Diffusion regulated growth characteristics of a spherical prevascular carcinoma

Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Quantitative analysis of tumour spheroid structure

Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure; in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time; however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.

An Adaptive Robust Control Strategy in a Cancer Tumor-Immune System under Uncertainties

We propose an adaptive robust control for a second order nonlinear model of the interaction between cancer and immune cells of the body to control the growth of cancer and maintain the number of immune cells in an appropriate level. Most of the control approaches are based on minimizing the drug dosage based on an optimal control structure. However, in many cases, measuring the exact quantity of the model parameters is not possible. This is due to limitation in measuring devices, variational and undetermined characteristics of micro-environmental factors. It is of great importance to present a control strategy that can deal with these unknown factors in a nonlinear model.

On the morphological stability of multicellular tumour spheroids growing in porous media

Multicellular tumour spheroids (MCTSs) are extensively used as in vitro system models for investigating the avascular growth phase of solid tumours. In this work, we propose a continuous growth model of heterogeneous MCTSs within a porous material, taking into account a diffusing nutrient from the surrounding material directing both the proliferation rate and the mobility of tumour cells. At the time scale of interest, the MCTS behaves as an incompressible viscous fluid expanding inside a porous medium. The cell motion and proliferation rate are modelled using a non-convective chemotactic mass flux, driving the cell expansion in the direction of the external nutrients' source. At the early stages, the growth dynamics is derived by solving the quasi-stationary problem, obtaining an initial exponential growth followed by an almost linear regime, in accordance with experimental observations. We also perform a linear-stability analysis of the quasi-static solution in order to investigate the morphological stability of the radially symmetric growth pattern. We show that mechano-biological cues, as well as geometric effects related to the size of the MCTS subdomains with respect to the diffusion length of the nutrient, can drive a morphological transition to fingered structures, thus triggering the formation of complex shapes that might promote tumour invasiveness. The results also point out the formation of a retrograde flow in the MCTS close to the regions where protrusions form, that could describe the initial dynamics of metastasis detachment from the in vivo tumour mass. In conclusion, the results of the proposed model demonstrate that the integration of mathematical tools in biological research could be crucial for better understanding the tumour's ability to invade its host environment.

Scalable stirred-suspension bioreactor culture of human pluripotent stem cells

Advances in stem cell biology have afforded promising results for the generation of various cell types for therapies against devastating diseases. However, a prerequisite for realizing the therapeutic potential of stem cells is the development of bioprocesses for the production of stem cell progeny in quantities that satisfy clinical demands. Recent reports on the expansion and directed differentiation of human embryonic stem cells (hESCs) in scalable stirred-suspension bioreactors (SSBs) demonstrated that large-scale production of therapeutically useful hESC progeny is feasible with current state-of-the-art culture technologies. Stem cells have been cultured in SSBs as aggregates, in microcarrier suspension and after encapsulation. The various modes in which SSBs can be employed for the cultivation of hESCs and human induced pluripotent stem cells (hiPSCs) are described. To that end, this is the first account of hiPSC cultivation in a microcarrier stirred-suspension system. Given that cultured stem cells and their differentiated progeny are the actual products used in tissue engineering and cell therapies, the impact of bioreactor's operating conditions on stem cell self-renewal and commitment should be considered. The effects of variables specific to SSB operation on stem cell physiology are discussed. Finally, major challenges are presented which remain to be addressed before the mainstream use of SSBs for the large-scale culture of hESCs and hiPSCs.

Mechanistic modelling of dynamic MRI data predicts that tumour heterogeneity decreases therapeutic response

BACKGROUND

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) contains crucial information about tumour heterogeneity and the transport limitations that reduce drug efficacy. Mathematical modelling of drug delivery and cellular responsiveness based on underutilised DCE-MRI data has the unique potential to predict therapeutic responsiveness for individual patients.

METHODS

To interpret DCE-MRI data, we created a modelling framework that operates over multiple time and length scales and incorporates intracellular metabolism, nutrient and drug diffusion, trans-vascular permeability, and angiogenesis. The computational methodology was used to analyse DCE-MR images collected from eight breast cancer patients at Baystate Medical Center in Springfield, MA.

RESULTS

Computer simulations showed that trans-vascular transport was correlated with tumour aggressiveness because increased vessel growth and permeability provided more nutrients for cell proliferation. Model simulations also indicate that vessel density minimally affects tissue growth and drug response, and nutrient availability promotes growth. Finally, the simulations indicate that increased transport heterogeneity is coupled with increased tumour growth and poor drug response.

CONCLUSION

Mathematical modelling based on DCE-MRI has the potential to aid treatment decisions and improve overall cancer care. This model is the critical first step in the creation of a comprehensive and predictive computational method.

