Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO₂ Profiles

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).