Related papers: Evolutionary dynamics in vascularised tumours unde…
Tumors are defined by their intense proliferation, but sometimes cancer cells turn senescent and stop replicating. In the stochastic cancer model in which all cells are tumorigenic, senescence is seen as the result of random mutations,…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and…
A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of…
Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
Despite recent advances in the field of Oncoimmunology, the success potential of immunomodulatory therapies against cancer remains to be elucidated. One of the reasons is the lack of understanding on the complex interplay between tumor…
Mathematical modelling of tumor growth is one of the most useful and inexpensive approaches to determine and predict the stage, size and progression of tumors in realistic geometries. Moreover, these models has been used to get an insight…
A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate…
Neuroblastoma is a paediatric extracranial solid cancer that arises from the developing sympathetic nervous system and is characterised by an abnormal distribution of cell types in tumours compared to healthy infant tissues. In this paper,…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
Tumor heterogeneity is a complex and widely recognized trait that poses significant challenges in developing effective cancer therapies. In particular, many tumors harbor a variety of subpopulations with distinct therapeutic response…
This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
Phenotypic heterogeneity along the epithelial-mesenchymal (E-M) axis contributes to cancer metastasis and drug resistance. Recent experimental efforts have collated detailed time-course data on the emergence and dynamics of E-M…
We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may…
Development of resistance limits transferability of most anticancer therapies into curative treatment and understanding mechanisms beyond it remains a big challenge. Many high resolution experimental observations show enormous intratumor…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…