Arakelyan, L., Vainstein, V., Agur, Z., A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth. Angiogenesis 5:3 (2002), 203–214, 10.1023/a:1023841921971.
Adam, J.A., Nicola, B., A Survey of Models for Tumor–Immune System Dynamics. 2012, Modeling and Simulation in Science, Engineering and Technology, Birkhaüser.
Alfonso, J.C.L., Jagiella, N., Nunez, L., Herrero, M.A., Drasdo, D., Estimating dose painting effects in radiotherapy: a mathematical model. PLoS One, 9(2), 2014, e89380, 10.1371/journal.pone.0089380.
Altrock, P.M., Liu, L.L., Michor, F., The mathematics of cancer: integrating quantitative models. Nat. Rev. Cancer 15:12 (2015), 730–745, 10.1038/nrc4029.
Anderson, A.R.A., Chaplain, M.A.J., Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60 (1998), 857–899, 10.1006/bulm.1998.0042.
Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C., Thompson, A.M., Mathematical modelling of tumour invasion and metastasis. J. Theor. Med. 2 (2000), 129–154, 10.1080/10273660008833042.
Anderson, A.R.A., A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math. Med. Biol. 22:2 (2005), 163–186, 10.1093/imammb/dqi005.
Araujo, R.P., McElwain, D.L., A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol. 66:5 (2004), 1039–1091, 10.1016/j.bulm.2003.11.002.
Araujo, A., Cook, L.M., Lynch, C.C., Basanta, D., Size Matters: Metastatic cluster size and stromal recruitment in the establishment of successful prostate cancer to bone metastases. Bull. Math. Biol. 80 (2018), 1046–1058, 10.1007/s11538-018-0416-4.
ASME V&V 40, Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices. 2018 https://www.asme.org/codes-standards/find-codes-standards/v-v-40-assessing-credibility-computational-modeling-verification-validation-application-medical-devices.
Athale, C.A., Mansury, Y., Deisboeck, T.S., Simulating the impact of a molecular “decision-process” on cellular phenotype and multicellular patterns in brain tumors. J. Theor. Biol. 223 (2005), 469–481, 10.1016/j.jtbi.2004.10.019.
Athale, C.A., Deisboeck, T.S., The effects of EGF-receptor density on multiscale tumor growth patterns. J. Theor. Biol. 238:4 (2006), 771–779, 10.1016/j.jtbi.2005.06.029.
Balding, D., McElwain, D.L.S., A mathematical model of tumour-induced capillary growth. J. Theor. Biol. 114:1 (1985), 53–73, 10.1016/S0022-5193(85)80255-1.
Balkwill, F.R., Capasso, M., Hagemann, T., The tumor microenvironment at a glance. J. Cell. Sci. 125 (2012), 5591–5596, 10.1242/jcs.116392.
Baratchart, E., A Quantitative Study of the Metastatic Process through Mathematical Modeling. 2016, Computation [stat.CO], Université de Bordeaux.
Bauer, A.L., Jackson, T.L., Jiangy, Y., A cell-based model exhibiting branching and Anastomosis during tumor-induced angiogenesis. Biophys. J. 92 (2007), 3105–3121, 10.1529/biophysj.106.101501.
Behinaein, B., Rudie, K., Sangrar, W., Petri net siphon analysis and graph theoretic measures for identifying combination therapies in cancer. IEEEACM Trans. Comput. Biol. Bioinform. 15:1 (2018), 231–243, 10.1109/TCBB.2016.2614301.
Belfatto, A., Jereczek-Fossa, B.A., Baroni, G., Cerveri, P., Model-supported radiotherapy personalization: in silico test of hyper- and hypo-fractionation effects. Front. Physiol., 9, 2018, 1445, 10.3389/fphys.2018.01445.
Bellomo, N., Preziosi, L., Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comput. Model. 32:3–4 (2000), 413–452, 10.1016/S0895-7177(00)00143-6.
Benecchi, L., Neuro-fuzzy system for prostate cancer diagnosis. Urology 68:2 (2006), 357–361, 10.1016/j.urology.2006.03.003.
Bentley, K., Franco, C.A., Philippides, A., Blanco, R., Dierkes, M., Gebala, V., Gerhardt, H., The role of differential VE-cadherin dynamics in cell rearrangement during angiogenesis. Nat. Cell Biol. 16:4 (2014), 309–321, 10.1038/ncb2926.
Benzekry, S., Lamont, C., Beheshti, A., Tracz, A., Ebos, J.M.L., Hlatky, L., Hahnfeldt, P., “Classical mathematical models for description and prediction of experimental tumor growth. PLoS Comput. Biol., 10(8), 2014, e1003800, 10.1371/journal.pcbi.1003800.
Benzekry, S., Tracz, A., Mastri, M., Corbelli, R., Barbolosi, D., Ebos, J.M., Modeling spontaneous metastasis following surgery: an in vivo-in silico approach. Cancer Res. 76:3 (2016), 535–547, 10.1158/0008-5472.CAN-15-1389.
Brady, R., Enderling, H., Mathematical models of Cancer: when to predict novel therapies, and when not to. Bull. Math. Biol. 81 (2019), 3722–3731, 10.1007/s11538-019-00640-x.
Breward, C.J.W., Byrne, H.M., Lewis, C.E., The role of cell–cell interactions in a two-phase model for avascular tumour growth. J. Math. Biol. 45 (2002), 125–152, 10.1007/s002850200149.