Modeling progression in radiation-induced lung adenocarcinomas

Quantitative multistage carcinogenesis models are used in radiobiology to estimate cancer risks and latency periods (time from exposure to clinical cancer). Steps such as initiation, promotion and transformation have been modeled in detail. However, progression, a later step during which malignant cells can develop into clinical symptomatic cancer, has often been approximated simply as a fixed lag time. This approach discounts important stochastic mechanisms in progression and evidence on the high prevalence of dormant tumors. Modeling progression more accurately is therefore important for risk assessment. Unlike models of earlier steps, progression models can readily utilize not only experimental and epidemiological data but also clinical data such as the results of modern screening and imaging. Here, a stochastic progression model is presented. We describe, with minimal parameterization: the initial growth or extinction of a malignant clone after formation of a malignant cell; the likely dormancy caused, for example, by nutrient and oxygen deprivation; and possible escape from dormancy resulting in a clinical cancer. It is shown, using cohort simulations with parameters appropriate for lung adenocarcinomas, that incorporating such processes can dramatically lengthen predicted latency periods. Such long latency periods together with data on timing of radiation-induced cancers suggest that radiation may influence progression itself.

Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

Incorporating energy metabolism into a growth model of multicellular tumor spheroids

Diffusion limitations in tumors create regions that are deficient in essential nutrients and contain a large number of quiescent and dying cells. Chemotherapeutic compounds are not effective against quiescent cells and therefore have reduced efficacy against tumors with extensive quiescence. We have formulated a mathematical model that predicts the extent and location of quiescence in multicellular spheroids. Multicellular spheroids are in vitro models of in vivo tumor growth that have proven to be useful experimental systems for studying radiation therapy, drug penetration, and novel chemotherapeutic strategies. Our model incorporates a realistic description of primary energy metabolism within reaction-diffusion equations to predict local glucose, oxygen, and lactate concentrations and an overall spheroid growth rate. The model development is based on the assumption that local cellular growth and death rates are determined by local ATP production generated by intracellular energy metabolism. Dynamic simulation and parametric sensitivity studies are used to evaluate model behavior, including the spatial distribution of proliferating, quiescent, and dead cells for different cellular characteristics. Using this model we have determined the critical cell survival parameters that have the greatest impact on overall spheroid physiology, and we have found that oxygen transport has a greater effect than glucose transport on the distribution of quiescent cells. By predicting the extent of quiescence based on individual cellular characteristic alone this model has the potential to predict therapeutic efficiency and can be used to design effective chemotherapeutic strategies.

Modeling positive regulatory feedbacks in cell–cell interactions

Our current understanding of molecular mechanisms of cellular regulation still does not support quantitative predictions of the overall growth kinetics of normal or malignant tissues. However, discernment of the role of growth-factor mediated cell-cell communication in tissue kinetics is possible by the use of simple mathematical models. Here we discuss the design and use of mathematical models in quantifying the contribution of autocrine and paracrine (i.e., humoral) interactions to the kinetics of tissue growth. We present models that include a humorally mediated regulatory feedback among cells built into phenomenological mathematical models of growth. Application of these models to data exemplifies the finite contributions of positive feedback in cell-cell interactions to the overall tissue growth. In addition, we propose a perturbation approach to allow separation of cell-cell interactions dependent on the perturbing agent (such as hormone antagonists in hormone-dependent tissues) from cell-cell interactions independent of it.

Competition effects in the dynamics of tumor cords

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.

Modeling tumor growth and irradiation response in vitro--a combination of high-performance computing and web-based technologies including VRML visualization

A simplified three-dimensional Monte Carlo simulation model of in vitro tumor growth and response to fractionated radiotherapeutic schemes is presented in this paper. The paper aims at both the optimization of radiotherapy and the provision of insight into the biological mechanisms involved in tumor development. The basics of the modeling philosophy of Duechting have been adopted and substantially extended. The main processes taken into account by the model are the transitions between the cell cycle phases, the diffusion of oxygen and glucose, and the cell survival probabilities following irradiation. Specific algorithms satisfactorily describing tumor expansion and shrinkage have been applied, whereas a novel approach to the modeling of the tumor response to irradiation has been proposed and implemented. High-performance computing systems in conjunction with Web technologies have coped with the particularly high computer memory and processing demands. A visualization system based on the MATLAB software package and the virtual-reality modeling language has been employed. Its utilization has led to a spectacular representation of both the external surface and the internal structure of the developing tumor. The simulation model has been applied to the special case of small cell lung carcinoma in vitro irradiated according to both the standard and accelerated fractionation schemes. A good qualitative agreement with laboratory experience has been observed in all cases. Accordingly, the hypothesis that advanced simulation models for the in silico testing of tumor irradiation schemes could substantially enhance the radiotherapy optimization process is further strengthened. Currently, our group is investigating extensions of the presented algorithms so that efficient descriptions of the corresponding clinical (in vivo) cases are achieved.

