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  • Articles  (89)
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  • Articles  (89)
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  • Springer  (89)
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  • 1
    ISSN: 1435-604X
    Keywords: Mathematical model ; Laser surgery ; Optical fibres ; Tumours ; Thermal diffusion ; Multiple fibres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics , Technology
    Notes: Abstract A mathematical model is employed to discuss the region treated by local hyperthermia, when the source of heat is a laser whose energy is directed into the treatment region through four optical fibres ending at the corners of a square. If treatment is over a period that is substantially longer than the time for the temperature distribution to reach equilibrium, a steady state model using four point sources can be employed to obtain a general idea of the temperatures reached and the region treated for different power levels and sizes of square. For shorter times, and for more accurate estimation of the regions treated, numerical calculation on a computer is essential. The details of the calculation depend on individual cases, but we demonstrate here that such computations are possible, and present a series of typical results. A comparison is made with the results of a series of experiments on canine liver, showing that it is possible to obtain good qualitative and numerical agreement.
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  • 2
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    Lasers in medical science 4 (1989), S. 55-64 
    ISSN: 1435-604X
    Keywords: Laser hyperthermia ; Mathematical model ; Tumours ; Optical coefficients ; Optical fibres ; Thermal diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics , Technology
    Notes: Abstract A time dependent mathematical model of optical energy transfer and heat conduction in tissue with strong anisotropic scattering is used to analyse the results of experiments (1) in which the livers of rats were treated by local laser hyperthermia. Good qualitative agreement to the temperature distribution is possible, but satisfactory quantitative agreement is only possible if allowance is made for temperature dependence of the optical and thermal parameters. Analysis of the volume of tissue killed by the treatment shows a marked departure from the rule used in conventional hyperthermia to determine the region treated; the reason for this is not clear, but a number of possibilities are suggested.
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  • 3
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    Journal of marine science and technology 1 (1996), S. 75-84 
    ISSN: 1437-8213
    Keywords: monitoring ; modeling ; environmental preservation ; navigation ; nazardous spills ; tidal prediction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The improved monitoring and modeling capability resulting from recent technological advances in oceanographic sensors, computer processing power, and telecommunications can play a major role in environmental preservation. In particular, this capability can help improve: safe navigation and thus the prevention of maritime accidents that lead to hazardous spills; the effective cleanup of hazardous spills when they do occur; the real-time assessment of water quality problems; the assessment of long-term trends and variability due to both anthropogenic and climate change effects; and the understanding of key physical, chemical, and ecological processes.
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  • 4
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    Plasma chemistry and plasma processing 10 (1990), S. 133-150 
    ISSN: 1572-8986
    Keywords: Induction plasma ; modeling ; chemical equilibrium ; silicon nitride synthesis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A mathematical model is presented for the numerical simulation of the flow, temperature, and concentration fields in an rf plasma chemical reactor. The simulation is performed assuming chemical equilibrium. The extent of validity of this assumption is discussed. The system considered is the reaction of SiCl4 and NH3 for the production of Si3N4.
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  • 5
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    Plasma chemistry and plasma processing 10 (1990), S. 151-166 
    ISSN: 1572-8986
    Keywords: Induction plasma ; modeling ; chemical kinetics ; dissociation of silicon tetrachloride
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A kinetic model has been developed for the prediction of the concentration gelds in an rf plasma reactor. A sample calculation for a SiCl4/H2 system is then performed. The model considers the mixing processes along with the kinetics of seven reactions involving the decomposition of these reactants. The results obtained are compared to those assuming chemical equilibrium. The predictions indicate that an equilibrium assumption will result in lower predicted temperature fields in the reactor. Furthermore, for the chemical system considered here, while differences exist between the concentration fields obtained by the two models, the differences are not substantial.
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  • 6
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    Plasma chemistry and plasma processing 10 (1990), S. 167-188 
    ISSN: 1572-8986
    Keywords: Nonequilibrium plasma ; modeling ; RF plasma sintering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Plasma sintering experiments in this laboratory at reduced pressures revealed efficient heating of the ceramic sample due to recombination of dissociated and/or ionized species on the surface. For establishing a model for this plasma sintering process, it is necessary to first consider the plasma itself. Therefore, a suitable model for an RF inductively coupled plasma has been developed considering reduced pressures. As the pressure decreases, the electron density also decreases at a fixed electron temperature, causing substantial deviations from chemical equilibrium. Due to the poor collisional coupling between electrons and heavy particles at reduced pressures, large deviations from kinetic equilibrium have also to be expected. The model is based on a rotationally symmetric plasma contained in a quartz tube. The power level ranges from 1.5 to 3 kW and the operating pressure is varied from 1 to 0.01 atm. Both deviations from chemical and kinetic equilibrium are included in this model. Thermodynamic and transport properties for two-temperature plasmas are used for this modeling work. The results indicate that for pressures below 0.1 atm, there is a strong ambipolar flux of charge carriers to the confining walls, leading to significant variations of the temperature across the tube. The electron temperature increases rapidly as the pressure decreases, whereas the heavy-particle temperature decreases.
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  • 7
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    Plasma chemistry and plasma processing 10 (1990), S. 189-206 
    ISSN: 1572-8986
    Keywords: Thermal plasmas ; modeling ; heat and mass transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The present analysis is restricted to the wall region for a confined gas plasma and applied specifically to an argon plasma. The wall may be either positive or negative in potential with respect to the plasma, and the electric current may flow either parallel or normal to the wall. Estimates of the Debye shielding distance and the mean free path of various components are made to obtain the range of validity of the analysis, in addition to the situation where the wall acts like a cathode, an anode, or an electrical insulation. Analysis is for a one-dimensional case with an outer boundary, where the plasma temperature is specified. The computational domain is split into a continuum region, where both equilibrium compositions for a two-temperature plasma and a chemically reacting plasma are studied, and a free-fall region. The results allow a quantitative assessment of temperature nonequilibrium and electrical potential distribution in the free-fall region.
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  • 8
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    Plasma chemistry and plasma processing 10 (1990), S. 207-229 
    ISSN: 1572-8986
    Keywords: Plasma etching ; modeling ; SF6 ; O2 ; gas-phase reactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A model has been developed to describe the chemistry which occurs in SF6/O2 plasmas and the etching of silicon in these plasmas. Emphasis is placed nn the gas-phase free radical reactions, and the predictions n( the model are compared with experimental results. Forty-seven reactions are included, although a subset of 18 reactions describes the chemistry equally well. Agreement between the calculated and measured concentrations of stable products downstream of the plasma is better than a factor of 2. The need for additional kinetic data and fàr well-characterized diagnostic studies of SF6/O2 plasmas is discussed.
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  • 9
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    Plasma chemistry and plasma processing 10 (1990), S. 305-319 
    ISSN: 1572-8986
    Keywords: Thermal plasma sintering ; reduced pressures ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Numerical simulation of the thermal behavior of sintering specimen under RF plasma conditions at reduced pressure is considered. A two-dimensional approach is adopted for describing flow, temperature, and electromagnetic fields in the reactor with appropriate boundary conditions. Slip boundary conditions are imposed for the velocity field at the sample surface and at the wall of the reactor, and corresponding jump boundary conditions are specified for the temperature field. Simple kinetic theory is employed for the calculation of the heat flux from the plasma to the specimen. The so-called capture-radiative-cascade model is adopted for ionization and recombination processes. The results indicate that ion-electron surface recombination is the dominant heat transfer mechanism to the sintering specimen under reduced pressure conditions.
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  • 10
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    Plasma chemistry and plasma processing 10 (1990), S. 377-399 
    ISSN: 1572-8986
    Keywords: Resist etching ; radical concentration ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract During the etching of AZ 1350 photoresist in O2 and O2/CF4 discharges, ground-state concentrations of atoms (O, F, and H), and small radicals (OH, HO2, RO2) were measured in the discharge afterglow by EPR spectroscopy. In the case of CF4/O2 discharges, the dependence of O and F atom concentrations on the etch time reflects both surfäce oxidation and fluorination reactions in accordance with existing etch models. In the case of high-rate resist etching in pure O2 discharges, high concentrations of product radicals (H, OH and HO2) were detected and compared with resist free O2/H2O discharges. Kinetic modeling of the afterglow reactions reveals that the mean lifetime and, accordingly, the diffusion length of the etchant species O(3P) is drastically reduced in rapid reactions with OH and HO2. The results are used to simulate both etch homogeneity and the loading effect in a simple etch model.
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  • 11
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    Plasma chemistry and plasma processing 11 (1991), S. 103-128 
    ISSN: 1572-8986
    Keywords: RF plasma torch ; injection probe ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Flow, temperature, and electromagnetic (EM) fields in a radio-frequency thermal plasma torch designed for the preparation of superconducting powders or films have been analysed by using a new two-dimensional modeling approach with the electric field intensity as the fundamental EM field variable. The insertion of a stainless steel injection tube into the torch leads to large induction currents in this tube. Although such large induction currents cause pronounced changes of the EM fields near the injection tube, flow and temperature fields are little affected. There exists only one large toroidal vortex in the upper part of the present torch, while the maximum temperature appears at an off-axis location within the coil region.
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  • 12
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    Plasma chemistry and plasma processing 11 (1991), S. 129-150 
    ISSN: 1572-8986
    Keywords: Thermal plasma reactor ; transferred arc ; converging wall ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract In this paper the behavior of an arc in a transferred-arc plasma reactor with a converging wall geornetrr and flow through a hollow cathode is investigated numerically with emphasis on the fluid dynamics. The general conservation equations and auxiliary relations for the calculation domain are established based on reasonable assumptions Then, the coupled nonlinear differential equations are solved with suitable boundary conditions and temperature-dependent argon plasma properties at atmospheric pressure, by employing an efficient finite-difference method. The results, for a hollow cathode geornetrr with low injection flow rates, clear/y demonstrate the existence of the Maecker elect which is responsible Joy the formation of two recirculation zones. As the plasma gas flow rate is increased, the downstream recirculation zoner is swept away leaving only an upstream recirculation zone.
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  • 13
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    Plasma chemistry and plasma processing 11 (1991), S. 229-249 
    ISSN: 1572-8986
    Keywords: Thermal plasma reactor ; counterflow ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Modeling of a counterflow plasma reactor is presented, using liquid injection for the synthesis of fine particles. An experimental reactor has been developed in this laboratory, and feasibility has been demonstrated for synthesizing advanced ceramic powders. The flow field calculations show two major recirculating regions which are of importance for increasing the particles' residence time inside of the reactor. In addition, the temperature within these recirculation zones remains relatively uniform. For simulation, water droplet trajectories have been calculated for droplets produced by an injection probe. It is shown that the droplets in a size range below 50 μm in diameter will follow the streamlines and evaporate completely within a short traveling distance. This finding suggests that this reactor configuration provides a favorable environment for the synthesis of fine particles using liquid precursors.
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  • 14
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    Plasma chemistry and plasma processing 3 (1983), S. 163-192 
    ISSN: 1572-8986
    Keywords: RF plasma ; plasma polymerization ; modeling ; theoretical
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A theoretical model has been developed to describe the deposition of polymer occurring in a capacitatively coupled, low-pressure, RF discharge sustained in ethane. The reaction mechanism chosen for this model assumes that polymer formation is controlled by the formation of free radicals in the plasma and the subsequent reaction of these species at the surface of the electrodes used to sustain the plasma. Convective and diffusive transport is taken to occur in the direction parallel to the electrodes. Diffusive transport perpendicular to the electrodes is considered to be rapid, and hence the gradients in this direction are taken to be negligible. Both the composition of the gas leaving the plasma reactor and the axial profile of polymer deposition rate within the reactor, observed experimentally, are predicted accurately by the model. Results obtained from the model have also been used to estimate the kinetic chain length and degree of unsaturation in the polymer. Both predictions are found to be in reasonable agreement with experimental observations.
