Mathematical Oncology 2013

  • Alberto d'Onofrio
  • Alberto Gandolfi

Table of contents

  1. Front Matter
    Pages i-x
  2. Cancer Onset and Early Growth

    1. Front Matter
      Pages 1-1
    2. Antonio Fasano, Alessandro Bertuzzi, Carmela Sinisgalli
      Pages 27-61
  3. Tumor and Inter-Cellular Interactions

    1. Front Matter
      Pages 107-107
    2. Marina Dolfin, Mirosław Lachowicz, Zuzanna Szymańska
      Pages 151-180
    3. Irina Kareva, Kathleen P. Wilkie, Philip Hahnfeldt
      Pages 181-196
  4. Anti-Tumor Therapies

About this book


With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways.

Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways.

Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.


Anticancer therapy Mathematical biology and medicine Mathematical modeling Stochasticity Systems biology Tumor

Editors and affiliations

  • Alberto d'Onofrio
    • 1
  • Alberto Gandolfi
    • 2
  1. 1.International Prevention Research InstituteLyonFrance
  2. 2.Istituto di Analisi dei Sistemi ed Informatica "Antonio Ruberti"—CNRRomeItaly

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-0457-0
  • Online ISBN 978-1-4939-0458-7
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • About this book