Mathematical Models in Cancer Research

Chaplain, M. A. J.

doi:10.1002/0470025077.chap60

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…Besides, it would be necessary to take into account spatial migration of cell populations during the process of invasion (see, e.g. [8]). Therefore, the system of Equations (1) - (7) is valid for the description of early stages of the tumour growth when the processes of angiogenesis, invasion and metastasis are not of critical importance.…”

Section: Modelmentioning

confidence: 99%

Modelling of Anti‐Tumour Immune Response: Immunocorrective Effect of Weak Centimetre Electromagnetic Waves

Isaeva

Osipov

2008

Computational and Mathematical Methods in Medicine

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We formulate the dynamical model for the anti-tumour immune response based on intercellular cytokine-mediated interactions with the interleukin-2 (IL-2) taken into account. The analysis shows that the expression level of tumour antigens on antigen presenting cells has a distinct influence on the tumour dynamics. At low antigen presentation, a progressive tumour growth takes place to the highest possible value. At high antigen presentation, there is a decrease in tumour size to some value when the dynamical equilibrium between the tumour and the immune system is reached. In the case of the medium antigen presentation, both these regimes can be realized depending on the initial tumour size and the condition of the immune system. A pronounced immunomodulating effect (the suppression of tumour growth and the normalization of IL-2 concentration) is established by considering the influence of low-intensity electromagnetic microwaves as a parametric perturbation of the dynamical system. This finding is in qualitative agreement with the recent experimental results on immunocorrective effects of centimetre electromagnetic waves in tumour-bearing mice.

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Section: Modelmentioning

confidence: 99%

Modelling of Anti‐Tumour Immune Response: Immunocorrective Effect of Weak Centimetre Electromagnetic Waves

Isaeva

Osipov

2008

Computational and Mathematical Methods in Medicine

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“…This does not mean, however, that a delay in the vaccination is not dangerous. In fact, as mentioned above, we do not take into account the angiogenesis, which begins at certain size of the tumor and provokes its further explosion [2,7]. In other words, the existence of the saturation level does not imply the termination of the tumor growth.…”

Section: Vaccine Therapymentioning

confidence: 99%

“…To simplify analysis, we reduced the model to three equations incorporating the most important modern concepts of tumor-immune dynamics including the influence of IL-2 dynamics (see [22] for details). Notice also that we do not consider the spatial migration of cell populations that is of most importance for modeling of angiogenesis (vascular growth), invasion and metastasis (see, e.g., [7]).…”

Section: Introductionmentioning

confidence: 99%

Different Strategies for Cancer Treatment: Mathematical Modelling

Isaeva

Osipov

2008

Computational and Mathematical Methods in Medicine

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We formulate and analyse a mathematical model describing immune response to avascular tumour under the influence of immunotherapy and chemotherapy and their combinations as well as vaccine treatments. The effect of vaccine therapy is considered as a parametric perturbation of the model. In the case of a weak immune response, neither immunotherapy nor chemotherapy is found to cause tumour regression to a small size, which would be below the clinically detectable threshold. Numerical simulations show that the efficiency of vaccine therapy depends on both the tumour size and the condition of immune system as well as on the response of the organism to vaccination. In particular, we found that vaccine therapy becomes more effective when used without time delay from a prescribed date of vaccination after surgery and is ineffective without preliminary treatment. For a strong immune response, our model predicts the tumour remission under vaccine therapy. Our study of successive chemo/immuno, immuno/chemo and concurrent chemoimmunotherapy shows that the chemo/immuno sequence is more effective while concurrent chemoimmunotherapy is more sparing.

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