| [1] | Moding EJ, Kastan MB, Kirsch DG (2013) Strategies for optimizing the response of cancer and normal tissues to radiation. Nat Rev Drug Discov 12: 526–42. doi: 10.1038/nrd4003
|
| [2] | Amini A, Lou F, Correa AM, Baldassarre R, Rimner A, et al. (2013) Predictors for locoregional recurrence for clinical stage iii-n2 non-small cell lung cancer with nodal downstaging after induction chemotherapy and surgery. Ann Surg Oncol 20: 1934–40. doi: 10.1245/s10434-012-2800-x
|
| [3] | Paulsson AK, McMullen KP, Peiffer AM, Hinson WH, Kearns WT, et al.. (2012) Limited margins using modern radiotherapy techniques does not increase marginal failure rate of glioblastoma. Am J Clin Oncol 1.
|
| [4] | Gerlinger M, Rowan AJ, Horswell S, Larkin J, Endesfelder D, et al. (2012) Intratumor heterogeneity and branched evolution revealed by multiregion sequencing. N Engl J Med 366: 883–92. doi: 10.1056/nejmoa1113205
|
| [5] | Sottoriva A, Spiteri I, Piccirillo SG, Touloumis A, Collins VP, et al. (2013) Intratumor heterogeneity in human glioblastoma reects cancer evolutionary dynamics. Proc Natl Acad Sci U S A 110: 4009–14. doi: 10.1073/pnas.1219747110
|
| [6] | Marusyk A, Polyak K (2010) Tumor heterogeneity: causes and consequences. Biochim Biophys Acta 1805: 105–17. doi: 10.1016/j.bbcan.2009.11.002
|
| [7] | Marusyk A, Almendro V, Polyak K (2012) Intra-tumour heterogeneity: a looking glass for cancer? Nat Rev Cancer 12: 323–34. doi: 10.1038/nrc3261
|
| [8] | Bao S, Wu Q, McLendon RE, Hao Y, Shi Q, et al. (2006) Glioma stem cells promote radioresistance by preferential activation of the dna damage response. Nature 444: 756–60. doi: 10.1038/nature05236
|
| [9] | van der Heide UA, Houweling AC, Groenendaal G, Beets-Tan RG, Lambin P (2012) Functional mri for radiotherapy dose painting. Magn Reson Imaging 30: 1216–23. doi: 10.1016/j.mri.2012.04.010
|
| [10] | Bentzen SM, Gregoire V (2011) Molecular imaging-based dose painting: a novel paradigm for radiation therapy prescription. Semin Radiat Oncol 21: 101–10. doi: 10.1016/j.semradonc.2010.10.001
|
| [11] | International Commission on Radiation Units & Measurements (ICRU) (1993) Prescribing, recording, and reporting photon beam therapy. In: International commission on radiation units and measurements, Bethesda MD, USA: ICRU report 50.
|
| [12] | ICRU (1999) Prescribing, recording, and reporting photon beam therapy (supplement to icru report 50). In: International commission on radiation units and measurements, Bethesda MD, USA: ICRU report 62.
|
| [13] | ICRU (2010) Prescribing, recording, and reporting imrt. In: International commission on radiation units and measurements, Washington DC, USA: ICRU report 83.
|
| [14] | Malinen E, S？vik A, Hristov D, Bruland ？S, Olsen DR (2006) Adapting radiotherapy to hypoxic tumours. Phys Med Biol 51: 4903–21. doi: 10.1088/0031-9155/51/19/012
|
| [15] | Piccirillo SG, Combi R, Cajola L, Patrizi A, Redaelli S, et al. (2009) Distinct pools of cancer stemlike cells coexist within human glioblastomas and display different tumorigenicity and independent genomic evolution. Oncogene 28: 1807–11. doi: 10.1038/onc.2009.27
|
| [16] | Moore N, Lyle S (2011) Quiescent, slow-cycling stem cell populations in cancer: a review of the evidence and discussion of significance. J Oncol 2011.
