Periodic auto-immune hemolytic anemia: An induced dynamical disease. (English) Zbl 0414.92012


92Cxx Physiological, cellular and medical topics
34C25 Periodic solutions to ordinary differential equations
35B32 Bifurcations in context of PDEs
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[1] Chow, S. N. and J. Mallet-Paret. 1978. ”The Fuller Index and Global Hopf Bifurcation.”J. Diff. Equns,29, 66–85. · Zbl 0369.34020
[2] Cronin, J. 1977. ”Mathematical Aspects of Periodic Catatonic Schizophrenia.”Bull. Math. Biol.,39, 187–199. · Zbl 0366.92007
[3] Dormer, P. 1973. ”Kinetics of Erythropoietic Cell Proliferation in Normal and Anemic Man: A New Approach Using Quantitative14C-Autoradiography.”Prog. Histochem. Cytochem.,6, 1–83.
[4] Giblett, E. R., D. H. Coleman, P. Pirzio-Biroli, D. M. Donohue, A. G. Motulsky and C. A. Finch. 1956. ”Erythrokinetics: Quantitative Measurements of Red Cell Production and Destruction in Normal Subjects and Patients with Anemia.”Blood,11, 291–309.
[5] Glass, L. and M. C. Mackey. 1978. ”Pathological Conditions Resulting from Instabilities in Physiological Control System.”Ann. N.Y. Acad. Sci., (in press). · Zbl 0427.92004
[6] Gurel, O. 1975. ”Limit Cycles and Bifurcations in Biochemical Dynamics.”Biosystems,7, 83–91.
[7] Hayes, N. D. 1950. ”Roots of the Trancendental Equation Associated with a Certain Difference-Differential Equation.”J. Lond. Math. Soc.,25, 226–232. · Zbl 0038.24102
[8] Hodgson, G. and I. Eskuche. 1966. ”Aplication de la teoria de control al estudio de la eritropoyesis.”Arch. Biol. Med. Exp.,3, 85–92.
[9] Mackey, M. C. 1978a. ”A Unified Hypothesis for the Origin of Aplastic Anemia and Periodic Haematopoiesis.”Blood,51, 941–956.
[10] Mackey, M. C. 1978b. ”Dynamic Haematological Diseases of Stem Cell Origin.” InProceedings Second International Colloquium on Physical and Chemical Information Transfer in the Regulation of Aging. (ed. J. Vassileva-Popova) Plenum Press, New York (in press).
[11] Mackey, M. C. and L. Glass. 1977. ”Oscillation and Chaos in Physiological Control Systems.”Science,197, 287–289. · Zbl 1383.92036
[12] May, R. M. 1978. ”Dynamical Diseases.”Nature,272, 673–674.
[13] Morley, A. 1970. ”Periodic Diseases Physiological Rhythms and Feedback Control–A Hypothesis.”Aust. Ann. Med.,3, 244–249.
[14] Orr, J. S., J. Kirk, K. G. Gray and J. R. Anderson. 1968. ”A Study of the Interdependence of Red Cell and Bone Marrow Stem Cell Populations.”Br. J. Haemat.,15, 23–34.
[15] Wazewska-Czyzewska M. and A. Lasota. 1976. ”Matematyczyne problemy dynamiki ukladu krwinek czewonych.” Roczniki Polskiego Towarzystwa Matematycznego, Seria III: Matamatyka Stosowana VI, 23–40.
[16] Wintrobe, M. M. 1976.Clinical Hematology. Lea and Febiger, Philadelphia.
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