Math. Model. Nat. Phenom.
Volume 15, 2020
Reviews in mathematical modelling
Article Number 21
Number of page(s) 12
Published online 12 March 2020
  1. Z. Agur, M. Elishmereni and Y. Kheifetz, Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration. Wiley Interdiscip. Rev. Syst. Biol. Med. 6 (2014) 239–253. [CrossRef] [PubMed] [Google Scholar]
  2. J.C.L. Alfonso, K. Talkenberger, M. Seifert, B. Klink, A. Hawkins-Daarud, K.R. Swanson, H. Hatzikirou and A. Deutsch, The biology and mathematical modelling of glioma invasion: a review. J. Roy. Soc. Interface 14 (2017) 20170490. [CrossRef] [PubMed] [Google Scholar]
  3. P.M. Altrock, L.L. Liu and F. Michor, The mathematics of cancer: integrating quantitative models. Nat. Rev. Cancer 15 (2015) 730–745. [Google Scholar]
  4. V. Andasari, R.T. Roper, M.H. Swat and M.A.J. Chaplain, Integrating intracellular dynamics using compucell3d and bionetsolver: applications to multiscale modelling of cancer cell growth and invasion. PLOS ONE 7 (2012) 1–17. [Google Scholar]
  5. A.R.A. Anderson and P.K. Maini, Mathematical oncology. Bull. Math. Biol. 80 (2018) 945–953. [Google Scholar]
  6. A.L. Baldock, R.C. Rockne, A.D. Boone, M.L. Neal, A. Hawkins-Daarud, D.M. Corwin, C.A. Bridge, L.A. Guyman, A.D. Trister, M.M. Mrugala, J.K. Rockhill and K.R. Swanson, From patient-specific mathematical neuro-oncology to precision medicine. Front. Oncol. 3 (2013) 62. [CrossRef] [PubMed] [Google Scholar]
  7. A. Ballesta and J. Clairambault, Physiologically based mathematical models to optimize therapies against metastatic colorectal cancer: a mini-review. Curr. Pharmaceut. Des. 20 (2014) 37–48. [CrossRef] [Google Scholar]
  8. A. Ballesta, Q. Zhou, X. Zhang, H. Lv and J.M. Gallo, Multiscale design of cell-type specific pharmacokinetic/ pharmacodynamic models for personalized medicine: application to temozolomide in brain tumors. CPT Pharmacometr. Syst. Pharmacol. 3 (2014) e112. [CrossRef] [Google Scholar]
  9. A. Ballesta, P.F. Innominato, R. Dallmann, D.A. Rand and F.A. Levi, Systems chronotherapeutics. Pharmacolog. Rev. 69 (2017) 161–199. [CrossRef] [PubMed] [Google Scholar]
  10. P. Ballet, SimCells, an advanced software for multicellular modeling: application to tumoral and blood vessel co-development, Working paper (unpublished) (2018). [Google Scholar]
  11. D. Barbolosi, J. Ciccolini, B. Lacarelle, F. Barlési and N. André, Computational oncology-mathematical modelling of drug regimens for precision medicine. Nat. Rev. Clin. Oncol. 13 (2016) 242–254. [Google Scholar]
  12. D. Basanta and A.R.A. Anderson, Homeostasis back and forth: an ecoevolutionary perspective of cancer. Cold Spring Harbor Perspect. Med. 7 (2017) a028332. [CrossRef] [Google Scholar]
  13. B. Bedessem and S. Ruphy, Smt or toft? How the two main theories of carcinogenesis are made (artificially) incompatible. Acta Biotheor. 63 (2015) 257–267. [CrossRef] [PubMed] [Google Scholar]
  14. B. Bedessem and S. Ruphy, Smt and toft integrable after all: a reply to bizzarri and cucina. Acta Biotheor. 65 (2017) 81–85. [CrossRef] [PubMed] [Google Scholar]
  15. M. Bizzarri and A. Cucina, Smt and toft: why and how they are opposite and incompatible paradigms. Acta Biotheor. 64 (2016) 221–239. [CrossRef] [PubMed] [Google Scholar]
  16. M. Block, Physiologically based pharmacokinetic and pharmacodynamic modeling in cancer drug development: status, potential and gaps. Exp. Opin. Drug Metab. Toxicol. 11 (2015) 743–756. [CrossRef] [Google Scholar]
