Green’s function method for simulation of oxygen transport to tissue

In the Green’s function method for simulating oxygen transport from a network of vessels to a finite volume of tissue, a numerical method is used in which vessels are treated as distributions of oxygen sources and the tissue is represented as a distribution of oxygen sinks.

We have developed implementations of this method in FORTRAN and C. This version gives the ‘infinite-domain solution’, in which the network of vessels and the associated oxygen-consuming tissue domain are effectively embedded in an infinite domain without other oxygen sources or sinks. The tissue domain is defined by the region of oxygen-consuming tissue, and no explicit boundary condition is applied on the boundaries of this domain. Such an approach has two advantages: it is applicable to tissue domains of arbitrary shape, and it avoids artifacts that can occur when specific boundary conditions, such as the no-flux condition, are imposed.

The method is described in the following publication: Secomb, T.W., Hsu, R., Park, E.Y.H. and Dewhirst, M.W. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Annals of Biomedical Engineering, 32: 1519-1529 (2004).

C version 1.0, May 1, 2008 (instructions and download)

C version 2.0, May 1, 2010 (instructions and download)

C version 3.0, May 17, 2011 (instructions and download)

 

Publications
Our publications showing simulations of oxygen transport by networks of microvessels include:
Hsu, R. and Secomb, T.W. A Green's function method for analysis of oxygen delivery to tissue by microvascular networks. Math. Biosciences. 96: 61-78 (1989).
Hsu, R. and Secomb, T.W. Analysis of oxygen exchange between arterioles and surrounding capillary-perfused tissue. J. Biomech. Eng. 114: 227-231 (1992).
Secomb, T.W., Hsu, R., Dewhirst, M.W., Klitzman, B. and Gross, J.F. Analysis of oxygen transport to tumor tissue by microvascular networks. Int. J. Rad. Onc. Biol. Phys. 25: 481-489 (1993).
Secomb, T.W. and Hsu, R. Simulation of oxygen transport in skeletal muscle: diffusive exchange between arterioles and capillaries. Am. J. Physiol. 267, H1214-1221 (1994).
Secomb, T.W., Hsu, R., Ong, E.T., Gross, J.F. and Dewhirst, M.W. Analysis of the effects of oxygen supply and demand on hypoxic fraction in tumors. Acta Oncologica 34, 313-316 (1995).
Secomb, T.W., Hsu, R., Braun, R.D., Ross, J.R., Gross, J.F. and Dewhirst, M.W. Theoretical simulation of oxygen transport to tumors by three-dimensional networks of microvessels. In "Oxygen Transport to Tissue XX," ed. A.G. Hudetz and D.F. Bruley. Plenum, New York, 1998, pp. 629-634.
Secomb, T.W., Hsu, R., Beamer, N.B. and Coull, B.M. Theoretical simulation of oxygen transport to brain by networks of microvessels: effects of oxygen supply and demand on tissue hypoxia. Microcirculation 7, 237-247 (2000).
Kavanagh, B.D., Secomb, T.W., Hsu, R., Lin, P.-S., Venitz, J. and Dewhirst, M.W. A theoretical model for the effects of reduced hemoglobin-oxygen affinity on tumor oxygenation. Int. J. Rad. Onc. Biol. Phys. 53, 172-179 (2002).
Secomb, T.W., Hsu, R. and Dewhirst, M.W. Synergistic effects of hyperoxic gas breathing and reduced oxygen consumption on tumor oxygenation: A theoretical model. Int. J. Rad. Onc. Biol. Phys., 59: 572-578 (2004).
Secomb, T.W., Hsu, R., Park, E.Y.H. and Dewhirst, M.W. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Annals of Biomedical Engineering, 32: 1519-1529 (2004).

Updated April 5, 2010

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