Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan Toward understanding the boundary propagation speeds in tumor growth models. (English) Zbl 1472.35404 SIAM J. Appl. Math. 81, No. 3, 1052-1076 (2021). MSC: 35Q92 35K55 35B25 35B40 35C07 76D27 76S05 76M20 92C50 92C37 35R35 PDFBibTeX XMLCite \textit{J.-G. Liu} et al., SIAM J. Appl. Math. 81, No. 3, 1052--1076 (2021; Zbl 1472.35404) Full Text: DOI arXiv
Perrillat-Mercerot, Angélique; Miranville, Alain; Bourmeyster, Nicolas; Guillevin, Carole; Naudin, Mathieu; Guillevin, Rémy What mathematical models can or cannot do in glioma description and understanding. (English) Zbl 1451.92104 Discrete Contin. Dyn. Syst., Ser. S 13, No. 8, 2165-2193 (2020). MSC: 92C32 92C55 92C50 35Q92 PDFBibTeX XMLCite \textit{A. Perrillat-Mercerot} et al., Discrete Contin. Dyn. Syst., Ser. S 13, No. 8, 2165--2193 (2020; Zbl 1451.92104) Full Text: DOI
Michel, T.; Fehrenbach, J.; Lobjois, V.; Laurent, J.; Gomes, A.; Colin, T.; Poignard, Clair Mathematical modeling of the proliferation gradient in multicellular tumor spheroids. (English) Zbl 1406.92059 J. Theor. Biol. 458, 133-147 (2018). MSC: 92C15 92C37 35Q92 PDFBibTeX XMLCite \textit{T. Michel} et al., J. Theor. Biol. 458, 133--147 (2018; Zbl 1406.92059) Full Text: DOI HAL
Ilieş, Iulian; Sipahi, Rifat; Zupanc, Günther K. H. Growth of adult spinal cord in knifefish: development and parametrization of a distributed model. (English) Zbl 1394.92018 J. Theor. Biol. 437, 101-114 (2018). MSC: 92C15 35K57 PDFBibTeX XMLCite \textit{I. Ilieş} et al., J. Theor. Biol. 437, 101--114 (2018; Zbl 1394.92018) Full Text: DOI
Viger, Louise; Denis, Fabrice; Draghi, Clément; Ménard, Thibault; Letellier, Christophe Spatial avascular growth of tumor in a homogeneous environment. (English) Zbl 1368.92090 J. Theor. Biol. 416, 99-112 (2017). MSC: 92C50 PDFBibTeX XMLCite \textit{L. Viger} et al., J. Theor. Biol. 416, 99--112 (2017; Zbl 1368.92090) Full Text: DOI
Al-Mamun, Mohammed A.; Brown, Louise J.; Hossain, M. A.; Fall, Charles; Wagstaff, L.; Bass, Rosemary A hybrid computational model for the effects of maspin on cancer cell dynamics. (English) Zbl 1411.92077 J. Theor. Biol. 337, 150-160 (2013). MSC: 92C37 68Q80 PDFBibTeX XMLCite \textit{M. A. Al-Mamun} et al., J. Theor. Biol. 337, 150--160 (2013; Zbl 1411.92077) Full Text: DOI
Sciumè, G.; Gray, W. G.; Ferrari, M.; Decuzzi, P.; Schrefler, Bernard A. On computational modeling in tumor growth. (English) Zbl 1349.92013 Arch. Comput. Methods Eng. 20, No. 4, 327-352 (2013). MSC: 92-08 92C50 92C30 92C37 PDFBibTeX XMLCite \textit{G. Sciumè} et al., Arch. Comput. Methods Eng. 20, No. 4, 327--352 (2013; Zbl 1349.92013) Full Text: DOI
André, N.; Barbolosi, D.; Billy, F.; Chapuisat, G.; Hubert, F.; Grenier, E.; Rovini, A. Mathematical model of cancer growth controled by metronomic chemotherapies. (English. French summary) Zbl 1336.92035 ESAIM, Proc. 41, 77-94 (2013). MSC: 92C50 PDFBibTeX XMLCite \textit{N. André} et al., ESAIM, Proc. 41, 77--94 (2013; Zbl 1336.92035) Full Text: DOI
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît Composite waves for a cell population system modeling tumor growth and invasion. (English) Zbl 1346.92017 Chin. Ann. Math., Ser. B 34, No. 2, 295-318 (2013). MSC: 92C10 35J60 35K57 74J30 35C07 PDFBibTeX XMLCite \textit{M. Tang} et al., Chin. Ann. Math., Ser. B 34, No. 2, 295--318 (2013; Zbl 1346.92017) Full Text: DOI
