Theoretical Models of Microvascular Oxygen Transport to Tissue

References

• Bakalova R. Ultra-fast biosensors and multi-photon microscopy in the future of brain studies. Cell Mol Neurobiol 2007; 27: 359–365
   Google Scholar
• Beard DA. Computational framework for generating transport models from databases of microvascular anatomy. Ann Biomed Eng 2001; 29: 837–843
   PubMed Web of Science ®Google Scholar
• Beard DA. Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism. PLoS Comput Biol :e 2006; 2: 107
   Google Scholar
• Beard DA, Bassingthwaighte JB. Modeling advection and diffusion of oxygen in complex vascular networks. Ann Biomed Eng 2001; 29: 298–310
   PubMed Web of Science ®Google Scholar
• Beard DA, Schenkman KA, Feigl EO. Myocardial oxygenation in isolated hearts predicted by an anatomically realistic microvascular transport model. Am J Physiol Heart Circ Physiol 2001; 285: H1826–1836
   Google Scholar
• Bos C, Hoofd L, Oostendorp T. The effect of separate red blood cells on capillary tissue oxygenation calculated with a numerical model. IMA J Math Appl Med Biol 1996; 13: 259–274
   Google Scholar
• Bos C, Hoofd L, Oostendorp T. Mathematical model of erythrocytes as point-like sources. Math Biosci 1995; 125: 165–189
   Google Scholar
• Bruley DF. Modeling oxygen transport: development of methods and current state. Adv Exp Med Biol 1994; 345: 33–42
   Google Scholar
• Chen X, Buerk DG, Barbee KA, Jaron D. A model of NO/O2 transport in capillary-perfused tissue containing an arteriole and venule pair. Ann Biomed Eng 2007; 35: 517–529
   Google Scholar
• Clark A, Jr, Federspiel WJ Clark PA Cokelet GR 1985. Oxygen delivery from red cells. Biophys J 47:171–181.
   PubMedGoogle Scholar
• Cole RH, Vandegriff KD, Szeri AJ, Savas O, Baker DA, Winslow RM. A quantitative framework for the design of acellular hemoglobins as blood substitutes: implications of dynamic flow conditions. Biophys Chem 2007; 128: 63–74
   Google Scholar
• Dash RK, Bassingthwaighte JB. Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG, and temperature levels. Ann Biomed Eng 2004; 32: 1676–1693
   Google Scholar
• Dash RK, Bassingthwaighte JB. Simultaneous blood-tissue exchange of oxygen, carbon dioxide, bicarbonate, and hydrogen ion. Ann Biomed Eng 2006; 34: 1129–1148
   Google Scholar
• Eggleton CD, Vadapalli A, Roy TK, Popel AS. Calculations of intracapillary oxygen tension distributions in muscle. Math Biosci 2000; 167: 123–143
   PubMed Web of Science ®Google Scholar
• Ellis CG, Bateman RM, Sharpe MD, Sibbald WJ, Gill R. Effect of a maldistribution of microvascular blood flow on capillary O2 extraction in sepsis. Am J Physiol Heart Circ Physiol 2002; 282: H156–H164
   PubMedGoogle Scholar
• Ellis CG, Ellsworth ML, Pittman RN. Determination of red blood cell oxygenation in vivo by dual video densitometric image analysis. Am J Physiol 1990; 258: H1216–H1223
   PubMed Web of Science ®Google Scholar
• Ellsworth ML, Popel AS, Pittman RN. Assessment and impact of heterogeneities of convective oxygen transport parameters in capillaries of striated muscle: experimental and theoretical. Microvasc Res 1998; 35: 341–362
   Google Scholar
• Federspiel WJ, Popel AS. A theoretical analysis of the effect of the particulate nature of blood on oxygen release in capillaries. Microvasc Res 1986; 32: 164–189
   PubMed Web of Science ®Google Scholar
• Fletcher JE, Schubert RW. Axial diffusion and wall permeability effects in perfused capillary-tissue structures. Biosystems 1987; 20: 153–174
   Google Scholar
