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.     

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.     

Mathematical modelling of the Warburg effect in tumour cords

The model proposed here links together two approaches to describe tumours: a continuous medium to describe the movement and the mechanical properties of the tissue, and a population dynamics approach to represent internal genetic inhomogeneity and instability of the tumour. In this way one can build models which cover several stages of tumour progression. In this paper we focus on describing transition from aerobic to purely glycolytic metabolism (the Warburg effect) in tumour cords. From the mathematical point of view this model leads to a free boundary problem where domains in contact are characterized by different sets of equations. Accurate stitching of the solution was possible with a modified ghost fluid method. Growth and death of the cells and uptake of the nutrients are related through ATP production and energy costs of the cellular processes. In the framework of the bi-population model this allowed to keep the number of model parameters relatively small.     

Mesenchymal stem cells modified to express lentivirus TNF‐α Tumstatin45–132 inhibit the growth of prostate cancer

Mesenchymal stem cells (MSCs) are a potential novel delivery system for cell‐based gene therapies. Although tumour necrosis factor (TNF)‐α has been shown to have antitumour activity, its use in therapy is limited by its systemic toxicity. For the present study, we designed lentivirus‐mediated signal peptide TNF‐α‐Tumstatin_45–132‐expressing mesenchymal stem cells (SPTT‐MSCs) as a novel anti‐cancer approach. We evaluated the effects of this approach on human prostate cancer cells (PC3 and LNCaP) by co‐culturing them with either SPTT‐MSCs or supernatants from their culture medium in vitro. The antitumour effects and possible mechanisms of action of SPTT‐MSCs were then determined in PC3 cells in vivo. The results showed that efficient TNF‐α‐Tumstatin_45–132‐expressing MSCs had been established, and demonstrated that SPTT‐MSCs inhibited the proliferation of and induced apoptosis in prostate cancer cells and xenograft tumours. As would be expected, given the properties of the individual proteins, the TNF‐α‐Tumstatin_45–132 fusion exerted potent cytotoxic effects on human prostate cancer cells and tumours via the death receptor‐dependent apoptotic pathway and via antiangiogenic effects. Our findings suggest that SPTT‐MSCs have significant activity against prostate cancer cells, and that they may represent a promising new therapy for prostate cancer.     

Paradoxes of tumour complexity: somatic selection,vulnerability by design,or infectious aetiology?

The aetiology of cancer involves intricate cellular and molecular mechanisms that apparently emerge on the short timescale of a single lifetime. Some of these traits are remarkable not only for their complexity, but also because it is hard to conceive selection pressures that would favour their evolution within the local competitive microenvironment of the tumour. Examples include ‘niche construction’ (re‐programming of tumour‐specific target sites) to create permissive conditions for distant metastases; long‐range feedback loops of tumour growth; and remarkably ‘plastic’ phenotypes (e.g. density‐dependent dispersal) associated with metastatic cancer. These traits, which we term ‘paradoxical tumour traits’, facilitate the long‐range spread or long‐term persistence of the tumours, but offer no apparent benefit, and might even incur costs in the competition of clones within the tumour. We discuss three possible scenarios for the origin of these characters: somatic selection driven by specific selection regimes; non‐adaptive emergence due to inherent vulnerabilities in the organism; and manipulation by putative transmissible agents that contribute to and benefit from these traits. Our work highlights a lack of understanding of some aspects of tumour development, and offers alternative hypotheses that might guide further research.     

Growth and Vascular Structure of Human Melanoma Xenografts

Abstract The growth and the vascular structure of five human melanomas grown in athymic nude mice were studied. Four growth parameters (tumour volume doubling time, fraction of cells in S-phase, growth fraction, cell-loss factor) were analysed against each of four vascular parameters (length of vessels with diameters in the range 5–15 μm, total vessel length, total vessel surface, total vessel volume-all per unit of histologically intact tumour volume). Statistically significant linear correlations between the parameters were found for any of the combinations. However, there was a consistent trend in the data: the tumour volume doubling time and the cell-loss factor tended to decrease while the fraction of cells in S-phase and the growth fraction tended to increase with increasing vascular density, whichever vascular parameter was considered. This finding indicates that the vascular density is among the factors which are decisive for the growth rate of tumours. However, the present work does not exclude the possibility that intrinsic properties of the tumour cells may also be important.     