  17. A. Bouchnita, N. Eymard, T.K. Moyo, M.J. Koury and V. Volpert, Bone marrow infiltration by multiple myeloma causes anemia by reversible disruption of erythropoiesis. Am. J. Hematol. 91 (2016) 371–378. [CrossRef] [PubMed] [Google Scholar]
  18. A. Bouchnita, F.-E. Belmati, R. Aboulaich, M.J. Koury and V. Volpert, A hybrid computation model to describe the progression of multiple myeloma and its intra-clonal heterogeneity. Computation 5 (2017) 16. [CrossRef] [Google Scholar]
  19. S. Brueningk, G. Powathil, P. Ziegenhein, J. Ljaz, I. Rivens, S. Nill, M. Chaplain, U. Oelfke and G. Ter Haar Combining radiation with hyperthermia: a multiscale model informed by in vitro experiments. J. Roy. Soc. Interface 15 (2018) 20170681. [CrossRef] [Google Scholar]
  20. F. Caraguel, A.C. Lesart, F. Estève, B. van der Sanden and A. Stéphanou, Towards the design of a patient-specific virtual tumour. Comput. Math. Methods Med. 2016 (2016) 7851789. [CrossRef] [PubMed] [Google Scholar]
  21. L. Carrara, S.M. Lavezzi, E. Borella, G. De Nicolao, P. Magni and I. Poggesi, Current mathematical models for cancer drug discovery. Exp. Opin. Drug Discov. 12 (2017) 785–799. [Google Scholar]
  22. M.A.J. Chaplain, The mathematical modelling of tumour angiogenesis and invasion. Acta Biotheor. 43 (1995) 387–402. [CrossRef] [PubMed] [Google Scholar]
  23. T. Colin, F. Cornelis, J. Jouganous, M. Martin and O. Saut, Patient specific image driven evaluation of the aggressiveness of metastases to the lung. Med. Image Comput. Comput. Assist Interv. 17 (2014) 553–560. [PubMed] [Google Scholar]
  24. L.M. Cook, A. Araujo, J.M. Pow-Sang, M.M. Budzevich, D. Basanta and C.C. Lynch, Predictive computational modeling to define effective treatment strategies for bone metastatic prostate cancer. Sci. Rep. 6 (2016) 29384. [CrossRef] [PubMed] [Google Scholar]
  25. C. Davis, H. Naci, E. Gurpinar, E. Poplavska and A. Pinto, Availability of evidence of benefits on overall survival and quality of life of cancer drugs approved by European medicines agency: retrospective cohort study of drug approvals 2009–13. BMJ 359 (2017) j4530. [Google Scholar]
  26. H. Enderling and K.A. Rejniak, Simulating cancer: computational models in oncology. Front. Oncol. 3 (2013) 233. [PubMed] [Google Scholar]
  27. E.W. Esch, A. Bahinski and D. Huh, Organs-on-chips at the frontiers of drug discovery. Nat. Rev. Drug Discov. 14 (2015) 248–260. [PubMed] [Google Scholar]
  28. N. Eymard, V. Volpert, P. Kurbatova, V. Volpert, N. Bessonov, K. Ogungbenro, L. Aarons, P. Janiaud, P. Nony, A. Bajard, S. Chabaud, Y. Bertrand, B. Kassai, C. Cornu, P. Nony and CRESim project group, Mathematical model of t-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients. Math. Med. Biol. 35 (2018) 25–47. [Google Scholar]
  29. J. Foo and F. Michor, Evolution of acquired resistance to anti-cancer therapy. J. Theor. Biol. 355 (2014) 10–20. [CrossRef] [PubMed] [Google Scholar]
  30. J.A. Gallaher, P.M. Enriquez-Navas, K.A. Luddy, R.A. Gatenby and A.R.A. Anderson, Spatial heterogeneity and evolutionary dynamics modulate time to recurrence in continuous and adaptive cancer therapies. Cancer Res. 78 (2018) 2127–2139. [Google Scholar]
  31. E. Garralda, R. Dienstmann and J. Tabernero, Pharmacokinetic/pharmacodynamic modeling for drug development in oncology. Am. Soc. Clin. Oncol. Annu. Meet. 37 (2017) 210–215. [Google Scholar]
