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PubMed1988

[Parametric identification of mathematical models of population genetics taking into account the geographical dispersion in finite samples].

A method for parameter identification of population genetics' mathematical models, taking account of geographical disperse at limited samples of experimental data on mutant frequency values has been developed. The existence of the MLS (method of the least squares) estimations of the models' parameters studied has been proved, zero approach of the looked for estimations found and the iterative procedure of making them precise shown. A means of building up the a posteriori function of probability density of the zero and following approximations of the models' parameters is pointed out. The possibility of application of the proposed method to find estimations of mathematical models' parameters of population genetics, taking account of geographical disperse, has been shown on the particular example.

Animals↗

PubMedDate not supplied

Coupling basin- and site-scale inverse models of the Española aquifer.

Large-scale models are frequently used to estimate fluxes to small-scale models. The uncertainty associated with these flux estimates, however, is rarely addressed. We present a case study from the Española Basin, northern New Mexico, where we use a basin-scale model coupled with a high-resolution, nested site-scale model. Both models are three-dimensional and are analyzed by codes FEHM and PEST. Using constrained nonlinear optimization, we examine the effect of parameter uncertainty in the basin-scale model on the nonlinear confidence limits of predicted fluxes to the site-scale model. We find that some of the fluxes are very well constrained, while for others there is fairly large uncertainty. Site-scale transport simulation results, however, are relatively insensitive to the estimated uncertainty in the fluxes. We also compare parameter estimates obtained by the basin- and site-scale inverse models. Differences in the model grid resolution (scale of parameter estimation) result in differing delineation of hydrostratigraphic units, so the two models produce different estimates for some units. The effect is similar to the observed scale effect in medium properties owing to differences in tested volume. More important, estimation uncertainty of model parameters is quite different at the two scales. Overall, the basin inverse model resulted in significantly lower estimates of uncertainty, because of the larger calibration dataset available. This suggests that the basin-scale model contributes not only important boundary condition information but also improved parameter identification for some units. Our results demonstrate that caution is warranted when applying parameter estimates inferred from a large-scale model to small-scale simulations, and vice versa.

Calibration↗

PubMed1989

Parameter space boundaries for unidentifiable compartmental models.

Methods for dealing with unidentifiable compartmental models are first reviewed, emphasizing the parameter interval analysis and exhaustive modeling approaches. More general methods are presented for generating the set of all nonnegative parameter solutions that localize the parameters within bounded regions of parameter space and extend previously published parameter bounding strategies. Each point of these regions is an equivalent solution of the parameter identification problem. If a point on the boundary is selected, at least one of the parameters vanishes and an equivalent submodel is obtained. This property shows the close relationship between the exhaustive modeling and parameter interval analysis approaches.

Mathematics↗

PubMed2005

Kinetic modeling of lipase catalyzed hydrolysis of (R/S)-1-methoxy-2-propyl-acetate as a model reaction for production of chiral secondary alcohols.

The Candida antarctica lipase B catalyzed kinetic resolution of (R/S)-1-methoxy-2-propyl-acetate was studied as a model system for the biocatalytic production of chiral secondary alcohols. For this purpose, a kinetic model is proposed involving both enantiomers of this reaction using model discrimination and parameter identification. Starting from a ping-pong bi-bi mechanism, a simplified model with sensitive parameters was derived for the R- and S-enantiomer, respectively. It was validated at pH 7.0, using time-course measurements at varying temperatures (30-60 degrees C) and initial substrate conditions (0.05-1.5 M). This model was then used for mechanistic interpretation of the kinetic resolution on a biochemical level. The effect of temperature on kinetic parameters and enantiomeric ratio was investigated and compared to findings from the field of molecular modeling to obtain a better understanding of the reaction system for process design. Values of 21.2 and 9.7 kJmol-1 were determined for the enthalpic (DeltaR-S DeltaH ++ degrees) and the entropic (-T x DeltaR-S DeltaS ++ degrees) contribution of the difference in transition state energy of both enantiomers at 30 degrees C. High enantiomeric ratio's (E of 47-110) especially at lower temperatures, in addition to enzyme activity at a wide pH range, indicate this biotransformation is a promising example for the industrial production of chiral secondary alcohols.

Fungal Proteins↗

PubMed2003

Continuous-time identification of gene expression models.

