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PubMed2003

Linear regression with spatial constraint to generate parametric images of ligand-receptor dynamic PET studies with a simplified reference tissue model.

For the quantitative analysis of ligand-receptor dynamic positron emission tomography (PET) studies, it is often desirable to apply reference tissue methods that eliminate the need for arterial blood sampling. A common technique is to apply a simplified reference tissue model (SRTM). Applications of this method are generally based on an analytical solution of the SRTM equation with parameters estimated by nonlinear regression. In this study, we derive, based on the same assumptions used to derive the SRTM, a new set of operational equations of integral form with parameters directly estimated by conventional weighted linear regression (WLR). In addition, a linear regression with spatial constraint (LRSC) algorithm is developed for parametric imaging to reduce the effects of high noise levels in pixel time activity curves that are typical of PET dynamic data. For comparison, conventional weighted nonlinear regression with the Marquardt algorithm (WNLRM) and nonlinear ridge regression with spatial constraint (NLRRSC) were also implemented using the nonlinear analytical solution of the SRTM equation. In contrast to the other three methods, LRSC reduces the percent root mean square error of the estimated parameters, especially at higher noise levels. For estimation of binding potential (BP), WLR and LRSC show similar variance even at high noise levels, but LRSC yields a smaller bias. Results from human studies demonstrate that LRSC produces high-quality parametric images. The variance of R(1) and k(2) images generated by WLR, WNLRM, and NLRRSC can be decreased 30%-60% by using LRSC. The quality of the BP images generated by WLR and LRSC is visually comparable, and the variance of BP images generated by WNLRM can be reduced 10%-40% by WLR or LRSC. The BP estimates obtained using WLR are 3%-5% lower than those estimated by LRSC. We conclude that the new linear equations yield a reliable, computationally efficient, and robust LRSC algorithm to generate parametric images of ligand-receptor dynamic PET studies.

Adult↗

PubMed2002

Pedestrian risk decrease with pedestrian flow. A case study based on data from signalized intersections in Hamilton, Ontario.

A unique database provided information on pedestrian accidents, intersection geometry and estimates of pedestrian and vehicle flows for the years 1983-1986 for approximately 300 signalized intersections in Hamilton, Ont., Canada. Pedestrian safety at semi-protected schemes, where left-turning vehicles face no opposing traffic but have potential conflicts with pedestrians, were compared with pedestrian safety at normal non-channelized signalized approaches, where right-turning vehicles have potential conflicts with pedestrians. Four different ways of estimating hourly flows for left- and right-turning vehicles were explored. Hourly flows were estimated for periods of 15 min, hours, two periods a day (a.m. and p.m.) and the 'daily' period (7 h). Parameter estimates were somewhat affected by the time period used for flow estimation. However, parameter estimates seem to be affected far more by the traffic pattern (left- or right-turning traffic), even though approaches were selected such that the situation for left- and right-turning turning traffic was similar (no opposing traffic, no advanced green or other separate phases and no channelization). Left-turning vehicles caused higher risks for pedestrians than right-turning vehicles. At low vehicular flows right turns and semi-protected left turns seemed to be equally safe for pedestrians. When risks for pedestrians were calculated as the expected number of reported pedestrian accidents per pedestrian, risk decreased with increasing pedestrian flows and increased with increasing vehicle flow. As risk decreases with increasing pedestrian flows, promoting walking will have a positive effect on pedestrian risk at signalized intersections.

Accidents, Traffic↗

PubMed1996

Bayesian procedures for the estimation of mutation rates from fluctuation experiments.

Bayesian procedures are developed for estimating mutation rates from fluctuation experiments. Three Bayesian point estimators are compared with four traditional ones using the results of 10,000 simulated experiments. The Bayesian estimators were found to be at least as efficient as the best of the previously known estimators. The best Bayesian estimator is one that uses (1/m2) as the prior probability density function and a quadratic loss function. The advantage of using these estimators is most pronounced when the number of fluctuation test tubes is small. Bayesian estimation allows the incorporation of prior knowledge about the estimated parameter, in which case the resulting estimators are the most efficient. It enables the straightforward construction of confidence intervals for the estimated parameter. The increase of efficiency with prior information and the narrowing of the confidence intervals with additional experimental results are investigated. The results of the simulations show that any potential inaccuracy of estimation arising from lumping together all cultures with more than n mutants (the jackpots) almost disappears at n = 70 (provided that the number of mutations in a culture is low). These methods are applied to a set of experimental data to illustrate their use.

Bacteria↗

PubMed2006

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system.

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.

Antiretroviral Therapy, Highly Active↗

PubMed2006

Differential scanning calorimetry as a tool to estimate binding parameters in multiligand binding proteins.

