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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 49 (1987), S. 153-169 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulatein vivo transmural accumulation of an intravenously injected tracer in the aortic wall of experimental animals. Parameters have been included to represent the following processes that affect tracer distribution: permeation of the blood-tissue interface, diffusion through the layers of the artery wall,convective solute drag through the same, and degradation. Of particular interest for thein vivo situation situation is the inclusion of boundary conditions that account for the variation in the plasma concentration of injected tracer as a function of time. Two analytical solutions are presented. The first describes a system in which two boundaries must be delineated; it pertains if the tracer is allowed to circulate until it enters the avascular media of the artery wall both across its luminal boundary and from the capillaries in its outer layer. The second applies to shorter duration experiments in which entry across only the luminal boundary is considered. A limiting case of the solution for short circulation times is presented, compared with a previously published solution, and examined for its potential utility in parameter estimation. Because of its treatment of time-dependent boundary conditions, the model has unique application toin vivo experiments related to macromolecular transport in atherosclerosis that may otherwise elude proper interpretation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 39 (1977), S. 117-128 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A diffusion model of tumor growth, vascularization and necrosis is used to analyze experimental data describing the temporal changes in tumor cell and blood vessel radial distributions in a host-tissue field transplanted with a fibrosarcoma. The experimental results showed a peak density of vessels occurring at the advancing migration front of the tumor and a decline in the vessel surface area at the tumor center with time. The peak density of tumor cells shifts away from the tumor center with time. These dynamic changes can be explained by a mathematical model which views the process as one of diffusion and proliferation in time and space. Coupled diffusion equations with nonlinear source and sink terms describe the proliferation, death, and migration of tumor cells and vascular surface area. The concept of an angiogenic factor elaborated by tumor cells is incorporated.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 18 (1990), S. 37-56 
    ISSN: 1573-9686
    Keywords: Ventilatory system ; Respiratory mechanics ; Model simulations ; Rib cage ; Static relaxation ; Abdominal compression ; Mueller maneuver ; Diaphragmatic isometric inspiration ; Paradoxical breathing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A mathematical model of chest wall mechanics, based on a phenomenological approach to force balances, provides a quantitative framework for analyzing many types of chest wall movements by using orthogonal displacement coordinates. The moveable components of the ventilatory system include the rib cage, diaphragm, and abdomen. A distinction is made between the lung-apposed and diaphragm-apposed actions on the rib cage. The model equations are derived from “pressure” balances and geometrical relations of the compartments; the stress-displacement relations are hyperbolic. With this model we simulated stiff and flaccid chest wall behavior under normal and constrained conditions associated with abdominal compression, a Mueller maneuver, and a diaphragmatic isometric inspiration. We also examined situations that produce paradoxical as well as orthodox inspiratory movements. The results of these simulations were quantitatively consistent with available data from the literature. A phenomenon predicted by the stiff-wall model during quasi-static inspiration is that the rib cage displacement is negligible near residual volume, but then increases dramatically with lung volume. Since this mathematical model has a sound physical basis and is more comprehensive than previous models, it can be used to predict and analyze the behavior of the chest wall under a wide variety of circumstances.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of biomedical engineering 19 (1991), S. 723-742 
    ISSN: 1573-9686
    Keywords: Cardiac output ; Acetylene-helium rebreathing ; Mathematical modeling ; Statistical analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A noninvasive method to estimate cardiac output $$\dot Q$$ without special patient cooperation was developed by modifying a previous acetylene-helium (C2H2−He) rebreathing technique (ART). Estimation of $$\dot Q$$ using ART is based on a single-compartment model that is valid only under prescribed breathing; e.g., fast, deep breathing, and emptying of the rebreathing bag on each breath. To make the ART less dependent on subject cooperation, a more sophisticated mathematical model and estimation method are needed. For this purpose, we modeled the C2H2 and He concentration dynamics at the mouth over successive breaths using a multi-compartment model. This model takes into account the effects of breathing pattern, compartmental volumes, and gas solubility. From computer simulations and sensitivity analysis, we found that $$\dot Q$$ could be estimated from the available data with adequate precision. Our model and estimation method were tested on a group of six normal adult subjects, at rest and during submaximal exercise (75 watts). Estimates of $$\dot Q$$ from our new method (6.5±0.4 L/min at rest, 12.5±0.4 L/min at 75 watts) were in agreement with those obtained using a previous ART (7.0±0.3 L/min at rest, 12.6±0.5 L/min at 75 watts). We conclude that this approach promises to provide reliable estimates of $$\dot Q$$ in patients (e.g., children and elderly), at rest and during exercise, without the need of prescribed breathing patterns or changes in rebreathing bag volume.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    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