|
| [17] | Vlashi E, Lagadec C, Vergnes L, Matsutani T, Masui K, et al. (2011) Metabolic state of glioma stem cells and nontumorigenic cells. Proc Natl Acad Sci U S A 108: 16062–7. doi: 10.1073/pnas.1106704108
|
| [18] | Drasdo D, H？hme S (2005) A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys Biol 2: 133–47. doi: 10.1088/1478-3975/2/3/001
|
| [19] | Anderson RA, Chaplain MAJ, Rejniak K, editors (2007) In: Single-cell-based models in biology and medicine, Birkhauser-Verlag, Basel, Boston and Berlin.
|
| [20] | Fowler JF (1989) The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 62: 679–94. doi: 10.1259/0007-1285-62-740-679
|
| [21] | Lee SP, Leu MY, Smathers JB, McBride WH, Parker RG, et al. (1995) Biologically effective dose distribution based on the linear quadratic model and its clinical relevance. Int J Radiat Oncol Biol Phys 33: 375–89. doi: 10.1016/0360-3016(95)00162-r
|
| [22] | Ramis-Conde I, Drasdo D, Anderson AR, Chaplain MA (2008) Modeling the inuence of the e-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. Biophys J 1: 155–165. doi: 10.1529/biophysj.107.114678
|
| [23] | Rietman EA, Friesen DE, Hahnfeldt P, Gatenby R, Hlatky L, et al.. (2013) An integrated multidisciplinary model describing initiation of cancer and the warburg hypothesis. Theor Biol Med Model 10.
|
| [24] | Gillies RJ, Verduzco D, Gatenby RA (2012) Evolutionary dynamics of carcinogenesis and why targeted therapy does not work. Nat Rev Cancer 12: 487–93. doi: 10.1038/nrc3298
|
| [25] | Preziosi L, Vitale G (2011) A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization. Math Models Methods Appl 21: 1901–32. doi: 10.1142/s0218202511005593
|
| [26] | Bellomo N, Delitala M (2008) From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Physics of Life Reviews 5: 183–206. doi: 10.1016/j.plrev.2008.07.001
|
| [27] | Anderson AR, Quaranta V (2008) Integrative mathematical oncology. Nat Rev Cancer 8: 227–34. doi: 10.1038/nrc2329
|
| [28] | Anderson AR, Weaver AM, Cummings PT, Quaranta V (2006) Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127: 905–15. doi: 10.1016/j.cell.2006.09.042
|
| [29] | Agur Z, Vuk-Pavlovi？ S (2012) Mathematical modeling in immunotherapy of cancer: personalizing clinical trials. Mol Ther 20: 1–2. doi: 10.1038/mt.2011.272
|
| [30] | Silva AS, Gatenby RA (2010) A theoretical quantitative model for evolution of cancer chemotherapy resistance. Biol Direct 5.
|
| [31] | Hoehme S, Brulport M, Bauer A, Bedawy E, Schormann W, et al. (2010) Prediction and validation of cell alignment along microvessels as order principle to restore tissue architecture in liver regeneration. Proc Natl Acad Sci U S A 107: 10371–6. doi: 10.1073/pnas.0909374107
|
| [32] | Enderling H, Park D, Hlatky L, Hahnfeldt P (2009) The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse. Math Model Nat Phenom 4: 117–33. doi: 10.1051/mmnp/20094305
|
| [33] | Kempf H, Bleicher M, Meyer-Hermann M (2010) Spatio-temporal cell dynamics in tumour spheroid irradiation. The European Physical Journal D 60: 177–93. doi: 10.1140/epjd/e2010-00178-4
|
| [34] | Zacharaki EI, Stamatakos GS, Nikita KS, Uzunoglu NK (2004) Simulating growth dynamics and radiation response of avascular tumour spheroids-model validation in the case of an emt6/ro multicellular spheroid. Comput Methods Programs Biomed 76: 193–206. doi: 10.1016/j.cmpb.2004.07.003
|
| [35] | Düchting W, Vogelsaenger T (1985) Recent progress in modelling and simulation of threedimensional tumor growth and treatment. Biosystems 18: 79–91. doi: 10.1016/0303-2647(85)90061-9
|
| [36] | Enderling H, Anderson AR, Chaplain MA, Munro AJ, Vaidya JS (2006) Mathematical modeling of radiotherapy strategies for early breast cancer. J Theor Biol 241: 158–71. doi: 10.1016/j.jtbi.2005.11.015
