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  • Articles  (36,230)
  • Springer  (31,731)
  • American Physical Society  (4,499)
  • 1970-1974  (36,230)
  • 1970  (36,230)
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  • 1970-1974  (36,230)
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  • 1
    Electronic Resource
    Electronic Resource
    The influence of noninstantaneous mixing on the measurement of fluxes of solute and water across a biological membrane (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 1-24 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The usual method of tracer analysis for calculating the flow across a biological membrance is based on the assumption that the compartments on either side are well-stirred. Thus, the validity of the rate of flow determination is questionable for cases where the distribution of tracer is not homogeneous. In this study, a mathematical model is developed for the purpose of estimating the effect of slow mixing on the calculation of the flow rate. The model is applied to the measurement of the rate of flow of aqueous humor through the living eye by use of a fluorescent dye as a tracer. A transit time of several minutes for the passage of fluorescein through the posterior chamber and an extended period of nonuniform distribution of fluorescein in the anterior chamber was observed. The effect of slow mixing on the calculated flow rate is compared to rates derived from equations based on the assumption of rapid mixing. Aqueous flow rates determined by the two methods were found to agree to within ≈20%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476789
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  • 2
    Electronic Resource
    Electronic Resource
    The dispersion of indicator in the cardio-pulmonary system (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 25-43 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper presents a three-parameter model of the mechanism of dispersion of an indicator in the cardio-pulmonary system, based on the postulates that this dispersion can be described by the one-dimensional diffusion equation and that dispersion continues past the sampling site. The model is tested using indicator dilution curves obtained from dogs, and the coefficient of diffusion is thus measured. It is found that this coefficient increases in magnitude non-linearly with increasing blood speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476790
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  • 3
    Electronic Resource
    Electronic Resource
    The effect of distension of the left ventricle of the heart on the length of the individual myocardial fibers (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 45-58 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476791
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  • 4
    Electronic Resource
    Electronic Resource
    The gas washout determination under a symmetry assumption (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 59-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In an open circuit gas washout determination the output of test substance is shown to be of the form ∑ i=0 ∞ A i λ i k on thekth expiration whereA i 〉0,i=1,2,... and 1 〉 λ1 ≥ λ2...≥ 0 provided the transition from inspiration to expiration has certain symmetry properties with the transition from expiration to inspiration. In general, no direct physical interpretation such as volume for theA t ’s or fraction of retained gas on expiration for the λ i is justified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476792
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  • 5
    Electronic Resource
    Electronic Resource
    Mathematical biology of automobile driving IV (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 71-78 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Previous studies by this author of the mathematical biology of automobile driving have emphasized only the biological aspects, except for such mechanical factors as the size of the car. Otherwise, the ideal case of an inertialess car was considered. In this paper the first step is made toward introducing the effects of the mass of the car and the side-slip of the tires when the direction of driving is even slightly altered and combining these with the previously studied biological aspects. Some tentative comparisons with available data are made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476794
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  • 6
    Electronic Resource
    Electronic Resource
    Relaxation methods for the determination of drug receptor affinities (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 65-69 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract According to the occupation theory of drug receptor interaction, the response is a functionf of the number of receptors occupied by drug molecules. Considerable controversy exists regarding assumptions about this function. Without knowledge of the nature of the function, it is not possible to determine directly the rate constants, and hence the affinity constant, in the reaction between the receptor and an agonist drug. Instead, indirect determinations involving the use of antagonists have been employed, limiting the determination of affinity to those agents for which specific antagonists exist. The present paper discusses a method for the direct determination of affinity of an agonist drug. It is a “relaxation method,” i.e., the equilibrium is perturbed and the kinetics of the restoration process are studied. Assuming only thatf is non-decreasing and approximately linear over a limited domain of concentrations, it is shown that the change in response obeys first order kinetics, permitting a determination of the rate constants from the time course of the restoration process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476793
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  • 7
    Electronic Resource
    Electronic Resource
    A remark on the course of development of organismic sets (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 79-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The basic postulate la, which governs the development of organismic sets, introduced previously (Bulletin of Mathematical Biophysics,31, 159–198, 1969), is generalized so as to contain also the rates of changes of the number and variety of differentQ-relations which determine an organismic set. It is thus brought closer to the Lagrangian principle in physics. It is pointed out that the postulate also provides a criterion of stability of an organismic set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476795
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  • 8
    Electronic Resource
    Electronic Resource
    In-vivo estimations of the nonlinear pressure-volume relationship of the aorta and instantaneous left ventricular volume (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 155-172 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is presented in this paper for the in-vivo estimation of the nonlinear pressure-volume relationship of the human aorta. The method is based on nonlinear elastic reservoir theory and utilizes clinical data that can be obtained with a high degree of accuracy, namely stroke volume, end diastolic ventricular volume and aortic pressure trace data. The computational procedure is described and then carried out for six cardiac patients. A method for the estimation of instantaneous left ventricular volume during the ejection period based on the considered nonlinear elastic reservoir theory is also presented. The method is applied for the six cardiac patients cited and the results compared with those obtained for the same subjects by a method of estimation based on linear elastic reservoir theory described in a previous paper by the author (1969).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476882
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  • 9
    Electronic Resource
    Electronic Resource
    The application of the minimal energy hypothesis to a casson fluid (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 249-262 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Deakin (1967b) suggested that flow of blood might obey a law of minimal energy dissipation. The present paper presents a simpler derivation of Deakin’s equations pointing out several previously unrecognized features. It is shown that these equations are unlikely to be applicable. In particular, the solution obtained by Deakin and Jones (1968) does not yield a true minimum for energy dissipation. The solution for which energy dissipation is actually minimized is shown to possess features which render it unlikely to apply to a real flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476889
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  • 10
    Electronic Resource
    Electronic Resource
    Some remarks on the Kedem-Katchalsky equations for non-electrolytes (1970)
    Springer
    Bulletin of mathematical biology 32 (1970), S. 237-247 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf sm andf sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL p .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476888
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