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  • 15
    ISSN: 1572-896X
    Keywords: particle population ; fluid mechanics ; flame synthesized aerosols ; CFD ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics , Technology
    Notes: Abstract The interaction of fluid mechanics and particle dynamics at the very early stages of flame synthesis largely affects the characteristics of the product powder. Detailed simulations provide a better understanding of these processes, which take place in a few milliseconds, and offer the possibility to influence the product characteristics by intelligent selection of the process parameters. The present paper reports on the simulation of titania powder formation by TiCl4 oxidation in an aerosol flow reactor. A commercially available fluid mechanics code is used for the detailed calculation of the fluid flow and the chemical reaction at non-isothermal conditions. This code is then interfaced with a model for aggregate particle dynamics neglecting the spread of the particle size distribution. The simulation shows the onset of the particle formation in the reactor and calculates the dynamic evolution of the aggregate particle size, number of primary particles per aggregate and the specific surface area throughout the reactor. The presented, newly developed calculation technique allows for the first time the simulation of particle formation processes under the authentic, complex conditions as found in actual aerosol reactors.
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  • 16
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    Plasma chemistry and plasma processing 7 (1987), S. 317-339 
    ISSN: 1572-8986
    Keywords: Plasma jets ; turbulence ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A mathematical representation is developed describing the temperature and the velocity profiles and mixing in a plasma jet discharging into ambient air. In the model, realistic allowance is made for turbulent behavior, the temperature-dependent property values, and also for the boundary conditions, including entrainment. The more precise definition of the boundary conditions, mixing, and entrainment are thought to be important novel features of this work. The theoretical predictions were found to be in good agreement with measurements reported by Vardelle regarding the behavior of a nitrogen plasma, but the agreement was less satisfactory for an argon plasma jet. Possible reasons for the discrepancy are discussed.
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  • 17
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    Plasma chemistry and plasma processing 13 (1993), S. 237-271 
    ISSN: 1572-8986
    Keywords: High-power transferred arc ; air plasma ; turbulence ; radiative transfer ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A physical model of two zones (constricted arc and cathode jet) of a 1-MW transferred arc in air is presented. It is based on the solution al conservation equations by a finite-differenee method. Turbulence is treated with Prandtl's approximation, whereas radiative transfer is solved considering a nonhontogeneous medium, with the hypothesis of gray spectral bands. The in of radiative transfer on the temperature field is illustrated using two-band and four-band radiation models. We also show the influence of several parameters on plasma jet properties: current intensity between 500 and 1500 A; gas mass /low rate between 10 and 90g/s, vortex injection. The arc characteristics are analyzed in accordance with physical mechanisms such as heat conduction, radiation, turbulence, convection, and miring of cold gas.
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  • 18
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    Plasma chemistry and plasma processing 16 (1996), S. 173-185 
    ISSN: 1572-8986
    Keywords: Diamond synthesis ; atomic hydrogen ; modeling ; mass spectrometry ; pulsed rf discharge
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The chemistry of hydrogen-rich hydrocarbon-hydrogen mixtures is of primary interest for the understanding of the low-pressure synthesis of diamond. We per formed experiments under well-defined conditions like temperature, pressure, initial gas composition, etc. The gas composition at the end of a flow reactor was analyzed by a calibrated mass spectrometer and compared to results obtained from the Chemkin computer code. Residence thne in the reactor as well as other process parameters were similar to those of diamond-growing PA CVD processes performed earlier with the same experimental set-rip. Modeling and experiment under isothermal conditions show quantitative agreement. We realized time-resolved mass .spectrometry by means of a helium-flushed gas sampling probe. There is evidence that the commonly used reaction kinetic data for the dissociation C2H6 (+ M) ⇔ 2CH,(+M) gives 2 too small C2H4 concentrations for hydrogen-rich conditions. This could be attributed to the poorly known third-body efficiencies of the H2 molecules compared to Ar or C2H6 from which kinetic data are commonly derived.
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  • 19
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    Plasma chemistry and plasma processing 17 (1997), S. 409-432 
    ISSN: 1572-8986
    Keywords: Plasma torch ; modeling ; laminar and turbulent flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A mathematical 2D representation is developed describing the temperature and the velocity profiles in a DC plasma torch and in the resulting plume. It is based on the resolution of conservation equations using the Simple method after Patankar. In the first part, we illustrate the effects of the turbulence, using, on the one hand, two Prandtl's mixing length models and, on the other hand, a standard k – ε model. We also show the influence of physical parameters like the inlet mass flow rate, the current intensity, and the kind of gas (argon or air) on the characteristics of the plasma. The second part of this study presents a comparison of the model with experimental results encountered in the literature. The profiles obtained at the exit of the torch are compared to the mathematical formulation used as boundary condition by the models taking into account only the plasma jet.
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  • 20
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    Plasma chemistry and plasma processing 17 (1997), S. 433-452 
    ISSN: 1572-8986
    Keywords: Laser Doppler anemometry ; fluidized plasma bed ; particles velocity distribution ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Laser Doppler anemometry (L.D.A.) is an efficient and nonintrusive technique. Today, improved in its configuration, the L.D.A. has been applied even in flowing plasmas. (1,2) In-flight simultaneous measurements were performed for local density and velocity of particle distribution. The measurements provide an insight into thermal and mass transfer, chemical reactivity, and the distribution of residence times of particles in a plasma fluidized bed. The difficulties of L.D.A. in a plasma fludized bed such as high emission intensity of the plasma torch, high temperature, high particle density, and large distribution of particle granulometry were overcomed in the present investigation. The aims achieved were the characterization of the plasma fluidized bed distribution together with accurate measurements of local particle density and velocity as measured by L.D.A.
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  • 21
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    Plasma chemistry and plasma processing 18 (1998), S. 73-89 
    ISSN: 1572-8986
    Keywords: Thermal plasma ; CVD ; modeling ; liquid precursor ; diamond
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract In this paper, a comprehensive model for thermal plasma chemical vapor deposition (TPCVD) with liquid feedstock injection is documented. The gas flow is assumed to be steady, of a single temperature. Radiation and charged species contributions are excluded, but extensive homogeneous and heterogeneous chemistry is included. The liquid phase is traced by considering individual droplets. Discussion on the model's application to diamond production from acetone in a hydrogen–argon plasma is included. The major conclusions are: (1) Liquid injection possesses a capability to deliver the hydrocarbon precursor directly onto the deposition target. (2) For the case of complete evaporation of the droplet before reaching the substrate, the deposition rate is similar to that obtained with gaseous precursors. (3) The computational results compare well with experimental data. The modeling results can be used to optimize the injection parameters with regard to the deposition rate.
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  • 22
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    Plasma chemistry and plasma processing 18 (1998), S. 189-214 
    ISSN: 1572-8986
    Keywords: Remote PECVD ; silicon dioxide ; modeling ; deposition rate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Plasma-enhanced chemical vapor deposition has become one of the most important thin film deposition technologies. To avoid direct plasma exposure the substrates may be placed in the remote region. A carrier gas conveys the plasma energy to the deposition area where the reactions with the monomer molecules take place. For the engineering of such a process the modeling of the achievable deposition rate is of great interest. Among different possibilities semiempirical models provide a fast and easily utilizable tool without intensive computer simulations or the necessity of detailed knowledge about the chemistry involved. From deposition experiments with oxygen and an organosilicon monomer (hexamethyldisiloxane, HMDSO) the remote composite parameter is suggested. It combines microwave power, monomer and carrier gas flow rate, and the distance of the substrate from the plasma source. This parameter was derived from the ratio between atomic oxygen and monomer flow rate. In the parameter range considered the deposition rate is described as well ordered and the energy- and monomer-deficient regions are clearly separated.
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  • 23
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    Plasma chemistry and plasma processing 18 (1998), S. 285-303 
    ISSN: 1572-8986
    Keywords: Fullerenes ; carbon arc ; plasma process ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A mathematical model of the carbon arc process for the synthesis of fullerenes (C 60 , C 70 ) is developed. The two-dimensional model solves for the velocities, temperature, and total concentration of carbon species. The net emission coefficient method is used for the radiation term. The carbon species conservation equations consider the evaporation of carbon from the anode, cathode surface deposition, and carbon condensation. The thermodynamic and transport properties are calculated as a function of temperature and carbon mass fraction, using the method of Chapman–Enskog. Erosion rates used by the model are determined experimentally. Calculated fields of the velocities, temperatures, carbon mass fraction and current intensity are presented. Comparison is made of the behavior of the arc at 1 and 4 mm interelectrode gaps, and between operation in argon and in helium. The results of simulations provide a justification for the higher yields observed in helium compared to the argon case.
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  • 24
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    Plasma chemistry and plasma processing 18 (1998), S. 325-362 
    ISSN: 1572-8986
    Keywords: Microwave plasma ; diamond deposition ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract One-dimensional transport models of moderate-pressure H 2 and H 2 /CH 4 plasmas obtained in a diamond deposition microwave reactor are presented. These models describe the plasma as a thermochemically nonequilibrium flow with three different energy modes. The solution of the one-dimensional plasma transport equations enabled the estimation of plasma species concentrations and temperatures on the axis of the reactor. As far as pure H 2 plasmas are concerned, results showed that the model predictions of gas and vibration temperatures are in good agreement with experimental measurements. The model also yields a relatively good qualitative prediction of the variations of H-atom mole fraction with the power density absorbed by the plasma. The results obtained for H 2 /CH 4 discharges showed that the model prediction on the variations of H-atom mole fraction with methane percentage in the discharge is in good qualitative agreement with experimental results. They also showed that methane is rapidly converted to acetylene before reaching the discharge zone. The concentrations of neutral hydrocarbon species in the reactor are mainly governed by thermal chemistry. The addition of methane strongly affects the ionization kinetics of the plasma. Three major ions are generally obtained in H 2 /CH 4 plasmas: C 2 H 2 + , C 2 H 3 + , and C 2 H 5 + . The relative predominance of these ions depends on the considered plasma region and on the discharge conditions. The ionic species concentrations are also mainly governed by chemistry, except very near the substrate surface. Finally the use of this transport model along with the surface chemistry model of Goodwin (1) enabled us to estimate the diamond growth rate for several discharge conditions.
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  • 25
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    Plasma chemistry and plasma processing 18 (1998), S. 429-446 
    ISSN: 1572-8986
    Keywords: Pulsed microwave discharge ; plasma ignition ; Ar/CF4 mixture ; plasma processing ; etching ; chemical kinetics ; modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The present work deals with a pulsed microwave discharge in an Ar/CF 4 gas mixture under a low pressure (1–10 mbar). The discharge chamber developed has a cylindrical geometry with a coupling window alternatively made of quartz or alumina. The setup allows one to investigate the plasma–wall interactions (here etching of the quartz window) and the ignition process of the pulsed microwave plasma. Microwave pulses with a duration of 50–200 μs and repetition rate between 1 and 10 kHz are typical for the experiments. The space-time behavior of the fluorine number density in the discharge has been investigated experimentally by optical actinometry. The discharge kinetics is modeled using electron-transport parameters and rate coefficients derived from solutions of the Boltzmann equation. Together with the solution of the continuity and electron balance equations and the rate equations describing the production of CF x (x=2, 3, 4) radicals and F atoms, a good agreement between experimental and theoretical data can be achieved.
