Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties

Cancer Informatics

Volumn 7, Issue , 2009, Pages 239-251

  Stamatakos, Georgios S ^a   Dionysiou, Dimitra D ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Cancer multiscale modeling; Computer models; Hypermatrix; In silico oncology; Oncosimulator; Operator notation; Radiobiology; Tumour growth; Tumour response to treatment

Indexed keywords

ALGORITHM; ARTICLE; CANCER RADIOTHERAPY; COMPUTER PROGRAM; MATHEMATICAL MODEL; SIMULATION; TREATMENT RESPONSE; TUMOR GROWTH; ANIMAL EXPERIMENT; ANIMAL MODEL; CANCER MODEL; CANCER SURGERY; COMPUTER MODEL; HEART; MATHEMATICS; NONHUMAN; RADIOBIOLOGY; RADIOTHERAPY; RELIABILITY;

EID: 77649251042     PISSN: 11769351     EISSN: 11769351     Source Type: Journal    
DOI: 10.4137/cin.s2712     Document Type: Article

References (47)

1. Kansal AR, Torquato S, Harsh GR, Chiocca EA, Deisboeck TS. Simulated brain tumour growth dynamics using a three-dimensional cellular automaton. J Theor Biol. 2000a;203:367-82.
2. Kansal AR, Torquato S, Harsh IV, Chiocca EA, Deisboeck TS. Cellular automaton of idealized brain tumour growth dynamics. BioSystems. 2000b;55:119-27.
3. Kraus M, Wolf B. Emergence of self-organization in tumour cells: relevance for diagnosis and therapy. Tumour Biol. 1993;14:338-53.
4. Jones B, Dale RG. Mathematical models of tumour and normal tissue response. Acta Oncol. 1999;38:883-93.
5. Duechting W, Ginsberg T, Ulmer W. Modelling of radiogenic responses induced by fractionated irradiation in malignant and normal tissue. Stem Cells. 1995;13(S1):301-6.
6. Kocher M, Treuer H. Reoxygenation of hypoxic cells by tumour shrinkage during irradiation. A computer simulation. Strahlentherapie und Onkologie. 1995;171:219-30.
7. Kocher M, Treuer H, Voges J, Hoevels M, Sturm V, Mueller RP. Computer simulation of cytotoxic and vascular effects of radiosurgery in solid and necrotic brain metastases, Radiother Oncol. 2000;54:149-56.
8. Swanson KR, Alvord Jr EC, Murray JD. Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br J Cancer. 2002;86:14-8.
9. Swanson KR, Bridge C, Murray JD, Alvord Jr EC. Virtual and real brain tumors: using mathematical modelling to quantify glioma growth and invasion. J Neurol Sci. 2003;216:1-10.
10. Mandonnet E, Delattre JY, Tanguy ML, Swanson KR, Carpentier AF, Duffau H, et al. Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann Neurol. 2003;53:524-8.
11. Byrne H, Matthews P. Assymetric growth of avascular solid tumours: exploiting symmetries. IMA J Mathematics Applied in Medicine and Biology. 2002;19:1-29.
12. Alarcon T, Byrne HM, Maini PK. A cellular automaton model for tumour growth in inhomogeneous environment. J Theor Biol. 2003;225:257-74.
13. Alarcon T, Byrne HM, Maini PK. Towards whole-organ modelling of tumour growth. Prog Biophys Mol Biol. 2004a;85:451-72.
14. Alarcon T, Byrne HM, Maini PK. A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells. J Theor Biol. 2004b; 229:395-411.
15. Wise SM, Lowengrub JS, Frieboes HB, Cristini V. Three-dimensional multispecies nonlinear tumor growth - I Model and numerical method. J Theor Biol. 2008;253:524-43.
16. Deisboeck TS, Zhang L, Yoon J, Costa J. In silico cancer modeling: is it ready for prime time? Nat Clin Pract Oncol. 2009;6:34-42.
