Heterogeneity is a hallmark of all cancers. Tumor heterogeneity is found at different levels—
interpatient, intrapatient, and intratumor heterogeneity. All of them pose challenges for …

Emergence of invasive behavior in cancer is life-threatening, yet ill-defined due to its
multifactorial nature. We present a multiscale mathematical model of cancer invasion, which …

We here propose a one-dimensional spatially explicit phenotype-structured model to
analyze selected aspects of avascular tumor progression. In particular, our approach …

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis
requires investigation of the impact of self-renewal on cancer expansion. To better …

Chemotherapeutics are often treated as having a lumped tumor effect, however, the growth
state and exposure for individual cancer cells ultimately determines the response of the …

From the perspectives of the thermodynamics of irreversible processes and the theory of
complex systems, a characterization of longevity and aging and their relationships with the …

In the last ten years, mixture theory has been applied with success to describe several
problems related to tumor growth, as reviewed by Ambrosi and Preziosi (2002), Araujo and …

A medically important feature of several types of tumors is their ability to “decide” between
staying at a primary site in the body or leaving it and forming metastases. The present …

It has long been recognized that the growth of tumor population depends on the initial age
distribution of the cells in the tumor and the age-dependent cellular birth rate. Deterministic …

Quantitative models from population biology and evolutionary game theory frame the tumor-
host interface as a dynamical microenvironment of competing tumor and normal …