Abstract
Myogenic and shear stress-sensitive mechanisms control the caliber of a small blood vessel in this modeling study. This blood vessel in our model was composed of a pressure-sensitive (myogenic) component and a series-connected shear-sensitive component. The response of this model to imposed pressure and the conditions that result in a stable steady-state vessel diameter were investigated. The requirement that the model parameters need to satisfy for a stable steady state to exist are expressed by the numerical solution of simultaneous nonlinear equations. Also, if a vessel is put into an initial state that is not an equilibrium state, then the system must occupy a range of initial conditions to arrive at a stable equilibrium. These are described graphically for three cases. In general, the initial shear stress should be higher than the equilibrium value of shear stress, and/or the initial transmural pressure should be low, compared with the imposed feed pressure. Increasing the imposed pressure on the vessel can lead to elimination of the equilibrium state and vasospasm, according to this model. When a stable steady state is not reached, the model predicts elimination of the vessel or vasospasm. The model is in qualitative agreement with experimental observations that, during angiogenesis, vessels with low flow are often eliminated.
Similar content being viewed by others
References
Davis, M. J.. Myogenic response gradient in an arteriolar network.Am. J. Physiol. 264 (Heart Circ. Physiol. 33): H2168-H2179, 1993.
Davis, M. J., and P. J. Sikes. Myogenic response of isolated arterioles: test for a rate-sensitive mechanism.Am. J. Physiol. 259 (Heart Circ. Physiol. 28):H1890-H1900, 1990.
Dinnar, U. Metabolic and mechanical control of the microcirculation. In: Interactive phenomena in the cardiac system, edited by S. Sideman and R. Beyar. New York: Plenum Press, 1993, pp. 243–254.
Griffith, T. M., and D. H. Edwards. Basal EDRF activity helps to keep the geometrical configuration of arterial bifurcations close to the Murray optimum.J. Theoret. Biol. 146: 545–573, 1990.
Hacking, W. J. G., E. VanBavel, and J. A. E. Spaan. Shear stress is not sufficient to control growth of vascular networks: a model study.Am. J. Physiol. 270 (Heart Circ. Physiol. 39):H364-H375, 1996.
Harrigan, T. P. Shear-controlled dilation in single or branched arterioles leads to unstable behavior, which can be stabilized by series fluid resistances. Proceedings of the ASME Bioengineering Conference BED, vol. 29, New York: American Society of Mechanical Engineers, 1995, pp. 527–528.
Holstein-Rathlou, N. H., and D. J. Marsh, A dynamic model of renal blood flow autoregulation.Bull. Math. Biol. 56:411–429, 1994.
Hudetz, A. G., and M. F. Kiani. The role of wall shear stress in microvascular network adaptation. In: Oxygen transport to tissue, vol. XIII edited by T. K. Goldsticket al.. New York: Plenum Press, 1992, pp. 31–39.
Hudlicka, O., and M. D. Brown. Physical forces and angiogenesis. In: Mechanoreception by the vascular wall. Mount Kisco, NY: Futura Publishing Co., Inc. 1993, pp. 197–241.
Kiani, M. F., A. R. Pries, L. L. Hsu, I. H. Sarelius, and G. R. Cokelet. Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms.Am. J. Physiol. 266 (Heart Circ. Physiol. 35):H1822-H1828, 1994.
Lee, R. M. K. W. Vascular remodeling in hypertension: its prevelance and possible mechanism. In: The resistance arteries, integration of regulatory pathways, edited by W. Halpern, J. A. Bevan, J. Brayden, H. Dustan, M. Nelson, and G. Osol. Totowa, NJ: Humana Press, 1994, pp. 197–213.
Norins, N. A., K. Wendelberger, R. G. Hoffmenn, P. A. Keller, and J. A. Madden. Effects of indomethacin on myogenic contractile activation and responses to changes in O2 and CO2 in isolated feline cerebral arteries.J. Cereb. Blood Flow Metab., 12:866–872, 1992.
Murray, C. D. The physiological principal of minimum work. I. The vascular system and the cost of blood volume.Proc. Natl. Acad. Sci. U.S.A. 12:207–214, 1926.
Pries, A. R., T. W. Secomb, P. Gaehtgens, and J. F. Gross. Blood flow in microvascular networks, experiments and simulation.Circ. Res. 67:826–834, 1990.
Pries, A. R., T. W. Secomb, and P. Gaehtgens. Design principles of vascular beds.Circ. Res. 77:1017–1023, 1995.
Rossotti, S., and J. Löfgren. Optimality principles and flow orderliness at the branching points of cerebral arteiresStroke 24:1029–1032, 1993.
Sherman, T. F., A. S. Popel, A. Koller, and P. C. Johnson. The cost of departure from optimal radii in microvascular networks.J. Theoret. Biol. 136:245–265, 1989.
Sun, D., G. Kaley, and A. Koller. Characteristics and origin of myogenic response in isolated gracilis muscle arterioles.Am. J. Physiol. 266 (Heart Circ. Physiol. 35):H1177-H1183, 1994.
Ursino, M., S. Cavalcanti, S. Bertuglia, and A. Colantuoni. Theoretical analysis of complex oscillations in multi-branched macrovascular networks.Microvasc. Res. 51:229–249, 1996.
Ursino, M., and G. Fabbri. Role of the myogenic mechanism in the genesis of microvascular oscillations (vasomotion): analysis with a mathematical model.Microvasc. Res. 43: 156–177, 1992.
Zamir, M. Optimality principles in arterial branching.J. Theoret. Biol. 62:227–251, 1976.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Harrigan, T.P. Regulatory interaction between myogenic and shear-sensitive arterial segments: Conditions for stable steady states. Ann Biomed Eng 25, 635–643 (1997). https://doi.org/10.1007/BF02684841
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02684841