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The basis of the present investigation was the establishment of an oncogene-dependent, genetically determined two-stage carcinogenesis in vitro model as multicellular spheroids. Spheroid formation was achieved with four rat embryo fibroblast cell lines, two of which represent the first step of malignant transformation, known as stage of immortalization. The ras-transfected counterparts of these two parental cell clones represent fully transformed phenotypes. The data obtained show that spheroid volume growth and cellular viability reflect the degree of tumorigenicity in vivo of the different fibroblast types investigated. In addition, ras-transfection alters not only the growth kinetics but also the cellular oxygen metabolism. Furthermore, the results demonstrate very clearly that different fibroblast clones at the same stage of malignant transformation may be characterized by an entirely different growth behavior, morphology and metabolic activity in spheroid culture. This is true, although these cells originate from the same primary cells, differ only in the step of immortalization, and were cultured as spheroids under identical environmental conditions.

A method for performing and evaluating autoradiography of diffusible 14C labeled substances in multicellular tumor spheroids is presented that allows one to obtain a diffusion coefficient of the substance investigated from each individual spheroid. Application of the method with 14C labeled L-glucose resulted in a glucose diffusion coefficient of 5 x 10(-6) cm2/s. It also revealed problems of the method at very short incubation times of about 10 s or less. These problems are most likely caused by the large penetration depth of beta particles irradiated by 14C labels (as compared to 3H labels) which tends to transform steep 14C concentration gradients into much more shallow optical density gradients during exposure. This transformation can be corrected for by deconvolution of the recorded optical density distributions. Basic data and mathematical tools necessary for the process of deconvolution are presently being developed. It is planned to use this method for determining diffusion coefficients of other substances of interest. One such group of substances are the metabolic waste products, most importantly lactate. Another group consists of larger molecules, e.g. peptides and comprises the various growth factors important in tumor biology. Since for members of this latter group little is known about their velocity of penetration into tissue, model calculations may be applied to predict a range of incubation times suitable for determining diffusion coefficients. Moreover, the algorithms for data analysis will have to be modified to allow for receptor binding of the substance under study.(ABSTRACT TRUNCATED AT 250 WORDS)

Organ surface PO2 measurement by oxygen sensitive electrodes has proved to be an efficient tool for monitoring changes in tissue oxygenation status. A parameter giving more direct information is the PO2 distribution within tissue cells which, however, can only be assessed by more invasive methods. The present study addresses the problem of relating electrode measured surface PO2 to muscle cell PO2. To that end, the magnitude of tissue volumes the PO2 in which electrodes are sensitive to, has been reassessed. It turned out that the measuring signal of current membrane covered PO2 electrodes is only sensitive to the PO2 within the muscle surface and not any deeper, thus rendering the measured PO2 an area weighted average over the surface PO2 rather than a spatial average. The consequences of this finding are illustrated in an example of a maximally working muscle. Under the assumption that there are capillaries located on the muscle surface or immediately beneath it, the PO2 predicted to be measured by a surface electrode is almost four times the average muscle fiber PO2. However, PO2 values actually measured by surface PO2 electrodes are even higher calling for further explanation, in which superficial blood vessels and surface fascia may play an important role. Quantitative information on vascular morphology near muscle surfaces is needed in order to more definitely determine the importance of mechanisms discussed, for experimental results.