Growth and vascular structure of human melanoma xenografts

The growth and the vascular structure of five human melanomas grown in athymic nude mice were studied. Four growth parameters (tumour volume doubling time, fraction of cells in S-phase, growth fraction, cell-loss factor) were analysed against each of four vascular parameters (length of vessels with diameters in the range 5-15 micron, total vessel length, total vessel surface, total vessel volume--all per unit of histologically intact tumour volume). Statistically significant linear correlations between the parameters were found for any of the combinations. However, there was a consistent trend in the data: the tumour volume doubling time and the cell-loss factor tended to decrease while the fraction of cells in S-phase and the growth fraction tended to increase with increasing vascular density, whichever vascular parameter was considered. This finding indicates that the vascular density is among the factors which are decisive for the growth rate of tumours. However, the present work does not exclude the possibility that intrinsic properties of the tumour cells may also be important.     

Coupled mathematical model of tumorigenesis and angiogenesis in vascular tumours

Objectives: Mathematical models are useful for studying vascular and avascular tumours, because these allow for more logical experimental design and provide valuable insights into the underlying mechanisms of their growth and development. The processes of avascular tumour growth and the development of capillary networks through tumour‐induced angiogenesis have already been extensively investigated, albeit separately. Despite the clinical significance of vascular tumours, few studies have combined these approaches to develop a single comprehensive growth and development model. Materials and methods: We develop a continuum‐based mathematical model of vascular tumour growth. In the model, angiogenesis is initiated through the release of angiogenic growth factors (AGFs) by cells in the hypoxic regions of the tumour. The nutrient concentration within the tumour reflects the influence of capillary growth and invasion induced by AGF. Results and conclusions: Parametric and sensitivity studies were performed to evaluate the influence of different model parameters on tumour growth and to identify the parameters with the most influence, which include the rates of proliferation, apoptosis and necrosis, as well as the diffusion of sprout tips and the size of the region affected by angiogenesis. An optimization was performed for values of the model parameters that resulted in the best agreement with published experimental data. The resulting model solution matched the experimental data with a high degree of correlation (r = 0.85).     

The multi-site tumour transplantation model for human endometrial carcinoma: a statistical evaluation

We studied the effect of multi-site tumour transplantation on tumour growth by implanting varying numbers of EnCa 101 human endometrial tumours in athymic mice. One treatment group received a single tumour per mouse, another group received two tumours per mouse and a third group received four tumours per mouse. Tumour growth was sustained in all animals by implantation of oestradiol-17 beta pellets. We observed positive correlation between tumours within the same mouse, which implies that individual tumours are not statistically independent. The correlation is sufficiently large that failure to account for it in statistical design and analysis could result in studies with insufficient power and in spurious assertions of significance. Regression modelling of tumour growth curves showed that mean tumour volume per animal is not affected by the number of tumours growing on the animal; that is, the data are consistent with the null hypothesis that mean tumour volume is the same regardless of the number of tumours present. Our results therefore suggest that the use of multiple tumours per animal can increase the precision of experiments without loss of validity and at relatively little cost. However, correct and efficient analysis of the data so obtained requires more sophisticated techniques than those--such as fixed-effects analysis of variance and the two sample t-test--that assume independence of tumours.     

CYTOKINETICS OF TUMOUR AND ENDOTHELIAL CELLS AND VASCULARIZATION OF LUNG METASTASES IN C3H/HE MICE

A model of lung metastases was developed using intravenous injection of tumour cell aggregates of spontaneous C3H/He mammary tumours in syngeneic mice. the growth rate of lung tumours decreased with increasing tumour volume, with mean host survival of 46 days. the cytokinetics of individual tumours ranging between 0.004 and 4.2 mm³ in volume were studied. the labelling index (LI) ranged between 12 and 17%, the DNA synthesis time (T_s) being 9–10 hr. the growth fraction (GF) ranged between 26 and 38%. the cell cycle time (T_c) was found to be 18–19 hr. the LI and the GF decreased with increasing tumour volume doubling time (T_d). No correlation was found between the tumour volume and T_c. the LI of endothelial cells within these tumours, ranging between 0.004 and 4.2 mm³ in volume was 14–15% and endothelial cell proliferation was not affected by tumour growth. Vascular parameters were also determined for these tumours as a function of tumour volume. Vascular volume increased with increasing tumour size while the percentage of capillary vessels decreased. the cellular volume to capillary volume ratio increased with increasing tumour volume. Necrosis was observed in 0.27 mm³ tumours and increased with increasing tumour size. The results from these studies suggested that the age-dependent decrease in proliferative activity of tumour cells growing in the lung is related to change in effective vascularity.     