Cell kinetics in a tumour cord

In some tumours, the viable cells grow around blood vessels forming cylindrical structures called tumour cords, which are surrounded by regions of necrosis. In the present paper, we propose a mathematical model for the cell kinetics in a tumour cord at the stationary state. Both proliferating cells and quiescent cells are considered, and the proliferating cell population is structured by age. Cell migration towards cord periphery is accounted for from a continuum viewpoint. The age distribution of proliferating cells, the fraction of cells in S phase, the growth fraction and the velocity along the cord radius are computed. The predictions of the model are compared with literature data obtained from two experimental rat hepatomas. The model was used to compute the profile of the oxygen tension within the cord. Possible modifications and extensions are also presented.

A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy

A mathematical model is developed that describes the reduction in volume of a vascular tumor in response to specific chemotherapeutic administration strategies. The model consists of a system of partial differential equations governing intratumoral drug concentration and cancer cell density. In the model the tumor is treated as a continuum of two types of cells which differ in their proliferation rates and their responses to the chemotherapeutic agent. The balance between cell proliferation and death within the tumor generates a velocity field which drives expansion or regression of the spheroid. Insight into the tumor's response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.

The effect of time delays on the dynamics of avascular tumor growth

During avascular tumor growth, the balance between cell proliferation and cell loss determines whether the colony expands or regresses. Mathematical models describing avascular tumor growth distinguish between necrosis and apoptosis as distinct cell loss mechanisms: necrosis occurs when the nutrient level is insufficient to sustain the cell population, whereas apoptosis can occur in a nutrient-rich environment and usually occurs when the cell exceeds its natural lifespan. Experiments suggest that changes in the proliferation rate can trigger changes in apoptotic cell loss and that these changes do not occur instantaneously: they are mediated by growth factors expressed by the tumor cells. In this paper, we consider two ways of modifying the standard model of avascular tumor growth by incorporating into the net proliferation rate a time-delayed factor. In the first case, the delay represents the time taken for cells to undergo mitosis. In the second case, the delay represents the time for changes in the proliferation to stimulate compensatory changes in apoptotic cell loss. Numerical and asymptotic techniques are used to show how a tumor's growth dynamics are affected by including such delay terms. In the first case, the size of the delay does not affect the limiting behavior of the tumor: it simply modifies the details of its evolution. In the second case, the delay can alter the tumor's evolution dramatically. In certain cases, if the delay exceeds a critical value, defined in terms of the system parameters, then the underlying radially symmetric steady state is unstable with respect to time-dependent perturbations. (For smaller delays, this steady state is stable). Using the delay as a measure of the speed with which a tumor adapts to changes in its structure, we infer that, for the second case, a highly responsive tumor (small delay) has a better chance of surviving than does a less-responsive tumor (large delay). We also conclude that the tumor's evolution depends crucially on the manner and speed with which it adapts to changes in its surroundings and composition.

Positive feedback and angiogenesis in tumor growth control

In vivo tumor growth data from experiments performed in our laboratory suggest that basic fibroblast growth factor (bFGF) and vascular endothelial growth factor (VEGF) are angiogenic signals emerging from an up-regulated genetic message in the proliferating rim of a solid tumor in response to tumor-wide hypoxia. If these signals are generated in response to unfavorable environmental conditions, i.e. a decrease in oxygen tension, then the tumor may play an active role in manipulating its own environment. We have idealized this type of adaptive behavior in our mathematical model via a parameter which represents the carrying capacity of the host for the tumor. If that model parameter is held constant, then environmental control is limited to tumor shape and mitogenic signal processing. However, if we assume that the response of the local stroma to these signals is an increase in the host's ability to support an ever larger tumor, then our models describe a positive feedback control system. In this paper, we generalize our previous results to a model including a carrying capacity which depends on the size of the proliferating compartment in the tumor. Specific functional forms for the carrying capacity are discussed. Stability criteria of the system and steady state conditions for these candidate functions are analyzed. The dynamics needed to generate stable tumor growth, including countervailing negative feedback signals, are discussed in detail with respect to both their mathematical and biological properties.

A patient-specific in vivo tumor model

A significant body of research, spanning approximately the last 25 years, has focused upon the task of developing a better understanding of tumor growth through the use of in vitro mathematical models. Although such models are useful for simulation, in vivo growth differs in significant ways due to the variety of competing biological, biochemical, and mechanical factors present in a living biological system. An in vivo, macroscopic, primary brain tumor growth model is developed, incorporating previous in vitro growth pattern research as well as scientific investigations into the biological and biochemical factors that affect in vivo neoplastic growth. The tumor growth potential model presents an integrated, universal framework that can be employed to predict the direction and extent of spread of a primary brain tumor with respect to time for a specific patient. This framework may be extended as necessary to include the results of current and future research into parameters affecting neoplastic proliferation. The patient-specific primary brain tumor growth model is expected to have multiple clinical uses, including: predictive modeling, tumor boundary delineation, growth pattern research, improved radiation surgery planning, and expert diagnostic assistance.

