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Mathematical Modeling (mathematical + modeling)
Selected AbstractsRe: Mathematical Modeling of Donor Skin,Sparing Full-Thickness Skin Grafts,Something Doesn't Add UpDERMATOLOGIC SURGERY, Issue 4 2010WANG QIANG MDArticle first published online: 30 MAR 2010 No abstract is available for this article. [source] Mathematical Modeling of Microbial Growth in Packaged Refrigerated Orange Juice Treated with Chemical PreservativesJOURNAL OF FOOD SCIENCE, Issue 5 2001S.C. Andrés ABSTRACT Microbial flora of refrigerated orange juice was analyzed during storage at 10 °C and the effects of the following factors were discussed: 1) the previous washing process of the orange peel, 2) the different levels of the added preservatives (citric acid, ascorbic acid, potassium sorbate, sodium benzoate), 3) the gaseous permeabilities of the packaging film. Gompertz equation was applied to model molds and yeasts growth for the different treatments and packaging conditions. The washing procedure with sodium hypochlorite extend 2,3 d the storage life of the juice (time to reach microbial counts of 106 CFU/ml) in both packaging films. The use of organic acids and potassium sorbate or sodium benzoate (1.66,6.94 mM) led to storage life values > 11 d in polyethylene and > 20 d in the low gaseous permeability film, maintaining good sanitary conditions. [source] Recent Advances in Mathematical Modeling of Flow and Heat Transfer Phenomena in Glass FurnacesJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 5 2002Manoj K. Choudhary This paper reviews significant advances in the mathematical modeling of flow and heat transfer phenomena in glass furnaces during the period 1996,2000. It describes developments in both the fundamental/scientific and practical aspects of modeling. The topics reviewed include developments in (a) model formulation and modeling techniques, (b) postprocessing modeling of glass quality and environmental emissions, (c) measurement of thermodynamic and transport properties of melt relevant to modeling, and (d) incorporation of model-based knowledge into process control schemes. These developments are critically examined and assessed from an industrial perspective, and topics needing further research and development efforts are identified. [source] Mathematical Modeling of Homopolymerization on Supported Metallocene CatalystsMACROMOLECULAR MATERIALS & ENGINEERING, Issue 5 2004Alessio Alexiadis Abstract Summary: In this paper, a mathematical model describing olefin polymerization with metallocene catalysts is presented. It is an improvement of a previous model, the "particle growth model" (PGM) proposed by, among others, one of the authors of the present work and derives from the so-called "multigrane model" (MGM). The main differences between this work and others is a more sophisticated approach to fragmentation with respect to the MGM. Additionally, there is a more specific modeling for the unfragmented core with respect to the PGM. The numerical results obtained by the model are compared with experimental data. The results of this work allow to extend the PGM to catalysts with lower activity. The importance of those catalysts depends on the fact that high activity catalysts could bring, in some cases, too poor polymer morphology. Geometrical representation of the micro- and macroparticle. [source] Mathematical Modeling of Atom-Transfer Radical CopolymerizationMACROMOLECULAR REACTION ENGINEERING, Issue 4 2007Mamdouh Al-Harthi Abstract A comprehensive mathematical model for atom transfer radical copolymerization in a batch reactor is presented using the concept of pseudo-kinetic rate constants and the method of moments. The model describes molecular weight, monomer conversion, polydispersity index, and copolymer composition as a function of polymerization time. Model predictions were compared with experimental data for styrene and butyl acrylate copolymerization and excellent agreement was obtained. We have also tested the model with styrene-acrylonitrile copolymerization data obtained in our laboratory. Finally, we used the model to study the effect of comonomer reactivity ratio, feed composition, activation and deactivation rate constants on the copolymer composition. [source] Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 , Numerical Inversion MethodsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 6 2010Mariano Asteasuain Abstract This is the first of two papers presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of the infinite mass balances describing the evolution of a two-dimensional distribution using 2D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2D pgfs are developed and carefully validated. The accuracy obtained with both methods was very satisfactory. The inversion formulas of both methods are simple and easy to implement. A simple copolymerization example is used to show the complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution. [source] Kinetic Study of the Thermopolymerization of Furfuryl Methacrylate in Bulk by Mathematical Modeling.MACROMOLECULAR THEORY AND SIMULATIONS, Issue 9 2009Part A: Simulation of Experimental Data, Sensitivity Analysis