Abstract
In continuation of previous work (Rashevsky,Some Medical Aspects of Mathematical Biology, Springfield, Ill.: Charles C. Thomas, 1964, Chap. 23 and Appendix 14), the study of the effects of the physical parameters of the cells of endocrine glands on the onset of sustained periodical oscillations in the interaction between the anterior pituitary and the thyroid hormones is generalized to include the possible effect of the intercellular fluid and of the degree of vascularization. Some conclusions of the previous study remain valid although some modifications must be made. A decreased relative volume of the intercellular fluid and an increased vascularization favor the conditions for sustained oscillations. The permeability of the cells and the permeability of the capillaries appear explicitly in the expressions which show the conditions for sustained periodicities.
Similar content being viewed by others
Literature
Danziger, L. and G. L. Elmergreen. 1954. “Mathematical Theory of Periodic Relapsing Catatonia.”Bull. Math. Biophysics,16, 15–21.
— 1956. “The Thyroid Pituitary Homeostatic Mechanism.”,18, 1–13.
— 1957. “Mathematical Models of Endocrine Systems.”,19, 9–18.
Rashevsky, N. 1960.Mathematical Biophysics: Physicomathematical Foundations of Biology. Volume II, 3rd ed. New York: Dover.
— 1963. “Mathematical Theory of the Effects of Cell Structure and of Diffusion Processes on the Homeostasis and Kinetics of the Endocrine System with Special Reference to Some Periodic Psychoses.” InNerve, Brain and Memory Models, Norbert Wiener and J. P. Schade, eds. Amsterdam: Elsevier Publishing Co., 244–256.
— 1964.Some Medical Aspects of Mathematical Biology. Springfield, Ill.: Charles C. Thomas, publisher.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rashevsky, N. Mathematical theory of the possible role of intercellular fluid and of vascularization on physiological periodicities. Bulletin of Mathematical Biophysics 29, 395–401 (1967). https://doi.org/10.1007/BF02476911
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02476911