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Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding…

Technological breakthroughs in spatial omics and artificial intelligence (AI) have the potential to transform the understanding of cancer cells and the tumor microenvironment. Here we review the role of AI in spatial omics, discussing the…

Quantitative Methods · Quantitative Biology 2025-07-01 Javad Noorbakhsh , Ali Foroughi pour , Jeffrey Chuang

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…

Mathematical Physics · Physics 2017-01-20 Andrea Tosin

Metastatic prostate cancer is one of the most common cancers in men. In the advanced stages of prostate cancer, tumours can metastasise to other tissues in the body, which is fatal. In this thesis, we performed a genetic analysis of…

Information Retrieval · Computer Science 2023-03-30 Yuxuan Li , Shi Zhou

The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment,…

Tissues and Organs · Quantitative Biology 2017-06-29 Anna Konstorum , Anthony T. Vella , Adam J. Adler , Reinhard Laubenbacher

A prototype for a web application was designed and implemented as a guide to be used by clinicians when designing the best drug therapy for a specific cancer patient, given biological data derived from the patients tumor tissue biopsy. A…

Molecular Networks · Quantitative Biology 2014-05-15 Elinor Velasquez , Jorge Soto-Andrade , Ben Bongalon

Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology.…

Other Quantitative Biology · Quantitative Biology 2023-01-27 Yue Wang

One of the key characteristics of cancer cells is an increased phenotypic plasticity, driven by underlying genetic and epigenetic perturbations. However, at a systems-level it is unclear how these perturbations give rise to the observed…

Molecular Networks · Quantitative Biology 2015-04-30 Andrew E. Teschendorff , Christopher R. S. Banerji , Simone Severini , Reimer Kuehn , Peter Sollich

We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi type branching process: We model individual cells which can either divide or…

Populations and Evolution · Quantitative Biology 2015-04-14 Benedikt Bauer , Reiner Siebert , Arne Traulsen

The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel…

Tissues and Organs · Quantitative Biology 2016-09-08 K. Bartha , H. Rieger

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…

Biological Physics · Physics 2024-12-05 Nonthakorn Olaranont , Chaozhen Wei , John Lowengrub , Min Wu

Cancer is a systemic heterogeneous disease involving complex molecular networks. Tumor formation involves epithelial-mesenchymal transition (EMT), which promotes both metastasis and plasticity of cancer cells. Recent experiments proposed…

Molecular Networks · Quantitative Biology 2023-05-23 Zihao Chen , Jia Lu , Xing-Ming Zhao , Haiyang Yu , Chunhe Li

It is a well-established fact that tumors up-regulate glucose consumption to meet increasing demands for rapidly available energy by switching to purely glycolytic mode of glucose metabolism. What is often neglected is that cytotoxic cells…

Tissues and Organs · Quantitative Biology 2014-07-31 Irina Kareva

The mitigation of stress is a key challenge for all biological systems. Conditions of unresolvable stress have been associated with a diverse array of pathologies, from cancer to post-traumatic stress disorder (PTSD). Here, I unify insights…

Cell Behavior · Quantitative Biology 2025-08-29 Jordan Strasser

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

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…

Cell Behavior · Quantitative Biology 2020-01-10 Jinzhi Lei

Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and…

Tissues and Organs · Quantitative Biology 2019-07-03 Robyn Shuttleworth , Dumitru Trucu

As immunotherapies become standard cancer treatments, it is increasingly important to identify a patient's immune profile, which encompasses the activity of immune cells within the tumor microenvironment and the presence of specific…

Genomics · Quantitative Biology 2026-03-31 Soham Chatterjee

The metabolic wiring of patient cells is altered drastically in many diseases, including cancer. Understanding the nature of such changes may pave the way for new therapeutic opportunities, as well as the development of personalized…

Molecular Networks · Quantitative Biology 2020-02-12 Ali Cakmak , M. Hasan Celik

We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…

Quantitative Methods · Quantitative Biology 2023-02-14 Bruce P. Ayati , Glenn F. Webb , Alexander R. A. Anderson