of Kinetic Parameters Abstract Mathematical modeling of the thermopolymerization of FM and CMFMA was carried out using a cross-linked kinetic model proposed for the photo-initiated polymerization of acryl-furanic compounds. In this model, the photochemical initiation step was substituted by a thermal one and it was assumed that the constant of radical termination was time-dependent, which allowed the gel effect (Trommsdorff) at high monomer conversion to be simulated. Optimization of all kinetic constants was achieved and the results of simulation suitably fitted the experimental data of the monomer conversion. The contribution of each step in the mechanism and its dependence on the experimental conditions were estimated by a sensitivity analysis technique. [source] Mathematical Modeling of Atom-Transfer Radical Polymerization Using Bifunctional InitiatorsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 3 2006Mamdouh Al-Harthi Abstract Summary: Bifunctional initiators can produce polymers with higher molecular weight at higher initiator concentrations than monofunctional initiators. In this study, we developed a mathematical model for ATRP with bifunctional initiators. The most important reactions in ATRP were included in the model. The method of moments was used to predict monomer conversion, average molecular weights and polydispersity index as a function of polymerization time in batch reactors. The model was used to understand the mechanism of ATRP and to quantify how polymerization conditions affect monomer conversion and polymer properties by examining the effect of several rate constants (activation, deactivation, propagation and chain termination) and of catalyst and initiator concentration on polymerization kinetics and polymer properties. When compared to monofunctional initiators, bifunctional initiators not only produce polymers with higher molecular weight averages at higher polymerization rates, but also control their molecular weight distributions more effectively. Effect of initial catalyst concentration on polydispersity index as a function of time. [source] Axial Distribution of Oxygen Concentration in Different Airlift Bioreactor Scales: Mathematical Modeling and SimulationCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 9 2006H. Znad Abstract Steady and unsteady state oxygen concentration distributions in the liquid and gas phases along the axial direction of different airlift bioreactor scales have been simulated for various gas flow rates and oxygen consumption rates by applying the axial dispersion model to the riser and the downcomer, and a complete mixing model for the top (separator) and the bottom sections of the bioreactor. The results show that the dissolved oxygen concentration is very low at the lower part of the downcomer when the rate of oxygen consumption by microorganisms is very high. Furthermore, the shorter (small) bioreactor shows relatively more uniform axial dissolved oxygen concentrations than the longer (large) bioreactor, due to the effect of the hydrostatic pressure along the bioreactor. One of the most important geometric factors for mass transfer is the reactor height, which dominates the mean pressure and thus influences the saturation concentration and mass transfer driving force. The presented model can be applied for modeling and scale-up of practical airlift bioreactors. [source] Experiment and Mathematical Modeling of Solid Formation at Spray DryingCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 5 2004P. Seydel The process of solid formation during spray drying has been described many times in the literature, however, a detailed mathematical description of the time-dependent process concerning the structure of the particles as a function of substance and process parameters is still not available. In the present work, a time-dependent and local modeling of the mass and energy transport processes during solid formation inside the droplet was carried out. The model was validated against reproducible experiments performed in a vertical pipe with single drop generation. [source] Mathematical and experimental insights into the development of the enteric nervous system and Hirschsprung's DiseaseDEVELOPMENT GROWTH & DIFFERENTIATION, Issue 4 2007Kerry A. Landman The vertebrate enteric nervous system is formed by a rostro-caudally directed invasion of the embryonic gastrointestinal mesenchyme by neural crest cells. Failure to complete this invasion results in the distal intestine lacking intrinsic neurons. This potentially fatal condition is called Hirschsprung's Disease. A mathematical model of cell invasion incorporating cell motility and proliferation of neural crest cells to a carrying capacity predicted invasion outcomes to imagined manipulations, and these manipulations were tested experimentally. Mathematical and experimental results agreed. The results show that the directional invasion is chiefly driven by neural crest cell proliferation. Moreover, this proliferation occurs in a small region at the wavefront of the invading population. These results provide an understanding of why many genes implicated in Hirschsprung's Disease influence neural crest population