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We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…

Optimization and Control · Mathematics 2016-08-02 Harald Garcke , Kei-Fong Lam , Elisabetta Rocca

Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables…

Cell Behavior · Quantitative Biology 2008-06-26 L. Leon Chen , Le Zhang , Jeongah Yoon , Thomas S. Deisboeck

Adaptive therapy is a dynamic cancer treatment protocol that updates (or "adapts") treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific…

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…

Tissues and Organs · Quantitative Biology 2013-12-09 F. S. Borges , K. C. Iarosz , H. P. Ren , A. M. Batista , M. S. Baptista , R. L. Viana , S. R. Lopes , C. Grebogi

Chimeric antigen receptor (CAR) T-cell based immunotherapy has shown its potential in treating blood cancers, and its application to solid tumors is currently being extensively investigated. For glioma brain tumors, various CAR T-cell…

Populations and Evolution · Quantitative Biology 2022-01-20 Runpeng Li , Prativa Sahoo , Dongrui Wang , Qixuan Wang , Christine E. Brown , Russell C. Rockne , Heyrim Cho

We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the…

Analysis of PDEs · Mathematics 2023-11-23 Abramo Agosti , Andrea Signori

Achieving effective synergy between radiotherapy and immunotherapy is critical for optimizing tumor control and treatment outcomes. To explore the underlying mechanisms of this synergy, we have investigated a novel treatment approach known…

Quantitative Methods · Quantitative Biology 2025-04-23 Yixun Xing , Casey Moore , Debabrata Saha , Dan Nguyen , MaryLena Bleile , Xun Jia , Robert Timmerman , Hao Peng , Steve Jiang

We study the effect of intratumor heterogeneity in the likelihood of cancer cells moving from a primary tumor to other sites in the human body, generating a metastatic process. We model different scenarios of competition between tumor cells…

Populations and Evolution · Quantitative Biology 2025-10-28 André Rocha , Claudia Manini , José I López , Annick Laruelle

The average treatment effect (ATE) is popularly used to assess the treatment effect. However, the ATE implicitly assumes a homogenous treatment effect even amongst individuals with different characteristics. In this paper, we mainly focus…

Methodology · Statistics 2016-03-10 Yunjian Yin , Lan Liu , Zhi Geng

Computational antibody CDR design methods condition on antigen structure to generate binding loops, yet existing architectures conflate two fundamentally distinct sub-problems: identifying which CDR positions will contact the antigen, and…

Machine Learning · Computer Science 2026-05-22 Mansoor Ahmed , Spencer VonBank , Nadeem Taj , Sujin Lee , Naila Jan , Murray Patterson

In this work, we combine a new form of the cell survival fraction developed in [29] with the Gompertz cell growth model. The result is an equation that models the cell growth/death under a radiation dose and can be applied in a conventional…

Biological Physics · Physics 2017-11-01 Diego Saldaña Ulloa

We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly,we develop it taking into account periodical immunotheraphy treatment with cytokines…

Mathematical Physics · Physics 2009-11-07 O. Sotolongo-Costa , L. Morales Molina , D. Rodriguez Perez , J. C. Antoranz , M. Chacon Reyes

The study of high-throughput genomic profiles from a pharmacogenomics viewpoint has provided unprecedented insights into the oncogenic features modulating drug response. A recent screening of ~1,000 cancer cell lines to a collection of…

In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors with radiotherapy influence. Under certain assumptions on the given data in the model, we prove existence and uniqueness of a weak…

Analysis of PDEs · Mathematics 2024-09-27 Marina Chugunova , Hangjie Ji , Roman Taranets , Nataliya Vasylyeva

Cancer arises from successive rounds of mutations which generate tumor cells with different genomic variation i.e. clones. For drug responsiveness and therapeutics, it is necessary to identify the clones in tumor sample accurately. Many…

Genomics · Quantitative Biology 2015-03-03 Gholamreza Haffari , Zhaoxiang Cai , Mohammad S. Rahman , Ann E. Nicholson

Objective Neoadjuvant chemotherapy (NACT) is one kind of treatment for advanced stage ovarian cancer patients. However, due to the nature of tumor heterogeneity, the clinical outcomes to NACT vary significantly among different subgroups.…

Computer Vision and Pattern Recognition · Computer Science 2024-07-04 Ke Zhang , Neman Abdoli , Patrik Gilley , Youkabed Sadri , Xuxin Chen , Theresa C. Thai , Lauren Dockery , Kathleen Moore , Robert S. Mannel , Yuchen Qiu

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific…

Tissues and Organs · Quantitative Biology 2023-02-28 Chloé Colson , Philip K. Maini , Helen M. Byrne

Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer stem cells (CSC). SC and CSC heterogeneity is manifested as diverse sub-populations with self-renewing and unique regeneration capacity. Moreover, the CSC progeny…

Molecular Networks · Quantitative Biology 2024-06-19 Chong Yu , Qiong Liu , Cong Chen , Jin Wang

Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given…

Quantitative Methods · Quantitative Biology 2013-12-31 Andrew Dhawan , Kamran Kaveh , Mohammad Kohandel , Siv Sivaloganathan

The efficacy of anti-cancer therapies is severely limited by the emergence of drug resistance. While genetic drivers are well-characterized, growing evidence suggests that non-genetic mechanisms, particularly those involving drug-tolerant…

Populations and Evolution · Quantitative Biology 2026-02-02 Xiyin Liang , Jinzhi Lei