Byrne, H.M., The effect of time delays on the dynamics of avascular tumor growth. Math. Biosci. 144 (1997), 83–117, 10.1016/S0025-5564(97)00023-0.
Byrne, H.M., A weakly nonlinear analysis of a model of avascular solid tumour growth. J. Math. Biol. 39 (1999), 59–89, 10.1007/s002850050163.
Byrne, H.M., Matthews, P., Asymmetric growth of models of avascular solid tumors: exploiting symmetries. IMA J. Math. Appl. Med. Biol. 19:1 (2002), 1–29, 10.1093/imammb/19.1.1.
Byrne, H.M., The importance of intercellular adhesion in the development of carcinomas. IMA J. Math. Appl. Med. Biol. 14:4 (1997), 305–323, 10.1093/imammb/14.4.305.
Byrne, H.M., Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Model. 24:12 (1997), 1–17, 10.1016/S0895-7177(96)00174-4.
Cancer Core Europe, Data Sharing Via Connected IT Systems. https://www.cancercoreeurope.eu/data-sharing.
Carlier, A., Vasilevich, A., Marechal, M., de Boer, R., Geris, L., In silico clinical trials for pediatric orphan diseases. Sci. Rep., 8, 2018, 2465, 10.1038/s41598-018-20737-y.
Chamseddine, B.M., Rejniak, K.A., Hybrid Modeling Frameworks of Tumor Development and Treatment. 2019, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 10.1002/wsbm.1461.
Chaplain, M.A.J., Stuart, A.M., A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. Math. Med. Biol. 10:3 (1993), 149–168, 10.1093/imammb/10.3.149.
Chaplain, M.A.J., Mathematical modelling of angiogenesis. J. Neurooncol. 50 (2000), 37–51, 10.1023/A:1006446020377.
Chaplain, M.A.J., Avascular growth, angiogenesis and vascular growth in solid tumours: the mathematical modelling of the stages of tumour development. Mathl. Comput. Modelling 23 (1996), 47–87, 10.1016/0895-7177(96)00019-2.
Cooper, A.K., Kim, P.S., A cellular automata and a partial diff; erential equation model of tumor–immune dynamics and chemotaxis. Eladdadi, A., Kim, P., Mallet, D., (eds.) Mathematical Modeling of Tumor–Immune System Dynamics, 2014, Springer Proceedings in Mathematics and Statistics, Springer, 21–46 107.
Crespo, I., Coukos, G., Doucey, M.-A., Xenarios, I., Modelling approaches to discovery in the tumor microenvironment. Journal of Cancer Immunology Therapy 1:1 (2018), 23–37.
Cristini, V., Lowengrub, J., Nie, Q., Nonlinear simulation of tumor growth. J. Math. Biol. 46 (2003), 191–224, 10.1007/s00285-002-0174-6.
Dagogo-Jack, I., Shaw, A., Tumour heterogeneity and resistance to cancer therapies. Nat. Rev. Clin. Oncol. 15:2 (2018), 81–94, 10.1038/nrclinonc.2017.166.
DeBerardinis, R.J., Chandel, N.S., Fundamentals of cancer metabolism. Sci. Adv., 2(5), 2016, e1600200, 10.1126/sciadv.1600200.
de Pillis, L.G., Radunskaya, A.E., A mathematical model of immune response to tumor invasion. Computational Fluid and Solid Mechanics, 2003, 1661–1668, 10.1016/B978-008044046-0.50404-8.
de Pillis, L.G., Radunskaya, A.E., Wiseman, C.L., A validated mathematical model of cell-mediated immune response to tumour growth. Cancer Res. 65:17 (2005), 7950–7958, 10.1158/0008-5472.CAN-05-0564.
de Pillis, L.G., Gu, W., Radunskaya, A.E., Mixed immunotherapy and chemotherapy of tumours modeling, applications and biological interpretations. J. Theor. Biol. 238:4 (2006), 841–862, 10.1016/j.jtbi.2005.06.037.
de Pillis, L.G., Fister, K.R., Gu, W., Collins, C., Daub, M., Gross, D., Mooree, J., Preskill, B., Mathematical model creation for cancer chemo-immunotherapy. Comput. Math. Methods Med. 10:3 (2009), 165–184, 10.1080/17486700802216301.
de Pillis, L.G., Eladdadi, A., Radunskaya, A.E., Modeling cancer-immune responses to therapy. J. Pharmacokinet. Pharmacodyn. 41:5 (2014), 461–478, 10.1007/s10928-014-9386-9.
Dingli, D., Michor, F., Antal, T., Pacheco, J.M., The emergence of tumor metastases. Cancer Biol. Ther. 6:3 (2007), 383–390, 10.4161/cbt.6.3.3720.
Dogra, P., Butner, J.D., Chuang, Y., Caserta, S., Goel, S., Brinker, C.J., Cristini, V., Wang, Z., Mathematical modeling in cancer nanomedicine: a review. Biomed. Microdevices, 21, 2019, 40, 10.1007/s10544-019-0380-2.
Dritschel, H., Waters, S.L., Roller, A., Byrne, H.M., A mathematical model of cytotoxic and helper T cell interactions in a tumour microenvironment. Lett. Biomath. 5:sup1 (2018), S36–S68, 10.1080/23737867.2018.1465863.