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A-2: Polymer Physics 6 (1968), S. 1149-1160 
    ISSN: 0449-2978
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A method for the theoretical analysis of branching in radical polymerization is presented which includes the dynamics of the process. In particular, the method is applied to a polymerization that occurs by decomposition of initiator, propagation, termination by radical combination, and chain transfer with polymer. By a numerical solution of the kinetic equations (suitably transformed), the time dependence of the number-average degree of polymerization (DP), the weight-average DP, the mean number of branches, and the monomer conversion are obtained. The parameters of the process, that is the rate coefficients and initial concentrations, have the following effects: (1) An increase in the chain transfer coefficient increases the ratio of weight-average to number-average Xw/Xn and the mean number of branches Xb, but does not change the number-average Xn. (2) For a given value of the chain transfer coefficient, a change in the parameters of the process such that Xn increases, causes Xw/Xn and Xb to increase also. (3) Chain transfer with polymer seems to produce relatively few polymer molecules having many branches and a large number of smaller polymer molecules having no branches; consequently, the polymer size (or molecular weight) distribution broadens.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 13 (1967), S. 319-326 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: For a number of polymerization models, we have developed equations that enable one to follow in time the moments of the polymer size distribution and the conversion. The exact and approximate solutions for the leading moments of the size distribution are presented for polymerization with initiation, propagation, and termination by combination. Approximate solutions for polymerizations with the additions of termination by disproportionation, chain transfer to monomer, and chain transfer to solvent show how these reactions decrease the average polymer size. From a simple model that exhibits autoacceleration a concomitant increase in the average polymer size also occurs.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 14 (1976), S. 402-407 
    ISSN: 1741-0444
    Keywords: Breathing pattern ; computer simulation ; Mathematical model ; Oxygen uptake ; Pulmonary transport
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Description / Table of Contents: Sommaire La montée d'oxygène pulmonaire a été analysée pour déterminer l'importance relative des paramètres caractérisant le mode de la respiration. On a simulé sur calculateur le transport d'oxygène pulmonaire en exploitant un modèle à compartiments multiples du poumon, en supposant l'absence de dérivations, une sortie cardiaque constante et une respiration d'oxygène de l'ordre de 21%. Des simulations de la montée d'oxygène dans les poumons relatives aux différents modes de respiration indiquent que les paramètres ayant le plus grand effet sur l'oxygène artériel sont le volume d'aspiration et le taux de respiration. Quand le volume de respiration et le ‘schéma’ de la respiration sont constants, c'est-à-dire, quand la ventilation est totale et constante, les variations, même extrêmes, du schéma du débit donnet lieu à des modifications relativement faibles de l'oxygène artériel. Pour une concentration d'oxygène inspiré donnée, des stratagèmes optima destinés à fournir un échange des gaz suffisant à l'aide d'un moyen de ventilation mécanique dans l'absence d'oedèmes ou d'atélectasie, peuvent être basés principalement sur les changements du volume d'aspiration et des taux de respiration.
    Abstract: Zusammenfassung Die Sauerstoffaufnahme der Lunge wurde analysiert, um die relative Bedeutung von Atmungsparametern festzulegen. Durch ein mehrteiliges Lungenmodell wurden Computersimulationen des Sauerstofftransports der Lunge erzielt. Dabei wurde von der Annahme ausgegangen, daß keine Umgehungen vorlagen, die Herzleistung konstant blieb und 21% Sauerstoff eingeatmet wurden. Eine Simulation der Sauerstoffaufnahme der Lunge durch verschiedenartige Atmung zeigte, daß Atmungsluftvolumen und Geschwindigkeit der Atmung die Parameter sind, die sich am stärksten auf den arteriellen PO2-Gehalt auswirken. Wenn Atmungsluftvolumen und Atmungsgeschwindigkeit konstant sind, d.h. bei konstanter Gesamtbeatmung, ergeben sich selbst bei extremen Schwankungen in der Form der Luftzufuhr relativ geringe Änderungen im arteriellen PO2-Gehalt. Bei einer bestimmten eingeatmeten Sauerstoffkonzentration lassen sich die optimalen Strategien zum Erzielen eines ausreichenden Gasaustausches durch mechanisch unterstützte Beatmung ohne wesentliche Oedeme oder Atelektasen in erster Linie durch eine Änderung des Atmungsluftvolumens und der Atmungsgeschwindigkeit erreichen.
