Karlfried Groebe

On the relation between size of necrosis and diameter of tumor spheroids

PURPOSE In many previous experimental studies on multicellular tumor spheroids, the spheroid diameter at which central necrosis develops has been determined to be twice the thickness of the viable cell rim measured at a later stage of spheroid growth. This procedure tacitly assumes that there is a linear relation between the diameter of necrosis and that of the whole spheroid over the entire range of emergence and growth of necrosis. However, some experimental investigations have demonstrated that necroses do not grow gradually with spheroid diameter, but show a rapid initial increase, once a few cells have died. The present article offers an explanation for this phenomenon, which is derived from basic diffusion theory. METHODS AND MATERIALS A theoretical relation between sizes of spheroids and of their central necroses is developed, which is based on the assumption that formation of necrosis is caused by depletion of substrates or accumulation of metabolic waste products. In a second part, the theoretical model is fitted to experimental data from the literature, and oxygen consumption rate as a function of spheroid size is determined. RESULTS It turns out that the model closely mimics the experimentally observed behavior described above. These experimental results, therefore, do not furnish any evidence for assuming other hypotheses of necrosis formation. Resulting O2 consumption rates are well in the range of previously published data. In all cases, approximations to the measured data are better than the corresponding linear squares fits. CONCLUSION At least in some tumor cell lines, depletion of substrates or accumulation of waste products can explain formation of necrosis without the assumption of any additional mechanisms. Moreover, the model presented in this article offers an alternative way of determining the turnover rate of a substrate or metabolic waste product provided that depletion/accumulation of this substance represents the cause for necrosis development.

Three-dimensional cell culture induces novel proliferative and metabolic alterations associated with oncogenic transformation.

To date, cell biological characteristics of oncogene‐transfected cells have been investigated either in relatively homogeneous monolayer cultures or in heterogeneous tumors in vivo. To evaluate the emergence of cellular heterogeneity during tumor formation, we have established a multicellular spheroid system from an oncogene‐dependent, genetically determined 2‐stage carcinogenesis model for 3‐dimensional growth under well‐defined conditions. The effect of T24Ha‐ras transfection on cellular growth, proliferation, cell viability and oxygenation was investigated using spontaneously immortalized (Rat1) and c‐myc‐transfected (M1) Fisher 344 rat embryo fibroblasts and a tumorigenic T24Ha‐ras‐transfected clone of each (Rat1‐T1 and MRI). Spheroid volume growth curves and [3H]thymidine autoradiographs clearly demonstrated that spheroids better reflect the degree of tumorigenicity in vivo as opposed to monolayer cultures. Studies on Rat1 and M1 aggregates showed that the potential for tumor formation of Rat1 cells might be manifested in vitro as an increased capability of the cells to survive in 3D culture. pO2 measurements confirmed that neither cell quiescence nor cell death in the pseudo‐normal cell aggregate types is due to an oxygen deficiency. In contrast, depletion of oxygen coincided with necrotic cell death in Rat1‐T1 spheroids and proliferation arrest in MRI cultures. Cell‐line‐specific attributes in 3D culture that were not specifically related to ras transfection of the cells included histological structure, development of necrosis and thickness of viable cell rim. However, growth behavior, proliferation characteristics and their association with the oxygen supply might be correlated with the extent of transformation.

Glucose diffusion coefficients determined from concentration profiles in EMT6 tumor spheroids incubated in radioactively labeled L-glucose.

