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  • Springer  (75.637)
  • 2015-2019
  • 1975-1979  (39.521)
  • 1970-1974  (36.116)
  • 1975  (39.521)
  • 1972  (36.116)
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  • 2015-2019
  • 1975-1979  (39.521)
  • 1970-1974  (36.116)
Jahr
  • 1
    Digitale Medien
    Digitale Medien
    Obituary of Nicolas Rashevsky (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. i 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02477019
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    On the stochastic theory of compartments: I. A single-compartment system (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 53-63 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02477024
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    A remark on sensory deprivation from the point of view of organismic sets (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 439-441 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476706
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Optimal branching structure of the vascular tree (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 431-438 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476705
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    First order kinetics in a distributed model (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 443-456 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In order to determine the kinetics of passage of a substance through an organ containing a tangle of vessels, we study the response of a tube to various inflows (perfusion, brief injection, ...). The introduction of the catabolic terms and of the spatial dependence between bulk concentration and surface concentration allows one to account for the difference of arteriovenous concentrations observed experimentally for many metabolites. The relationships between the physico-chemical parameters of the organ and the operational parameters of the model demonstrate the importance of the transit time through the considered vessels. If one considers the different pathways as independent, the introduction of the transit time distribution for an inert substance enables one to compute the response of the organ analytically or by recurrence, using convolution. The parameters of the model can be obtained by the moments method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476707
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Stochastic simulation of the gas diffusion in the air phase of the human lung (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 457-466 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The solution of the diffusion equation in the gas phase of the human lung is very difficult because of the structure of the bronchial tree. It is shown by means of physical arguments, how one can reduce the diffusion equation to a simple one-dimensional form. The solution is then obtained by a stochastic simulation, which is easily realized on a digital computer.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476708
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    A new mathematical model of the respiratory center (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 467-481 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A new mathematical model of the oscillatory behavior of the respiratory center has been developed based upon published records of neuronal activity during respiration in the pons and medulla. In contrast with a previous model, four, rather than two, networks are assumed to interact in the respiratory center so as to produce the respiratory oscillation. A mathematical description of this interaction, in the form of a set of four first-order, nonlinear, coupled differential equations, is derived; the behavior of the solutions of this system is studied qualitatively, and expressions for the durations of the inspiratory and expiratory phases are obtained in terms of some parameters. It is found that central and chemical influences drive the medullar neurons to a position somewhere between saturation and full cutoff, and the pontine neurons deeply into cutoff. The control of the duration of the different phases by these chemical and central means is discussed. In order to effect a decrease in the magnitude of the various times, the neurons have to be driven towards operating points of higher central facilitation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476709
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Digitale Medien
    Digitale Medien
    A mathematical model for calcium homeostasis (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 483-502 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In vivo control of calcium is analysed under the assumption that hormonal influences via plasma levels of parathormone and calcitonin are of prime (but not absolutely dominating) importance. A brief review concerning the physiological significance of body calcium and the mode of action of these two hormones is presented as an introduction to the basic philosophy of the study. A theoretical quasi-linear lumped-parameter model is developed to describe variations in ionic calcium, parathormone and calcitonin plasma concentrations to specific input stimuli. Formal evaluation of the system response requires the determination of ten constants, together with quantitation of ingested calcium entry into the plasma compartment which isindependent of hormonal influences. Values for various parameters are deduced from published data and experimental procedures are outlined to facilitate determination of the remaining unknowns. It is suggested that the proposed model should prove useful for investigations concerning general hormonal actions on calcium homeostatic mechanisms in both normal and diseased states, with particular reference to calcitonin.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476710
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    The struggle for life: III. A predator-prey chain (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 521-532 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Ann species predator-prey chain is analyzed to determine what oscillations occur in population sizes. It is found that only the populations of the first and second species in the chain must necessarily oscillate around the point of equilibrium if they do not come to equilibrium. The other species may or may not oscillate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476712
    Standort Signatur Erwartet Verfügbarkeit
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  • 10
    Digitale Medien
    Digitale Medien
    Mathematical models for exchange of substances in regional vascular beds— Measurement of the rates within vivo counters (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 503-520 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Sangren and Sheppard developed a mathematical model for first-order processes taking place in the regional circulation, applicable—for example—to tracer studies of potassium transport. It permits calculation of specific activity at any point along a “tube of flow” or in the cuff of tissue surrounding it as a function of time following a spike injection of tracer. In efforts to relate to the exchange a rate curves obtained within vivo counters pointed at the region of interest, we developed a compartment-system model of the process. In investigating the properties of the Sangren and Sheppard model integrated over an entire circulatory bed, as thein vivo counter would see it, we found that when the distribution of transit times of the “tubes of flow” can be approximated by an exponential sum, the solution reduces to that of the compartment system model. This results in an important simplification in the calculation, and insight into the assumptions underlying the two different models. A curve-fitting computer program for the compartment model has been written and applied to double-isotope studies of potassium transport in the hind leg of the dog.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476711
    Standort Signatur Erwartet Verfügbarkeit
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