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  • 26
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    Plasma chemistry and plasma processing 19 (1999), S. 341-362 
    ISSN: 1572-8986
    Keywords: Thermal rf plasma ; modeling ; spectroscopy ; plasma flash evaporation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The evaporation process of zirconia powders injected in a thermal rf plasma is investigated. Both model calculations and optical emission spectroscopy are used to study the evaporation behavior. Gas temperatures and velocity distributions are determined numerically from conservation laws and Maxwell equations. The influence of plasma and particle parameters on the thermal history of entrained particles is discussed. Asymmetric Abel inversion is applied to detect asymmetric emission profiles in the plasma source. Spectroscopic measurements reveal that evaporated zirconium is concentrated near the axis of the plasma. Numerical calculations show that line-integrated emission profiles can be used to distinguish the cases of complete and incomplete evaporation. Axial emission profiles confirm that the evaporation zone is shifted upstream of the plasma when smaller precursor particles are used.
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    Plasma chemistry and plasma processing 19 (1999), S. 467-486 
    ISSN: 1572-8986
    Keywords: He-plasma ; excitation spectra ; modeling ; comparison with experiments
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A collisional-radiative model was used to study the kinetics of an atmospheric pressure helium discharge. The electron kinetics was obtained from a two-term solution of the Boltzmann equation with electron–electron collisions included. The distribution of the helium electronic excited states was compared to measured values and used to calculate excitation temperatures. The results show that a unique value of the excitation temperature cannot be used to characterize the whole electronic states distribution, because the plasma is not in local thermodynamical equilibrium under the conditions considered. Other calculated discharge parameters, such as the electron temperature, the maintenance electric field, the density of metastable atoms in the 2 3 S state, and the ion densities are presented and compared to experimental data when available.
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    Plasma chemistry and plasma processing 19 (1999), S. 445-466 
    ISSN: 1572-8986
    Keywords: Dielectric barrier discharge ; CARS on N2 and NO ; NO reduction ; chemical and vibrational kinetics ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Dielectric barrier discharges (DBD) with planar- and knife-shaped electrodes are operated in N2O2NO mixtures under a pressure of 20 and 98 kPa. They are excited by means of consecutive unipolar or bipolar high-voltage pulse packages of 10 kV at a pulse repetition rate of 1 and 2 kHz. The rotational and vibrational excitation of N 2 molecules and the reduction of nitric oxide (NO) in the discharge have been investigated using coherent anti-Stokes Raman scattering (CARS) technique. Rotational (gas) temperatures near the room temperature and vibrational temperatures of about 800 K at atmospheric pressure and 1400 K at a pressure of 20 kPa are observed. Therefore, chemical reactions of NO with vibrationally excited N 2 are probably insignificant. One-dimensional kinetic models are developed that balance 35 chemical reactions between 10 species and deliver equations for the population density of excited vibrational levels of N 2 together with a solution of the Boltzmann equation for the electrons. A good agreement between measured vibrational temperatures of N 2 , the concentration of NO, and calculated data is achieved. Modeling of the plasma discharge verifies that a DBD operated with a N2NO mixture reduces the NO content, the simultaneous presence of O 2 , already 1%, is enough to prevent the NO reduction.
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    Plasma chemistry and plasma processing 20 (2000), S. 65-86 
    ISSN: 1572-8986
    Keywords: thermal plasma ; waste processing ; fly-ash vitrification ; optical emission spectroscopy ; volatilization ; lead ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Results are presented of optical emission spectroscopy (OES) application asa control tool to improve fly-ash plasma vitrification. A twin-torch plasmasystem has been used for the fly-ash processing, and a new OES method hasexamined metallic vapors above the melt. The method allows the study ofnonhomogeneous optically thin plasmas exhibiting a symmetry plane withoutsophisticated tomographic systems. The dc arc torches are mounted above acold crucible filled with a synthetic glass. The arc intensity is from200 to 400 Å. Argon is introduced into the torches along the cathodeand the anode, while argon, oxygen or hydrogen are injected through thelance between the torches. Local plasma temperatures above the melt havebeen evaluated using measured relative intensities of spectral lines ofthe plasma-forming gas. Metallic vapor concentration in the plasma isdeduced from the intensity ratio of the metal–gas spectral lines. Leadoxide has been used to study heavy-metal behavior at the fly-ash plasmavitrification. Distribution of the lead along the crucible surface,depending on the plasma-forming gas composition as well as the concentrationevolution with time, have been examined. The elemental analysis of theresultant glass has been measured by scanning electron microscopy (SEM)with energy-dispersive spectrometry (EDS). A predictive model has beenadapted to simulate the noncongruent vaporization of heavy metals from themelt. According to the data obtained, steep variations of the volatility ofthe elements depend strongly on reducing properties of gases controllingthe plasma composition near the melted surface. In addition, the melttemperature and the redox potential of the gas phase are found to be themost critical parameters.
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    Plasma chemistry and plasma processing 20 (2000), S. 521-553 
    ISSN: 1572-8986
    Keywords: thermal plasma ; transferred arc ; fumed silica ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The volatilization of quartz in a transferred arc plasma followed byquench and recondensation is a promising route to the production offumed silica. In this work, an existing model of a transferred arcwas modified and combined with a newly developed model of a moltensilica anode to predict the behavior of a transferred arc evaporatoras a function of current and plasma gas flow rate. The model predictstemperature, current, and flow fields in both the plasma and anode aswell as evaporation rates. Although quantitative agreement withexperimental results was not possible because of insufficient propertydata for silica at high temperature, the results were within an orderof magnitude of those measured experimentally. The model developed isuseful for the design and scaleup of this type of reactor.
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  • 31
    ISSN: 1572-8986
    Keywords: Methane ; acetylene ; kinetics ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract It is shown that it is basically possible to model plasma-chemical methane conversion using a kinetic concept regardless of the kind of plasma, i.e., the kind of activation. While the temporal plasma-chemical decomposition of methane is controlled by a first-order rate equation, the temporal product formation can be described by a set of first-order consecutive reactions. Prolonged portions of constant product concentrations in the temporal product formation curves were explained by the assumption of an equilibrium between forward and reverse reactions. The modeling revealed the special role of the re-formation of dissociated molecules.
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    Transport in porous media 7 (1992), S. 15-38 
    ISSN: 1573-1634
    Keywords: Porous media ; modeling ; scaling ; dimensionless numbers ; dominance
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    Topics: Geosciences , Technology
    Notes: Abstract A methodology for eliminating nondominant effects in models that describe transport phenomena in porous media is presented. The methodology is based on the introduction of dimensionless numbers and on a proper evaluation of the order of magnitude of terms. These dimensionless numbers are redefined as characteristics of transport and transformation phenomena in porous media. It is shown that different time scales and different length scales may have to be employed for different variables. A method for evaluating the order of magnitude of the error of prediction when terms are deleted, is presented.
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    Transport in porous media 41 (2000), S. 105-116 
    ISSN: 1573-1634
    Keywords: flow ; integration ; Gassmann ; acoustics ; reservoir ; characterization ; modeling ; simulation ; Newton–Raphson
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    Notes: Abstract Integrated flow modeling is the combination of a traditional flow simulator with a petrophysical model. By combining a petrophysical model with a traditional flow model, it is possible to perform calculations that improve our ability to monitor fluid movement in porous media. This paper outlines the formulation of an integrated flow model IFLO and its multi-variable, Newton–Raphson IMPES solution procedure. The benefits of integrated flow modeling and the underlying principles involved in the integration of a flow model with a petrophysical model are presented. Results from the IFLO model are used to illustrate the principles.
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    Transport in porous media 5 (1990), S. 27-47 
    ISSN: 1573-1634
    Keywords: Mathematical model ; percolation ; Monte Carlo ; viscous fingers ; Darcy ; relative permeability
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    Notes: Abstract The model described in this paper is an approach to simulating flow through porous media on a microscopic scale. It is based on a variation of diffusion limited aggregation. The model is shown to match coreflood average saturation profiles and production histories as predicted by Darcy's equations while generating saturation distributions resembling viscous fingering. The model also is shown to simulate the limiting cases of infinite mobility ratio and zero flow rates as previously modeled by diffusion limited aggregation and percolation theory. With some simplifying assumptions, differential equations very similar to Darcy's equations are derived from the microscopic interpretation of fluid behavior in porous media used in this model.
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    Journal of science education and technology 8 (1999), S. 3-19 
    ISSN: 1573-1839
    Keywords: levels ; complexity ; simulation ; modeling ; science education ; mathematics education ; dynamic systems ; systems thinking
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    Topics: Natural Sciences in General , Technology
    Notes: Abstract The concept of emergent "levels" (i.e., levels that arise from interactions of objects at lower levels) is fundamental to scientific theory. In this paper, we argue for an expanded role for this concept of levels in science education. We show confusion of levels (and "slippage" between levels) as the source of many of people's deep misunderstandings about patterns and phenomena in the world. These misunderstandings are evidenced not only in students' difficulties in the formal study of science but also in their misconceptions about experiences in their everyday lives. The StarLogo modeling language is designed as a medium for students to build models of multi-leveled phenomena and through these constructions explore the concept of levels. We describe several case studies of students working in StarLogo. The cases illustrate students' difficulties with the concept of levels, and how they can begin to develop richer understandings.
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    Journal of science education and technology 6 (1997), S. 173-191 
    ISSN: 1573-1839
    Keywords: Science education ; educational engineering ; modeling
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    Topics: Natural Sciences in General , Technology
    Notes: Abstract In this paper, we present a system for formally characterizing elements of an introductory science class, measuring the performance of a class based on this characterization, and modeling the value of the class based on the measurements. This system allows the iterative improvement of any educational presentation through a model, test, iterate cycle. We propose formal practices involved in iteratively improving an educational experience be called educational engineering.
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    Transport in porous media 35 (1999), S. 49-65 
    ISSN: 1573-1634
    Keywords: modeling ; biodegradation ; microbial transport ; dual-porosity ; kinetics.
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    Notes: Abstract A mathematical model describing microbial transport and growth in a heterogeneous aquifer domain, composed of overlapping subdomains of high-permeability and low-permeability materials, is developed. Each material is conceptually visualized as a continuum which occupies the entire considered spatial aquifer domain. Based on the assumption that advection in the low-permeability domain is negligible, the mathematical model is solved by using a publically available reactive transport code. The importance of modeling microbial transport and growth in such a dual-porosity system is demonstrated through a hypothetical case study.
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  • 38
    ISSN: 1573-1634
    Keywords: NAPLs ; radon ; modeling ; monitoring ; partitioning ; tracer ; emanation
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    Notes: Abstract The recently developed natural radon tracer method has potential as a rapid, low‐cost, nondestructive, and noninvasive method for quantifying NAPL contamination. In the subsurface, radon‐222 (radon) is produced by the decay of naturally occurring radium‐226 contained in the mineral fraction of aquifer solids. In groundwater radon occurs as a dissolved gas, with a half‐life of 3.83 days. In the absence of NAPL, the radon concentration in groundwater quickly reaches a maximum value that is determined by the mineral composition of the aquifer solids, which controls the rate of radon emanation. In the presence of NAPL, however, the radon concentration in the groundwater is substantially reduced due to the preferential partitioning of radon into the organic NAPL phase. A simple equilibrium model and supporting laboratory studies show the reduction in radon concentration can be quantitatively correlated with residual NAPL saturation. Thus, by measuring the spatial distribution in radon it may be possible to identify locations where residual NAPL is present and to quantify the NAPL saturation. When the basic processes of partitioning, radon emanation from the aquifer solids, and first‐order decay are incorporated into an advective/dispersive transport model, good agreement is obtained with the results of laboratory and field experiments. Model sensitivity analyses shows many factors can contribute to the radon concentration response, including the length of the NAPL zone, NAPL saturation, groundwater velocity, porosity, and radon emanation. Thus, care must be taken when applying the radon method to locate and quantify NAPL contamination in the subsurface.
