Related papers: Long-time Dynamics and Optimal Control of a Diffus…
Diffuse gliomas are malignant brain tumors that grow widespread through the brain. The complex interactions between neoplastic cells and normal tissue, as well as the treatment-induced changes often encountered, make glioma tumor growth…
In this paper, we tackle the problem of reconstructing earlier tumour configurations starting from a single spatial measurement at a later time. We describe the tumour evolution through a diffuse interface model coupling a…
We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is…
This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and…
The acid-mediated tumor invasion hypothesis proposes that altered glucose metabolism exhibited by the vast majority of tumors leads to increased acid (H+ ion) production which subsequently facilitates tumor invasion [1-3]. The…
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier--Stokes equations, nonlinearly…
We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The…
Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the critical role of treatment-holiday thresholds in adaptive therapy for…
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…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip…
In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
We present a phase-space analysis of a mathematical model of tumor growth with an immune responses. We consider mathematical analysis of the model equations with multipoint initial condition regarding to dissipativity, boundedness of…
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…