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PubMed2006

A process-based mathematical model on methane production with emission indices for control.

In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerability of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane production process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature effects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices.

Biomass↗

PubMed2002

Groundwater contamination downstream of a contaminant penetration site. II. Horizontal penetration of the contaminant plume.

Part I of this study (Rubin, H.; Buddemeier, R.W. Groundwater Contamination Downstream of a Contaminant Penetration Site Part 1: Extension-Expansion of the Contaminant Plume. J. of Environmental Science and Health Part A (in press).) addressed cases, in which a comparatively thin contaminated region represented by boundary layers (BLs) developed within the freshwater aquifer close to contaminant penetration site. However, at some distance downstream from the penetration site, the top of the contaminant plume reaches the top or bottom of the aquifer. This is the location of the "attachment point," which comprises the entrance cross section of the domain evaluated by the present part of the study. It is shown that downstream from the entrance cross section, a set of two BLs develop in the aquifer, termed inner and outer BLs. It is assumed that the evaluated domain, in which the contaminant distribution gradually becomes uniform, can be divided into two sections, designated: (a) the restructuring section, and (b) the establishment section. In the restructuring section, the vertical concentration gradient leads to expansion of the inner BL at the expense of the outer BL, and there is almost no transfer of contaminant mass between the two layers. In the establishment section, each of the BLs occupies half of the aquifer thickness, and the vertical concentration gradient leads to transfer of contaminant mass from the inner to the outer BL. By use of BL approximations, changes of salinity distribution in the aquifer are calculated and evaluated. The establishment section ends at the uniformity point, downstream from which the contaminant concentration profile is practically uniform. The length of the restructuring section, as well as that of the establishment section, is approximately proportional to the aquifer thickness squared, and is inversely proportional to the transverse dispersivity. The study provides a convenient set of definitions and terminology that are helpful in visualizing the gradual development of uniform contaminant concentration distribution in an aquifer subject to contaminant plume penetration. The method developed in this study can be applied to a variety of problems associated with groundwater quality, such as initial evaluation of field data, design of field data collection, the identification of appropriate boundary conditions for numerical models, selection of appropriate numerical modeling approaches, interpretation and evaluation of field monitoring results, etc.

Environmental Monitoring↗

PubMed2006

Spatial distribution and orientation of dermatan sulfate in human medial collateral ligament.

The proteoglycan decorin and its associated glycosaminoglycan (GAG), dermatan sulfate (DS), regulate collagen fibril formation, control fibril diameter, and have been suggested to contribute to the mechanical stability and material properties of connective tissues. The spatial distribution and orientation of DS within the tissue are relevant to these mechanical roles, but measurements of length and orientation from 2D transmission electron microscopy (TEM) are prone to errors from projection. The objectives of this study were to construct a 3D geometric model of DS GAGs and collagen fibrils, and to use the model to interpret TEM measurements of the spatial orientation and length of DS GAGs in the medial collateral ligament of the human knee. DS was distinguished from other sulfated GAGs by treating tissue with chondroitinase B, an enzyme that selectively degrades DS. An image processing pipeline was developed to analyze the TEM micrographs. The 3D model of collagen and GAGs quantified the projection error in the 2D TEM measurements. Model predictions of 3D GAG orientation were highly sensitive to the assumed GAG length distribution, with the baseline input distribution of 69+/-23 nm providing the best predictions of the angle measurements from TEM micrographs. The corresponding orientation distribution for DS GAGs was maximal at orientations orthogonal to the collagen fibrils, tapering to near zero with axial alignment. Sulfated GAGs that remained after chondroitinase B treatment were preferentially aligned along the collagen fibril. DS therefore appears more likely to bridge the interfibrillar gap than non-DS GAGs. In addition to providing quantitative data for DS GAG length and orientation in the human MCL, this study demonstrates how a 3D geometric model can be used to provide a priori information for interpretation of geometric measurements from 2D micrographs.

Chondroitinases and Chondroitin Lyases↗

PubMed1996

Cell cycle time of murine neopallial cells in vitro.