Single‐cell functional analysis of parathyroid adenomas reveals distinct classes of calcium sensing behaviour in primary hyperparathyroidism

Primary hyperparathyroidism (PHPT) is a common endocrine neoplastic disorder caused by a failure of calcium sensing secondary to tumour development in one or more of the parathyroid glands. Parathyroid adenomas are comprised of distinct cellular subpopulations of variable clonal status that exhibit differing degrees of calcium responsiveness. To gain a clearer understanding of the relationship among cellular identity, tumour composition and clinical biochemistry in PHPT, we developed a novel single cell platform for quantitative evaluation of calcium sensing behaviour in freshly resected human parathyroid tumour cells. Live‐cell intracellular calcium flux was visualized through Fluo‐4‐AM epifluorescence, followed by in situ immunofluorescence detection of the calcium sensing receptor (CASR), a central component in the extracellular calcium signalling pathway. The reactivity of individual parathyroid tumour cells to extracellular calcium stimulus was highly variable, with discrete kinetic response patterns observed both between and among parathyroid tumour samples. CASR abundance was not an obligate determinant of calcium responsiveness. Calcium EC50 values from a series of parathyroid adenomas revealed that the tumours segregated into two distinct categories. One group manifested a mean EC50 of 2.40 mM (95% CI: 2.37–2.41), closely aligned to the established normal range. The second group was less responsive to calcium stimulus, with a mean EC50 of 3.61 mM (95% CI: 3.45–3.95). This binary distribution indicates the existence of a previously unappreciated biochemical sub‐classification of PHPT tumours, possibly reflecting distinct etiological mechanisms. Recognition of quantitative differences in calcium sensing could have important implications for the clinical management of PHPT.     

Absent in melanoma 2 enhances anti‐tumour effects of CAIX promotor controlled conditionally replicative adenovirus in renal cancer

Conditionally replicative adenoviruses (CRAds) were promising approach for solid tumour treatment, but its oncolytic efficiency and toxicity are still not satisfactory for further clinical application. Here, we developed the CAIX promotor (CAIX^promotor)‐controlled CRAd armed with a tumour suppressor absent in melanoma 2 (AIM2) to enhance its oncolytic potency. The CAIX^promotor‐AIM2 adenoviruses (Ad‐CAIX^promotor‐AIM2) could efficiently express E1A and AIM2 in renal cancer cells. Compared with Ad‐CAIX^promotor, Ad‐CAIX^promotor‐AIM2 significantly inhibited cell proliferation and enhanced cell apoptosis and cell killing, thus resulting in the oncolytic efficiency in 786‐O cells or OSRC‐2 cells. To explore the therapeutic effect, various Ads were intratumourally injected into OSRC‐2‐xenograft mice. The tumour growth was remarkably inhibited in Ad‐CAIX^promotor‐AIM2‐treated group as demonstrated by reduced tumour volume and weight with a low toxicity. The inflammasome inhibitor YVAD‐CMK resulted in the reduction of anti‐tumour activity by Ad‐CAIX^promotor‐AIM2 in vitro or in vivo, suggesting that inflammasome activation response was required for the enhanced therapeutic efficiency. Furthermore, lung metastasis of renal cancer mice was also suppressed by Ad‐CAIX^promotor‐AIM2 treatment accompanied by the decreased tumour fossil in lung tissues. These results indicated that the tumour‐specific Ad‐CAIX^promotor‐AIM2 could be applied for human renal cancer therapy. The therapeutic strategy of AIM2‐based CRAds could be a potential and promising approach for the therapy of primary solid or metastasis tumours.     

Safe and effective treatment of spontaneous neoplasms with interleukin 12 electro‐chemo‐gene therapy

Electroporation improves the anti‐tumour efficacy of chemotherapeutic and gene therapies. Combining electroporation‐mediated chemotherapeutics with interleukin 12 (IL‐12) plasmid DNA produces a strong yet safe anti‐tumour effect for treating primary and refractory tumours. A previously published report demonstrated the efficacy of a single cycle of IL‐12 plasmid DNA and bleomycin in canines, and, similarly, this study further demonstrates the safety and efficacy of repeated cycles of chemotherapy plus IL‐12 gene therapy for long‐term management of aggressive tumours. Thirteen canine patients were enrolled in this study and received multiple cycles of electro‐chemo‐gene therapy (ECGT) with IL‐12 pDNA and either bleomycin or gemcitabine. ECGT treatments are very effective for inducing tumour regression via an antitumour immune response in all tested histotypes except for sarcomas, and these treatments can quickly eradicate or debulk large squamous cell carcinomas. The versatility of ECGT allows for response‐based modifications which can overcome treatment resistance for affecting refractory lesions. Importantly, not a single severe adverse event was noted even in animals receiving the highest doses of chemotherapeutics and IL12 pDNA over multiple treatment cycles. This report highlights the safety, efficacy and versatility of this treatment strategy. The data reveal the importance of inducing a strong anti‐tumour response for successfully affecting not only the treated tumours, but also non‐treated metastatic tumours. ECGT with IL12 pDNA plus chemotherapy is an effective strategy for treating multiple types of spontaneous cancers including large, refractory and multiple tumour burdens.     