size. In addition, during in vivo development the underlying gut tissues are growing simultaneously as the neural crest cell invasion proceeds. The interactions between proliferation, motility and gut growth dictate whether or not complete colonization is successful. Mathematical modeling provides insights into the conditions required for complete colonization or a Hirschsprung's-like deficiency. Experimental evidence supports the hypotheses suggested by the modeling. [source] Influence of heavy metals on microbial growth kinetics including lag time: Mathematical modeling and experimental verification,ENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 10 2009S. Sevinç, engör Abstract Heavy metals can significantly affect the kinetics of substrate biodegradation and microbial growth, including lag times and specific growth rates. A model to describe microbial metabolic lag as a function of the history of substrate concentration has been previously described by Wood et al. (Water Resour Res 31:553,563) and Ginn (Water Resour Res 35:1395,1408). In the present study, this model is extended by including the effect of heavy metals on metabolic lag by developing an inhibitor-dependent functional to account for the metabolic state of the microorganisms. The concentration of the inhibiting metal is explicitly incorporated into the functional. The validity of the model is tested against experimental data on the effects of zinc on Pseudomonas species isolated from Lake Coeur d'Alene sediments, Idaho, USA, as well as the effects of nickel or cobalt on a mixed microbial culture collected from the aeration tank of a wastewater treatment plant in Athens, Greece. The simulations demonstrate the ability to incorporate the effect of metals on metabolism through lag, yield coefficient, and specific growth rates. The model includes growth limitation due to insufficient transfer of oxygen into the growth medium. [source] Cell-free ethanol production: the future of fuel ethanol?JOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 2 2007Eric J. Allain Abstract The production of fuel ethanol from renewable resources as an economically viable alternative to gasoline is currently the subject of much research. Most studies seek to improve process efficiency by increasing the rate of ethanol production; ultimately, this approach will be limited by the selected ethanol-producing microorganism. Cell-free ethanol production, using only the enzymes involved in the conversion of glucose to ethanol, may offer a practical and beneficial alternative. Mathematical modeling of such a system has suggested that a cell-free process should be capable of producing ethanol much more efficiently than the microbial based process. This finding along with other potential benefits of a microorganism-free process suggests that a cell-free process might significantly improve the economy of fuel ethanol production and is a worthy target for further research. Copyright © 2007 Society of Chemical Industry [source] Mathematical modeling of gas-phase biofilter performanceJOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 7 2003Hasnaa Jorio Abstract In the present paper, a new mathematical model describing the physical, chemical and biological phenomena involved in the process of contaminant removal in biofilters is developed. In addition to the contaminant, the key components of the present theoretical model are carbon dioxide and oxygen. The model predicts the concentration profile of the key components in the gas phase, the biofilm and the sorption liquid retained in the solid particles composing the filter bed at both steady and transient regimes. The model equations were solved numerically and comparison between theory and experiment showed that the model results for styrene and carbon dioxide concentration profiles were in very good agreement with experimental data for the biofiltration of styrene vapors at steady state. The analysis of oxygen concentration profile in the biofilm predicted by the theoretical model revealed that oxygen limitation does not occur under the operating styrene biodegradation rate in the biofilter. Copyright © 2003 Society of Chemical Industry [source] Mathematical modeling of solid oxide fuel cells at high fuel utilization based on diffusion equivalent circuit modelAICHE JOURNAL, Issue 5 2010Cheng Bao Abstract Mass transfer and electrochemical phenomena in the membrane electrode assembly (MEA) are the core components for modeling of solid-oxide fuel cell (SOFC). The general MEA model is simply governed with the Stefan-Maxwell equation for multicomponent gas diffusion, Ohm's law for the charge transfer and the current-overpotential equation for the polarization calculation. However, it has obvious discrepancy at high-fuel utilization or high-current density. An advanced MEA model is introduced based on the diffusion equivalent circuit model. The main purpose is to correct the real-gas concentrations at the triple-phase boundary by assuming that the resistance of surface diffusion is in series with that of the gaseous bulk diffusion. Thus, it can obtain good prediction of cell performance in a wide range by avoiding the decrement of effective gas diffusivity via unreasonable increment of the electrode tortuosity in the general MEA model. The mathematical model has been validated in the cases of H2H2O, COCO2 and H2CO fuel system. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Mathematical modeling of water uptake through diffusion in 3D inhomogeneous swelling substratesAICHE JOURNAL, Issue 7 2009L. R. van den Doel Abstract Diffusion-driven water uptake in a substrate (imbibition) is a subject of great interest in the field of food technology. This is a particular challenge for rice grains that are preprocessed to accelerate the water uptake, i.e., to reduce the cooking time. Rice preprocessing disrupts the mesostructural order of starch and induces a microporous structure in the grains. The meso- and microstructural length scales have not been considered in joint approach until now. The (re)hydration of rice grains can be modeled by free (concentration-driven) diffusion or by water demand-driven diffusion. The latter is driven by the ceiling moisture content related to the extent of gelatinization of the rice substrate network. This network can be regarded as a fractal structure. As the spatial resolution of our models is limited, we choose to model the apparent water transport by a set of coupled partial differential equations (PDEs). Current models of water uptake are often limited to a single dimension, and the swelling of the substrate is not taken into account. In this article, we derive a set of PDEs to model water uptake in a three-dimensional (3D) inhomogeneous substrate for different types of water diffusion as well as the swelling of the substrate during water uptake. We will present simulation results for different 3D (macroscopic) structures and diffusion models and compare these results, qualitatively, with the experimental results acquired from magnetic resonance imaging. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Mathematical modeling of appendicular bone growth in glaucous-winged gullsJOURNAL OF MORPHOLOGY, Issue 1 2009James L. Hayward Abstract Development of locomotor activity is crucial in tetrapods. In birds, this development leads to different functions for hindlimbs and forelimbs. The emergence of walking and flying as very different complex behavior patterns only weeks after hatching provides an interesting case study in animal development. We measured the diaphyseal lengths and midshaft diameters of three wing bones (humerus, ulna, and carpometacarpus) and three leg bones (femur, tibiotarsus, and tarsometatarsus) of 79 juvenile (ages 0,42 days) and 13 adult glaucous-winged gulls (Larus glaucescens), a semiprecocial species. From a suite of nine alternative mathematical models, we used information-theoretic criteria to determine the best model(s) for length and diameter of each bone as a function of age; that is, we determined the model(s) that obtained the best tradeoff between the minimized sum of squared residuals and the number of parameters used to fit the model. The Janoschek and Holling III models best described bone growth, with at least one of these models yielding an R2 , 0.94 for every dimension except tarsometatarsus diameter (R2 = 0.87). We used the best growth models to construct accurate allometric comparisons of the bones. Early maximal absolute growth rates characterize the humerus, femur, and tarsometatarsus, bones that assume adult-type support functions relatively early during juvenile development. Leg bone lengths exhibit more rapid but less sustained relative growth than wing bone lengths. Wing bone diameters are initially smaller than leg bone diameters, although this relationship is reversed by fledging. Wing bones and the femur approach adult length by fledging but continue to increase in diameter past fledging; the tibiotarsus and tarsometatarsus approach both adult length and diameter by fledging. In short, the pattern of bone growth in this semiprecocial species reflects the changing behavioral needs of the developing organism. J. Morphol., 2009. © 2008 Wiley-Liss, Inc. [source] Spatially patterned gene expression for guided neurite extensionJOURNAL OF NEUROSCIENCE RESEARCH, Issue 4 2009Tiffany Houchin-Ray Abstract Axon pathfinding by localized expression of guidance molecules is critical for the proper development of the nervous system. In this report, we present a well-defined spatially patterned gene expression system to investigate neurite guidance in vitro. Nonviral gene delivery was patterned by combining substrate-mediated gene delivery with soft lithography techniques, and the amount of protein produced at the region of localized expression was varied by altering the vector concentration and the width of the pattern, highlighting the flexibility of the system. A neuronal coculture model was used to investigate responses to spatial patterns of nerve growth factor (NGF) expression. The soluble NGF gradient elicited a guidance cue, and the degree of guidance was governed by the distance a neuron was cultured from the pattern and the time between accessory cell and neuron seedings. A portion of the diffusible NGF bound to the culture surface in the extracellular space, and the surface-associated NGF