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At least 217 records · Page 12Linked to original sources
PubMed2006

Area-selective signal parameter estimation for two-dimensional MR spectroscopy data.

We consider the problem of parametric spectral analysis of two-dimensional (2D) magnetic resonance spectroscopy (MRS) data. Estimating the signal components from 2D MRS data is becoming common practice in many clinical MR applications. The most frequently used signal processing tool for this estimation problem is the non-parametric 2D-FFT. There are several alternative parametric methods available to perform this analysis, yet their computational complexity is generally rather high and it becomes prohibitive when the number of points in the measured data matrix is large. In this paper, we propose a novel signal parameter estimation technique which operates on a pre-specified sub-area of the 2D spectrum. This area-selective approach can be used either to estimate only the signal components of main interest in the data, or to compute signal parameter estimates of all present signal components as the computational burden for each sub-area is low. In the numerical example section we consider both simulated data and in vitro 1H data acquired from a 1.5 T MR scanner.

Algorithms↗
PubMedDate not supplied

Parameter estimation in cardiac ionic models.

We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler-Reuter (1977) ionic equations for the ventricular action potential. The estimation problem can be regarded as equivalent to the accurate reconstruction of ionic current kinetics and amplitudes in an excitable cell model, given only action potential experimental data. We show that in the Beeler-Reuter case, all ionic currents may be reasonably reconstructed using an experimental design consisting of action potential recordings perturbed by pseudo-random injection currents. The Beeler-Reuter model was parameterised into 63 parameters completely defining all membrane current amplitudes and kinetics. Total membrane current was fitted to model-generated experimental data using a 'data-clamp' protocol. The experimental data consisted of a default action-potential waveform and an optional series of perturbed waveforms generated by current injections. Local parameter identifiability was ascertained from the reciprocal condition value (1/lambda) of the Hessian at the known solution. When fitting to a single action potential waveform, the model was found to be over-determined, having a 1/lambda value of approximately 3.6e-14. This value improved slightly to approximately 1.4e-10 when an additional 2 perturbed waveforms were included in the fitting process, suggesting that the additional data did not overly improve the identifiability problem. The additional data, however, did allow the accurate reconstruction of all ionic currents. This indicates that by appropriate experimental design, it may be possible to infer the properties of underlying membrane currents from observation of transmembrane potential waveforms perturbed by pseudo-random currents.

Action Potentials↗
PubMed1991

Identification of compartmental models for perturbed cell populations using state-space parameter estimation techniques.

Multiple compartment models for describing synchronous cell kinetics in which cell populations are characterized by DNA content are reviewed. These models are useful for understanding and predicting a cell population's dynamic response to perturbations induced by drugs or radiation. A practical approach is proposed for determining the parameters of these models from empirical cell-cycle data. Specifically, a state-space parameter estimation algorithm based on the maximum likelihood method--developed and coded primarily for engineering applications and commercially available for personal computers and minicomputers--can be applied to DNA specific cell-cycle measurements from synchronized cell populations to produce model parameter estimates. This is demonstrated using published data from a cell-cycle experiment. The results show that the procedure works well, and that with careful experimental planning even better results should be possible. Since the compartmental model is often used to represent biological systems, this approach is widely applicable.

Algorithms↗
PubMed2001

Parameter estimation for suspended sediment transport processes under random waves.

This paper presents a parameter estimation method for suspended sediment transport processes subject to random wave environments. An objective function was constructed based on measurements of suspended sediment concentration profiles and the governing equation of sediment transport. The Chebyshev least square method was employed to approximate the process parameters, i.e. vertical eddy diffusivity (epsilon) and net vertical velocity (w). The objective function of sediment transport processes with Chebyshev's parameters is well posed and does not require boundary conditions. First, second, and third order epsilon and w Chebyshev orthogonal functions were determined for monochromatic (MONO), narrow-banded (NBR) and broad-banded (BBR) random wave conditions. In the BBR and NBR conditions, the best fit Chebyshev approximations of epsilon and w were 2nd degree, while the best approximations in the MONO condition were 2nd degree for epsilon and 1st degree for w. The Chebyshev method provides a quick, accurate and direct estimation of two prime parameters in sediment transport dynamics.

Journal Article↗
PubMed2005

Parameter estimation in modulated, unbranched reaction chains within biochemical systems.

