Migration and internalization of cells and polystyrene microspheres in tumor cell spheroids

The movement and internalization of ³H-labelled cells and of inert polystyrene microspheres within multicellular spheroids has been examined through histological sectioning and autoradiography. EMT6 and RIF-1 spheroids were cultured in spinner flasks for approx. 2.5 weeks. At this time, ³H-labelled cells and/or microspheres were allowed to adhere to the spheroid surface. Microspheres, ³H-labelled RIF-1 monolayer cells and ³H-labelled EMT6 monolayer cells were observed to move centripetally as a wave into EMT6 spheroids. In contrast, ³H-labelled trypsinized RIF-1 and EMT6 spheroid cells became mixed with the other non-labelled spheroid cells in homotypic RIF-1 and EMT6 spheroids, respectively. Reduction of spheroid growth by maintaining the spheroids at room temperature and by treatment with 2500 rads irradiation did not prohibit the internalization of ³H-labelled EMT6 cells and microspheres in EMT6 spheroids.     

Oscillating growth patterns of multicellular tumour spheroids

The growth kinetics of 9L (rat glioblastoma cell line) and U118 (human glioblastoma cell line) multicellular tumour spheroids (MTS) have been investigated by non-linear least square fitting of individual growth curves with the Gompertz growth equation and power spectrum analysis of residuals. Residuals were not randomly distributed around calculated growth trajectories. At least one main frequency was found for all analysed MTS growth curves, demonstrating the existence of time-dependent periodic fluctuations of MTS volume dimensions. Similar periodic oscillations of MTS volume dimensions were also observed for MTS generated using cloned 9L cells. However, we found significant differences in the growth kinetics of MTS obtained with cloned cells if compared to the growth kinetics of MTS obtained with polyclonal cells. Our findings demonstrate that the growth patterns of three-dimensional tumour cell cultures are more complex than has been previously predicted using traditional continuous growth models.     

Multicellular tumour spheroids derived from human brain tumours

Multicellular tumour spheroids were prepared from a total of 46 human brain tumour biopsies by collagenase digestion and plating into agar coated flasks. Both primary malignant and secondary tumours formed spheroids with some correlation between the malignancy of tumour and the ability to undergo spheroid formation. The spheroids were capable of progressive growth, the rate of which was dependent, to some extent, on environmental conditions and was reflected by an increase in cell number within the spheroids. Spheroids prepared in this way may prove to be useful models for in vitro chemosensitivity and the general biology of brain tumours.     

Effect of cytochalasin B, nocodazole and irradiation on migration and internalization of cells and microspheres in tumor cell spheroids

The effect of cytochalasin B (CB), nocodazole, and irradiation on the adherence and internalization of 3H-labeled EMT6 spheroid-derived single cells and inert microspheres in unlabeled, intact EMT6 multicellular spheroids has been examined. CB inhibited adhesion and internal migration, whereas nocodazole did not stop adhesion but did prevent later internalization. Treatment of labeled cells with 5, 15 and 25 Gy 250 kV X-rays before adherence did not effect their adherence or later internalization. The same radiation treatments administered to the spheroids either immediately before or after the introduction of unirradiated single cells did not affect adherence, but the depths reached by labeled cells and microspheres were reduced largely because of the consequent reduction in spheroid growth. Microsphere size (9, 15, or 25 microns) and surface charge (negative, or non-ionic) had minimal, if any, effect on the adherence and internalization of these particles.     

Residual stress generation and necrosis formation in multi-cell tumour spheroids

We consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition.     

Imaging growth dynamics of tumour spheroids using optical coherence tomography

Optical coherence tomography (OCT) was used to monitor the dynamics of tumour spheroid formation by the hanging drop method. In contrast to microscopy, the estimates obtained using OCT for the volume of the spheroid, were consistent with the measured changes in cell number as a function of time. The OCT images also revealed heterogeneous structures in the spheroids of ∼200 μm diameter. These corresponded to the necrotic regions identified by fluorescence of propidium iodide stained cells.     