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    Transport in porous media 41 (2000), S. 47-60 
    ISSN: 1573-1634
    Keywords: unsaturated flow ; peat ; filters ; septic ; modeling ; hydraulics ; soil moisture retention curve
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    Notes: Abstract Peat is an alternative filter medium for the treatment of various waste streams including septic tank effluent. The water holding capacity and adsorption capacity of peat make it a favorable filter medium over sand or gravel which are commonly used as the filter medium for the drainage field of septic systems. This paper presents the results of a field study to evaluate the hydraulics of a peat filter used to treat the septic tank effluent from a public school west of Ottawa, Canada. An experimental box was placed within the filter during its construction to provide access to the vertical profile of the peat layer. The filter is periodically pulsed with septic tank effluent, which is distributed over the top of the filter and flows vertically through the peat. The filter was instrumented with tensiometers and transducers to monitor the pore water pressures in response to a pulse of septic tank effluent. An in-depth study of the hydraulics of the system was completed. The soil moisture retention curve and the hydraulic conductivity as a function of density were determined in laboratory experiments. A one-dimensional unsaturated flow model was used to predict the pressure response due to a pulse. A comparison of the field and model results illustrates the impact of the density variations, and the corresponding hydraulic conductivity variations, on the model predictions. The compaction of the peat is an important design consideration for the filter since it directly impacts the flow characteristics and the hydraulic retention time within the filter.
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    Transport in porous media 24 (1996), S. 203-220 
    ISSN: 1573-1634
    Keywords: biotransformation ; halogenated solvents ; anaerobic processes ; modeling ; cometabolism
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    Topics: Geosciences , Technology
    Notes: Abstract In situ biorestoration is a groundwater remediation technique in which the indigenous aquifer bacteria are stimulated by injecting compounds to provide carbon source and energy. Stimulated bacteria may transform the target contaminants such as tetrachloroethylene (PCE) and trichloroethylene (TCE) into intermediate products. In this study, we developed a model to simulate the substrate-limited biotransformation of the halogenated solvents present in anoxic groundwater by sequential reductive dehalogenation under methanogenic conditions. The model consists of conservation of mass equations for the primary substrate, immobile indigenous biomass, organic solvents such as PCE and TCE, and their intermediate products trichloroethylene, dichloroethylene, and vinyl chloride. The utilization of primary substrate and the biotransformation of organic solvents are assumed to follow Monod kinetics. The limiting factor on bacterial growth is assumed to be the primary substrate. The microbial yield coefficient is determined from the stoichiometric equation describing the anaerobic process. The model is solved by using a finite difference technique. Results are presented for three different case studies: continuous injection of primary substrate (acetate), single-pulse injection, and double-pulse injection. The single-pulse or double-pulse injection techniques were found to be more effective than continuous injection of primary substrate. Double-pulse technique reduces the clogging of injection wells caused by excessive microbial growth around boreholes and achieves a more uniform distribution of microbial growth in the subsurface. In all cases target compounds were effectively removed. The results, however, indicate substantial levels of intermediate product accumulation. Numerical results of a simplified model which assumes an abundance of primary substrate and a constant population of biomass, compare favorably with experimental data reported in the literature.
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    Annals of biomedical engineering 13 (1985), S. 531-550 
    ISSN: 1573-9686
    Keywords: Input impedance ; Mathematical model ; Pulmonary circulation ; Pulmonary artery ; Ventricular septal defect
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    Topics: Medicine , Technology
    Notes: Abstract A mathematical model of the infant pulmonary vascular system was developed by altering an adult model to fit the hemodynamic properties of an infant pulmonary vascular bed. The model was designed for infants between the ages of 1 and 2 years with both normal and high mean pulmonary artery pressures (PAPs). The resulting infant model was evaluated on the basis of the computed parameters of cumulative length, volume and resistance of the pulmonary vascular bed, as well as on the basis of comparisons of the model spectra with actual computed spectra for ventricular septal defect patients who were of comparable age, had comparable mean PAPs and were not diagnosed as having pulmonary vascular disease. It was observed that the first minimum and first maximum in the modulus of the input impedance spectrum of the infant model for both normal and high mean PAPs occurred at a higher frequency than in the adult model. These observations led to the conclusion that there is a natural, age-related shift in the input impedance spectrum of infants which is not necessarily indicative of pulmonary impairment.
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    Annals of biomedical engineering 15 (1987), S. 139-155 
    ISSN: 1573-9686
    Keywords: Lung lymph ; Capillary permeability ; Pores ; Mathematical model
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    Topics: Medicine , Technology
    Notes: Abstract Mathematical models of solute and water exchange in the lung have been helpful in understanding factors governing the volume flow rate and composition of pulmonary lymph. As experimental data and models become more encompassing, parameter identification becomes more difficult. Pore sizes in these models should approach and eventually become equivalent to actual physiological pathway sizes as more complex and accurate models are tried. However, pore sizes and numbers vary from model to model as new pathway sizes are added. This apparent inconsistency of pore sizes can be explained if it is assumed that the pulmonary blood-lymph barrier is widely heteroporous, for example, being composed of a continuous distribution of pathway sizes. The sieving characteristics of the pulmonary barrier are reporduced by a log normal distribution of pathway sizes (log mean=−0.20, log s.d.=1.05). A log normal distribution of pathways in the microvascular barrier is shown to follow from a rather general assumption about the nature of the pulmonary endothelial junction.
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    Annals of biomedical engineering 17 (1989), S. 377-396 
    ISSN: 1573-9686
    Keywords: Periodic breathing ; Central apnea ; Sleep ; Mathematical model ; Hyperventilation ; Metabolic rate ; Asphyxia
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    Topics: Medicine , Technology
    Notes: Abstract Periodic breathing (recurrent central apneas) occurs frequently during sleep. Periodic breathing can arise as a result of unstable behavior of the respiratory control system. A mathematical model of the respiratory control system was used to investigate, systematically, the effect of severity of disturbances to respiration and certain system parameters on periodic breathing occurring during sleep. The model consisted of multi-compartment representation of O2 and CO2 stores, a peripheral controller sensitive to O2 and CO2, and a central controller sensitive to CO2. The effects of hypoxia and hypercapnia on the upper airway muscles were not considered in the model. Episodes of hyperventilation or asphyxia were used to disturb the control system and explore the boundaries of stable breathing. Circulation time and metabolic rate were also varied. Simulations with the model produced the following findings: The number of central apneas associated with periodic breathing were greater as circulation time increased; controller gain increases also made the number of apneas greater, although periodic breathing occurs with lower controller gains as circulation time increases. At each level of circulation time there was a range of controller gain changes which caused little change in the number of apneas. There were more apneas with hypoxia; also the number of apneas increased with sleep-associated reductions in metabolic rate. The more rapidly resting PCO2 rose at sleep onset, the greater the likelihood of recurrent apneas. Finally, the more intense the disturbance, the more apneas there were.
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    Annals of biomedical engineering 18 (1990), S. 123-133 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Macromolecules ; Dimension ; Sieving
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    Topics: Medicine , Technology
    Notes: Abstract The pulmonary microvasculature offers a heterogeneous barrier to the motion of large solutes as they pass between blood and lymph. While this barrier has been approximated by a few discrete pathways or by statistical ensembles of many pathways, these descriptions only partly capture the structural and functional properties of the pulmonary microcirculation. The concept that this barrier may be a fractal object is explored. Endothelial cleft geometry displays scaling in junctional path length and self-similarity in its spatial organization. It is shown that a fractal cleft produces heterogeneous spaces capable of transporting water and macromolecules. Cleft location, size, and depth are characterized, in part, by a fractal dimension of approximately 0.8. The consequences for transport through a fractal barrier are then determined. Predicted sieving of macromolecules by a fractal barrier is found to be consistent with lung microvascular transport data. Nonlinear transport phenomena are one consequence of a barrier having a fractional dimension.
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    Annals of biomedical engineering 19 (1991), S. 273-289 
    ISSN: 1573-9686
    Keywords: Vagal control ; Cardiac period ; SA node ; Mathematical model ; ACh release
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    Topics: Medicine , Technology
    Notes: Abstract In 12 dogs anesthetised with α-chloralose and urethane, and β-adrenergic blocked with propranolol, the cervical vagi were stimulated for 60 seconds with supramaximal constant current pulses at frequencies between 2.0 and 10 Hz. The time course of the recovery of the cardiac period response, after cessation of vagal stimulation, was analyzed using nonlinear curve fitting techniques. It was found that the recovery phase could be reliably fitted with a function consisting of the sum of up to three exponential terms. The first term has a moderate rate constant of 0.2260±0.0112 S−1 (SE) and is independent of vagal stimulus frequency and the preceding bradycardia. We propose that this term is associated with a recovery from the bradycardia with a rate constant indicative of the reduction of acetylchloline at the pacemaker caused by hydrolysis and washout. The second term has a small rate constant of 0.0499±0.0014 s−1 (SE) and a negative gain. This term describes the time course of the post vagal tachycardia observed at cessation of stimulation. It is also independent of stimulus frequency and the preceding bradycardia. The third term has a large and variable rate constant (range: 0.247–8.01 s−1) and becomes increasingly dominant when the preceding bradycardia is large. We propose that this third component arises from a rapid return of the pacemaker focus to the dominant location prior to vagal stimulation. The mathematical characterisation of this component is important to permit the accurate derivation of the time courses of the remaining two components. Curvilinear relationships exist between the gain parameters for each of the exponential terms and the preceding bradycardia.
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  • 46
    ISSN: 1573-9686
    Keywords: Circulation ; Modeling of circulation ; Mathematical model ; Electrical model ; Hydraulic model ; Modeling of physiological systems
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    Notes: Abstract Development, first of analog and later of digital computers, as well as algorithms for analysis of electrical circuits, stimulated the use of electrical circuits for modeling the circulation. The networks used as building blocks for electrical models can provide accurate representation of the hydrodynamic equations relating the inflow and outflow of individual segments of the circulation. These networks, however, can contain connections in which voltages and currents have no analogues in the circulation. Problems arise because (a) electrical current must flow in closed loops, whereas no such constraints exist for hydraulic models; and (b) electrical capacitors have a number of characteristics that are not analogous to those of hydraulic compliant chambers. Disregarding these differences can lead to erroneous results and misinterpretation of phenomena. To ensure against these errors, we introduce an imaginary electrical element, thenonlinear residual-charge capacitor (NRCC), with characteristics equivalent to those of a compliant chamber. If one uses appropriate circuit connections and incorporates the residual-charge capacitor, then all voltages and currents in the model are proper analogues of pressures and flows in the circulation. It is shown that the capacitive current represents the rate of change of volume of blood inside the vessel, as well as the rate of the corresponding displacement of volume of the surrounding tissue.
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    Annals of biomedical engineering 20 (1992), S. 517-531 
    ISSN: 1573-9686
    Keywords: Ion channel ; Kinetics ; Nonlinear dynamics ; Chaos ; Mathematical model
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    Topics: Medicine , Technology
    Notes: Abstract Models of the gating of ion channels have usually assumed that the switching between the open and closed states is a random process without a mechanistic basis. We explored the properties of a deterministic model of channel gating based on a chaotic dynamic system. The channel is modeled as a nonlinear oscillator, that has a potential function with two minima, which correspond to the stable open and closed states, and is driven by a periodic driving force. The properties of the model are like some properties of single channel data and unlike other properties. The model is like the data in that: the current switches between two well-defined states, this switching is nonperiodic, and there are subconductance states. These subconductance states are subharmonic resonances, due to the nonlinearities in the equation of the model, rather than stable conformational states due to local minima in the potential energy. The model is not like the data in that the current fluctuates too much within in each state and there are sometimes periodic fluctuations within a state. At the present time, the selection of the most appropriate channel model (Markov, chaotic, or other) is not possible, and in addition to chaotic models, other nonlinear models may be suitable.
