Interaction of Tumor with Its Micro-environment: A Mathematical Model

Yangjin Kim, Avner Friedman

Type: Article

Publication Date: 2009-11-11

Citations: 76

DOI: https://doi.org/10.1007/s11538-009-9481-z

View Publication

Locations

Bulletin of Mathematical Biology - View
PubMed - View

Similar Works

Action	Title	Year	Authors
+	Dynamics of tumor growth: a mathematical model.	1966	William C. Summers
+	Systems Biology of Tumor Microenvironment	2016	Katarzyna A. Rejniak
+	A simplified mathematical model of tumor growth	1986	John A. Adam
+	Mathematical model of the tumor cells’ population growth	2022	Nishant Namdev Himanshu Jain Arvind Kumar Sinha
+	Mathematical Modeling Of Cancerous Tumor For Reducing Growth As Consequence Of Cancer Treatment	2023	Govind Gond
+	Growth kinetics of heterogeneous tumors investigated by a mathematical model	1977	E.L. Orkina Oskar S. Frankfurt A.M. Petrovsky N.M. Emanuel
+	A Validated Mathematical Model of Tumor Growth Including Tumor–Host Interaction, Cell-Mediated Immune Response and Chemotherapy	2014	Álvaro G. López Jesús M. Seoane Miguel A. F. Sanjuán
+	Mathematical Modeling and Solution Landscape Reveal Cancer Progression Dynamics in Tumor Ecological Microenvironment	2025	Shun Wang Tengfei Wang Shuonan Wu Lei Zhang Xiufen Zou
+ PDF Chat	A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics	2014	Suzanne L. Weekes B. W. Barker Sarah Bober Karina Cisneros Justina Cline Amanda L. Thompson Lynn Hlatky Philip Hahnfeldt Heiko Enderling
+	Mathematical modeling of cellular interaction dynamics in multicellular tumor spheroids	1996	Željko Bajzer Miljenko Marušić Stanimir Vuk‐Pavlović
+	A Mathematical Model for Tumor Growth	2001	P. P. Delsanto Barbara Capogrosso-Sansone M. Scalerandi Guido Bongioannini M Magnano
+	Mathematical Modeling Of Tumor Growth	2015	Damla Kutluoğlu
+	MATHEMATICAL MODELING OF TUMOR GROWTH	2022	Sergey E. Dushin Irina I. Shpakovskaya Olga Albertovna Grafina
+	Mathematical modeling of controlled tumor cell growth in the process of personalized treatment	2024	Olga Albertovna Grafina S.E. Dushin Anna Meldo
+ PDF Chat	A mathematical model of tumor growth by diffusion	1988	John A. Adam
+	Mathematical Models Of Cancer Cells In Tumor Immune Interaction And Control Growth Of Cancer Cells With Chemotherapy	2022	Jitendra Singh
+	Mathematical and Computational Approach for Study of Tumor Growth	2022	Vikram Murthy PNS Lakshmi
+	MATHEMATICAL MODELING FOR TUMOR-IMMUNE INTERACTION	2010	Mustafa Mamat Edwin Setiawan Nugraha Agus Priyono Kartono
+	Mathematical models and simulation of tumor growth, radiation response, and micro-environment	2019	E Dahlman
+	A Hybrid Model for Tumor Growth	2011	Chen Zhan

Works That Cite This (48)

Action	Title	Year	Authors
+ PDF Chat	Modeling of Tumor Occurrence and Growth - I	2020	S.N. Antontsev А.А. Papin M.A. Tokareva E.I. Leonova E.A. Gridushko
+	How cancer-associated fibroblasts promote T-cell exclusion in human lung tumors: a physical perspective	2024	Joseph Ackermann C Bernard Philémon Sirven Hélène Salmon Massimiliano Fraldi Martine Ben Amar
+ PDF Chat	Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy	2018	Hang Xie Yang Jiao Qihui Fan Miaomiao Hai Jia-En Yang Zhijian Hu Yue Yang Jianwei Shuai Guo Chen Ruchuan Liu
+ PDF Chat	Inter-cellular signaling network reveals a mechanistic transition in tumor microenvironment	2012	Yu Wu Lana X. Garmire Rong Fan
+ PDF Chat	Data Driven Mathematical Model of FOLFIRI Treatment for Colon Cancer	2021	Aparajita Budithi Sumeyye Su Arkadz Kirshtein Leili Shahriyari
+ PDF Chat	Study of Tumor Growth under Hyperthermia Condition	2012	Qing Zhu Aili Zhang Ping Liu Lisa X. Xu
+	How cancer-associated fibroblasts promote T-cell exclusion in human lung tumors: a physical perspective	2024	Joseph Ackermann C Bernard Philémon Sirven Hélène Salmon Massimiliano Fraldi Martine Ben Amar
+	How cancer-associated fibroblasts promote T-cell exclusion in human lung tumors: a physical perspective	2024	Joseph Ackermann C Bernard Philémon Sirven Hélène Salmon Massimiliano Fraldi Martine Ben Amar
+	Supplementary Materials from A Spatio-Temporal Model of Macrophage-Mediated Drug Resistance in Glioma Immunotherapy	2023	Yongjiang Zheng Jiguang Bao Qiyi Zhao Tianshou Zhou Xiaoqiang Sun
+	Supplementary Materials from A Spatio-Temporal Model of Macrophage-Mediated Drug Resistance in Glioma Immunotherapy	2023	Yongjiang Zheng Jiguang Bao Qiyi Zhao Tianshou Zhou Xiaoqiang Sun

Works Cited by This (16)

Action	Title	Year	Authors
+	Partial Differential Equations	2022	Avner Friedman
+	Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development	1996	Mark A. J. Chaplain
+	Fractional step methods applied to a chemotaxis model	2000	Rebecca C. Tyson L. G. Stern Randall J. LeVeque
+	Chemical Control of Eukaryotic Cell Movement: A New Model	1993	Jonathan A. Sherratt E. Helene Sage J. D. Murray
+	ANALYSIS OF A MATHEMATICAL MODEL OF TUMOR LYMPHANGIOGENESIS	2004	Avner Friedman Georgios Lolas
+	Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis	1991	Cynthia L. Stokes Douglas A. Lauffenburger
+	Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields	2003	Patrick Namy Jacques Ohayon Philippe Tracqui
+	A stochastic model for adhesion-mediated cell random motility and haptotaxis	1993	Richard B. Dickinson Robert T. Tranquillo
+ PDF Chat	Investigating a simple model of cutaneous wound healing angiogenesis	2002	Eamonn A. Gaffney K. Pugh P. K. Maini Frank Arnold
+	Linear and Quasi-linear Equations of Parabolic Type	1968	O. Ladyženskaja V. A. Solonnikov N. Ural’ceva