EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 15 References
Cancer modelling
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Cancer modelling
Article Number 15
Number of page(s) 21
DOI https://doi.org/10.1051/mmnp/2022013
Published online 16 June 2022
  1. C. Bandt and B. Pompe, Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88 (2002) 174102. [CrossRef] [PubMed] [Google Scholar]
  2. D.A. Bratsun, D.V. Merkuriev, A.P. Zakharov and L.M. Pismen, Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue. J. Biol. Phys. 42 (2016) 107–132. [CrossRef] [PubMed] [Google Scholar]
  3. D.A. Bratsun, I.V. Krasnyakov and L.M. Pismen, Biomechanical modeling of invasive breast carcinoma under a dynamic change in cell phenotype: collective migration of large groups of cells. Biomech. Model. Mechanobiol. 19 (2020) 723–743. [CrossRef] [PubMed] [Google Scholar]
  4. A. Brazhe, Shearlet-based measures of entropy and complexity for two-dimensional patterns. Phys. Rev. E. 97 (2018) 061301. [CrossRef] [PubMed] [Google Scholar]
  5. P. Brodatz, Textures: A Photographic Album for Artists and Designers. Dover Publications, New York (1966). [Google Scholar]
  6. D. Chavey, Tilings by regular polygons - II: A catalog of tilings. Comput. Math. Appl. 17 (1989) 147–165. [CrossRef] [MathSciNet] [Google Scholar]
  7. C.A. Chung, T.H. Lin, S.D. Chen and H.I. Huang, Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs. J. Theor. Biol. 262 (2010) 267–278. [CrossRef] [Google Scholar]
  8. V. Cristini and J. Lowengrub, Multiscale Modeling of Cancer: an Integrated Experimental and Mathematical Modeling Approach. Cambridge University Press, Cambridge (2010). [Google Scholar]
  9. J.P. Crutchfield, Between order and chaos. Nat. Phys. 8 (2012) 17–24. [CrossRef] [Google Scholar]
  10. T.S. Deisboeck and G.S. Stamatakos, Multiscale Cancer Modeling. Chapman & Hall/CRC, Boca Raton (2011) [Google Scholar]
  11. E.V. Denisov, N.V. Litviakov, M.V. Zavyalova, V.M. Perelmuter, S.V. Vtorushin, M.M. Tsyganov, T.S. Gerashchenko, E.Yu. Garbukov, E.M. Slonimskaya and N.V. Cherdyntseva, Intratumoral morphological heterogeneity of breast cancer: neoadjuvant chemotherapy efficiency and multidrug resistance gene expression. Sci. Rep. 4 (2014) 4709. [Google Scholar]
  12. E. Denisov, T. Geraschenko, M. Zavyalova, N. Litviakov, M. Tsyganov, E. Kaigorodova, E. Slonimskaya, J. Kzhyshkowska, N. Cherdyntseva, V. Perelmuter, Invasive and drug resistant expression profile of different morphological structures of breast tumors. Neoplasma 62 (2015) 405–411. [CrossRef] [PubMed] [Google Scholar]
  13. D.L. Dexter, H.M. Kowalski, B.A. Blazar, Z. Fligiel, R. Vogel and G.H. Heppner, Heterogeneity of tumor cells from a single mouse mammary tumor. Cancer Res. 38 (1978) 3174–3181. [Google Scholar]
  14. D. Drasdo and M. Loeffler, Individual-based models to growth and folding in one-layered tissues: Intestinal crypts and early development. Nonlinear Anal. 47 (2001) 245–256. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Egeblad, E.S. Nakasone and Z. Werb, Tumors as organs: complex tissues that interface with the entire organism. Dev. Cell 18 (2010) 884–901. [CrossRef] [Google Scholar]
  16. R. Farhadifar, J.C. Roper, B. Aigouy, S. Eaton and F. Jülicher, The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr. Biol. 17 (2007) 2095–2104. [CrossRef] [Google Scholar]
  17. P. Friedl, J. Locker, E. Sahai and J.E. Segall, Classifying collective cancer cell invasion. Nat. Cell Biol. 14 (2012) 777–783. [CrossRef] [PubMed] [Google Scholar]
  18. T.S. Gerashchenko, M.V. Zavyalova, E.V. Denisov, N.V. Krakhmal, D.N. Pautova, N.V. Litviakov, S.V. Vtorushin, N.V. Cher-dyntseva and V.M. Perelmuter, Intratumoral morphological heterogeneity of breast cancer as an indicator of the metastatic potential and tumor chemosensitivity. Acta Nat. 9 (2017) 56–67. [CrossRef] [PubMed] [Google Scholar]
  19. C. Guillot and T. Lecuit, Mechanics of epithelial tissue homeostasis and morphogenesis. Science 340 (2013) 1185–1189. [CrossRef] [PubMed] [Google Scholar]
  20. K. Guo, D. Labate and W.-Q. Lim, Edge analysis and identification using the continuous shearlet transform. Appl. Comput. Harmon. Anal. 27 (2009) 24–46. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Hüauser and G. Steidl, Convex multiclass segmentation with shearlet regularization. Int. J. Comput. Math. 90 (2013) 62–81. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Hauser and G. Steidl, Fast finite shearlet transform: a tutorial. Available: http://arxiv.org/abs/1202.1773 (2014) [Google Scholar]
  23. L. He, L.R. Long, S. Antani and G.R. Thoma, Histology image analysis for carcinoma detection and grading. Comput. Methods Progr. Biomed. 107 (2012) 538–556. [CrossRef] [Google Scholar]
  24. G.H. Heppner, Tumor heterogeneity. Cancer Res. 44 (1984) 2259–2265. [Google Scholar]
