Mathematical modelling of tumour angiogenesis

• Autorzy: Poleszczuk J.

Identyfikatory

DOI

10.14708/ma.v41i1.382

Warianty tytułu

PL

Matematyczne modelowanie angiogenezy nowotworowej

• Języki publikacji: EN

Abstrakty

EN

Mathematical models are valuable tools for studying the underlying mechanisms of tumour progression. They enable us to explore possible radio-, chemo- and other various therapy combinations that until now have been only a promising hypotheses because of the huge costs of their clinical studies. Here we present a family of mathematical models of tumour angiogenesis, which give an accurate fit to biological data. In addition, after modifications they can describe the effect of anti-angiogenic treatment using various vessel targeting agents, as well as the impact of cytotoxic agents on proliferating cancer cells. We present two ways in which anti-angiogenic treatment can be incorporated into the model. In the first one, the agents directly target tumour vessels, whereas in the second one, they interfere with angiogenic signalling. We illustrate differences between these two approaches by presenting the results of fitting the corresponding models to the biological data.

PL

Modele matematyczne okazały się być cennym narzędziem do badania podstawowych mechanizmów progresji nowotworu. Modele pozwalają nam na badanie możliwości łączenia radioterapii, chemioterapii i innych metod leczenia, co do tej pory, z powodu bardzo wysokich kosztów badań klinicznych, było nieosiągalne. W pracy prezentujemy rodzinę matematycznych modeli angiogenezy nowotworowej, które okazały się dobrze odpowiadać wynikom przeprowadzonych eksperymentów biologicznych. Ponadto, po wprowadzeniu pewnych modyfikacji, modele te skutecznie opisują wpływ terapii antyangiogennej wykorzystującej leki o różnorakim sposobie działania. W pracy przedstawiamy dwa sposoby na uwzględnienie w modelu wpływu leków działających na naczynia krwionośne dostarczające w rejony nowotworu tlen i substancje odżywcze. Pierwszy sposób odnosi się do środków działających bezpośrednio na naczynia guza. Drugi opisuje środki wpływające na proangiogenna sygnalizacje. Różnice miedzy tymi dwoma podejściami ilustrujemy poprzez przedstawienie wyników dopasowywania modeli do danych eksperymentalnych.

Słowa kluczowe

EN

tumour angiogenesis; anti-angiogenic therapy; ODEs

PL

angiogeneza nowotworowa; terapia antyangiogenna; równania różniczkowe

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2013
• Tom: Vol. 41, No. 1
• Strony: 1--12
• Opis fizyczny: Bibliogr. 36 poz., rys., tab.

Twórcy

autor

Poleszczuk J.

• College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences The University of Warsaw Zwirki i Wigury 93, 02-089 Warsaw, Poland

Bibliografia

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