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    Annals of biomedical engineering 22 (1994), S. 184-193 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Factor XII ; Kallikrein ; HMWK ; Cascade ; Mass transfer
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    Topics: Medicine , Technology
    Notes: Abstract This work analyzes, for the first time, the combined role of blood flow, protein transport and the reaction network of the contact phase up to the “common pathway” of the blood coagulation cascade. The model is comprised of a set of 20 dominant reactions with 11 components. Systems of ODEs reducible to 4 coupled equations describe rigorously the dynamic behavior, while systems of algebraic equations, reducible to a single polynomial equation, model the steady state concentrations of the coagulants. The analysis showed that there is never more than onestable steady state. This is in contrast to the analysis of common pathway that gives rise to multiple concentration states. It also revealed a general robustness of the system to changes in procoagulant concentrations, inhibition rates and most activation rate constants. The system is largely impervious to the level of activated Factor XII, given that a trace (non-zero) level is present. In contrast, the system displays a dual response to flow and surface activity: A change in either of these factors alone can promote, have no effect on, or (in the case of flow) impede the progress of coagulation, depending on the value of the other factor. Their effects must therefore be examined in unison. These results may help resolve contradictory findings attributed to one or the other factor alone.
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  • 49
    ISSN: 1573-9686
    Keywords: Bioresorbable vascular graft ; Mechanical stress ; Mathematical model
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    Notes: Abstract Little attention has been given to the stresses within the wall of bioresorbable vascular prostheses and how they might affect the resorption process. We modeled the graft “complex” (inner tissue capsule, residual graft, and outer tissue capsule) as a three-layered compound tube under internal pressure. Using this biomechanical model, we studied the effects of alterations in the geometry (i. e., radius and thickness) and mechanical properties of each stratum on the overall transmural stress distribution. Hypothetical simulations were performed to investigate the possible-sequence of and alterations in the radial and circumferential stresses during the resorption process. Our results suggest that early in the resorption phase, the inner tissue capsule is subjected to compressive hoop stresses and concentrated, largemagnitude compressive radial stresses. This distribution gives way to the more typical distribution for a thick-walled tube when equilibration (i.e., complete resorption) is approached. The prediction of the compressive stresses in the pseudo-intima during early resorption parallels findings of an elevated mitotic index in that region at that time. This leads to a new hypothesis, namely, that compressive stresses, both in-plane and out-of-plane with respect to the regenerated vascular cells, participate in the resorption process of bioresorbable vascular grafts by modulating elevated cellular proliferative activity and may play an important role in other aspects of vascular cell biology. Results of recent experimentation support this hypothesis.
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    Annals of biomedical engineering 27 (1999), S. 208-218 
    ISSN: 1573-9686
    Keywords: Single cell model ; Multidrug resistance ; Cancer cell ; Drug influx and efflux ; Mathematical model ; Dynamic and steady-state simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Multidrug resistance (MDR) of some cancer cells is a major challenge for chemotherapy of systemic cancers to overcome. To experimentally uncover the cellular mechanisms leading to MDR, it is necessary to quantitatively assess both drug influx into, and efflux from, the cells exposed to drug treatment. By using a novel molecular microdelivery system to enforce continuous and adjustable drug influx into single cells by controlled diffusion through a gel plug in a micropipet tip, drug resistance studies can now be performed on the single cell level. Our dynamic model of this scheme incorporates drug delivery, diffusive mixing, and accumulation inside the cytoplasm, and efflux by both passive and active membrane transport. Model simulations using available experimental information on these processes can assist in the design of MDR related experiments on single cancer cells which are expected to lead to a quantitative evaluation of mechanisms. Simulations indicate that drug resistance of a cancer cell can be quantified better by its dynamic response than by steady-state analysis. © 1999 Biomedical Engineering Society. PAC99: 8717Aa, 8719Xx
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    Keywords: Thrombosis ; Mathematical model ; Thrombin ; Fluid dynamics ; Mass transport ; Platelets
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    Notes: Abstract To better understand the mechanisms leading to the formation and growth of mural thrombi on biomaterials, we have developed a two-dimensional computational model of platelet deposition and activation in flowing blood. The basic formulation is derived from prior work by others, with additional levels of complexity added where appropriate. It is comprised of a series of convection-diffusion-reaction equations which simulate platelet-surface and platelet-platelet adhesion, platelet activation by a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent thrombin generation, and thrombin inhibition by heparin. The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and resting and activated platelet-surface and platelet-platelet reaction rate constants. The model is formulated to simulate a wide range of biomaterials and complex flows. In this article we present the basic model and its properties; in Part II (Sorensen et al., Ann. Biomed. Eng. 27:449–458, 1999) we apply the model to experimental results for platelet deposition onto collagen. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8380Lz, 8717Aa, 8710+e, 8768+z
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  • 52
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    Keywords: Thrombosis ; Mathematical model ; Thrombin ; Fluid dynamics ; Mass transport ; Platelets
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    Notes: Abstract We have previously described the development of a two-dimensional computational model of platelet deposition onto biomaterials from flowing blood (Sorensen et al., Ann. Biomed. Eng. 27:436–448, 1999). The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and three platelet-deposition-related reaction rate constants. These parameters are estimated for platelet deposition onto a collagen substrate for simple parallel-plate flow of whole blood in both the presence and absence of thrombin. One set of experimental results is used as a benchmark for model-fitting purposes. The “trained” model is then validated by applying it to additional test cases from the literature for parallel-plate Poiseuille flow over collagen at both higher and lower wall shear rates, and in the presence of various anticoagulants. The predicted values agree very well with the experimental results for the training cases, and good reproduction of deposition trends and magnitudes is obtained for the heparin, but not the citrate, validation cases. The model is formulated to be easily extended to synthetic biomaterials, as well as to more complex flows. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8710+e, 8717Aa, 8768+z, 4760+i
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    Annals of biomedical engineering 28 (2000), S. 14-25 
    ISSN: 1573-9686
    Keywords: Coronary anatomy ; Finite element ; Network generation ; Mathematical model
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    Topics: Medicine , Technology
    Notes: Abstract A discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8718Bb, 0270Dh
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    Annals of biomedical engineering 28 (2000), S. 278-290 
    ISSN: 1573-9686
    Keywords: Dehydration ; Mathematical model ; Thermoregulation ; Cardiovascular ; Respiratory ; Body water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A model of the human body that integrates the variables involved in temperature regulation and blood gas transport within the cardiovascular and respiratory systems is presented here. It expands upon previous work to describe the competition between skin and muscles when both require increased blood flows during exercise and/or heat stress. First, a detailed study of the control relations used to predict skin blood flow was undertaken. Four other control relations employed in the model were also examined and modified as indicated by empirical results found in literature. Internal responses to exercise and/or heat stress can affect both thermoregulation and the cardiorespiratory system. Dehydration was studied in addition to complete water replacement during similar environmental and exercise situations. Control relations for skin blood flow and evaporative heat loss were modified and a water balance was added to study how the loss of water through sweat can be limiting. Runoff from sweating as a function of relative humidity was introduced along with evaporation, and these results were compared to data to validate the model. © 2000 Biomedical Engineering Society. PAC00: 8719Pp, 8719Uv, 8719Ff, 8710+e
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    Annals of biomedical engineering 28 (2000), S. 495-511 
    ISSN: 1573-9686
    Keywords: Heart ; Epicardial and endocardial differences ; Vascular growth model ; Mathematical model ; Computer simulation ; Constrained constructive optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of “staged growth” guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 8719Hh, 4760+i
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  • 56
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    Keywords: Mathematical model ; Receptor ; Renin ; Kinetic analysis
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    Notes: Abstract Numerous studies have demonstrated changes in receptor number, protein concentration, or mRNA levels and have proposed that these subcellular changes produce physiologic effects. To date, no adequate mathematical analysis has been available to provide a framework for interpretation of such data. In the present study we have combined measurements of angiotensin receptor protein levels with the development of a mathematical model that includes two receptors with opposing actions for a single ligand. This model was used to quantify the net, physiologic response of each receptor population to ANG II stimulation and the effect of altering the expression of receptor populations by a physiologic stimulus. Altered sodium intake was used as the physiologic stimulus and quantification of Western blot analysis and revealed that high sodium diet significantly suppressed AT1 receptor protein in the adrenal gland and aorta and augmented AT2 receptor protein in the aorta. A high sodium diet did not significantly alter AT2 receptor protein in the adrenal gland. Modeling the measured sodium-induced changes in receptor concentration demonstrated that small, subcellular changes in receptor concentration can have a large impact on the net physiologic effect. This model for dual receptor–single ligand interactions should be amenable for other systems. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8714Ee
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    Transport in porous media 13 (1993), S. 205-220 
    ISSN: 1573-1634
    Keywords: Dual-porosity ; fractures ; gravitational forces ; homogenization ; modeling ; validation
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    Topics: Geosciences , Technology
    Notes: Abstract Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual-porosity model was derived in Part I of this work from the microscopic model by two-scale mathematical homogenization. In this paper, we show that the dual-porosity model predicts well the behavior of the microscopic model by comparing their computed solutions in certain reasonable test cases. Homogenization gives a complex formula for a key parameter in the dual-porosity model; herein a simple approximation to this formula is presented. The third model considered is a single-porosity model with averaged parameters. It is shown that this type of model cannot predict the behavior of the microscopic flow.
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    Transport in porous media 13 (1993), S. 179-203 
    ISSN: 1573-1634
    Keywords: Dual-porosity ; fractures ; gravitational forces ; homogenization ; modeling
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    Topics: Geosciences , Technology
    Notes: Abstract We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.
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    Transport in porous media 28 (1997), S. 233-251 
    ISSN: 1573-1634
    Keywords: capillary pressure ; conservation equations ; constitutive equations ; liquid water ; modeling ; thermodynamic equilibrium
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    Notes: Abstract In this paper some considerations are presented about the equations needed to set up a model of the process of heat and mass transfer in porous media. A clear classification is made of the various types of equations used and of their physical meaning. Special attention is paid to the thermodynamic equilibrium equations and to their derivation since they are too often taken for granted. The importance of the various transport mechanisms (of mass and energy) is analyzed and the consequences that can arise when some term is neglected are indicated.
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    Transport in porous media 28 (1997), S. 285-306 
    ISSN: 1573-1634
    Keywords: fissured media ; homogenization ; dual porosity ; modeling ; microstructure ; porous media
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    Topics: Geosciences , Technology
    Notes: Abstract Totally fissured media in which the individual cells are isolated by the fissure system are effectively described by double porosity models with microstructure. Such models contain the geometry of the individual cells in the medium and the flux across their interface with the fissure system which surrounds them. We extend these results to a dual-permeability model which accounts for the secondary flux arising from direct cell-to-cell diffusion within the solid matrix. Homogenization techniques are used to construct a new macroscopic model for the flow of a single phase compressible fluid through a partially fissured medium from an exact but highly singular microscopic model, and it is shown that this macroscopic model is mathematically well posed. Preliminary numerical experiments illustrate differences in the behaviour of solutions to the partially fissured from that of the totally fissured case.
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    Transport in porous media 4 (1989), S. 199-212 
    ISSN: 1573-1634
    Keywords: Mathematical model ; borehole coal mining system ; sorption phenomenon of methane in coal ; methane flow in porous coal seams
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    Topics: Geosciences , Technology
    Notes: Abstract Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.
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  • 62
    ISSN: 1573-1839
    Keywords: virtual reality ; modeling ; constructionism ; astronomy
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    Topics: Natural Sciences in General , Technology
    Notes: Abstract In this manuscript we describe an introductory astronomy course for undergraduate students in which we moved from the large-lecture format to one in which students were immersed in a technologically-rich, inquiry-based, participatory learning environment. Specifically, undergraduate students used 3-D modeling tools to construct virtual reality models of the solar system, and in the process, build rich understandings of various astronomical phenomena. For this study, primarily naturalistic inquiry was used to gain a holistic view of this semester-long course. These data are presented as two case studies focusing on: (1) the role of the teacher in this participatory learning environment; (2) the particular dynamics that formed in each group; (3) the modeling process; (4) the resources used, specifically student-developed inscriptions; and (5) the role of technology and whether learning the technology interfered with learning astronomy. Results indicated that VR can be used effectively in regular undergraduate university courses as a tool through which students can develop rich understandings of various astronomical phenomena.
