealing: Practice versus theory
Simulated annealing (SA) presents an optimization technique with several striking positive and negative features. Perhaps its most salient feature, statistically promising to deliver an optimal solution, in current practice is often spurned to use instead modified faster algorithms, ''simulated quenching'' (SQ). Using the author's Adaptive Simulated Annealing (ASA) code, some examples are given which demonstrate how SQ can be much faster than SA without sacrificing accuracy.
21864171
Handbook of Parametric and Nonparametric Statistical Procedures
described and related to one another and to the different resampling methods is also notable. This is especially useful for the book’s target audience, for whom such concepts may not yet have taken root. On the computational side, the book may be a little less satisfying. Stepby-step computational algorithms are at some times inef cient and at other times cryptic so that an individual with little programming experience might have dif culty applying them. This problem is substantially offset by the presence of numerous detailed examples solved using existing software, providing readers roughly equal exposure to S-PLUS, SC, and Resampling Stats. Unfortunately, these examples often require large, complex programs, demonstrating as much as anything a need for better resampling software. On the whole, Data Analysis by Resampling is a useful and clear introduction to resampling. It would make an ambitious second course in statistics or a good third or later course. It is quite well suited for self-study by an individual with just a few previous statistics courses. Although it would be miscast as a graduate-level textbook or as a research reference—for one thing it lacks a thorough bibliography to make up for its surface treatment of many of the topics it covers—it is a very nice book for any reader seeking an introductory book on resampling.
23703317
Decreased Hydrodynamic Resistance in the Two‐Phase Flow of Blood Through Small Vertical Tubes at Low Flow Rates
The aggregation of red blood cells in blood flowing through small tubes at very low shear rates leads to the two-phase flow of an inner core of rouleaux surrounded by a cell-depleted peripheral layer. The formation of this layer is known to be accompanied by a decrease in hydrodynamic resistance to flow. To quantitate this effect, we measured the pressure gradient, flow rate, and the radius of the red blood cell core in suspensions flowing through tubes of 172-μm radius at mean linear flow rates (Ū) from 50 to 0.15 tube diameters · sec−1. Washed red blood cells were suspended in 1.5% buffered dextran 110 at hematocrits of 34–52%. Using syringe pumps, blood flowed from a stirred reservoir through a vertical 12-cm length of tube in either the upward or downward direction. The pressure drop was measured with transducers. Mean values in distributions in the core radius were obtained by analyzing cine films of flow taken through a microscope with flow in the upward direction, measuring the core radius at five equally spaced axial positions of the tube in each of 100 frames. At 34% and 46% hematocrit, the hydrodynamic resistance increased as Ū decreased from 50 sec−1, reaching a maximum at Ū∼2 sec−1. It then decreased to a minimum at Ū<0.5 sec−1 as the red blood cell core formed in the tube, and the mean core radius/tube radius ratio decreased from 0.98 to 0.74 with marked axial fluctuations at the lower Ū. At higher hematocrits, both the increase and decrease in hydrodynamic resistance were greater. In a red blood cell albumin–saline suspension, where there is no aggregation of red blood cells and no two-phase flow, hydrodynamic resistance increases linearly with decreasing Ū. The experimental results were compared with the predictions of a two-phase steady-flow model, assuming axisymmetric flow of a core surrounded by cell-free suspending medium. Two models were considered, one in which the core is solid, the other in which the rheological properties of the suspension in the core are given by the Quemada equation. The effects of sedimentation of the core resulting in a zero net flow pressure gradient were taken into account. Provided that an experimentally extrapolated value for the zero pressure gradient was used, the Quemada-fluid model gave good agreement with the experimentally observed core radius as a function of Ū and hematocrit.
45704931
A derivation of mean residence time.
MRT was derived as the mean value of the continuously distributed random variable residence time. Provide that elimination kinetics is linear and that elimination takes place exclusively from the central compartment, MRT can be calculated from the ratio AUMC/AUC. In this case, MRT is a drug (and formulation) related constant MRT may also be determined when the elimination kinetics is nonlinear. The meaning of those MRT values, however, remains limited because they depend on the dose applied.