Modern biology is increasingly developing techniques for measuring time series of global gene expression and of many simultaneous proteins or metabolites. These data contain valuable information on the dynamics of cells, which has to be extracted with computational means. Given a suitable mathematical model, this extraction is in principle a straightforward regression task, but the complexity and nonlinearity of the differential equations that describe biological systems cause severe difficulties when the systems are of realistic size. We propose a method of stepwise regression that can be applied effectively to linear portions of pathways. The method may be combined with other estimation methods and either directly yields reasonable parameter estimates or at least provides appropriate start values for subsequent nonlinear search algorithms. We illustrate the method with the analysis of in vivo NMR data describing the dynamics of glycolytic metabolites in Lactococcus lactis.

Algorithms↗
PubMedDate not supplied

Improving a regional model using reduced complexity and parameter estimation.

The availability of powerful desktop computers and graphical user interfaces for ground water flow models makes possible the construction of ever more complex models. A proposed copper-zinc sulfide mine in northern Wisconsin offers a unique case in which the same hydrologic system has been modeled using a variety of techniques covering a wide range of sophistication and complexity. Early in the permitting process, simple numerical models were used to evaluate the necessary amount of water to be pumped from the mine, reductions in streamflow, and the drawdowns in the regional aquifer. More complex models have subsequently been used in an attempt to refine the predictions. Even after so much modeling effort, questions regarding the accuracy and reliability of the predictions remain. We have performed a new analysis of the proposed mine using the two-dimensional analytic element code GFLOW coupled with the nonlinear parameter estimation code UCODE. The new model is parsimonious, containing fewer than 10 parameters, and covers a region several times larger in areal extent than any of the previous models. The model demonstrates the suitability of analytic element codes for use with parameter estimation codes. The simplified model results are similar to the more complex models; predicted mine inflows and UCODE-derived 95% confidence intervals are consistent with the previous predictions. More important, the large areal extent of the model allowed us to examine hydrological features not included in the previous models, resulting in new insights about the effects that far-field boundary conditions can have on near-field model calibration and parameterization. In this case, the addition of surface water runoff into a lake in the headwaters of a stream while holding recharge constant moved a regional ground watershed divide and resulted in some of the added water being captured by the adjoining basin. Finally, a simple analytical solution was used to clarify the GFLOW model's prediction that, for a model that is properly calibrated for heads, regional drawdowns are relatively unaffected by the choice of aquifer properties, but that mine inflows are strongly affected. Paradoxically, by reducing model complexity, we have increased the understanding gained from the modeling effort.

Microcomputers↗
PubMed2005

Ultrasonic data compression via parameter estimation.

Ultrasonic imaging in medical and industrial applications often requires a large amount of data collection. Consequently, it is desirable to use data compression techniques to reduce data and to facilitate the analysis and remote access of ultrasonic information. The precise data representation is paramount to the accurate analysis of the shape, size, and orientation of ultrasonic reflectors, as well as to the determination of the properties of the propagation path. In this study, a successive parameter estimation algorithm based on a modified version of the continuous wavelet transform (CWT) to compress and denoise ultrasonic signals is presented. It has been shown analytically that the CWT (i.e., time x frequency representation) yields an exact solution for the time-of-arrival and a biased solution for the center frequency. Consequently, a modified CWT (MCWT) based on the Gabor-Helstrom transform is introduced as a means to exactly estimate both time-of-arrival and center frequency of ultrasonic echoes. Furthermore, the MCWT also has been used to generate a phase x bandwidth representation of the ultrasonic echo. This representation allows the exact estimation of the phase and the bandwidth. The performance of this algorithm for data compression and signal analysis is studied using simulated and experimental ultrasonic signals. The successive parameter estimation algorithm achieves a data compression ratio of (1-5N/J), where J is the number of samples and N is the number of echoes in the signal. For a signal with 10 echoes and 2048 samples, a compression ratio of 96% is achieved with a signal-to-noise ratio (SNR) improvement above 20 dB. Furthermore, this algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements ranging from 10 to 60 dB for composite signals having SNR as low as -10 dB.

Algorithms↗
PubMed2006

Registration of MR prostate images with biomechanical modeling and nonlinear parameter estimation.