  32. P. Gerlee and A.R.A. Anderson, Evolution of cell motility in an individual-based model of tumour growth. J. Theor. Biol. 259 (2009) 67–83. [CrossRef] [PubMed] [Google Scholar]
  33. A. Ghaffarizadeh, R. Heiland, S.H. Friedman, S.M. Mumenthaler and P. Macklin, PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput. Biol. 14 (2018) e1005991. [Google Scholar]
  34. N. Glade and A. Stéphanou, Le vivant discret et continu – Modes de représentation en biologie théorique. Editions Matériologiques, Paris (2013). [Google Scholar]
  35. F. Graner and J.A. Glazier, Simulation of biological cell sorting using a two-dimensional extended potts model. Phys. Rev. Lett. 69 (1992) 2013–2016. [CrossRef] [PubMed] [Google Scholar]
  36. J.A. Grogan, A.J. Connor, B. Markelc, R.J. Muschel, P.K. Maini, H.M Byrne and J. Pitt-Francis, Microvessel chaste: an open library for spatial modeling of vascularized tissue. Biophys. J. 112 (2017) 1767–1772. [CrossRef] [PubMed] [Google Scholar]
  37. S. Hamis, P. Nithiarasu and G.G. Powathil, What does not kill a tumour may make it stronger: in silico insights into chemotherapeutic drug resistance. J. Theor. Biol. 454 (2018) 253–267. [CrossRef] [PubMed] [Google Scholar]
  38. L. Hutchinson and R. Kirk, High drug attrition rates: where are we going wrong? Nat. Rev. Clin. Oncol. 8 (2011) 189–190. [Google Scholar]
  39. P.R. Jackson, J. Juliano, A. Hawkins-Daarud, R.C. Rockne and K.R. Swanson, Patient-specific mathematical neuro-oncology: using a simple proliferation and invasion tumor model to inform clinical practice. Bull. Math. Biol. 77 (2015) 846–856. [Google Scholar]
  40. A.M. Jarrett, E.A.B.F. Lima, D.A. Hormuth, M.T. McKenna, X. Feng, D.A. Ekrut, A.C.M. Resende, A. Brock and T.E. Yankeelov, Mathematical models of tumor cell proliferation: a review of the literature. Exp. Rev. Anticancer Therapy (2018) 1–16. [Google Scholar]
  41. Z. Ji, K. Yan, W. Li, H. Hu and X. Zhu, Mathematical and computational modeling in complex biological systems. BioMed Res. Int. 2017 (2017) 5958321. [Google Scholar]
  42. A. Karolak, D.A. Markov, L.J. McCawley and K.A. Rejniak, Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues. J. Roy. Soc. Interface 15 (2018) 20170703. [CrossRef] [Google Scholar]
  43. Y. Kim, G. Powathil, H. Kang, D. Trucu, H. Kim, S. Lawler and M. Chaplain, Strategies of eradicating glioma cells: a multi-scale mathematical model with mir-451-ampk-mtor control. PLoS ONE 10 (2015) e0114370j. [Google Scholar]
  44. I. Kola and J. Landis, Can the pharmaceutical industry reduce the attrition rates? Nat. Rev. Drug Discov. 3 (2004) 711–715. [CrossRef] [PubMed] [Google Scholar]
  45. N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlović and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models. PLOS ONE 5 (2010) 1–8. [Google Scholar]
  46. P. Kurbatova, S. Bernard, N. Bessonov, F. Crauste, I. Denim, C. Dumontet, S. Fischer and V. Volpert, Hybrid model of erythtropoiesis and leukemia treatment with cytosine arabinoside. SIAM J. Appl. Math. 71 (2011) 2246–2268. [Google Scholar]
  47. A.K. Laird, Dynamics of tumor growth. Br. J. Cancer 13 (1964) 490–502. [CrossRef] [PubMed] [Google Scholar]
  48. A.C. Lesart, B. van der Sanden, L. Hamard, F. Estève and A. Stéphanou, On the importance of the submicrovascular network in a computational model of tumour growth. Microvasc. Res. 84 (2012) 188–204. [Google Scholar]