• Gardner JD, Schubert RW. Evaluation of myoglobin function in the presence of axial diffusion. Adv Exp Med Biol 1997; 411: 157–169
   PubMed Web of Science ®Google Scholar
• Gayeski TE, Honig CR. O2 gradients from sarcolemma to cell interior in red muscle at maximal VO2. Am J Physiol 1986; 251: H789–H799
   Google Scholar
• Goldman D, Bateman RM, Ellis CG. Effect of decreased O2 supply on skeletal muscle oxygenation and O2 consumption during sepsis: role of heterogeneous capillary spacing and blood flow. Am J Physiol Heart Circ Physiol 2006; 290: H2277–H2285
   PubMed Web of Science ®Google Scholar
• Goldman D, Bateman RM, Ellis CG. Effect of sepsis on skeletal muscle oxygen consumption and tissue oxygenation: interpreting capillary oxygen transport data using a mathematical model. Am J Physiol Heart Circ Physiol 2004; 287: H2535–H2544
   PubMed Web of Science ®Google Scholar
• Goldman D, Popel AS. A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport. J Theor Biol 2000; 206: 181–194
   PubMed Web of Science ®Google Scholar
• Goldman D, Popel AS. A computational study of the effect of vasomotion on oxygen transport from capillary networks. J Theor Biol 2001; 209: 189–199
   Google Scholar
• Golub AS, Barker MC, Pittman RN. PO2 profiles near arterioles and tissue oxygen consumption in rat mesentery. Am J Physiol Heart Circ Physiol 2007; 293: H1097–H1106
   Google Scholar
• Golub AS, Popel AS, Zheng L, Pittman RN. Analysis of phosphorescence in heterogeneous systems using distributions of quencher concentration. Biophys J 1997; 73: 452–465
   PubMed Web of Science ®Google Scholar
• Greene AS Tonellato PJ Zhang Z Lombard JH Cowley AW, Jr. 1992. Effect of microvascular rarefaction on tissue oxygen delivery in hypertension. Am J Physiol 262: H1486–H1493.
   Google Scholar
• Groebe K. An easy-to-use model for O2 supply to red muscle. Validity of assumptions, sensitivity to errors in data. Biophys J 1995; 68: 1246–1269
   PubMed Web of Science ®Google Scholar
• Groebe K. A versatile model of steady state O2 supply to tissue. Application to skeletal muscle. Biophys J 1990; 57: 485–498
   Google Scholar
• Groebe K, Thews G. Effects of red cell spacing and red cell movement upon oxygen release under conditions of maximally working skeletal muscle. Adv Exp Med Biol 1989; 248: 175–185
   Google Scholar
• Groebe K, Thews G. Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle. Respir Physiol 1990; 79: 255–278
   Google Scholar
• Gutierrez G. The rate of oxygen release and its effect on capillary O2 tension: a mathematical analysis. Respir Physiol 1986; 63: 79–96
   Google Scholar
• Hellums JD, Nair PK, Huang NS, Ohshima N. Simulation of intraluminal gas transport processes in the microcirculation. Ann Biomed Eng 1996; 24: 1–24
   PubMedGoogle Scholar
• Hoofd L. Calculation of oxygen pressures in tissue with anisotropic capillary orientation. I. Two-dimensional analytical solution for arbitrary capillary characteristics. Math Biosci 1995; 129: 1–23
   Google Scholar
• Hoofd L. Calculation of oxygen pressures in tissue with anisotropic capillary orientation. II. Coupling of two-dimensional planes. Math Biosci 1995; 129: 25–39
   Google Scholar
• Hoofd L, Turek Z. Effect of realistic capillary spacing on pO2 calculations in dog gracilis muscle. Med Biol Eng Comput 1994; 32: 436–439
   Google Scholar
• Hoofd L, Turek Z. Realistic modelling of capillary spacing in dog gracilis muscle greatly influences the heterogeneity of calculated tissue oxygen pressures. Adv Exp Med Biol 1996; 388: 333–340
   Google Scholar
• Hsu R, Secomb TW. Analysis of oxygen exchange between arterioles and surrounding capillary-perfused tissue. J Biomech Eng 1992; 114: 227–231
