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PubMed2001

4D maximum a posteriori reconstruction in dynamic SPECT using a compartmental model-based prior.

A 4D ordered-subsets maximum a posteriori (OSMAP) algorithm for dynamic SPECT is described which uses a temporal prior that constrains each voxel's behaviour in time to conform to a compartmental model. No a priori limitations on kinetic parameters are applied; rather, the parameter estimates evolve as the algorithm iterates to a solution. The estimated parameters and time-activity curves are used within the reconstruction algorithm to model changes in the activity distribution as the camera rotates, avoiding artefacts due to inconsistencies of data between projection views. This potentially allows for fewer, longer-duration scans to be used and may have implications for noise reduction. The algorithm was evaluated qualitatively using dynamic 99mTc-teboroxime SPECT scans in two patients, and quantitatively using a series of simulated phantom experiments. The OSMAP algorithm resulted in images with better myocardial uniformity and definition, gave time-activity curves with reduced noise variations, and provided wash-in parameter estimates with better accuracy and lower statistical uncertainty than those obtained from conventional ordered-subsets expectation-maximization (OSEM) processing followed by compartmental modelling. The new algorithm effectively removed the bias in k21 estimates due to inconsistent projections for sampling schedules as slow as 60 s per timeframe, but no improvement in wash-out parameter estimates was observed in this work. The proposed dynamic OSMAP algorithm provides a flexible framework which may benefit a variety of dynamic tomographic imaging applications.

Algorithms↗

PubMed2002

Statistical estimation of parameters in a disease transmission model: analysis of a Cryptosporidium outbreak.

Population dynamic models, commonly used tools in the study of epidemics and other complex population processes, are implicit non-linear mathematical equations. Inference based on such models can be difficult due to the problems associated with high dimensional parameters that may be non-identified and complex likelihood functions that are difficult to maximize. To address a problem of non-identifiability due to collinearity of parameter estimates in a mathematical model of the 1993 Milwaukee Cryptosporidium parvum outbreak, we examined the utility of a constrained profile likelihood approach. This method was used to study two parameters of interest from the mathematical model: (i). the rate of secondary transmission; (ii). the proportional increase in primary transmission due to water treatment failure. The estimated values of these parameters were shown to depend strongly on poorly understood aspects of Cryptosporidium epidemiology such as asymptomatic proportion and the population immune status. Our analysis demonstrated that the combination of a disease transmission model and a constrained profile likelihood procedure provides an effective approach for inference and estimation of important parameters regulating infectious disease outbreaks.

Animals↗

PubMed1990

Atmospheric deposition, resuspension, and root uptake of Pu in corn and other grain-producing agroecosystems near a nuclear fuel facility.

Plutonium released to the environment may contribute to dose to humans through inhalation or ingestion of contaminated foodstuffs. Plutonium contamination of agricultural plants may result from interception and retention of atmospheric deposition, resuspension of Pu-bearing soil particles to plant surfaces, and root uptake. Plutonium on vegetation surfaces may be transferred to grain surfaces during mechanical harvesting. Data obtained from corn grown near the U.S. Department of Energy's H-Area nuclear fuel chemical separations facility on the Savannah River Site were used to estimate parameters of a simple model of Pu transport in agroecosystems. The parameter estimates for corn were compared to those previously obtained for wheat and soybeans. Despite some differences in parameter estimates among crops, the relative importances of atmospheric deposition, resuspension, and root uptake were similar among crops. For even small deposition rates, the relative importances of processes for Pu contamination of corn grain should be: transfer of atmospheric deposition from vegetation surfaces to grain surfaces during combining greater than resuspension of soil to grain surfaces greater than root uptake. Approximately 3.9 X 10(-5) of a year's atmospheric deposition is transferred to grain. Approximately 6.2 X 10(-9) of the Pu inventory in the soil is resuspended to corn grain, and a further 7.3 X 10(-10) of the soil Pu inventory is absorbed and translocated to grains.

Air Pollution, Radioactive↗

PubMed1999

Modelling the growth of a methanotrophic biofilm: estimation of parameters and variability.