Influence of stem-cell cycle time on accelerated re-population during radiotherapy in head and neck cancer

Objectives

Tumour re‐population during radiotherapy was identified as an important reason for treatment failure in head and neck cancers. The process of re‐population is suggested to be caused by various mechanisms, one of the most plausible one being accelerated division of stem‐cells (i.e. drastic shortening of cell cycle duration). However, the literature lacks quantitative data regarding the length of tumour stem‐cell cycle time during irradiation.

Materials and methods

The presented work suggests that if accelerated stem‐cell division is indeed a key mechanism behind tumour re‐population, the stem‐cell cycle time can drop below 10 h during radiotherapy. To illustrate the possible implications, the mechanism of accelerated division was implemented into a Monte Carlo model of tumour growth and response to radiotherapy. Tumour response to radiotherapy was simulated with different stem‐cell cycle times (between 2 and 10 h) after the initiation of radiotherapy.

Results

It was found that very short stem‐cell cycle times lead to tumour re‐population during treatment, which cannot be overcome by radiation‐induced cell kill. Increasing the number of radiation dose fractions per week might be effective, but only for longer cell cycle times.

Conclusion

It is of crucial importance to quantitatively assess the mechanisms responsible for tumour re‐population, given that conventional treatment regimens are not efficient in delivering lethal doses to advanced head and neck tumours.     

Invasion and metastasis.

Malignant tumours cause sickness and death largely because they invade and metastasize. Such spread is made possible by many cellular properties, including the ability of neoplastic cells to move and to release degradative enzymes. These properties enable tumour cells to break free of the primary tumour, penetrate blood or lymphatic vessels and, after being transported to distant sites, pass out of the vessels to establish new tumours. Not all cells in a tumour, however, are able to metastasize, so the process tends to select for greater malignancy in the secondary tumour. The heterogeneity of tumours probably accounts for the difficulty of providing effective treatment, in that the various subpopulations of cells arising from each tumour vary in their responses to chemotherapeutic agents. We do not yet understand the process sufficiently to treat cancer patients by interfering selectively with the metastatic mechanisms.     

PV1 down‐regulation via shRNA inhibits the growth of pancreatic adenocarcinoma xenografts

PV1 is an endothelial‐specific protein with structural roles in the formation of diaphragms in endothelial cells of normal vessels. PV1 is also highly expressed on endothelial cells of many solid tumours. On the basis of in vitro data, PV1 is thought to actively participate in angiogenesis. To test whether or not PV1 has a function in tumour angiogenesis and in tumour growth in vivo, we have treated pancreatic tumour‐bearing mice by single‐dose intratumoural delivery of lentiviruses encoding for two different shRNAs targeting murine PV1. We find that PV1 down‐regulation by shRNAs inhibits the growth of established tumours derived from two different human pancreatic adenocarcinoma cell lines (AsPC‐1 and BxPC‐3). The effect observed is because of down‐regulation of PV1 in the tumour endothelial cells of host origin, PV1 being specifically expressed in tumour vascular endothelial cells and not in cancer or other stromal cells. There are no differences in vascular density of tumours treated or not with PV1 shRNA, and gain and loss of function of PV1 in endothelial cells does not modify either their proliferation or migration, suggesting that tumour angiogenesis is not impaired. Together, our data argue that down‐regulation of PV1 in tumour endothelial cells results in the inhibition of tumour growth via a mechanism different from inhibiting angiogenesis.     

