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PubMed2004

Dynamic diffusion model for tracing the real-time potential response of polymeric membrane ion-selective electrodes.

A numerical solution for the prediction of the time-dependent potential response of a polymeric-based ion-selective electrode (ISE) is presented. The model addresses short- and middle-term potential drifts that are dependent on changes in concentration gradients in the aqueous sample and organic membrane phase. This work has important implications for the understanding of the real-time response behavior of potentiometric sensors with low detection limits and with nonclassical super-Nernstian response slopes. As a model system, the initial exposure of membranes containing the well-examined silver ionophore O,O' '-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene was monitored, and the large observed potential drifts were compared to theoretical predictions. The model is based on an approximate solution of the diffusion equation for both aqueous and organic diffusion layers using a numerical scheme (finite difference in time and finite elements in space). The model may be evaluated on the basis of experimentally available parameters and gives time-dependent information previously inaccessible with a simpler steady-state diffusion model. For the cases studied, the model gave a very good correlation with experimental data, albeit with lower than expected diffusion coefficients for the organic phase. This model may address numerous open questions regarding the response time and memory effects of low-detection-limit ion-selective electrodes and for other membrane electrodes where ion fluxes are relevant.

Diffusion↗
PubMed2006

Classification of phase transitions in reaction-diffusion models.

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of nonequilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the "coordinate"- to the "phase"-space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero "energy." We identify four families of topologically distinct classes of phase portraits stable upon renormalization group transformations.

Journal Article↗
PubMed2000

TGFbeta2 acts as an "activator" molecule in reaction-diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture.

It was previously speculated that TGFbeta acts as an "activator"-molecule in chondrogenic pattern formation in the limb micromass culture system, but its precise role and relationship with the cell sorting phenomenon have not been properly studied. In the present study, we examined whether the TGFbeta2 molecule satisfies the necessary conditions for an "activator"-molecule in the reaction-diffusion model. Firstly, we showed that TGFbeta2 became localized at chondrogenic sites during the establishment of a chondrogenic pattern, and exogenous TGFbeta2 promoted chondrogenesis when added in the culture medium. Secondly, TGFbeta2 protein was shown to promote the production of its own mRNA after 3 hr, indicating that a positive feedback mechanism exists which may be responsible for the emergence of the chondrogenic pattern. We then found that when locally applied with beads, TGFbeta2 suppressed chondrogenesis around the beads, indicating it induces the lateral inhibitory mechanism, which is a key element for the formation of the periodic pattern. We also examined the possible effects of TGFbeta2 on the cell sorting phenomenon and found that TGFbeta2 exerts differential chemotactic activity on proximal and distal mesenchyme cells of the limb bud, and at very early phases of differentiation TGFbeta2 promotes the expression of N-cadherin protein which is known to be involved in pattern formation in this culture system. These findings suggest that TGFbeta2 acts as an "activator"-like molecule in chondrogenic pattern formation in vitro, and is possibly responsible for the cell sorting phenomenon.

Animals↗
PubMed2001

Diffusion model of pain language and quality of life in orofacial pain patients.

AIMS: To address the following questions: (1) Which words are preferred by different groups of orofacial pain patients to describe their pain experience? (2) Is it possible, based on such descriptions, to obtain a clinical differential diagnosis in these patients? (3) Is there any relationship between the verbal description of pain and self-rated quality of life (QOL)? (4) Can a pattern of modulation of pain language by affective variables (diffusion model) be recognized in orofacial pain patients, as it has in other chronic pain patients? and (5) If so, what might be the clinical usefulness of assessing pain language in these patients? METHODS: A total of 332 consecutive orofacial pain patients filled out an Italian Pain Questionnaire (the Italian analog of the McGill Pain Questionnaire) and were then divided into 6 diagnostic subgroups (sample 1) based on history and clinical findings. In a double-blind setting, the distribution of pain descriptors and indexes was statistically evaluated. From sample 1, a randomly selected sample of 121 patients (sample 2) also filled out a QOL categorical scale. The results of both tests in this sample were compared statistically. RESULTS: Some significant differences among diagnostic subgroups were found for choice of descriptors and for pain intensity. When a patient's pain description was compared to the corresponding self-evaluation of QOL, a self-perceived worsening of QOL revealed a good correlation with an increase in the number of words chosen, pain intensity, and affective and sensory pain descriptors. A similar significant association was found between self-assessed anxiety and/or depression and the same items. CONCLUSION: Although trends in patients' choice of descriptors were evident, differential diagnosis based on only a pain questionnaire was not possible in the different groups of orofacial pain patients examined in this study. The present study suggests the presence of a phenomenon of diffusion in the language of those patients who were experiencing a worsening of their QOL as a result of pain and consequent psychologic distress. This observation can be of clinical usefulness by enhancing the sensitivity of the clinician to the suffering and affective distress experienced by the patient, and it also can be helpful in refining the therapeutic approach for each individual patient.