  25. H. Honda, T. Nagai and M. Tanemura, Two different mechanisms of planar cell intercalation leading to tissue elongation. Dev. Dyn. 237 (2008) 1826–1836. [CrossRef] [Google Scholar]
  26. L.J. Kleinsmith, Principles of cancer biology. Pearson Benjamin Cummings (2006). [Google Scholar]
  27. Y.L. Klimontovich, Decrease in entropy in the process of self-organization. S-theorem. Sov. Tech. Phys. Lett. 9 (1983) 606–610. [Google Scholar]
  28. N.V. Krakhmal, M.V. Zavyalova, E.V. Denisov, S.V. Vtorushin and V.M. Perelmuter, Cancer invasion: patterns and mechanisms. Acta Nat. 7 (2015) 17–28. [CrossRef] [PubMed] [Google Scholar]
  29. I.V. Krasnyakov, D.A. Bratsun and L.M. Pismen, Mathematical modelling of epithelial tissue growth. Russ. J. Biomech. 24 (2020) 375–388. [Google Scholar]
  30. G. Kutyniok and D. Labate, Shearlets. Multiscale analysis for multivariate data. Birkhüauser Boston, Boston (2012). [Google Scholar]
  31. S. Lamouille, J. Xu and R. Derynck, Molecular mechanisms of epithelial-mesenchymal transition. Nat. Rev. Mol. Cell Biol. 15 (2014) 178–196. [CrossRef] [PubMed] [Google Scholar]
  32. J. Lober, F. Ziebert and I.S. Aranson, Collisions of deformable cells lead to collective migration. Sci. Rep. (2015) 9172. [CrossRef] [Google Scholar]
  33. R. Lopez-Ruiz, Y.L. Mancini and X. Calbet, A statistical measure of complexity. Phys. Lett. A. 209 (1995) 321–326. [CrossRef] [Google Scholar]
  34. J. Makki, Diversity of breast carcinoma: histological subtypes and clinical relevance. Clin. Med. Insights Pathol. 8 (2015) 23–31. [Google Scholar]
  35. L.M. Merlo, J.W. Pepper, B.J. Reid and C.C. Maley, Cancer as an evolutionary and ecological process. Nat. Rev. Cancer 6 (2006) 924–935. [Google Scholar]
  36. B.E. Miller, F.R. Miller and G.H. Heppner, Interactions between tumor subpopulations affecting their sensitivity to the antineoplastic agents cyclophosphamide and methotrexate. Cancer Res. 41 (1981) 4378–4381. [Google Scholar]
  37. I. Mizeva, V. Dremin, E. Potapova, E. Zherebtsov, I. Kozlov and A. Dunaev, Wavelet analysis of the temporal dynamics of the laser speckle contrast in human skin. IEEE Trans. Biomed. Eng. 67 (2020) 1882–2889. [Google Scholar]
  38. R. Polikar, A. Topalis, D. Green, J. Kounios and C.M. Clark, Comparative multiresolution wavelet analysis of ERP spectral bands using an ensemble of classifiers approach for early diagnosis of Alzheimer's disease. Comput. Biol. Med. 37 (2007) 542–558. [CrossRef] [Google Scholar]
  39. G.E. Powell and I.C. Percival, A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems. J. Phys. A: Math. Gen. 12 (1979) 2053–2071. [CrossRef] [Google Scholar]
  40. I. Prigogine and G. Nicolis, Self-Organization in Non-Equilibrium Systems. Wiley (1977). [Google Scholar]
  41. H.V. Ribeiro, L. Zunino, E.K. Lenzi, P.A. Santoro and R.S. Mendes, Complexity-entropy causality plane as a complexity measure for two-dimensional patterns. PLoS ONE 7 (2012) e40689. [CrossRef] [PubMed] [Google Scholar]
  42. O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Plastino and M.A. Fuentes, Distinguishing Noise from Chaos. Phys. Rev. Lett. 99 (2007) 154102. [CrossRef] [PubMed] [Google Scholar]
  43. I. Ruben, R.-R. Reinaldo, V.-R. Fernando et al., Tumor growth modelling by cellular automata. Math. Mech. Complex Syst. 5 (2017) 239–259. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Salm and L.M. Pismen, Chemical and mechanical signaling in epithelial spreading. Phys. Biol. 9 (2012) 026009. [CrossRef] [PubMed] [Google Scholar]
  45. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27 (1948) 379–423. [CrossRef] [Google Scholar]
  46. H.P. Sinn and H. Kreipe, A brief overview of the WHO classification of breast tumors, 4th edition, focusing on issues and updates from the 3rd edition. Breast Care 8 (2013) 149–154. [CrossRef] [PubMed] [Google Scholar]
  47. K-Y. Su and W-L. Lee, Fourier transform infrared spectroscopy as a cancer screening and diagnostic tool: a review and prospects. Cancers 12 (2020) 115. [CrossRef] [Google Scholar]
  48. D. Tabassum and K. Polyak, Tumorigenesis: it takes a village. Nat. Rev. Cancer 8 (2015) 473–483. [CrossRef] [PubMed] [Google Scholar]
  49. I. Viktorinova, L. Pismen, B. Aigouy and C. Dahmann, Modeling planar polarity of epithelia: the role of signal relay in collective cell polarization. J.R. Soc. Interface. 8 (2011) 1059–1063. [CrossRef] [PubMed] [Google Scholar]
  50. M. Zanin, L. Zunino, O.A. Rosso and D. Papo, Permutation entropy and its main biomedical and econophysics applications: a review. Entropy 14 (2012) 1553–1577. [CrossRef] [Google Scholar]
  51. L. Zunino and H.V. Ribeiro, Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane. Chaos Solitons Fract. 91 (2016) 679–688. [CrossRef] [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.