Feedback and Control

  • Russell K. Hobbie
  • Bradley J. Roth


We now turn to the way in which the body regulates such things as temperature, oxygen concentration in the blood, cardiac output, number of red or white blood cells, and blood concentrations of substances like calcium, sodium, potassium and glucose. Each of these is regulated by a feedback loop. A feedback loop exists if variable x determines the value of variable y, and variable y in turn determines the value of variable x.


Feedback Loop Operating Point Bifurcation Diagram Thyroid Stimulate Hormone Chaotic Behavior 
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  1. Bartlett, A. A., and T. J. Braun (1983). Death in a hot tub: the physics of heat stroke. Am. J. Phys. 51(2): 127–132.CrossRefADSGoogle Scholar
  2. Begon, M., M. Mortimer, and D. J. Thompson (1996). Population Ecology: A Unified Study of Animals and Plants, 3rd ed. Cambridge, MA, Blackwell Science.Google Scholar
  3. Bub, G., A. Shrier, and L. Glass (2002). Spiral wage generation in heterogeneous excitable media. Phys. Rev. Lett. 88.058101.CrossRefADSGoogle Scholar
  4. Epstein, A. E., and R. E. Ideker (1995). Ventricular fibrillation. In D. P. Zipes and J. Jalife, eds. Cardiac Electrophysiology: From Cell to Bedside, 2nd ed. Philadelphia, Saunders, pp. 927–933.Google Scholar
  5. Epstein, I. R., K. Kustin, P. De Kepper, and M. Orban (1983). Oscillating chemical reactions. Sci. Am. March: 112–123.Google Scholar
  6. Fox, J. J., E. Bodenschatz and R. F. Gilmour, Jr. (2002). Period-doubling instability and memory in cardiac tissue. Phys. Rev. Lett. 89.138101.CrossRefADSGoogle Scholar
  7. Garfinkel, A., M. L. Spano, W. L. Ditto, and J. N. Weiss (1992). Controlling cardiac chaos. Science 257: 1230–1235.CrossRefADSGoogle Scholar
  8. Garfinkel, A., Y.-H. Kim, O. Voroshilovsky, Z. Qu, J. R. Kil, M.-H. Lee, H. S. Karagueuzian, J. N. Weiss, and P.-S. Chen (2000). Preventing ventricular fibrillation by flattening cardiac restitution. Proc. Natl. Acad. Sci. USA 97: 6061–6066CrossRefADSGoogle Scholar
  9. Ginzburg, L. and M. Colyvan (2004). Ecological Orbits: How Planets Move and Populations Grow. Oxford. Oxford University Press.Google Scholar
  10. Glass, L., and M. C. Mackey (1988). From Clocks to Chaos. Princeton, NJ, Princeton University Press.MATHGoogle Scholar
  11. Glass, L., Y. Nagai, K. Hall, M. Talajic, and S. Nattel (2002). Predicting the entrainment of reentrant cardiac waves using phase resetting curves. Phys. Rev. E, 65.021908.CrossRefADSGoogle Scholar
  12. Guevara, M. R., L. Glass, and A. Shrier (1981). Phase-locking, period-doubling bifurcations and irregular dynamics in periodically stimulated cardiac cells. Science 214: 1350–1353.CrossRefADSGoogle Scholar
  13. Guyton, A. C., J. W. Crowell, and J. W. Moore (1956). Basic oscillating mechanism of Cheyne–Stokes breathing. Am. J. Physiol. 187: 395–398.Google Scholar
  14. Hastings, H. M., F. H. Fenton, S. J. Evans, O. Hotomaroglu, J. Geetha, K. Gittelson, J. Nilson, and A. Garfinkel (2000). Alternans and the onset of ventricular fibrillation. Phys. Rev. E 62: 4043–4048.CrossRefADSGoogle Scholar
  15. Hayes, N. D. (1950). Roots of the transcendental equation associated with a certain difference-differential equation. J. London Math. Soc. 25: 226–232.MATHCrossRefMathSciNetGoogle Scholar
  16. Hilborn, R. C. (2000). Chaos and Nonlinear Dynamics, 2nd. ed. New York, Oxford University Press.MATHCrossRefGoogle Scholar
  17. Kaplan, D., and L. Glass (1995). Understanding Nonlinear Dynamics. New York, Springer.MATHGoogle Scholar
  18. Keener, J. P., and A. V. Panfilov (1995). Three-dimensional propagation in the heart: The effects of geometry and fiber orientation on propagation in the myocardium. In D. P. Zipes and J. Jalife, eds. Cardiac Electrophysiology: From Cell to Bedside, 2nd ed. Philadelphia, Saunders, pp. 335–348.Google Scholar
