Computational Models of Vascularization and Therapy in Tumor Growth - Mechanical and Chemical Signaling in Angiogenesis - page 223

new hypotheses and, in the case of therapies for instance, to predict and optimize
treatment outcomes in patients.
Most models in biology rely on the description, using continuous or discrete
mathematical tools, of the time-course of one or several biological entities. Their aim
is to 'capture' the dynamics of a process, which by definition evolve in time. Almost
all biological processes are characterized by particular dynamics. Computational
modeling relies on the premise that integrating the dynamics of a process can provide
benefits in its understanding in comparison to classical static analysis.
An illustrative example is the successful use of changes in hematological vari-
ables on a continuous scale for assessing anticancer drug toxicity in early phase
clinical trials. To appreciate the amplitude of myelosuppression following the
administration of chemotherapy, clinicians used to consider the nadir (minimum)
value of neutrophils or leukocytes. But in doing so, relevant information regarding
the time course of hematological variables and duration of neutropenia was wasted.
A predictive model of the time-course of leukocyte and neutrophil counts was
developed and can be used for optimizing the design of clinical trials in oncology [ 1 ].
Often, however, the modeler faces some difficulties accessing data since ex-
perimentalists may sometimes omit the time factor when studying a biological
process. As already stated, in the example of myelosuppression, the minimal value
of neutrophil counts assessed at a given time was considered to evaluate the
toxicity induced by the drug. To give a parallel example, the efficacy of anticancer
drugs is still nowadays appreciated in early phase clinical trials by measuring the
change in tumor size before and at a given time point after treatment. This is the
base of the Response Evaluation Criteria in Solid Tumors (RECIST) [ 2 , 3 ]. In
preclinical experiments also, biologists often analyze the change of a biological
marker at a given time point and not in a dynamic way. These limitations can be
however, explained by the cost and time required for repeated measurements
(using repeated MRI for instance to assess tumor size evolution during treatment).
More generally, in the drug development process, the development of com-
putational models can facilitate the continuous integration of available information
related to a drug or disease in order to describe and predict the behavior of studied
systems and to address questions researchers, regulators and public health care
bodies face when bringing drugs to patients.
The aim of the present chapter is to provide a partial and short overview of
modeling efforts in the study of the process of angiogenesis and tumor growth.
Models range from simple formalisms describing the time-course of a morphological
variable, such as the tumor volume, to the description of molecular signaling
pathways relevant to the process of angiogenesis.
2 Simple Computational Modeling in Oncology
The modeling of tumor growth started in 1964 when tumor cells in vitro were
shown to grow following Gompertzian kinetics [ 4 ].