supported neuron survival and neurite outgrowth. However, the surface-bound NGF gradient alone did not elicit a guidance signal, and in fact masked the guidance cue by soluble NGF gradients. Mathematical modeling of NGF diffusion was used to predict the concentration gradients, and both the absolute and fractional gradients capable of guiding neurites produced by patterned gene expression differed substantially from the values obtained with existing engineered protein gradients. Spatially patterned gene expression provides a versatile tool to investigate the factors that may promote neurite guidance. © 2008 Wiley-Liss, Inc. [source] Mathematical modeling of 13C label incorporation of the TCA cycle: The concept of composite precursor functionJOURNAL OF NEUROSCIENCE RESEARCH, Issue 15 2007Kai Uffmann Abstract A novel approach for the mathematical modeling of 13C label incorporation into amino acids via the TCA cycle that eliminates the explicit calculation of the labeling of the TCA cycle intermediates is described, resulting in one differential equation per measurable time course of labeled amino acid. The equations demonstrate that both glutamate C4 and C3 labeling depend in a predictible manner on both transmitochondrial exchange rate, VX, and TCA cycle rate, VTCA. For example, glutamate C4 labeling alone does not provide any information on either VX or VTCA but rather a composite "flux". Interestingly, glutamate C3 simultaneously receives label not only from pyruvate C3 but also from glutamate C4, described by composite precursor functions that depend in a probabilistic way on the ratio of VX to VTCA: An initial rate of labeling of glutamate C3 (or C2) being close to zero is indicative of a high VX/VTCA. The derived analytical solution of these equations shows that, when the labeling of the precursor pool pyruvate reaches steady state quickly compared with the turnover rate of the measured amino acids, instantaneous labeling can be assumed for pyruvate. The derived analytical solution has acceptable errors compared with experimental uncertainty, thus obviating precise knowledge on the labeling kinetics of the precursor. In conclusion, a substantial reformulation of the modeling of label flow via the TCA cycle turnover into the amino acids is presented in the current study. This approach allows one to determine metabolic rates by fitting explicit mathematical functions to measured time courses. © 2007 Wiley-Liss, Inc. [source] Role of mathematical modeling on the optimal control of HIV-1 pathogenesisAICHE JOURNAL, Issue 3 2006Marcel Joly Abstract Mathematical modeling of HIV-1 infection has proven to be instrumental for the modern understanding basis of the AIDS pathogenesis, since it offers the unique means to adequately pose hypotheses concerning AIDS dynamics and treatment protocols. Focusing on the HIV-1 subtype-B epidemic, a comprehensive review and discussion of the state-of-the-art in the area is presented. Based on recent results, this multidisciplinary study is then extended to a more in-depth view at the cellular and molecular biology levels that address key issues concerned with the natural history of AIDS, as the basic human anatomic model, the host cell entry of HIV-1, the quantification the HIV-1 infectivity in terms of viral coreceptor specificity, as well as regulation and expression of CCR5 and CXCR4 molecules on the target cell, the T-lymphocyte generation and infection models, and the immune response model. In the sequence, modeling techniques for AIDS pathogenesis are revised and models concerned with either the general HIV-1 dynamics or specifically related to the HIV-1 primary infection are discussed. Ultimately, a general framework for the real-world problem of optimizing the highly active antiretroviral therapy (HAART) benefits is proposed regarding the important questions associated with the drug chemotherapy resistance, side effects and costs. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Mathematical modeling of 980-nm and 1320-nm endovenous laser treatmentLASERS IN SURGERY AND MEDICINE, Issue 3 2007Serge R. Mordon PhD Abstract Background and Objectives Endovenous laser treatment (ELT) has been proposed as an alternative in the treatment of reflux of the great saphenous vein (GSV) and small saphenous vein (SSV). Numerous studies have since demonstrated that this technique is both safe and efficacious. ELT was presented initially using diode lasers of 810 nm, 940 nm, and 980 nm. Recently, a 1,320-nm Nd:YAG laser was introduced for ELT. This study aims to provide mathematical modeling of ELT in order to compare 980 nm and 1,320 nm laser-induced damage of saphenous veins. Study Design/Materials and Methods The model is based on calculations describing light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation, and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma, Inc., Arlington, MA). Calculations were performed so as to determine the damage induced in the intima tunica, the externa tunica and inside the peri-venous tissue for 3 mm and 5 mm vessels (considered after tumescent anesthesia) and different linear endovenous energy densities (LEED) usually reported in the literature. Results