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  • Springer  (52,321)
  • Wiley-Blackwell  (10,008)
  • American Geophysical Union  (2,869)
  • Copernicus
  • 1985-1989  (65,252)
  • 1986  (65,252)
Collection
Keywords
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Years
  • 1985-1989  (65,252)
Year
  • 1
    Electronic Resource
    Electronic Resource
    An equation for flow in the renal proximal tubule (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 29-57 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460061
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  • 2
    Electronic Resource
    Electronic Resource
    Seventeenth Annual Meeting of the Classification Society of North America (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 105-105 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460066
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial: Software Survey Section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460067
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  • 4
    Electronic Resource
    Electronic Resource
    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 97-103 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460065
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 125-136 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460018
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  • 6
    Electronic Resource
    Electronic Resource
    Multiple stable equilibria in a predator-prey system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 137-148 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460019
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  • 7
    Electronic Resource
    Electronic Resource
    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 107-124 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460017
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  • 8
    Electronic Resource
    Electronic Resource
    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 167-187 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460021
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  • 9
    Electronic Resource
    Electronic Resource
    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460023
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  • 10
    Electronic Resource
    Electronic Resource
    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 213-228 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460024
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