Tumor Development Under Combination Treatments with Anti-angiogenic Therapies - Mathematical Methods and Models in Biomedicine - page 300

Tumor Development Under Combination
Treatments with Anti-angiogenic Therapies

Urszula Ledzewicz, Alberto d'Onofrio, and Heinz Schattler

1 Introduction

Tumors are a family of high-mortality diseases, each differing from the other, but all
exhibiting a derangement of cellular proliferation and characterized by a remarkable
lack of symptoms [ 52 ] and by time courses that, in a broad sense, may be classified
as nonlinear. As a consequence, despite the enormous strides in prevention and, to
a certain extent, cure, cancer is one of the leading causes of death worldwide, and,
unfortunately, is likely to remain so for many years to come [ 4 , 53 ].
Phenomenal progress in the field of molecular biology has qualitatively
suggested how the macroscopic complexity of tumor behavior reflects the intricacy
of its underlying deregulating microscopic biochemical mechanisms. At an inter-
cellular level, considering tumor cell populations as ecosystems [ 57 ], further sources
of complexity arise from its internal cell-to-cell cooperative and competitive
interactions [ 41 ]. Additional interactions, which are critically relevant for the
survival of a cancer, are its relationships with external populations, such as blood
vessels, lymphatic vessels and with the cells of the immune system. Moreover,
the responses of tumor cells (TCs) to these interactions are characterized by a
considerable evolutionary ability via changes by means of mutations to enhance

U. Ledzewicz ( )
Department of Mathematics and Statistics, Southern Illinois University Edwardsville,
Edwardsville, IL, 62026, USA
e-mail: [e-mail]
A. d'Onofrio
Department of Experimental Oncology, European Institute of Oncology, 20139 Milan, Italy
e-mail: [e-mail]
H. Schattler
Department of Electrical and Systems Engineering, Washington University, St. Louis, MO,
63130, USA
e-mail: [e-mail]