Calculations were performed for two different vein diameters: 3 mm and 5 mm and with LEED typically reported in the literature. For 980 nm, LEED: 50 to 160 J/cm (CW mode, 2 mm/second pullback speed, power: 10 W to 32 W) and for 1,320 nm, LEED: 50 to 80 J/cm (pulsed mode, pulse duration 1.2 milliseconds, peak power: 135 W, repetition rate 30 Hz to 50 Hz). Discussion and Conclusion Numerical simulations are in agreement with LEED reported in clinical studies. Mathematical modeling shows clearly that 1,320 nm, with a better absorption by the vessel wall, requires less energy to achieve wall damage. In the 810,1,320-nm range, blood plays only a minor role. Consequently, the classification of these lasers into hemoglobin-specific laser wavelengths (810, 940, 980 nm) and water-specific laser wavelengths (1,320 nm) is inappropriate. In terms of closure rate, 980 nm and 1,320 nm can lead to similar results and, as reported by the literature, to similar side effects. This model should serve as a useful tool to simulate and better understand the mechanism of action of the ELT. Lasers Surg. Med. 39:256,265, 2007. © 2007 Wiley-Liss, Inc. [source] Vascular response to laser photothermolysis as a function of pulse duration, vessel type, and diameter: Implications for port wine stain laser therapyLASERS IN SURGERY AND MEDICINE, Issue 2 2002Sol Kimel PhD Abstract Background and Objective Treatment of port wine stains (PWS) by photothermolysis can be improved by optimizing laser parameters on an individual patient basis. We have studied the critical role of pulse duration (tp) on the treatment efficacy. Study Design/Materials and Methods The V-beam laser (Candela) allowed changing tp over user-specified discrete values between 1.5 and 40 milliseconds by delivering a series of 100 microsecond spikes. For the 1.5 and 3 millisecond pulses, three spikes were observed at intervals tp/2 and for tp,,,6 milliseconds, four spikes separated by tp/3. The ScleroPlus laser (Candela) has a smooth output over its fixed 1.5 milliseconds duration. Blood vessels in the chick chorioallantoic membrane (CAM) were irradiated at fixed wavelength (595 nm), spot size (7 mm), radiant exposure (15 Jcm,2), and at variable tp. The CAM contains an extensive microvascular network ranging from capillaries with diameter D,<,30 ,m to blood vessels of D,,,120 ,m. The CAM assay allows real-time video documentation, and observation of blood flow in pre-capillary arterioles (A) and post-capillary venules (V). Vessel injury was graded from recorded videotapes. Mathematical modeling was developed to interpret results of vessel injury when varying tp and D. A modified thermal relaxation time was introduced to calculate vessel wall temperature following laser exposure. Results Arterioles. For increasing tp, overall damage was found to decrease. For fixed tp, damage decreased with vessel size. Venules. For all D, damage was smaller than for corresponding arterioles. There was no dependence of damage on tp. For given tp, no variation of damage with D was observed. Photothermolysis due to spiked (V-beam) vs. smooth (Scleroplus) delivery of laser energy at fixed tp (1.5 milliseconds), showed similar vessel injuries for al values of D (P>0.05). Conclusions The difference between initial arteriole and venule damage could be explained by the threefold higher absorption coefficient at 595 nm in (oxygen-poor!) arterioles. In human patients, PWS consist of ectatic venules (characterized by higher absorption), so that these considerations favor the use of 595-nm irradiation for laser photothermolysis. For optimal treatment of PWS it is proposed that tp be between 0.1 and 1.5 milliseconds. This is based on a modified relaxation time ,d,, defined as the time required for heat conduction into the full thickness of the vessel wall, which is assumed to have a thickness ,D ,,0.1D. The corresponding ,d, will be a factor of about six smaller than given in the literature. For vessels with D between 30 and 300 ,m, ,d, ranges from 0.1 to 1.5 milliseconds. Lasers Surg. Med. 30:160,169, 2002. © 2002 Wiley-Liss, Inc. [source] Kinetic Study of the Thermopolymerization of Furfuryl Methacrylate in Bulk by Mathematical Modeling.MACROMOLECULAR THEORY AND SIMULATIONS, Issue 9 2009Part A: Simulation of Experimental Data, Sensitivity Analysis of Kinetic Parameters Abstract Mathematical modeling of the thermopolymerization of FM and CMFMA was carried out using a cross-linked kinetic model proposed for the photo-initiated polymerization of acryl-furanic compounds. In this model, the photochemical initiation step was substituted by a thermal one and it was assumed that the constant of radical termination was time-dependent, which allowed the gel effect (Trommsdorff) at high monomer conversion to be simulated. Optimization of all kinetic constants was achieved and the results of simulation suitably fitted the experimental data of the monomer conversion. The contribution of each step in the mechanism and its dependence on the experimental conditions were estimated by a sensitivity analysis technique. [source] Mathematical modeling of boundary conditions for laser-molecule time-dependent Schrödinger equations and some aspects of their numerical computation,One-dimensional caseNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Emmanuel Lorin Abstract This article deals with boundary conditions for time-dependent Schrödinger equations for molecules excited by intense and ultrashort electric fields. On the basis of Volkov wavefunctions, we propose an original boundary condition design that allows to reduce spurious reflections at the domain boundary and allows to take at least partially, plasma effects into account. