Authors: Lorenzi, Tommaso, Venkataraman, Chandrasekhar, Lorz, Alexander, Chaplain, Mark A. J.

Superior Title: Lorenzi , T , Venkataraman , C , Lorz , A & Chaplain , M A J 2018 , ' The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity ' , Journal of Theoretical Biology , vol. 451 , pp. 101-110 . https://doi.org/10.1016/j.jtbi.2018.05.002

Subject Terms: Intratumour heterogeneity, Phenotypic selection, Mathematical oncology, Partial differential equations, Finite element methods

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Availability: https://doi.org/10.1016/j.jtbi.2018.05.002
https://risweb.st-andrews.ac.uk/portal/en/researchoutput/the-role-of-spatial-variations-of-abiotic-factors-in-mediating-intratumour-phenotypic-heterogeneity(b481322d-6719-49d7-bf85-0bde5937637f).html
https://research-repository.st-andrews.ac.uk/bitstream/10023/17662/1/Manuscript_revised_PURE.pdf

Authors: Lorenzi, Tommaso, Venkataraman, Chandrasekhar, Lorz, Alexander, Chaplain, Mark A. J.

Contributors: EPSRC, University of St Andrews. Applied Mathematics

Subject Terms: Intratumour heterogeneity, Phenotypic selection, Mathematical oncology, Partial differential equations, Finite element methods, HA Statistics, RC0254 Neoplasms. Tumors. Oncology (including Cancer), QA Mathematics, DAS, SDG 3 - Good Health and Well-being, HA, RC0254, QA

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Relation: Journal of Theoretical Biology; Lorenzi , T , Venkataraman , C , Lorz , A & Chaplain , M A J 2018 , ' The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity ' , Journal of Theoretical Biology , vol. 451 , pp. 101-110 . https://doi.org/10.1016/j.jtbi.2018.05.002; PURE: 252985123; PURE UUID: b481322d-6719-49d7-bf85-0bde5937637f; Scopus: 85046750884; ORCID: /0000-0001-5727-2160/work/55378933; WOS: 000434002000010; http://hdl.handle.net/10023/17662; https://doi.org/10.1016/j.jtbi.2018.05.002; 642866; EP/N014642/1

Availability: https://doi.org/10.1016/j.jtbi.2018.05.002
http://hdl.handle.net/10023/17662

Authors: Chaplain, Mark A. J.¹ (AUTHOR), Lorenzi, Tommaso¹ (AUTHOR), Macfarlane, Fiona R.¹ (AUTHOR) frm3@st-andrews.ac.uk

Superior Title: Journal of Mathematical Biology. Jan2020, Vol. 80 Issue 1/2, p343-371. 29p.

Subject Terms: *CELL populations, *PARTIAL differential equations, *NONLINEAR differential equations, *CELLULAR evolution

Authors: Lorenzi, Tommaso, Venkataraman, Chandrasekhar, Lorz, Alexander, Chaplain, Mark A. J.

Contributors: EPSRC, University of St Andrews. Applied Mathematics

Subject Terms: Intratumour heterogeneity, Phenotypic selection, Mathematical oncology, Partial differential equations, Finite element methods, HA Statistics, RC0254 Neoplasms. Tumors. Oncology (including Cancer), SDG 3 - Good Health and Well-being, SDG 13 - Climate Action, HA, RC0254

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Relation: Lorenzi , T , Venkataraman , C , Lorz , A & Chaplain , M A J 2017 ' The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity ' University of St Andrews .; PURE: 249738933; PURE UUID: afac6412-c7b0-4641-a521-9a937ed8a812; ORCID: /0000-0001-5727-2160/work/55379071; http://hdl.handle.net/10023/10685; EP/N014642/1

Availability: http://hdl.handle.net/10023/10685

Authors: Bitsouni, Vasiliki, Trucu, Dumitru, Chaplain, Mark A J, Eftimie, Raluca

Superior Title: Mathematical Medicine & Biology: A Journal of the IMA; Dec2018, Vol. 35 Issue 4, p541-577, 37p

Subject Terms: CANCER cells, CELL growth, MATHEMATICAL models, PARTIAL differential equations, CELL differentiation

Authors: Enderling, Heiko, Anderson, Alexander R. A., Chaplain, Mark A. J., Rowe, Glenn W. A.

Superior Title: Enderling , H , Anderson , A R A , Chaplain , M A J & Rowe , G W A 2006 , ' Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology ' , Mathematical Biosciences and Engineering , vol. 3 , no. 4 , pp. 571-582 .

Subject Terms: Visualisation, Adaptive marching cubes, Transparency blending, Partial differential equations, Mathematical models, Tumour growth and invasion

Availability: https://risweb.st-andrews.ac.uk/portal/en/researchoutput/visualisation-of-the-numerical-solution-of-partial-differential-equation-systems-in-three-space-dimensions-and-its-importance-for-mathematical-models-in-biology(9e77e5b9-ad44-401a-9ffd-0e39db92f7db).html
http://aimsciences.org/index.html

Authors: Matzavinos, Anastasios, Chaplain, Mark A. J.