Adolescent↗
PubMed2005

Nonlocal polymerization-driven diffusion-model-based examination of the scaling law for holographic data storage.

For the first time to our knowledge, a detailed theoretical basis is provided for the well-known inverse-square scaling law of holographic diffraction, which states that replay diffraction efficiency eta = gamma/M2, where M is the number of gratings stored and gamma is a constant system parameter. This law is shown to hold for photopolymer recording media governed by the predictions of the nonlocal polymerization-driven diffusion model. On the basis of the analysis, we (i) propose a media inverse scaling law, (ii) relate gamma to photopolymer material parameters and the hologram geometry and replay conditions, and (iii) comment on the form and validity of the diffraction efficiency inverse-square scaling law for higher-diffraction-efficiency gratings.

Journal Article↗
PubMed1993

Analysis of skin penetration enhancement based on a two-layer skin diffusion model with polar and nonpolar routes in the stratum corneum: dose-dependent effect of 1-geranylazacycloheptan-2-one on drugs with different lipophilicities.

The effects of 1-geranylazacycloheptan-2-one (GACH) on the in vitro skin penetration of seven drugs with various lipophilicities were studied. The penetration of drugs from aqueous vehicle through the guinea pig skin was increased depending on the pretreatment dose of GACH. The largest enhancement was observed for 5-fluorouracil (5-FU) and a bell-shaped relationship was obtained between enhancement ratio and the octanol/water partition coefficients of drugs. Further, Laplace transformed equations for percutaneous absorption of drug were derived from Fick's second law based on a two-layer skin diffusion model with polar and nonpolar routes in the stratum corneum. Through curve-fitting of their equations to penetration profiles using a nonlinear regression program MULTI(FILT) combined with a fast inverse Laplace transform (FILT) algorithm, the action mechanism of GACH was discussed in terms of its effect on the partitioning and diffusivity of drugs in each domain. With an increase in pretreatment dose of GACH, the estimated partition parameters of drugs into the nonpolar route increased but their diffusivities were little affected. The analysis based on a linear free-energy relationship suggested that the increase in partitioning of drugs into the nonpolar route was explained by its increasing polarity with GACH pretreatment.

Algorithms↗
PubMed1993

A diffusion model of early visual search: theoretical analysis and experimental results.

Meinecke (1989, Exp. 1, cond. HO) showed that the detectability of a visual target embedded in a linear noise array decreases with increasing retinal eccentricity, while the reaction time (RT) of the hits increases. One of the most interesting features of her results was that the RT of the correct rejections is consistently larger than the RT for signals presented near the fovea. This finding suggests that initially visual attention is concentrated near the fixation point and then diffuses across the stimulus array to perform a serial, exhaustive search. We present a diffusion model of early visual-search processes that quantitatively describes this evolution of attention in time and space; in contrast to most previous conceptions, it is based on a genuine relation between the spatial and temporal dimensions of the search processes performed. The model predicts quantitatively both detection performance and RT. We conducted an experiment similar to that of Meinecke (1989), but with an additional variation of the presentation time. All the main features of the 189 predictions could be explained by the model. The interpretation of the four model's parameters is discussed in some detail and compared with previous estimates of the microscopic search speed derived from alternative models. Finally, we consider some possible modifications related to results of Kehrer (1987, 1989), and some generalizations to multi target detection and two-dimensional stimulus arrays.

Adult↗
PubMed2002

A reaction-diffusion model for interference in meiotic crossing over.