  19. Khoo, M. C. K. (2000). Physiological Control Systems: Analysis, Simulation and Estimation. New York, IEEE.Google Scholar
  20. Mackey, M. C., and L. Glass (1977). Oscillation and chaos in physiological control systems. Science 197: 287–289.CrossRefADSGoogle Scholar
  21. May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature (London) 261: 459–467.CrossRefADSGoogle Scholar
  22. Mercader, M. A., D. C. Michaels, and J. Jalife (1995). Reentrant activity in the form of spiral waves in mathematical models of the sinoatrial node. In D. P. Zipes and J. Jalife, eds. Cardiac Electrophysiology: From Cell to Bedside, 2nd ed. Philadelphia, Saunders, pp. 389–403.Google Scholar
  23. Mielczarek, E. V., J. S. Turner, D. Leiter, and L. Davis (1983). Chemical clocks: Experimental and theoretical models of nonlinear behavior. Am. J. Phys. 51(1): 32–42.CrossRefADSGoogle Scholar
  24. Mines, G. R. (1914). On circulating excitation of heart muscles and their possible relation to tachycardia and fibrillation. Trans. R. Soc. Can. 4: 43–53.Google Scholar
  25. Patton, H. D., A. F. Fuchs, B. Hille, A. M. Scher, and R. F. Steiner, eds. (1989). Textbook of Physiology, 21st ed. Philadelphia, Saunders.Google Scholar
  26. Pertsov, A. M., and J. Jalife (1995). Three-dimensional vortex-like reentry. In D. P. Zipes and J. Jalife, eds. Cardiac Electrophysiology: From Cell to Bedside, 2nd ed. Philadelphia, Saunders, pp. 403–410.Google Scholar
  27. Riggs, D. S. (1970). Control Theory and Physiological Feedback Mechanisms. Baltimore, Williams and Wilkins.Google Scholar
  28. Stark, L. (1957). A servoanalytic study of consensual pupil reflex to light. J. Neurophys. 20: 17–26.Google Scholar
  29. Stark, L. (1968). Neurological Control Systems: Studies in Bioengineering. New York, Plenum, pp. 73–84.Google Scholar
  30. Stark, L. W. (1984). The pupil as a paradigm for neurological control systems. IEEE Trans. Biomed. Eng. 31: 919–924.CrossRefGoogle Scholar
  31. Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos. Reading, MA, Addison-Wesley.Google Scholar
  32. Winfree, A. T. (1987). When Time Breaks Down. Princeton, NJ, Princeton University Press.Google Scholar
  33. Winfree, A. T. (1994a). Electrical turbulence in three-dimensional heart muscle. Science 266: 1003–1006.CrossRefADSGoogle Scholar
  34. Winfree, A. T. (1994b). Persistent tangled vortex rings in generic excitable media. Nature 371: 233–236.CrossRefADSGoogle Scholar
  35. Winfree, A. T. (1995). Theory of spirals. In D. P. Zipes and J. Jalife, eds. Cardiac Electrophysiology: From Cell to Bedside, 2nd ed., Philadelphia, Saunders, pp. 379–389.Google Scholar
  36. Winfree, A. T. (2001). The Geometry of Biological Time. 2nd. ed. New York, Springer.MATHGoogle Scholar
  37. Witkowski, F. X., K. M. Kavanagh, P. A. Penkoske, and R. Plonsey (1993). In vivo estimation of cardiac transmembrane current. Circ. Res. 72(2): 424–439.Google Scholar
  38. Witkowski, F. X., R. Plonsey, P. A. Penkoske, and K. M. Kavanagh (1994). Significance of inwardly directed transmembrane current in determination of local myocardial electrical activation during ventricular fibrillation. Circ. Res. 74(3): 507–524.Google Scholar
  39. Witkowski, F. X., K. M. Kavanagh, P. A. Penkoske, R. Plonsey, M. L. Spano, W. L. Ditto, and D. T. Kaplan (1995). Evidence for determinism in ventricular fibrillation. Phys. Rev. Lett. 75(6): 1230–1233.CrossRefADSGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Russell K. Hobbie
    • 1
  • Bradley J. Roth
    • 2
  1. 1.Professor of Physics, Emeritus University of Minnesota
  2. 2.Associate Professor of Physics Oakland UniversityOakland

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