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.     

Behaviour of Listeria monocytogenes under combined chilling processes

The behaviour of Listeria monocytogenes under chilling processes was investigated. Growth kinetics were measured at 7 degrees C in TSBYE culture medium as a function of pH (7.2 and 6.2), pre-incubation temperatures (4 or 7 degrees C), cooling (0.05 or 0.1 degree C min-1) and freezing (0 and -5 degrees C) treatments. Growth curves generated were fitted by Gompertz and Baranyi functions. The Baranyi function gave better parameter estimation values than the Gompertz equation which over-estimated the specific growth rate values. Listeria monocytogenes grew at 7 degrees C without a lag phase, except when the sub-culture was performed at 37 degrees C, whereas the specific growth rate was affected by the chilling processes. In fact, L. monocytogenes grew slightly faster at 7 degrees C when a 4 degrees C pre-incubation treatment was applied than with a 7 degrees C pre-incubation treatment. These results suggest that to mimic the processes of contamination in industry, predictive microbiology studies with L. monocytogenes should be performed with organisms cultured at low temperatures.     

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PurposeTo develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.MethodsCells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.ResultsSimulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.ConclusionsThe model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.     

Modeling mass transfer in hepatocyte spheroids via cell viability, spheroid size, and hepatocellular functions

Hepatocyte aggregation into spheroids attributes to their increased activity, but in the absence of a vascular network the cells in large spheroids experience mass transfer limitations. Thus, there is a need to define the spheroid size which enables maximal cell viability and productivity. We developed a combined theoretical and experimental approach to define this optimal spheroid size. Hepatocyte spheroids were formed in alginate scaffolds having a pore diameter of 100 microm, in rotating T-flasks or spinners, to yield a maximal size of 100, 200, and 600 microm, respectively. Cell viability was found to decrease with increasing spheroid size. A mathematical model was constructed to describe the relationship between spheroid size and cell viability via the oxygen mass balance equation. This enabled the prediction of oxygen distribution profiles and distribution of viable cells in spheroids with varying size. The model describes that no oxygen limitation will take place in spheroids up to 100 microm in diameter. Spheroid size affected the specific rate of albumin secretion as well; it reached a maximal level, i.e., 60 microg/million cells/day in 100-microm diameter spheroids. This behavior was depicted in an equation relating the specific albumin secretion rate to spheroid size. The calculated results fitted with the experimental data, predicting the need for a critical number of viable hepatocytes to gain a maximal albumin secretion. Taken together, the results on mass transport in spheroids and its effects on cell viability and productivity provide a useful tool for the design of 3D scaffolds with pore diameters of 100 microm.     

Recombinant human Erythropoietin enhanced the cytotoxic effects of tamoxifen toward the spheroid MCF-7 breast cancer cells

Erythropoietin (EPO) is widely used to treat anemia in patients undergoing chemotherapy for cancers. The main objective of this study was to investigate the effect of rHuEPO on the response of spheroid breast cancer, MCF-7, cells to tamoxifen treatment. The MCF-7 spheroids were treated with 10 mg/mL tamoxifen in combination with either 0, 10, 100 or 200 IU/mL rHuEPO for 24, 48 or 72 h. The viability of the MCF-7 cells was determined using the annexin-V, cell cycle, caspases activation and acridine orange/propidium iodide staining. rHuEPO-tamoxifen combination significantly (p greater than 0.05) increased the number of spheroid MCF-7 cells entering early apoptotic phase after 12 h and late apoptotic phase after 24 h of treatment; primarily the result of the antiproliferative effect tamoxifen. Tamoxifen alone significantly (p < 0.05) increased the caspase-3 and −9 activities in the spheroid MCF-7 cells by 200 to 550% of the control. Combination rHuEPO and tamoxifen produced much lesser effect on the caspase-8 activity. The rHuEPO in the combination treatment had concentration-dependently caused decrease in the caspase activities. rHuEPO-tamoxifen combination markedly increased MCF-7 cells entering the SubG0/G1 phase of the cell cycle by more than 500% of the control, while decreasing those entering the G2 + M and S phases by 50%. After 72 h, the combination treatment produced greater (p < 0.05) change in the SubG0/G1 phase than tamoxifen treatment alone. Morphologically, spheroid MCF-7 cells subjected to combination rHuEPO-tamoxifen treatment showed nuclear condensation and margination, cytoplasmic blebbing, necrosis, and early and late apoptosis. Thus, the study showed that rHuEPO-tamoxifen combination induced apoptosis in the spheroid MCF-7 cells. The apoptotic effect of the rHuEPO-tamoxifen combination treatment on the MCF-7 cells was greater than that produced by tamoxifen alone. The rHuEPO-tamoxifen treatment enhanced the caspase-independent apoptotic effects of tamoxifen on the spheroid MCF-7 cells.     