|
| [37] | Enderling H, Chaplain MAJ, Anderson ARA, Vaidya JS (2007) A mathematical model of breast cancer development, local treatment and recurrence. J Theor Biol 2: 245–259. doi: 10.1016/j.jtbi.2006.12.010
|
| [38] | Enderling H, Chaplain MAJ, Hahnfeldt P (2010) Quantitative modeling of tumor dynamics and radiotherapy. Acta Biotheor 4: 341–353. doi: 10.1007/s10441-010-9111-z
|
| [39] | Cappuccio A, Herrero MA, Nú？ez L (2009) Tumour radiotherapy and its mathematical modelling. Contemporary Mathematics 492: 77–102. doi: 10.1090/conm/492/09632
|
| [40] | O’Rourke SF, McAneney H, Hillen T (2009) Linear quadratic and tumour control probability modelling in external beam radiotherapy. J Math Biol 4–5: 799–817. doi: 10.1007/s00285-008-0222-y
|
| [41] | Rockne R, Alvord ECJ, Rockhill JK, Swanson KR (2009) A mathematical model for brain tumor response to radiation therapy. J Math Biol 4–5: 561–578. doi: 10.1007/s00285-008-0219-6
|
| [42] | Rockne R, Rockhill JK, Mrugala M, Spence AM, Kalet I, et al. (2010) Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach. Phys Med Biol 12: 3271–3285. doi: 10.1088/0031-9155/55/12/001
|
| [43] | Gao X, McDonald JT, Hlatky L, Enderling H (2013) Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. Cancer Res 73: 1481–90. doi: 10.1158/0008-5472.can-12-3429
|
| [44] | Vainstein V, Kirnasovsky OU, Kogan Y, Agur Z (2012) Strategies for cancer stem cell elimination: insights from mathematical modeling. J Theor Biol 298: 32–41. doi: 10.1016/j.jtbi.2011.12.016
|
| [45] | Dionysiou DD, Stamatakos GS, Gintides D, Uzunoglu N, Kyriaki K (2008) Critical parameters determining standard radiotherapy treatment outcome for glioblastoma multiforme: a computer simulation. Open Biomed Eng J 2: 43–51. doi: 10.2174/1874120700802010043
|
| [46] | Dahlberg WK, Azzam EI, Yu Y, Little JB (1999) Response of human tumor cells of varying radiosensitivity and radiocurability to fractionated irradiation. Cancer Res 59: 5365–9.
|
| [47] | Allam A, Taghian A, Gioioso D, Duffy M, Suit HD (1993) Intratumoral heterogeneity of malignant gliomas measured in vitro. Int J Radiat Oncol Biol Phys 27: 303–8. doi: 10.1016/0360-3016(93)90241-m
|
| [48] | Stupp R, Hegi ME (2007) Targeting brain-tumor stem cells. Nat Biotechnol 25: 193–4. doi: 10.1038/nbt0207-193
|
| [49] | Clarke MF, Dick JE, Dirks PB, Eaves CJ, Jamieson CH, et al. (2006) Cancer stem cells–perspectives on current status and future directions: Aacr workshop on cancer stem cells. Cancer Res 66: 9339–44. doi: 10.1158/0008-5472.can-06-3126
|
| [50] | Bonnet D, Dick JE (1997) Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat Med 3: 730–7. doi: 10.1038/nm0797-730
|
| [51] | Li L, Neaves WB (2006) Normal stem cells and cancer stem cells: the niche matters. Cancer Res 66: 4553–57. doi: 10.1158/0008-5472.can-05-3986
|
| [52] | Dembinski JL, Krauss S (2009) Characterization and functional analysis of a slow cycling stem cell-like subpopulation in pancreas adenocarcinoma. Clin Exp Metastasis 26: 611–23. doi: 10.1007/s10585-009-9260-0
|
| [53] | Roesch A, Fukunaga-Kalabis M, Schmidt EC, Zabierowski SE, Brafford PA, et al. (2010) A temporarily distinct subpopulation of slow-cycling melanoma cells is required for continuous tumor growth. Cell 141: 583–94. doi: 10.1016/j.cell.2010.04.020
|
| [54] | Moore N, Houghton J, Lyle S (2012) Slow-cycling therapy-resistant cancer cells. Stem Cells Dev 21: 1822–30. doi: 10.1089/scd.2011.0477
|
| [55] | Richichi C, Brescia P, Alberizzi V, Fornasari L, Pelicci G (2013) Marker-independent method for isolating slow-dividing cancer stem cells in human glioblastoma. Neoplasia 15: 840–7.
