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PubMed1999

Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models.

We introduce a formalism for the reconstruction of bifurcation diagrams from noisy time series. The method consists in finding a parametrized predictor function whose bifurcation structure is similar to that of the given system. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropriate model that best represents all the given time series is selected. A nonlinear autoregressive model with polynomial terms is employed in this study. The identification of the bifurcation parameters from among the many model parameters is done in the second stage. The algorithm works well even for a limited number of time series.

Journal Article↗
PubMed2003

New parameters in identification of right ventricular myocardial infarction and proximal right coronary artery lesion.

OBJECTIVE: The diagnosis of right ventricular myocardial infarction (RVMI) accompanied by acute inferior myocardial infarction (MI) is still a problem that we encounter. This study was designed to find out the usefulness both of peak myocardial systolic velocity (Sm) and of the myocardial performance index (MPI) of the right ventricle measured by pulsed-wave tissue Doppler imaging (TDI) in assessing right ventricular function. METHODS: Sixty patients who experienced a first acute inferior MI (mean [+/- SD] age, 57 +/- 9 years) were prospectively assessed. An ST-segment elevation of >or= 0.1 mV in V(4)-V(6)R lead derivations was defined as an RVMI. From the echocardiographic apical four-chamber view, the Sm, the peak early diastolic velocity, peak late diastolic velocity, the ejection time, the isovolumetric relaxation time, and the contraction time of the right ventricle were recorded at the level of the tricuspid annulus by using TDI. Then, the MPI was calculated. The patients were classified into the following three groups, according to the localization of the infarct-related artery (IRA) detected using coronary angiography: group I, proximal right coronary artery; group II, distal right coronary artery; and group III, circumflex coronary artery. RESULTS: RVMIs were detected in sixteen patients, and the IRA in 27 patients was the proximal right coronary artery. The right ventricular Sm was observed to be significantly low in patients with RVMIs and those in group I compared to those without RVMIs and those in groups II and III (10.9 +/- 1.3 vs 14.3 +/- 3.2 cm/s, respectively [p < 0.001]; 11.5 +/- 2.5 vs 15.1 +/- 3 cm/s, respectively; and 14.9 +/- 2.6 cm/s, respectively [p < 0.001]). In the diagnosis of RVMI, the values for sensitivity, specificity, negative predictive value, and positive predictive value of Sm < 12 cm/s were 81%, 82%, 92%, and 62% respectively, and in the diagnosis of the proximal right coronary artery as the IRA, those values were 63%, 88%, 74%, and 81%, respectively. The MPI was high in the same patient groups (0.83 +/- 0.12 vs 0.57 +/- 0.11 in those patients without RVMI, respectively, [p < 0.001]; 0.74 +/- 0.13 vs 0.56 +/- 0.15 in group II and 0.54 +/- 0.07 in group III, respectively [p < 0.001]). The sensitivity, specificity, negative predictive value, and positive predictive value of an MPI of > 0.70 in the diagnosis of RVMI were calculated as 94%, 80%, 97%, and 63%, respectively, and in the diagnosis of the proximal right coronary artery as the IRA, those values were 78%, 91%, 83%, and 88% respectively. CONCLUSIONS: An Sm <12 cm/s and an MPI > 0.70 obtained by TDI may define RVMI concomitant with acute inferior MI, and the IRA.

Case-Control Studies↗
PubMed1993

Real-time identification of parameters of the ARMA model of the human EEG waveforms.

Electroencephalogram (EEG) can provide important information about the functioning of the human brain. In particular, the EEG waveforms manifest certain changes due to application of drugs, such as general anesthetics. Measurement of the changes in the EEG waveforms in real time, may therefore be used to determine the global effects of the administered drug. Among numerous mathematical techniques used in the analysis of the EEG waveforms, perhaps, the fast Fourier transform (FFT) is the most widely used. Recently some researchers have suggested the use of the autoregressive moving average (ARMA) model for the EEG analysis. In this method the coefficients of the ARMA model are identified and used to describe the waveform. We consider a first order ARMA model, and use the Extended Least Squares (ELS) and its recursive version (RELS) for parameter estimation. The identified parameters are then used to describe the time-domain or the frequency-domain properties of the EEG waveforms. Since the parameters of the model may change with time, a forgetting factor is incorporated in the RELS algorithm to allow for tracking of time varying parameters. The advantage of recursive estimation of the coefficients of the ARMA model over the non-recursive estimation and the FFT method, is substantial reduction in computation as well as its capability to track the time varying process.

Algorithms↗
PubMedDate not supplied

Identification power of a standardized HPLC-DAD system for systematic toxicological analysis.