19960924
Measurement of glomerular filtration rate: single injection plasma clearance method without urine collection.
Glomerular filtration rate (GFR) can be calculated from the plasma clearance of any of several radiopharmaceuticals that are excreted by glomerular filtration. Simplified methods have been proposed that require only one or two plasma samples in lieu of a more complete clearance curve. We examined the error introduced by this simplification. Forty patients were studied using a dual-isotope technique employing [99mTc]DTPA and [169Yb]DTPA, obtaining eight plasma samples for each clearance curve at intervals from 10 to 240 min after injection. Data were fit to several empirical or semiempirical formulae and also to a two-compartment computer model that permitted GFR estimation from only one or two data points. The computer model gave good fit, but so did several simpler methods. The error that results from replacing the complete clearance curve by a single 3-hr sample was about 8 ml/min (residual s.d.). By using two samples (at 1 and 3 hr), the error could be reduced to 4 ml/min. Recommended one- and two-sample methods are presented.
20940393
A Bayesian regression model for plasma clearance.
UNLABELLED
Nonlinear Bayesian regression permits curve fitting to a group of subjects simultaneously rather than individually. We evaluated this approach for interpreting plasma clearance curves with the goal of reducing curve-fitting failures and dealing objectively with problem datasets that may arise in clinical settings.


METHODS
(99m)Tc-Diethylenetriaminepentaacetic acid plasma clearance curves from 79 subjects were analyzed. The data typically comprised 7-9 samples obtained from 5-10 to 180-240 min after injection. A 2-compartment model was fitted by Bayesian regression to yield compartmental hyperparameters V1, L21, and L12 corresponding to the volume of the compartment into which tracer was injected and the transfer rates from compartment 1 to compartment 2 and from compartment 2 to compartment 1, respectively. This also yielded a clearance estimate for each subject.


RESULTS
Estimated hyperparameters were V1 = 8.9 L, L21 = 0.026 min(-1), and L12 = 0.040 min(-1). Conventional methods led to fitting failures in 2 of the 79 subjects but there were no failures with the Bayesian method. The hyperparameters were used to calculate the glomerular filtration rate for each subject from a single plasma sample with a root-mean-square error of 7.3 mL/min, which was not significantly different from the widely used Christensen-Groth formula.


CONCLUSION
Fewer fitting failures were encountered than with conventional methods, offering an objective means of dealing with problem data. This conceptually simple model can be used directly to calculate clearance from a single plasma sample. It requires only the 3 parameters described above, whereas the Christensen-Groth method requires 6 parameters.
17425892
Guidelines for glomerular filtration rate determination in children.
The purpose of this guideline is to offer to the nuclear medicine team a framework, which could prove helpful in daily practice. This guideline contains information related to the procedure and indications of measurement of glomerular filtration rate using blood samples in children. The present document is inspired by the report of the Radionuclides in Nephrourology Committee on renal clearance , but contains information more specifically adapted to the European practice e.g. the choice of tracer. This guideline summarises the views of the Paediatric Committee of the European Association of Nuclear medicine. It should be taken in the context of ”good practice” of nuclear medicine and local regulation.
209832610
The Monte Carlo method.
Abstract We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.
33770871
Pharmacokinetic model identification and parameter estimation as an ill-posed problem
SummaryFor model identification and parameter estimation in the framework of linear pharmacokinetics it is most often assumed that the disposition function is a finite sum of exponential functions with time constants λi and associated coefficients Ci. Least-square fitting procedures are used to estimate the coefficients Ci and the corresponding discrete locations λi on the λ-axes.This work presents an alternative approach. It does not assume that the non-zero coefficients are located at sharply defined values of λ, but that they are represented by a continuous function h(λ), the spectrum of the disposition function. This turns the non-linear least-square problem into a linear problem, which is known to be as so-called “ill-posed”. Regularisation methods have been developed in recent years as suitable tools for the treatment of such ill-posed problems.Application of Tikhonov regularisation to the case of the bolus kinetics of propofol in 8 volunteers is demonstrated. In 7 of the 8 cases a spectrum with 4 to 5 peaks was found, and in one volunteer there were only 2 peaks. All spectra with more than 2 peaks showed negative values of h(λ).The method used is described and the results are compared with those of conventional compartment analysis.