Extracellular matrix density regulates the formation of tumour spheroids through cell migration

In this work, we show how the mechanical properties of the cellular microenvironment modulate the growth of tumour spheroids. Based on the composition of the extracellular matrix, its stiffness and architecture can significantly vary, subsequently influencing cell movement and tumour growth. However, it is still unclear exactly how both of these processes are regulated by the matrix composition. Here, we present a centre-based computational model that describes how collagen density, which modulates the steric hindrance properties of the matrix, governs individual cell migration and, consequently, leads to the formation of multicellular clusters of varying size. The model was calibrated using previously published experimental data, replicating a set of experiments in which cells were seeded in collagen matrices of different collagen densities, hence producing distinct mechanical properties. At an initial stage, we tracked individual cell trajectories and speeds. Subsequently, the formation of multicellular clusters was also analysed by quantifying their size. Overall, the results showed that our model could accurately replicate what was previously seen experimentally. Specifically, we showed that cells seeded in matrices with low collagen density tended to migrate more. Accordingly, cells strayed away from their original cluster and thus promoted the formation of small structures. In contrast, we also showed that high collagen densities hindered cell migration and produced multicellular clusters with increased volume. In conclusion, this model not only establishes a relation between matrix density and individual cell migration but also showcases how migration, or its inhibition, modulates tumour growth.     

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis

Objectives: Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large‐scale volume oscillations in MTS, reported several years ago by two independent groups ( 1 , 2 ), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours ‘in vivo’. Materials and methods: Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN). Results: Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well‐defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation. Conclusions: Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.     

Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures

In this paper we adapt an avascular tumour growth model to compare the effects of drug application on multicell spheroids and on monolayer cultures. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generates volume changes described by a velocity field. The drug is modelled as an externally applied, diffusible material capable of killing cells, both linear and Michaelis-Menten kinetics for drug action on cells being studied. Numerical solutions of the resulting system of partial differential equations for the multicell spheroid case are compared with closed form solutions of the monolayer case, particularly with respect to the effects on the cell kill of the drug dosage and of the duration of its application. The results show an enhanced survival rate in multicell spheroids compared to monolayer cultures, consistent with experimental observations, and indicate that the key factor determining this is drug penetration. An analysis of the large time tumour spheroid response to a continuously applied drug at fixed concentration reveals up to three stable large time solutions, namely the trivial solution (i.e. a dead tumour), a travelling wave (continuously growing tumour) and a sublinear growth case in which cells reach a pseudo-steady-state in the core. Each of these possibilities is formulated and studied, with the bifurcations between them being discussed. Numerical solutions reveal that the pseudo-steady-state solutions persist to a significantly higher drug dose than travelling wave solutions.     

The effect of combined heat and ultrasound on multicellular tumour spheroids

The effect of combined ultrasound and heat treatments on Chinese hamster multicellular spheroids of varying size was investigated using growth rate, single cell survival and ultrastructural damage as endpoints. Ultrasonic irradiation at 37 degrees C had no effect on the growth rate of 200-730 microns spheroids. Similarly there was no effect on the growth rate of 350 microns spheroids when irradiated during a 60 min exposure to 41.5 degrees C. However, spheroids of 200-700 mm diameter showed growth delay when held at 43 degrees C for 1 h. The effect was enhanced with concomitant ultrasound irradiation but was not dependent on spheroid size. When 200 and 400 microns spheroids held at 43 degrees C for 60 min were irradiated with different ultrasonic intensities a dose-dependent decrease in surviving fraction and a dose-dependent increase in growth delay was obtained. When surviving fraction was plotted as a function of growth delay a good correlation was obtained, suggesting that the combination of heat and ultrasound irradiation does not produce cytostasis in the surviving cells of either 200 or 400 microns spheroids. At the ultrastructural level increased cytoplasmic vacuolation was the only result of ultrasonic irradiation at 37 degrees C. Exposure to 43 degrees C for 60 min was required to elicit thermal damage. This took the form of membrane evagination at the spheroid surface, vacuolation of the cytoplasm, grouping of organelles around the periphery of the nucleus, and fragmentation of the nucleolus. These effects were enhanced with concomitant ultrasonic irradiation but other features were also noted, viz. disaggregation of polyribosomes, dilation of the rough endoplasmic reticulum and blebbing of the nuclear membrane. Damage was independent of spheroid size. These results are in agreement with previous data obtained from single-cell studies. Indicating that there is a non-thermal, non-cavitational component to the cell killing in multicellular spheroids resulting from combined heat and ultrasound treatment.     