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) have been shown to be very useful for identifying prostate cancers. For high sensitivity, the MRI/MRSI examination is often acquired with an endorectal probe that may cause a substantial deformation of the prostate and surrounding soft tissues. Such a probe is removed prior to radiation therapy treatment. To register diagnostic probe-in magnetic resonance (MR) images to therapeutic probe-out MR images for treatment planning, a new deformable image registration method is developed based on biomechanical modeling of soft tissues and estimation of uncertain tissue parameters using nonlinear optimization. Given two-dimensional (2-D) segmented probe-in and probe-out images, a finite element method (FEM) is used to estimate the deformation of the prostate and surrounding tissues due to displacements and forces resulting from the endorectal probe. Since FEM requires tissue stiffness properties and external force values as input, the method estimates uncertain parameters using nonlinear local optimization. The registration method is evaluated using images from five balloon and five rigid endorectal probe patient cases. It requires on average 37 s of computation time on a 1.6 GHz Pentium-M PC. Comparing the prostate outline in deformed probe-out images to corresponding probe-in images, the method obtains a mean Dice Similarity Coefficient (DSC) of 97.5% for the balloon probe cases and 98.1% for the rigid probe cases. The method improves significantly over previous methods (P < 0.05) with greater improvement for balloon probe cases with larger tissue deformations.

Algorithms↗
PubMed2001

A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry.

A linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) identification algorithm is developed for modeling time series data. The new algorithm is based on the concepts of affine geometry in which the salient feature of the algorithm is to remove the linearly dependent ARMA vectors from the pool of candidate ARMA vectors. For noiseless time series data with a priori incorrect model-order selection, computer simulations show that accurate linear and nonlinear ARMA model parameters can be obtained with the new algorithm. Many algorithms, including the fast orthogonal search (FOS) algorithm, are not able to obtain correct parameter estimates in every case, even with noiseless time series data, because their model-order search criteria are suboptimal. For data contaminated with noise, computer simulations show that the new algorithm performs better than the FOS algorithm for MA processes, and similarly to the FOS algorithm for ARMA processes. However, the computational time to obtain the parameter estimates with the new algorithm is faster than with FOS. Application of the new algorithm to experimentally obtained renal blood flow and pressure data show that the new algorithm is reliable in obtaining physiologically understandable transfer function relations between blood pressure and flow signals.

Algorithms↗
PubMed2006

Evaluation of isotopic enrichment factors for the biodegradation of chlorinated ethenes using a parameter estimation model: toward an improved quantification of biodegradation.

A model was developed to predict the concentrations of chlorinated ethenes and ethene during sequential reductive dechlorination of tetrachloroethene (PCE) from stable carbon isotope values using Rayleigh model principles and specified isotopic enrichment factors for each step of dechlorination. The model was tested using three separate datasets of concentration and isotope values measured during three experiments involving the degradation of PCE to vinyl chloride (VC), trichloroethene (TCE) to ethene, and cis-1,2-dichloroethene (cDCE) to ethene. The model was then coupled to a parameter estimation method to estimate values for the isotopic enrichment factors of TCE, cDCE, and VC when they are intermediates in the dechlorination to ethene. The enrichment factors estimated for TCE and cDCE when they were intermediates in biodegradation experiments were close to or within the published range of enrichment factors determined from experiments where TCE or cDCE were the initial substrates. In contrast, the enrichment factors determined by parameter estimation for experiments in which VC was an intermediate in biodegradation experiments were consistently more negative (by approximately 10 per thousandth) than the most negative published enrichment factor determined from experiments where VC was the initial substrate. This finding suggests that the range of enrichment factors for VC dechlorination may not be as narrow as previously suggested (-21.5 per thousandth to -26.6 per thousandth) and that fractionation during VC dechlorination when VC is an intermediate compound may be significantly larger than when VC is the initial substrate. These findings have important implications both for the current practice of extrapolating laboratory-derived isotopic enrichment factors to quantify biodegradation of chlorinated ethenes in the field and for understanding the details of enzymatic reductive dechlorination.

Biodegradation, Environmental↗
PubMedDate not supplied

Parameter estimation in distributed models of blood-tissue exchange: a Monte Carlo strategy to assess precision.

