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PubMed2004

Isometric graphing and multidimensional scaling for reaction-diffusion modeling on regular and fractal surfaces with spatiotemporal pattern recognition.

Heterogeneous surface reactions exhibiting complex spatiotemporal dynamics and patterns can be studied as processes involving reaction-diffusion mechanisms. In many realistic situations, the surface has fractal characteristics. This situation is studied by isometric graphing and multidimensional scaling (IGMDS) of fractal surfaces for extracting geodesic distances (i.e., shortest scaled distances that obtain edges of neighboring surface nodes and their interconnections) and the results obtained used to model effects of surface diffusion with nonlinear reactions. Further analysis of evolved spatiotemporal patterns may be carried out by IGMDS because high-dimensional snapshot data can be efficiently projected to a transformed subspace with reduced dimensions. Validation of the IGMDS methodology is carried out by comparing results with reduction capabilities of conventional principal component analysis for simple situations of reaction and diffusion on surfaces. The usefulness of the IGMDS methodology is shown for analysis of complex patterns formed on both regular and fractal surfaces, and using generic nonlinear reaction-diffusion systems following FitzHugh Nagumo and cubic reaction kinetics. The studies of these systems with nonlinear kinetics and noise show that effects of surface disorder due to fractality can become very relevant. The relevance is shown by studying properties of dynamical invariants in IGMDS component space, viz., the Lyapunov exponents and the KS entropy for interesting situations of spiral formation and turbulent patterns.

Diffusion↗
PubMed2005

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces.

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.

Colloids↗
PubMed2003

Direct estimation of Cole parameters in multifrequency EIT using a regularized Gauss-Newton method.

A major drawback of electrical impedance tomography is the poor quality of the conductivity images, i.e., the low spatial resolution as well as large errors in the reconstructed conductivity values. The main reason is the necessity for regularization of the ill-conditioned inverse problem which results in excessive spatial low-pass filtering. A novel regularization method (SMORR (spectral modelling regularized reconstructor)) is proposed, which is based on the inclusion of spectral a priori information in the form of appropriate tissue models (e.g. Cole models). This approach reduces the ill-posedness of the inverse problem, when multifrequency data are available. An additional advantage is the direct reconstruction of the (physiological) tissue parameters of interest instead of the conductivities. SMORR was compared with posterior fitting of a Cole model to the conductivity spectra obtained with a classical iterative reconstruction scheme at various frequencies. SMORR performed significantly better than the reference method concerning robustness against noise in the data.

Algorithms↗
PubMed2006

Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem.

Procrustes analysis involves finding the optimal superposition of two or more "forms" via rotations, translations, and scalings. Procrustes problems arise in a wide range of scientific disciplines, especially when the geometrical shapes of objects are compared, contrasted, and analyzed. Classically, the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms. Despite its widespread use, the ordinary unweighted least-squares (LS) criterion can give erroneous solutions when the errors have heterogeneous variances (heteroscedasticity) or the errors are correlated, both common occurrences with real data. In contrast, maximum likelihood (ML) estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation. Here we provide a complete solution to the nonisotropic ML Procrustes problem assuming a matrix Gaussian distribution with factored covariances. Our analysis generalizes, simplifies, and extends results from previous discussions of the ML Procrustes problem. An iterative algorithm is presented for the simultaneous, numerical determination of the ML solutions.

Algorithms↗
PubMed1984

Cross validation of model predicting (ir)regularity of dental attendance.

A theoretical model developed for the prediction of (ir)regular dental attendance was evaluated with loglinear models (logit approach). The model found is identical to the model developed previously. The prediction of (ir)regularity, however, proved to be unsatisfactory. The disappointing result is attributed to the difficulty of measuring the predictors adequately, and to the possibility that additional variables might be needed.

Dental Care↗
PubMed1992

The mobile order theory versus UNIFAC and regular solution theory-derived models for predicting the solubility of solid substances.

The theory of mobile order of Huyskens is tested against the UNIFAC model, the regular solution model, and the extended Hildebrand or Hansen solubility approaches in predicting the solubility of naphthalene in both polar and nonpolar solvents at 40 degrees C. While all models correctly predict the solubility in nonpolar and moderately polar solvents, a substantial improvement is achieved by Huyskens' model, particularly in alcohols. This improvement originates from the correct description of the entropy effects as well as of the hydrophobic effects in the particular case of the alcohols. The model necessitates the knowledge of only one parameter not known a priori, i.e., the naphthalene modified nonspecific solubility parameter, the value of which is deduced from its solubility in hexane.

Models, Chemical↗
PubMed2006

A segmentation-based regularization term for image deconvolution.

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.