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] An optimization procedure for the pultrusion process based on a finite element formulationPOLYMER COMPOSITES, Issue 3 2002R. M. L. Coelho Composite materials are manufactured by different processes. In all, the process variables have to be analyzed in order to obtain a part with uniform mechanical properties. In the pultrusion process, two variables are the most important: the pulling speed of resin-impregnated fibers and the temperature profile (boundary condition) imposed on the mold wall. Mathematical modeling of this process results in partial differential equations that are solved here by a detailed procedure based on the Galerkin weighted residual finite element method. The combination of the Picard and Newton-Raphson methods with an analytical Jacobian calculation proves to be robust, and a mesh adaptation procedure is presented in order to avoid integration errors during the process optimization. The two earlier-mentioned variables are optimized by the Simulated Annealing method with some constraints, such as a minimum degree of cure at the end of the process, and the resin degradation (the part temperature cannot be higher than the resin degradation temperature at any time during the whole process). Herein, the proposed objective function is an economic criterion instead of the pulling speed of resin-impregnated fibers, used in the majority of papers. [source] Mathematical modeling for the ionic inclusion process inside conducting polymer-based thin-filmsPOLYMER ENGINEERING & SCIENCE, Issue 11 2008Saptarshi Majumdar Ionic inclusion inside thin conducting polymer (CP) film is a major and common feature for actuator as well as membrane-based drug release. In this study, an electro-active polymeric thin-film system has been conceptualized. PNP-electro-neutrality (Poisson,Nernst, Planck) based modeling framework with customized boundary conditions is used to depict the electrochemical phenomena. In dynamic model, kinetics of probable redox reactions is included along with electro-migration and diffusion terms in the overall PNP framework. At steady state, interfacial voltage seems to hold the critically important role, while ionic migration and reaction kinetics play very crucial roles in determining the dynamics of such systems. The validated model predicts that lowering in the standard potential of the polymeric electrode accelerates the process of ionic ingress. Higher ionic flux is obtained using slower voltage scan. Variation of diffusivity shows the large spectrum of relatively unexplored dynamics for such electro-active thin-film-based system. The significance is in designing actuator- or membrane-based controlled molecular release systems. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers [source] Differential expression of cardiac mitochondrial proteinsPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 3 2008Julia R. Smith Abstract Mitochondria were isolated from whole hearts of Dahl salt sensitive (SS) and chromosome 13 consomic control (SS.13BN/Mcwi) rats using a mechanical homogenization process followed by density centrifugation. The proteins present in the two mitochondria preparations were quantified; equal amounts of protein from each sample were taken and trypsinized in the presence of either 16O or 18O before pooling. Incorporation of one or two 18O atoms at the C-terminus of the peptide cleaved by trypsin allows the distinction between the two samples. The proteins were identified by automated MS/MS sequencing and relative amounts of each protein assessed by comparison of the intensities of the constituent peptides. Relative quantification was performed using the ZoomQuant (v1.24) software. Nine proteins were found to be differentially expressed. Electron transfer flavoprotein alpha (P13803, ETFA) protein expression was two-fold lower in the SS compared to the SS.13BN. This was confirmed by Western blot and 2-DE gel quantification. Potential functional implications of this differential expression include an impaired capacity of the heart to oxidize fatty acids in the SS strain compared to the control. Mathematical modeling of mitochondrial electron transport predicted that the observed change in ETFA expression may result in decreased activity of the electron transport chain. [source] Mathematical modeling of the circadian rhythm of key neuroendocrine,immune system players in rheumatoid arthritis: A systems biology approachARTHRITIS & RHEUMATISM, Issue 9 2009Michael Meyer-Hermann Objective Healthy subjects and patients with rheumatoid arthritis (RA) exhibit circadian rhythms of the neuroendocrine,immune system. Understanding circadian dynamics is complex