17. Stamatakos G, Dionysiou D, Nikita K, Zamboglou N, Baltas D, Pissakas G, et al. In vivo tumour growth and response to radiation therapy: a novel algorithmic description. Int J Radiat Oncol Biol Phys. 2001;51 Suppl 1:240.
18. Stamatakos GS, Dionysiou DD, Zacharaki EI, Mouravliansky NA, Nikita K, Uzunoglu N. In silico radiation oncology: combining novel simulation algorithms with current visualization techniques. Proc. IEEE 2002;90, (11):1764-77.
19. Stamatakos GS, Antipas VP, Uzunoglu NK, Dale RG. A four dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density. Brit J Radiology. 2006a;79:389-400.
20. Stamatakos GS, Antipas VP, Uzunoglu NK. Simulating chemotherapeutic schemes in the individualized treatment context: The paradigm of glioblastoma multiforme treated by temozolomide in vivo. Comput Biol Med. 2006b;36:1216-34.
21. Stamatakos GS, Antipas VP, Uzunoglu NK. A spatiotemporal, patient individualized simulation model of solid tumor response to chemotherapy in vivo: the paradigm of glioblastoma multiforme treated by temozolomide. IEEE Trans Biomed Engineering. 2006c;53:(8):1467-77.
22. Stamatakos GS. Towards a collaborative formulation of the Mathematical Principles of Natural Philosophy: Living Matter. The paradigm of In Silico Oncology. DIMACS Workshop on Computational Tumor Modeling, DIMACS Center, Rutgers University, Piscataway, NJ, USA. 2006d. http://dimacs.rutgers. edu/Workshops/TumorModeling/abstracts.html.
23. Dionysiou DD, Stamatakos GS, Uzunoglu NK, Nikita KS, Marioli A. A four-dimensional simulation model of tumour response to radiotherapy in vivo: parametric validation considering radiosensitivity, genetic profile and fractionation. J Theor Biol. 2004;230:1-20.
24. Dionysiou DD, Stamatakos GS, Uzunoglu NK, Nikita KS. A computer simulation of in vivo tumour growth and response to radiotherapy: New algorithms and parametric results. Computers in Biology and Medicine. 2006;36:448-64
25. Dionysiou DD, Stamatakos GS, Gintides D, Uzunoglu N, Kyriaki K. Critical Parameters Determining Standard Radiotherapy Treatment Outcome for Glioblastoma Multiforme: A Computer Simulation. The Open Biomedical Engineering Journal. 2008;2:43-51.
26. Dionysiou DD, Stamatakos GS. Applying a 4D multiscale in vivo tumor growth model to the exploration of radiotherapy scheduling: the effects of weekend treatment gaps and p53 gene status on the response of fast growing solid tumors. Cancer Informatics. 2006;2:113-21.
27. Stamatakos GS, Uzunoglu N. Computer Simulation of Tumour Response to Therapy. Cancer Bioinformatics: from therapy design to treatment. Edited by Sylvia Nagl. John Wiley & Sons, Ltd., Chichester, UK. 2006.
28. Kolokotroni EA, Stamatakos GS, Dionysiou DD, Georgiadi E Ch, Desmedt Ch, Graf NM. Translating Multiscale Cancer Models into Clinical Trials: Simulating Breast Cancer Tumor Dynamics within the Framework of the "Trial of Principle" Clinical Trial and the ACGT Project. Proc. 8th IEEE International Conference on Bioinformatics and Bioengineering (BIBE 2008), Athens, Greece, 2008 Oct 8-10. IEEE Catalog Number: CFP08266, ISBN: 978-1-4244-2845-8, Library of Congress: 2008907441, Paper No. BE-2.1.1, length: 8 pages (in electronic format). 2008.