  49. W.B. Looney, J.S. Trefil, J.C. Schaffner, C.J. Kovacs and H.A. Hopkins, Solid tumor models for the assessment of different treatment modalities: I. Radiation-induced changes in growth rate characteristics of a solid tumor model. Proc. Natl. Acad. Sci. U.S.A. 72 (1975) 2662–2666. [Google Scholar]
  50. P. Macklin, M.E. Edgerton, A.M. Thompson and V. Cristini, Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): from microscopic measurements to macroscopic predictions of clinical progression. J. Theor. Biol. 301 (2012) 122–140. [CrossRef] [PubMed] [Google Scholar]
  51. P. Macklin, H.B. Frieboes, J.L. Sparks, A. Ghaffarizadeh, S.H. Friedman, E.F. Juarez, E. Jonckheere and S.M. Mumenthaler, Progress towards computational 3-d multicellular systems biology. Adv. Exp. Med. Biol. 936 (2016) 225–246. [CrossRef] [PubMed] [Google Scholar]
  52. S.C. Massey, R.C. Rockne, A. Hawkins-Daarud, J. Gallaher, A.R.A. Anderson, P. Canoll and K.R. Swanson, Simulating PDGF-driven glioma growth and invasion in an anatomically accurate brain domain. Bull. Math. Biol. 80 (2018) 1292–1309. [Google Scholar]
  53. G.R. Mirams, C.J. Arthurs, M.O. Bernabeu, R. Bordas, J. Cooper, A. Corrias, Y. Davit, S.J. Dunn, A.G. Fletcher, D.G. Harvey, M.E. Marsh, J.M. Osborne, P. Pathmanathan, J. Pitt-Francis, J. Southern, N. Zemzemi and D.J. Gavaghan, Chaste: an open source c++ library for computational physiology and biology. PLOS Comput. Biol. 9 (2013) 1–8. [Google Scholar]
  54. M. Montévil and A. Pocheville, The hitchhiker’s guide to the cancer galaxy. How two critics missed their destination. Orgnisms. J. Biol. Sci. 1 (2017) 37–48. [Google Scholar]
  55. M.M. Palm, M.G. Dallinga, E. van Dijk, I. Klaassen, R.O. Schlingemann and R.M.H. Merks, Computational screening of tip and stalk cell behavior proposes a role for apelin signaling in sprout progression. PLOS ONE 11 (2016) 1–31. [Google Scholar]
  56. A.R. Perestrelo, A.C.P. Águas, A. Rainer and G. Forte, Microfluidic organ/body-on-a-chip devices at the convergence of biology and microengineering. Sensors (Basel, Switzerland) 15 (2015) 31142–31170. [CrossRef] [PubMed] [Google Scholar]
  57. R.K. Perez, R. Kang, R. Chen, J.G. Castellanos, A.R. Milewski and A.R. Perez, Computational oncology. J. Oncopathol. Clin. Res. 2 (2018). [Google Scholar]
  58. J. Pitt-Francis, P. Pathmanathan, M.O. Bernabeu, R. Bordas, J. Cooper, A.G. Fletcher, G.R. Mirams, P. Murray, J.M. Osborne, A. Walter, S.J. Chapman, A. Garny, I.M.M. van Leeuwen, P.K. Maini, B. Rodriguez, S.L. Waters, J.P. Whiteley, H.M. Byrne and D.J. Gavaghan, Chaste: a test-driven approach to software development for biological modelling. Comp. Phys. Commun. 180 (2009) 2452–2471. [CrossRef] [Google Scholar]
  59. J. Poleszczuk, R. Walker, E.G. Moros, K. Latifi, J.J. Caudell and H. Enderling, Predicting patient-specific radiotherapy protocols based on mathematical model choice for proliferation saturation index. Bull. Math. Biol. 80 (2018) 1195–1206. [Google Scholar]
  60. M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov and A. Stéphanou, A computational framework to assess the efficacy of cytotoxic molecules and vascular disrupting agents against solid tumours. MMNP 7 (2012) 49–77. [Google Scholar]
  61. G.G. Powathil, M. Swat and M.A.J. Chaplain, Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling. Semin. Cancer Biol. 30 (2015) 13–20. [CrossRef] [PubMed] [Google Scholar]
  62. G.G. Powathil, A.J. Munro, M.A.J. Chaplain and M. Swat, Bystander effects and their implications for clinical radiation therapy: insights from multiscale in silico experiments. J. Theor. Biol. 401 (2016) 1–14. [CrossRef] [PubMed] [Google Scholar]