This article discusses the growth of methanotrophic biofilms. Several independent biofilm growths scenarios involving different inocula were examined. Biofilm growth, substrate removal and product formation were monitored throughout the experiments. Based on the oxygen consumption it was concluded that heterotrophs and nitrifiers co-existed with methanotrophs in the biofilm. Heterotrophic biomass grew on soluble polymers formed by the hydrolysis of dead biomass entrapped in the biofilm. Nitrifier populations developed because of the presence of ammonia in the mineral medium. Based on these experimental results, the computer program AQUASIM was used to develop a biological model involving methanotrophs, heterotrophs and nitrifiers. The modelling of six independent growth experiments showed that stoichiometric and kinetic parameters were within the same order of magnitude. Parameter estimation yielded an average maximum growth rate for methanotrophs, micron, of 1.5 +/- 0.5 d-1, at 20 degrees C, a decay rate, bm, of 0.24 +/- 0.1 d-1, a half saturation constant, KS(CH4), of 0.06 +/- 0.05 mg CH4/L, and a yield coefficient, YCH4, of 0.57 +/- 0.04 g X/g CH4. In addition, a sensitivity analysis was performed on this model. It indicated that the most influential parameters were those related to the biofilm (i.e. density; solid-volume fraction; thickness). This suggests that in order to improve the model, further research regarding the biofilm structure and composition is needed.

Biodegradation, Environmental↗

PubMed2005

A new method for estimating joint parameters from motion data.

Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.

Adult↗

PubMed2006

Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models.

The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a chi(2) test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator-prey type system.

Algorithms↗

PubMed2005

Pre-eclampsia and fetal growth restriction: how morphometrically different is the placenta?

Both pre-eclampsia (PET) and fetal growth restriction (FGR) pose a heavy burden on fetal and maternal health and may disrupt pregnancy outcome. Using design based stereological techniques, placental vascular and villous morphology were assessed to determine the individual role played by both PET and FGR on placental growth during the third trimester. The following placentas delivered between 25 and 41 weeks of gestation were included into the study; controls (n=16), PET (n=20), FGR (n=17) and PET-FGR (n=16). Each placenta was uniformly randomly sampled and the sampled tissue processed to paraffin. Sections were stained with a CD34 antibody and the following morphometric parameters estimated: volumes, surface areas, length, diameters and the shape factor of the villous (terminal and intermediate) and vascular placental features. For stereologically estimated parameters pure PET had an effect on IVS and terminal villi volume only. FGR alone or when coexisting with PET contributed towards significant reductions in volumetric and surface area terminal villous and vascular features. FGR factors also contributed towards a significant reduction in the lengths of all parameters estimated and in the terminal villi diameter. Additionally, FGR was associated with a significant difference in shape factor indices for both intermediate and terminal villi. This study has shown that PET on its own has limited influence on the placental morphology studied, since the vascular features estimated do not differ stereologically from age matched normal controls. However, placental morphology is different between PET and PET-FGR and between PET-FGR and FGR. PET and FGR may have a cumulative effect on placental villous and vascular morphology as seen in the PET-FGR but there is no synergistic effect. These morphological abnormalities may have major physiological implications in terms of placental function and fetal growth.

Adult↗

PubMed1991

A reduced sampling schedule for estimating the parameters of the glucose minimal model from a labeled IVGTT.

The minimal model of tracer glucose disappearance allows the measurement in man of important metabolic parameters from a labeled IVGTT (intravenous glucose tolerance test). Usually 30 blood samples are drawn to measure the insulin and the labelled glucose concentration time courses, which provide the data base for the model identification. In this paper, we address the problem of reducing the number of blood samples withdrawn without, however, deteriorating parameter estimation. By using a stepwise approach, largely based on optimal experiment design theory, we have derived a reliable reduced sampling schedule, which comprises only 14 total samples. The practical application of this reduced schedule has been validated by applying it in a new set of human experiments, completely independent of the ones used in the design phase.

Blood Glucose↗

PubMed2004

Estimation of parameters for a mathematical model of growth hormone secretion.