Dudek, A., Gupta, K., Ramakrishnan, S., Mukhopadhyay, D., Tumor angiogenesis. J. Oncol., ID761671, 2010, 10.1155/2010/761671.
Edelman, L.B., Eddy, J.A., Price, N.D., In silico models of cancer. WIREs Systems Biology and Medicine 2:4 (2010), 438–459, 10.1002/wsbm.75.
Eftimie, R., Bramson, J.L., Earn, D.J.D., Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73:1 (2011), 2–32, 10.1007/s11538-010-9526-3.
Eladdadi, A., Kim, P., Mallet, D., Mathematical Modeling of Tumor–Immune System Dynamics. 2014, Springer Proceedings in Mathematics and Statistics, Springer 107.
Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Munro, A.J., Vaidya, J.S., Mathematical modelling of radiotherapy strategies for early breast cancer. J. Theor. Biol. 241:1 (2006), 158–171, 10.1016/j.jtbi.2005.11.015.
Enderling, H., Chaplain, M.A.J., Anderson, A.R.A., Vaidya, J.S., A mathematical model of breast condecancer development, local treatment and recurrence. J. Theor. Biol., 246(2), 2007, 10.1016/j.jtbi.2006.12.010 pp. 21, 245-21259.
EOSC, European Open Science Cloud. 2020, European Commission accessed 23/01/2020 https://ec.europa.eu/research/openscience/index.cfm?pg=open-science-cloud.
Ferreira, S.C. Jr, Martins, M.L., Vilela, M.J., Reaction-diffusion model for the growth of avascular tumor. Physical Review E covering statistical, nonlinear, biological, and soft matter physics, 65, 2002, 021907, 10.1103/PhysRevE.65.021907.
Franssen, L.C., Lorenzi, T., Burges, A.E.F., Chaplain, M.A.J., “A mathematical framework for modelling the metastatic spread of Cancer. Bull. Math. Biol. 81 (2018), 1965–2010, 10.1007/s11538-019-00597-x.
Friedman, A., Lolas, G., Analysis of a mathematical model of tumor lymphangiogenesis. Math. Model. Methods Appl. Sci. 15:1 (2005), 95–107, 10.1142/S0218202505003915.
Friedman, A., Hao, W., The role of exosomes in pancreatic Cancer microenvironment. Bull. Math. Biol. 80:5 (2018), 1111–1133, 10.1007/s11538-017-0254-9.
Gardner, S.N., Modeling multi-drug chemotherapy:tailoring treatment to individuals. J. Theor. Biol. 214 (2002), 181–207, 10.1006/jtbi.2001.2459.
Geris, L., Gomez-Cabrero, D., (eds.) Uncertainty in Biology: A Computational Modeling Approach, 2016, Studies in Mechanobiology, Tissue Engineering and Biomaterials, Springer.
Ghadiri, M., Heidari, M., Marashi, S.-M., Mousavi, S.H., A multiscale agent-based framework integrated with a constraint-based metabolic network model of cancer for simulating avascular tumor growth. Molecular BioSystem 13:9 (2017), 1888–1897, 10.1039/c7mb00050b.
Gombert, A.K., Nielsen, J., Mathematical modelling of metabolism. Current Opinion in Current Biotechnology 11:2 (2000), 180–186, 10.1016/S0958-1669(00)00079-3.
Gompertz, B., “XXIV. On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies”, (In a Letter to Francis Baily, Esq. F. R. S. & C, 115). 1825, Philosophical Transaction Royal Society, 10.1098/rstl.1825.0026.
Graner, F., Glazier, J.A., Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69:13 (1992), 785–790, 10.1103/PhysRevLett.69.2013.
Greenspan, H., Models for the growth of a solid tumor by diffusion. Stud. Appl. Math. 51 (1972), 317–340, 10.1002/sapm1972514317.
Greenspan, H., On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56:1 (1976), 229–242, 10.1016/s0022-5193(76)80054-9.
Hamis, S., Nithiarasu, P., Powathil, G.G., What does not kill a tumour may make it stronger: in silico insights into chemotherapeutic drug resistance. J. Theor. Biol. 454 (2018), 253–267, 10.1016/j.jtbi.2018.06.014.
Hanahan, D., Weinberg, R.A., The hallmarks of Cancer. Cell 100 (2000), 57–70, 10.1016/S0092-8674(00)81683-9.
Hanahan, D., Weinberg, R.A., The hallmarks of Cancer: the next generation. Cell 144:5 (2011), 647–674, 10.1016/j.cell.2011.02.013.
Hauth, J., Grey-Box Modelling for Nonlinear Systems. 2008, Dissertation im Fachbereich Mathematik der Technischen Universität Kaiserslautern.
Hénin, E., Meille, C., Barbolosi, D., et al. Revisiting dosing regimen using PK/PD modeling: the MODEL1 phase I/II trial of docetaxel plus epirubicin in metastatic breast cancer patients. Breast Cancer Research and Treatments 156 (2016), 331–341, 10.1007/s10549-016-3760-9.
Hinow, P., Gerlee, P., McCawley, L.J., Quaranta, V., Ciobanu, M., Wang, S., Graham, J.M., Ayati, B.P., Claridge, J., Swanson, K.R., Loveless, M., Anderson, A.R.A., A spatial model of tumor-host interaction: application of chemotherapy. Math. Biosci. Eng. 6:3 (2009), 521–546, 10.3934/mbe.2009.6.521.
