Abstract
The flow in a vessel able to regulate its lumen under the action of mechanical stimuli, the variation of the pressure difference between the inner and outer surfaces of the vessel wall and the blood flow velocity, is described. This ability is determined by the effect of the mechanical stimuli on the degree of activation of smooth muscle cells in the vessel wall. In order to describe the active properties of the wall, two controlling parameters which have the sense of the concentration of free calcium ions in the cytoplasm of smooth muscle cells and the average concentration of nitric oxide in the smooth muscle layer, are introduced. The approach proposed makes it possible to estimate both the degree of participation of each mechanical stimulus in vessel lumen regulation and the result of interaction of two differently directed vascular responses. The calculations show that both the magnitude and direction of the radius response to a mechanical stimulus depend on the initial state of the vessel wall. The role of the vessel wall sensitivity to mechanical stimuli in the stabilization of the blood flow-rate and the variation of the radius along the vessel is considered.
Similar content being viewed by others
References
V.M. Khayutin and A.N. Rogoza, “Regulation of Blood Vessels Caused by Mechanical Forces Applied to Them,” in Manual of Physiology. Physiology of Blood Circulation: Regulation of Circulation (Nauka, Leningrad, 1986) [in Russian], pp. 37–66.
J.F. Brekke, N.I. Gokina, and G. Osol, “Vascular Smooth Muscle Cell Stress as a Determinant of Cerebral Artery Myogenic Tone,” Amer. J. Physiol. Heart Circ. Physiol. 283, H2210–H2216 (2002).
M.A. Hill, H. Zou, S.J. Potocnik, G.A. Meininger, and M.J. Devis, “Invited Review: Arteriolar Smooth Muscle Mechanotransduction: Ca2+ Signaling Pathways Underlying Myogenic Reactivity,” J. Appl. Physiol. 91(2), 973–983 (2001).
A. M. Melkumyants and S. A. Balashov, Mechanosensitivity of the Arterial Endothelium (Triada, Tver, 2005) [in Russian].
M. Kimura, H.H. Dietrich, and R.G. Dacey, “Nitric Oxide Regulates Cerebral Arteriolar Tone in Rats, Stroke 25(11), 2227–2233 (1994).
S.A. Regirer and N.Kh. Shadrina, ’Mathematical Models of Nitric Oxide Transport in a Blood Vessel,” Biophysics 50(3), 454–472 (2005).
G.J. Lagaud, P.L. Skarsgard, I. Laher, and C. van Breemen, “Heterogeneity of Endothelium-Dependent Vasodilation in Pressurized Cerebral and Small Mesenteric Resistance Arteries of the Rat,” J. Pharmacol. and Experim. Therapeutics 290(2), 832–839 (1999).
N.A. Kudryashov and I.L. Chernyavskii, “Numerical Simulation of the Process of Autoregulation of the Arterial Blood Flow,” Fluid Dynamics 43(1), 32–48 (2008).
S. Payne, H. Morris, and A. Rowley, “A Combined Haemodynamic and Biochemical Model of Cerebral Autoregulation,” in Proc. 27th IEEE EMBS Conf. Shanghai, China, pp. 2295–2298 (2005).
N.Kh. Shadrina, “Mathematical Modeling of Vascular Response to Mechanical Stimuli,” in Modern Problems of Biomechanics, Vol. 11 (Moscow University Press, Moscow, 2006), pp. 64–78.
T.W. Secomb, “Theoretical Models for Regulation of Blood Flow,” Microcirculation 15(8), 765–775 (2008).
N.Kh. Shadrina and V.A. Buchin, “Mathematical Modeling of the Response of a Resistive Vessel to Pressure, Biophysics 54(2), 188–192 (2009).
S.A. Regirer, “Resistance Blood Vessel as a Nonlinear Mechanical System,” Izv. Vuzov, Prikl. Nelin. Dinamika 2(3–4), 77–85 (1994).
H.J. Knot and M.T. Nelson, “Regulation of Arterial Diameter and Wall [Ca2+] in Cerebral Arteries of Rat by Membrane Potential and Intravascular Pressure,” J. Physiol. 508(1), 199–209 (1998).
M. Kelm, M. Feelisch, R. Spahr, H. Piper, E. Noack, and J. Schrader, “Quantitative and Kinetic Characterization of Nitric Oxide and EDRF Released from Cultured Endothelial Cells,” Biochem. Biophys. Res. Commun. 154(1), 236–244 (1988).
K.M. Arthurs, L.C. Moore, C.S. Peskin, E.B. Pitman, and H.E. Layton, “Modeling Arteriolar Flow and Mass Transport Using the Immersed Boundary Method,” J. Comput. Phys. 147(2), 402–440 (1998).