One crossover point between a pair of homologous chromosomes in meiosis appears to interfere with occurrence of another in the neighborhood. It has been revealed that Drosophila and Neurospora, in spite of their large difference in the frequency of crossover points, show very similar plots of coincidence-a measure of the interference-against the genetic distance of the interval, defined as one-half the average number of crossover points within the interval. We here propose a simple reaction-diffusion model, where a "randomly walking" precursor becomes immobilized and matures into a crossover point. The interference is caused by pair-annihilation of the random walkers due to their collision and by annihilation of a random walker due to its collision with an immobilized point. This model has two parameters-the initial density of the random walkers and the rate of its processing into a crossover point. We show numerically that, as the former increases and/or the latter decreases, plotted curves of the coincidence vs. the genetic distance converge on a unique curve. Thus, our model explains the similarity between Drosophila and Neurospora without parameter values adjusted finely, although it is not a "genetic model" but is a "physical model," specifying explicitly what happens physically.

Crossing Over, Genetic↗
PubMed2006

Film-pore-concentration-dependent surface diffusion model for the adsorption of dye onto palm kernel shell activated carbon.

The rate of dye adsorption from aqueous effluents onto palm kernel shell (PKS) activated carbon has been studied experimentally using the batch adsorption method. The adsorption rates of methylene blue on PKS for systems of different initial dye concentrations are modeled using a film-pore-concentration dependent surface diffusion (FPCDSD) model. The FPCDSD model is sufficiently general and can be reduced easily to describe other simplified models. Using the FPCDSD model, only a single set of mass transfer parameters is required to describe the methylene blue/PKS system for different initial concentrations. A different set of mass transfer parameters are needed to obtain the best fitting if the pore diffusion is not included in the model.

Journal Article↗
PubMed1997

An in vitro diffusion model for the study of calcification of bovine pericardium tissue.

Bovine pericardium (BP) is extensively used for the production of heart valve bioprostheses. BP has excellent mechanical properties but a limited lifespan because of intrinsic subsurface calcification in vivo. In this study, the in vitro mineralization of BP was investigated by a novel diffusion cell model. In two sets of experiments, glutaraldehyde-treated BP membranes were placed between two compartments, both of which contained calcium phosphate solutions made by equilibration of octacalcium phosphate (Exp I) or dicalcium phosphate dihydrate (Exp II) in phosphoric acid. The movement of calcium (Ca), phosphate (P), and protons through the BP membrane was followed throughout the diffusion process. Histology, scanning electron microscopy, wet chemical analysis, and energy dispersive X-ray analyses provided good evidence of subsurface mineralization of BP that resembled in vivo mineral deposition. Energy dispersive x-ray microanalyses found a Ca/P heterogeneity of the early subsurface mineral that formed in the membrane. The use of a diffusion cell to model BP calcification under well-characterized conditions has led to in vitro mineralization that more closely matches that observed in vivo. The results suggest that this in vitro diffusion model can be used to study the mechanism of pathological mineralization. This model has the potential to provide rapid, inexpensive, basic information about the mineralization process.

Animals↗
PubMed2001

Two-species D-dimensional diffusive model and its mapping onto a growth model.

In this work, we consider a diffusive two-species d-dimensional model and study it in great detail. Two types of particles, with hard core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density, the instantaneous, as well as noninstantaneous, two-point correlation functions for various initial conditions. We study the impact of correlations in the initial state on the dynamics. Finally, we map the one-dimensional version of the model under consideration onto a restricted solid-on-solid growth model with three states and solve its dynamics.

Journal Article↗
PubMed2006

Dual diffusion model for single-cell recording data from the superior colliculus in a brightness-discrimination task.

Monkeys made saccades to one of two peripheral targets based on the brightness of a central stimulus. Task difficulty was manipulated by varying the ratio of stimulus black-and-white pixels. Correct response probability for two monkeys varied directly with difficulty. Deep layer SC neurons exhibited robust presaccadic activity the magnitude of which was unaffected by task difficulty when the stimulus specified a saccade toward a target within the neuron's response field. Activity after stimuli specifying saccades to targets outside the response field was affected by task difficulty, increasing as the task became more difficult. A quantitative model derived from studies of human decision-making was fit to the behavioral data. The model assumes that information from the stimulus drives two independent diffusion processes. Simulated paths from the model were compared with neuron activity, assuming that firing rate is linearly related to position in the accumulation process. The firing rate data show delayed availability of discriminative information for fast, intermediate, and slow decisions when activity is aligned on the stimulus and very small differences in discriminative information when aligned on the saccade. The model produces exactly these patterns of results. The accumulation process is highly variable, allowing the process both to make errors, as is the case for the behavioral performance, and also to account for the firing rate results. Thus the dual diffusion model provides a quantitative account for both the behavior in a simple decision-making task as well as the patterns of activity in competing populations of neurons.