Disaggregated glial cells from newborn CD1 mouse neopallia were cultured in low concentration (4.2 x 10(3) cells/cm2) for 72 hr and then either pulse labeled with BrdU by one 2-hr pulse at various times of culturing or continuously labeled for various lengths of time. At the end of incubation, the cells were fixed and immunoreacted with BrdU. All BrdU+ and BrdU- cell nuclei were counted in an area of 4.84 cm2. A three-compartment model for interpretation of the experimental data was developed consisting of active proliferating cells, non-active cells with proliferating potential, and nonproliferating cells. The model is based on assumptions of time invariance of culture conditions, random re-entry of cells into cell cycle and random exit from the proliferating pool. Furthermore, it is assumed that average values are representative for describing the numbers of cells in specific compartments as functions of time. A set of relationships representing the numbers of labeled cells for pulse labeling and continuous labeling assays is derived from these assumptions and the generally accepted representation of cell progress through the cell cycle, i.e., a genetically predetermined sequence of post-mitosis rest phase, S-phase, pre-mitosis rest phase, and mitosis. These relationships are used to evaluate the S-phase time tau s and cell cycle time tau c of proliferating cells. Under our particular conditions, we obtain approximately tau s = 8 hr and tau c = 16 hr, respectively. The applicability of the model and possible distorting factors are discussed.

Animals↗

PubMed1991

Domain of validity of classical models of leucine metabolism assessed by compartmental modeling.

Whole-body modeling of in vivo leucine (an essential amino acid) metabolism is fundamentally difficult due to the complexity of the system. This has favored the use of two simple kinetic models, the so-called primary and reciprocal pool models, to interpret tracer data, but their domain of validity is uncertain. We define here the error of these two approaches by using comprehensive compartmental models of leucine metabolism as true representations of the leucine system. Of particular interest is the comparison of the two simple models with an 11-compartment model characterized by a rich intracellular compartmentation that has recently been proposed as a sound physiological description of the system. Formulas are derived that define in structural terms the error of the primary and reciprocal pool models.

Humans↗

PubMed2000

A new dose model for assessment of health risk due to contaminants in air.

The problem of making quantitative assessments of the risks associated with human exposure to toxic contaminants in the environment is a pressing one. This study demonstrates the capability of a new computational technique involving the use of fuzzy logic and neural networks to produce realistic risk assessments. The systematic analysis of human exposure involves the use of measurements and models, the results of which are sometimes used in regulatory decisions or in the drafting of legislation. Because of limited scientific understanding, however, interpretation of models often involves substantial uncertainty. Extensive measurement programs can be very expensive. The high complexity and inherent heterogeneity of exposure analysis is still a major challenge. The approach to this challenge tested here is to use a new model incorporating sophisticated artificial intelligence algorithms. Exposure assessment often requires that a number of factors be evaluated, including exposure concentrations, intake rates, exposure times, and frequencies. These factors are incorporated into a system that can "learn" the relevant relationships based on a known data set. The results can then be applied to new data sets and thus be applied widely without the need for extensive measurements. In this analysis, an example is developed for human health risk through inhalation exposure to benzene from vehicular emissions in the cities of Auckland and Christchurch, New Zealand. Risk factors considered were inhaled contaminant concentration, age, body weight, and activity patterns of humans. Three major variables affecting the inhaled contaminant concentration were emissions (mainly from motor vehicles), meteorology (wind speed, temperature, and atmospheric stability), and site factors (hilly, flat, etc.). The results are preliminary and used principally to demonstrate the technique, but they are very encouraging.

Age Factors↗

PubMed2000

GRid-INdependent descriptors (GRIND): a novel class of alignment-independent three-dimensional molecular descriptors.

Traditional methods for performing 3D-QSAR rely upon an alignment step that is often time-consuming and can introduce user bias, the resultant model being dependent upon and sensitive to the alignment used. There are several methods which overcome this problem, but in general the necessary transformations prevent a simple interpretation of the resultant models in the original descriptor space (i.e. 3D molecular coordinates). Here we present a novel class of molecular descriptors which we have termed GRid-INdependent Descriptors (GRIND). They are derived in such a way as to be highly relevant for describing biological properties of compounds while being alignment-independent, chemically interpretable, and easy to compute. GRIND are obtained starting from a set of molecular interaction fields, computed by the program GRID or by other programs. The procedure for computing the descriptors involves a first step, in which the fields are simplified, and a second step, in which the results are encoded into alignment-independent variables using a particular type of autocorrelation transform. The molecular descriptors so obtained can be used to obtain graphical diagrams called "correlograms" and can be used in different chemometric analyses, such as principal component analysis or partial least-squares. An important feature of GRIND is that, with the use of appropriate software, the original descriptors (molecular interaction fields) can be regenerated from the autocorrelation transform and, thus, the results of the analysis represented graphically, together with the original molecular structures, in 3D plots. In this respect, the article introduces the program ALMOND, a software package developed in our group for the computation, analysis, and interpretation of GRIND. The use of the methodology is illustrated using some examples from the field of 3D-QSAR. Highly predictive and interpretable models are obtained showing the promising potential of the novel descriptors in drug design.