Generation of Multicellular Tumor Spheroids with Microwell-Based Agarose Scaffolds for Drug Testing

Three dimensional multicellular aggregate, also referred to as cell spheroid or microtissue, is an indispensable tool for in vitro evaluating antitumor activity and drug efficacy. Compared with classical cellular monolayer, multicellular tumor spheroid (MCTS) offers a more rational platform to predict in vivo drug efficacy and toxicity. Nevertheless, traditional processing methods such as plastic dish culture with nonadhesive surfaces are regularly time-consuming, laborious and difficult to provide uniform-sized spheroids, thus causing poor reproducibility of experimental data and impeding high-throughput drug screening. In order to provide a robust and effective platform for in vitro drug evaluation, we present an agarose scaffold prepared with the template containing uniform-sized micro-wells in commercially available cell culture plates. The agarose scaffold allows for good adjustment of MCTS size and large-scale production of MCTS. Transparent agarose scaffold also allows for monitoring of spheroid formation under an optical microscopy. The formation of MCTS from MCF-7 cells was prepared using different-size-well templates and systematically investigated in terms of spheroid growth curve, circularity, and cell viability. The doxorubicin cytotoxicity against MCF-7 spheroid and MCF-7 monolayer cells was compared. The drug penetration behavior, cell cycle distribution, cell apoptosis, and gene expression were also evaluated in MCF-7 spheroid. The findings of this study indicate that, compared with cellular monolayer, MCTS provides a valuable platform for the assessment of therapeutic candidates in an in vivo-mimic microenvironment, and thus has great potential for use in drug discovery and tumor biology research.     

Growth inhibition of estrogen receptor-positive and aromatase-positive human breast cancer cells in monolayer and spheroid cultures by letrozole, anastrozole, and tamoxifen

Two third-generation aromatase inhibitors, letrozole and anastrozole, and the antiestrogen tamoxifen, were compared for growth-inhibiting activity in two estrogen receptor (ER)-positive aromatase-overexpressing human breast cancer cell lines, MCF-7aro and T-47Daro. Inhibition of hormone (1 nM testosterone)-stimulated proliferation was evaluated in both monolayer cultures and in three-dimensional spheroid cultures. Letrozole and anastrozole were also compared for effectiveness of aromatase inhibition, and relative affinity for aromatase, under both monolayer and spheroid growth conditions. Letrozole was an effective inhibitor of MCF-7aro monolayer cell proliferation, with an estimated 50% inhibitory concentration (IC50) of 50-100 nM, whereas an IC50 was not reached with anastrozole at any concentration tested (100-500 nM). An IC50 of tamoxifen was 1000 nM. Proliferation of T-47Daro monolayer cells was more sensitive to inhibition by all three agents; as with MCF-7aro cells, letrozole was the most effective inhibitor. MCF-7aro spheroids were slightly less sensitive than monolayer cells proliferation-inhibiting effects of letrozole (IC50 about 200 nM), and there was no significant inhibition with 100-200 nM anastrozole or 200-1000 nM tamoxifen. Letrozole and anastrozole significantly inhibited T-47Daro spheroid cell proliferation, at 15-25 and 50 nM, respectively, consistent with the greater sensitivity of T-47Daro monolayer cells to inhibition of proliferation by these agents. Tamoxifen failed to significantly inhibit T-47Daro spheroid cell proliferation over a 100-500 nM concentration range. Determination of aromatase inhibition in monolayers of both cell lines by a direct-access microsomal assay and an intact-cell assay revealed that letrozole was more active than anastrozole in monolayers of both cell lines and in both assays. In MCF-7aro spheroids following cell lysis, only letrozole significantly inhibited aromatase activity, supporting the conclusion that letrozole binds stronger to aromatase than anastrozole does. Our results demonstrate that MCF-7aro and T-47Daro spheroids could be a suitable model for evaluation of growth-inhibitory effects of agents used in hormonal therapy of breast cancer.     