Latest Global Cancer Data:Cancer Burden Rises to 18.1 Million New Cases and 9.6 Million Cancer Deaths in 2018. 2018, International Agency for Research on Cancer (World Health Organization) Press release n. 263, 12 september.
Iwata, K., Kawasaki, K., Shigesada, N., A dynamical model for the growth and size distribution of multiple metastatic tumors”. J. Theor. Biol. 203:2 (2000), 177–186, 10.1006/jtbi.2000.1075.
Isaeva, O.G., Osipov, V.A., Different strategies for cancer treatment: mathematical modelling. Comput. Math. Methods Med. 10:4 (2009), 253–272, 10.1080/17486700802536054.
Jackson, M., Marks, L., May, G.H.W., Wilson, J.B., The genetic basis of disease. Essays Biochem. 62 (2018), 643–723, 10.1042/EBC20170053.
Jarrett, A.M., Lima, E.A.B.F., Hormuth, D.A., McKenna, M.T., Feng, X., Ekrut, D.A., Resende, A.C.M., Brock, A., Yankeelov, T.E., Mathematical models of tumor cell proliferation: a review of the literature. Expert Rev. Anticancer Ther. 18:12 (2018), 1271–1286, 10.1080/14737140.2018.1527689.
Jean-Quartier, C., Jeanquartier, F., Jurisica, I., Holzinger, A., In silico cancer research towards 3R. BMC Cancer, 18, 2018, 408, 10.1186/s12885-018-4302-0.
Jiang, P., Sellers, W.R., Liu, X.S., Big data approaches for modeling resistance to Cancer drugs. Annu. Rev. Biomed. Data Sci. 1 (2018), 1–27, 10.1146/annurev-biodatasci-080917-013350.
Jones, A.F., Byrne, H.M., Gibson, J.S., Dold, J.W., Mathematical model for the stress induced during avascular tumor growth. J. Math. Biol. 40 (2000), 473–499, 10.1007/s002850000033.
Kather, J.N., Poleszczuk, J., Suarez-Carmona, M., et al. In silico modeling of immunotherapy and stroma-targeting therapies in human colorectal cancer. Cancer Res. 77 (2017), 6442–6452, 10.1158/0008-5472.CAN-17-2006.
Kempf, H., Bleicher, M., Meyer-Hermann, M., Spatio-temporal cell dynamics in tumour spheroid irradiation. Eur. Phys. J. 60 (2010), 177–193, 10.1140/epjd/e2010-00178-4.
Kiran, K.L., Lakshminarayanan, S., Optimization of chemotherapy and immunotherapy: in silico analysis using pharmacokinetic-pharmacodynamic and tumor growth models. J. Process Control 23:3 (2013), 396–403, 10.1016/j.jprocont.2012.12.006.
Komarova, N.L., Wodarz, D., Targeted Cancer Treatment In Silico: Small Molecules Inhibitors and Oncolytic Viruses. 2014, Modeling and Simulation in Science, Engineering and Technology, Birkhaüser.
Konstorum, A., Mathematical Modeling of Tumor-Microenvironment Dynamics. 2015, UC Irvine Electronic Theses and Dissertations.
Kovatchev, B.P., Breton, M., Man, C.D., Cobelli, C., In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes”. J. Diabetes Sci. Technol. 3:1 (2009), 44–55, 10.1177/193229680900300106.
Kozłowska, E., Färkkilä, A., Vallius, T., et al. Mathematical modeling predicts response to chemotherapy and drug combinations in ovarian Cancer. Cancer Res. 78:14 (2018), 4036–4044, 10.1158/0008-5472.CAN-17-3746.
Kuemmel, C., Yang, Y., Zhang, X., Florian, J., Zhu, H., Tegenge, M., Huang, S.M., Wang, Y., Morrison, T., Zineh, I., Consideration of a credibility assessment framework in model-informed drug development: potential application to physiologically-based pharmacokinetic modeling and simulation. CPT Pharmacometrics Syst. Pharmacol. 9:1 (2020), 21–28, 10.1002/psp4.12479.
Kunz, M., Jeromin, J., Fuchs, M., Christoph, J., Veronesi, G., Flentje, M., Nietzer, S., Dandekar, G., Dandekar, T., In silico signaling modeling to understand cancer pathways and treatment responses. Brief. Bioinformatics, bbz033, 2019, 10.1093/bib/bbz033.
Lamouille, S., Xu, J., Derynck, R., Molecular mechanisms of epithelial–mesenchymal transition. Nat. Rev. Mol. Cell Biol. 15:3 (2014), 178–196, 10.1038/nrm3758.
Lugano, R., Ramachandran, M., Dimberg, A., Tumor angiogenesis: causes, consequences, challenges and opportunities. Cell. Mol. Life Sci., 2019, 10.1007/s00018-019-03351-7.
Macklin, P., Lowengrub, J.S., Nonlinear simulation of the effect of microenvironment on tumor growth. J. Theor. Biol. 245:4 (2007), 677–704, 10.1016/j.jtbi.2006.12.004.
Magi, S., Iwamoto, K., Okada-Hatakeyama, M., Current status of mathematical modeling of cancer – from the viewpoint of cancer hallmarks. Curr. Opin. Syst. Biol. 2 (2017), 39–48, 10.1016/j.coisb.2017.02.008.
Mahasa, K.J., Ouifki, R., Eladdadi, A., de Pillis, L.G., Mathematical model of tumor–immune surveillance. J. Theor. Biol. 404 (2016), 312–330, 10.1016/j.jtbi.2016.06.012.