One objective of systems biology is to create predictive, quantitative models of the transcriptional regulation networks that govern numerous cellular processes. Gene expression measurements, as provided by microarrays, are commonly used in studies that attempt to infer the regulation underlying these processes. At present, most gene expression models that have been derived from microarray data are based in discrete-time, which have limited applicability to common biological data sets, and may impede the integration of gene expression models with other models of biological processes that are formulated as ordinary differential equations (ODEs). To overcome these difficulties, a continuous-time approach for process identification to identify gene expression models based in ODEs was developed. The approach utilizes the modulating functions method of parameter identification. The method was applied to three simulated systems: (1) a linear gene expression model, (2) an autoregulatory gene expression model, and (3) simulated microarray data from a nonlinear transcriptional network. In general, the approach was well suited for identifying models of gene expression dynamics, capable of accurately identifying parameters for small numbers of data samples in the presence of modest experimental noise. Additionally, numerous insights about gene expression modeling were revealed by the case studies.

Data Interpretation, Statistical↗

PubMed2006

Fast gradient elution reversed-phase liquid chromatography with diode-array detection as a high-throughput screening method for drugs of abuse. II. Data analysis.

In Part I of this work, we developed a method for the detection of drugs of abuse in biological samples based on fast gradient elution liquid-chromatography coupled with diode array spectroscopic detection (LC-DAD). In this part of the work, we apply the chemometric method of target factor analysis (TFA) to the chromatograms. This algorithm identifies the target compounds present in chromatograms based on a spectral library, resolves nearly co-eluting components, and differentiates between drugs with similar spectra. The ability to resolve highly overlapped peaks using the spectral data afforded by the DAD is what distinguishes the present method from conventional library searching methods. Our library has a mean list length (MLL) of 1.255 and a discriminating power of 0.997 when both retention index and spectral factors are considered. The algorithm compares a library of 47 different compounds of toxicological relevance to unknown samples and identifies which compounds are present based on spectral and retention index matching. The application of a corrected retention index for identification rather than raw retention times compensates for long-term and column-to-column retention time shifts and allows for the use of a single library of spectral and retention data. Training data sets were used to establish the search and identification parameters of the method. A validation data set of 70 chromatograms was used to calculate the sensitivity (correct identification of positives) and specificity (correct identification of negatives) of the method, which were found to be 92% and 94%, respectively.

Algorithms↗

PubMed2004

Experimental on-line identification of an electromechanical system.

Identification of electromechanical systems operating in open-loop or closed-loop conditions has long been of prime interest in industrial applications. This paper presents experimental on-line identification of an electromechanical system represented by a digital input/output model. The paper also bridges the theory and practice gap for applied researchers. Studies are carried out by formulating the mathematical model using differential equations and experimental discrete-time identification using on-line plant input-output data. A recursive least-squares method is used to estimate the unknown parameters of the system. Discrete-time data for the parameter identification are obtained experimentally from a setup constructed in the laboratory. A root-mean-square error criterion is used for model validation. Results are presented which show variations in parameters of the electromechanical system. It is demonstrated that identified model output and actual system output match. All tests are performed with no previous results from finite element simulations.

Journal Article↗

PubMed1980

Measurement of cerebral blood flow in the pig by the Xe-133 clearance technique. Failure of the two-compartmental clearance model.

The Xe-133 clearance technique is used to measure cerebral blood flow in the pig, which often serves as an experimental animal for cardiovascular research. The clearance curves are fitted by a two-exponential model. However, the fitted parameters are incompatible with a two-compartmental model: the values found for the parameters depend on the length of the clearance curve analysed. The discrepancies are thought to be consequences of the heterogeneity of cerebral blood flow and of mathematical problems of parameter identification. The non-validity of the relative weight of the fast clearance component as an anatomical or functional parameter is demonstrated. The use of the mean time constant, mean transit time, mean decay constant and initial slope for determination of cerebral blood flow rates is discussed. The mean cerebral blood flow of the anaesthetized pig measured by the clearance technique is found to be lower than the blood flow measured by means of a flow probe around the common carotid artery (with the external carotid artery tied off). The existence of a significant arteriovenous shunt flow is postulated.

Animals↗

PubMed1980

Dynamics of ventilation, heart rate, and gas exchange: sinusoidal and impulse work loads in man.

Dynamic characteristics of ventilation, heart rate, and gas exchange in response to sinusoidally varying work loads were analyzed in four male subjects, exercising in the upright position on a bicycle ergometer. Mean work-load and sinusoidal amplitude were about 1.5 and 0.9 W/kg, fat-free mass), respectively. Seven different frequencies were used, the periods ranging from 12 to 0.75 min. To further investigate the linearity of the variables under study, 10-s impulse loads were also applied to three of the four subjects. Harmonic analysis of the sine-wave data and comparison of the sine-wave fundamental responses with the impulse frequency responses showed that only O2 uptake behaves in a linear fashion. Ventilation and CO2 production showed quasi- to nonlinear behaviors, whereas the responses of heart rate and alveolar partial pressures were clearly dependent on the type of forcing used. By means of mathematical parameter identification techniques, it was found that the individual frequency responses of O2 uptake could be almost completely described by a four-parameter transfer function with parameter values showing second-order underdamped to critically damped dynamics.

