Related papers: Morphology transitions induced by chemotherapy in …

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…

In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of…

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…

We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…

Adaptive therapy is a recent paradigm in cancer treatment aiming at indefinite, safe containment of the disease when cure is judged unattainable. In modeling this approach, inherent limitations arise due to the structure of the vector…

In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…

Cytotoxic chemotherapy is a common treatment for advanced prostate cancer. These tumors are also known to rely on angiogenesis, i.e., the growth of local microvasculature via chemical signaling produced by the tumor. Thus, several clinical…

We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…

In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient…

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or…

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype…

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the…

Histopathological evidence supports the idea that the emergence of phenotypic heterogeneity and resistance to cytotoxic drugs can be considered as a process of adaptation, or evolution, in tumor cell populations. In this framework, can we…

In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…

Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells…

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific…

We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…