A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth

The rates of consumption of oxygen and glucose by EMT6/Ro cells in multicellular spheroids were measured at various times during normal growth. In situ spheroid cellular consumption rates were similar to those of exponentially growing single cells up to a spheroid diameter of 150 micron. Further growth resulted in decreases in the rates of both oxygen and glucose consumption which were correlated with the increase in spheroid diameter and cell number. At a diameter of 1300 micron, both rates of cellular consumption had decreased by a factor of 2.5. The rates of consumption per unit of nonnecrotic spheroid volume decreased in a similar manner. Measurements with single cells demonstrated that the rate of oxygen consumption was coupled with glucose concentration, and vice versa. The rates of consumption for cells dissociated from small spheroids indicated that there was some effect of the spheroid environment. As the spheroids grew, however, association in the spheroid structure accounted for a smaller proportion of the total observed reduction in the rates of nutrient consumption. The presence of central necrosis also appeared to have no effect on the rates of consumption of these nutrients. Spheroid-derived cells showed a decrease in cell volume with growth as the cells accumulated in a quiescent state. Measurements with single cells demonstrated that oxygen and glucose consumption were correlated with cell volume and with the development of nonproliferating cells. We conclude that the observed decrease in oxygen and glucose consumption with growth in spheroids is largely due to the progressive accumulation of cells in a quiescent state characterized by an inherently lower cellular rate of nutrient utilization.     

PATTERNS OF GROWTH IN BIRDS. II. GROWTH RATE AND MODE OF DEVELOPMENT

This analysis was initiated to examine the relationship between the rate of growth in birds and their development of mature function. The literature was surveyed for data on growth and development, and the growth curves of 81 species were chosen for the analysis. Growth curves of most species were fitted with the Gompertz equation, and the rate constants of the equation were used as an index of the growth rate. For those species whose curves were fitted better by other equations, with a slightly different form, appropriate conversion factors, derived in this paper, were employed.
Among species with similar modes of development, growth rate decreases with increasing body weight in an allometric manner, with slopes of –0.26 to –0.42, depending on the group. Between groups, the rate of growth in body weight was found to be closely associated with the rate of development of function, in particular, the acquisition of flight. Among those species that can walk at an early age, but acquire flight relatively late, the rate of growth depends primarily on the relative size of the musculature of the lower extremities.
Data are presented to refute the hypotheses that growth rate is adjusted to nestling mortality, or that the energy requirements of the young (and hence their growth rates) are balanced against brood size. It is concluded that most species grow at some physiologically maximum rate, but as yet it is not possible to distinguish between limitation of growth rate at the level of the organism or at the level of the tissue.     

Shedding of mitotic cells from the surface of multicell spheroids during growth

During the growth of EMT6/Ro mammary tumor multicell spheroids, a large number of cells are shed into the suspension medium. The rate of cell shedding was 218 cells per square millimeter of spheroid surface per hour, or up to 1.5% of the total spheroid cell content per hour. Shed cells had a clonogenic capacity equal to that of exonential monolayer cultures and were further characterized by volume distribution, mitotic index, flow cytoflurometry, and autoradiography. The results indicated that cells are released from the spheroid surface at mitosis, presumably due to a loosening of the cell-to-cell attachment during this cycle phase. These mitotic cells, when placed in monolayer culture, attached and grew synchronously with a cell cycle time of about 13 hours. Shed cells kept in suspension culture had a similar cell cycle time, but these cells reaggregated immediately after mitosis. The results indicated that cell shedding and reaggregation both occur near the time of mitosis and are intrinsic factors regulating the initiation and subsequent growth of multicell spheroids. Although these studies were done with spheroids cultured in vitro, shedding of mitotic cells may play an important role in the in vivo process of metastasis.     