Streaming of labelled cells in the conjunctival epithelium

This study examines epithelial cell streaming and turnover in normal rat bulbar conjunctiva. Twenty seven male adult random-bred Hebrew rats weighing between 250–300 g, were injected i.p. with [³H]-thymidine. Three rats were killed at various times, thereafter from 1 h to 28 days. The enucleated eyes were fixed in formalin, cut into 5 μ thick sections, dipped into liquid emulsion, exposed for three weeks and stained with haematoxylin and eosin. Conjunctival epithelium was scanned from the limbus and outward, using an ocular micrometer grid with 10 x 10 divisions. In each consecutive field the grid was positioned along the basement membrane which was defined as the x-axis. The y-axis extended from the basement membrane outward. The x, y coordinate of each nucleus with three grains or more and its grain content were recorded along the entire epithelium. Conjunctival epithelium is divided into two cell kinetic compartments: a progenitor (P), along the basal and supra basal layer, in which cells proliferate, and a non proliferating Q-compartment, in the layers above. One hour after labelling most of the labelled cells were in the basal and supra basal layers. From then onward labelled cells streamed along both axes. Their x-velocity was 10·5±2·4 μ/day and the y-velocity 9·3 ± 5·4 μ/day. Cells are eliminated at the epithelial surface which is the outer Q-compartment boundary. Basal cell turnover was estimated from grain count dilution curves. The time it takes for the grains in a cell to reach half of their initial value was 8·3 days. It is closely related to the cell's generation time. The present study demonstrates that conjunctival epithelium in the rat streams along two axes, x, and y: 1 The x-axis extends along the basal layer, from the limbus and outward. 2 The y-axis extends from the basal layer into the layers above it. Cells first stream along the x-direction and then turn y-ward. Since cells are ultimately exfoliated from the conjunctival surface, and since the conjunctiva maintains steady state, we propose that stem cells located in the limbus generate transitional cells that stream along the two axes. Macroscopically the limbus is circular, and the stem cells are situated around the cornea. Each stem cell and its streaming progeny can be viewed as a conjunctival epithelial unit. We propose that conjunctival and corneal epithelium, are the descendants of an uncommitted stem cell that generates two differentiation pathways, a corneal and a conjunctival.     

Modelling and detecting tumour oxygenation levels

Tumours that are low in oxygen (hypoxic) tend to be more aggressive and respond less well to treatment. Knowing the spatial distribution of oxygen within a tumour could therefore play an important role in treatment planning, enabling treatment to be targeted in such a way that higher doses of radiation are given to the more radioresistant tissue. Mapping the spatial distribution of oxygen in vivo is difficult. Radioactive tracers that are sensitive to different levels of oxygen are under development and in the early stages of clinical use. The concentration of these tracer chemicals can be detected via positron emission tomography resulting in a time dependent concentration profile known as a tissue activity curve (TAC). Pharmaco-kinetic models have then been used to deduce oxygen concentration from TACs. Some such models have included the fact that the spatial distribution of oxygen is often highly inhomogeneous and some have not. We show that the oxygen distribution has little impact on the form of a TAC; it is only the mean oxygen concentration that matters. This has significant consequences both in terms of the computational power needed, and in the amount of information that can be deduced from TACs.     