Butyrophenones↗

PubMed1995

Nonlinear autoregressive analysis of the 3/s ictal electroencephalogram: implications for underlying dynamics.

In a previous study, nonlinear autoregressive (NLAR) models applied to ictal electroencephalogram (EEG) recordings in six patients revealed nonlinear signal interactions that correlated with seizure type and clinical diagnosis. Here we interpret these models from a theoretical viewpoint. Extended models with multiple nonlinear terms are employed to demonstrate the independence of nonlinear dynamical interactions identified in the 'NLAR fingerprint' of patients with 3/s seizure discharges. Analysis of the role of periodicity in the EEG signal reveals that the fingerprints reflect the dynamics not only of the periodic discharge itself, but also of the fluctuations of each cycle about an average waveform. A stability analysis is used to make qualitative inferences concerning the network properties of the ictal generators. Finally, the NLAR fingerprint is analyzed in the context of Volterra-Weiner theory.

Electroencephalography↗

PubMed1985

Model-independent electron spin resonance for measuring order of immobile components in a biological assembly.

A model-independent description of the angular orientation distribution of elements in an ordered biological assembly is applied to the electron spin resonance (ESR) technique. As in a previous model-independent treatment of fluorescence polarization (Burghardt, T.P., 1984, Biopolymers, 23:2383-2406) the elemental order is described by an angular distribution of molecular frames with one frame fixed in each element of the assembly. The distribution is expanded in a complete orthonormal set of functions. The coefficients of the series expansion (the order parameters) describe the orientation distribution of the elements in the assembly without reference to a model and can be obtained from the observed spectrum. The method establishes the limitations of ESR in detecting order in the assembly by determining which distribution coefficients the technique can detect. A method of determining the order parameters from an ESR spectra, using a set of ESR basis spectra, is developed. We also describe a treatment that incorporates the actual line shape measured from randomly oriented, immobile elements. In this treatment, no model-dependent assumptions about the line shape are required. We have applied the model-independent analysis to ESR spectra from spin-labeled myosin cross-bridges in muscle fibers. The results contain detailed information on the spin-probe angular distribution and differ in interesting ways from previous model-dependent interpretations of the spectra.

Animals↗

PubMed2005

Non-quadratic-intensity dependence of two-photon absorption induced fluorescence of organic chromophores in solution.

We have provided a model to interpret the non-quadratic-intensity dependence behavior commonly observed in the two-photon fluorescence (TPF) experiment excited with high laser intensity. The model also provides one with a different technique to measure the two-photon absorption cross section of an organic chromophore in solution. In contrast to the commonly used low intensity technique that depends on the quadratic-intensity law, the present technique is based on the non-quadratic-intensity dependence of two-photon fluorescence. Auxiliary data such as two-photon quantum efficiency and fluorescence collection efficiency, essential in the low intensity method, are not required in the present technique. TPF measurements of Rhodamine B in methanol are carried out to demonstrate the validity of the present method. The method is used to determine the two-photon absorption cross section of a new chromophore attached with tricyano-derivatized furan as the electron acceptor. The two-photon absorption cross section measured using this method is also compared with that using a conventional transmission technique.

Journal Article↗

PubMed1987

[The results of research on the biological effects of neutrons].

A study was made of the peculiarities of the biological effect of neutrons as compared to gamma-radiation. A number of biological models were proposed for interpretation of the phenomenon: a biophysical model of mutations and cell inactivation, a model for interpretation of the formation of a radioresistant and radiosensitive fraction.

Animals↗

PubMed2004

Perimetric defects and ganglion cell damage: interpreting linear relations using a two-stage neural model.