due to the nonlinear behavior of the neuroendocrine,immune network. This study was undertaken to seek and test a mathematical model for studying this network. Methods We established a quantitative computational model to simulate nonlinear interactions between key factors in the neuroendocrine,immune system, such as plasma tumor necrosis factor (TNF), plasma cortisol (and adrenal cholesterol store), and plasma noradrenaline (NA) (and presynaptic NA store). Results The model was nicely fitted with measured reference data on healthy subjects and RA patients. Although the individual circadian pacemakers of cortisol, NA, and TNF were installed without a phase shift, the relative phase shift between these factors evolved as a consequence of the modeled network interactions. Combined long-term and short-term TNF increase (the "RA model") increased cortisol plasma levels for only a few days, and cholesterol stores started to become markedly depleted. This nicely demonstrated the phenomenon of inadequate cortisol secretion relative to plasma TNF levels, as a consequence of adrenal deficiency. Using the RA model, treatment with glucocorticoids between midnight and 2:00 AM was found to have the strongest inhibitory effect on TNF secretion, which supports recent studies on RA therapy. Long-term reduction of TNF levels by simulation of anti-TNF therapy normalized cholesterol stores under "RA" conditions. Conclusion These first in silico studies of the neuroendocrine,immune system in rheumatology demonstrate that computational biology in medicine, making use of large collections of experimental data, supports understanding of the pathophysiology of complex nonlinear systems. [source] Mathematical modeling of reactive transport of anti-tumor drugs through electro-active membranesASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2009Parag Saurabh Abstract We present a mathematical modeling and design of an implantable polymer membrane-based drug-release device that uses alternate voltage scans across the electro-active membrane for delivery and reactive uptake of anionic anti-tumor drugs. Our mathematical model comprises Poisson,Boltzmann, Nernst,Planck and Diffusion,Reaction equations written for three compartments, namely, the drug reservoir, the polymer membrane and the diseased tissue, with the governing equations for the compartments being linked to each other through the boundary conditions. An analytical solution for the three-compartment model has been obtained using Laplace transforms and residue integration. We use this solution to quantify the various parameters controlling the spatiotemporal dynamics of drug delivery and analyze the efficacy of the reactive transport process for an anionic chemotherapeutic drug, Irinotecan-HCl, commercially also known as CPT-11. We show that a ,smart pill' with optimal drug efficacy may be designed by altering the thickness and the diffusivity of the electro-active membrane, and by tuning the applied voltage and the duration of the positive and the negative voltage scans such that the drug concentration in the tumor tissue is maintained within its therapeutic range. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Dynamic culture of droplet-confined cell arraysBIOTECHNOLOGY PROGRESS, Issue 1 2010Elisa Cimetta Abstract Responding to the need of creating an accurate and controlled microenvironment surrounding the cell while meeting the requirements for biological processes or pharmacological screening tests, we aimed at designing and developing a microscaled culture system suitable for analyzing the synergic effects of extracellular matrix proteins and soluble environments on cell phenotype in a high-throughput fashion. We produced cell arrays deposing micrometer-scale protein islands on hydrogels using a robotic DNA microarrayer, constrained the culture media in a droplet-like volume and developed a suitable perfusion system. The droplet-confined cell arrays were used either with conventional culture methods (batch operating system) or with automated stable and constant perfusion (steady-state operating system). Mathematical modeling assisted the experimental design and assessed efficient mass transport and proper fluidodynamic regimes. Cells cultured on arrayed islands (500 ,m diameter) maintained the correct phenotype both after static and perfused conditions, confirmed by immunostaining and gene expression analyses through total RNA extraction. The mathematical model, validated using a particle tracking experiment, predicted the constant value of velocities over the cell arrays (less than 10% variation) ensuring the same mass transport regime. BrdU analysis on an average of 96 cell spots for each experimental condition showed uniform expression inside each cell island and low variability in the data (average of 13%). Perfused arrays showed longer doubling times when compared with static cultures. In addition, perfused cultures showed a reduced variability in the collected data, allowing to detect statistically significant differences in cell behavior depending on the spotted ECM protein. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010 [source] | |||||||||||||||||||||||||||||||||||||