A mathematical model of glioma growth: the effect of extent of surgical resection

Abstract. We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.     

Characteristics of tumour vessels in cytological squash smears of astrocytic tumours

S. Sato, Y. Sato, K. Marutsuka, H. Takeshima and Y. Asada Characteristics of tumour vessels in cytological squash smears of astrocytic tumours Objective: Smear preparations are useful tools from which to diagnose brain tumours intraoperatively. Although vascular proliferation is histologically a key feature of high‐grade astrocytoma, the characteristics of tumour vessels in smear preparations have not been determined. Methods: We examined the density and morphological parameters (area, width, nuclear layer and branches of vessel wall) of tumour vessels in squash smears of 43 primary astrocytomas (grade II diffuse astrocytomas, n = 9; grade III anaplastic astrocytomas, n = 13; grade IV glioblastomas, n = 21) and normal brain tissues (n = 11). Results: Vessel density and all morphological parameters were significantly higher in grade IV than in the other grades of tumours and in normal brain tissue. Vessel area, width and nuclear layer were greater in grade III than in normal brain tissue. The sensitivity and specificity of these vessel parameters for astrocytomas were 75–100% and 82–100%, respectively. Conclusions: Tumour vessel evaluations from squash smears provide useful information for the intraoperative diagnosis and grading of astrocytic tumours.     

Prognostic significance of DNA ploidy and proliferation rate in human astrocytic gliomas

DNA ploidy and the proliferative potential in 75 gliomas were investigated using bromodeoxyuridine labelling index (BrdUrd LI), S-phase fraction (SPF) and argyrophilic nucleolar organizer regions (AgNOR) technique. There were 53 highly malignant (AIII-AIV), and 22 low-grade (AI-AII) gliomas. One fragment of the tumour was fixed in Carnoy's solution for AgNOR test, while the other fragments were used for flow cytometric determination of the labelling index, SPF and DNA ploidy. For the BrdUrdLI, tumour samples from each patient were incubated in vitro for one hour at 37 degrees C with BrdUrd using the high pressure oxygen method. The tumours showed variability in the BrdUrdLI values, SPF and AgNOR counts/cell nucleus. The same percentage of DNA aneuploidy (55%) was found in high-grade as well as in low-grade gliomas. Univariate analysis showed that patients with grade I & II gliomas had significantly higher 3-year survival rate (p = 0.0193) than those with grade III and grade IV gliomas. Also patients with lower proliferation rate of tumours (BrdUrdLI < or =2.3% and AgNOR counts < or =2.6%/cell) had higher 3-year survival rate (p<0.03), which can be helpful in prognosis. Tumour ploidy or SPF had no influence on patients' survival (p = 0.7908). Cox multivariate analysis showed that only patients' age > 45 years and high tumour grade (III and IV) were significant unfavourable prognostic factors in terms of patients' survival.     

Apoptosis and cell proliferation correlated with tumour grade in peritoneal fluids of patients with serous ovarian cancer

A. Kalogeraki, I. Karvela‐Kalogeraki, P. E. Petraki, I. Zois, D. Tamiolakis and E. N. Stathopoulos
Apoptosis and cell proliferation correlated with tumour grade in peritoneal fluids of patients with serous ovarian cancer Objective: Apoptosis and cell proliferation in peritoneal fluids of patients with ovarian serous adenocarcinoma have not been well described in cytology. To investigate the contribution of cell death to the growth of this tumour we analysed both apoptosis and cell proliferation in peritoneal fluids of patients with ovarian serous adenocarcinoma. Methods: We studied 40 tumours from 40 patients with ovarian serous adenocarcinoma. Twelve tumours were high grade, 13 were moderately differentiated and 15 were poorly differentiated. The detection of DNA fragments in situ using the terminal deoxyribonucleotidy transferase (TDT)‐mediated dUTP‐digoxigenin nick‐end labelling (TUNEL) assay was applied to investigate active cell death (apoptosis), and the MIB‐1 antigen was used to investigate cell proliferation. Results: The TUNEL indices were 0.29 ± 0.05, 0.79 ± 0.10 and 2.1 ± 0.90 in Grade I, Grade II and Grade III ovary carcinomas, respectively. The MIB‐1 antigen labelling indices were 6.5 ± 0.09, 12.9 ± 3 and 25.8 ± 6.2, respectively, in the same order of tumour differentiation. The differences in both TUNEL and MIB‐1 labelling indices were statistically significant between Grade I, Grade II and Grade III carcinomas and there was a positive correlation between the two indices (P < 0.001). Conclusions: Apoptosis and cell proliferation increased as the grade of tumour increased in ovarian serous adenocarcinoma, suggesting a rapid turnover of the tumour cells in tumours of higher grade, and may play an important role in the growth and the extension of such cancer cells in the peritoneal cavity.     