PURPOSE: To better understand the relations between glaucomatous perimetric defects and ganglion cell damage, a neural model was developed to interpret empiric findings on linear relations between perimetric defects and measures of ganglion cell loss. METHODS: A two-stage model computed responses of ganglion cell mosaics (first stage), then computed perimetric sensitivity in terms of processing by spatial filters (second stage) that pool the ganglion cell responses. Cell death and dysfunction were introduced in a local patch of the first-stage ganglion cell mosaic, and perimetric defect depth was computed for the corresponding region of the visual field. Calculations were performed for both sparse and dense ganglion cell mosaics and for spatial filters with peak frequencies from 0.5 to 4.0 cyc/deg. RESULTS: The model yielded nonlinear functions for perimetric defect depth in decibel versus the percentage of ganglion cell damage, but functions for lower spatial frequencies became linear when perimetric defect was expressed as a percentage of normal. The relations between perimetric defects and percentage of ganglion cell loss were determined primarily by spatial tuning of the second-stage spatial filters. For averaging sensitivities across different visual field locations, linear units (arithmetic mean) can more closely approximate mean ganglion cell loss than decibel units (geometric mean). Fits to data from experimental glaucoma required ganglion cell dysfunction in addition to ganglion cell loss. CONCLUSIONS: Pooling by second-stage spatial filters can account for empiric findings of linear relations between perimetric defects and measures of ganglion cell loss.

Glaucoma↗

PubMed1989

Structures of actomyosin crossbridges in relaxed and rigor muscle fibers.

It was shown previously that a significant fraction of the myosin crossbridges is attached to actin in the skinned rabbit psoas fibers under relaxed conditions at low ionic strength and low temperature (Brenner, B., M. Schoenberg, J. M. Chalovich, L. E. Greene, and E. Eisenberg. 1982. Proc. Natl. Acad. Sci. USA. 79:7288-7291; Brenner, B., L. C. Lu, and R. J. Podolsky. 1984. Biophys. J. 46:299-306). In the present work, the structure of the attached crossbridges in the relaxed state between ionic strengths of 20 and 100 mM, as compared with that in the rigor state, is further examined by equatorial x-ray diffraction. Mass distributions projected along the fiber axis are reconstructed based on the first five equatorial reflections such that the spatial resolution is 128 A. The fraction of crossbridges attached under relaxed conditions are estimated to be in the range of 30% (at 100 mM ionic strength) and 60% (at 20 mM). The reconstructed density maps suggest that in the relaxed state, upon attachment the part of the crossbridge that centers around the thin filament is small, and the attachment does not significantly alter the center of mass of the myosin head distribution around the thick filament backbone. In contrast, accretion of mass in the rigor state occurs in a wider region surrounding the thin filament. In this case, mass in the surface region of the thick filament backbone is shifted slightly outward, probably by approximately 10 A. A schematic model for interpreting the present data is presented.

Actomyosin↗

PubMed1987

Evidence implicating alpha-2 adrenergic receptors in the anticonvulsant action of intranigral muscimol.

The effects of systemically administered catecholamine receptor antagonists on the anticonvulsant action produced by local application of a gamma-aminobutyric acid agonist, muscimol, to the substantia nigra of rats were studied. Both electroshock and kindled seizures were studied. Two alpha-2 receptor antagonists, idazoxan and yohimbine, blocked the anticonvulsant action of intranigral muscimol in the electroshock model. Neither a beta nor an alpha-1 adrenergic nor a dopamine-2 receptor antagonist blocked this action. In contrast to electroshock seizures, an alpha-2 antagonist only partially reversed the anticonvulsant action of intranigral muscimol in the kindling model. We interpret the data to indicate that the interaction of norepinephrine with alpha-2 receptors is required for the anticonvulsant action of intranigral muscimol in the electroshock model. The only partial reversal found in the kindling model suggests that nigral control of seizure propagation involves more than alpha-2 receptor mediated neurotransmission.

Animals↗

PubMed1995

Interpretation of serological surveillance data for measles using mathematical models: implications for vaccine strategy.

Serological surveillance of measles immunity has been carried out in England since 1986/7. Results from sera collected in 1989-91 revealed that the proportion of school age children who were susceptible to measles was increasing, following the introduction of the measles, mumps and rubella vaccination programme in October 1988. Mathematical models are used to interpret these data and determine whether this increasing susceptibility is sufficient to allow a resurgence of disease from the low levels achieved by 1993. The models summarize serological profiles by a single parameter, the reproduction number R, which quantifies the level of herd immunity in the population. Results showed that there was cause for concern over the levels of susceptibility to measles, with an epidemic of over 100,000 cases likely in 1995/6. These predictions are consistent with trends in the incidence and age distribution of measles and have enabled the planning of a major vaccination campaign.

