Abstract
The goal of this study was to investigate the complex co-transport of nitric oxide (NO) and oxygen (O2) in a paired arteriole–venule, surrounded by capillary-perfused tissue using a computer model. Blood flow was assumed to be steady in the arteriolar and venular lumens and to obey Darcy’s law in the tissue. NO consumption rate was assumed to be constant in the core of the arteriolar and venular lumen and to decrease linearly to the endothelium. Average NO consumption rate by capillary blood in a unit tissue volume was assumed proportional to the blood flux across the volume. Our results predict that: (1) the capillary bed, which connects the arteriole and venule, facilitates the release of O2 from the vessel pair to the surrounding tissue; (2) decreasing the distance between arteriole and venule can result in a higher NO concentration in the venular wall than in the arteriolar wall; (3) in the absence of capillaries in the surrounding tissue, diffusion of NO from venule to arteriole contributes little to NO concentration in the arteriolar wall; and (4) when capillaries are added to the simulation, a significant increase of NO in the arteriolar wall is observed.
Similar content being viewed by others
References
Boegehold M. A. (1996) Shear-dependent release of venular nitric oxide: effect on arteriolar tone in rat striated muscle. Am. J. Physiol. 271(2 Pt 2):H387–395
Bohlen H. G. (1998) Mechanism of increased vessel wall nitric oxide concentrations during intestinal absorption. Am. J. Physiol. 275(2 Pt 2):H542–550
Brinck H., Werner J. (1994) Estimation of the thermal effect of blood flow in a branching countercurrent network using a three-dimensional vascular model. J. Biomech. Eng. 116(3):324–330
Brown G. C. (2001) Regulation of mitochondrial respiration by nitric oxide inhibition of cytochrome c oxidase. Biochim. Biophys. Acta. 1504(1):46–57
Buerk D. G., Saidel G. M. (1977) A comparison of two nonclassical models for oxygen consumption in brain and liver tissue. Adv. Exp. Med. Biol. 94:225–232
Buerk D. G., Bridges E. W. (1986) A simplified algorithm for computing the variation in oxyhemoglobin saturation with pH, PCO2, T and DPG. Chem. Eng. Commun. 47:113–124
Buerk D. G. (2001) Can we model NO biotransport? A survey of mathematical models for a simple diatomic molecule with surprisingly complex biological activities. Ann. Rev. Biomed. Eng. 3:109–143
Carlsen E., Comroe J. H. (1958) The rate of uptake of carbon monoxide and of nitric oxide by normal human erythrocytes and experimentally produced spherocytes. J. Gen. Physiol. 42(1):83–107
Chen K., Popel A. S. (2006) Theoretical analysis of biochemical pathways of nitric oxide release from vascular endothelial cells. Free. Radic. Biol. 41(4):668–80
Chen X., Jaron D., Barbee K. A., Buerk D. G. (2006) The influence of radial RBC distribution, blood velocity profiles, and glycocalyx on coupled NO/O2 transport. J. Appl. Physiol. 100(2):482–492
Davis M. J., Ferrer P. N., Gore R. W. (1986) Vascular anatomy and hydrostatic pressure profile in the hamster cheek pouch. Am. J. Physiol. 250(2 Pt 2):H291–303
Ellsworth M. L., Pittman R. N. (1990) Arterioles supply oxygen to capillaries by diffusion as well as by convection. Am. J. Physiol. 258(4 Pt 2):H1240–1243
Fagan K. A., Tyler R. C., Sato K., Fouty B. W., Morris K. G. Jr., Huang P. L., Mcmurtry I. F., Rodman D. M. (1999) Relative contributions of endothelial, inducible, and neuronal NOS to tone in the murine pulmonary circulation. Am. J. Physiol. 277(3 Pt 1):L472–478
Fåhraeus R. (1928) Die Strömungsverhältnisse und die Verteilung der Blutzellen im Gefässystem. Klin. Wochenschr. 7:100–106
Falcone J. C., Bohlen H. G. (1990) EDRF from rat intestine and skeletal muscle venules causes dilation of arterioles. Am. J. Physiol. 258(5 Pt 2):H1515–1523
Falcone J. C., Meininger G. A. (1997) Arteriolar dilation produced by venule endothelium-derived nitric oxide. Microcirculation 4(2):303–310
Forstermann U., Closs E. I., Pollock J. S., Nakane M., Schwarz P., Gath I., Kleinert H. (1994) Nitric oxide synthase isozymes. Characterization, purification, molecular cloning, and functions. Hypertension 23(6 Pt 2):1121–1131
Granger H. J., Shepherd A. P. Jr. (1973) Intrinsic microvascular control of tissue oxygen delivery. Microvasc. Res. 5(1):49–72
House S. D., Lipowsky H. H. (1987) Microvascular hematocrit and red cell flux in rat cremaster muscle. Am. J. Physiol. 252(1 Pt 2):H211–222
Hsu R., Secomb T. W. (1992) Analysis of oxygen exchange between arterioles and surrounding capillary-perfused tissue. J. Biomech. Eng. 114:227–231
Kashiwagi S., Kajimura M., Yoshimura Y., Suematsu M. (2002) Nonendothelial source of nitric oxide in arterioles but not in venules: alternative source revealed in vivo by diaminofluorescein microfluorography. Circ. Res. 91(12):e55–64