Animals↗
PubMedDate not supplied

[Traveling waves in cross-diffusion models of population dynamics].

"Traveling wave"--type solutions of some models with cross-diffusion were considered. It was shown that "cross-diffusion" terms, as opposed to "diffusion" terms, do not increase the dimensionality of the automodel system. The bifurcation approach was used to study the dependence of the wave solutions on the parameters of the models being considered, and the waves were classified. It was shown that, at the same parameter values, both "fast" and "slow" waves can exist and that these waves are described by different automodel systems.

Models, Theoretical↗
PubMed1993

A theoretical study of rotational diffusion models for rod-shaped viruses. The influence of motion on 31P nuclear magnetic resonance lineshapes and transversal relaxation.

Information about the interaction between nucleic acids and coat proteins in intact virus particles may be obtained by studying the restricted backbone dynamics of the incapsulated nucleic acids using 31P nuclear magnetic resonance (NMR) spectroscopy. In this article, simulations are carried out to investigate how reorientation of a rod-shaped virus particle as a whole and isolated nucleic acid motions within the virion influence the 31P NMR lineshape and transversal relaxation dominated by the phosphorus chemical shift anisotropy. Two opposite cases are considered on a theoretical level. First, isotropic rotational diffusion is used as a model for mobile nucleic acids that are loosely or partially bound to the protein coat. The effect of this type of diffusion on lineshape and transversal relaxation is calculated by solving the stochastic Liouville equation by an expansion in spherical functions. Next, uniaxial rotational diffusion is assumed to represent the mobility of phosphorus in a virion that rotates as a rigid rod about its length axis. This type of diffusion is approximated by an exchange process among discrete sites. As turns out from these simulations, the amplitude and the frequency of the motion can only be unequivocally determined from experimental data by a combined analysis of the lineshape and the transversal relaxation. In the fast motional region both the isotropic and the uniaxial diffusion model predict the same transversal relaxation as the Redfield theory. For very slow motion, transversal relaxation resembles the nonexponential relaxation as observed for water molecules undergoing translational diffusion in a magnetic field gradient. In this frequency region T2e is inversely proportional to the cube root of the diffusion coefficient. In addition to the isotropic and uniaxial diffusion models, a third model is presented, in which fast restricted nucleic acid backbone motions dominating the lineshape are superimposed on a slow rotation of the virion about its length axis, dominating transversal relaxation. In an accompanying article the models are applied to the 31P NMR results obtained for bacteriophage M13 and tobacco mosaic virus.

Bacteriophages↗
PubMed2002

Y genetic data support the Neolithic demic diffusion model.

There still is no general agreement on the origins of the European gene pool, even though Europe has been more thoroughly investigated than any other continent. In particular, there is continuing controversy about the relative contributions of European Palaeolithic hunter-gatherers and of migrant Near Eastern Neolithic farmers, who brought agriculture to Europe. Here, we apply a statistical framework that we have developed to obtain direct estimates of the contribution of these two groups at the time they met. We analyze a large dataset of 22 binary markers from the non-recombining region of the Y chromosome (NRY), by using a genealogical likelihood-based approach. The results reveal a significantly larger genetic contribution from Neolithic farmers than did previous indirect approaches based on the distribution of haplotypes selected by using post hoc criteria. We detect a significant decrease in admixture across the entire range between the Near East and Western Europe. We also argue that local hunter-gatherers contributed less than 30% in the original settlements. This finding leads us to reject a predominantly cultural transmission of agriculture. Instead, we argue that the demic diffusion model introduced by Ammerman and Cavalli-Sforza [Ammerman, A. J. & Cavalli-Sforza, L. L. (1984) The Neolithic Transition and the Genetics of Populations in Europe (Princeton Univ. Press, Princeton)] captures the major features of this dramatic episode in European prehistory.

Animals↗
PubMed2000

A simplified approach for modeling diffusion into cells.