2208295
A Simplex Method for Function Minimization
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
121589596
Ridge regression: biased estimation for nonorthogonal problems
In multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X′X. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.
6657901
Guidelines for the measurement of glomerular filtration rate using plasma sampling
These guidelines have been adopted by the British Nuclear Medicine Society.
23656896
A Power Law for Determining Renal Sufficiency Using Volume of Distribution and Weight from Bolus 99mTc-DTPA, Two Blood Sample, Pediatric Data
Objectives: (1) Explore power laws for estimating the one-compartment glomerular filtration rate (G<sub>1</sub>), i.e., E(G<sub>1</sub>), as functions of compartment volume (V), patient mass (W), age (A), height (H) and sex (S). (2) Propose a renal sufficiency index, RSI=G<sub>1</sub>/E(G<sub>1</sub>). (3) Present the best estimator, E(G<sub>1</sub>) = f(V,W) = 10.988 V<sup>0.64717</sup>W<sup>0.20185</sup>. (4) Present the first clinical application of RSI, prediction of relative bone age (RBA = E(A)/A). Methods: 130 <sup>99m</sup>Tc-DTPA imaging and G<sub>1</sub> studies were screened to find 44 normal studies in children 1.46 to 18.5 years old. Results: E(G<sub>1</sub>) formulae of the body surface area type, i.e., f(W,H,S) and F(W,H), were found to be statistically unwarranted. Statistically acceptable formulae, in descending adjusted R<sup>2</sup>, were f(V,W), f(V,A), f(V,H), f(V), f(W,A,H), f(W), f(H) and f(A). Kleiber's law, E(G<sub>1</sub>) prop W<sup>frac34</sup>, seems to confirm the previously reported relationship GFR<sub>inulin</sub> ap 0.87G<sub>1</sub>. Our best G<sub>1</sub> estimator, f(V,W), may be related to a physiological volume. RSI as predicted by f(V,W) had the smallest relative standard deviation, 11.3%, no regression bias and good agreement with clinical classification at 95% specificity. RBA was found to be correlated with RSI, with a peak at 88% E(RSI), with RSI accounting for 25% of its variance. Conclusions: Our best RSI predictor, RSI = 90.927gammaV<sup>0.35283</sup>W<sup>-0.20185</sup>, should be capable of detecting mildly reduced (14.1%) renal sufficiency.
29451718
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.
9378873
Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals
The fact that metabolic rate scales as the three-quarter power of body mass (M) in unicellular, as well as multicellular, organisms suggests that the same principles of biological design operate at multiple levels of organization. We use the framework of a general model of fractal-like distribution networks together with data on energy transformation in mammals to analyze and predict allometric scaling of aerobic metabolism over a remarkable 27 orders of magnitude in mass encompassing four levels of organization: individual organisms, single cells, intact mitochondria, and enzyme molecules. We show that, whereas rates of cellular metabolism in vivo scale as M−1/4, rates for cells in culture converge to a single predicted value for all mammals regardless of size. Furthermore, a single three-quarter power allometric scaling law characterizes the basal metabolic rates of isolated mammalian cells, mitochondria, and molecules of the respiratory complex; this overlaps with and is indistinguishable from the scaling relationship for unicellular organisms. This observation suggests that aerobic energy transformation at all levels of biological organization is limited by the transport of materials through hierarchical fractal-like networks with the properties specified by the model. We show how the mass of the smallest mammal can be calculated (≈1 g), and the observed numbers and densities of mitochondria and respiratory complexes in mammalian cells can be understood. Extending theoretical and empirical analyses of scaling to suborganismal levels potentially has important implications for cellular structure and function as well as for the metabolic basis of aging.
