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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…

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…

Tissues and Organs · Quantitative Biology 2013-06-21 Sebastien Benzekry , Philip Hahnfeldt

We investigate a method of selectively targeting cancer cells by means of ultrasound harmonic excitation at their resonance frequency, which we refer to as oncotripsy. The geometric model of the cells takes into account the cytoplasm,…

Biological Physics · Physics 2020-07-21 Stefanie Heyden , Michael Ortiz

In this paper, a reaction-diffusion system modeling injection of a chemotherapeutic drug on the surface of a living tissue during a treatment for cancer patients is studied. The system describes the interaction of the chemotherapeutic drug…

Analysis of PDEs · Mathematics 2024-08-20 Jeff Morgan , Bao Quoc Tang , Hong-Ming Yin

In the study of therapeutic strategies for the treatment of cancer, eco-evolutionary dynamics are of particular interest, since characteristics of the tumour population, interaction with the environment and effects of the treatment,…

Populations and Evolution · Quantitative Biology 2023-07-19 Giulia Chiari , Giada Fiandaca , Marcello Edoardo Delitala

The primary objective of phase I oncology studies is to establish the safety profile of a new treatment and determine the maximum tolerated dose (MTD). This is motivated by the development of cytotoxic agents based on the underlying…

Applications · Statistics 2023-02-10 Yiding Zhang , Zhixing Xu , Hui Quan , Ji Lin

Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors,…

Computational Engineering, Finance, and Science · Computer Science 2012-08-21 Giulio Caravagna , Alex Graudenzi , Marco Antoniotti , Giancarlo Mauri , Alberto d'Onofrio

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of…

Tissues and Organs · Quantitative Biology 2015-10-07 H. Hatzikirou , J. C. L. Alfonso , S. Muhle , C. Stern , S. Weiss , M. Meyer-Hermann

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…

Tissues and Organs · Quantitative Biology 2015-07-24 A. I. Reppas , J. C. L. Alfonso , H. Hatzikirou

Personalized cancer treatments based on the molecular profile of a patient's tumor are an emerging and exciting class of treatments in oncology. As genomic tumor profiling is becoming more common, targeted treatments to specific molecular…

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…

Oncolytic virotherapy - the use of viruses that specifically kill tumor cells - is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral…

Tissues and Organs · Quantitative Biology 2015-06-15 Leticia R Paiva , Hallan S Silva , Silvio C Ferreira , Marcelo L Martins

We propose a novel computational framework leveraging hypergraph theory to analyse cancer stem cell markers (CSCMs) across multiple organs. Hypergraphs provide a robust representation of CSCM co-expression patterns, capturing their complex…

Biological Physics · Physics 2025-08-01 David H. Margarit , Gustavo Paccosi , Marcela V. Reale , Lilia M. Romanelli

The majority of cancer-related fatalities are due to metastatic disease. In chemoradiotherapy, chemotherapeutic agents are administered along with radiation to increase damage to the primary tumor and control systemic disease such as…

Optimization and Control · Mathematics 2016-11-16 Hamidreza Badri , Ehsan Salari , Yoichi Watanabe , Kevin Leder

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…

Artificial Intelligence · Computer Science 2022-05-18 Alexander Brownlee , Martin Pelikan , John McCall , Andrei Petrovski

The development of oncology drugs progresses through multiple phases, where after each phase a decision is made about whether to move a molecule forward. Early phase efficacy decisions are often made on the basis of single arm studies based…

Applications · Statistics 2023-04-17 Ulrich Beyer , David Dejardin , Matthias Meller , Kaspar Rufibach , Hans Ulrich Burger

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.…

Other Quantitative Biology · Quantitative Biology 2026-03-02 Tarini Kumar Dutta , Silmera A Sangma , Janice Moore , Meir Shillor

Protontherapy is hadrontherapy fastest-growing modality and a pillar in the battle against cancer. Hadrontherapy superiority lies in its inverted depth-dose profile, hence tumour-confined irradiation. Protons, however, lack distinct…

The aim of this chapter is to provide a brief introduction into the basics of a top-down multilevel tumor dynamics modeling method primarily based on discrete entity consideration and manipulation. The method is clinically oriented, one of…

Medical Physics · Physics 2010-09-14 Georgios Stamatakos

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…

Tissues and Organs · Quantitative Biology 2019-06-10 Ahmed M. Fouad