Related papers: A Mathematical Programming Approach to the Fractio…
In this article, we focus on determining a minimum-cost treatment program aimed at maintaining the size of a cancerous tumor at a level that allows the patient to live comfortably. At each predetermined point in a treatment horizon, the…
Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular…
Mechanical force is tightly connected to human health status, and the occurrence of disease can generally be ascribed to certain loss of force balance. However, the role of mechanical approaches in tumor therapy is largely neglected, while…
Delineating and planning with respect to regions suspected to contain microscopic tumor cells is an inherently uncertain task in radiotherapy. The recently proposed \textit{clinical target distribution} (CTD) is an alternative to the…
The predicted increase in the number of patients receiving radiation therapy (RT) to treat cancer calls for an optimized use of resources. To manually schedule patients on the linear accelerators delivering RT is a time-consuming and…
Although optimal control theory has been used for the theoretical study of anti-cancerous drugs scheduling optimization, with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously…
In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints,…
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 formulate and analyze a mathematical model describing immune response to avascular tumor under the influence of immunotherapy and chemotherapy and their combinations as well as vaccine treatments. The effect of vaccine therapy is…
A component which suffers radiation damage usually also becomes radioactive, since the source of activation and radiation damage is the interaction of the material with particles from an accelerator or with reaction products. However, the…
Geometric uncertainty can degrade treatment quality in radiation therapy. While margins and robust optimization mitigate these effects, they provide only implicit control over clinical goal fulfillment probability. We therefore develop a…
Accurately linking microscopic energy deposition from ionizing radiation to emergent biological outcomes remains a central challenge in radiobiological modelling, particularly when stochastic damage induction, cell-cycle dynamics, and…
The number of cancer cases per year is rapidly increasing worldwide. In radiation therapy (RT), radiation from linear accelerators is used to kill malignant tumor cells. Scheduling patients for RT is difficult both due to the numerous…
We continue our study of a model for cancer treatment, constructed in Dutta et. al., 2025, by adding Virotherapy to the Chemotherapy and Immunotherapy studied there. It is a dynamical system model for the spread of cancer in healthy tissue.…
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 combination of cytotoxic therapies and anti-angiogenic agents is emerging as a most promising strategy in the treatment of malignant tumors. However, the timing and sequencing of these treatments seem to play essential roles in…
Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof…
Doctors are well aware that sometimes cancer treatments not only fail, but even work backwards, i.e. they make the treated tumor grow. In this work we present a mathematical perspective on this paradox in the case of chemotherapy, by…
Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects such as DNA mutation or bystander…
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design…