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  • 1
    ISSN: 1432-1238
    Keywords: Tracheal gas insufflation ; Mathematical model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Objective To investigate the theoretical interactions between ventilator settings, tracheal gas insufflation (TGI), and alveolar ventilation. Design We derived differential equations governing compartmental volume changes in a one-compartment model of TGI-assisted ventilation and equations governing gas dilution in the airway proximal to the TGI catheter and the additional CO2 clearing ventilation arising from this dilution. This additional ventilation was called proximal ventilation. Validation was conducted in a mechanical lung analog. Model predictions for proximal ventilation were then generated over wide ranges of frequency, duty cycle, and tidal volume. Results Significant interactions were identified between ventilator settings and proximal ventilation. The persistence of end-expiratory flow from the lung decreased proximal dilution by fresh gas and thereby reduced TGI-aided proximal ventilation. Changes in end-expiratory lung flow resulting from alterations in ventilator settings were correlated inversely with proximal ventilation. Conclusions During TGI with constant catheter flow, ventilator settings that promote end-expiratory flow of gas from the lung diminish proximal ventilation. When frequency increases, the decrease in dilution efficiency of the individual breath is partially offset by the increase in cycle number, an effect which is magnified by any concomitant decrease in inspired tidal volume. Prolongation of the duty cycle tends to decrease proximal ventilation. Increases in expiratory resistance, including those arising from the external ventilator circuit or the endotracheal tube, also impair proximal ventilation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial-boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial-boundary-value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L2 on errors in the geometry.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0138-4988
    Keywords: Life Sciences ; Life Sciences (general)
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Notes: Understanding both the qualitative and quantitative transient responses to inlet flow and substrate step functions has been a relatively unsolved problem for continuous fermentation processes. This study of transient responses and simple descriptive models suggests that the saturation constant of the MONOD equation is a variable. Thatf variable depends on the rate constants of parallel biochemical pathways leading to cell growth, the concentration of cells themselves, and the concentration of all products in the culture. Mechanisms for describing the hysteresis behavior of the growth rate funcion are postulated in terms of the underlying molecular biology of the microbial system.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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