Distributed parameter models of blood-tissue exchange are increasingly used to interpret multiple tracer dilution data in regional kinetic studies. To derive a measure of the precision with which the model parameters are estimated is therefore of paramount importance. The standard approach to deriving precision of estimates does not take into account the fact that some of the model parameters are fixed. Thus, the precision of parameter estimates is not realistic and, in all likelihood, it is overestimated. The aim of this study is to describe a Monte Carlo method devised to obtain a theoretically sound measure of the precision of estimates, which takes into account both measurement error and the uncertainty associated with the fixed parameters. The fixed parameter values are taken from a probability distribution. By letting the fixed parameters vary according to their distribution, a large number of synthetic datasets is generated. Noise is then added. Estimating the parameters in each of these synthetic datasets allows the derivation of a Monte Carlo mean and standard deviation, which provides a realistic measure of precision. The methodology is illustrated for a simulated data case study dealing with the estimation of the capillary permeability-surface area product in a two tracer experiment.

Animals↗
PubMed2004

Use of an anaerobic sequencing batch reactor for parameter estimation in modelling of anaerobic digestion.

The model structure in anaerobic digestion has been clarified following publication of the IWA Anaerobic Digestion Model No. 1 (ADM1). However, parameter values are not well known, and uncertainty and variability in the parameter values given is almost unknown. Additionally, platforms for identification of parameters, namely continuous-flow laboratory digesters, and batch tests suffer from disadvantages such as long run times, and difficulty in defining initial conditions, respectively. Anaerobic sequencing batch reactors (ASBRs) are sequenced into fill-react-settle-decant phases, and offer promising possibilities for estimation of parameters, as they are by nature, dynamic in behaviour, and allow repeatable behaviour to establish initial conditions, and evaluate parameters. In this study, we estimated parameters describing winery wastewater (most COD as ethanol) degradation using data from sequencing operation, and validated these parameters using unsequenced pulses of ethanol and acetate. The model used was the ADM1, with an extension for ethanol degradation. Parameter confidence spaces were found by non-linear, correlated analysis of the two main Monod parameters; maximum uptake rate (k(m)), and half saturation concentration (K(S)). These parameters could be estimated together using only the measured acetate concentration (20 points per cycle). From interpolating the single cycle acetate data to multiple cycles, we estimate that a practical "optimal" identifiability could be achieved after two cycles for the acetate parameters, and three cycles for the ethanol parameters. The parameters found performed well in the short term, and represented the pulses of acetate and ethanol (within 4 days of the winery-fed cycles) very well. The main discrepancy was poor prediction of pH dynamics, which could be due to an unidentified buffer with an overall influence the same as a weak base (possibly CaCO3). Based on this work, ASBR systems are effective for parameter estimation, especially for comparative wastewater characterisation. The main disadvantages are heavy computational requirements for multiple cycles, and difficulty in establishing the correct biomass concentration in the reactor, though the last is also a disadvantage for continuous fixed film reactors, and especially, batch tests.

Acetates↗
PubMed1995

Analytic solution of the Variable-Volume Double-Pool urea kinetics model applied to parameter estimation in hemodialysis.

An analytic solution of the Variable-Volume Double-Pool urea kinetics model and its application to the estimation of clinically relevant parameters of the patient-machine system, are presented. These include the urea distribution volume and generation rate and the mean dialyzer clearance. The estimation of these parameters is based on the assumption of constant values for the diffusion coefficient between the two pools and the intra-extracellular volume ratio. Results obtained by computer simulations show that the effect of a +/- 50% variation of these parameters influences the estimates less than standard measurement errors. Starting from these results, four methods to in vivo estimate the urea distribution volume and generation rate from blood samples are compared. Two methods are based on the analytic solution of the double-pool model using seven samples (reference method) or three samples (new clinical method). The remaining methods are based on urea mass-balance and are largely used in the clinical practice. These last techniques differ from each other for the blood sample taken at the end of the treatment or 30 min later. The results obtained from hemofiltration sessions show that the urea generation rate is accurately estimated by all methods. The total distribution volume is still accurately estimated by the new clinical method while it is systematically underestimated by the urea mass-balance when the blood sample at the end of dialysis is used. Instead, a high overcompensation results using the blood sample taken 30 min after the end of dialysis. Finally, the new clinical method also provides reliable estimates for the dialyzer clearance starting from only three blood samples all taken during dialysis.

Algorithms↗
PubMed1993

Pharmacokinetic model identification and parameter estimation as an ill-posed problem.

