title: 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.
authors.affiliation: Department of Basic Sciences, Faculty of Sciences, Universidad del Bío-Bío, Campus Fernando May, Av. Andrés Bello s/n, Casilla 447 Chillán, Chile. pcumsille@ubiobio.cl.|Centre for Biotechnology and Bioengineering, University of Chile, Beaucheff 851, Santiago, Chile. pcumsille@ubiobio.cl.|Group of Applied Mathematics (GMA), Chillán, Chile. pcumsille@ubiobio.cl.|Group of Investigation in Tumor Angiogenesis (GIANT), Chillán, Chile. pcumsille@ubiobio.cl.
authors.forename: Patricio
authors.initials: P
authors.lastname: Cumsille
authors.affiliation: Department of Basic Sciences, Faculty of Sciences, Universidad del Bío-Bío, Campus Fernando May, Av. Andrés Bello s/n, Casilla 447 Chillán, Chile. acoronel@ubiobio.cl.|Group of Applied Mathematics (GMA), Chillán, Chile. acoronel@ubiobio.cl.
authors.forename: Aníbal
authors.initials: A
authors.lastname: Coronel
authors.affiliation: Centre for Biotechnology and Bioengineering, University of Chile, Beaucheff 851, Santiago, Chile. cconca@dim.uchile.cl.|Department of Mathematical Engineering (DIM) and Center for Mathematical Modelling (CMM), University of Chile, (UMI CNRS 2807), Beaucheff 851, Correo 3 Santiago, P.O. Box 170-3, Chile. cconca@dim.uchile.cl.
authors.forename: Carlos
authors.initials: C
authors.lastname: Conca
authors.affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie and Mathematical Neuroscience Team, CIRB, Collège de France, (UMR CNRS 7598), 4 place de Jussieu, Paris, F-75005, France. cristobal.quininao@college-de-france.fr.
authors.forename: Cristóbal
authors.initials: C
authors.lastname: Quiñinao
authors.affiliation: Department of Basic Sciences, Faculty of Sciences, Universidad del Bío-Bío, Campus Fernando May, Av. Andrés Bello s/n, Casilla 447 Chillán, Chile. cescudero@ubiobio.cl.|Group of Investigation in Tumor Angiogenesis (GIANT), Chillán, Chile. cescudero@ubiobio.cl.|Group of Research and Innovation in Vascular Health (GRIVAS Health), Chillán, Chile. cescudero@ubiobio.cl.
authors.forename: Carlos
authors.initials: C
authors.lastname: Escudero
mesh_terms: D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply*; D009389:Neovascularization, Pathologic