CELL PROLIFERATION OF CARCINOMA IN BILHARZIAL BLADDER: AN AUTORADIOGRAPHIC STUDY

The rate of cell production in thirty-five cases of carcinoma in Bilharzial bladder was evaluated from the labelling index after in vitro incubation with [³H]TdR. Squamous cell carcinoma was the most frequent histological type in this series and had a median LI of 8.0% which corresponds to a potential doubling time of 5.9 days. In squamous cell tumours the LI increased with the histological grade. Transitional cell tumours had a somewhat greater LI. In all histological types the LI was significantly greater in the deep infiltrating parts of the tumour than in the superficial parts. The discrepancy between the estimated potential doubling time and the growth rate normally attributed to such tumours suggests the existence of an extensive cell loss factor. Areas of focal or diffuse mucosal hyperplasia were associated with increased LI.     

The labelled mitosis curve for a population consisting of fast and slowly cycling cells

In studies of tumour growth, and particularly of tumour treatment with phase-specific chemotherapeutic agents, the fraction labelled mitosis technique is frequently used to estimate the kinetic properties of the cell population making up the tumour. We show here that the FLM technique is in principle very insensitive to the behaviour of slowly cycling cells, even if these constitute a large proportion of the total cell population. Furthermore, since the rate of DNA synthesis is frequently lower in slowly growing cells than in those growing rapidly, there is a higher probability of labelling error associated with the former cells. In view of these theoretical and experimental considerations, it is suggested that considerable caution be used when applying the FLM technique to heterogeneous cell populations such as those of solid tumours.     

Do poor-prognosis breast tumours express membrane cofactor proteins (CD46)?

CD46 or membrane cofactor protein (MCP) is a complement regulatory protein that has been identified on all nucleated cells and which protects them from attack by autologous complement. Breast carcinomas are reported to consistently express CD46.Aim and methods: Our previous immunohistochemical study showed that in breast carcinomas, loss of CD59 and CD55 correlated with poor survival. This study aimed to investigate the prognostic significance of CD46 on breast tumours using a rabbit polyclonal anti-CD46 antibody with a standard immunohistochemistry method. A total of 510 breast tissues from patients with primary operable breast cancer diagnosed between 1987 and 1992 had previously been included in tissue microarrays. They included patients 70 years of age or less (mean = 54 years) with a long-term follow-up (median = 82 months).Results: Immunohistochemical study revealed that 507/510 (99.4%) of breast tumours expressed CD46. Strong immunoreactivity was exhibited by 136/510 (27%) tumours, while moderate and weak staining was observed in 43% and 29% of tumours, respectively. Intensity of CD46 expression was significantly associated with tumour grade (p<0.05), histological type of tumour (p<0.001) and tumour recurrence (p<0.05). There was no correlation with lymph node stage or the presence of vascular invasion, nor with patient age or menopausal status. Interestingly, as most tumours expressed CD46, it would appear that poor-prognosis tumours that lose CD55 and CD59 still express CD46.Conclusion: Breast tumours express high levels of CD46 that correlates with tumour grade and recurrence. It is therefore likely that loss of CD55 and CD59 could be compensated by expression of CD46. However, loss of CD55 and CD59, even for tumours that still express CD46, is still associated with a poor prognosis. This may suggest that CD46 alone can protect from complement lysis but that loss of CD55 and CD59 are associated with other roles in immune regulation.     

Paraoxonase 192 gene polymorphism and serum paraoxonase activity in high grade gliomas and meningiomas

The purpose of this study was to demonstrate the relationship between serum PON1 activity and PON 192 polymorphism in brain tumours. The distribution of PON 192 polymorphism in 42 high grade gliomas and 42 meningiomas were determined by polymerase chain reaction--based restriction fragment length polymorphism analysis and compared with 50 healthy control subjects. Serum paraoxonase1 activities were also measured and compared in the same population. We found that in both tumour groups serum PON1 activity was significantly lower than the control group (p < 0.001), but did not differ between meningiomas and high grade gliomas. There was no significant difference either in distribution of the AA, AB and BB genotypes or in the allelic frequencies, between the patient group and control subjects (p > 0.05). Our results suggest that serum PON1 as a part of the lipid peroxidation scavenging systems might be involved in the tumourigenesis of brain tumours.     