High-performance liquid chromatography with photodiode-array detection (HPLC-DAD) provides two identification parameters: retention and UV spectral data. The identification power of these two parameters, expressed in standardized form (retention index and absorption maximum with the highest wavelength), is calculated using two approaches: discriminating power (DP) and mean list length (MLL). Our own HPLC database, which comprises data for more than 370 substances, is used as the basis of calculations. The identification power of both parameters applied separately is low but increases substantially when the combination of retention and spectral data is applied. Additionally, the DP and MLL values obtained for 56 acidic or neutral and 76 basic drugs examined by means of HPLC-DAD and other analytical methods (thin-layer chromatography, gas chromatography (GC), and ultraviolet (UV) detection) are compared. The on-line combination of HPLC retention index values and UV spectra, registered by means of DAD, creates an identification system in which the identification potential is slightly lower than the off-line combination of capillary GC and UV spectroscopy.

Chromatography, Gas↗
PubMed2005

Modelling approach in cell/material interactions studies.

Based on our experiments, we propose a statistical modeling approach of the in vitro interactions between biological objects and materials. The objective of this paper is to provide basic principles for developing more ambitious experiments comparing the simultaneous influence of more than one or two parameters on various observations, taking advantage of convenient statistical and mathematical techniques for the treatment of measured data. Analyzing some examples of our own experiments, the essential features needed for modeling cell/material interaction studies are presented. Firstly, we describe the initial process of designing appropriate experiments that allow for comprehensive modeling. In the second part, we illustrate the different applications of a specific statistical modeling technique, the bootstrap protocol, on either the amplification of data, the elimination of correlation existing between measured parameters or, out of a set of parameters, identification of the most relevant parameter for further statistical analysis. Finally, based on recent statistical analysis tools such as the bootstrap, we illustrate the relative influence of biological and physical parameters in phenomenological studies of cell/material interactions.

Biocompatible Materials↗
PubMed1983

Oral glucose tolerance test and insulin sensitivity in low insulin responders.

Oral and iv glucose tolerance, insulin response to iv and oral glucose load as well as insulin sensitivity were evaluated in 58 'low insulin responders'. They were selected from a group of 226 healthy subjects with normal fasting blood glucose and normal iv glucose tolerance test on the basis of a low insulin response during a standardized glucose infusion test (GIT). The insulin response to GIT was analysed by parameter identification in a mathematical model (parameter KI). Insulin sensitivity was also measured by computer analysis of GIT (parameter KG) and, in a limited group of subjects, by a somatostatin infusion test. Thirty-three low insulin responders had normal OGTT, whereas 5 demonstrated borderline-1, 16 borderline-2, and 4 decreased OGTT. The first group of subjects demonstrated normal or enhanced insulin sensitivity. Borderline and decreased OGTT, in most instances, was accompanied by decreased insulin sensitivity, implying that a subgroup of low insulin responders exhibited signs of both impaired insulin response to glucose and insulin resistance. Since these defects characterize manifest type-2 diabetes, these subjects possibly may run a high risk to develop this type of diabetes. On the other hand, low insulin response in combination with increased insulin sensitivity may reflect adaptation of the secretory capacity of B-cells to the need of insulin.

Adult↗
PubMed2005

Phenotype analysis using network motifs derived from changes in regulatory network dynamics.

The intrinsic dynamic response of a transcriptional regulatory network depends directly on molecular interactions in the cellular transcription, translation, and degradation machineries. These interactions can be incorporated into dynamic mathematical models of the biochemical system using the biophysical relationship with the model parameters. Modifications of such interactions bring changes to the biological behavior of the cells, and therefore, many normal and pathological cellular states depend on them. It is important for analysis, prediction, diagnosis, and treatment of cellular function to have an experimentally derived model with parameters that adequately represent the molecular interactions of interest. Finding the model and parameters of a transcriptional regulatory network is a difficult task that has been approached at different levels and with different techniques. We develop here a new analysis method (based on previous work on network inference, modeling, and parameter identification) that finds the most changed parameters from yeast oligonucleotide microarray expression patterns in cases where a phenotype difference exists between two samples. We then relate and examine the changed parameters with their associated genes, corresponding genetic functional categories, and particular subnetworks and connectivities. The biophysical bases for these changes are also identified by studying the relationship of the changed parameters with the transcription, translation, and degradation mechanisms. The method is improved to cases where there are two or more transcription factors influencing transcription, and a statistical analysis is performed to give a measurement of the uniqueness and robustness of the parameter fit.

Algorithms↗
PubMed1988

Quantitative characterization of diet effects on glucose tolerance in rabbits.

Normal, atherogenic and butter-enriched diets were given to three groups of rabbits during six months. The effects of the three forms of diet after six months were examined with the intravenous glucose tolerance test, which was evaluated by computer-aided model-fitting and parameter identification. Long-term effects are reflected in parameters such as pancreas sensitivity and the glucose utilization rate constant as a measure of peripheral insulin sensitivity. In these terms, the atherogenic diet caused a diminution of both pancreatic and peripheral sensitivity, whereas the butter-enriched diet led to an increase in glucose utilization and a decrease in pancreatic sensitivity relative to the system parameters of the normally fed control animals. Related to the findings about metabolic regulation are indications for an endocrinological approach to the problems of cholesterogenesis and atheroma formation.