Growth of necrotic tumors in the presence and absence of inhibitors

A mathematical model is presented for the growth of a multicellular spheroid that comprises a central core of necrotic cells surrounded by an outer annulus of proliferating cells. The model distinguishes two mechanisms for cell loss: apoptosis and necrosis. Cell loss due to apoptosis is defined to be programmed cell death, occurring, for example, when a cell exceeds its natural lifespan, whereas cell death due to necrosis is induced by changes in the cell's microenvironment, occurring, for example, in nutrient-depleted regions. Mathematically, the problem involves tracking two free boundaries, one for the outer tumor radius, the other for the inner necrotic radius. Numerical simulations of the model are presented in an inhibitor-free setting and an inhibitor-present setting for various parameter values. The effects of nutrients and inhibitors on the existence and stability of the time-independent solutions of the model are studied using a combination of numerical and asymptotic techniques.

Growth of nonnecrotic tumors in the presence and absence of inhibitors

In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed range of parameters, which corresponds to a balance between cell proliferation and cell death. Stability analysis, based on a two-timing method, suggests that, where it exists, the nontrivial solution is stable and the trivial solution unstable. Otherwise, the trivial solution is stable. Modification to these characteristic states brought about by the presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the treatment of cancer are also discussed.

From passive diffusion to active cellular migration in mathematical models of tumour invasion

Mathematical models of tumour invasion appear as interesting tools for connecting the information extracted from medical imaging techniques and the large amount of data collected at the cellular and molecular levels. Most of the recent studies have used stochastic models of cell translocation for the comparison of computer simulations with histological solid tumour sections in order to discriminate and characterise expansive growth and active cell movements during host tissue invasion. This paper describes how a deterministic approach based on reaction-diffusion models and their generalisation in the mechano-chemical framework developed in the study of biological morphogenesis can be an alternative for analysing tumour morphological patterns. We support these considerations by reviewing two studies. In the first example, successful comparison of simulated brain tumour growth with a time sequence of computerised tomography (CT) scans leads to a quantification of the clinical parameters describing the invasion process and the therapy. The second example considers minimal hypotheses relating cell motility and cell traction forces. Using this model, we can simulate the bifurcation from an homogeneous distribution of cells at the tumour surface toward a nonhomogeneous density pattern which could characterise a pre-invasive stage at the tumour-host tissue interface.

Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions

To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.

Growth factors and growth control of heterogeneous cell populations

In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth. Bull. math. Biol. 53, 639-656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a "triad" of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.

Equilibrium model of a vascularized spherical carcinoma with central necrosis--some properties of the solution

Properties of the solutions of a nonlinear time-independent diffusion equation are studied. The equation arises in a model of a spherically symmetric vascularized carcinoma with a central necrotic core. The boundary value problem as posed possesses a constant solution when the nutrient consumption rate and deposition rate (from the vascular network) are equal. This solution can lose uniqueness at a critical tumor dimension which corresponds to the onset of instability with respect to deviations from that uniform equilibrium state.

Cell migration in multicell spheroids: swimming against the tide

Multicell spheroids, small spherical clusters of cancer cells, have become an important in vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.

Biological response of multicellular EMT6 spheroids to exogenous lactate

The influence of elevated lactate concentrations, as found in tumor microregions, on cellular growth, viability, and metabolic state was studied employing the multicellular spheroid model. Spheroids of EMT6/Ro cells were cultured at 37 degrees C in 5% or 20% (v/v) oxygen, using stirred media with various concentrations of exogenous lactate ranging from 0.0 mM (standard conditions) to 20.0 mM. Elevated concentrations of exogenous lactate led to a considerable decrease of the maximum spheroid diameter at growth saturation, e.g., for 20% O2 from around 1700 microns to 700 microns in 0.0 and 20.0 mM lactate respectively. Histological investigations showed that the thickness of the viable cell rim was increased by elevated lactate concentrations in 20% O2, whereas this correlation was reversed in 5% O2. Cultivation of spheroids in increasing lactate concentrations was associated with a shift of metabolic pathways from net production to increased utilization of lactate in both 20% and 5% O2, as determined by standard enzymatic assays. Oxygen tension (PO2) values measured with micro-electrodes were less in spheroids cultured in high lactate (9.0 and 20.0 mM) than under standard conditions, irrespective of the external oxygen concentration. This finding reflected a substantial increase in the cellular O2 consumption with elevated external lactate levels. At given lactate concentrations, respiration rates that were derived from measured PO2 distributions by theoretical considerations were significantly lower in 5% O2 than in 20% O2.