A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection,design and delivery

Abstract. Motivated by the recent development of highly specific agents for brain tumours, we develop a mathematical model of the spatio-temporal dynamics of a brain tumour that receives an infusion of a highly specific cytotoxic agent (e.g. IL-4-PE, a cytotoxin comprised of IL-4 and a mutated form of Pseudomonas exotoxin). We derive an approximate but accurate mathematical formula for the tumour cure probability in terms of the tumour characteristics (size at time of detection, proliferation rate, diffusion coefficient), drug design (killing rate, loss rate and convection constants for tumour and tissue), and drug delivery (infusion rate, infusion duration). Our results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required. The most important levers to improve tumour cure appear to be earlier detection, higher infusion rate, lower drug clearance rate and better convection into tumour, but not tissue. In contrast, the tumour cure probability is less sensitive to a longer infusion duration and enhancements in drug potency and drug specificity.     

Ki-67 labelling index in human brain tumours

The proliferative potential in 157 brain tumours was investigated using Ki-67 labelling index (Ki-67LI). There were 46 patients with low grade gliomas (Al & All), 82 with high grade gliomas (AIII & AIV) and 29 with metastatic tumours. Tumour fragments used for assessment of Ki-67LI were fixed in formalin. Ki-67 antigen was visualised on paraffin sections using DAKO Rabbit Anti-Human Ki-67 antigen. The Ki-67LI was calculated as the percentage of Ki-67 labelled cells. The tumours showed variability in the Ki-67LI values. Significantly higher mean Ki-67LI was found for highly malignant (AIII & AIV) than for low grade gliomas (Al & All). For metastatic tumours, the mean values of Ki-67LI were significantly higher than for gliomas. Moreover, Ki-67LI of metastatic tumours were significantly higher than for high grade gliomas.     

Estimating the selective advantage of mutant p53 tumour cells to repeated rounds of hypoxia

The tumour suppressor gene, p53, plays an important role in tumour development. Under low levels of oxygen (hypoxia), cells expressing wild-type p53 undergo programmed cell death (apoptosis), whereas cells expressing mutations in the p53 gene may survive and express angiogenic growth factors that stimulate tumour vascularization. Given that cells expressing mutations in the p53 gene have been observed in many forms of human tumour, it is important to understand how both wild-type and mutant cells react to hypoxic conditions. In this paper a mathematical model is presented to investigate the effects of alternating periods of hypoxia and normoxia (normal oxygen levels) on a population of wild-type and mutant p53 tumour cells. The model consists of three coupled ordinary differential equations that describe the densities of the two cell types and the oxygen concentration and, as such, may describe the growth of avascular tumours in vitro and/or in vivo. Numerical and analytical techniques are used to determine how changes in the system parameters influence the time at which mutant cells become dominant within the population. A feedback mechanism, which switches off the oxygen supply when the total cell density exceeds a threshold value, is introduced into the model to investigate the impact that vessel collapse (and the associated hypoxia) has on the time at which the mutant cells become dominant within vascular tumours growing in vivo. Using the model we can predict the time it takes for a subpopulation of mutant p53 tumour cells to become the dominant population within either an avascular tumour or a localized region of a vascular tumour. Based on independent experimental results, our model suggests that the mutant population becomes dominant more quickly in vivo than in vitro (12 days vs 17 days).     

Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion

Abstract. Objectives: Tumour progression has been described as a sequence of traits or phenotypes that cells have to acquire if the neoplasm is to become an invasive and malignant cancer. Although genetic mutations that lead to these phenotypes are random, the process by which some of these mutations become successful and cells spread is influenced by tumour microenvironment and the presence of other cell phenotypes. It is thus likely that some phenotypes that are essential in tumour progression will emerge in the tumour population only with prior presence of other different phenotypes. Materials and methods: In this study, we use evolutionary game theory to analyse the interactions between three different tumour cell phenotypes defined by autonomous growth, anaerobic glycolysis, and cancer cell invasion. The model allows us to understand certain specific aspects of glioma progression such as the emergence of diffuse tumour cell invasion in low‐grade tumours. Results: We have found that the invasive phenotype is more likely to evolve after appearance of the glycolytic phenotype which would explain the ubiquitous presence of invasive growth in malignant tumours. Conclusions: The result suggests that therapies, which increase the fitness cost of switching to anaerobic glycolysis, might decrease probability of the emergence of more invasive phenotypes.     