25279865
D-optimal designs for parameter estimation for indirect pharmacodynamic response models
This report generates efficient experimental designs (dose, sampling times) for parameter estimation for four basic physiologic indirect pharmacodynamic response (IDR) models. The principles underlying IDR models and their response patterns have been well described. Each IDR model explicitly contains four parameters, kin (production), kout (loss), Imax/Smax (capacity) and IC50/SC50 (sensitivity). The pharmacokinetics of an IV dose of drug described by a monoexponential function of time with two parameters, V and kel, is assumed. The random errors in the response variable are assumed to be additive, independent, and normal with zero mean and variance proportional to some power of the mean response. Optimal design theory was used extensively to assess the role of both dose and sampling times. Our designs were generated in Mathematica (ADAPT 5 typically produces identical results). G-optimality was used to verify that the generated designs were indeed D-optimal. Such designs are efficient and robust when good prior knowledge of the estimated parameters is available. The efficiency of unconstrained D-optimal designs (4 dose, sampling time pairs) does not improve much when the drug doses are allowed to differ, compared with constrained single dose designs (4 sampling times) with one maximal feasible dose. Also, explored were efficiencies of alternative study designs and results from parameter misspecification. This analysis substantiates the importance of larger doses yielding greater certainty in parameter estimation in pharmacodynamics.
23922619
Estimation of Glomerular Filtration Rate from Plasma Clearance of 51-Chromium Edetic Acid
The glomerular filtration rate was estimated by a single compartment analysis of the rate of fall of plasma concentration of 51-chromium edetic acid after a single intravenous injection. This slope clearance consistently overestimated the simultaneously determined standard urinary clearance, but could be used to predict the latter with an accuracy of ±9% (95% confidence limits). The coefficient of variation of replicate estimates of the slope clearance in the same individual was 3·9%; thus two estimates of glomerular filtration rate by this technique which differ by 11% have a 95% probability of reflecting a genuine difference. The method requires an intravenous injection and blood samples at 2 and 4 hours; urine samples are not required. It is simple, safe, and precise, and is applicable to children.
42693791
Optimum sample times for single-injection, multisample renal clearance methods.
The best choice of sample times for measuring renal function in adults by single-injection multisample plasma clearance methods was determined by Monte Carlo simulation, using a two-compartment model with parameters chosen to fit average values (from published clinical studies) for each of the three radiopharmaceuticals 99mTc-MAG3, 99mTc-DTPA and 131I-ortho-iodohippurate. Random errors were added and the simulated data were then fit to a two-exponential model using a weighted nonlinear curve fitting method. The calculated clearance values were compared with the original values to determine random and systematic errors for different selections of sample time for each radiopharmaceutical at various levels of renal function. The results show that for research-level accuracy with a GFR agent such as 99mTc-DTPA, plasma sampling must begin by 10 min after injection and continue at least 3 hr (in adults). With an ERPF agent such as 99mTc-MAG3 or 131I-OIH, sampling must begin by 5 min and continue for at least 90 min. Six logarithmically distributed samples are sufficient.
9250442
Anaphylaxis to intravenous sinistrin
1. Hauben M, Reich L. Safety related drug-labeling changes: findings from two data mining algorithms. Drug Saf 2004;27:735-44. 2. Hauben M, Reich L. Drug-induced pancreatitis: lessons in data mining. Br J Clin Pharmacol 2004;58:560-2. DOI 10. 1111/j.1365-2125.2004.02176 3. Matsui A, Matsuo H, Hitomi T, Sasaki S, Maeda M, Sawada Y. Prediction of catalepsies induced by amiodarone, aprindine and procaine: similarity in conformation of diethylaminoethyl side chain. J Pharmacol Exp Ther 1998;287:725-32. 4. Matsuo H, Matsui A, Risa N, Takanaga H, Inoue N, Hattori F, et al. Propiverine-induced parkinsonism: a case report and a pharmacokinetic/pharmacodynamic study in mice. Pharm Res 2000;17:565-71. 5. Sawada Y, Nasu R, Matsuo H, Ohtani H. Relationship between structure and drug-induced parkinsonism (letter). Ann Pharmacother 2000;34:668. DOI 10.1345/aph.19253
39226536
Anaphylactic reaction to intravenous sinistrin (Inutest)
Inulin clearance is the 'gold standard' for the determination of glomerular filtration rate, This is the first report of anaphylaxis following intravenous administration of inulin.