Countercurrent exchange in the inner renal medulla: Vasa recta-descending limb systemPalatt, Paul J.;Saidel, Gerald M.
doi: 10.1007/BF02575187pmid: 4777228
Abstract A model of countercurrent exchange has been developed to simulate transport of salt, urea and water among vasa recta and descending limbs of the loop of Henle in the inner medulla. These vessels are abstracted as three concentric cylinders: the inne one represents descending vasa recta, the middle one represents ascending vasa recta and the outer one represents descending limbs. The capillary plexus, which connects the ascending and descending vasa recta, is modeled as a series of well-mixe compartments. Multicomponent transport equations for the sytem are derived from steady state mass balances and simple passive flux relations. The resulting set of nonlinear equations are solved numerically by an iterative Gauss-Seidel algorithm with under-relaxation. Simulations yield the salt and urea concentrations as well as volume flow rates in all tubes and compartments. The simulations indicate that solute concentrations can increase monotonically toward the papillae even if all transport processes within the exchanger are passive and source fluxes decrease monotonically toward the papillae.
Snail population in running waterCoutinho, A. Bezerra;Coutinho, F. A. Bezerra
doi: 10.1007/BF02575188pmid: N/A
Abstract A model developed in a previous paper (Coutinho and Coutinho,Bull. Math. Biophysics,30, 553–563, 1968) is used to study populations ofBiomphalaria glabrata in fast-flowing rivers and channels. The results obtained are in good qualitative agreement with the phenomena experimentally observed, and suggest that the use of artificial channels can be a very useful tool for the experimental study of some important aspects of ecology of theBiomphalaria glabrata.
Filtres passe-bande chimiques et oscillations non periodiquesHyver, C.
doi: 10.1007/BF02575189pmid: 4777229
Abstract In this note some of the basic hypotheses used by N. Rashevsky in his studies of nonperiodic oscillations in cerebral wave patterns (Bull. Math. Biophys., Vol.33, 1971) are reconsidered. The concept of chemical pass-band filters is suggested to develop models which account for several aspects of the electrical cortex activity rhythms. A very simple system is then used to demonstrate that certain non-linearities might explain the disappearance of the alpha rhythm as well as the appearance of waves at different frequencies.
Forced vibrations of a circular muscle ringDelsemme, Pierre;Vayo, H. Westcott
doi: 10.1007/BF02575190pmid: 4777230
Abstract We consider the small radial displacement of a circular ring of cardiac muscle subjected to periodic forcing. The ring in question is that in the middle layer, at the transverse midsection, of the left ventricle. We show that the ring reacts in a periodic manner when forced in a periodic manner. This is accomplished by writing the differential equation for the ring and solving it for two cases-one for constant and one for variable ring thickness.
On adjoint dynamical systemsBâianu, Ion;Scripcariu, Dragoş
doi: 10.1007/BF02575191pmid: 4798205
Abstract Transformations of dynamical systems are discussed in terms of adjoint, simple adjoint and weak adjoint functors. The relevance of this approach to interpretations of nuclear transplant experiments is suggested, and three new theorems concerning the development of biological systems are presented. Another three theorems concerning adjoint dynamical systems are proved. The connection of these results with the theory of organismic sets developed by Rashevsky (1966, 1967a-c, 1968a-c, 1969a-c, 1971a, b) is also investigated.
Statistical theory of persuasion in tripartite negotiationsHenderson, G. P.;Cervin, V. B.
doi: 10.1007/BF02575192pmid: 4777231
Abstract The interaction of three neutral subjects discussing a question is analyzed. The course of the debate is described by three first-order differential equations with coefficients depending on the characteristics of the subjects. Under plausible assumptions the equations are linear and can be solved explicitly. In general, the opinions of the participants approach a common limiting value which is a weighted average of their initial opinions. Special cases are considered in which one or two subjects keep their opinions constant during the discussion. The case of a coalition of two subjects against the third is shown to reduce to a two-party situation. A method of fitting the model to experimental data is suggested. Preliminary trials indicate that it is possible to obtain numerical observations to test this model of a three-party debate.
Flow in tubules due to ciliary activityBlake, John
doi: 10.1007/BF02575194pmid: 4777233
Abstract A simplified model for cilia-induced flows in tubules is presented. Each cilium is a long slender body which is constrained to move similar to its beat. An array of cilia is defined and coordinated in such a way as to represent the metachronal wave. The velocity field is represented by a distribution of viscous fluid singularities (Stokes flow) along the centerline of each slender body. The total mean velocity field due to all the cilia is obtained. It is found that backflow (reflux) can occur near the walls for cilia exhibiting antiplectic metachronism. Maximum flow rates are obtained for cilia whose length is 0.3 to 0.6 the radius of the tube.