   Google Scholar
• Hsu R, Secomb TW. A Green's function method for analysis of oxygen delivery to tissue by microvascular networks. Math Biosci 1989; 96: 61–78
   PubMedGoogle Scholar
• Huang NS, Hellums JD. A theoretical model for gas transport and acid/base regulation by blood flowing in microvessels. Microvasc Res 1994; 48: 364–388
   PubMed Web of Science ®Google Scholar
• Hudetz AG. Mathematical model of oxygen transport in the cerebral cortex. Brain Res 1999; 817: 75–83
   Google Scholar
• Japee SA, Pittman RN, Ellis CG. A new video image analysis system to study red blood cell dynamics and oxygenation in capillary networks. Microcirculation 2005; 12: 489–506
   PubMed Web of Science ®Google Scholar
• Ji JW, Tsoukias NM, Goldman D, Popel AS. A computational model of oxygen transport in skeletal muscle for sprouting and splitting modes of angiogenesis. J Theor Biol 2006; 241: 94–108
   Google Scholar
• Kang KA, Bruley DF, Bicher H. A computer simulation of simultaneous heat and oxygen transport during heterogeneous three dimensional tumor hyperthermia. Adv Exp Med Biol 1988; 222: 747–756
   Google Scholar
• Kavanagh BD, Secomb TW, Hsu R, Lin PS, Venitz J, Dewhirst MW. A theoretical model for the effects of reduced hemoglobin-oxygen affinity on tumor oxygenation. Int J Radiat Oncol Biol Phys 2002; 53: 172–179
   Google Scholar
• Kirkpatrick JP, Brizel DM, Dewhirst MW. A mathematical model of tumor oxygen and glucose mass transport and metabolism with complex reaction kinetics. Radiat Res 2003; 159: 336–344
   PubMed Web of Science ®Google Scholar
• Klitzman B, Popel AS, Duling BR. Oxygen transport in resting and contracting hamster cremaster muscles: experimental and theoretical microvascular studies. Microvasc Res 1983; 25: 108–131
   Google Scholar
• Krogh A. The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J Physiol 1919; 52: 409–415
   PubMedGoogle Scholar
• Kuo L, Pittman RN. Effect of hemodilution on oxygen transport in arteriolar networks of hamster striated muscle. Am J Physiol 1988; 254: H331–H339
   Google Scholar
• Lagerlund TD, Low PA. Axial diffusion and Michaelis-Menten kinetics in oxygen delivery in rat peripheral nerve. Am J Physiol 1991; 260: R430–R440
   Google Scholar
• Lagerlund TD, Low PA. Mathematical modeling of time-dependent oxygen transport in rat peripheral nerve. Comput Biol Med 1993; 23: 29–47
   Google Scholar
• Lamkin-Kennard KA, Buerk DG, Jaron D. Interactions between NO and O2 in the microcirculation: a mathematical analysis. Microvasc Res 2004; 68: 38–50
   Google Scholar
• Li Z, Yipintsoi T, Bassingthwaighte JB. Nonlinear model for capillary-tissue oxygen transport and metabolism. Ann Biomed Eng 1997; 25: 604–619
   Google Scholar
• Lin PC, Kreutzer U, Jue T. Anisotropy and temperature dependence of myoglobin translational diffusion in myocardium: implication for oxygen transport and cellular architecture. Biophys J 2007; 92: 2608–2620
   Google Scholar
• MacGabhann F, Ji JW, Popel AS. Multi-scale computational models of pro-angiogenic treatments in peripheral arterial disease. Ann Biomed Eng 2007; 35: 982–994
   Google Scholar
• McGuire BJ, Secomb TW. Estimation of capillary density in human skeletal muscle based on maximal oxygen consumption rates. Am J Physiol Heart Circ Physiol 2003; 285: H2382–H2391
   Google Scholar
• McGuire BJ, Secomb TW. A theoretical model for oxygen transport in skeletal muscle under conditions of high oxygen demand. J Appl Physiol 2001; 91: 2255–2265
   PubMed Web of Science ®Google Scholar