|
| [56] | Bansal A, Ramalingam S, Anant S (2013) Cancer stem cells in the origin and transformation of barrett’s esophagus: Current knowledge and areas of uncertainty. Immunogastroenterology 2: 9–21. doi: 10.7178/ig.26
|
| [57] | Chen J, Li Y, Yu TS, McKay RM, Burns DK, et al. (2012) A restricted cell population propagates glioblastoma growth after chemotherapy. Nature 488: 522–26. doi: 10.1038/nature11287
|
| [58] | Hegedüs B, Czirók A, Fazekas I, B’abel T, Madar’asz E, et al. (2000) Locomotion and proliferation of glioblastoma cells in vitro: statistical evaluation of videomicroscopic observations. J Neurosurg 92: 428–34. doi: 10.3171/jns.2000.92.3.0428
|
| [59] | Stamatakos GS, Antipas VP, Uzunoglu NK, Dale RG (2006) A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density. Br J Radiol 79: 389–400. doi: 10.1259/bjr/30604050
|
| [60] | Baumann M, Krause M, Hill R (2008) Exploring the role of cancer stem cells in radioresistance. Nat Rev Cancer 8: 545–54. doi: 10.1038/nrc2419
|
| [61] | Enderling H, Hlatky L, Hahnfeldt P (2013) Cancer stem cells: A minor cancer subpopulation that redefines global cancer features. Front Oncol 3.
|
| [62] | Enderling H, Hlatky L, Hahnfeldt P (2009) Migration rules: tumours are conglomerates of selfmetastases. Br J Cancer 100: 1917–25.
|
| [63] | Pine SR, Ryan BM, Varticovski L, Robles AI, Harris CC (2010) Microenvironmental modulation of asymmetric cell division in human lung cancer cells. Proc Natl Acad Sci U S A 107: 2195–200. doi: 10.1073/pnas.0909390107
|
| [64] | Knoblich JA (2010) Asymmetric cell division: recent developments and their implications for tumour biology. Nat Rev Mol Cell Biol 11: 849–60. doi: 10.1038/nrm3010
|
| [65] | Visvader JE, Lindeman GJ (2008) Cancer stem cells in solid tumours: accumulating evidence and unresolved questions. Nat Rev Cancer 8: 755–68. doi: 10.1038/nrc2499
|
| [66] | Das S, Srikanth M, Kessler JA (2008) Cancer stem cells and glioma. Nat Clin Pract Neurol 4: 427–35. doi: 10.1038/ncpneuro0862
|
| [67] | Barendsen GW, Bree CV, Franken NA (2001) Importance of cell proliferative state and potentially lethal damage repair on radiation effectiveness: implications for combined tumor treatments (review). Int J Oncol 19: 247–56. doi: 10.3892/ijo.19.2.247
|
| [68] | Allalunis-Turner MJ, Barron GM 3rd, Day RS, Fulton DS, Urtasun RC (1992) Radiosensitivity testing of human primary brain tumor specimens. Int J Radiat Oncol Biol Phys 23: 339–43. doi: 10.1016/0360-3016(92)90751-3
|
| [69] | Taghian A, Ramsay J, Allalunis-Turner MJ, Budach W, Gioioso D, et al. (1993) Intrinsic radiation sensitivity may not be the major determinant of the poor clinical outcome of glioblastoma multiforme. Int J Radiat Oncol Biol Phys 25: 243–9. doi: 10.1016/0360-3016(93)90345-v
|
| [70] | Araujo RP, McElwain DL (2004) A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull Math Biol 66: 1039–91. doi: 10.1016/j.bulm.2003.11.002
