nonlinear diffusion
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We extended the linearized model of electromigration, which is used by PeakMaster, by calculation of nonlinear dispersion and diffusion of zones. The model results in the continuity equation for the shape function ϕ(x,t) of the zone: ϕ(t) = -(v(0) + v(EMD) ϕ)ϕ(x) + δϕ(xx) that contains linear (v(0)) and nonlinear migration (v(EMD)), diffusion (δ), and subscripts x and t stand for partial derivatives. It is valid for both analyte and system zones, and we present equations how to calculate characteristic zone parameters. We solved the continuity equation by Hopf-Cole transformation and applied it for two different initial conditions-the Dirac function resulting in the Haarhoff-van der Linde (HVL) function and the rectangular pulse function, which resulted in a function that we denote as the HVLR function. The nonlinear model was implemented in PeakMaster 5.3, which uses the HVLR function to predict the electropherogram for a given background electrolyte and a composition of the sample. HVLR function also enables to draw electropherograms with significantly wide injection zones, which was not possible before. The nonlinear model was tested by a comparison with a simulation by Simul 5, which solves the complete nonlinear model of electromigration numerically.
BACKGROUND: Diffusion tensor imaging (DTI) is now widely used in neurosurgery to preoperatively delineate the course of the pyramidal tract. OBJECTIVE: To evaluate the accuracy of the method by comparison with subcortical electrical stimulation and to evaluate the influence of the distance of the pyramidal tract from the tumor on the resection extent and postoperative clinical deficits. METHODS: A diffusion tensor imaging depiction of the pyramidal tract was used in preoperative planning and intraoperative navigation in 72 cases. In 36 cases, subcortical electrical stimulation was used during the resection. The preoperative tumor-to-tract distance was compared with the stimulation result, the extent of resection, and the short-term postoperative course. RESULTS: A significant nonlinear relationship between the tract-to-tumor distance and the probability of a motor response to subcortical stimulation was observed. The largest preoperatively measured tumor-to-tract distance with a positive stimulation result was 8 mm. Moreover, we observed a trend toward transient postoperative motor deterioration in patients with tumors close to the pyramidal tract. Resection extent was not significantly affected by the tumor-to-tract distance. CONCLUSION: Despite methodological obstacles, reasonable accuracy of the diffusion tensor imaging reconstructions of the pyramidal tracts was confirmed by our study. The occurrence of transient postoperative motor deterioration is higher in patients with tumors located close to the pyramidal tract.
- MeSH
- difuzní magnetická rezonance metody MeSH
- elektrodiagnostika metody MeSH
- hluboká mozková stimulace metody MeSH
- lidé středního věku MeSH
- lidé MeSH
- nádory mozku patologie chirurgie MeSH
- předoperační péče metody MeSH
- pyramidové dráhy patologie MeSH
- reprodukovatelnost výsledků MeSH
- senzitivita a specificita MeSH
- Check Tag
- lidé středního věku MeSH
- lidé MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- klinické zkoušky kontrolované MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein-Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.
- MeSH
- akční potenciály fyziologie MeSH
- algoritmy MeSH
- financování organizované MeSH
- lidé MeSH
- membránové potenciály fyziologie MeSH
- modely neurologické MeSH
- nervové vedení fyziologie MeSH
- neurony fyziologie MeSH
- refrakterní doba elektrofyziologická fyziologie MeSH
- stochastické procesy MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
The theory of glucose-responsive composite membranes for the planar diffusion and reaction process is extended to a microsphere membrane. The theoretical model of glucose oxidation and hydrogen peroxide production in the chitosan-aliginate microsphere has been discussed in this manuscript for the first time. We have successfully reported an analytical derived methodology utilizing homotopy perturbation to perform the numerical simulation. The influence and sensitive analysis of various parameters on the concentrations of gluconic acid and hydrogen peroxide are also discussed. The theoretical results enable to predict and optimize the performance of enzyme kinetics.
Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction-diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing's original thesis to a far wider and more realistic class of systems.
- MeSH
- biologické modely * MeSH
- difuze MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Due to dramatic effects of even small changes in mobile phase composition on the retention, separations of high-molecular compounds are very difficult, if possible at all, at isocratic conditions and need gradient elution. The theory of gradient elution for small molecules is well established, however its applications to reversed-phase gradient separations of biopolymers are not straightforward because of specific problems, such as slow diffusion, limited accessibility of the stationary phase for larger molecules, or possible sample conformation changes during the elution. Theoretical prediction of gradient data needs the parameters of model retention equations to be known, which however cannot be determined at isocratic conditions. The present work overviews the attempts at implementation of the conventional gradient theory developed for low-molecular compounds to the description and prediction of gradient separations of peptides and proteins on various types of HPLC columns: conventional analytical columns packed with wide-pore fully porous, fused-core superficially porous and non-porous particles; silica-based monolithic columns and organic-polymer poly(alkylmethacrylate) and poly(styrene-divinylbenzene) monolithic columns in capillary and disc formats. The attention is focused on the determination of the parameters necessary to predict gradient retention times (volumes) and bandwidths using the theoretical model equations. The accuracy of the prediction of protein retention on totally porous columns improves if size exclusion effect is taken into account, but this is not necessary with non-porous or superficially porous particles. Band dispersion effects counteracting band compression in gradient elution depend on the type of column, on the protein and on the gradient volume (steepness) and complicate the prediction of band broadening in gradient chromatography of proteins, however the conventional gradient model can be employed to estimate the effects of changing gradient parameters on the bandwidths, as well as on the elution times (volumes) of proteins.
CRC series in pure and applied physics
1st ed. 550 s.
... Selecting the Mth Largest 431 -- 8.6 Determination of Equivalence Classes 439 -- 9 Root Finding and Nonlinear ... ... Newton-Raphson Method Using Derivative 456 -- 9.5 Roots of Polynomials 463 -- 9.6 Newton-Raphson Method for Nonlinear ... ... Systems of Equations 473 -- 9.7 Globally Convergent Methods for Nonlinear Systems of Equations 477 - ... ... Straight-Line Data with Errors in Both Coordinates 785 -- 15.4 General Linear Least Squares 788 -- 15.5 Nonlinear ... ... Equations 1024 -- 20.0 Introduction 1024 -- 20.1 Flux-Conservative Initial Value Problems 1031 -- 20.2 Diffusive ...
3rd ed. xxi, 1235 s. : il. ; 27 cm + 1 CD-ROM
- MeSH
- matematické výpočty počítačové MeSH
- matematika MeSH
- numerická analýza pomocí počítače * MeSH
- Publikační typ
- monografie MeSH
... Vaccination 122 -- 8 Spatial spread 125 -- 8.1 Posing the problem 125 -- 8.2 Warming up: the linear diffusion ... ... reflections suggesting robustness 128 -- 8.4 Linear structured population models 130 -- 8.5 The nonlinear ...
Wiley series in mathematical and computational biology
1st ed. xvi, 303 s.
Biological Physics Series
3rd ed. xii, 575 s., obr.