• Nair PK, Hellums JD, Olson JS. Prediction of oxygen transport rates in blood flowing in large capillaries. Microvasc Res 1989; 38: 269–285
   Google Scholar
• Nair PK, Huang NS, Hellums JD, Olson JS. A simple model for prediction of oxygen transport rates by flowing blood in large capillaries. Microvasc Res 1990; 39: 203–211
   Google Scholar
• Page TC, Light WR, Hellums JD. Prediction of microcirculatory oxygen transport by erythrocyte/hemoglobin solution mixtures. Microvasc Res 1998; 56: 113–126
   PubMed Web of Science ®Google Scholar
• Papadopoulos S, Endeward V, Revesz-Walker B, Jurgens KD, Gros G. Radial and longitudinal diffusion of myoglobin in single living heart and skeletal muscle cells. Proc Natl Acad Sci U S A 2001; 98: 5904–5909
   PubMed Web of Science ®Google Scholar
• Piiper J, Scheid P. Diffusion limitation of O2 supply to tissue in homogeneous and heterogeneous models. Respir Physiol 1991; 85: 127–136
   Google Scholar
• Pittman RN. Oxygen transport and exchange in the microcirculation. Microcirculation 2005; 12: 59–70
   PubMed Web of Science ®Google Scholar
• Popel AS. Theory of oxygen transport to tissue. Crit Rev Biomed Eng 1989; 17: 257–321
   PubMed Web of Science ®Google Scholar
• Popel AS, Charny CK, Dvinsky AS. Effect of heterogeneous oxygen delivery on the oxygen distribution in skeletal muscle. Math Biosci 1986; 81: 91–113
   Google Scholar
• Popel AS, Pittman RN, Ellsworth ML. Rate of oxygen loss from arterioles is an order of magnitude higher than expected. Am J Physiol 1989; 256: H921–H924
   PubMed Web of Science ®Google Scholar
• Pries AR, Secomb TW, Gaehtgens P, Gross JF. Blood flow in microvascular networks. Experiments and simulation. Circ Res 1990; 67: 826–834
   PubMed Web of Science ®Google Scholar
• Salathe EP. Mathematical analysis of oxygen concentration in a two-dimensional array of capillaries. J Math Biol 2003; 46: 287–308
   Google Scholar
• Salathe EP. A mathematical method for determining oxygen distribution in skeletal muscle with multiple capillaries and axial diffusion. Proc R Soc Lond A Math Phys Eng 2005; 461: 975–1004
   Google Scholar
• Salathe EP. Mathematical modeling of oxygen transport in skeletal muscle. Math Biosci 1982; 58: 171–184
   Google Scholar
• Schacterle RS, Adams JM, Ribando RJ. A theoretical model of gas transport between arterioles and tissue. Microvasc Res 1991; 41: 210–228
   Google Scholar
• Schumacker PT, Samsel RW. Analysis of oxygen delivery and uptake relationships in the Krogh tissue model. J Appl Physiol 1989; 67: 1234–1244
   PubMedGoogle Scholar
• Secomb TW, Hsu R. Simulation of O2 transport in skeletal muscle: diffusive exchange between arterioles and capillaries. Am J Physiol Heart Circ Physiol 1994; 267: H1214–H1221
   PubMed Web of Science ®Google Scholar
• Secomb TW, Hsu R, Beamer NB, Coull BM. Theoretical simulation of oxygen transport to brain by networks of microvessels: effects of oxygen supply and demand on tissue hypoxia. Microcirculation 2000; 7: 237–247
   PubMed Web of Science ®Google Scholar
• Secomb TW, Hsu R, Dewhirst MW, Klitzman B, Gross JF. Analysis of oxygen transport to tumor tissue by microvascular networks. Int J Radiat Oncol Biol Phys 1993; 25: 481–489
   PubMed Web of Science ®Google Scholar
• Secomb TW, Hsu R, Park EY, Dewhirst MW. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng 2004; 32: 1519–1529
   PubMed Web of Science ®Google Scholar
• Sharan M Jones MD, Jr, Koehler RC Traystman RJ Popel AS 1989. A compartmental model for oxygen transport in brain microcirculation. Ann Biomed Eng 17:13–38.