The stability of proteins and their interactions with other molecules is a topic of special interest in biochemistry because many cellular processes depend on that. New methods and approaches are constantly developed to elucidate the energetics of biomolecular recognition. In this sense, the application of the theory of macromolecular unfolding linked to ligand binding to differential scanning calorimetry (DSC) has proved to be a useful tool to simultaneously characterize the energetics of unfolding and binding. Although the general theory is well known, the applicability of DSC to study the interaction of biomolecules is not common. In the current work, we estimated the binding parameters of 8-anilinonaphthalene-1-sulfonic acid to human serum albumin using DSC. This model system was chosen due to both the complex stoichiometry and the moderate binding constants. From DSC curves acquired at different ligand concentrations, we obtained the number of bound ligands, the binding constants, and the binding enthalpy for each independent binding site. Compared with those parameters determined by titration calorimetry, the results highlight the potentiality of DSC to estimate binding parameters in multiligand binding proteins.

Anilino Naphthalenesulfonates↗

PubMed2000

Confidence images for MR spectroscopic imaging.

Automated spectral analysis and estimation of signal amplitudes from magnetic resonance data generally constitutes a difficult nonlinear optimization problem. Obtaining a measure of the degree of confidence that one has in the estimated parameters is as important as the estimates themselves. This is particularly important if clinical diagnoses are to be based on estimated metabolite levels, as in applications of MR Spectroscopic Imaging for human studies. In this report, a standard method of obtaining confidence intervals for nonlinear estimation is applied to simulated data and short-TE clinical proton spectroscopic imaging data sets of human brain. So-called "confidence images" are generated to serve as visual indicators of how much trust should be placed in interpretation of spatial variations seen in images derived from fitted metabolite parameter estimates. This method is introduced in a Bayesian framework to enable comparison with similar techniques using Cramer-Rao bounds and the residuals of fitted results.

Bayes Theorem↗

PubMed2000

Detection of areas with viable remnant tumor in postchemotherapy patients with Ewing's sarcoma by dynamic contrast-enhanced MRI using pharmacokinetic modeling.

An approach is presented for monitoring the effects of neoadjuvant chemotherapy in patients with Ewing's sarcoma using dynamic contrast-enhanced perfusion magnetic resonance (MR) images. For that purpose, we modify the three-compartment pharmacokinetic permeability model introduced by Tofts et al. (Magn Reson Med 1991;17:357-67) to a two-compartment model. Perfusion MR images acquired using an intravenous injection with Gadolinium (Gd-DTPA) are analyzed with this two-compartment pharmacokinetic model as well as the with an extended pharmacokinetic model that includes the (local) arrival time t(0) of the tracer as an endogenous (estimated) parameter. For each MR section, a wash-in parameter associated with each voxel is estimated twice by fitting each of the two pharmacokinetic models to the dynamic MR signal. A comparison of the two wash-in parametric images (global versus local arrival time) with matched histologic macroslices demonstrates a good correspondence between areas with viable remnant tumor and a high wash-in rate. This can be explained by the high number and permeability of the (leaking) capillaries in viable tumor tissue. The novel pharmacokinetic model based on a local arrival time of tracer results in the best fit of the wash-in rate, the most important factor discerning viable from nonviable tumor components. However, parameter estimates obtained with this model are also more sensitive to noise in the MR signal. The novel pharmacokinetic model resulted in a sensitivity between 0.22 and 0.60 and a specificity between 0.61 and 1. The model based on a global arrival time gave sensitivities between 0.33 and 0.77 and specificities between 0.58 and 0.99. Both statistics are computed as the fraction of correctly labeled voxels (viable or nonviable tumor) within a specified ROI, which delineates the tumor. We conclude that the added value of estimating the local arrival time of tracer first manifests itself for moderate noise levels in the MR signal. The novel pharmacokinetic model should moreover be preferred when pharmacokinetic modeling is applied on the average signal intensity within a ROI, where noise has less effect on the fitted parameters.

Adolescent↗

PubMed2004

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model.

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

Animals↗

PubMed2006

A computationally efficient approach to the estimation of two- and three-dimensional hidden Markov models.

Statistical modeling methods are becoming indispensable in today's large-scale image analysis. In this paper, we explore a computationally efficient parameter estimation algorithm for two-dimensional (2-D) and three-dimensional (3-D) hidden Markov models (HMMs) and show applications to satellite image segmentation. The proposed parameter estimation algorithm is compared with the first proposed algorithm for 2-D HMMs based on variable state Viterbi. We also propose a 3-D HMM for volume image modeling and apply it to volume image segmentation using a large number of synthetic images with ground truth. Experiments have demonstrated the computational efficiency of the proposed parameter estimation technique for 2-D HMMs and a potential of 3-D HMM as a stochastic modeling tool for volume images.

Algorithms↗

PubMed1988

Solubility and related physicochemical properties of narcotic analgesics.