|
| [71] | Lowengrub JS, Frieboes HB, Jin F, Chuang YL, Li X, et al. (2010) Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity 23: R1–R9. doi: 10.1088/0951-7715/23/1/r01
|
| [72] | Moreira J, Deutsch A (2002) Cellular automaton models of tumor development: a critical review. Advs Complex Syst 5: 1–21. doi: 10.1142/s0219525902000572
|
| [73] | Sottoriva A, Verhoeff JJ, Borovski T, McWeeney SK, Naumov L, et al. (2010) Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res 70: 46–56. doi: 10.1158/0008-5472.can-09-3663
|
| [74] | Düchting W, Lehrig R, Rademacher G, Ulmer W (1989) Computer simulation of clinical irradiation schemes applied to in vitro tumor spheroids. Strahlenther Onkol 165: 873–8.
|
| [75] | Dormann S, Deutsch A (2002) Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol 2: 393–406.
|
| [76] | Ribba B, Marron K, Agur Z, Alarcón T, Maini PK (2005) A mathematical model of doxorubicin treatment efficacy for non-hodgkin’s lymphoma: investigation of the current protocol through theoretical modelling results. Bull Math Biol 67: 79–99. doi: 10.1016/j.bulm.2004.06.007
|
| [77] | Maini PK, Gatenby RA (2006) Some mathematical modelling challenges and approaches in cancer. In: Nagl S, editor, Cancer Bioinformatics: From Therapy Design to Treatment, Chichester, UK: John Wiley and Sons, Ltd. 95–107. doi:10.1002/0470032898.ch5.
|
| [78] | Alfonso JCL, Buttazzo G, García-Archilla B, Herrero MA, Nú？ez L (2012) A class of optimization problems in radiotherapy dosimetry planning. Discr Cont Dyn Systems B 17: 1651–72. doi: 10.3934/dcdsb.2012.17.1651
|
| [79] | Cappuccio A, Herrero MA, Nú？ez L (2009) Biological optimization of tumor radiosurgery. Med Phys 36: 98–104. doi: 10.1118/1.2986141
|
| [80] | Radszuweit M, Block M, Hengstler JG, Sch？ll E, Drasdo D (2009) Comparing the growth kinetics of cell populations in two and three dimensions. Phys Rev E Stat Nonlin Soft Matter Phys 79: 051907. doi: 10.1103/physreve.79.051907
|
| [81] | Block M, Sch？ll E, Drasdo D (2007) Classifying the growth kinetics and surface dynamics in growing cell populations. Phys Rev Lett 99: 248101–104. doi: 10.1103/physrevlett.99.248101
|
| [82] | Cruchten SV, Broeck WVD (2002) Morphological and biochemical aspects of apoptosis, oncosis and necrosis. Anat Histol Embryol 31: 214–23. doi: 10.1046/j.1439-0264.2002.00398.x
|
| [83] | Bursch W, Kleine L, Tenniswood M (1990) The biochemistry of cell death by apoptosis. Biochem Cell Biol 68: 1071–4. doi: 10.1139/o90-160
|
| [84] | Goergen JL, Marc A, Engasser JM (1993) Determination of cell lysis and death kinetics in continuous hybridoma cultures from the measurement of lactate dehydrogenase release. Cytotechnology 11: 189–95. doi: 10.1007/bf00749869
|
| [85] | Wells JE, Russell JB (1996) The effect of growth and starvation on the lysis of the ruminal cellulolytic bacterium fibrobacter succinogenes. Appl Environ Microbiol 62: 1342–6.