Method for generation of homogeneous multicellular tumor spheroids applicable to a wide variety of cell types

Multicellular tumor spheroids (MCTS) are used as organotypic models of normal and solid tumor tissue. Traditional techniques for generating MCTS, such as growth on nonadherent surfaces, in suspension, or on scaffolds, have a number of drawbacks, including the need for manual selection to achieve a homogeneous population and the use of nonphysiological matrix compounds. In this study we describe a mild method for the generation of MCTS, in which individual spheroids form in hanging drops suspended from a microtiter plate. The method has been successfully applied to a broad range of cell lines and shows nearly 100% efficiency (i.e., one spheroid per drop). Using the hepatoma cell line, HepG2, the hanging drop method generated well-rounded MCTS with a narrow size distribution (coefficient of variation [CV] 10% to 15%, compared with 40% to 60% for growth on nonadherent surfaces). Structural analysis of HepG2 and a mammary gland adenocarcinoma cell line, MCF-7, composed spheroids, revealed highly organized, three-dimensional, tissue-like structures with an extensive extracellular matrix. The hanging drop method represents an attractive alternative for MCTS production, because it is mild, can be applied to a wide variety of cell lines, and can produce spheroids of a homogeneous size without the need for sieving or manual selection. The method has applications for basic studies of physiology and metabolism, tumor biology, toxicology, cellular organization, and the development of bioartificial tissue.     

Development of Multicellular Tumor Spheroid (MCTS) Culture from Breast Cancer Cell and a High Throughput Screening Method Using the MTT Assay

In comparison to monolayer cells, MCTS has been claimed as more suitable candidate for studying drug penetration due to the high resemblance to solid tumors. However, the cultivation of MCTS is cumbersome, time consuming, and most technique fail to generate spheroids with uniform sizes. Therefore, the application of spheroid cultures in high throughput screening has been rather limiting. Besides, the lack of a well established screening protocol method that is applicable to spheroid could also be attributed to this limitation. Here we report a simple way of cultivating homogenous MCTS cultures with compact and rigid structure from the MCF-7 cells. Besides, we had also made some modifications to the standard MTT assay to realize high throughput screening of these spheroids. Using the modified protocol, tamoxifen showed cytotoxicity effect towards MCTS cultures from MCF-7 with high consistency. The results correlated well with the cultures' response assessed by LDH release assay but the latter assay was not ideal for detecting a wide range of cytotoxicity due to high basal background reading. The MTT assay emerged as a better indicator to apoptosis event in comparison to the LDH release assay. Therefore, the method for spheroid generation and the modified MTT assay we reported here could be potentially applied to high throughput screening for response of spheroid cultures generated from MCF-7 as well as other cancer cell lines towards cytotoxic stimuli.     

In situ oxygen consumption rates of cells in V-79 multicellular spheroids during growth

The rate of consumption of oxygen by V-79 cells in multicellular spheroids was measured as a function of the spheroid diameter. In situ consumption was equal to that of exponentially growing cells for spheroids less than 200 micron in diameter. The rate of oxygen consumption decreased for cells in spheroids between 200 and 400 micron diameter to a value one-fourth the initial, then remained constant with further spheroid growth. Comparison of consumption rates for spheroid-derived cells before and after dissociation from the spheroid structure indicated that the spheroid microenvironment accounted for only 20% of the change in oxygen consumption rate. Cell-cell contact, cell packing, and cell volume were not critical parameters. Plateau-phase cells had a fivefold lower rate of oxygen consumption than exponential cells, and it is postulated that the spheroid quiescent cell population accounts for a large part of the intrinsic alteration in oxygen consumption of cells in spheroids. Some other mechanism must be involved in the regulation of cellular oxygen consumption in V-79 spheroids to account for the remainder of the reduction observed in this system.     

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.     

Recovery from potentially lethal damage and recruitment time of noncycling clonogenic cells in 9L confluent monolayers and spheroids

Cells that have been grown as multicell tumor spheroids exhibit radioresistance compared to the same cells grown in monolayers. Comparison of potentially lethal damage (PLD) repair and its kinetics was made between 9L cells grown as spheroids and confluent monolayers. Survival curves of cells plated immediately after irradiation showed the typical radioresistance associated with spheroid culture compared to plateau-phase monolayers. The dose-modification factor for spheroid cell survival is 1.44. Postirradiation incubations in normal phosphate-buffered saline (PBS), conditioned media, or 0.5 M NaCl in PBS reduced the differences in radiosensitivity between the two culture conditions. Postirradiation treatment in PBS or conditioned medium promoted repair of potentially lethal damage, and 0.5 M NaCl prevented the removal of PLD and allowed the fixation of damage resulting in lower survival. Survival of spheroid and monolayer cells after hypertonic NaCl treatment was identical. NaCl treatment reduced Do more than it did the shoulder (Dq) of the survival curve. PLD repair kinetics measured after postirradiation incubation in PBS followed by hypertonic NaCl treatment was the same for spheroids and for plateau-phase monolayers. The kinetics of PLD repair indicates a biphasic phenomenon. There is an initial fast component with a repair half-time of 7.9 min and a slow component with a repair half-time of 56.6 min. Most of the damage (59%) is repaired slowly. Since the repair capacity and kinetics are the same for spheroids and monolayers, the radioresistance of spheroids cannot be explained on this basis. Evidence indicates that the time to return from a Go (noncycling G1 cells) state to a proliferative state (recruitment) for cells from confluent monolayers and from spheroids after dissociation by protease treatment may be the most important determinant of the degree of PLD repair that occurs. Growth curves and flow cytometry cell cycle analysis indicate that spheroid cells have a lag period for reentry into a proliferative state. Since plating efficiency remains high and unchanging during this period, one cannot account for the delay on the basis of the existence of a large fraction of Go cells which are not potentially clonogenic. The cell cycle progression begins in 6-8 h for monolayer cells and in 14-15 h for spheroids. It is hypothesized that the slower reentry of spheroid cells into a cycling phase allows more time for repair than for the rapidly proliferating monolayer cells.     