Kavdia M., Popel A. S. (2006) Venular Endothelium Derived NO Can Affect Paired Arteriole: A Computational Model. Am. J. Physiol. Heart Circ. Physiol. 290(2):H716–23
Kobayashi H., Takizawa N. (2002) Imaging of oxygen transfer among microvessels of rat cremaster muscle. Circulation 105:1713–1719
Kurihara N., Alfie M. E., Sigmon D. H., Rhaleb N. E., Shesely E. G., Carretero O. A. (1998) Role of nNOS in blood pressure regulation in eNOS null mutant mice. Hypertension 32(5):856–861
Lamkin-Kennard K. A., Buerk D. G., Jaron D. (2004) Interactions between NO and O2 in the Microcirculation: A mathematical Analysis. Microvasc. Res. 68:38–50
Lash J. M., Bohlen H. G. (1987) Perivascular and tissue PO2 in contracting rat spinotrapezius muscle. Am. J. Physiol. 252(6 Pt 2):H1192–1202
Long D. S., Smith M. L., Pries A. R., Ley K., Damiano E. R. (2004) Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution. Proc. Natl. Acad. Sci. USA 101(27):10060–10065
Mitchell D., Tyml K. (1996) Nitric oxide release in rat skeletal muscle capillary. Am. J. Physiol. 270(5 Pt 2):H1696–1703
Nase G. P., Tuttle J., Bohlen H. G. (2003) Reduced perivascular PO2 increases nitric oxide release from endothelial cells. Am. J. Physiol. Heart Circ. Physiol. 285:H507–H515
Nellore K., Harris N. (2004) Nitric oxide measurements in rat mesentery reveal disrupted venulo-arteriolar communication in diabetes. Microcirculation 11:415–423
Popel A. S., Pittman R. N., Ellsworth M. L. (1989) Rate of oxygen loss from arterioles is an order of magnitude higher than expected. Am. J. Physiol. 256(3 Pt 2):H921-H924
Rengasamy A., Johns R. A. (1996) Determination of K m for oxygen of nitric oxide synthase isoforms. J. Pharmacol. Exp. Ther. 276(1):30–33
Saito Y., Eraslan A., Hester R. L. (1993) Importance of venular flow in control of arteriolar diameter in hamster cremaster muscle. Am. J. Physiol. 265(4 Pt 2):H1294–1300
Secomb T. W., Hsu R. (1994) Simulation of O2 transport in skeletal muscle: diffusive exchange between arterioles and capillaries. Am. J. Physiol. 267(3 Pt 2):H1214–1221
Sharan M., Popel A. S. (1988) A mathematical model of countercurrent exchange of oxygen between paired arteriole and venules. Math. Biosci. 91:17–34
Tateishi N., Suzuki Y., Soutani M., Maeda N. (1994) Flow dynamics of erythrocytes in microvessels of isolated rabbit mesentery: cell-free layer and flow resistance. J. Biomech. 27(9):1119–1125
Thomas D. D., Liu X., Kantrow S. P., Lancaster J. R. Jr. (2001) The biological lifetime of nitric oxide: implications for the perivascular dynamics of NO and O2. Proc. Natl. Acad. Sci. USA 98(1):355–360
Tsai A. G., Friesenecker B., Mazzoni M. C., Kerger H., Buerk D. G., Johnson P. C., Intaglietta M. (1998) Microvascular and tissue oxygen gradients in the rat mesentery. Proc. Natl. Acad. Sci. USA 95:6590–6595
Tsoukias N. M., Popel A. S. (2003) A model of nitric oxide capillary exchange. Microcirculation 10(6):479–495
Vadapalli A., Pittman R. N., Popel A. S. (2000) Estimating oxygen transport resistance of the microvascular wall. Am. J. Physiol. Heart Circ. Physiol. 279:657–671
Vaughn M. W., Kuo L., Liao J. C. (1998) Estimation of nitric oxide production and reaction rates in tissue by use of a mathematical model. Am. J. Physiol. 274(6 Pt 2):H2163–2176
Vukosavljevic N., Jaron D., Barbee K. A., Buerk D. G. (2006) Quantifying the l-arginine paradox in vivo. Microvasc Res. 71(1):48–54
Wagner L., Hoey J. G., Erdely A., Boegehold M. A., Baylis C. (2001) The nitric oxide pathway is amplified in venular vs arteriolar cultured rat mesenteric endothelial cells. Microvasc. Res. 62(3):401–409
Weerappuli D. P. V., Popel A. S. (1989) A model of oxygen exchange between an arteriole or venule and the surrounding tissue. J. Biomech. Eng. 111:24–31
Weinbaum S., Xu L. X., Zhu L., Ekpene A. (1997) A new fundamental bioheat equation for muscle tissue: part I - blood perfusion term. J. Biomech. Eng. 119:278–288
Whorton A. R., Simonds D. B., Piantadosi C. A. (1997) Regulation of nitric oxide synthesis by oxygen in vascular endothelial cells. Am. J. Physiol. 272(6 Pt 1):L1161–1166
Ye G. F., Moore T. W., Buerk D. G., Jaron D. (1994) A compartmental model for oxygen-carbon dioxide coupled transport in the microcirculation. Ann. Biomed. Eng. 22(5):464–479
Acknowledgment
This work is supported by: NIH/HL 068164 and NSF/BES 0301446.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, X., Buerk, D.G., Barbee, K.A. et al. A Model of NO/O2 Transport in Capillary-perfused Tissue Containing an Arteriole and Venule Pair. Ann Biomed Eng 35, 517–529 (2007). https://doi.org/10.1007/s10439-006-9236-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-006-9236-z