The bulletin of mathematical biophysics

, Volume 16, Issue 1, pp 15–21 | Cite as

Mathematical theory of periodic relapsing catatonia

  • Lewis Danziger
  • George L. Elmergreen


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.


Equilibrium Point Thyrotropin Basal Metabolic Rate Equilibrium Level Typical Trajectory 
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Copyright information

© Univerisity of Chicago 1954

Authors and Affiliations

  • Lewis Danziger
    • 1
  • George L. Elmergreen
    • 1
  1. 1.Milwaukee Sanitarium, WauwatosaWisconsin and University of WisconsinMilwaukee

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