G. Osol and W. Halpern, “Myogenic Properties of Cerebral Blood Vessels from Normotensive and Hypertensive Rats,” Amer. J. Physiol. Heart Circ. Physiol. 249(5), H914–H921 (1985).
G.L Baumbach, J.G. Walmsley, and M.N. Hart, “Composition and Mechanics of Cerebral Arterioles in Hypertensive Rats,” Amer. J. Pathol. 133(3), 464–471 (1988).
T. Malinski, Z. Taha, S. Grunfeld, S. Patton, M. Kapturczak, and P. Tomboulian, “Diffusion of Nitric Oxide in the Aorta Wall Monitored in Situ by Porphyrinic Microsensors,” Biochem. Biophys. Res. Commun. 193(3), 1076–1082 (1993).
M. Kavdia and A.S. Popel, “Contribution of nNOS and eNOS-Derived NO to Microvascular Smooth Muscle NO Exposure,” J. Appl. Physiol. 97(1), 293–301 (2004).
R.S. Lewis and W.M. Deen, “Kinetics of the Reaction of Nitric Oxide with Oxygen in Aqueous Solutions,” Chem. Res. Toxicol. 7(4), 568–574 (1994).
M.W. Vaughn, L. Kuo, and J.C. Liao, “Estimation of Nitric Oxide Production and Reaction Rates in Tissue by Use of a Mathematical Model,” Amer. J. Physiol. Heart Circ. Physiol. 274(6) H2163–H2176 (1998).
N.M. Tsoukias, M. Kavdia, and A.S. Popel, “A Theoretical Model of Nitric Oxide Transport in Arterioles: Frequency vs. Amplitude-Dependent Control of cGMP Formation, Amer. J. Physiol. Heart Circ. Physiol. 286, H1043–H1056 (2004).
M. Kavdia and A.S. Popel, “Wall Shear Stress Differentially AffectsNO Level in Arterioles for Volume Expanders and Hb-Based O2 Carriers,” Microvasc. Res. 66, 49–58 (2003).
A.J. Kanai, H.C. Strauss, G.A. Truskey, A.L. Crews, S. Grunfeld, and T. Malinski, “Shear Stress Induces ATP-Independent Transient Nitric Oxide Release from Vascular Endothelial Cells, Measured Directly with Porphyrinic Microsensor, Circulat. Res. 77(2), 284–293 (1995).
M. Sharan and A.S. Popel, “A Two-Phase Model for Flow of Blood in Narrow Tubes with Increased Effective Viscosity near the Wall,” Biorheol. 38, 415–428 (2001).
A.F. Voevodin and S.M. Shugrin, Numerical Methods of Calculating One-Dimensional Systems (Nauka, Novosibirsk, 1981) [in Russian].
N. Thorin-Trescases, J.A. Bevan, and W.J. Pearce, “High Levels of Myogenic Tone Antagonize the Dilator Response to Flow of Small Rabbit Cerebral Arteries,” Stroke 29, 1194–1201 (1998).
R.S. Reneman and A.P.G. Hoeks, “Wall Shear Stress as Measured in Vivo: Consequences for Design of the Arterial System,” Med. Biol. Eng. Comput. 46(5), 499–507 (2008).
J.-L. Garcia-Roldan and J.A. Bevan, “Augmentation of Endothelium-Independent Flow Constriction in Pial Arteries at High Intravascular Pressures,” Hypertension 17(6), 870–874 (1991).
M.E. Ward, L. Yan, S. Kelly, and M.R. Angle, “Flow Modulation of Pressure-Sensitive Tone in Rat Pial Arterioles: Role of the Endothelium,” Anesthesiol. 93(6), 1456–1464 (2000).
K.A. Shoshenko, A.S. Golub, V.I. Brod, et al., Architectonics of Vascular Bed (Nauka, Novosibirsk, 1982) [in Russian].
K. Tyml, D. Anderson, D. Lidington, and H.M. Ladak, “A New Method for Assessing Arteriolar Diameter and Hemodynamic Resistance Using Image Analysis of Vessel Lumen,” Amer. J. Physiol. Heart Circ. Physiol. 284(5), H1721–H1728 (2003).
E. Bakker, J. Versluis, P. Sipkema, and E. VanBavel, “Different Structural Adaptation to Haemodynamics along Single Rat Cremaster Arterioles,” J. Physiol. 548(Pt 2), 549–555 (2003).
Additional information
Original Russian Text © V.A. Buchin, N.Kh. Shadrina, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 2, pp. 52–64.
Rights and permissions
About this article
Cite this article
Buchin, V.A., Shadrina, N.K. Regulation of the lumen of a resistance blood vessel by mechanical stimuli. Fluid Dyn 45, 211–222 (2010). https://doi.org/10.1134/S0015462810020067
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462810020067