Mahlbacher, G.E., Reihmer, K.C., Frieboes, H.B., Mathematical modeling of tumor-immune cell interactions. J. Theor. Biol. 469 (2019), 47–60, 10.1016/j.jtbi.2019.03.002.
Malinzi, J., Mathematical analysis of a mathematical model of chemovirotherapy: effect of drug infusion method. Comput. Math. Methods Med., 2019, 10.1155/2019/7576591.
Mallet, D.G., De Pillis, L.G., A cellular automata model of tumor–immune system interactions. J. Theor. Biol. 239:3 (2006), 334–350, 10.1016/j.jtbi.2005.08.002.
Mansury, Y., Deisboeck, T.S., The impact of “search precision” in an agent-based tumor model. J. Theor. Biol. 224:3 (2003), 325–337, 10.1016/S0022-5193(03)00169-3.
Mansury, Y., Kimura, M., Lobo, J., Deisboeck, T.S., Emerging patterns in tumor systems: simulating the dynamics of multicellular clusters with an agent-based spatial agglomeration model. J. Theor. Biol. 219:3 (2002), 343–370, 10.1006/jtbi.2002.3131.
Mantzari, N.V., Webb, S., Othmer, H.G., Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol. 49 (2004), 111–187, 10.1007/s00285-003-0262-2.
Marcu, L.G., Marcu, D., In silico modelling of radiation effects towards personalised treatment in radiotherapy. IM17 Physics Conference AIP Conference Proceedings, 1916, 10.1063/1.5017440 040001-1–040001-040007, 2017.
Mardis, E.R., Insights from large-scale Cancer genome sequencing. Annu. Rev. Cancer Biol. 2 (2018), 429–444, 10.1146/annurev-cancerbio-050216-122035.
Markert, E.K., Vazquez, A., Mathematical models of cancer metabolism. Cancer Metab., 3, 2015, 14, 10.1186/s40170-015-0140-6.
Martínez-González, A., Calvo, G.F., Pérez Romasanta, L.A., Perez Garcia, V.M., Hypoxic cell waves around necrotic cores in glioblastoma: a biomathematical model and its therapeutic implications. Bull. Math. Biol. 74 (2012), 2875–2896, 10.1007/s11538-012-9786-1.
Mbeunkui, F., Johann, D.J. Jr., Cancer and the tumor microenvironment: a review of an essential relationship. Cancer Chemother. Pharmacol. 63:4 (2009), 571–582, 10.1007/s00280-008-0881-9.
McAneney, H., O'Rourke, S.F.C., Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy. Phys. Med. Biol., 52(4), 2007, 10.1088/0031-9155/52/4/012 1039.
McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A., Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol. 64 (2002), 673–702, 10.1006/bulm.2002.0293.
McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., “Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241:3 (2006), 564–589, 10.1016/j.jtbi.2005.12.022.
McKinney, S.M., Sieniek, M., Godbole, V., et al. International evaluation of an AI system for breast cancer screening. Nature 577:7788 (2020), 89–94, 10.1038/s41586-019-1799-6.
Meaney, C., Powathil, G.G., Yaromina, A., Dubois, L.J., Lambin, P., Kohandel, M., Role of hypoxia-activated prodrugs in combination with radiation therapy: an in silico approach”. Math. Biosci. Eng. 16:6 (2019), 6257–6273, 10.3934/mbe.2019312.
Medina, M.A., Mathematical modeling of Cancer metabolism. Crit. Rev. Oncol. Hematol. 124 (2018), 37–40, 10.1016/j.critrevonc.2018.02.004.
Metzcar, J., Wang, Y., Heiland, R., Macklin, P., A review of cell-based computational modeling in Cancer biology. Jco Clin. Cancer Inform. 3 (2019), 1–13, 10.1200/CCI.18.00069.
Michor, F., Nowak, M.A., Iwasa, Y., Stochastic dynamics of metastasis formation. J. Theor. Biol. 240:4 (2006), 521–530, 10.1016/j.jtbi.2005.10.021.
Moran, P.A.P., The Statistical Processes of Evolutionary Theory. 1962, Clarendon Press, Oxford.
Moreira, J., Deutsch, A., Cellular automaton models of tumor development: a critical review. Adv. Complex Syst. 5:2–3 (2002), 1–21, 10.1142/S0219525902000572.
Musuamba Tshinanu, F., Bursi, R., Manolis, E., Karlsson, K., Kulesza, A., Courcelles, E., Boissel, J.P., Lesage, L., Crozatier, C., Voisin, E., Rousseau, C., Marchal, T., Alessandrello, R., Geris, L., Verifying and Validating Quantitative Systems Pharmacology and in Silico Models in Drug Development: Current Needs, Gaps and Challenges. 2020, CPT Pharmacometrics and Systems Pharmacology.
Newton, P.K., Mason, J., Bethel, K., Bazhenova, L.A., Nieva, J., et al. A stochastic markov chain model to describe lung Cancer growth and metastasis. PLoS One, 7(4), 2012, e34637, 10.1371/journal.pone.0034637.g002.
Newton, P.K., Mason, J., Bethel, K., et al. Spreaders and sponges define metastasis in lung cancer: a Markov chain Monte Carlo mathematical model. Cancer Res. 73:9 (2013), 2760–2769, 10.1158/0008-5472.CAN-12-4488.