Heart Rate↗

PubMed2003

[Use of national French health insurance register to identify the current address of a cohort].

BACKGROUND: The aim of the study was to assess the efficiency of the Registre National Inter-régimes des bénéficaires de l'Assurance-Maladie (RNIAM), which is the French register of health insurance, in order to identify the present address of subjects who have lived in the Beaumont-Hague county, France, between 1978 and 1998, when they were less than 25 years old. METHODS: A cohort of 4,118 persons was defined by consulting school and civil status registers from three villages. We drew at random 824 subjects and between October 2000 and August 2001, we asked the RNIAM to locate them. For each subject, the usual identification parameters (first name, last name, birth date and eventually birth place) were provided. In case of a doubt concerning these parameters, a second request was undertaken with a slight modification. RESULTS: Altogether, 94.5% of the included people were identified by the RNIAM. Identification was better for people born in France than for those born abroad (97% versus 52%) and 84.5% of people were linked to a health insurance regimen. The RNIAM was able to identify a correct address for 68.7% of the subjects. CONCLUSION: The RNIAM seems promising for further epidemiological investigations. Nonetheless, it still remains insufficient by itself to identify addresses. Other means (tax records) should be evaluated and associated with the register data.

Adolescent↗

PubMed2003

A method for assessing the statistical significance of mass spectrometry-based protein identifications using general scoring schemes.

This paper investigates the use of survival functions and expectation values to evaluate the results of protein identification experiments. These functions are standard statistical measures that can be used to reduce various protein identification scoring schemes to a common, easily interpretably representation. The relative merits of scoring systems were explored using this approach, as well as the effects of altering primary identification parameters. We would advocate the widespread use of these simple statistical measures to simplify and standardize the reporting of the confidence of protein identification results, allowing the users of different identification algorithms to compare their results in a straightforward and statistically significant manner. A method is described for measuring these distributions using information that is being discarded by most protein identification search engines, resulting in accurate survival functions that are specific to any combination of scoring algorithms, sequence databases, and mass spectra.

Mass Spectrometry↗

PubMed2003

Dynamical modelling of a waste stabilisation pond.

This paper is concerned with the dynamical modelling and the parameter identification of a waste stabilisation pond. First, a dynamical model of the pond is proposed, based on mass balances in the first basin. It involves a reaction network involving eight (bio)chemical reactions, and in particular the (chemical or biochemical) oxidation of H(2)S. The height of the pond is divided into two layers: the upper layer (approximate depth: 0.8 m), and the lower layer (about 0.2 m). Three microorganism populations are considered: microalgae and aerobic bacteria (in the upper layer), and sulphate-reducing anaerobic bacteria (in the lower layer). The Droop model is introduced to emphasise the potential activity of microalgae when daylight has disappeared (sunset). The transport of organic matter between the two layers is also considered in the model. The derivation is based on collected data and intensive follow-up of a specific pond at the village of Rethondes in Northern France. The parameters of the model are then identified on the basis of these data by considering data in spring, summer and autumn. The calibration of the model parameters is a challenging problem because of the large number of parameters, the limited number of available experimental data and the model complexity. The objective in the identification procedure was thus limited to obtain the largest number of unique values for the parameters in the three instances.

Bacteria, Aerobic↗

PubMed1999

Identification of electrically stimulated quadriceps muscles in paraplegic subjects.

This work establishes a method for the noninvasive in vivo identification of parametric models of electrically stimulated muscle in paralyzed individuals, when significant inertial loads and/or load transitions are present. The method used differs from earlier work, in that both the pulse width and stimulus period (interpulse interval) modulation are considered. A Hill-type time series model, in which the output is the product of two factors (activation and torque-angle) is used. In this coupled model, the activation dynamics depend upon velocity. Sequential nonlinear least squares methods are used in the parameter identification. The ability of the model, using identified time-varying parameters, to accurately predict muscle torque outputs is evaluated, along with the variability of the identified parameters. This technique can be used to determine muscle parameter models for biomechanical computer simulations, and for real-time adaptive control and monitoring of muscle response variations such as fatigue.

Algorithms↗

PubMed2002

Modeling acidogenic and sulfate-reducing processes for the determination of fermentable fractions in wastewater.