A method is presented that allows to calculate distributions of ventilation from measured time courses of inert gas washout. In the mathematical description of the washout process a discontinuous algorithm is applied: For each individual breath inspiratory and expiratory tidal volumes, endexpiratory alveolar volume, and dead space inspiration are taken into account. Furthermore, volume reduction of the alveolar gas according to the gas exchange ratio is considered. Commonly in ventilation analysis, the specific ventilation serves as abscissa of the density of the ventilation distribution. As at a given location the specific ventilation changes with varying tidal volumes even if the distribution pattern of the ventilation amongst the lung remains unchanged, the normalized specific ventilation is newly introduced instead. This quantity is defined to be the ratio of regional alveolar ventilation and regional endexpiratory alveolar volume divided by the total alveolar ventilation. The normalized specific ventilation reflects the distribution of the ventilation independently of variations in tidal volume and respiratory frequency. Furthermore, it allows direct comparison of ventilation distributions that are determined at varying alveolar ventilations. Ventilation distributions are approximated by the transformed beta distribution which is parameterized by its mean, variance, and skewness. In order to evaluate simplifications introduced in former studies and to quantify their effects on the resulting ventilation distributions, washout time courses are generated in a computer simulation from the comprehensive discontinuous algorithm and are used to recover ventilation distributions by means of accordingly simplified algorithms. Furthermore, the influence of errors that may occur in the measurement of tidal volumes are assessed. The results of these studies are summarized as follows: Serious errors are introduced in the recovered distributions if ventilation is modelled as a continuous process and if physiological variations in tidal volumes or endexpiratory alveolar volumes or dead space inspiration are neglected. Modelling the entire dead space as common dead space or as local dead space only, entails significant errors as well. Statistical errors of 2% in the measured volumes practically do not have any impacts on the recovered distributions whereas systematic errors significantly deteriorate the results. In conclusion, in ventilation analysis it is essential to apply a discontinuous description of the inert gas washout process that accounts for dead space inspiration and variations in the above mentioned quantities. In addition it is important to obtain all measured values with the highest achievable precision.

Honig and collaborators reported striking contradictions in current understanding of O2 supply to working skeletal muscle. Therefore we re-examined the problem by means of a new composite computer simulation. As inclusion of erythrocytic O2 desaturation and oxygen transport and consumption inside the muscle cell into a single model would entail immense numerical difficulties, we broke up the whole process into its several components: O2 desaturation of erythrocytes O2 transport and consumption in muscle fiber capillary transit time characterizing the period of contact between red cell and muscle fiber. "Erythrocyte model" as well as "muscle fiber model" both consist of a central core cylinder surrounded by a concentric diffusion layer representing the extracellular resistance to O2 diffusion (Fig. 1). Resistance layers in both models are to be conceived of as one and the same anatomical structure--even though in each model their shape is adapted to the respective geometry. By means of this overlap region a spatial connexion between both is given, whereas temporal coherence governing O2 fluxes and red cell spacing is derived from capillary transit time. Analysis of individual components is outlined as follows: Assuming axial symmetry of the problem a numerical algorithm was employed to solve the parabolic system of partial differential equations describing red cell O2 desaturation. Hb-O2 reaction kinetics, free and facilitated O2 diffusion in axial and radial directions, and red cell movement in capillary were considered. Resulting time courses of desaturation, which are considerably faster than the ones computed by Honig et al., are given in the following table (see also Fig. 3). (Formula: see text) Furthermore, we studied the respective importance of the several processes included in our model: Omission of longitudinal diffusion increased desaturation time by 15% to 23%, whereas effects of reaction kinetics and axial movement were 5% and 2% respectively. For time courses see Fig. 2. Nature and magnitude of extra-erythrocytic resistance to O2 diffusion playing a prominent part in O2 desaturation are scarcely explored. Calculated desaturation times based upon our new estimates (line 3 of above table) correspond well, however, with findings by Sinha, who observed 1.75 to 4-fold prolongation in omental and mesenteric capillaries compared to desaturation through equivalent plasma layers. The 3-dimensional elliptic system of partial differential equations describing stationary O2 transport through resistance layer and subsequent free and facilitated O2 diffusion and O2 consumption in muscle fiber was solved analytically.(ABSTRACT TRUNCATED AT 400 WORDS)

RBC spacing in capillaries plays an important role in that it determines the total number of RBCs contained in a capillary and, therefore, the total O2 flux out of the capillary. The detrimental effects of increased RBC spacing upon capillary O2 release are in part compensated for by enhanced O2 release out of single RBCs due to improved diffusion geometry and RBC movement. Non-uniformity of O2 flux brought about by the particulate nature of blood is considerably smaller than calculations which do not consider RBC movement indicate. It creates oscillations in the O2 supply to the tissue, the periodicity of which is fast, however, compared to the time constant of the PO2 decay in a temporarily unsupplied tissue. We conclude that non-uniformity of O2 flux out of capillaries due to large inter-erythrocytic plasma gaps does not play an important role for tissue O2 supply as long as average RBC spacing is sufficiently small to guarantee an appropriate overall capillary O2 flux.