Algorithms↗
PubMed2005

A clockwork hypothesis: synaptic release by rod photoreceptors must be regular.

We can see at light intensities much lower than an average of one photon per rod photoreceptor, demonstrating that rods must be able to transmit a signal after absorption of a single photon. However, activation of one rhodopsin molecule (Rh*) hyperpolarizes a mammalian rod by just 1 mV. Based on the properties of the voltage-dependent Ca2+ channel and data on [Ca2+] in the rod synaptic terminal, the 1 mV hyperpolarization should reduce the rate of release of quanta of neurotransmitter by only 20%. If quantal release were Poisson, the distributions of quantal count in the dark and in response to one Rh* would overlap greatly. Depending on the threshold quantal count, the overlap would generate too frequent false positives in the dark, too few true positives in response to one Rh*, or both. Therefore, quantal release must be regular, giving narrower distributions of quantal count that overlap less. We model regular release as an Erlang process, essentially a mechanism that counts many Poisson events before release of a quantum of neurotransmitter. The combination of appropriately narrow distributions of quantal count and a suitable threshold can give few false positives and appropriate (e.g., 35%) efficiency for one Rh*.

Calcium Channels↗
PubMed1987

Solution structure of [d(GGTATACC)]2: wrinkled D structure of the TATA moiety.

Phase-sensitive two-dimensional nuclear Overhauser effect spectra of [d(GGTATACC)]2 in aqueous deuterium oxide solution at four mixing times were quantified to give all nonoverlapping cross-peak intensities. A structural model for [d(GGTATACC)]2 was built in which the GG- and -CC moieties were in the B-DNA form, while the middle -TATA- moiety was in the wrinkled-D form (BDB model). This model was subjected to energy refinement by molecular mechanics calculations with the program AMBER. Counterions (Na+) were added to neutralize the charges, and water molecules were placed bridging across the minor groove. A complete relaxation matrix analysis was used to calculate two-dimensional nuclear Overhauser effect spectra of [d(GGTATACC)]2 from the above models (before and after energy refinement) and from four other [d(GGTATACC)]2 structural models: regular A, crystalline A, regular B, and energy-minimized B. Among them, the energy-minimized BDB model yielded a set of theoretical spectra that gave the best fit to the experimental spectra. It was also the energetically most stable. Therefore, it is a good representation of the ensemble- and time-averaged structure of the octamer in solution. This model has backbone torsion angles similar to those of B-form DNA in the GG- and -CC moieties and torsion angles similar to those of wrinkled D form DNA in the -TATA- moiety. The base stacking and base pairing are not interrupted at the junctions between the two structural moieties. Its minor groove is narrower than that of B DNA, and the solvent-accessible surface of the minor groove forms a closed hydration tunnel in the middle -TATA- segment.

Adenine↗
PubMedDate not supplied

A computer model for intracellular pH regulation in Chinese hamster ovary cells.

A single-cell model for Chinese hamster ovary (CHO) cells has been extended to study the regulation of intracellular pH. This model provides for the first time a direct mechanistic linkage between intracellular pH control and cellular metabolism. Among the known mechanisms that regulate and disturb pHi, the Na/H antiport, effect of lactate and ammonia, proton leakage, and external pH have been included in the model. The ability of the model to predict both steady-state and transient pHi has been tested against experimental studies. The "regular model" that has been used to predict cell growth in suspension and batch cultures can predict the steady-state pHi and the transient response of pHi to an alkaline load well, but it had to be modified in terms of the maximum activity of the Na/H antiport in order to simulate the transient response of pHi to an acid load. The modification indicates the possibility that a cell could activate the Na/H antiport under acute acid load but return to its basal level of Na/H antiport activity under steady-state conditions, even when the cell interior is under low-pH conditions (6.7-7.0).

Amino Acids↗
PubMedDate not supplied

Mathematical modelling of bacterial growth at subinhibitory levels of aminoglycosides.

The subinhibitory effect of antibiotics has often been studied without any clear theoretical framework; we have chosen to use mathematical bacterial growth modelling as a useful tool to analyse these biological states in a more rigorous manner. Since their mode of action and molecular target are relatively well known, aminoglycosides were well suited for this more sophisticated study of subinhibitory action. We have shown that two models (the Monod and the logistic models) regularly used in bacteriology, were adequate to describe these effects in a glucose-limited medium. A change of model, according to antibiotic concentration, revealed the existence of two separate actions. At lower concentrations, inhibition affected mainly glucose use, the substrate remained limiting and growth mode did not change. As soon as the concentration exceeded a threshold, growth was totally disturbed, probably through a physiological "catastrophe". This threshold can be used to estimate bacterial susceptibility to these antibiotics.

Aminoglycosides↗