  63. S. Prokopiou, E.G. Moros, J. Poleszczuk, J. Caudell, J.F. Torres-Roca, K. Latifi, J.K. Lee, R. Myerson, L.B. Harrison and H. Enderling, A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation. Radiat. Oncol. 10 (2015) 159. [CrossRef] [PubMed] [Google Scholar]
  64. C. Sonnenschein and A.M. Soto, Carcinogenesis explained within the context of a theory of organisms. Progr. Biophys. Molec. Biol. 122 (2016) 70–76. [CrossRef] [Google Scholar]
  65. A.M. Soto and C. Sonnenschein, The tissue organization field theory of cancer: a testable replacement for the somatic mutation theory. BioEssays 33 (2011) 332–340. [CrossRef] [PubMed] [Google Scholar]
  66. A. Stéphanou and V. Volpert, Hybrid modelling in biology: a classification review. MMNP 11 (2016) 37–48. [EDP Sciences] [Google Scholar]
  67. A. Stéphanou, S.R. McDougall, A.R.A. Anderson and M.A.J. Chaplain, Mathematical modelling of flow in 2d and 3d vascular networks: applications to antiangiogenic and chemotherapeutic drug stategies. Math. Comp. Model. 41 (2005) 1137–1156. [CrossRef] [Google Scholar]
  68. A. Stéphanou, A.C. Lesart, J. Deverchère, A. Juhem, A. Popov and F. Estève, How tumour-induced vascular changes alter angiogenesis: Insights from a computational model. J. Theor. Biol. 419 (2017) 211–226. [CrossRef] [PubMed] [Google Scholar]
  69. A. Stéphanou, E. Fanchon, P.F. Innominato and A. Ballesta, Systems biology, systems medicine, systems pharmacology: the what and the why. Acta Biotheor. 66 (2018) 345–365. [CrossRef] [PubMed] [Google Scholar]
  70. M.H. Swat, G.L. Thomas, J.M. Belmonte, A. Shirinifard, D. Hmeljak and J.A. Glazier, Multi-scale modeling of tissues using compucell3d. In Vol. 110 of Computational Methods in Cell Biology. Edited by Anand R. Asthagiri and Adam P. Arkin. Academic Press (2012) 325–366. [CrossRef] [Google Scholar]
  71. I.M.M. Van Leeuwen, G.R. Mirams, A. Walter, A. Fletcher, P. Murray, J. Osborne, S. Varma, S.J. Young, J. Cooper, B. Doyle, J. Pitt-Francis, L. Momtahan, P. Pathmanathan, J.P. Whiteley, S.J. Chapman, D.J. Gavaghan, O.E. Jensen, J.R. King, P.K. Maini, S.L. Waters and H.M. Byrne, An integrative computational model for intestinal tissue renewal. Cell Proliferation 42 (2009) 617–636. [CrossRef] [PubMed] [Google Scholar]
  72. C.H. Wang, J.K. Rockhill, M. Mrugala, D.L. Peacock, A. Lai, K. Jusenius, J.M. Wardlaw, T. Cloughesy, A.M. Spence, R. Rockne, E.C. Alvord Jr. and K.R. Swanson, Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. Cancer Res. 69 (2009) 9133–9140. [Google Scholar]
  73. K.K. Winner, M.P. Steinkamp, R.J. Lee, M. Swat, C.Y. Muller, M.E. Moses, Y. Jiang and B.S. Wilson, Spatial modeling of drug delivery routes for treatment of disseminated ovarian cancer. Cancer Res. 76 (2016) 1320–1334. [Google Scholar]
  74. T.E. Yankeelov, Integrating imaging data into predictive biomathematical and biophysical models of cancer. ISRN Biomath. 2012 (2012). [Google Scholar]
  75. T.E. Yankeelov, R.G. Abramson and C.C. Quarles, Quantitative multimodality imaging in cancer research and therapy. Nat. Rev. Clin. Oncol. 11 (2014) 670–680. [Google Scholar]
  76. T.E. Yankeelov, G. An, O. Saut, E.G. Luebeck, A.S. Popel, B. Ribba, P. Vicini, X. Zhou, J.A. Weis, K. Ye and G.M. Genin, Multi-scale modeling in clinical oncology: opportunities and barriers to success. Ann. Biomed. Eng. 44 (2016) 2626–2641. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.