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    Journal of science education and technology 6 (1997), S. 193-211 
    ISSN: 1573-1839
    Keywords: Science education ; educational engineering ; modeling
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    Topics: Natural Sciences in General , Technology
    Notes: Abstract This article extends and refines the modeling system presented previously (Stewart, 1997). The initial system was sufficient for the optimization of delivery of education at a departmental level. This system is greatly more powerful, precise, and scientific, and fulfills the role of a modeling system for the research and development of educational practices. The model is applied to two widely diverse educational processes, Student Actions and Do Homework Problem, establishing the formalism and demonstrating its usefulness. The use of a rigorous computational syntax imposes completeness criteria on the modeling itself and uniformity. Experimental definition of the formation process of the patterns allows anyone to introduce new features of a model. This and the uniformity allows the models to become the property of the education community, not merely a single researcher, in the same way that mathematical models allow scientists to utilize and build upon previous research.
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    Journal of science education and technology 6 (1997), S. 297-314 
    ISSN: 1573-1839
    Keywords: Science education ; educational engineering ; modeling
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    Topics: Natural Sciences in General , Technology
    Notes: Abstract This paper presents a measurement of the time and resources committed to traditional student actions such as reading and working homework. The perception of the educational value of each basic action for both students and faculty is captured. From this information, basic educational efficiencies are computed for a traditional mechanics course and a non-traditional hands-on Electricity and Magnetism course. The calculations show an allocation of resources in the traditional course which uses the most student time in the least educationally valuable activity. The computed efficiencies also show overseen student note-taking as potentially a very valuable general tool. The techniques presented allow any institution to carry out quantitative educational engineering of their course offerings at the highest level.
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    Plasma chemistry and plasma processing 9 (1989), S. 45-71 
    ISSN: 1572-8986
    Keywords: Thermal plasma flows ; particulates ; three-dimensional effects ; swirl component ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Injection of particulate matter into a thermal plasma represents one of the approaches used in thermal plasma processing. The injected particles are usually treated as a dispersed phase, governed by the equation of motion and the rate equations for heat and mass transfer in Lagrangian coordinates. A stochastic approach is introduced to take particle dispersion into account due to turbulent fluctuations by randomly sampling instantaneous flow fields. Three-dimensional effects are also considered which are mainly due to particle injection and the presence of a swirl component. A modified approach for investigating noncontinuum effects on plasma-particle heat transfer is proposed, incorporating both electric and aerodynamic effects on the boundary layer around a particle immersed into a thermal plasma. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.
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    Plasma chemistry and plasma processing 9 (1989), S. 291-328 
    ISSN: 1572-8986
    Keywords: Thermal plasma jets ; turbulence ; vortex flow ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract This work is concerned with analytical studies of thermal plasma jets, which are finding increasing interest for thermal plasma processing. A two-dimensional model for turbulent plasma jets with superimposed vortex flow has been developed, incorporating multiple time scales for velocity and temperature fluctuations and a density-weighted averaging for the density fluctuation effect. Results show that adding swirl to the flow field for confined and free jets induces strong axial and radial pressure gradients near the nozzle exit, causing a rapid decay of the axial velocity with increasing distance from the nozzle. Comparisons with cold flow show similar trends close to the nozzle exit, but further downstream, the axial velocities increase again, especially for larges swirl numbers. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.
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    Plasma chemistry and plasma processing 3 (1983), S. 259-273 
    ISSN: 1572-8986
    Keywords: Electric arcs ; thermal plasmas ; contaminants ; modeling
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract Plasmas consisting of a high-ionization-potential component mixed with a low-ionization-potential contaminant are common in industrial processes. Modeling results are presented for a sodium-contaminated nitrogen plasma column operating either in a free-burning (low-temperature) mode or operating in a constricted (high-temperature) mode. At sufficiently high plasma temperatures, the behavior is dominated by the high-ionization-potential component's properties. The low-ionization-potential contaminant's properties determine the low-temperature plasma behavior even when the contaminant is present in relatively small quantities.
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    Annals of biomedical engineering 14 (1986), S. 383-400 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Protein ; Platelets ; Embolization ; Artificial surface
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    Topics: Medicine , Technology
    Notes: Abstract A theoretical model for the deposition and detachment of protein and platelets on biomaterial surfaces is presented here. This work is an extension of themodel previously reported (12). Two mechanisms of protein and platelet removal are assumed: (1) A characteristic time elapses before adsorbed protein detaches from the surface, carrying away platelets and protein which have deposited on top of it; and (2) thrombi that attain a critical size are subject to hydrodynamic forces which embolize them from the surface. A theoretical distribution of thrombus sizes is assumed. Analysis of the effects of varying model parameters on predicted protein and platelet deposition reveals that the addition of the embolization process does not change the overall structure of the deposition profiles, but does significantly affect the finer details.
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    Annals of biomedical engineering 21 (1993), S. 435-458 
    ISSN: 1573-9686
    Keywords: Coronary circulation ; Mathematical model ; Coronary compression ; Ischemia ; Collaterals
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    Notes: Abstract The dynamics of the transmyocardial coronary flow patterns during normal and ischemic conditions are complex and relatively inaccessible to measurements. Therefore, theoretical analyses are needed to help in understanding these phenomena. The proposed model employs compartmental division to three layers, each with four vessel-size compartments which are characterized by resistance and compliance. These compartments are subjected to the extravascular compressive pressure (ECP) generated by cardiac contraction, which by modifying the transmural pressure causes changes in cross-sectional area of the vessels in each compartment continuously determining the resistance and capacitance values. Autoregulation and collaterals are also included in order to simulate the flow patterns during regional ischemia. Using these features, the model predicts the typical out of phase arterial and venous flow patterns. Systolic collapse of the large intramyocardial veins during the normal cycle, as well as systolic arteriolar collapse during ischemia are predicted. The transmural flow during ischemia is characterized by alternating flows between the layers. The ECP is considered here is two ways: (a) as a function of left ventricle (LV) pressure, decreasing linearly from endocardium to epicardium and (b) as the interstitial fluid pressure, employing a multilayer muscle-collagen model of the LV. While both of these approaches can describe the dynamics of coronary flow under normal conditions, only the second approach predicts the large compressive effects due to high ECP obtained at very low cavity pressure, resulting from significant muscle shortening and radial collagen stretch. This approach, combining a detailed description of transmural coronary circulation interacting with the contracting myocardium agrees with many observations on the dynamics of coronary flow and suggests that the type of LV mechanical model is important for that interaction.
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    ISSN: 1573-9686
    Keywords: Invasion ; Collagen gel ; Mathematical model ; Metastasis ; Migration ; Cell tracking
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Anin vitro assay proposed to systematically characterize and compare cell invasion under different conditions is the collagen gel invasion assay where cells, initially seeded onto the surface of a type I collagen gel, penetrate the surface and migrate within the gel over time. Using simplifying assumptions about cell transport across the gel surface and migration within the gel, we formulate and solve a mathematical model of this assay which predicts the resulting cell distribution based on three phenomenological parameters characterizing the ability of cells to penetrate the gel surface interface, migrate randomly within the gel, and return to the gel surface. An index of cell invasiveness is defined based on these parameters that reflects the overall ability of cells to transport across the gel surface interface, that is, invade the gel. Cell concentration profiles predicted by the model correspond well to measured profiles for murine melanoma cells invading gels supplemented with extracellular matrix proteins fibronectin and type IV collagen as well as unsupplemented gels, allowing these parameters to be estimated by a nonlinear regression fit of the model solution to the measured profiles. Our analysis suggests that type IV collagen and fibronectin primarily modulate cell transport across the gel surface interface rather than migration within the gel. Further, we validate the key model assumptions and obtain independent, direct estimates of model parameters by time-lapse video microscopy and digital image analysis of cell penetration of the gel surface and migration within the gel during the assay.
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    Annals of biomedical engineering 23 (1995), S. 48-60 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Soluble gas exchange ; Alcohol breath test
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    Topics: Medicine , Technology
    Notes: Abstract A previously developed mathematical model that describes the relationship between blood alcohol (ethanol) concentration and the concentration of alcohol in the exhaled breath at end-exhalation (BrAC) has been used to quantitate the effect of pretest breathing conditios on BrAC. The model was first used to “condition” the airways with different breathing maneuvers prior to simulating a single exhalation maneuver, the maneuver used in standard breath alcohol testing. On inspiration, the alcohol in the air reaches local equilibrium with the alcohol in the bronchial capillary bed prior to entering the alveolar region. On expiration, approximately 50% of the alcohol absorbed on inspiration is desorbed back to the airways. BrAC correlates with the amount of alcohol that is desorbed to the airways. The six pretest breathing conditions and the percent change in BrAC relative to the control maneuver were: hyperventilation (−4.4%), hypoventilation (3.7%), hot-humid air (−2.9%), hot-dry air (0.66%), cold-humid air (0.13%), and cold-dry air (0.53%). The mechanism underlying these responses is not due to changes in breath temperature, but, rather to changes in the axial profile of alcohol content in the mucous lining of the airways.
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    Annals of biomedical engineering 23 (1995), S. 164-177 
    ISSN: 1573-9686
    Keywords: Arterial system ; Mathematical model ; Total arterial compliance ; Aortic characteristic impedance ; Nonlinear pressure-volume relationship ; Parameter estimation ; Energy balance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steadystate periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.
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    Annals of biomedical engineering 23 (1995), S. 299-307 
    ISSN: 1573-9686
    Keywords: Signal transduction ; Antagonist ; Mathematical model ; Diffusion ; Computer simulation ; Smooth muscle cells ; Phenylephrine ; Prazosin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Cells have evolved elaborate strategies for sensing, responding to, and interacting with their environment. In many systems, interaction of cell surface receptors with extracellular ligand can activate cellular signal transduction pathways leading to G-protein activation and calcium mobilization. In BC3H1 smooth muscle-like cells, we find that the speed of calcium mobilization as well as the fraction of cells which mobilize calcium following phenylephrine stimulation is dependent upon receptor occupation. To determine whether receptor inactivation affects calcium mobilization, we use the receptor antagonist prazosin to block a fraction of cell surface receptors prior to phenylephrine stimulation. For cases of equal receptor occupation by agonist, cells with inactivated or blocked receptors show diminished calcium mobilization following phenylephrine stimulation as compared to cells without inactivated receptors. Ligand/receptor binding and two-dimensional diffusion of receptors and G-proteins in the cell membrane are studied using a Monte Carlo model. The model is used to determine if receptor inactivation affects G-protein activation and thus the following signaling events for cases of equal equilibrium receptor occupation by agonist. The model predicts that receptor inactivation by antagonist binding results in lower G-protein activation not only by reducing the number of receptors able to bind agonist but also by restricting the movement of agonist among free receptors. The latter process is important to increasing the access of bound receptors to G-proteins.