The physicochemical properties of select opioid and anilinopiperidine narcotic analgesics were investigated. The solubilities of the narcotics in hexane and water and, for morphine, in other organic solvents were determined. Regular solution theory seems to be applicable to the solubility behavior of morphine in solvents that lack strong dipoles and hydrogen bonds. A best-fit solubility parameter of 13.2 (cal/cm3)1/2 for morphine was determined from its solubilities in London solvents and its ideal solubility. Calculation of morphine's solubility parameter from its hexane solubility alone and its melting properties gave a corresponding delta 2 value. These measured solubility parameters were appreciably larger than the solubility parameter estimated from molar attraction constants. Solubility parameters of hydromorphone, codeine, fentanyl, and sufentanil were also calculated from respective hexane solubilities, melting points, and heats of fusion and were 11.7, 10.9, 9.8, and 9.7 (cal/cm3)1/2. For these compounds, experimental solubility parameters agreed with solubility parameters estimated from molar attraction constants. Because meperidine, fentanyl, and sufentanil exhibit low levels of intracrystalline cohesion, as reflected in low melting points and relatively modest heats of fusion, theoretically projected ideal solubilities and actual solubilities in organic solvents measured for them were considerably higher than determined for morphine and its analogues. Consistent with the solubilities, the octanol-water partition coefficients of the two 4-anilinopiperidine analogues and of meperidine were several orders of magnitude larger than those of the opioids, evidencing the fact that meperidine, fentanyl, and sufentanil are substantially more lipophilic than the opioids.

Analgesics, Opioid↗

PubMed2004

Functional CT in lung with a conventional scanner: simulations and sampling considerations.

Due to rapid transit times, motion artefacts from breathing and the low signal intensity, functional computed tomography (f-CT) studies in lung tissue remain challenging with conventional CT scanners. The purpose of this study is to examine the accuracy of parameter estimates when performing deconvolution analysis with signals from lung tissue. The effects of partial volume averaging in lung tissue, differing transit times, variable vascular and capillary responses, expected noise levels, differing sampling rate and durations were simulated on a computer. Deconvolution using singular-value decomposition (SVD) analysis was performed for realistic lung signals using published and measured values of the arterial input and noise levels. The accuracy, bias and variance of the estimated residue functions and their associated parameter estimates were evaluated. We find that f-CT signals may be measured and analysed using SVD and other deconvolution approaches. Functional CT signals in the lung may be analysed provided that the rise and fall of the tissue and input curves are well sampled (regardless of sampling rate) and noise levels in the lung ROI tissue are approximately 20 HU or less, even for regions of interest that are mostly occupied by air. Estimates of the mean tissue transit time (MTT) are insensitive to air volume. Other decovolution methods such as fast Fourier transform methods provide more accurate estimates of PBF, whereas SVD approaches provide more accurate estimates of pulmonary blood volume and MTT. F-CT of the lung with a conventional scanner should be possible, when the extra dose is not a consideration.

Computer Simulation↗

PubMed2002

NONMEM and NPEM2 population modeling: a comparison using tobramycin data in neonates.

Nonlinear mixed effects modeling (NONMEM) and nonparametric expectation maximization (NPEM2) have both been used in population modeling of tobramycin. We compared both methods for differences in population pharmacokinetic parameters in relation to error models used. Predictive performance was compared between models. A group of 470 neonates who had received tobramycin according to a gestational age (GA)-dependent dosing interval was analyzed according to a one-compartment model with NONMEM and NPEM2. Additional models were constructed where the assay error pattern in NPEM2 mimicked NONMEM residual error and vice versa. Individual pharmacokinetic parameter estimates were compared. Predictive performance was evaluated in a separate group of 61 patients. Population estimates and variation coefficients (CV) for optimal models were NONMEM K(el) 0.071 h(-1) (27%), V(d) 0.59 L/kg (9%); NPEM2 K(el) 0.079 h(-1) (42%), V(d) 0.65 L/kg (48%). Forcing NONMEM to use the NPEM2 error pattern as residual error or vice versa resulted in smaller differences in CVs of the estimates. NONMEM gave less bias (P < 0.05) than NPEM2 and comparable precision with this approach. In conclusion NONMEM and NPEM2 are dissimilar in population estimates. Differences in ranges of pharmacokinetic parameter estimates between NONMEM and NPEM2 are largely determined by the method of incorporating error patterns in both programs.

Bias↗

PubMed2004

Synchronization-based estimation of all parameters of chaotic systems from time series.

By a simple combination of adaptive scheme and linear feedback with the updated feedback strength, for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically. This approach supplies a systematic and analytical procedure for estimating parameters from time series, and it is simple to implement in practice. In addition, this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system. Lorenz and Rössler hyperchaos systems are used to illustrate the validity of this technique.