For 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 lambda i and associated coefficients Ci. Least-square fitting procedures are used to estimate the coefficients Ci and the corresponding discrete locations lambda i on the lambda-axes. This work presents an alternative approach. It does not assume that the non-zero coefficients are located at sharply defined values of lambda, but that they are represented by a continuous function h(lambda), 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". Regularization methods have been developed in recent years as suitable tools for the treatment of such ill-posed problems. Application of Tikhonov regularization 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(lambda). The method used is described and the results are compared with those of conventional compartment analysis.

Humans↗
PubMed2002

Genetic parameter estimation for milk yield over multiple parities and various lengths of lactation in Danish Jerseys by random regression models.

The objectives of this study were to test for heterogeneity of genetic and environmental variance among completed and extended records from different lactations or different days in milk (DIM) and to build a model that accounts for this heterogeneity. A total of 147,457 305-d milk yield records from Danish Jersey cows calving between 1984 and early 1999 from two regions of Denmark were used in this study. Results showed that DIM and parity influenced parameters estimated from an animal model with repeated records. Therefore, the data were analyzed using random-regression models that allow the covariance between measurements to change gradually with DIM and parity. Random regressions were fitted for additive genetic effects and permanent environmental effects using second- or third-order normalized Legendre polynomials for DIM and parity. Variances of random-regression coefficients associated with all orders of the polynomials were significant. Based on these parameter estimates, a covariance function (CF) was defined. The CF showed that the heritability decreases over parities, but within each parity heritability increases with DIM, whereas variance of permanent environmental effects increases over parities and decreases with DIM. Generally, genetic correlations were higher between records with similar DIM and parity. The results indicate that there are problems with the extension procedure used to predict 305-d milk yields. Using the covariance functions estimated in this study, breeding values could be predicted that take into account the covariance structure between records from different parities and different DIM.

Analysis of Variance↗
PubMedDate not supplied

Cell population modeling and parameter estimation for continuous cultures of Saccharomyces cerevisiae.

Saccharomyces cerevisiae is known to exhibit sustained oscillations in chemostats operated under aerobic and glucose-limited growth conditions. The oscillations are reflected both in intracellular and extracellular measurements. Our recent work has shown that unstructured cell population balance models are capable of generating sustained oscillations over an experimentally meaningful range of dilution rates. A disadvantage of such unstructured models is that they lack variables that can be compared directly to easily measured extracellular variables. Thus far, most of our work in model development has been aimed at achieving qualitative agreement with experimental data. In this paper, a segregated model with a simple structured description of the extracellular environment is developed and evaluated. The model accounts for the three most important metabolic pathways involved in cell growth with glucose substrate. As compared to completely unstructured models, the major advantage of the proposed model is that predictions of extracellular variables can be compared directly to experimental data. Consequently, the model structure is well suited for the application of estimation techniques aimed at determining unknown model parameters from available extracellular measurements. A steady-state parameter selection method developed in our group is extended to oscillatory dynamics to determine the parameters that can be estimated most reliably. The chosen parameters are estimated by solving a nonlinear programming problem formulated to minimize the difference between predictions and measurements of the extracellular variables. The efficiency of the parameter estimation scheme is demonstrated using simulated and experimental data.

Cell Count↗
PubMed2002

Strategies to improve neuroreceptor parameter estimation by linear regression analysis.

In an attempt to improve neuroreceptor distribution volume (V) estimates, the authors evaluated three alternative linear methods to Logan graphical analysis (GA): GA using total least squares (TLS), and two multilinear analyses, MA1 and MA2, based on mathematical rearrangement of GA equation and two-tissue compartments, respectively, using simulated and actual PET data of two receptor tracers, [(18)F]FCWAY and [(11)C]MDL 100,907. For simulations, all three methods decreased the noise-induced GA bias (up to 30%) at the expense of increased variability. The bias reduction was most pronounced for MA1, moderate to large for MA2, and modest to moderate for TLS. In addition, GA, TLS, and MA1, methods that used only a portion of the data (T > t*, chosen by an automatic process), showed a small underestimation for [(11)C]MDL 100,907 with its slow kinetics, due to selection of t* before the true point of linearity. These noniterative methods are computationally simple, allowing efficient pixelwise parameter estimation. For tracers with kinetics that permit t* to be accurately identified within the study duration, MA1 appears to be the best. For tracers with slow kinetics and low to moderate noise, however, MA2 may provide the lowest bias while maintaining computational ease for pixelwise parameter estimation.

Basal Ganglia↗