Adolescent↗

PubMed1997

Partition of perceived space within the fusional area on the basis of apparent fronto-parallel plane criterion.

The relationship between visual space and physical space was investigated by means of the apparent fronto-parallel plane percept. A set of curves in physical space, corresponding to fronto-parallel planes perceived in front or behind a given fixation point, was determined. The curvature at the apex of these curves follows a hyperbolic law that depends on the distance between the perceived plane and the fixation point. Our results are interpreted by distinguishing absolute disparity, which sets the position of the perceived plane, from relative disparity measured by adjusting in this plane eccentric vertical lines. We show that Foley's model, which interprets the shape of the apparent fronto-parallel planes on the mis-evaluation of egocentric distance, works for absolute disparity judgements, but seems to be inadequate for relative disparity judgements in our experimental conditions.

Humans↗

PubMed2004

The spin-unrestricted molecular Kohn-Sham solution and the analogue of Koopmans's theorem for open-shell molecules.

Spin-unrestricted Kohn-Sham (KS) solutions are constructed from accurate ab initio spin densities for the prototype doublet molecules NO(2), ClO(2), and NF(2) with the iterative local updating procedure of van Leeuwen and Baerends (LB). A qualitative justification of the LB procedure is given with a "strong" form of the Hohenberg-Kohn theorem. The calculated energies epsilon(isigma) of the occupied KS spin orbitals provide numerical support to the analogue of Koopmans' theorem in spin-density functional theory. In particular, the energies -epsilon(ibeta) of the minor spin (beta) valence orbitals of the considered doublet molecules correspond fairly well to the experimental vertical ionization potentials (VIPs) I(i) (1) to the triplet cationic states. The energy -epsilon(Halpha) of the highest occupied (spin-unpaired) alpha orbital is equal to the first VIP I(H) (0) to the singlet cationic state. In turn, the energies -epsilon(ialpha) of the major spin (alpha) valence orbitals of the closed subshells correspond to a fifty-fifty average of the experimental VIPs I(i) (1) and I(i) (0) to the triplet and singlet states. For the Li atom we find that the exact spin densities are represented by a spin-polarized Kohn-Sham system which is not in its ground state, i.e., the orbital energy of the lowest unoccupied beta spin orbital is lower than that of the highest occupied alpha spin orbital ("a hole below the Fermi level"). The addition of a magnetic field in the -z direction will shift the beta levels up so as to restore the Aufbau principle. This is an example of the nonuniqueness of the mapping of the spin density on the KS spin-dependent potentials discussed recently in the literature. The KS potentials may no longer go to zero at infinity, and it is in general the differences nu(ssigma)( infinity )-epsilon(isigma) that can be interpreted as (averages of) ionization energies. In total, the present results suggest the spin-unrestricted KS theory as a natural one-electron independent-particle model for interpretation and assignment of the experimental photoelectron spectra of open-shell molecules.

Journal Article↗

PubMed2000

Applied pharmacoeconomics: modeling data from internal and external sources.

The use and application of techniques for modeling data obtained from various data sources are discussed. Modeling with internal and external data has become a popular way for health care organizations to apply pharmacoeconomics to pharmacy practice. Modeling studies use existing clinical and epidemiologic data to project the effect of a clinical, policy, or medication decision on a patient, population, or organization. Although several modeling techniques have been used in health care, the most common approaches are to modify and adapt existing models or to develop a unique model to answer questions of interest in a specific practice setting. Typically, an economic model developed by adapting an existing one will use either the clinical decision-analysis or Markov modeling technique. Regardless of the technique used, external data must be carefully evaluated to ensure that the data are appropriate for use in making decisions at a specific organization. For example, cost data must be analyzed to ensure that the calculations are reproducible. Also, it must be acknowledged that this strategy may not always be appropriate. The use of modeling techniques can assist decision-makers in making more informed clinical, policy, and medication decisions in real-world settings. Caution is required when adapting and interpreting existing models to ensure appropriate application in a specific organization.

Algorithms↗