The biochemical acidogenic potential (BAP) of a wastewater is the maximum concentration of volatile fatty acids (VFAs) that can be measured at the end of an anaerobic fermentation test. A model was constructed to describe the acidogenic reactions occurring during BAP tests and to divide the BAP into organic fractions. The model was calibrated with a set of specific experiments highlighting the role of sulfate-reducing bacteria on acidogenic processes, which description was necessary for correct parameter identification. The model could describe acidogenic fermentation processes, with or without sulfate reduction, at 20 degrees C, for 13 wastewaters of different origin, composition, and settleability using the same optimized parameters. A simplified version of the model, without sulfate reduction, was able to describe VFA production by the adjustment of only three variables: readily fermentable organic matter (Sf), anaerobically hydrolyzable organic matter (Xf), and heterotrophic acidogenic biomass (Xha), which proved to be coherent with the experimental BAP value. The combination of the BAP test and the model developed in this study resulted in a new reliable tool to characterize wastewater under anaerobic conditions. As VFAs are the main substrates for phosphate-accumulating organisms (PAOs), the use of organic fractions VFA, Sf, Xf, and Xha in wastewater treatment plant modeling could improve the predictability and optimization of enhanced biological phosphorus removal (EBPR) processes.

Bacteria, Anaerobic↗

PubMed2001

Partition coefficients of alkyl aromatic hydrocarbons and esters in a hexane-acetonitrile system.

Partition coefficients (Kp) in a heterogeneous system consisting of two immiscible organic solvents can be successfully used for a supplementary identification parameter in qualitative GC and GC-MS analysis of organic compounds. For rapid addition to database of Kp values, calculation methods based on the well-known 'retention-structure relationships' approach can be used. This paper reports the experimentally determined and calculated Kp values for 252 compounds including alkyl aromatic hydrocarbons and esters. It is shown that for group identification of components it is desirable to use not the Kp values themselves but the parameter j which is a combination of K, and gas chromatographic retention indices: j = kI - log Kp.

Acetonitriles↗

PubMed1980

Pharmacokinetics in nonlinear and partially compartmentalized systems.

The pharmacokinetics of complex systems both linear and nonlinear, compartmentalized, distributed, and partially compartmentalized are reviewed. The two problems considered are: 1) the prediction of concentration or pharmacological effects, and 2) the determination of the input (absorption, dosage schedule) from a given set of measured or desired concentrations. These problems are solved using the super-position integral in linear time-invariant systems by i) integration and ii) deconvolution respectively. Time-varying systems are dealt with by using tracer methods. Nonlinear systems are defined as systems with concentration-dependent parameters. The examples of Michaelis-Menten kinetics, tissue binding, and threshold effects are considered. Approaches to solutions of these problems are generally model-dependent and achieved through i) system identification (parameter estimation), ii) linearization for limiting cases, and iii) tracer techniques. Tracer techniques effectively linearize a nonlinear system so that some variable-dependent parameters can be measured. It is suggested that some of the more general techniques used in the study of metabolic systems may be useful in pharmacokinetics.

Drug Administration Schedule↗

PubMed1982

Role of longitudinal diffusion in the extravascular pulmonary space on parameter estimates derived from data of multiple indicator dilution.

A mathematical model of transcapillary exchange has been developed that considers in detail the role of axial diffusion in the extravascular tissue region on estimates of such physiological parameters as lung water (VE) and pulmonary capillary permeability-surface area products (PS), obtained from multiple indicator dilution studies. The experimental cases considered correspond to two animal models of pulmonary oedema in which the integrity of the pulmonary capillary membrane is disrupted and the effects of extravascular axial diffusion may be important. A novel feature of the computational scheme is the use of an Array Processor in the solution of the governing equations, initial and boundary conditions. Computer time is reduced to 2-3 min for parameter identification, thereby allowing a wide range of values for extravascular axial diffusion coefficients (D'/L2) to be studied at little computational expense. The results indicate that diffusion in the extravascular region does not influence parameter estimates for PS to urea. A statistical correlation is suggested between values for VE, PS to water, and D'/L2.

Animals↗

PubMed2000

Application of a sensorial response model to the design of an oral liquid pharmaceutical dosage form.

In this paper, we discuss the application of a compartmental model to study the sensorial response, in terms of taste intensity versus time, in an oral solution for pharmaceutical use. The numerical model was developed from sensorial response curves obtained by a panel of three trained individuals. Parameter identification was carried out by means of a least-squares procedure that obtained the linear coefficients in the model by solving an exact linear least-squares problem conditional on the values of the nonlinear parameters for each iteration. Thus, nonlinear estimation was done in terms of the first-order kinetic parameters only, and ill-conditioning of the Hessian matrix present in these models was solved. Results of modeling for a set of formulations were used to determine the effects of various ingredients (sweeteners and an essence) on a baseline unflavored formulation of acetaminophen in a mixture of cosolvents. The first moment of the area under the curve of taste intensity versus time was found to be the best global indicator of taste for the purpose of product design. It was found that a mixture of sweeteners and an essence was the most efficient way of masking the bitter taste of this active ingredient.

Acetaminophen↗