Tosin, Andrea Initial/boundary-value problems of tumor growth within a host tissue. (English) Zbl 1259.35212 J. Math. Biol. 66, No. 1-2, 163-202 (2013). MSC: 35Q92 35B45 92B05 35K51 35K65 PDFBibTeX XMLCite \textit{A. Tosin}, J. Math. Biol. 66, No. 1--2, 163--202 (2013; Zbl 1259.35212) Full Text: DOI arXiv
Chatelain, Clément; Ciarletta, Pasquale; Ben Amar, Martine Morphological changes in early melanoma development: influence of nutrients, growth inhibitors and cell-adhesion mechanisms. (English) Zbl 1397.92318 J. Theor. Biol. 290, 46-59 (2011). MSC: 92C50 92C15 35Q92 92C17 PDFBibTeX XMLCite \textit{C. Chatelain} et al., J. Theor. Biol. 290, 46--59 (2011; Zbl 1397.92318) Full Text: DOI HAL
Escher, Joachim; Matioc, Anca-Voichita Bifurcation analysis for a free boundary problem modeling tumor growth. (English) Zbl 1231.35319 Arch. Math. 97, No. 1, 79-90 (2011). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35R35 35B32 35Q92 92C50 PDFBibTeX XMLCite \textit{J. Escher} and \textit{A.-V. Matioc}, Arch. Math. 97, No. 1, 79--90 (2011; Zbl 1231.35319) Full Text: DOI arXiv
D’onofrio, Alberto; Cerrai, Paola A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy. (English) Zbl 1165.92308 Math. Comput. Modelling 49, No. 5-6, 1156-1163 (2009). MSC: 92C50 PDFBibTeX XMLCite \textit{A. D'onofrio} and \textit{P. Cerrai}, Math. Comput. Modelling 49, No. 5--6, 1156--1163 (2009; Zbl 1165.92308) Full Text: DOI
Pindera, Maciej Z.; Ding, Hui; Chen, Zhijian Convected element method for simulation of angiogenesis. (English) Zbl 1194.92044 J. Math. Biol. 57, No. 4, 467-495 (2008). MSC: 92C50 35K57 62M99 92C15 65C20 35Q92 65N99 PDFBibTeX XMLCite \textit{M. Z. Pindera} et al., J. Math. Biol. 57, No. 4, 467--495 (2008; Zbl 1194.92044) Full Text: DOI
Saadatmandi, Abbas; Dehghan, Mehdi Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method. (English) Zbl 1151.92017 Commun. Numer. Methods Eng. 24, No. 11, 1467-1474 (2008). MSC: 92C50 65C20 35K20 35K15 35Q92 PDFBibTeX XMLCite \textit{A. Saadatmandi} and \textit{M. Dehghan}, Commun. Numer. Methods Eng. 24, No. 11, 1467--1474 (2008; Zbl 1151.92017) Full Text: DOI
Panovska, Jasmina; Byrne, Helen M.; Maini, Philip K. A theoretical study of the response of vascular tumours to different types of chemotherapy. (English) Zbl 1148.92020 Math. Comput. Modelling 47, No. 5-6, 560-579 (2008). MSC: 92C50 35K50 35Q92 92C37 35K57 65C20 PDFBibTeX XMLCite \textit{J. Panovska} et al., Math. Comput. Modelling 47, No. 5--6, 560--579 (2008; Zbl 1148.92020) Full Text: DOI
Fasano, A.; Bertuzzi, A.; Gandolfi, A. Mathematical modelling of tumour growth and treatment. (English) Zbl 1387.92050 Quarteroni, Alfio (ed.) et al., Complex systems in biomedicine. Milano: Springer (ISBN 978-88-470-0394-1/hbk). 71-108 (2006). MSC: 92C50 PDFBibTeX XMLCite \textit{A. Fasano} et al., in: Complex systems in biomedicine. Milano: Springer. 71--108 (2006; Zbl 1387.92050) Full Text: DOI
Foryś, U.; Mokwa-Borkowska, A. Solid tumour growth analysis of necrotic core formation. (English) Zbl 1080.92039 Math. Comput. Modelling 42, No. 5-6, 593-600 (2005). MSC: 92C50 65C20 PDFBibTeX XMLCite \textit{U. Foryś} and \textit{A. Mokwa-Borkowska}, Math. Comput. Modelling 42, No. 5--6, 593--600 (2005; Zbl 1080.92039) Full Text: DOI
Kolev, M.; Kozłowska, E.; Lachowicz, M. A mathematical model for single cell cancer– immune system dynamics. (English) Zbl 1085.92019 Math. Comput. Modelling 41, No. 10, 1083-1095 (2005). MSC: 92C50 45K05 37N25 PDFBibTeX XMLCite \textit{M. Kolev} et al., Math. Comput. Modelling 41, No. 10, 1083--1095 (2005; Zbl 1085.92019) Full Text: DOI