Here, we describe partial calibration of a parsimonious mathematical model of growth hormone (GH) secretion. From first principles, we derived a model of the effects on GH secretion from pituitary somatotrophs of stimulation by GH-releasing factor (GRF) or GH secretagogue, and of inhibition by somatostatin. We obtained a concise model by collapsing the many processes of the signal transduction cascade into a single step broadly reflecting the initial binding of GRF to its receptors. In the model, GH secretion is proportional to the rate of binding of GRF to activatable receptors. Desensitization occurs because of reduction of free receptors/available effector units, and resensitization occurs as those lost are replaced. This replacement is speeded up in the presence of somatostatin, which also inhibits GH secretion by reducing the constant of proportionality between the rate of GH secretion and the rate of GRF binding. We derived simple mathematical equations for the rate of GH secretion and cumulative secretion. Using these, we tested the model against data obtained from experiments performed in vitro, and made it quantitative using rigorous statistical approaches to optimize parameter estimates. The behaviour of the calibrated model matches experimental observations closely.

Algorithms↗

PubMed2000

[Rheologic properties of viscoelastic materials--identification of models and estimation of parameters].

The methodology of description and quantification of mechanical properties of visco-elastic materials is particularly important for drug production as well as for pharmaceutical applications. Of similar importance is this methodology for biomechanics and other biological disciplines, as many biological materials belong to the category of visco-elastic bodies. Methods derived from the theory of elastic bodies or hydrodynamics are not adequate for the quantification of mechanical properties of these materials. Application of more general rheological methods is necessary in these cases. In rheology, the so-called creep curves are most frequently used as a source of information on the mechanical behavior of visco-elastic materials. Further, for more exact analysis, rheological models are often derived from the creep curves. Classical methods of identification and parameter estimation of rheological models are not sufficiently general and do not derive all information involved in creep curves. A significant contribution is the application of the general theory of systems, theory of system identification, and mathematical methodology of Laplace transformation to this field. Practical application of these methods is often relatively simple. The paper presents the necessary theoretical background and a practical guide for utilization of this methodology.

Elasticity↗

PubMed1992

Estimation of parameters of allometric equations.

Accurate parameter estimation of allometric equations is a question of considerable interest. Various techniques that address this problem exist. In this paper it is assumed that the measured values are normally distributed and a maximum likelihood estimation approach is used. The computations involved in this procedure are reducible to relatively simple forms, and an efficient numerical algorithm is used. A listing of the computer program is included as an appendix.

Algorithms↗

PubMed2002

Linear phase correction models for synchronization: parameter identification and estimation of parameters.

Linear phase correction models for synchronized tapping and their stochastic properties are presented. In the most general form they include a central timer, a motor execution, and a phase correction mechanism that acts on the physical or the perceived asynchrony. A central issue of the article is how to identify and estimate the model parameters from the data. Monte Carlo simulations show serious problems of parameter interdependency.

Humans↗

PubMed2005

Evaluation of Bayesian estimation of pharmacokinetic parameters.

The validity of pharmacokinetic parameters estimated by the maximum a posteriori probability (MAP) Bayesian method was investigated by simulation studies. A 1-compartment model with bolus intravenous administration was used as a pharmacokinetic model, and the coefficients of variation for the parameters and residual error were set at 30% and 10%, respectively. The accuracy of the posterior modes of pharmacokinetic parameters estimated by the MAP Bayesian method was assessed by the difference between the true value and the estimated value. The results showed that the accuracy of the Bayesian estimation depended on sampling times and on the differences between the prior means and individual true parameter values. For assessing the reliability and accuracy of the Bayesian estimation, the authors suggest using the whole posterior distribution of the pharmacokinetic parameters to describe the 95th percentile range for predicted blood concentration profiles. The authors believe that the proposed procedures provide helpful information for evaluating the Bayesian estimation of pharmacokinetic profiles.

Bayes Theorem↗

PubMed1984

Problems and pitfalls in estimating average pharmacokinetic parameters.

The problems of obtaining optimal average parameter estimates (APE) from experimental pharmacokinetic data are considered. Four different approaches, three parametric and one non-parametric tests, are compared, using selected individual alcohol concentration data. Pooling the raw data for estimating APE can obscure individual pharmacokinetic characteristics, whereas averaging individual parameter estimates (IPE) exposes unique statistical problems. Furthermore, careful consideration should be given to weighting procedures. The advantages and shortcomings of all four methods are discussed. It is concluded that none can be considered as a universally applicable statistical method in view of the purpose for which the information, derived from a set of data, e.g. an alcohol-kinetic study, is required.