Niculescu, I., Textor, J., de Boer, R.J., Crawling and gliding: a computational model for shape-driven cell migration. PLoS Comput. Biol., 11(10), 2015, e1004280, 10.1371/journal.pcbi.1004280.
Nielsen, J., Systems biology of metabolism: a driver for developing personalized and precision medicine. Cell Metabolism Perspective 25:3 (2017), 572–579, 10.1016/j.cmet.2017.02.002.
Niida, A., Nagayama, S., Miyano, S., Mimori, K., Understanding intratumor heterogeneity by combining genome analysis and mathematical modeling. Wiley Cancer Science, 2018, 10.1111/cas.13510.
Nilsson, A., Nielsen, J., Genome scale metabolic modeling of cancer. Metab. Eng. 43 (2017), 103–112, 10.1016/j.ymben.2016.10.022 part B.
Norton, L., Simon, R., The Norton-Simon hypothesis revisited. Cancer Treat. Rep. 70 (1986), 163–169.
Norton, K.A., Gong, C., Jamalian, S., Popel, A.S., Multiscale agent-based and hybrid modeling of the tumor immune microenvironment. Processes (Basel), 7(1), 2019, 37, 10.3390/pr7010037.
Orme, M.E., Chaplain, M.A.J., Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. Math. Med. Biol. 14:3 (1997), 189–205, 10.1093/imammb/14.3.189.
Pamuk, S., A mathematical model for capillary formation and development in tumor angiogenesis: a review. Chemotherapy 52 (2006), 35–37, 10.1159/000090241.
Peirce, S.M., Computational and mathematical modeling of angiogenesis. Microcirculation 15:8 (2008), 739–751, 10.1080/1073968080222033.
Pappalardo, F., Russo, G., Tshinanu, F.M., Viceconti, M., In silico clinical trials: concepts and early adoptions. Brief Bioinform. 20:5 (2019), 1699–1708, 10.1093/bib/bby043.
Passini, E., Britton, O.J., Lu, H.R., Rohrbacher, J., Hermans, A.N., Gallacher, D.J., Greig, R.J.H., Bueno-Orovio, A., Rodriguez, B., Human in silico drug trials demonstrate higher accuracy than animal models in predicting clinical pro-arrhythmic cardiotoxicity. Front. Physiol., 8, 2017, 668, 10.3389/fphys.2017.00668.
Pathmanathan, P., Gray, R.A., Romero, V.J., Morrison, T.M., Applicability analysis of validation evidence for biomedical computational models. J. Verif. Valid. Uncertain. Quantif., 2(2), 2017, 021005, 10.1115/1.4037671.
Perez-Garcıa, V.M., Ayala-Hernandez, L.E., Belmonte-Beitia, J., Schucht, P., Murek, M., Raabe, A., et al. Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas. PLoS Comput. Biol., 15(7), 2019, e1006778, 10.1371/journal.pcbi.1006778.
Pérez-García, V.M., Bogdanska, M., Martínez-González, A., et al. Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications. Math. Med. Biol. 32:3 (2015), 307–329, 10.1093/imammb/dqu009.
Pérez Romasanta, L., Belmonte Beitia, J., Martínez González, A., Fernández Calvo, G., Pérez García, V.M., Mathematical model predicts response to radiotherapy of grade II gliomas. Rep. Pract. Oncol. Radiother., 18, 2013, S63, 10.1016/j.rpor.2013.03.732.
Pepper, M.S., Lolas, G., The lymphatic vascular system in lymphangiogenesis invasion and metastasis a mathematical approach. Selected Topics in Cancer Modeling, 2008, Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, 10.1007/978-0-8176-4713-1_10.
Perumpanani, A.J., Sherratt, J.A., Norbury, J., Byrne, H.M., Biological inferences from a mathematical model for malignant invasion. Invasion Metastasis 16 (1996), 209–221.
Perumpanani, A.J., Sherratt, J.A., Norbury, J., Byrne, H.M., A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion. Physica D 126:3–4 (1999), 145–159, 10.1016/S0167-2789(98)00272-3.
Pinho, S.T.R., Rodrigues, D.S., Mancera, P.F.A., A mathematical model of chemotherapy response to tumour growth. Can. Appl. Math. Q., 19, 2011, 4.
Powathil, G.G., Kohandel, M., Sivaloganathan, S., Oza, A., Milosevic, M., Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy. Phys. Med. Biol. 52:11 (2007), 3291–3306, 10.1088/0031-9155/52/11/023.
Powathil, G.G., Adamson, D.J.A., Chaplain, M.A.J., Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: clinical insights from a computational model. PLoS Comput. Biol., 9(7), 2013, e1003120, 10.1371/journal.pcbi.1003120.
Qutub, A.A., Gabhann, F.M., Karagiannis, E.D., Vempati, P., Popel, A.S., Multiscale Models of Angiogenesis: Integration of Molecular Mechanisms with Cell- and Organ-Level Models. IEEE Eng. Med. Biol. Mag. 28:2 (2009), 14–31, 10.1109/MEMB.2009.931791.
Ramis-Conde, I., Drasdo, D., Anderson, A.R.A., Chaplain, M.A.J., Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. Biophys. J. 95:1 (2008), 155–165, 10.1529/biophysj.107.114678.
Ramis-Conde, I., Chaplain, M.A.J., Anderson, A.R.A., Drasdo, D., Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis. Phys. Biol., 6(1), 2009, 016008, 10.1088/1478-3975/6/1/016008.