Animals↗
PubMed1978

Personalized, electro-kinematic, neuromuscular model of a human forearm.

Electromyography, the recording of muscular activity, is of importance in industrial, biomechanical, and sports research as well as in medical diagnoses. When a muscle is activated, an electric potential in the order of microvolts (muV) is generated. This potential can be picked up, amplified, and displayed on an oscilloscope or strip chart recorder. Researchers have developed ways of analyzing these signals in terms of their characteristics. A numerical index, which reflects the basic characteristics of the electromyogram, mainly amplitude, frequency, and duration, can be used to provide quantitative information. The method used in this work for EMG processing consisted of filtering, rectification, and integration over very small intervals of time. Both analog and digital filtering proved necessary. Angular accelerometer and rotational potentiometer data were used in conjunction with limb inertia parameters obtained from existing biochemical models for the individual tested for obtaining the torques as a function of time. A system parameter identification method was used to determine the muscle parameters, such as occur in the single muscle Hill model, of four muscle groups for a human arm. The main results consist of personalized arm muscle group models. It was concluded that the method provided excellent (fit) personalized arm muscle group models under dynamic conditions. This method could lead to fundamental scientific information about a living muscle group from experiments in vivo.

Electromyography↗
PubMed2003

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms.

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges.

Acetates↗
PubMed1999

Evaluation of capillary electrophoretic techniques towards systematic toxicological analysis.

Two capillary electrophoresis (CE) methods were evaluated for their suitability in systematic toxicological analysis (STA). A test set of 25 barbiturates was analysed using capillary zone electrophoresis (CZE) and micellar electrokinetic chromatography (MEKC). Buffers used consisted of 90 mM borate set at pH 8.4 (CZE) and 20 mM phosphate, 50 mM sodium dodecyl sulphate set at pH 7.5 (MEKC). All analyses were carried out using fused silica capillaries using an electric field strength of 52.6 kV/m. The use of a reproducible identification parameter is very important in STA as it influences the identification power (IP). To deal with the poor reproducibility of the migration time, we introduced the corrected effective mobility. Inter-day reproducibilities of the latter parameter were < 0.6% for CZE and < 0.5% for MEKC, using daily prepared buffers. The IP of the methods was expressed by calculation of the discriminating power and the mean list length. Data obtained were compared to gas chromatographic and high-performance liquid chromatographic data, and correlations between all methods were calculated. It was shown that little correlation exists between chromatographic and electrophoretic techniques. The results indicated that CE has a good identification power for the application in STA, especially when a combination of methods having a low correlation is used.

Barbiturates↗
PubMed2000

A closed-loop model of the canine cardiovascular system that includes ventricular interaction.

A closed-loop model of cardiopulmonary circulation has been developed for the study of right-left ventricular interaction under physiologically normal and altered conditions. The core model provides insight into the effects of ventricular interaction and pericardial mechanics on hemodynamics. The complete model contains realistic descriptions of (a) the interacting ventricular free walls and septum, (b) the atria, (c) the pericardium, and (d) the systemic and pulmonary vascular loads. The current analysis extends previous work on ventricular interaction and pericardial influence under isolated heart conditions to loading conditions imposed by a closed-loop model of the circulation. A nonlinear least-squares parameter identification method (Levenberg-Marquardt algorithm) is used, together with parameter sensitivity analysis, to estimate the values of key parameters associated with the ventricular and circulation models. Pressure measurements taken at several anatomical locations in the circulation during open-chest experiments on dogs are used as data in the identification process. The complete circulatory model, including septal and pericardial coupling, serves as a virtual testbed for assessing the global affects of localized mechanical or hemodynamic alterations. Studies of both direct and series ventricular interaction, as well as the effect of the pericardium on cardiac performance, are accomplished with this model. Alterations in model parameter values are used to predict the impact of disease and/or clinical interventions on steady-state hemodynamic performance. Additionally, a software package titled CardioPV has been developed to integrate the complete model with data acquisition tools and a sophisticated graphical user interface. The complete software package enables users to collect experimental data, use the data to estimate model parameters, and view the model outputs in an online setting.

Animals↗
PubMed2006

Computational analysis of CFSE proliferation assay.

CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogenous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitro: (1) the total number of live cells, (2) the total number of dead but not disintegrated cells and (3) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth- and death rate "functions". It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance-covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback-Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g. the loss of confidence in the parameter estimates starting around the sixth division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.

Cell Growth Processes↗
PubMedDate not supplied

Identification of three-element windkessel model: comparison of time and frequency domain techniques.

The problem of the parameter identification of the three-element windkessel model is studied. Minimization by least-square technique--LSQ--in time domain and frequential techniques--FFT--are compared. Continuous pressure and flow curves were recorded in the proximal aorta of an open chest dog. Comparison shows very high correlations between the parameter estimations obtained by LSQ and FFT methods. However, systematic differences appear between the calculated values, but do not seem to endanger physiological interpretation of the results.

Animals↗