    Notes: Abstract Pulmonary oxygen uptake has been analysed to determine the relative importance of breathing pattern parameters. Computer simulations of pulmonary oxygen transport were obtained with a multicompartment model of the lung, assuming an absence of shunts, constant cardiac output, and 21% inspired oxygen. Simulations of oxygen uptake in the lung for various breathing patterns showed that the parameters having the greatest effect on the arterial PO2 are the tidal volume and breathing rate. At a constant tidal volume and breathing rate, that is a constant total ventilation, even extreme variations in the shape of the flow pattern produce relatively small changes in arterial Po2. At a given inspired oxygen concentration, optimal strategies to provide sufficient gas exchange with mechanically aided ventilation in the absence of significant oedema or aetelectasis can be based primarily on changes in tidal volume and breathing rates.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 14 (1976), S. 408-426 
    ISSN: 1741-0444
    Keywords: Renal transport ; Urea ; Simulation ; Digital computer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Description / Table of Contents: Sommaire Un modèle mathématique des processus de transport dans les membres ascendants (AL), les canaux collecteurs (CD) et le plexus capillaire-instertitium (ICP) autour de la substance médullaire rénale a été développé et utilisé pour l'étude des mécanismes qui peuvent intervenir dans la régulation tubulaire rénale de l'excrétion d'urée. Des équations d'équilibre de corps dissous et d'eau pour des compartiments d'une parfaite homogénéité en série décrivent les processus de transport dans l'ensemble AL, CD et ICP. Les types de corps dissous considérés sont l'urée, le sel (NaCl) et un ‘corps dissous non-réabsorbable’ qui tient compte des substances diverses accumulées dans les CD. Les équations de transport de membranes utilisées dans le modèle décrivent le mouvement du corps dissous sous forme de diffusion passive, trainée de dissolvant et transport actif; et le mouvement d'eau par osmose. Les paramètres du modèle sont évalués à partir de données expérimentales publiées. Des solutions en calculateur numérique des équations du modèle indiquent que pratiquement toutes les constatations expérimentales concernant la régulation de l'excrétion d'urée s'expliquent par une augmentation de la trainée dissolvante de l'urée à partir des CD corticaux et médullaires. On évite ainsi la nécessité de postuler le transport actif d'urée à partir des CD pour expliquer la régulation de l'excrétion d'urée.
    Abstract: Zusammenfassung Es wurde ein mathematisches Modell des Transportvorganges in den aufsteigenden Gliedmaßen (AL), Sammelkanälen (CD) und in dem sie umgebenden Interstitial-Kapillarplexus (ICP) der Nierenrinde entwickelt und auf die Untersuchung des Mechanismus angewandt, der evtl. für die Regulierung der Harnstoffausscheidung durch die Nierenkanäle gilt. Die Transportvorgänge in den AL, CD und ICP werden durch Gleichungen für die gelösten Stoffe und den Wasserausgleich für perfekt gemischte, in Serien geschaltete Zellen beschreiben. Bei den berücksichtigten gelösten Stoffen handelt es sich um Harnstoff, Salz (NaCl) und einen idealisierten ‘nichtresorbierbaren gelösten Stoff’, der für verschiedene Substanzen gilt, die sich in den CD ansammeln. Die im Modell verwendeten Membranentransportgleichungen beschreiben die Bewegung der gelösten Stoffe durch passive Diffusion, Lösungsmittelaustrag und aktiven Transport sowie Wasserbewegung durch Osmose. Die Modellparameter werden durch veröffentlichte experimentelle Daten beurteilt. Aus digitalen Rechnerlösungen der Modellgleichungen geht hervor, daß sich fast alle experimentellen Beobachtungen, die sich auf die Regulierung der Harnstoffausscheidung beziehen, durch eine Steigerung des Lösungsmittelaustrages des Harnstoffes aus den kortikalen und Nierenrinden-CD erklären lassen. Daher ist die Notwendigkeit, einen aktiven Transport des Harnstoffes von den CD anzunehmen, um die Regulierung der Harnstoffausscheidung zu erklären, überflüssig.
    Notes: Abstract A mathematical model of transport processes in the ascending limbs (a.l.), collecting ducts (c.d.), and surrounding interstitium-capillary plexus (i.c.p.) of the renal medulla has been developed and applied to an investigation of mechanisms which may be involved in renal tubular regulation of urea excretion. Solute and water balance equations for perfectly-mixed compartments in series describe the transport processes in the a.l., c.d., and i.c.p. Solute species considered are urea, salt (NaCl), and an idealised ‘nonreabsorbable solute’ which accounts for miscellaneous substances accumulated in the c.d. The membrane transport equations used in the model describe solute movement by passive diffusion, solvent drag, and active transport; and water movement by osmosis. Model parameters are evaluated from published experimental data. Digital computer solutions of the model equations indicate that virtually all experimental observations pertaining to the regulation of urea excretion can be explained by an increase in the solvent drag of urea from the cortical and medullary c.d. Therefore, the need to postulate an active transport of urea from the c.d. to explain the regulation of urea excretion is obviated.
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