Computational Modelling of Metastasis Development in Renal Cell Carcinoma

The biology of the metastatic colonization process remains a poorly understood phenomenon. To improve our knowledge of its dynamics, we conducted a modelling study based on multi-modal data from an orthotopic murine experimental system of metastatic renal cell carcinoma. The standard theory of metastatic colonization usually assumes that secondary tumours, once established at a distant site, grow independently from each other and from the primary tumour. Using a mathematical model that translates this assumption into equations, we challenged this theory against our data that included: 1) dynamics of primary tumour cells in the kidney and metastatic cells in the lungs, retrieved by green fluorescent protein tracking, and 2) magnetic resonance images (MRI) informing on the number and size of macroscopic lesions. Critically, when calibrated on the growth of the primary tumour and total metastatic burden, the predicted theoretical size distributions were not in agreement with the MRI observations. Moreover, tumour expansion only based on proliferation was not able to explain the volume increase of the metastatic lesions. These findings strongly suggested rejection of the standard theory, demonstrating that the time development of the size distribution of metastases could not be explained by independent growth of metastatic foci. This led us to investigate the effect of spatial interactions between merging metastatic tumours on the dynamics of the global metastatic burden. We derived a mathematical model of spatial tumour growth, confronted it with experimental data of single metastatic tumour growth, and used it to provide insights on the dynamics of multiple tumours growing in close vicinity. Together, our results have implications for theories of the metastatic process and suggest that global dynamics of metastasis development is dependent on spatial interactions between metastatic lesions.     

Experimental chemotherapy and concepts related to the cell cycle

Scheduling of chemotherapy is limited by damage to normal tissues, and tolerated schedules are dependent on normal tissue recovery. Most anticancer drugs are more toxic to proliferating cells and the fall and recovery of granulocyte counts after chemotherapy may be explained by the effect of drugs on rapidly proliferating precursor cells in the bone marrow. It is argued that serious toxicity due to myelosuppression most often occurs because of damage to proliferating precursors that may be recognized in bone marrow rather than to stem cells. In contrast, therapy that is aimed at producing cure or long-term remission of tumours must be directed at killing tumour stem cells. The evidence that tumours contain a limited population of cells which can repopulate the tumour after treatment (and are therefore tumour stem cells) is reviewed critically. While there is quite strong evidence for a limited population of target cells, evidence from studies on metastases suggests that the tumour cells which may express this stem cell property may change with time. The stem cell concept has major implications for predictive assays. Although colony-forming assays appear to have a sound biological background for predicting tumour response, technical problems prevent them from being used routinely in patient management. Cells in tumours are known to be heterogeneous and at least three types of heterogeneity may influence tumour response to drug treatment: the development of subclones with differing properties including drug resistance; variation in cellular properties due to differentiation during clonal expansion; and variation in properties due to nutritional status and micro-anatomy. Heterogeneity in drug distribution within solid tumours may occur because of limited drug penetration from blood vessels, and nutrient-deprived cells in solid tumours may be expected to escape the toxicity of some anticancer drugs as well as being resistant to radiation because of hypoxia. This may occur both because nutrient-deprived cells have a low rate of cell proliferation, and also because of poor drug penetration to them. There is a need for improved understanding of the mechanisms that lead to cell death in tumours. If these mechanisms were understood, it might be possible to simulate them by therapeutic manoeuvres. Recent research from our laboratory suggests that the combination of low extracellular pH and hypoxia may be very toxic to cells in nutrient-deprived regions. Drugs which limit the cell's ability to survive in regions of acid pH may provide strategy for therapy of nutrient-deprived cells.     

Assessment of vascularity in histological sections: effects of methodology and value as an index of angiogenesis in breast tumours

The aims of this study were to (a) determine how the quantification of blood vessels in histological sections (vascularity) is affected by the methodology used and (b) assess the value of vascularity as an index of angiogenesis by comparing tumour and normal breast tissue. Archival specimens of breast, lung and oral carcinoma, oral dysplasia and normal breast tissue were used to test the effects of the following experimental variables on vascularity: pretreatment of the sections (enzymatic digestion, heating), endothelial markers (von Willebrand factor and CD31 antibodies), method of quantification (highest microvascular density, average microvascular density and microvascular volume) and interobserver variations. All the variables examined significantly affected the estimated vascularity; this depended on the type of tissue and method used. The pretreatment of the sections before staining was the most important variable, altering the vascularity ranking of the tumours. Vascularity in breast tumours was similar to that of the normal breast intralobular stroma, suggesting that an area of high microvascular density in the tumour does not necessarily represent tumour-induced angiogenesis. Contradictory results have been published regarding the value of vascularity as a tumour prognostic factor. Our results suggest that statistically significant differences in vascularity values are most likely to arise from failure to optimize the staining protocol and from the method used to assess vascularity. © 1998 Chapman & Hall