The migration of cells in multicell tumor spheroids

A mathematical model is proposed to explain the observed internalization of microspheres and 3H-thymidine labelled cells in steady-state multicellular spheroids. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. In addition, a very simple model of the progress of the cells through the cell cycle is considered. Cells are divided into two classes, those proliferating (being in G1, S, G2 or M phases) and those that are quiescent (being in G0). Furthermore, the two categories are presumed to have different chemotactic responses to the nutrient gradient. The model accounts for the spatial and temporal variations in the cell categories together with mitosis, conversion between categories and cell death. Numerical solutions demonstrate that the model predicts the behavior similar to existing models but has some novel effects. It allows for spheroids to approach a steady-state size in a non-monotonic manner, it predicts self-sorting of the cell classes to produce a thin layer of rapidly proliferating cells near the outer surface and significant numbers of cells within the spheroid stalled in a proliferating state. The model predicts that overall tumor growth is not only determined by proliferation rates but also by the ability of cells to convert readily between the classes. Moreover, the steady-state structure of the spheroid indicates that if the outer layers are removed then the tumor grows quickly by recruiting cells stalled in a proliferating state. Questions are raised about the chemotactic response of cells in differing phases and to the dependency of cell cycle rates to nutrient levels.     

Increased radioresistance of cells in cultured multicell spheroids

Using the Chinese hamster cell line B14 FAF28, several specific properties of the contact effect (CE) of radiation action in spheroids were investigated. CE was found to "protect" the spheroid cells against several types of radiation-induced cytogenetic misfunctions such as blockage in S and G2+M-phase, mutagenesis, and chromosome damage. However, repair of DNA strand-breaks was the same in monolayers and spheroids. Furthermore, CE is a property of the single cell and does not depend on the proliferative status (cycling or non-cycling) of the cells. We conclude that CE is the result of a physiological modification of the cells occurring during growth in the three-dimensional spheroid matrix and requiring metabolic cooperation and cyclic AMP for its induction.     

Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids

In order to determine the role of micromilieu in tumour spheroid growth, a mathematical model was developed to predict EMT6/Ro spheroid growth and microenvironment based upon numerical solution of the diffusion/reaction equation for oxygen, glucose, lactate ion, carbon dioxide, bicarbonate ion, chlorine ion and hydrogen ion along with the equation of electroneutrality. This model takes into account the effects of oxygen concentration, glucose concentration and extracellular pH on cell growth and metabolism. Since independent measurements of EMT6/Ro single cell growth and metabolic rates, spheroid diffusion constants, and spinner flask mass transfer coefficients are available, model predictions using these parameters were compared with published data on EMT6/Ro spheroid growth and micro-environment. The model predictions of reduced spheroid growth due to reduced cell growth rates and cell shedding fit experimental spheroid growth data below 700 microns, but overestimated the spheroid growth rate at larger diameters. Predicted viable rim thicknesses based on predicted near zero glucose concentrations fit published viable rim thickness data for 1000 microns spheroids grown at medium glucose concentrations of 5.5 mM or less. However, the model did not accurately predict the onset of necrosis. Moreover, the model could not predict the observed decreases in oxygen and glucose metabolism seen in spheroids with time, nor could it predict the observed growth plateau. This suggests that other unknown factors, such as inhibitors or cell-cell contact effects, must also be important in affecting spheroid growth and cellular metabolism.     

Forecasting the growth of multicell tumour spheroids: implications for the dynamic growth of solid tumours

The growth dynamics of multicell tumour spheroids (MTS) were analysed by means of mathematical techniques derived from signal processing theory. Volume vs. time trajectories of individual spheroids were fitted with the Gompertz growth equation and the residuals (i.e. experimental volume determinations minus calculated values by fitting) were analysed by fast fourier transform and power spectrum. Residuals were not randomly distributed around calculated growth trajectories demonstrating that the Gompertz model partially approximates the growth kinetics of three-dimensional tumour cell aggregates. Power spectra decreased with increasing frequency following a 1/f(delta) power-law. Our findings suggest the existence of a source of 'internal' variability driving the time-evolution of MTS growth. Based on these observations, a new stochastic Gompertzian-like mathematical model was developed which allowed us to forecast the growth of MTS. In this model, white noise is additively superimposed to the trend described by the Gompertz growth equation and integrated to mimic the observed intrinsic variability of MTS growth. A correlation was found between the intensity of the added noise and the particular upper limit of volume size reached by each spheroid within two MTS populations obtained with two different cell lines. The dynamic forces generating the growth variability of three-dimensional tumour cell aggregates also determine the fate of spheroid growth with a strong predictive significance. These findings suggest a new approach to measure tumour growth potential.