Abstract
Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to characterize oxygen transport and consumption in spheroids. Busch et al. (1982) proposed employing, piecewise, either first order or Michaelis-Menten oxygen consumption kinetics in the diffusion equation. They, however, gave no evidence that this was appropriate and their study contains insufficient data to enable evaluation of the methods. Grossmann, Carlsson and Acker (1983) solved the steady state diffusion equation with an oxygen consumption rate that was linear with the radius. This appears not to be generally applicable because a later analysis (Grossmann et al., 1984) shows a nonlinear dependence on radius. A semianalytical approach to the evaluation of PO2 profiles in spheroids, including a diffusiondepleted ‘stagnant’ layer of medium, has been proposed (Mueller-Klieser, 1984). This features a constant, zero order oxygen consumption rate in the viable region and a uniform Krogh’s diffusion constant throughout the spheroid. In a preliminary study, Groebe and Mueller-Klieser (1986) included this approach in a nonlinear regression analysis taking into account experimental errors during the PO2 measurements in the spheroids. Jurman (1986) extended the nonlinear regression to include two compartments in the viable region (see below).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Busch, N.A., Bruley, D.F. and Bicher, H.I. (1982). Identification of viable regions in ‘in vivo’ spheroidal tumors: a mathematical investigation. In: Hyperthermia. Eds Bicher, H.I. and Bruley, D.F., Plenum Press, New York and London, ( Adv. Exp. Med. Biol. 157, 1–7 ).
Carlsson, J., Stalnacke, C.G., Acker, H., Haji-Karim, M., Nilsson, S. and Larsson, B. (1979). The influence of oxygen on viability and nproliferation in cellular spheroids. Int. J. Radiat. Oncol. Biol. Phys. 5, 2011–2020.
Franko, A.J. and Sutherland, R.M. (1979). Oxygen diffusion distance and development of necrosis and multicell spheroids. Radiat. Res. 79, 439–453.
Freyer, J.P. and Sutherland, R.M. (1980). Selective dissociation and characterization of cells from different regions of multicell tumor spheroids. Cancer Res. 40, 3956–3965.
Groebe, K. and Mueller-Klieser, W. (1986). Non-linear regression analysis of PO2-profiles in multicellular spheroids. Abstracts of the 24th Annual Mtg Radiation Research Soc., Las Vegas, p. 123.
Grossmann, U., Carlsson, J. and Acker, H. (1983). Oxygen consumption profiles inside cellular spheroids calculated from P02-profiles. In: Oxygen Transport to Tissue-IV. Eds Bicher, H.I. and Bruley, D.F., Plenum Press, New York and London, ( Adv. Exp. Med. Biol. 159, 477–480 ).
Grossmann, U., Winkler, P., Carlsson, J. and Acker, H. (1984). Local variations of oxygen consumption within multicellular spheroids calculated from measured PO2-profiles. In: Oxygen Transport to Tissue-V. Eds Lubbers, D.W., Acker, H., Leniger-Follert, E. and Goldstick, T.K., Plenum Press, New York and London, ( Adv. Exp. Med. Biol. 169, 719–728 ).
Jurman, L.A. (1986). Oxygen consumption and transport in multicellular tumor spheroids analyzed using a multiple compartment diffusion model. M.S. thesis, Chemical Engineering Department, Northwestern University, Evanston, IL 60201, U.S.A.
Kaufman, N., Bicher, H.I., Hetzel, F.W. and Brown, M. (1981). A system of determining the pharmacology of indirect radiation sensitizer drugs on multicellular spheroids. Cancer Clin. Trials, 4, 199–204.
Mueller-Klieser, W. (1984). Method for determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids. Biophys. J. 46, 343–348.
Mueller-Klieser, W., Bourrat, B., Gabbert, H. and Sutherland, R.M. (1985). Changes in O2 consumption of multicellular spheroids during development of necrosis. In: Oxygen Transport to Tissue-VII. Eds Kreuzer, F., Cain, S.M. Turek, Z. and Goldstick, T.K., Plenum Press, New York and London, ( Adv. Exp. Med. Biol. 191, 775–784 ).
Mueller-Klieser, W., Freyer, J.P. and Sutherland, R.M. (1986). Influence of glucose and oxygen supply conditions on the oxygenation of multicellular spheroids. Br.J. Cancer, 53, 345–353.
Mueller-Klieser, W. and Sutherland, R.M. (1982a). Influence of convection in the growth medium on oxygen tensions in multicellular tumor spheroids. Cancer Res. 42, 237–242.
Mueller-Klieser, W. and Sutherland, R.M. (1982b). Oxygen tensions in multicell spheroids of two cell lines. Br. J. Cancer, 45, 256–264.
Robinson, B. (1982). NLREG - Nonlinear regression subroutine package, VCC No. 328, Vogelback Computing Center, Northwestern University, Evanston, IL 60201, U.S.A.
Sutherland, R.M., McCredie, J.A. and Inch, W.R. (1971). Growth of multicellular spheroids in tissue culture as a model of nodular carcinomas. J1 Natl. Cancer Inst. 46, 113–120.
Sutherland, R.M., Sordat, B., Bamat, J., Gabbert, H., Bourrat, B. and Mueller-Klieser, W. (1986). Oxygenation and differentiation in multicell spheroids of human colon carcinoma. Cancer Res. (in press).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Goldstick, T.K., Mueller-Klieser, W., Bourrat, B., Jurman, L.A. (1987). Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles. In: Silver, I.A., Silver, A. (eds) Oxygen Transport to Tissue IX. Advances in Experimental Medicine and Biology, vol 215. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7433-6_46
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7433-6_46
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-7435-0
Online ISBN: 978-1-4684-7433-6
eBook Packages: Springer Book Archive