|
| [86] | Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81: 2340–61. doi: 10.1021/j100540a008
|
| [87] | Bortz AB, Kalos MH, Lebowitz JL (1975) New algorithm for monte-carlo simulations of ising spin systems. J Comput Phys 17: 10–18. doi: 10.1016/0021-9991(75)90060-1
|
| [88] | Fuller CD, Choi M, Forthuber B, Wang SJ, Rajagiriyil N, et al.. (2007) Standard fractionation intensity modulated radiation therapy (imrt) of primary and recurrent glioblastoma multiforme. Radiat Oncol 2.
|
| [89] | Narayana A, Yamada J, Berry S, Shah P, Hunt M, et al. (2006) Intensity-modulated radiotherapy in high-grade gliomas: clinical and dosimetric results. Int J Radiat Oncol Biol Phys 64: 892–7. doi: 10.1016/j.ijrobp.2005.05.067
|
| [90] | Stupp R, Tonn JC, Brada M, Pentheroudakis G (2010) Esmo guidelines working group. highgrade malignant glioma: Esmo clinical practice guidelines for diagnosis, treatment and follow-up. Ann Oncol 21.
|
| [91] | Korolev KS, Müller MJI, Karahan N, Murray AW, Hallatschek O, et al. (2012) Selective sweeps in growing microbial colonies. Phys Biol 9: 026008. doi: 10.1088/1478-3975/9/2/026008
|
| [92] | Barendsen GW (1982) Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Int J Radiat Oncol Biol Phys 8: 1981–97. doi: 10.1016/0360-3016(82)90459-x
|
| [93] | Emami B, Lyman J, Brown A, Coia L, Goiten M, et al. (1991) Tolerance of normal tissue to therapeutic radiation. Int J Radiat Oncol Biol Phys 21: 109–22.
|
| [94] | Grimm J, LaCouture T, Croce R, Yeo I, Zhu Y, et al. (2011) Dose tolerance limits and dose volume histogram evaluation for stereotactic body radiotherapy. J Appl Clin Med Phys 12: 267–92.
|
| [95] | Dale R (2007) In: Radiobiological modelling in radiation oncology, London, UK: The British Institute of Radiology.
|
| [96] | Buatti JM, Marcus RB, Mendenhall WM, Friedman WA, Bova FJ (1996) Accelerated hyperfractionated radiotherapy for malignant gliomas. Int J Radiat Oncol Biol Phys 34: 785–92. doi: 10.1016/0360-3016(95)02157-4
|
| [97] | Chaffer CL, Brueckmann I, Scheel C, Kaestli AJ, Wiggins PA, et al. (2011) Normal and neoplastic nonstem cells can spontaneously convert to a stem-like state. Proc Natl Acad Sci U S A 108: 7950–5. doi: 10.1073/pnas.1102454108
|
| [98] | Tang DG (2012) Understanding cancer stem cell heterogeneity and plasticity. Cell Res 22: 457–72. doi: 10.1038/cr.2012.13
|
| [99] | Meacham CE, Morrison SJ (2013) Tumour heterogeneity and cancer cell plasticity. Nature 501: 328–37. doi: 10.1038/nature12624
|
| [100] | Lengauer C, Kinzler KW, Vogelstein B (1998) Genetic instabilities in human cancers. Nature 396: 643–9. doi: 10.1038/25292
|
| [101] | Wang J, Guo LP, Chen LZ, Zeng YX, Lu SH (2007) Identification of cancer stem cell-like side population cells in human nasopharyngeal carcinoma cell line. Cancer Res 67: 3716–24. doi: 10.1158/0008-5472.can-06-4343
|
| [102] | Gatenby RA (2009) A change of strategy in the war on cancer. Nature 459: 508–9. doi: 10.1038/459508a
|
| [103] | Tixier F, Rest CCL, Hatt M, Albarghach N, Pradier O, et al. (2011) Intratumor heterogeneity characterized by textural features on baseline 18f-fdg pet images predicts response to concomitant radiochemotherapy in esophageal cancer. J Nucl Med 52: 369–78. doi: 10.2967/jnumed.110.082404
|
