Proposal of a hybrid approach for tumor progression and tumor-induced angiogenesis

Abstract

One of the main challenges in cancer modelling is to improve the knowledge of tumor progression in areas related to tumor growth, tumor-induced angiogenesis and targeted therapies efficacy. For this purpose, incorporate the expertise from applied mathematicians, biologists and physicians is highly desirable. Despite the existence of a very wide range of models, involving many stages in cancer progression, few models have been proposed to take into account all relevant processes in tumor progression, in particular the effect of systemic treatments and angiogenesis. Composite biological experiments, both in vitro and in vivo, in addition with mathematical modelling can provide a better understanding of theses aspects. In this work we proposed that a rational experimental design associated with mathematical modelling could provide new insights into cancer progression. To accomplish this task, we reviewed mathematical models and cancer biology literature, describing in detail the basic principles of mathematical modelling. We also analyze how experimental data regarding tumor cells proliferation and angiogenesis in vitro may fit with mathematical modelling in order to reconstruct in vivo tumor evolution. Additionally, we explained the mathematical methodology in a comprehensible way in order to facilitate its future use by the scientific community.

Fig. 1

Plot of the different tumor growth laws. Exponential growth law (solid-dotted line); logistic growth (solid line); general growth law (α=0.5, circles and α=2.0, crosses); Gompertzian growth law (dots). Parameter values: k=0.1, θ=1.0, N ₀=0.1

Fig. 2

Four snapshots of tumor evolution in absence of treatment at times t=10,70,159 and 250 [12 h]. (Left) Spatial distribution of proliferative plus quiescent tumor cells. (Right) Spatial distribution of endothelial cells

Fig. 3

Three layers fully developed distribution of the tumor at time t=270[12 h]. Spatial distribution of proliferative cells (up), quiescent cells (middle) and necrotic cells (down)

Fig. 4

Different cell proliferation in ovarian cancer cells. Two cell lines derived from human ovarian cancers were used (HEY and UCI). Cells were cultured under 21 % and 5 % oxygen during 0, 3, 6, 12 and 24 hours. Cell proliferation was analyzed by bromouridine incorporation as previously reported [58]. Data is presented as the logarithm of t ₅₀ (replication time) ± SEM. N=4 per group and analyzed time. * p<0.05 vs HEY at 21 % oxygen. ** p<0.05 vs UCI at 21 % oxygen