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Mathematical theory of periodic relapsing catatonia

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Abstract

Two first-order, non-linear differential equations are presented to describe the interaction of the thyroid and pituitary glands and to explain some of the phenomena of periodic relapsing catatonia. Topographical study of these equations shows a mechanism in which either random fluctuations of hormone levels or system stability may occur. The variations in hormone concentrations are assumed to be caused by system malfunction, while stability is shown to result from the administration of exogenous thyroid which, if supplied at an optimum rate, suppresses the output of both glands. The system, under treatment, shows a zero level of thyrotropin and a thyroid concentration which is larger than the equilibrium level in the untreated system. The theory is consistent with what is known of the course and proper treament of periodic relapsing catatonia.

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Literature

  • Danziger L., J. A. Kindwall, and W. R. Lewis. 1948. “Periodic Catatonia. Simplified Diagnosis and Treatment”.Dis. Nerv. Syst.,9, 330–33.

    Google Scholar 

  • Gjessing, R. 1939. “Beitrage zur Kenntnis der Pathophysiologie periodisch Katatoner Zustande”.Archiv f. Psychiat.,109, 525–95.

    Article  Google Scholar 

  • Gornall, A. G., B. Eglitis, A. Miller, A. B. Stokes, and J. G. Dewan, 1953. “Long-term Clinical and Metabolic Observations in Periodic Catatonia”Am. Jour. Psychiat.,109, 584–94.

    Google Scholar 

  • Langmuir, I. 1916. “The Constitution and Fundamental Properties of Solids and Liquids”.Jour. Am. Chem. Soc.,38, 2221–95.

    Article  Google Scholar 

  • Mall, G. 1952. “Beitrag die Gjessingschen Thyroxinbehandlung der periodischen Katatonien”.Archiv f. Psychiat.,187, 381–403.

    Article  Google Scholar 

  • Minorsky, N. 1947.Introduction to Non-Linear Mechanics. Ann Arbor, Mich.: Edwards Brothers.

    Google Scholar 

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Authors and Affiliations

  1. Milwaukee Sanitarium, Wauwatosa, Wisconsin and University of Wisconsin, Milwaukee, Wisconsin

    Lewis Danziger & George L. Elmergreen

Authors
  1. Lewis Danziger
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  2. George L. Elmergreen
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Read before the American Chemical Society, Chicago, Ill., September 11, 1953.

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Danziger, L., Elmergreen, G.L. Mathematical theory of periodic relapsing catatonia. Bulletin of Mathematical Biophysics 16, 15–21 (1954). https://doi.org/10.1007/BF02481809

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  • DOI: https://doi.org/10.1007/BF02481809

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