Chaotic oscillations in microvessel arterial networks
A mathematical model of a multibranched microvascular network was used to study the mechanisms underlying irregular oscillations (vasomotion) observed in arteriolar microvessels. The network's layout included three distinct terminal arteriolar branches originating from a common parent arteriole. The biomechanical model of the single microvessel was constructed to reproduce the time pattern of the passive and active (myogenic) response of arterioles in the hamster cheek pouch to a step-wise arterial pressure change. Simulation results indicate that, as a consequence of the myogenic reflex, each arteriole may behave as an autonomous oscillator, provided its intraluminal pressure lies within a specific range. In the simulated network, the interaction among the various oscillators gave rise to a complex behavior with many different oscillatory patterns. Analysis of model bifurcations, performed with respect to the arterial pressure level, indicated that modest changes in this parameter caused the network to shift between periodic, quasiperiodic, and chaotic behavior. When arterial pressure was changed from approximately 60–150 mm Hg, the model exhibited a classic route toward chaos, as in the Ruelle-Takens scenario. This work reveals that the nonlinear myogenic mechanism is able to produce the multitude of different oscillatory patterns observedin vivo in microvascular beds, and that irregular microvascular fluctuations may be regarded as a form of deterministic chaos.
KeywordsVasomotion Chaos Nonlinear dynamics Myogenic reflex microvascular networks
Unable to display preview. Download preview PDF.
- 2.Arnold, V. I.Geometrical Methods in the Theory of Ordinary Differential Equations. New York: Springer-Verlag, 1993.Google Scholar
- 6.Casti, J. L.Alternate Realities: Mathematical Models of Nature and Man. New York: John Wiley & Sons, 1989, pp. 253–280.Google Scholar
- 11.Fung, Y. C.Biomechanics: Mechanical Properties of Living Tissues. New York, Berlin: Springer-Verlag, 1981, pp. 41–50.Google Scholar
- 16.Intaglietta, M., and G. A. Breit. Chaos and microcirculatory control. In:Capillary Functions and White Cell Interaction, edited by H. Messmer, Prog. Appl. Microcirc. 18. Basel, Switzerland: S. Karger, 1991, pp. 22–32.Google Scholar
- 23.Parker, T. S., and L. O. Chuas,Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag, 1989.Google Scholar
- 24.Perko, L.Differential Equations and Dynamical Systems. New York: Springer-Verlag, 1991.Google Scholar
- 28.Sparrow, C.The Lorenz Equations: Biforcations, Chaos and Strange Attractors. Berlin, New York: Springer-Verlag, 1982, 27 pp.Google Scholar