Identification of Viable Regions in “In Vitro” Spheroidal Tumors: A Mathematical Investigation

Busch, Nathan A.; Bruley, Duane F.; Bicher, Haim I.

doi:10.1007/978-1-4684-4388-2_1

Cited by 4 publications

(2 citation statements)

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“…7a and 7b, respectively, gives a value of Q/Ks. Ks may then be derived from the flux boundary condition at the spheroid surface Since KM is known, Ks can be determined by measuring the Po2 gradients inside and outside the spheroid at the spheroid surface, as suggested by Bush et al (1982). Depending on the accuracy required, the procedures described in the two preceding paragraphs may be used to precisely determine the oxygen consumption rate and Krogh's diffusion constant in a few individual spheroids.…”

Section: Discussionmentioning

confidence: 99%

“…Since both Q and K are not known, neither of these quantities can be unequivocally determined from steady state P02 profiles in spheroids. A theoretical approach to determining Q from steady state P02 profiles in spheroids has been published recently (Bush et al, 1982), however, neither numerical results nor data on the accuracy of the method are given to permit further evaluation.…”

Section: Introductionmentioning

confidence: 99%

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Method for the determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids

Mueller‐Klieser¹

1984

Biophysical Journal

129

103

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A method has been developed for the quantitative evaluation of oxygen tension (PO2) distributions in multicellular spheroids measured with O2-sensitive microelectrodes. The experimental data showed that multicellular tumor spheroids in stirred growth media were characterized by a diffusion-depleted zone surrounding the spheroids. This zone was elicited by an unstirred layer of medium next to the spheroid leading to a continuous decrease in the PO2 values from the bulk medium towards the spheroid surface. Theoretical considerations demonstrate that the volume-related O2 consumption rate, Q, in the spheroids can be assessed by measuring the PO2 gradient in the diffusion-depleted zone outside the spheroids. Accordingly, Krogh's diffusion constant, KS, in the spheroids can be determined through measuring the PO2 gradient within the spheroids. The results obtained suggest that multicellular spheroids represent useful in vitro tumor models for the experimental and theoretical analysis of the interrelationship among O2 supply to tumor cells, O2 metabolism in tumors tissue, and the responsiveness of cancer cells to treatment.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%