A model of oxygen diffusion in absorbing tissue

Liapis, Athanasios I.; Lipscomb, G. Glenn; Crosser, O.K.; Tsiroyianni-Liapis, E.

doi:10.1016/0270-0255(82)90014-8

Cited by 26 publications

(31 citation statements)

References 11 publications

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“…The diffusion-consumption of oxygen in absorbing tissue consists in finding the free boundary x=s(t) and the concentration C(x,t) such that they satisfy the following conditions (Crank & Gupta, 1972;Crank, 1984;Liapis et al, 1982):…”

Section: The Oxygen Diffusion-consumption Problem and Its Relationshimentioning

confidence: 99%

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia¹

2011

Advanced Topics in Mass Transfer

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Section: The Oxygen Diffusion-consumption Problem and Its Relationshimentioning

confidence: 99%

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia¹

2011

Advanced Topics in Mass Transfer

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“…Hansen and Hougaard [6] used an integral equation for the function defining the position of the moving boundary and an integral formula for the concentration distribution. More references to this problem may be found in References [5,[7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Crank and Gupta [2] also employed an uniform space grid moving with the boundary and the necessary interpolations are performed with either cube splines or polynomials, 856 V. GÜLKAÇ Reynolds and Dalton [3] also developed the heat balance integral method, Noble [4] suggested repeated spatial subdivision, Liapis et al [5] proposed an orthogonal collocation for solving the partial differential equation of the diffusion of oxygen in absorbing tissue. Hansen and Hougaard [6] used an integral equation for the function defining the position of the moving boundary and an integral formula for the concentration distribution.…”

Section: Introductionmentioning

confidence: 99%

Comparative study between two numerical methods for oxygen diffusion problem

Gülkaç

2008

Commun. Numer. Meth. Engng.

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SUMMARYTwo approximate numerical solutions of the oxygen diffusion problem are defined using three time-level of Crank-Nicolson equation and Gauss-Seidel iteration for three time-level of implicit method.Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem is mathematically formulated through two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is searched, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is searched. The results obtained by three time-level of implicit method and Gauss-Seidel iteration for three time-level of implicit method and the results gave a good agreement with the previous methods (J.

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“…Crank and Gupta [10] also employed a uniform space grid moving with the boundary and necessary interpolations are performed with either cube splines or polynomials. In this direction Noble suggested the repeated spatial subdivision [20], the heat balance integral method defined by Reynolds and Dalton [22], an orthogonal collocation for solving the partial differential equation of the diffusion of oxygen in absorbing tissue described by Liapis et al [16]. Two numerical methods for solving the oxygen diffusion problem were proposed by Gülkaç [14].…”

Section: Introductionmentioning

confidence: 99%