29. Georgiadi E Ch, Stamatakos GS, Graf NM, et al. Multilevel Cancer Modeling in the Clinical Environment: Simulating the Behavior of Wilms Tumor in the Context of the SIOP 2001/GPOH Clinical Trial and the ACGT Project. Proc. 8th IEEE International Conference on Bioinformatics and Bioengineering (BIBE 2008), Athens, Greece, 2008 Oct 8-10. IEEE Catalog Number: CFP08266, ISBN: 978-1-4244-2845-8, Library of Congress: 2008907441, Paper No. BE-2.1.2, length: 8 pages (in electronic format). 2008.
30. Eves H. Foundations and Fundamental Concepts of Mathematics. Third Edition. Dover, Mineola, US. 1990.
31. Schiff LI. Quantum Mechanics. Third Edition. McGraw Hill Kogakusha, Tokyo. 1981. pp. 148-86.
32. Morse PM, Feshbach H. Methods of Theoretical Physics. Mc Graw-Hill, New York. 1953.
33. Miller GA. Groups which are the products of two permutable proper subgroups. PNAS. 1935;21:469-72.
34. Werner-Wasik M, Scott CB, Nelson DF, et al. Final report of a phase I/II trial of hyperfractionated and accelerated hyperfractionated radiation therapy with carmustine for adults with supratentorial malignant gliomas. Cancer. 1996;77:1535-43.
35. Haas-Kogan DA, Yount G, Haas M, et al; p53-dependent G1 arrest and p53 independent apoptosis influence the radiobiologic response of glioblastoma. Int J Radiat Oncol Biol Phys. 1996;36:95-103.
36. Tribius S, Pidel A, Casper D. ATM protein expression correlates with radioresistance in primary glioblastoma cells in culture. Int J Radiat Oncol Biol Phys. 2001;50:511-23.
37. Katzung BG, (Ed.). Basic and Clinical Pharmacology, 8th ed, New York: McGraw-Hill/Lange Medical Books. 2001.
38. Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62:679-94.
39. Steel G. (Ed.). Basic Clinical Radiobiology. Arnold, London, UK. 2002.
40. Dillehay LE. A model of cell killing by low-dose-rate radiation including repair of sublethal damage, G2 block, and cell division. Rad Res. 1990;124:201-7.
41. Hegedues B, Czirok A, Fazekas I, Babel T, Madarasz E, Viscsek T. Locomotion and proliferation of glioblastoma cells in vitro: statistical evaluation of videomicroscopic observations. J Neurosurgery. 2000;92:428-34.
42. Duechting W, Ulmer W, Lehrig R, Ginsberg T, Dedeleit E. Computer simulation and modelling of tumour spheroid growth and their relevance for optimization of fractionated radiotherapy. Strahlenther Onkol. 1992;168:354-60.
43. Huang P, Allam A, Perez L, Taghian A, Freeman J, Suit H. The effect of combining recombinant human tumor necrosis factor-alpha with local radiation on tumor control probability of a human glioblastoma multiforme xenograft in nude mice. Int J Radiat Oncol Biol Phys. 1995;32(1):93-8.
44. Nakajima M, Nakasu S, Morikawa S, Inubushi T. Estimation of volume doubling time and cell loss in an experimental rat glioma model in vivo. Acta Neurochir. 1998;140:607-13.
45. Perez C, Brady L, (Eds.). Principles and Practice of Radiation Oncology. Philadelphia: Lippincott-Raven. 1998.
46. Antipas VP, Stamatakos GS, Uzunoglu NK. A patient-specific in vivo tumor and normal tissue model for prediction of the response to radiotherapy: a computer simulation approach. Methods Inf Med. 2007;46:367-75.
47. Stamatakos GS, Dionysiou DD, Graf NM, et al. The Oncosimulator: a multilevel, clinically oriented simulation system of tumor growth and organism response to therapeutic schemes. Towards the clinical evaluation of in silico oncology. Proceedings of the 29th Annual International Conference of the IEEE EMBS Cite Internationale, August 23-26, SuB07.1: 6628-6631, Lyon, France. 2007.