Kolev, M. A mathematical model of cellular immune response to leukemia. (English) Zbl 1080.92042 Math. Comput. Modelling 41, No. 10, 1071-1081 (2005). MSC: 92C50 45K05 65C20 PDFBibTeX XMLCite \textit{M. Kolev}, Math. Comput. Modelling 41, No. 10, 1071--1081 (2005; Zbl 1080.92042) Full Text: DOI
Pamuk, Serdal Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source. (English) Zbl 1072.92027 Math. Biosci. 189, No. 1, 21-38 (2004). MSC: 92C50 35Q92 65C20 PDFBibTeX XMLCite \textit{S. Pamuk}, Math. Biosci. 189, No. 1, 21--38 (2004; Zbl 1072.92027) Full Text: DOI
d’Ónofrio, Alberto; Gandolfi, Alberto Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). (English) Zbl 1050.92039 Math. Biosci. 191, No. 2, 159-184 (2004). MSC: 92C50 37N25 34C60 34D23 34D05 PDFBibTeX XMLCite \textit{A. d'Ónofrio} and \textit{A. Gandolfi}, Math. Biosci. 191, No. 2, 159--184 (2004; Zbl 1050.92039) Full Text: DOI
Bellomo, N.; Bellouquid, A.; De Angelis, E. The modelling of the immune competition by generalized kinetic (Boltzmann) models: Review and research perspectives. (English) Zbl 1022.92012 Math. Comput. Modelling 37, No. 1-2, 65-86 (2003). MSC: 92C50 35Q92 92C30 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Math. Comput. Modelling 37, No. 1--2, 65--86 (2003; Zbl 1022.92012) Full Text: DOI
Ambrosi, D.; Preziosi, L. On the closure of mass balance models for tumor growth. (English) Zbl 1016.92016 Math. Models Methods Appl. Sci. 12, No. 5, 737-754 (2002). MSC: 92C50 92C10 74F20 74L15 PDFBibTeX XMLCite \textit{D. Ambrosi} and \textit{L. Preziosi}, Math. Models Methods Appl. Sci. 12, No. 5, 737--754 (2002; Zbl 1016.92016) Full Text: DOI
Primicerio, M.; Talamucci, F. Discrete and continuous compartmental models of cellular populations. (English) Zbl 1016.92009 Math. Models Methods Appl. Sci. 12, No. 5, 649-663 (2002). MSC: 92C37 37N25 47G20 34K60 PDFBibTeX XMLCite \textit{M. Primicerio} and \textit{F. Talamucci}, Math. Models Methods Appl. Sci. 12, No. 5, 649--663 (2002; Zbl 1016.92009) Full Text: DOI
D’Acunto, B.; De Angelis, M. A phase-change problem for an extended heat conduction model. (English) Zbl 1002.80014 Math. Comput. Modelling 35, No. 7-8, 709-717 (2002). MSC: 80A22 35K10 35R35 PDFBibTeX XMLCite \textit{B. D'Acunto} and \textit{M. De Angelis}, Math. Comput. Modelling 35, No. 7--8, 709--717 (2002; Zbl 1002.80014) Full Text: DOI
Delitala, M. Critical analysis and perspectives on kinetic (cellular) theory of immune competition. (English) Zbl 1003.92019 Math. Comput. Modelling 35, No. 1-2, 63-75 (2002). MSC: 92C50 92C37 37N25 45K05 PDFBibTeX XMLCite \textit{M. Delitala}, Math. Comput. Modelling 35, No. 1--2, 63--75 (2002; Zbl 1003.92019) Full Text: DOI
De Angelis, Elena; Mesin, L. Modelling of the immune response: Conceptual frameworks and applications. (English) Zbl 1013.92016 Math. Models Methods Appl. Sci. 11, No. 9, 1609-1630 (2001). MSC: 92C37 92C50 92C30 PDFBibTeX XMLCite \textit{E. De Angelis} and \textit{L. Mesin}, Math. Models Methods Appl. Sci. 11, No. 9, 1609--1630 (2001; Zbl 1013.92016) Full Text: DOI
Bellomo, N.; Preziosi, L. Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. (English) Zbl 0997.92020 Math. Comput. Modelling 32, No. 3-4, 413-452 (2000). MSC: 92C50 35Q92 PDFBibTeX XMLCite \textit{N. Bellomo} and \textit{L. Preziosi}, Math. Comput. Modelling 32, No. 3--4, 413--452 (2000; Zbl 0997.92020) Full Text: DOI