Regulation of the intracellular concentration of substrates is essential for the maintenance of a stable cellular environment. Diffusion and reaction processes supply and consume substrates within cells and determine their steady-state concentrations. To realistically represent these processes by computer simulation they must be modeled in three dimensions. Yet three-dimensional models are inherently computing intensive. This study describes a method, which substantially simplifies the modeling of diffusion into a polyhedral body (a cube), that was used as a model representation of a cell. The method is applied to a case study of oxygen diffusion into nitrogen-fixing, rhizobia-infected cells in legume nodules. The method involved generating a one-dimensional representation of the three-dimensional problem to provide a "surface area profile" of three-dimensional diffusion. The one-dimensional models were significantly easier to program, several orders of magnitude faster to solve and in this study were validated by assessing their results against those of comparable three-dimensional models of diffusion into the same body. The results show the one-dimensional method to be a close approximation of a three-dimensional source-sink problem with systematic differences below 10% for fractional oxygenation of leghemoglobin, cell respiration and nitrogenase activity. Larger differences between models (up to 45%) in the predicted average and innermost O(2)concentrations had no effects on the physiological conclusions of the study, but were attributed to the poorer resolution of the three- than the one-dimensional model, and to an inherent simplification in the derivation of the one-dimensional surface area profiles. The one-dimensional modeling approach was found to be a simple, yet powerful tool for the study of diffusion and reaction in biological systems.

Cell Membrane Permeability↗
PubMed2005

Morphogen gradient formation in a complex environment: an anomalous diffusion model.

Current models of morphogen-induced patterning assume that morphogens undergo normal, or Fickian, diffusion, although the validity of this assumption has never been examined. Here we argue that the interaction of morphogens with the complex extracellular surrounding may lead to anomalous diffusion. We present a phenomenological model that captures this interaction, and derive the properties of the morphogen profile under conditions of anomalous (non-Fickian) diffusion. In this context we consider the continuous time random walk formalism and extend its application to account for degradation of morphogen particles. We show that within the anomalous diffusion model, morphogen profiles are fundamentally distinct from the corresponding Fickian profiles. Differences were found in several key aspects, including the role of degradation in determining the profile, the rate by which it spreads in time and its long-term behavior. We analyze the effect of an abrupt change in the extracellular environment on the concentration profiles. Furthermore, we discuss the robustness of the morphogen distribution to fluctuations in morphogen production rate, and describe a feedback mechanism that can buffer such fluctuations. Our study also provides rigorous criteria to distinguish experimentally between Fickian and anomalous modes of morphogen transport.

Algorithms↗
PubMed2005

Modelling diffusive O(2) supply to isolated preparations of mammalian skeletal and cardiac muscle.

The purpose of this study was to use A. V. Hill's equation describing diffusion of O(2) into cylindrical muscles to assess the adequacy of O(2) supply for commonly used isolated preparations of mammalian cardiac and skeletal muscles. The diffusion equation was solved numerically to give the maximum, steady state O(2) diffusion distances (i.e. the distance from the surface of the muscle to the radial location where P(O(2)) is 0) for both resting and contracting muscles and for a range of temperatures. Non-steady state solutions for the rest-to-work transition were also determined to estimate how long contractile activity could be continued before anoxia develops at the muscle centre. The influence on muscle oxygenation of myoglobin-facilitated O(2) diffusion was also assessed. The analysis was performed for typical sized, whole muscles from adult rats and mice, for frog sartorius muscle and for a range of temperatures. Muscle O(2) consumption rates were taken from the literature. The results indicated that (1) diffusive O(2) supply would be adequate to support resting metabolism of soleus and EDL muscles of rat and mouse but may not be adequate to support the transient high resting metabolic rate of papillary muscles shortly after dissection, (2) during steady contractile activity of soleus and EDL muscles, particularly those from the rat, over a reasonable range of duty cycles, adequate O(2) supply could only be ensured if the radii of preparations was substantially smaller than those of whole muscles and (3) for cardiac muscles, diffusive O(2) supply could only support steady-state metabolism at twitch frequencies <1 Hz for whole papillary muscles from rat and <3 Hz for those from mouse. Reducing experimental temperature markedly enhances O(2) supply to skeletal, but not cardiac, muscle. O(2) supply from myoglobin had only minimal effects on oxygenation under typical isolated muscle conditions.

Animals↗