Journal Article↗

PubMed2004

Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents.

The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.

Antineoplastic Agents↗

PubMed1998

Estimation of genetic parameters for scrotal circumference, age at puberty in heifers, and hip height in Brahman cattle.

Genetic parameters were estimated for scrotal circumference (SC; n=287), age at puberty in heifers (AP; n=292), and hip height in both sexes (HH; n=684) for Brahman cattle born from 1984 to 1994 at the Subtropical Agricultural Research Station, Brooksville, Florida. Age at puberty was defined as the age (days) at first detected ovulatory estrus. Measurements of SC and HH were taken at 18 mo of age. Fixed effects considered in the SC model were year of birth (YOB), age of dam (AOD), and age at measurement (AGE) as a linear covariate. Fixed effects fitted to the AP model were YOB and AOD. Fixed effects in the HH model were YOB, sex, AOD, and AGE as a linear covariate. Variances and covariances were estimated using REML with a derivative-free algorithm and fitting a multiple trait animal model. Estimates of heritability for SC, AP, and HH were .28, .42, and .65, respectively. Estimates of genetic correlations between SC and AP, SC and HH, and AP and HH were -.32, .19, and .25, respectively. Estimates of environmental correlations were .19 between SC and HH, and -.13 between AP and HH. Estimates of genetic parameters indicate a favorable genetic relationship between SC in Brahman bulls and AP in Brahman heifers under subtropical conditions. There was also evidence that selecting Brahman bulls for HH would not adversely affect SC but would have some detrimental effect on AP in female progeny.

Age Factors↗

PubMed1995

Blood volume modeling and refilling rate estimation in hemodialysis by continuous hemoglobin monitoring.

Eleven bicarbonate hemodialyses (HD) of 6 patients under constant ultrafiltration were continuously monitored with an optical Hb-meter, considered to be a marker of blood volume (BV) changes. A theoretical model was fed experimental data for prediction of blood volume and estimation of vascular parameters, and a time course of rate of refilling was extrapolated. The adequacy of the model was very good for the time course of BV prediction (r2 = 0.85-0.95, n = 11) and for plasma protein concentration (r2 = 0.83-0.86, n = 2). Parameters estimated included (mean-DS): filtration coefficient (Cf) = 0.22 (0.16) dl/min*mmHg, transcapillary hydrostatic pressure (DP) = 17.80 (3.44) mmHg and protein concentration of the refilling fluid (Cref) = 0.45 (0.30) g/dl. In conclusion our study has shown that the model chosen fits the observed BV profile well in all cases, thus the Hb data series can be used for BV dynamic modeling and for estimation of vascular parameters.

Adult↗

PubMed2004

An integrated model for the analysis of pharmacokinetic data from microdialysis experiments.

PURPOSE: To develop an integrated model for microdialysis data that incorporates all data including the recovery measurements in one model, and to compare this model to a previous model and the results from a noncompartmental analysis. METHODS: The models were developed in NONMEM. The modes of analysis were compared with respect to parameter estimates, model structures, gained mechanistic insight, and practical aspects. RESULTS: Both modeling approaches resulted in similar model structures. The parameter estimates in blood and brain from the models and the results from the noncompartmental analysis were comparable. Using the integrated model all data, that is, the total arterial concentrations, the venous and brain dialysate concentrations, and the recovery measurements, were analyzed simultaneously. CONCLUSION: The theoretical benefits of the integrated model are related to the inclusion of the recovery in the model and the use of all collected data as it was observed. Thus, all data are described in a single model, corrections for the recovery and the protein binding are done within the model, and the dialysate observations are described by the integral over each collection interval. Thereby, the variability and the uncertainty in the model parameters are handled correctly to give more reliable parameter estimates.

Animals↗

PubMed1994

Predictive performance of the Bayesian analysis: effects of blood sampling time, population parameters, and pharmacostatistical model.

The present paper reports theoretical equations for the predictive performance of the Bayesian forecasting method. The precision of parameter estimates and predicted concentrations for an individual was described by general equations with the aid of a variance-covariance matrix of parameter estimates that involved the Bayes theorem. The equations were applied to assess the predictive performance of the one-point Bayesian method in association with blood sampling time, the population parameters, and the pharmacostatistical model. The simulation study showed that the prediction error in parameter estimates essentially depended upon the sampling time but the magnitude of dependency was affected by the size of inter- and intraindividual variances. With a smaller value of interindividual variance, the dependency on sampling time was less apparent. Effects of sampling time were further examined using clinical data obtained from 20 patients taking theophylline, and the results were in good agreement with the theoretical consideration. The present general equations are useful to investigate the sampling strategy as well as structural and variance modeling on the predictive performance of the Bayesian method.

Adult↗