Studies of a Hybrid and Multiscale Tumor Growth Model using Isogeometric Analysis
Paulo Wander Barbosa1; Adriano M. de A. Côrtes2; Lucia Catabriga1
1 Universidade Federal do Espírito Santo; 2 Universidade Federal do Estado do Rio de Janeiro
doi:10.20906/CPS/CILAMCE2017-1192
Resumo
The World Health Organization indicates that each year 8.8 million people die of cancer. Trying to reduce this alarming number of deaths, and minimize the patient suffering, the scientific community is collaborating on researches able to improve the understanding of the cancer dynamics and enhance the different treatments available. Many mathematical models of tumors growth have been developed in the last decades, with great potential to accelerate drug development and optimize treatments.The onset and the development of the tumor in the body is quite complex and involves a large amount of events at different scales: molecular, cellular, and tissue scales. In the early stage, called avascular stage, the tumor cells feed on nutrients that are available in the host tissue and that have penetrated of the tumor surface. In the case of solid tumors growth, e.g. carcinomas, the clustering of tumor cells prevents the nutrients from reaching the nucleus by diffusion, forming three regions: proliferative layer, hypoxic layer and necrotic nucleus. This privation of nutrients triggers the production of angiogenic factors by the hypoxic tumor cells, which induce angiogenesis, the process in which new blood vessels are formed from preexisting ones through migration and proliferation mechanisms. Angiogenesis is one of the hallmarks of cancer [1], additionally the connection of the tumor with blood vessels generates the opportunity for tumor cells to fall into the bloodstream and migrate to other organs. A mathematical model describing the aforementioned events taking place in the growth process, characterized by the interplay between the three scales, is a challenging task. Models based on a system of partial differential equations coupled with an agent-based model are commom in the literature [2]. For example, [3,4] based their hybrid model, incorporating the avascular and vascular phases, in [5]. In this work, we discuss the implementation of a hybrid and multiscale tumor growth model[3,4,5], using the high performance Iso
Palavras-chave: Tumor growth; Angiogenesis; Phase-field models