Prostate‐specific membrane antigen expression in the vasculature of primary lung carcinomas associates with faster metastatic dissemination to the brain

Glioblastomas and brain metastases (BM) of solid tumours are the most common central nervous system neoplasms associated with very unfavourable prognosis. In this study, we report the association of prostate‐specific membrane antigen (PSMA) with various clinical parameters in a large cohort of primary and secondary brain tumours. A tissue microarray containing 371 cases of ascending grades of gliomas pertaining to astrocytic origin and samples of 52 cases of primary lung carcinomas with matching BM with follow‐up time accounting to 10.4 years was evaluated for PSMA expression using immunohistochemistry. In addition, PSMA expression was studied in BM arising from melanomas and breast carcinomas. Neovascular expression of PSMA was evident alongside with high expression in the proliferating microvasculature of glioblastomas when compared to the tumour cell expression. This result correlated with the results obtained from the in silico (cancer genome databases) analyses. In gliomas, only the vascular expression of PSMA associated with poor overall survival but not the tumour cell expression. In the matched primary lung cancers and their BM (n = 52), vascular PSMA expression in primary tumours associated with significantly accelerated metastatic dissemination to the brain with a tendency towards poor overall survival. Taken together, we report that the vascular expression of PSMA in the primary and secondary brain tumours globally associates with the malignant progression and poor outcome of the patients.     

A mathematical model of the treatment and survival of patients with high-grade brain tumours

More years of life per patient are lost as the result of primary brain tumours than any other form of cancer. The most aggressive of these is known as glioblastoma (GBM). The median survival time of patients with GBM is under 10 months and the outlook has hardly improved over the past 20 years. Generally, these tumours are remarkably resistant to radiotherapy and yet about 2-3% of all GBMs appear to be cured.The objectives of this study were to formulate a mathematical and phenomenological model of tumour growth in a population of patients with GBM to predict survival, and to use the model to extract biological information from clinical data.The model describes the growth of the tumour and the resulting damage to the normal brain using simple concepts borrowed from chemical reaction engineering. Death is assumed to result when the amount of surviving normal brain falls to a critical level. Radiotherapy is assumed to destroy tumour but not healthy brain. Simple rules are included to represent approximately the clinician's decisions about what type of treatment to offer each patient. A population of patients is constructed by assuming that key parameters can be sampled from statistical distributions. Following Monte Carlo simulation, the model can be fitted to data from clinical trials.The model reproduces clinical data extremely accurately. This suggests that the long-term survivors are not a separate sub-population but are the ‘lucky tail’ of a unimodal distribution. The estimated values of radiation sensitivity (represented as SF2, the survival fraction after 2 Gy) suggest the presence of severe hypoxia, which renders cells less sensitive to radiation. The model can predict the probable age distribution of tumours at presentation. The model shows the complicated effects of waiting times for treatment on the survival outcomes, and is used to predict the effects of escalation of radiotherapy dose.The model may aid the design of clinical trials using radiotherapy for patients with GBM, especially in helping to estimate the size of trial required. It is also designed in a generic form, and might be applicable to other tumour types.     

Impact of myo‐inositol trispyrophosphate (ITPP) on tumour oxygenation and response to irradiation in rodent tumour models

Tumour hypoxia is a well‐established factor of resistance in radiation therapy (RT). Myo‐inositol trispyrophosphate (ITPP) is an allosteric effector that reduces the oxygen‐binding affinity of haemoglobin and facilitates the release of oxygen by red blood cells. We investigated herein the oxygenation effect of ITPP in six tumour models and its radiosensitizing effect in two of these models. The evolution of tumour pO₂ upon ITPP administration was monitored on six models using 1.2 GHz Electron Paramagnetic Resonance (EPR) oximetry. The effect of ITPP on tumour perfusion was assessed by Hoechst staining and the oxygen consumption rate (OCR) in vitro was measured using 9.5 GHz EPR. The therapeutic effect of ITPP with and without RT was evaluated on rhabdomyosarcoma and 9L‐glioma rat models. ITPP enhanced tumour oxygenation in six models. The administration of 2 g/kg ITPP once daily for 2 days led to a tumour reoxygenation for at least 4 days. ITPP reduced the OCR in six cell lines but had no effect on tumour perfusion when tested on 9L‐gliomas. ITPP plus RT did not improve the outcome in rhabdomyosarcomas. In 9L‐gliomas, some of tumours receiving the combined treatment were cured while other tumours did not benefit from the treatment. ITPP increased oxygenation in six tumour models. A decrease in OCR could contribute to the decrease in tumour hypoxia. The association of RT with ITPP was beneficial for a few 9L‐gliomas but was absent in the rhabdomyosarcomas.     