Superior Title: Matzavinos , A & Chaplain , M A J 2004 , ' Travelling wave analysis of a model of the immune response to cancer ' , Comptes Rendus Biologies , vol. 327 , no. 11 . https://doi.org/10.1016/j.crvi.2004.07.016

Subject Terms: Travelling waves, Mathematical modelling, Partial differential equations, Cancer dormancy, Tumour cells, Bifurcations

Availability: https://doi.org/10.1016/j.crvi.2004.07.016
https://risweb.st-andrews.ac.uk/portal/en/researchoutput/travelling-wave-analysis-of-a-model-of-the-immune-response-to-cancer(6ee528ad-bb49-4a28-8cce-b39e3f96375d).html

Authors: Morel, J.-M., Takens, F., Teissier, B., Friedman, Avner, Chaplain, Mark, Matzavinos, Anastasios

Superior Title: Tutorials in Mathematical Biosciences III; 2005, p131-183, 53p

Authors: Sturrock, Marc, Terry, Alan, Xirodimas, Dimitris, Thompson, Alastair, Chaplain, Mark

Superior Title: Bulletin of Mathematical Biology; Jul2012, Vol. 74 Issue 7, p1531-1579, 49p

Subject Terms: NUCLEAR membranes, ACTIVE biological transport, CELL morphology, MICROTUBULES, PROTEASOMES, PARTIAL differential equations, P53 protein

Authors: Colin, Thierry^Aff5, Michel, Thomas^Aff6, Poignard, Clair^Aff7

Contributors: Suzuki, Takashi, editor^Aff1, Poignard, Clair, editor^Aff2, Chaplain, Mark, editor^Aff3, Quaranta, Vito, editor^Aff4

Superior Title: Methods of Mathematical Oncology : Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020. 370:15-49

Authors: Wilson, Anna^Aff5, Williams, Thomas^Aff5, Sfakianakis, Nikolaos^Aff5

Contributors: Suzuki, Takashi, editor^Aff1, Poignard, Clair, editor^Aff2, Chaplain, Mark, editor^Aff3, Quaranta, Vito, editor^Aff4

Superior Title: Methods of Mathematical Oncology : Fusion of Mathematics and Biology, Osaka, Japan, October 26–28, 2020. 370:173-192

Authors: Villa, Chiara¹ (AUTHOR) cv23@st-andrews.ac.uk, Gerisch, Alf² (AUTHOR), Chaplain, Mark A.J.¹ (AUTHOR)

Superior Title: Journal of Theoretical Biology. Feb2022, Vol. 534, pN.PAG-N.PAG. 1p.

Subject Terms: *PARTIAL differential equations, *NEOVASCULARIZATION, *PROGENITOR cells, *CHEMOTAXIS, *ENDOTHELIAL cells, *NUMERICAL solutions to differential equations

Authors: Villa, Chiara

Contributors: Chaplain, Mark, Lorenzi, Tommaso, University of St Andrews. School of Mathematics and Statistics

Subject Terms: Mathematical modelling, Partial differential equations, Mathematical biology, Cancer, Vasculogenesis, Pattern formation, Adaptive dynamics, Hamilton-Jacobi formalism, Linear stability analysis, Numerical simulation

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Relation: Villa, C., Chaplain, M. A. J., & Lorenzi, T. (2020). Evolutionary dynamics in vascularised tumours under chemotherapy: mathematical modelling, asymptotic analysis and numerical simulations. Vietnam Journal of Mathematics, First Online. https://doi.org/10.1007/s10013-020-00445-9 [http://hdl.handle.net/10023/20767 : Open Access version]; Villa, C., Chaplain, M. A., & Lorenzi, T. (2021). Modeling the emergence of phenotypic heterogeneity in vascularized tumors. SIAM Journal on Applied Mathematics, 81(2), 434-453. https://doi.org/10.1137/19M1293971 [http://hdl.handle.net/10023/24165 : Open Access version]; Villa, C., Gerisch, A., & Chaplain, M. A. J. (2021). A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis. Journal of Theoretical Biology, In Press, [110963]. https://doi.org/10.1016/j.jtbi.2021.110963 [http://hdl.handle.net/10023/26476 : Open Access version]; Villa, C., Chaplain, M. A. J., Gerisch, A., & Lorenzi, T. (2021). Mechanical models of pattern and form in biological tissues: the role of stress-strain constitutive equations. Bulletin of Mathematical Biology, 83, [80]. https://doi.org/10.1007/s11538-021-00912-5 [http://hdl.handle.net/10023/23254 : Open Access version]; http://hdl.handle.net/10023/20767; http://hdl.handle.net/10023/24165; http://hdl.handle.net/10023/26476; http://hdl.handle.net/10023/23254; https://doi.org/10.17630/sta/616

Availability: https://doi.org/10.17630/sta/616