Rejniak, K.A., McCawley, K.J., Current trends in mathematical modeling of tumor–microenvironment interactions: a survey of tools and applications. Exp. Biol. Med. 235 (2010), 411–423, 10.1258/ebm.2009.009230.
Rejniak, K.A., Anderson, A.R.A., Hybrid models of tumor growth. WIREs Systems Biology and Medicine 3:1 (2011), 115–125, 10.1002/wsbm.102.
Resendis-Antonio, O., Gonzalez-Torres, C., Jaime-Munoz, G., Hernandez-Patino, C.E., Salgado-Muno, C.F., Modeling metabolism: a window toward a comprehensive interpretation of networks in cancer. Semin. Cancer Biol. 30 (2015), 79–87, 10.1016/j.semcancer.2014.04.003.
Ribba, B., Boetsch, C., Nayak, T., et al. Prediction of the optimal dosing regimen using a mathematical model of tumor uptake for immunocytokine-based Cancer immunotherapy. Clin. Cancer Res. 24:14 (2018), 3325–3333, 10.1158/1078-0432.CCR-17-2953.
Robertson-Tessi, M., El-Kareh, A., Goriely, A., A mathematical model of tumor-immune interactions. J. Theor. Biol. 294 (2012), 56–73, 10.1016/j.jtbi.2011.10.027.
Roy, M., Finley, S.D., Computational model predicts the effects of targeting cellular metabolism in pancreatic Cancer. Front. Physiol., 8, 2017, 217, 10.3389/fphys.2017.00217.
Sachs, R.K., Hahnfeld, P., Brenner, D.J., The link between low-let dose–response relations and the underlying kinetics of damage production/repair/misrepair. Int. J. Radiat. Biol. 72:4 (1997), 351–374, 10.1080/095530097143149.
Saidel, G.M., Liotta, L.A., Kleinerman, J., System dynamics of metastatic process from an implanted tumor. J. Theor. Biol. 56:2 (1976), 417–434, 10.1016/s0022-5193(76)80083-5.
San Lucas, F.A., Fowler, J., Chang, K., Kopetz, S., Vilar, E., Scheet, P., Cancer in silico drug discovery: a systems biology tool for identifying candidate drugs to target specific molecular tumor subtypes. Mol. Cancer Ther. 13:12 (2014), 3230–3324, 10.1158/1535-7163.MCT-14-0260.
Schuster, S., Boley, D., Moller, P., Stark, H., Kaleta, C., Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production. Biochem. Soc. Trans. 43:6 (2015), 1187–1194, 10.1042/BST20150153.
Scianna, M., Bell, C.G., Preziosi, L., A review of mathematical models for the formation of vascular networks. J. Theoretical Theory 333 (2013), 174–209, 10.1016/j.jtbi.2013.04.037.
Scott, J.G., Gerlee, P., Basanta, D., Fletcher, A.G., Maini, P.K., Anderson, A.R.A., Mathematical modeling of the metastatic process. Experimental Metastasis: Modeling and Analysis, 2013, 189–208, 10.1007/978-94-007-7835-1_9.
Scott, J.G., Fletcher, A.G., Maini, P.K., Anderson, A.R.A., Gerlee, P., A filter-flow perspective of haematogenous metastasis offers a non-genetic paradigm for personalised cancer therapy. Eur. J. Cancer 50:17 (2014), 3068–3075, 10.1016/j.ejca.2014.08.019.
Shahi, P.K., Pineda, I.F., Tumoral angiogenesis: review of the literature. Cancer Invest. 26:1 (2008), 104–108, 10.1080/07357900701662509.
Shamsi, M., Saghafan, M., Dejam, M., Sanati-Nezhad, A., Mathematical modeling of the function of warburg effect in tumor microenvironment. Sci. Rep., 8(1), 2018, 8903, 10.1038/s41598-018-27303-6.
Sherratt, J.A., Chaplain, M.A.J., A new mathematical model for avascular tumour growth. J. Math. Biol. 43 (2001), 291–312, 10.1007/s002850100088.
Skipper, H.E., Kinetics of mammary tumor cell growth and implications for treatment. Cancer 28 (1971), 1479–1499.
Stanta, G., Bonin, S., Overview on clinical relevance of intra-tumor heterogeneity. Front. Med. (Lausanne), 5, 2018, 85, 10.3389/fmed.2018.00085.
Stein, S., Zhao, R., Haeno, H., Vivanco, I., Michor, F., Mathematical modeling identifies optimum lapatinib dosing schedules for the treatment of glioblastoma patients. PLoS Comput Biology, 14(1), 2018, e1005924, 10.1371/journal.pcbi.1005924.
Steinway, S.N., Zañudo, J.G.T., Ding, W., Rountree, C.B., Feith, D.J., Loughran, T.P. Jr., Albert, R., Network modeling of TGFβ signaling in hepatocellular carcinoma epithelial-to-Mesenchymal transition reveals joint sonic hedgehog and wnt pathway activation. Cancer Res., 74(21), 2014, 10.1158/0008-5472.CAN-14-0225.
Stephanou, A., McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Mathematical modelling of flow in 2D and 3D vascular networks: applications to antiangiogenic and chemotherapeutic drug strategies. Math. Comput. Model. 41:10 (2005), 1137–1156, 10.1016/j.mcm.2005.05.008.
