Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion

We propose a mathematical modelling system to investigate the dynamic process of tumour cell proliferation, death and tumour angiogenesis by fully coupling the vessel growth, tumour growth and blood perfusion. Tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the updated vasculature. The domains of intravascular, transcapillary and interstitial fluid flow were coupled in the model to provide a comprehensive solution of blood perfusion variables. An estimation of vessel collapse is made according to the wall shear stress criterion to provide feedback on vasculature remodelling. The simulation can show the process of tumour angiogenesis and the spatial distribution of tumour cells for periods of up to 24 days. It can show the major features of tumour and tumour microvasculature during the period such as the formation of a large necrotic core in the tumour centre with few functional vessels passing through, and a well circulated tumour periphery regions in which the microvascular density is high and associated with more aggressive proliferating cells of the growing tumour which are all consistent with physiological observations. The study also demonstrated that the simulation results are not dependent on the initial tumour and networks, which further confirms the application of the coupled model feedback mechanisms. The model enables us to examine the interactions between angiogenesis and tumour growth, and to study the dynamic response of a solid tumour to the changes in the microenvironment. This simulation framework can be a foundation for further applications such as drug delivery and anti-angiogenic therapies.     

Enhanced lymphocyte-mediated killing of tumour cells after tumour irradiation in vivo.

The effect of local X-irradiation of a syngeneic carcinoma of fibrosarcoma growing in the leg of W/Fu rats on the ability of host spleen lymphocytes to kill syngeneic and allogeneic tumour cells in vitro was examined. Lymphocytotoxicity was found to be enhanced one day after local X-irradiation (4000 R) when compared with unirradiated tumour-bearing rats (p = 0.05 to 0.01). This enhancing effect of local irradiation was not observed when the lymphocytes were tested 1 week or later after X-irradiation, nor when normal legs of non-tumour bearing rats were irradiated. Mechanisms which might possibly explain these results are a reduction in release of tumour-specific antigen which can act as an inhibitor of cell-mediated cytotoxicity, or depletion of suppressor cells in the lymphocyte population. These findings may be relavant to clinical studies of cellular immunity in patients undergoing radiotherapy of malignant tumours.     

Lectin-induced apoptosis of tumour cells

The mechanisms of cytotoxic activity of Griffonia simplicifolia1-B₄ (GS1B₄) and wheat germ agglutinin (WGA) lectins againstvarious murine tumour cell lines were studied. Tumour cellsthat lack lectin-binding carbohydrates were resistant to lysisby these lectins. However, YAC-1 cells that expressed GS1B⁴lectin-binding sites showed low sensitivity to lysis. To furtheranalyse the relative importance of cell surface carbohydratesin lectin cytotoxicity, BL6–8 melanoma cells, which donot express the     

Mathematical modelling of tumour acidity

Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as the existence of the benign steady state, or predicted incorrectly the size of the inter-tissue gap. Here we show that taking proper account of quiescence ameliorates these drawbacks as well as revealing novel behaviour. The simplicity of the model allows us to fully identify the key parameters controlling different aspects of behaviour.     

Electrostatic potentials of tumour promoters

Molecular-modelling studies and quantum-chemical calculations have been undertaken on a variety of structurally unrelated tumour promoters. The modelling studies reveal some broad areas of agreement in the associated electrostatic potentials for the molecules TPA, teleocidin, aplysiatoxin and ingenol. Azulene-type derivatives were used as models for inactive and active tumour promoters in the quantum chemical studies. The results obtained from these calculations of the electrostatic potentials show very little difference between active and inactive compounds, thus suggesting that other factors are of importance in these systems.     

Relationship between tumour aromatase activity, tumour characteristics and response to therapy

Aromatase activity has been measured in human breast cancers by incubating tumour minces with [7-³H]testosterone and characterizing purified oestradiol (E₂) fractions by chemical derivative formation. Of 247 primary tumours, 178 showed evidence of oestrogen biosynthesis, levels varying between 0.5 and 12.5 fmol E₂ produced/h/g tissue. These values were quantitatively small but at least comparable with those in other peripheral tissues. There was no correlation between presence or level of aromatase activity and the histopathology of the tumours although oestrogen biosynthesis was more likely to be present in more cellular tumours. Aromatase activity was also unrelated to age, menopausal status, lymph node status and T stage of the patient from which the tumour was derived. In a subgroup of patients presenting without clinical evidence of distant metastatic disease, no significant relation was detected between tumour aromatase and disease-free interval, but tumours without aromatase activity were associated with increased survival at 36 months after primary treatment. A statistically significant correlation was also detected between the presence of tumour aromatase and oestrogen receptors. Furthermore, in small subgroups of patients with “advanced” breast cancer tumour aromatase was related to response to aminoglutethimide but not tamoxifen therapy. Whilst these results do not conclusively define a role for local synthesis of oestrogen in the progression of breast cancer, this possibility still exists and further studies on tumour aromatase are warranted.