Bifurcation analysis of nephron pressure and flow regulation

Chaos

Volumn 6, Issue 3, 1996, Pages 280-287

  Barfred, Mikael ^a   Mosekilde, Erik ^a   Holstein Rathlou, Niels Henrik ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001309046     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166175     Document Type: Article

References (33)

1. L. Glass and M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton University Press, Princeton, NJ, 1988).
2. E. Mosekilde and O. G. Mouritsen, Modeling the Dynamics of Biological Systems, Nonlinear Phenomena and Pattern Formation (Springer-Verlag, Berlin, 1995).
3. W. F. Crowley and J. G. Hofler, The Episodic of Hormones (Wiley, New York, 1987).
4. G. Leng, Pulsatility in Neuroendocrine Systems (CRC Press, Boca Raton, FL, 1988).
5. J. E. Levine, Pulsatility in Neuroendocrine Systems, Methods in Neurosciences (Academic, New York, 1994), Vol. 20.
6. A. Goldbeter, Cell to Cell Signalling: From Experiments to Theoretical Models (Academic, London, 1989).
7. L. C. Moore, "Tubuloglomerular feedback and SNGFR autoregulation in the rat," Am. J. Physiol. 247, F267-F276 (1984).
8. P. P. Leyssac and L. Baumbach, "An oscillating intratubular pressure response to alterations in Henle loop flow in the rat kidney," Acta Physiol. Scand. 117, 415-419 (1983).
9. N.-H. Holstein-Rathlou and P. P. Leyssac, "TGF-mediated oscillations in the proximal intratubular pressure: Difference between spontaneous hypertensive rats and Wistar-Kyoto rats," Acta. Physiol. Scand. 126, 333-339 (1986).
10. P. P. Leyssac and N.-H. Holstein-Rathlou, "Effects of various transport inhibitors on oscillating TGF pressure responses in the rate," Pfluegers Archiv. 407, 285-291 (1986).
11. K.-P. Yip, N.-H. Holstein-Rathlou, and D. J. Marsh, "Chaos in blood flow control in genetic and renovascular hypertensive rats," Am. J. Physiol. 261, F400-F408 (1991).
12. N.-H. Holstein-Rathlou and P. P. Leyssac, "Oscillations in the proximal intratubular pressure: A mathematical model," Am. J. Physiol. 252, F560-F572 (1987).
13. K. S. Jensen, E. Mosekilde, and N.-H. Holstein-Rathlou, "Self-sustained oscillations and chaotic behavior in kidney pressure regulation," Mondes Develop. 54/55, 91-109 (1986).
14. K. S. Jensen, N.-H. Holstein-Rathlou, P. P. Leyssac, E. Mosekilde, and D. R. Rasmussen, "Chaos in a system of interacting nephrons," in Chaos in Biological Systems, edited by H. Degn, A. V. Holden, and L. F. Olsen (Plenum, New York, 1987), pp. 23-32
15. N.-H. Holstein-Rathlou, "Synchronization of proximal intratubular pressure oscillations: Evidence for interaction between nephrons," Pfluegers Archiv. 408, 438-443 (1987).
16. N.-H. Holstein-Rathlou and D. J. Marsh, "Oscillations of tubular pressure, flow, and distal chloride concentration in rats," Am. J. Physiol. 256, F1007-F1014 (1989).
17. N.-H. Holstein-Rathlou and D. J. Marsh, "A dynamic model of the tubuloglomerular feedback mechanism," Am. J. Physiol. 258, F1448-F1459 (1990).
18. N.-H. Holstein-Rathlou, A. J. Wagner, and D. J. Marsh, "Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats," Am. J. Physiol. 260, F53-F68 (1991).
19. N.-H. Holstein-Rathlou and D. J. Marsh, "A dynamic model of renal blood flow autoregulation," Bull. Math. Biol. 56, 411-429 (1994).
20. R. Feldberg, M. Colding-Jørgensen, and N.-H. Holstein-Rathlou, "An analysis of the interaction between tubuloglomerular feedback and the myogenic response in renal blood flow autoregulation," Am. J. Physiol. 269, F581-F593 (1995).
21. C. Casellas and L. C. Moore, "Autoregulation and tubuloglomerular feedback in juxtamedullary glomerular arterioles," Am. J. Physiol. 258, F666-F669 (1990).
22. D. A. Haberle and J. M. Davis, "Interrelationship between proximal tubular hydrodynamics and tubuloglomerular feedback in the rat kidney," Kidney Int. 22, Suppl. 12, S193-S197 (1982).
23. J. Briggs, "A simple steady-state model for feedback control of glomerular filtration rate," Kidney Int. 22, Suppl. 12, S143-S150 (1982).
24. R. Feldberg, M. Colding-Jørgensen, and N.-H. Holstein-Rathlou, "A model of the myogenic response in small arteries and arterioles," in Proceedings of the 1st Copenhagen Symposium on Computer Simulation in Biology, Ecology and Medicine, edited by E. Mosekilde (The Society for Computer Simulation, San Diego, 1993), pp. 110-114.
25. L. O. Chua, M. Komuro, and T. Matsumoto, "The double scroll family, parts I and II," IEEE Trans. Circ. Syst. CAS-33, 1072-1118 (1986).
26. L. Glass and R. Perez, "Fine structure of phase locking," Phys. Rev. Lett. 48, 1772-1775 (1982).
27. M. Schell, S. Fraser, and R. Kapral, "Subharmonic bifurcation in the sine map: An infinite hierarchy of cusp bistabilities," Phys. Rev. A 28, 373-378 (1983).
28. J. P. Carcasses, C. Mira, M. Bosch, C. Simó, and J. C. Tatjer, "Crossroad area-Spring area transition (I) parameter plane representation," Int. J. Bifurc. Chaos 1, 183-196 (1991).
29. A. P. Kuznetsov, S. P. Kuznetsov, and I. R. Sataev, "From bimodal one-dimensional maps to Hénon-like two-dimensional maps: Does quantitative universality survive?," Phys. Lett. A 184, 413-421 (1994).
30. R. S. MacKay and C. Tresser. "Some flesh on the skeleton: The bifurcation structure of bimodal maps," Physica D 27, 412-422 (1987).
31. M. Rosenbaum and D. Race, "Frequency-response characteristics of vascular resistance vessels," Am. J. Physiol. 215, 1397-1402 (1968).
32. Y.-C. B. Fung, Biomechanics. Mechanical Properties of Living Tissues (Springer, New York, 1981).
33. R. J. Paul, "Smooth muscle: Mechano-chemical energy conversion relations between metabolism and contractibility," in Physiology of the Gastrointestinal Tract, edited by L. R. Johnson (Raven, New York, 1981), pp. 269-288.