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    Annals of biomedical engineering 26 (1998), S. 166-178 
    ISSN: 1573-9686
    Keywords: ARDS ; Intravenous oxygenation ; Artificial lung ; Mathematical model ; Model ; Gas exchange ; Oxygenator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Acute respiratory distress syndrome (ARDS) is a pulmonary edemic condition which reduces respiratory exchange in 150,000 people per year in the United States. The currently available therapies of mechanical ventilation and extracorporeal membrane oxygenation are associated with high mortality rates, so intravenous oxygenation represents an attractive, alternative support modality. We are developing an intravenous membrane oxygenator (IMO) device intended to provide 50% of basal oxygen and carbon dioxide exchange requirements for ARDS patients. A unique aspect of the IMO is its use of an integral balloon to provide active mixing. This paper describes a mathematical model which was developed to quantify and optimize the gas exchange performance of the IMO. The model focuses on balloon activated mixing, uses a lumped compartment approach, and approximates the blood-side mass transfer coefficients with cross-flow correlations. IMO gas exchange was simulated in water and blood, for a variety of device geometries and balloon pulsation rates. The modeling predicts the following: (1) gas exchange efficiency is reduced by a buildup of oxygen in the fluid near the fibers; (2) the IMO gas exchange rate in blood is normally about twice that in water under comparable conditions; (3) a balloon diameter of about 1.5 cm leads to optimal gas exchange performance; and (4) in vivo positioning can affect gas exchange rates. The numerically predicted gas transfer rates correlate closely with those experimentally measured in vitro for current IMO prototypes. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 8790+y, 8265Fr
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  • 75
    ISSN: 1573-9686
    Keywords: Oxygen transport ; Microcirculation ; Cerebral circulation ; Hypoxia ; Carbon monoxide ; Mathematical model ; Computer simulation ; Anemia ; Hematocrit ; Brain
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Cerebral blood flow (CBF) increases as arterial oxygen content falls with hypoxic (low PO2), anemic (low hemoglobin) and carbon monoxide (CO) (high carboxyhemoglobin) hypoxia. Despite a higher arterial PO2, CO hypoxia provokes a greater increase in CBF than hypoxic hypoxia. We analyzed published data using a compartmental mathematical model to test the hypothesis that differences in PO2 in tissue, or a closely related vascular compartment, account for the greater response to CO hypoxia. Calculations showed that tissue, but not arteriolar, PO2 was lower in CO hypoxia because of the increased oxyhemoglobin affinity with CO hypoxia. Analysis of studies in which oxyhemoglobin affinity was changed independently of CO supports the conclusion that changes in tissue PO2 (or closely related capillary or venular PO2) are predictive of alterations in CBF. We then sought to determine the role of tissue PO2 in anemic hypoxia, with no change in arterial and little, if any, change in venous PO2. Calculations predict a small fall in tissue PO2 as hematocrit decreases from 55% to 20%. However, calculations show that changes in blood viscosity can account for the increase in CBF in anemic hypoxia over this range of hematocrits. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 8722-q, 8745Ft
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  • 76
    ISSN: 1573-9686
    Keywords: Mathematical model ; Parameter estimation ; Flow heterogeneity ; Skeletal muscle ; Glucose ; Blood flow heterogeneity ; Modeling transcapillary exchange
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Distributed models of blood-tissue exchange are widely used to measure kinetic events of various solutes from multiple tracer dilution experiments. Their use requires, however, a careful description of blood flow heterogeneity along the capillary bed. Since they have mostly been applied in animal studies, direct measurement of the heterogeneity distribution was possible, e.g., with the invasive microsphere method. Here we apply distributed modeling to a dual tracer experiment in humans, performed using an intravascular (indocyanine green dye, subject to distribution along the vascular tree and confined to the capillary bed) and an extracellular ([3H]-D-mannitol, tracing passive transcapillary transfer across the capillary membrane in the interstitial fluid) tracer. The goal is to measure relevant parameters of transcapillary exchange in human skeletal muscle. We show that assuming an accurate description of blood flow heterogeneity is crucial for modeling, and in particular that assuming for skeletal muscle the well-studied cardiac muscle blood flow heterogeneity is inappropriate. The same reason prevents the use of the common method of estimating the input function of the distributed model via deconvolution, which assumes a known blood flow heterogeneity, either defined from literature or measured, when possible. We present a novel approach for the estimation of blood flow heterogeneity in each individual from the intravascular tracer data. When this newly estimated blood flow heterogeneity is used, a more satisfactory model fit is obtained and it is possible to reliably measure parameters of capillary membrane permeability-surface product and interstitial fluid volume describing transcapillary transfer in vivo. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 8722Fy
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  • 77
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    Annals of biomedical engineering 26 (1998), S. 1036-1043 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Perfusion ; Diffusion ; Collagen ; Nitric oxide (NO) inhibition ; Platelet adhesion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Nitric oxide (NO) is a simple biological molecule which inhibits adhesion and aggregation of platelets. A novel NO delivery device has been developed to quantitatively study the effects of NO concentration and flux on the adhesion of platelets to a surface. The slit-flow device is lined with a protein-coated membrane through which NO gas permeates into a perfusing platelet suspension. A model predicting spatial NO concentrations and fluxes within the flow slit was validated. At a wall shear rate of 250s-1, platelet adhesion was inhibited 87% relative to controls for exposures as low as 0.1 ppm NO. Corresponding model predictions of the aqueous NO concentration and fluxes at the surface were 0.15 nM, and between 0.5 and 1.1 nanomoles cm-2 s-1, respectively. Endo-thelial cells, which release NO to inhibit platelet adhesion in vivo, generate NO at an estimated flux similar to the above values. At a NO exposure of 0.02 ppm, platelet inhibition was only 10%. The delivery device is useful for other studies in which a knowledge of the spatial NO fluxes or concentrations is desired. Knowledge of these fluxes or concentrations is beneficial towards the design of biomaterials incorporating NO to inhibit platelet adhesion. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8722Fy, 8780+s, 8710+e, 8380Lz
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  • 78
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    Annals of biomedical engineering 26 (1998), S. 1044-1054 
    ISSN: 1573-9686
    Keywords: Lung ; Gas exchange ; Mathematical model ; O2 and CO2 transfer ; Microporous hollow fibers
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    Topics: Medicine , Technology
    Notes: Abstract An intravascular gas exchange device for the treatment of respiratory failure consisted of a multitude of blind-ended hollow fibers glued in a pine-needle arrangement to a central gas supply catheter. It has previously been shown that gas desorption rates can be significantly enhanced by cycling gas pressure between a hypobaric level of 130 and an ambient level of 775 Torr. In this study, influences of the cycling frequency (f) and the cycle fraction during which hypobaric pressure is applied (Θ) were investigated. Rates of O2 desorption from O2-saturated water and CO2 desorption from CO2-saturated water into a manifold containing 198 fibers, 380 μm in diameter, were measured over a range of f from 0.2 to 1.0 Hz, Θ from 0.1 to 0.8, and fiber lengths from 4 to 16 cm. Relative to operation at ambient pressure, pressure cycling increased O2 transfer 3–4 times and CO2 transfer 4–6 times when the water flowed over the fiber manifold at 2.3 l/min. Transfer rates were relatively insensitive to f and Θ with 80–90% of maximum enhancement obtained when Θ was as low as 0.2. Transfer rates increased continuously with fiber length, implying that pressure cycling reduced the intra-fiber resistance to gas diffusion. A mathematical diffusion model which utilized only two adjustable parameters, a mass transfer coefficient for O2 and for CO2, simulated the trends exhibited by desorption data. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8790+y
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  • 79
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    Annals of biomedical engineering 26 (1998), S. 911-913 
    ISSN: 1573-9686
    Keywords: Physiological database ; Mathematical model ; Physiome: microcirculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Presented is a discussion of steps towards the creation of a database of the microcirculation encompassing anatomical and functional experimental data, and conceptual and computational models. The discussion includes issues of database utility, organization, data deposition, and linkage to other databases. The database will span levels from gene to tissue and will serve both research and educational purposes. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 0130Cc
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  • 80
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    Annals of biomedical engineering 26 (1998), S. 914-930 
    ISSN: 1573-9686
    Keywords: Flow distribution ; Axial diffusion ; Mathematical model ; Perfusion heterogeneity ; Relative dispersion ; Heterogeneity ; Capillary transit times ; Indicator dilution
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract To mathematically model multiple indicator dilution (MID) data for the purpose of estimating parameters descriptive of indicator-tissue interactions, it is necessary to account for the effects of the distribution of capillary transit times, hc(t) In this paper, we present an efficient approach for incorporating hc(t) in the mathematical modeling of MID data. In this method, the solution of the model partial differential equations obtained at different locations along the model capillary having the longest transit time provides the outflow concentrations for all capillaries. When weighted by hc(t) these capillary outflow concentrations provide the outflow concentration versus time curve for the capillary bed. The method is appropriate whether the available data on capillary dispersion are in terms of capillary transit time or relative flow distributions, and whether the dispersion results from convection time differences among heterogeneous parallel pathways or axial diffusion along individual pathways. Finally, we show that the knowledge of a relationship among the moments of hc(t) rather than hc(t) per se, is sufficient information to account for the effect of hc(t) in the mathematical modeling interpretation of MID data. This relationship can be determined by including a flow-limited indicator in the injected bolus, thus providing an efficient means for obtaining the experimental data sufficient to account for capillary flow and transit time heterogeneity in MID modeling. © 1998 Biomedical Engineering Society. PAC98: 8745Ft, 8710+e, 0230Jr
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  • 81
    ISSN: 1573-9686
    Keywords: Cardiopulmonary resuscitation ; Mathematical model ; Intrathoracic pressure
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Whether blood flow during cardiopulmonary resuscitation (CPR) results from intrathoracic pressure fluctuations or direct cardiac compression remains controversial. We developed a mathematical model that predicts that blood flow due to intrathoracic pressure fluctuations should be insensitive to compression rate over a wide range but dependent on the applied force and compression duration. If direct compression of the heart plays a major role, however, the model predicts that flow should be dependent on compression rate and force, but above a threshold, insensitive to compression duration. These differences in hemodynamics produced by changes in rate and duration form a basis for determining whether blood flow during CPR results from intrathoracic pressure fluctuations or from direct cardiac compression. The model was validated for direct cardiac compression by studying the hemodynamics of cyclic cardiac deformation following thoracotomy in four anesthetized, 21–32-kg dogs. As predicted by the model, there was no change in myocardial or cerebral perfusion pressures when the duration of compression was increased from 15% to 45% of the cycle at a constant rate of 60/min. There was, however, a significant increase in perfusion pressures when rate was increased from 60 to 150/min at a constant duration of 45%. The model was validated for intrathoracic pressure changes by studying the hemodynamics produced by a thoracic vest (vest CPR) in eight dogs. The vest contained a bladder that was inflated and deflated. Vest CPR changed intrathoracic pressure without direct cardiac compression, since sternal displacement was 〈0.8 cm. As predicted by the model and opposite to direct cardiac compression, there was no change in perfusion pressures when the rate was increased from 60 to 150/min at a constant duration of 45% of the cycle. Manual CPR was then studied in eight dogs. There was no surgical manipulation of the chest. Myocardial and cerebral blood flows were determined with radioactive microspheres and behaved as predicted from the model of intrathoracic pressure, not direct cardiac compression. At nearly constant peak sternal force (378–426 N), flow was significantly increased when the duration of compression was increased from short (13%–19% of the cycle) to long (40%–47%), at a rate of 60/min. Flow was unchanged, however, for an increase in rate from 60 to 150/min at constant compression duration. In addition, myocardial and cerebral flow correlated with their respective perfusion pressures. Thus vital organ perfusion pressures and flow for manual external chest compression are dependent on the duration of compression, but not on rates of compression of 60 and 150/min. These data are of course similar to those produced by vest CPR, where intrathoracic pressure is manipulated without sternal displacement, and to those predicted for movement of blood by intrathoracic pressure changes. These data are, however, opposite to those produced by cardiac deformation and to those predicted for movement blood by direct cardiac compression. We conclude that intrathoracic pressure fluctuations generate blood flow during manual CPR.