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)

Oxygen transport to tissue XVIII

Assessment of Dysoxia. Calcium-Dependent 02 Sensitivity of Cat Carotid Body D.G. Buerk, et al. Myocardial Hypoxia-Ischemia. Coronary Flow Response After Myocardial Ischemia May Predict Level of Functional Recovery R.J.F. Houston, et al. Tissue Oxygen Distribution. The S Factor -- A New Derived Hemodynamic Oxygenation Parameter -- A Useful Tool for Simplified Mathematical Modeling of Global Problems of Oxygen Transport K. Farrell, T. Wasser. Tissue Oxygenation in Tumors. Can NMR Diffusion-Weighted Imaging Provide Quantitative Information on Tumor Interstitial pO2? J.F. Dun, et al. Oxygen Supply-Demand. Peripheral Perfusion & Tissue Oxygenation Improvement Induced By Antihypertensive Medication Combined with Lipoidoproteinosis Treatment G. Cicco, et al. Angiogenesis & Microcirculation. Modification of Low Density Lipoproteins by Erythrocytes and Hemoglobin Under Hypoxic Conditions C. Balagopalakrishna, et al. Oxygen Carriers. Anticoagulants & Tissue Oxygenation. Near Infrared Spectroscopy. Nitric Oxide & Free Radicals. Measurement of Tissue Oxygen. 68 Additional Articles. Index.

Basic Mechanisms of Diffusive and Diffusion-Related Oxygen Transport in Biological Systems: A Review

In mammals, energy metabolism of active tissues requires permanent availability of oxygen. Because cessation of O 2 supply results in loss of organ function within seconds or minutes, continual feed of adequate amounts of O 2 to tissue is the most vital task for living organisms. For many years, it therefore has been one of the greatest challenges to physiologists to understand the mechanisms provided by nature to satisfy this need for oxygen.

Precapillary Servo Control of Blood Pressure and Postcapillary Adjustment of Flow to Tissue Metabolic Status A New Paradigm for Local Perfusion Regulation

BACKGROUND There are several shortcomings in current understanding of how the microvasculature maintains tissue homeostasis. Presently unresolved issues include (1) integration of the potentially conflicting needs for capillary perfusion and hydrostatic pressure regulation, (2) an understanding of signal transmission pathways for conveying information about tissue energetic status from undersupplied tissue sites to the arterioles, (3) accounting for the experimentally observed interrelations between precapillary and postcapillary resistances, and (4) an explanation of how precise local adjustment of perfusion to metabolic demands is achieved. METHODS AND RESULTS A novel conceptualization of how local microvascular control mechanisms are coordinated is proposed, according to which blood flow is adjusted to the metabolic needs of the tissue by the venules. Arteriolar action is merely called on for controlling capillary pressure through myogenic response and shear stress-induced vasodilation. A mathematical model of this theory is introduced and evaluated using well-established experimental data from the literature on regulating mechanisms of microvessel diameters exclusively. The model results demonstrate the suggested mode of microvascular operation to be functional and efficient under conditions present in vivo. Moreover, the predicted vascular responses are large enough to cover the entire range observed in exercising skeletal muscle during adjustment of perfusion to higher performance levels. CONCLUSIONS Precapillary pressure regulation combined with postcapillary adjustment of perfusion to tissue metabolic status is suitable to resolve the above shortcomings in our current understanding of microvascular control. With mathematical modeling based on experimental data, this mode of microvascular operation is shown to be functional and effective in controlling muscle microcirculation.

Oncogene-Associated Growth Behavior and Oxygenation of Multicellular Spheroids from Rat Embryo Fibroblasts

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.

Relating measuring signals from PO2 electrodes to tissue PO2: a theoretical study.

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.

Theoretical Analysis of Factors Influencing Recovery of Ventilation Distributions from Inert Gas Washout Data

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.

Is the division of heated tissue into temperature equivalent zones suitable for estimation of tumor blood flow from thermal clearance curves

Problems arising during application of a method proposed recently to predict tissue blood flow from measured thermal clearance curves have been discussed here. In this method, the treated tissue is divided into temperature equivalent zones with the aim to improve the mathematical description of experimental washout curves compared to descriptions based on monoexponential temperature decay. However, when applying the mathematical procedure suggested, any blood flow can be calculated by variation of the number of isothermal zones chosen. Unfortunately, to date no method for determination of the proper division of the treated tissue into temperature equivalent zones is available. Thus, any choice of the number of temperature equivalent zones is arbitrary. Therefore, we suggest that other investigators should not follow the analysis recently proposed for the determination of blood flow from thermal washout curves.