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

Abstract

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.

Necrotic core in EMT6/Ro tumour spheroids: Is it caused by an ATP deficit?

“…We remark that the values of the diffusivities (see Table 1) guarantee that the contribution of the extracellular liquid flow to metabolite transport is negligible. Experimental observations that evidenced the presence of concentration gradients in a layer surrounding the surface of tumour spheroids (Mueller-Klieser and Sutherland, 1982, Mueller-Klieser, 1984, Groebe and Mueller-Klieser, 1991, led us to prescribe the concentrations in the culture medium at a fixed distance L from the spheroid surface. These concentrations obey the following equations:…”

“…The growth characteristics and the metabolism of the EMT6/Ro spheroid (mouse mammary carcinoma cells) have been extensively investigated (Mueller-Klieser and Sutherland, 1982, Mueller-Klieser, 1984, Freyer and Sutherland, 1985, Freyer and Sutherland, 1986a, Casciari et al, 1988, Freyer, 1988, Walenta et al, 1990, Freyer et al, 1991, Casciari et al, 1992, Casciari et al, 1992a. In Freyer and Sutherland (1986a) in particular, the radius of the necrotic core for spheroids of different size and under different oxygen and glucose concentrations in the medium were reported.…”

“…We used this data as a constraint on the value of the unknown parameters. The thickness of the unstirred layer around the spheroid has been found to range from 60 − 80 μm (Groebe and Mueller-Klieser, 1991) to 100 − 200 μm (Mueller-Klieser, 1984), hence we assumed L = 80 μm.…”

Modeling of oxygen transport across tumor multicellular layers

“…No microscopic visualization of the MCL or insert is necessary to prepare the MCL for measurement. Second, the PO 2 data measured from a spheroid must be recorded along a radial course through the center in order to be properly described by the diffusion model (Mueller-Klieser, 1984). If the electrode does not enter the spheroid perpendicular to the surface, then the profile does not follow the radial coordinates described in the model.…”

“…The in vitro model that has been most commonly used to study oxygen metabolism and transport in tumor parenchyma is the 3-D tumor spheroid. PO 2 can be measured in tumor spheroids using oxygen microelectrodes (Acker et al, 1983,Mueller-Klieser, 1984, and the recorded PO 2 profiles can be fitted to oxygen diffusion models to determine oxygen consumption rates (Mueller-Klieser, 1984,MuellerKlieser et al, 1986,Mueller-Klieser and Sutherland, 1984,Sutherland et al, 1986. These measurements can be technically challenging, because the spheroids are positioned on an O 2 -permeable membrane and are held in place by a glass micropipette (Mueller-Klieser and Sutherland, 1982).…”