DNA ploidy and pS2 protein expression in breast cancer

The DNA content of ductal breast carcinomas of varying histological grade was measured using static image cytometry and correlated with pS₂ expression in the tumour cells. Our study was performed on imprint of surgical biopsies of 60 women with ductal breast cancer. A statistically significant difference was observed between pS₂⁺ expression and grade of malignancy ( P <0.001). The percentage of euploid tumours significantly decreased from grade I to grade II to grade III ( P =0.01). The percentage of aneuploid tumours increased from pS₂⁺ to pS₂⁻ breast tumours ( P <0.001). These findings may be indicative of pS₂ and DNA ploidy alterations and tumour aggressiveness.     

DNA Ploidy,Bromodeoxyuridine labelling index,S-phase fraction and AgNOR counts in brain tumours

DNA ploidy and the proliferative potential in 88 brain tumours were investigated using the bromodeoxyuridine labelling index (BrdUrd LI), S-phase fraction (SPF) and an argyrophilic nucleolar organizer regions (AgNOR) technique. The study included 65 highly malignant (AIII–AIV), and 23 low-grade (AI–AII) gliomas. One fragment of the tumour was fixed in Carnoy's solution for AgNOR test, while the other fragments were used for flow cytometric determination of the labelling index, SPF and DNA ploidy. For the BrdUrdLl, tumour samples from each patient were incubated in vitro for one hour at 37°C with BrdUrd using a high pressure oxygen method. After fixation and staining, the percentages of BrdUrd-labelied cells (BrdUrdLI) and unlabelled S-phase cells (SPF) were evaluated. The tumours showed variability in the BrdUrdLI values, SPF and AgNOR counts/cell nucleus. However, grade dependent differences in the proliferating rate were only found to exist on the basis of BrdUrdLI and AgNOR counts. The same percentage of DNA aneuploidy (56 %) was found in high-grade as well as in low-grade gliomas. A linear – regression analysis showed a significant correlation between the results of three applied methods: BrdUrdLl, SPF and AgNOR counts.     

Lipids,Mitochondria and Cell Death: Implications in Neuro-oncology

Polyunsaturated fatty acids (PUFAs) are known to inhibit cell proliferation of many tumour types both in vitro and in vivo. Their capacity to interfere with cell proliferation has been linked to their induction of reactive oxygen species (ROS) production in tumour tissues leading to cell death through apoptosis. However, the exact mechanisms of action of PUFAs are far from clear, particularly in brain tumours. The loss of bound hexokinase from the mitochondrial voltage-dependent anion channel has been directly related to loss of protection from apoptosis, and PUFAs can induce this loss of bound hexokinase in tumour cells. Tumour cells overexpressing Akt activity, including gliomas, are sensitised to ROS damage by the Akt protein and may be good targets for chemotherapeutic agents, which produce ROS, such as PUFAs. Cardiolipin peroxidation may be an initial event in the release of cytochrome c from the mitochondria, and enriching cardiolipin with PUFA acyl chains may lead to increased peroxidation and therefore an increase in apoptosis. A better understanding of the metabolism of fatty acids and eicosanoids in primary brain tumours such as gliomas and their influence on energy balance will be fundamental to the possible targeting of mitochondria in tumour treatment.     

Cell proliferation of carcinoma in Bilharzial bladder: an autoradiographic study

The rate of cell production in thirty-five cases of carcinoma in Bilharzial bladder was evaluated from the labelling index after in vitro incubation with [3H]TdR. Squamous cell carcinoma was the most frequent histological type in this series and had a median LI of 8.0% which corresponds to a potential doubling time of 5.9 days. In squamous cell tumours the LI increased with the histological grade. Transitional cell tumours had a somewhat greater LI. In all histological types the LI was significantly greater in the deep infiltrating parts of the tumour than in the superficial parts. The discrepancy between the estimated potential doubling time and the growth rate normally attributed to such tumours suggests the existence of an extensive cell loss factor. Areas of focal or diffuse mucosal hyperplasia were associated with increased LI.     

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.