Related papers: An Optimal Control Strategy for Mathematically Mod…
This paper deals with the classic radiotherapy dose fractionation problem for cancer tumors concerning the following goals: a) To maximize the effect of radiation on the tumor, restricting the effect produced to the organs at risk (healing…
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species -- namely immune cells. We run six…
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…
In this paper, a new stochastic framework to determine optimal combination therapies in colon cancer-induced immune response is presented. The dynamics of colon cancer is described through an It\"o stochastic process, whose probability…
In this paper, a methodology is proposed that enables to analyze the sensitivity of the outcome of a therapy to unavoidable high dispersion of the patient specific parameters on one hand and to the choice of the parameters that define the…
Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML…
Despite the remarkable advances in cancer diagnosis, treatment, and management that have occurred over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by…
Cancer is a term used to refer to a large set of diseases. The cancerous cells grow and divide and, as a result, they form tumours that grow in size. The immune system recognise the cancerous cells and attack them, though, it can be…
In radiation therapy, mathematical methods have been used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to critical surrounding structures minimal. This optimization problem…
The challenge of removing cancerous cells lies in the limitation of organ at risk, which restricts the ability to increase the radiation dose adequately for enhancing treatment effectiveness. This survey provides a comprehensive overview of…
In this paper we consider optimal control problems for a parabolic system modeling a therapy, based on oncolytic viruses, for the glioma brain cancer. Using several techniques typical of functional analysis, we prove the global in time well…
A distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cahn--Hilliard equation for the tumour fraction coupled with a…
We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of…
It is possible to find the optimized radiation dose per session for a radiotherapy (RT) treatment, using a population dynamics model. This has already been done in a previous work for a protocol with 30 sessions and a fixed dose per…
Therapies such as combined-hyperthermia-radiotherapy (CHR) take advantage of excellent radiosensitization properties of hyperthermia and treat of tumors with both radiation and heat. To appropriately model a CHR treatment, features like…
Chemotherapy treatment for cancer is a complex optimisation problem with a large number of interacting variables and constraints. A number of different probabilistic algorithms have been applied to it with varying success. In this paper we…
We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…
This paper proposes a general framework for probabilistic certification of cancer therapies. The certification is defined in terms of two key issues which are the tumor contraction and the lower admissible bound on the circulating…
Radiation therapy is a critical component of cancer treatment. However, the delivery of radiation poses inherent challenges, particularly in minimizing radiation exposure to healthy organs surrounding the tumor site. One significant…
Drug resistance is still a major challenge in cancer therapy. Drug combination is expected to overcome drug resistance. However, the number of possible drug combinations is enormous, and thus it is infeasible to experimentally screen all…