Qualitative mathematical models of endocrine systems.

Some qualitative dynamical models of endocrine systems are considered and analyzed, with the reproductive endocrine system as an example. The models considered are systems of nonlinear ordinary differential equations describing the rates of change of the hormonal concentrations with time. This type of general approach, which requires only the incorporation of the basic qualitative features of the interactions present in the underlying system into the model, is a potentially powerful tool for elucidating possible mechanisms for observed qualitative patterns of hormonal dynamics.

[1]  R. J. Bogumil,et al.  Mathematical studies of the human menstrual cycle. II. Simulation performance of a model of the human menstrual cycle. , 1972, The Journal of clinical endocrinology and metabolism.

[2]  H. Othmer The qualitative dynamics of a class of biochemical control circuits , 1976, Journal of mathematical biology.

[3]  W R Smith,et al.  Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion. , 1980, Bulletin of mathematical biology.

[4]  K Grant-Brown,et al.  Physiological aspects of the steroid hormone-gonadotropin interrelationship. , 1977, International review of physiology.

[5]  N B Schwartz,et al.  A model for the regulation of ovulation in the rat. , 1969, Recent progress in hormone research.

[6]  D. Bolt,et al.  Changes in the concentration of luteinizing hormone in plasma of rams following administration of oestradiol, progesterone or testosterone. , 1971, Journal of reproduction and fertility.

[7]  John J. Tyson,et al.  Existence of periodic solutions for negative feedback cellular control systems , 1977 .

[8]  W. Bremner,et al.  Prolonged intravenous infusions of LH-releasing hormone into normal men. , 1977, Hormone and metabolic research = Hormon- und Stoffwechselforschung = Hormones et metabolisme.

[9]  L. Shotkin A model for the effect of daily injections of gonadal hormones on LH levels in recently-castrated adult rats and its comparison with experiment. , 1974, Journal of theoretical biology.

[10]  W R Smith,et al.  Hypothalamic regulation of pituitary secretion of luteinizing hormone. , 1976, Bulletin of mathematical biology.

[11]  L. Shotkin,et al.  A model for LH levels in the recently-castrated adult rat and its comparison with experiment. , 1974, Journal of theoretical biology.

[12]  A Arimura Hypothalamic gonadotropin-releasing hormone and reproduction. , 1977, International review of physiology.

[13]  R. J. Bogumil,et al.  Mathematical studies of the human menstrual cycle. I. Formulation of a mathematical model. , 1972, The Journal of clinical endocrinology and metabolism.

[14]  P. Rapp,et al.  Analysis of biochemical phase shift oscillators by a harmonic balancing technique , 1976, Journal of mathematical biology.

[15]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.