Computers↗

PubMed2003

A new approach of fitting biomass dynamics models to data.

A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The data assimilation method provides a novel and computationally efficient procedure for combining all available information, i.e., the data and the model in the analysis of a resource system. This technique will be used to analyze data for the North-east Arctic cod stock. Two alternative population growth models: the logistic and the Gompertz model are used for estimating parameters of simple bioeconomic models by the method of constrained least squares. Estimates of the parameters of the models dynamics are reasonable and can be accepted. The main inference from the work is that the average fishing mortality is found to be significantly above the maximum sustainable yield value.

Animals↗

PubMed1988

The ascertainment sampling problem and estimation of genetic parameters when parental haplotypes are known.

Comparisons of bias and standard errors of genetic parameter estimates arising from various estimation procedures are made by using contrived genetic data in which parental haplotypes are known in addition to the haplotypes of affected sibs. These comparisons show that knowledge of parental haplotypes can reduce standard errors of genetic parameter estimates by between 10% and 45% as compared to estimates when parental information is not available. The added information does not appear to change the standard errors of ascertainment-assumption-free estimates relative to those from classical methods. This implies that the decision to accept possible bias arising from a classical estimation method or to accept slightly increased standard errors under an ascertainment-assumption-free approach is comparable to that involved when parental haplotypes are unknown.

Biometry↗

PubMedDate not supplied

KINFIT: a non linear least-squares computer program for the estimation of pharmacokinetic parameters after intravenous administration.

KINFIT is a nonlinear least-squares computer program designed to allow pharmacokinetic modeling of experimental data and to obtain pertinent parameter estimates based on the derived values. It is written in Visual BASIC for the Microsoft Windows graphical environment. Drug concentrations in blood, plasma, or serum with time following intravenous administration are input and a linear or semi-logarithmic plot of the data appears on the display. On command, polyexponential coefficients and exponents are computed and a non linear curve is fitted through the data set. Results from statistical tests are printed to determine goodness of fit. Commonly calculated pharmacokinetic parameters are also calculated and appear on the output. The execution of KINFIT is demonstrated for time courses of ampicillin in man. KINFIT was compared with the widely available ESTRIP and RSTRIP computer programs and gave parameter estimates that were very similar, although not identical.

Ampicillin↗

PubMed1988

A minimal model of liver glycogen metabolism; feasibility for predicting flux rates.

A minimal model of glycogen metabolism can allow the estimation of the flux rates in the glycogen pathway from the time course of the intermediates in the pathway, measured during substrate administration and hormonal stimulation. The comprehensive model of El-Refai & Bergman (Am. J. Physiol. 231, 1608, 1976) consisting of six compartments and 26 non-estimable parameters has successfully accounted for the responses of hepatic glycogenic intermediates in response to a glucose load in hepatocytes (Katz et al., J. biol. Chem. 253, 4530, 1978), in perfused liver (Nordlie et al., J. biol. Chem. 255, 1834, 1980) and during refeeding in vivo (Van DeWerve & Jeanrenaud, Am. J. Physiol. 247, E271, 1984). The comprehensive model is here reduced to a minimal model, consisting of five compartments representing extracellular and intracellular glucose, glucose-phosphate, uridine diphosphate glucose (UDPG), glycogen, and five parameters estimated from the hepatic response to a given stimulus. Estimation of these parameters requires the measurement of the net hepatic glucose balance, the net gluconeogenic flux, and the time course of glycogenic intermediates responding to a hormone or substrate stimulus. The hepatic glycogenolytic response predicted by the comprehensive model in response to an increase in glucagon is closely fitted by the minimal model. When Gaussian distributed random error was added, 0-5% SD in the glucose and glycogen compartments and 0-10% SD in the glucose-phosphate and UDPG compartments, the hepatic response predicted by the minimal model was virtually free of the added error, and the model parameters were found to be within 30% of their true values. When the minimal model was used to interpret the experimental response to an increase in glucose concentration it predicted that: (1) glucokinase can phosphorylate glucose at rates similar to maximal rates of net glycogen synthesis; (2) futile cycling at the glycogen/glucose-1-phosphate level can limit glycogen synthesis; and (3) glucose-6-phosphatase inhibition by glucose has a significant role in net glycogen synthesis.

Animals↗