Stephanou, A., McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Mathematical modelling of the influence of blood rheological properties upon adaptive tumour-induced angiogenesis. Math. Comput. Model. 44:1–2 (2006), 96–123, 10.1016/j.mcm.2004.07.021.
Sun, X., Hu, B., Mathematical modeling and computational prediction of cancer drug resistance. Briefings in Bioinformics 19 (2018), 1382–1399, 10.1093/bib/bbx065.
Suzuki, T., Minerva, D., Nishiyama, K., Koshikawa, N., Chaplain, M.A.J., Study on the tumor-induced angiogenesis using mathematical models. Wiley Cancer Science 109:1 (2017), 15–23, 10.1111/cas.13395.
Swanson, K.R., Harpold, H.L., Peacock, D.L., et al. Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: a proof of principle. Clin. Oncol. (R Coll Radiol) 20:4 (2008), 301–308, 10.1016/j.clon.2008.01.006.
Swanson, K.R., Quantifying glioma cell growth and invasion in vitro. Mathematical and Computer Modeling 47:5–6 (2008), 638–648.
Swanson, K.R., Alvord, E.C., Murray, J.D., Dynamics of a model for brain tumors reveals a small window for therapeutic intervention. Discrete and Continuous Dynamical Systems-Series B. 4:1 (2004), 289–295.
Swanson, K.R., Bridge, C., Murray, J.D., Alvord, E.C. Jr, “Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216:1 (2003), 1–10, 10.1016/j.jns.2003.06.001.
Swanson, K.R., Jr Alvord, E.C., Murray, J.D., Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br. J. Cancer 86:1 (2002), 14–18, 10.1038/sj.bjc.6600021.
Swanson, K.R., Jr Alvord, E.C., Murray, J.D., “Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery. Acta Biotheor. 50:4 (2002), 223–237.
Szabo, A., Merks, R.M.H., Cellular Potts modeling of tumor growth, tumor invasion, and tumor evolution. Front. Oncol., 3, 2013, 87, 10.3389/fonc.2013.00087.
Tabassum, S., Binti Rosli, N., Binti Mazalan, M.S.A., Mathematical modeling of Cancer growth process: a review. J. Phys. Conf. Ser., 1366(1), 2019, 10.1088/1742-6596/1366/1/012018.
Traina, T.A., Theodoulou, M., Feigin, K., et al. Phase I study of a novel capecitabine schedule based on the Norton-Simon mathematical model in patients with metastatic breast cancer. J. Clin. Oncol. 26:11 (2008), 1797–1802, 10.1200/JCO.2007.13.8388.
Traina, T.A., Dugan, U., Higgins, B., et al. Optimizing chemotherapy dose and schedule by Norton-Simon mathematical modeling. Breast Dis. 31:1 (2010), 7–18, 10.3233/BD-2009-0290.
Usher, J.R., Some mathematical models for Cancer chemotherapy. Comput. Math. With Appl. 28:9 (1994), 73–80, 10.1016/0898-1221(94)00179-0.
Van Sint Jan, S., Geris, L., Modelling towards a more holistic medicine: the Virtual Physiological Human (VPH). Morphologie 103:343 (2019), 127–130, 10.1016/j.morpho.2019.10.044.
Vermolen, F.J., Particle methods to solve modelling problems in wound healing and tumor growth. Comput. Part. Mech. 2 (2015), 381–399, 10.1007/s40571-015-0055-6.
Vermolen, F.J., van der Meijden, R.P., van Es, M., et al. Towards a mathematical formalism for semi-stochastic cell-level computational modeling of tumor initiation. Ann. Biomed. Eng. 43 (2015), 1680–1694, 10.1007/s10439-015-1271-1.
Viceconti, M., Henney, A., Morley-Fletcher, E., In silico clinical trials: how computer simulation will transform the biomedical industry. Int. J. Clin. Trials 3:2 (2016), 37–46, 10.18203/2349-3259.ijct20161408.
Vilanova, G., Colominas, I., Gomez, H., A mathematical model of tumour angiogenesis: growth, regression and regrowth. J. R. Soc. Interface, 14, 2017, 20160918, 10.1098/rsif.2016.0918.
Vinay, D.S., et al. Immune evasion in cancer: mechanistic basis and therapeutic strategies. Semin. Cancer Biol. 35:Supplement (2015), S185–S198, 10.1016/j.semcancer.2015.03.004.
Von Bertalanffy, L., Quantitative laws in metabolism and growth. Q. Rev. Biol., 32(3), 1957.
Wang, S., Schättler, H., Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Math. Biosci. Eng., 13(6), 2016, 10.3934/mbe.2016040.
Warburg, O., On the origin of Cancer cells. Science 123:3191 (1956), 309–314, 10.1126/science.123.3191.309.
Werner, H.M., Mills, G.B., Ram, P.T., Cancer Systems Biology: a peek into the future of patient care?. Nat. Rev. Clin. Oncol. 11:3 (2014), 167–176, 10.1038/nrclinonc.2014.6.
West, G., Brown, J., Enquist, B., A general model for ontogenetic growth. Nature 413 (2001), 628–631, 10.1038/35098076.
Yin, A., Moes, D.J.A.R., van Hasselt, J.G.C., Swen, I.J., Guchelaar, H.-J., A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT Pharmacometrics Syst. Pharmacol. 8 (2019), 720–737, 10.1002/psp4.12450.