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  • 82
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    Annals of biomedical engineering 17 (1989), S. 13-38 
    ISSN: 1573-9686
    Keywords: Oxygen transport ; Microcirculation ; Cerebral circulation ; Carbon monoxide ; Mathematical model ; Computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A compartmental model is formulated for oxygen transport in the cerebrovascular bed of the brain. The model considers the arteriolar, capillary and venular vessels. The vascular bed is represented as a series of compartments on the basis of blood vessel diameter. The formulation takes into account such parameters as hematocrit, vascular diameter, blood viscosity, blood flow, metabolic rate, the nonlinear oxygen dissociation curve, arterial PO2, P50 (oxygen tension at 50% hemoglobin saturation with O2) and carbon monoxide concentration. The countercurrent diffusional exchange between paired arterioles and venules is incorporated into the model. The model predicts significant longitudinal PO2 gradients in the precapillary vessels. However, gradients of hemoglobin saturation with oxygen remain fairly small. The longitudinal PO2 gradients in the postcapillary vessels are found to be very small. The effect of the following variables on tissue PO2 is studied: blood flow, PO2 in the arterial blood, hematocrit, P50, concentration of carbon monoxide, metabolic rate, arterial diameter, and the number of perfused capillaries. The qualitative features of PO2 distrbution in the vascular network are not altered with moderate variation of these parameters. Finally, the various types of hypoxia, namely hypoxic, anemic and carbon monoxide hypoxia, are discussed in light of the above sensitivity analysis.
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  • 83
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    Annals of biomedical engineering 16 (1988), S. 445-461 
    ISSN: 1573-9686
    Keywords: Periodic breathing ; Respiratory control ; Mathematical model ; CO2 mass transport ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A stability analysis of respiratory chemical control is developed using a mathematical model of CO2 mass transport dynamics. Starting with a 3-compartment model of CO2 stores that distinguishes alveolar, muscle, and other tissue, model reduction techniques are applied to obtain a first-order representation of the respiratory plant. This model contains an effective tissue volume for CO2, whose derived value is much smaller than previously predicted. To investigate oscillatory instabilities, a controller which incorporates only peripheral chemoreceptor responses was added to the first-order plant model. An explicit stability index (SI) is obtained analytically from a linearized version of this model. SI varies directly with the controller gain and circulation delay time and inversely with the effective tissue volume and inspired CO2 concentration. Numerical simulations using the first-order nonlinear model show that SI is a good predictor of system stability. According to the linearized model, the system is stable for SI〈1; from the nonlinear model, the system is stable for SI〈1.1. For typical normal adults, the SI value is well within the stable region.
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  • 84
    ISSN: 1573-9686
    Keywords: SA node ; Mathematical model ; Vagal control ; ACh
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract We present a new mathematical model for vagal control of rabbit sinoatrial (SA) node electrical activity based on the DiFrancesco-Noble equations. The original equations were found to be unstable, resulting in progressive cycle by cycle depletion or accumulation of ions in intra- and extracellular compartments. This problem was overcome by modifying the maximum Na−K pump current and the time constant for uptake of intracellular calcium. We also included a formulation for the acetylcholine (ACh)-activated potassium current which was consistent with experimental data. This formulation was based on kinetics first proposed by Osterrieder and later modified by Yanagihara. The resulting model exhibits cycle-cycle ionic stability, and includes an ACh-activated potassium current which accurately reproduces experimentally observed effects of vagal stimulation on both the membrane potential and its timederivative. Simulations were performed for both brief-burst and prolonged vagal stimulation using simplified square wave profiles for the concentration of ACh in the synaptic cleft space. This protocol permits the isolation of cardiac period dynamics caused by changes in membrane potential and intra- and extracellular ionic concentrations from those caused by other mechanisms including the dynamics of ACh release, diffusion, hydrolysis and washout. Simulation results for the effects of brief-burst single cycle stimulation on the cardiac period agree closely with experimental data reported in the literature, accurately reproducing changes in membrane potential and the phasic dependency of the response to the position of vagal stimulus bursts within the cycle. Simulation of the effects of prolonged vagal stimulation accurately reproduced the steady-state characteristics of heart period response, but did not yield the complex multimodal dynamics of the recovery phase, or the pronounced post vagal tachycardia observed experimentally at the termination of the stimulus. Our results show that the major chronotropic effects of vagal stimulation on the SA cell membrane can be explained in terms of the ACh-activated potassium current. The effects of this membrane current however are generally fast acting and cannot contribute to any long lasting dynamics of the cardiac period response. The modified DiFrancesco-Noble model presented in this article provides a valuable theoretical tool for further analysis of the dynamics of vagal control of the cardiac pacemaker.
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  • 85
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    Annals of biomedical engineering 26 (1998), S. 28-36 
    ISSN: 1573-9686
    Keywords: Mathematical model ; Tissue factor ; Wall shear rate ; FXa generation ; TF:FVIIa ; Rat ; Vascular ; Smooth muscle ; Factor X ; Coagulation ; Clot
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A computational model was developed to investigate the contribution of classical mass transport and flow parameters to factor X (FX) activation by the tissue factor–factor VIIa complex (TF:VIIa) on one wall of a parallel-plate flow chamber. The computational results were compared to previously obtained experimental data for the generation of factor Xa (FXa) by TF:VIIa on the surface of cultured rat vascular smooth muscle cells. In this study, the complete steady-state convection–diffusion equation was solved using the commercial software package, FLUENT (Fluent Inc., Lebanon, New Hampshire). A user-defined subroutine interfaced with FLUENT implemented the surface reaction which was modeled using classical Michaelis–Menten reaction kinetics. The numerical solutions were obtained for 12 cases which used combinations of three wall shear rates and four reaction rates. The numerically obtained fluxes for a given reaction rate displayed a wall shear rate dependence which ranged from classical kinetic reaction control (no dependence) to pure diffusional control (maximum dependence). The experimental data, however, were not represented by numerical data generated using a single reaction rate. The three numerically obtained fluxes which corresponded most closely to the experimental fluxes were determined using three different V max values. This finding supports the hypothesis that there may be a direct effect of flow on the TF:VIIa complex or the cell membrane. © 1998 Biomedical Engineering Society. PAC98: 8722-q, 8710+e
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  • 86
    ISSN: 1573-9686
    Keywords: Mannitol ; Deconvolution ; Mathematical model ; Transport function ; Recirculation ; Indicator dilution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The transport function of an indicator through an organ allows the calculation of important physiological parameters, but its estimation, especially in the presence of recirculation, can be difficult. In this paper, we estimate the transport function of 3H-mannitol (an extracellular tracer of glucose) in the human leg skeletal muscle. To do so, an indicator bolus is administered into the femoral artery and its recirculating dilution curves are nonuniformly sampled in both the femoral artery and the femoral vein. A new deconvolution-based method is used to simultaneously estimate the indicator transport function and the organ plasma flow. Subsequently, the indicator mean transit time and distribution volume are calculated. The reliability of the method is assessed by Monte Carlo simulation. The ability to estimate parameters, like mean transit time and extracellular distribution volume, is critical to the study of pathophysiologic states such as diabetes, insulin resistance, and hypertension. © 1998 Biomedical Engineering Society. PAC98: 8710+e, 0270Lq, 8745Hw
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  • 87
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    Annals of biomedical engineering 26 (1998), S. 417-430 
    ISSN: 1573-9686
    Keywords: Capillary permeability ; Acute respiratory distress syndrome ; Mathematical model ; Alloxan lung injury ; Pulmonary edema ; Lung fluid balance ; Indicator dilution: optical ; Indicator dilution: radioisotope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The objective of this study was a validation of an optical multiple indicator dilution technique for measuring microvascular exchange parameters in edematous lungs by comparison to conventional radioisotope multiple indicator dilution methods. Six anesthetized dogs were studied at baseline and after alloxan infusion to increase capillary permeability. In addition, 11 isolated, perfused dog lungs were studied at baseline and after edema was created by increasing venous pressure or by infusing alloxan to increase vascular permeability. Increased capillary permeability from alloxan infusion led to increases in most but not all capillary exchange parameters as analyzed by mathematical models and measured by both optical and radioisotope methods. Increased vascular pressure led to increased edema but no significant increases in capillary exchange parameters. Two-way analysis of variance (ANOVA; variations in baseline versus pressure or alloxan and variation in optical versus radioisotope for each transport parameter derived from the mathematical models) indicated few significant differences in capillary exchange parameters between optical and radioisotope measures. Newman–Keuls multiple comparison tests did uncover some variations between a few of the group-mean values derived from optical and radioisotope methods. However, optical and radioisotope parameter measurements were highly correlated for all studies regardless of the mathematical model used for analysis.
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  • 88
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    Annals of biomedical engineering 27 (1999), S. 525-537 
    ISSN: 1573-9686
    Keywords: Biosensors ; Mathematical model ; Algorithms ; Inverse problems ; Input estimation ; Regularization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract An approach for inference of blood glucose concentrations in real time is considered. First, a model that predicts the subcutaneous glucose concentration from the blood glucose concentration is presented. The model includes diffusive transport from the blood to the subcutaneous tissue and reactive-like cellular uptake of glucose. Next, the Phillips-Tikhonov regularization method is considered to solve the real-time input estimation problem that determines the blood glucose concentration given the subcutaneous glucose concentration. The inverse problem is regularized by imposing a smoothing condition to obtain a stable solution. Three different penalization functionals were considered in evaluating the regularization method using a synthetic function that approximates the subcutaneous glucose response to an oral glucose tolerance test in a human subject. Various levels of either white noise or time-correlated noise were superimposed onto the synthetic response to evaluate the sensitivity of the inverse to measurement error. For inversion assuming only diffusive transport, the optimal time interval of integration of previous subcutaneous measurements was found to be about 1.5/ $$\hat \alpha $$ , where $$\hat \alpha $$ -1 is the dominant time constant for the exchange of glucose between the blood and subcutaneous tissue. The optimal sampling rate was found to be 54 $$\hat \alpha $$ . Linear regularizations based on minimization of first or second derivatives of the blood glucose concentration were found to be satisfactory, each yielding a minimum error that was about 50% greater than the measurement error. Including nonlinear, reactive-like uptake of glucose was found to decrease the error magnification factor slightly. Both the model and the inverse method relating blood and subcutaneous glucose concentrations are successfully applied to experimental measurements using glucose biosensors reported by Schmidtke et al. (Proc. Natl. Acad. Sci. USA 95:294–299, 1998). © 1999 Biomedical Engineering Society. PAC99: 8780-y, 8717Aa
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    Journal of engineering mathematics 34 (1998), S. 277-300 
    ISSN: 1573-2703
    Keywords: modeling ; supercell storm ; nonlinear ; inertial oscillation ; mesonetwork data.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The pulsing inertial oscillation (PIO) model is a nonlinear, time-dependent, translating vortex solution of the inviscid, compressible fluid dynamic equations in the middle troposphere. The translation of this vortex during a pulse is strikingly similar to that of a supercell storm – a rotating thunderstorm that can generate tornadoes and hail. Two studies were performed to test the hypothesis that some supercell storms are manifestations of a PIO pulse. The first study applied the model to an intense interior draft whose buoyancy was bounded by a temperature excess of ± 12 K. The peak updraft speed achieved was 41·5 m s−1 and the peak Rossby number was 92·9. The study also pointed to an advanced concept for attaining higher values. The second study applied the PIO model to a supercell storm as a whole and succeeded in replicating its bulk properties, such as mesocylonic circulation, net mass and moisture influxes, and time track. This study also identified a critical feature of the PIO model that could be tested against storm data: The average vertical draft is downward before the turn in the storm track and upward afterwards. In the conventional theory, the average vertical draft is upward from storm inception until dissipation. These differing draft predictions were compared with the best available data, which are surface mesonetwork data. These data were found to support the PIO model. However, surface data alone are not conclusive, and further measurements are warranted.
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