   PubMed Web of Science ®Google Scholar
• Sharan M, Selvakumar S. The effects of chemical kinetics on oxygen delivery to tissue. Math Biosci 1992; 108: 253–277
   PubMed Web of Science ®Google Scholar
• Sharma GC, Jain M. A computational solution of mathematical model for oxygen transport in peripheral nerve. Comput Biol Med 2004; 34: 633–645
   PubMed Web of Science ®Google Scholar
• Styp-Rekowska B, Disassa NM, Reglin B, Ulm L, Kuppe H, Secomb TW, Pries AR. An imaging spectroscopy approach for measurement of oxygen saturation and hematocrit during intravital microscopy. Microcirculation 2007; 14: 207–221
   Web of Science ®Google Scholar
• Sullivan JP, Gordon JE, Palmer AF. Simulation of oxygen carrier mediated oxygen transport to C3A hepatoma cells housed within a hollow fiber bioreactor. Biotechnol Bioeng 2006; 93: 306–317
   PubMed Web of Science ®Google Scholar
• Teboh-Ewungkem MI, Salathe EP. The role of counter-current exchange in preventing hypoxia in skeletal muscle. Bull Math Biol 2006; 68: 2191–2204
   Google Scholar
• Thomas DD Liu X Kantrow SP Lancaster JR, Jr. 2001. The biological lifetime of nitric oxide: implications for the perivascular dynamics of NO and O2. Proc Natl Acad Sci U S A 98:355–360.
   PubMed Web of Science ®Google Scholar
• Tozer GM, Ameer-Beg SM, Baker J, Barber PR, Hill SA, Hodgkiss RJ, Locke R, Prise VE, Wilson I, Vojnovic B. Intravital imaging of tumour vascular networks using multi-photon fluorescence microscopy. Adv Drug Deliv Rev 2005; 57: 135–152
   PubMed Web of Science ®Google Scholar
• Tsai AG, Friesenecker B, Mazzoni MC, Kerger H, Buerk DG, Johnson PC, Intaglietta M. Microvascular and tissue oxygen gradients in the rat mesentery. Proc Natl Acad Sci U S A 1998; 95: 6590–6595
   PubMed Web of Science ®Google Scholar
• Tsoukias NM, Goldman D, Vadapalli A, Pittman RN, Popel AS. A computational model of oxygen delivery by hemoglobin-based oxygen carriers in three-dimensional microvascular networks. J Theor Biol 2007; 248: 657–674
   PubMed Web of Science ®Google Scholar
• Vadapalli A, Goldman D, Popel AS. Calculations of oxygen transport by red blood cells and hemoglobin solutions in capillaries. Artif Cells Blood Substit Immobil Biotechnol 2002; 30: 157–188
   PubMed Web of Science ®Google Scholar
• Vadapalli A, Pittman RN, Popel AS. Estimating oxygen transport resistance of the microvascular wall. Am J Physiol Heart Circ Physiol 2000; 279: H657–H671
   PubMed Web of Science ®Google Scholar
• Varghese HJ, MacKenzie LT, Groom AC, Ellis CG, Chambers AF, MacDonald IC. Mapping of the functional microcirculation in vital organs using contrast-enhanced in vivo video microscopy. Am J Physiol Heart Circ Physiol 2005; 288: H185–H193
   Google Scholar
• Voter WA, Gayeski TE. Determination of myoglobin saturation of frozen specimens using a reflecting cryospectrophotometer. Am J Physiol 1995; 269: H1328–H1341
   Google Scholar
• Wang CH, Popel AS. Effect of red blood cell shape on oxygen transport in capillaries. Math Biosci 1993; 116: 89–110
   PubMedGoogle Scholar
• Weerappuli DP, Pittman RN, Popel AS. Effect of convection in capillaries on oxygen removal from arterioles in striated muscle. J Theor Biol 1990; 147: 275–288
   Google Scholar
• Weerappuli DP, Popel AS. A model of oxygen exchange between an arteriole or venule and the surrounding tissue. J Biomech Eng 1989; 111: 24–31
   Google Scholar
• Whiteley JP, Gavaghan DJ, Hahn CE. Mathematical modelling of oxygen transport to tissue. J Math Biol 2002; 44: 503–522
   PubMed Web of Science ®Google Scholar
• Wieringa PA, Stassen HG, Van Kan JJ, Spaan JA. Oxygen diffusion in a network model of the myocardial microcirculation. Int J Microcirc Clin Exp 1993; 13: 137–169
   Google Scholar