Use of a laser diffraction particle sizer for the measurement of mean diameter of multicellular tumor spheroids

Summary Increasing use is being made of tumor cell lines cultured as cell aggregates (generally referred to as multicellular spheroids) in in vitro radiosensitivity and/or chemosensitivity tests. Conventional procedures for the determination of mean spheroid diameters for the construction of growth delay curves employ a microscope-image analyzer. However, this approach can prove excessively time consuming when large numbers of samples have to be, measured. We have, therefore, been exploring the use of a Laser Diffraction Particle Sizer, the Malvern 2600 long bench model, for the measurement of mean spheroid diameter and size distribution. We report here a direct comparison between measurements carried out by the instrument and under the microscope. Also a comparison of growth curves for six cell lines constructed from measurements by the microscope and by the instrument. A number of factors that might affect the accuracy of spheroid diameter measurement by the instrument have been investigated: The effect of stirring to maintain the spheroids in suspension during measurement. Sampling error due to removal of a series of spheroid samples from culture flasks for measurement. Optimum number of scans to be carried out by the instrument to reach a constant value for mean diameter, and minimum SE of the mean. This research was supported by the Yorkshire Cancer Research Campaign, Horrogate HG1 5LQ, United Kingdom, and by the Hospital Research Fund, Cookridge Hospitatl, Leeds LS16 6QB, United Kingdom.     

Proliferation-associated oxygen consumption and morphology of tumor cells in monolayer and spheroid culture.

The oxygen consumption rate, proliferative activity, and morphology of EMT6/Ro mouse mammary sarcoma cells in monolayer and multicellular spheroid culture have been investigated in a comparative study. During the transition of monolayer cells from the exponential into the plateau growth phase, there is a distinct decrease in the cellular volume that is associated with a corresponding decrease in the proliferative and respiratory activity of the cells. The decline in cell volume is mainly due to a decrease in the content of cytoplasm, whereas the size of the nucleus is only slightly reduced. A concomitant decrease in the number of mitochondria per cell obviously accounts for the reduction in cellular oxygen uptake. Despite a continuous decrease of cell proliferation from the surface to interior regions of EMT6 spheroids reflected by a gradient in tritiated thymidine labeling, volume-related oxygen consumption is rather uniform in viable regions of these aggregates. The finding can be explained by the results of the morphometric evaluation showing a uniform volume density of mitochondria, i.e., of oxygen-consuming sites within these spheroids.     

Modelling cacao pod growth: implications for disease control

Cacao trees are affected by diseases that attack either their vegetative parts, their fruits or both. In cacao pod diseases, several factors are involved in disease susceptibility, such as the fruiting cycle, fruit size, age, position on the tree and cacao genotype. To gain a clearer understanding of how these characteristics influence cacao pod diseases, four models describing pod growth in several cacao genotypes were evaluated. Three models used to estimate pod volume or surface area were also compared. Observed pod growth was of a sigmoid form and fitted best to the Richards model, well to the Logistic and Beta growth models, and least to the Gompertz model. Pod volume and probably pod surface area were best estimated using a prolate spheroid model. Pod growth models can help improve pod disease management and thereby cacao production. They can help to predict yield, as well as provide information for the timing and frequency of control operations. Information on pod size, surface area and susceptibility will help to improve dose transfer and spray deposit studies intended to optimise control efficiency.