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Understanding Drug Resistance in Breast Cancer with Mathematical Oncology

  • Risk, Prevention, and Screening (TA Patel, Section Editor)
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Abstract

Chemotherapy is the mainstay of treatment for the majority of patients with breast cancer but results in only 26 % of patients with distant metastasis living 5 years past treatment in the United States, largely because of drug resistance. The complexity of drug resistance calls for an integrated approach of mathematical modeling and experimental investigation to develop quantitative tools that reveal insights into drug resistance mechanisms, predict chemotherapy efficacy, and identify novel treatment approaches. This paper reviews recent modeling work for understanding cancer drug resistance through the use of computer simulations of molecular signaling networks and cancerous tissues, with a particular focus on breast cancer. These mathematical models are developed by drawing on current advances in molecular biology, physical characterization of tumors, and emerging drug delivery methods (eg, nanotherapeutics). We focus our discussion on representative modeling works that have provided quantitative insight into chemotherapy resistance in breast cancer and how drug resistance can be overcome or minimized to optimize chemotherapy treatment. We also discuss future directions of mathematical modeling in understanding drug resistance.

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References

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  1. Siegel R, Naishadham D, Jemal A. Cancer statistics, 2012. CA-Cancer J Clin. 2012;62:10–29.

    Article  PubMed  Google Scholar 

  2. Kitano H. Cancer as a robust system: implications for anticancer therapy. Nat Rev Cancer. 2004;4:227–35.

    Article  CAS  PubMed  Google Scholar 

  3. Pasquier J, Magal P, Boulange-Lecomte C, Webb G, Le Foll F. Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model. Biol Direct. 2011;6:5. doi:10.1186/1745-6150-6-5.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  4. Daniel C, Bell C, Burton C, Harguindey S, Reshkin SJ, Rauch C. The role of proton dynamics in the development and maintenance of multidrug resistance in cancer. Biochim Biophys Acta. 1832;2013:606–17. doi:10.1016/j.bbadis.2013.01.020.

    Google Scholar 

  5. Garraway LA, Janne PA. Circumventing cancer drug resistance in the era of personalized medicine. Cancer Discov. 2012;2:214–26. doi:10.1158/2159-8290.CD-12-0012.

    Article  CAS  PubMed  Google Scholar 

  6. Cancer Multidrug Resistance. Nature Biotechnol. 2000;18(Suppl):IT18–20. doi:10.1038/80051.

    Google Scholar 

  7. Minchinton AI, Tannock IF. Drug penetration in solid tumours. Nat Rev Cancer. 2006;6:583–92.

    Article  CAS  PubMed  Google Scholar 

  8. Tannock IF, Lee CM, Tunggal JK, Cowan DSM, Egorin MJ. Limited penetration of anticancer drugs through tumor tissue a potential cause of resistance of solid tumors to chemotherapy. Clin Cancer Res. 2002;8:878–84.

    CAS  PubMed  Google Scholar 

  9. Trédan O, Galmarini CM, Patel K, Tannock IF. Drug resistance and the solid tumor microenvironment. J Natl Cancer Inst. 2007;99:1441–54.

    Article  PubMed  Google Scholar 

  10. Cristini V, Lowengrub J. Multiscale modeling of cancer: an integrated experimental and mathematical modeling approach. Cambridge, UK: Cambridge University Press; 2010.

  11. Hatzikirou H, Chauviere A, Bauer AL, Leier A, Lewis MT, Macklin P, et al. Integrative physical oncology. Wiley Interdiscip Rev Syst Biol Med. 2012;4:1–14. doi:10.1002/wsbm.158.

    Article  PubMed Central  PubMed  Google Scholar 

  12. Marx V. Biology: the big challenges of big data. Nature. 2013;498:255–60. doi:10.1038/498255a.

    Article  CAS  PubMed  Google Scholar 

  13. Deisboeck TS, Wang Z, Macklin P, Cristini V. Multiscale cancer modeling. Annu Rev Biomed Eng. 2011;13:127–55. doi:10.1146/annurev-bioeng-071910-124729.

    Article  CAS  PubMed  Google Scholar 

  14. Lowengrub JS, Frieboes HB, Jin F, Chuang YL, Li X, Macklin P, et al. Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity. 2010;23:R1–91. doi:10.1088/0951-7715/23/1/r01.

    Article  PubMed Central  PubMed  Google Scholar 

  15. Rejniak KA, Anderson AR. Hybrid models of tumor growth. Wiley Interdiscip Rev Syst Biol Med. 2011;3:115–25. doi:10.1002/wsbm.102.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  16. Tracqui P. Biophysical models of tumour growth. Rep Prog Phys. 2009;72.

  17. Kim M, Gillies RJ, Rejniak KA. Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues. Front Oncol. 2013;3:278. doi:10.3389/fonc.2013.00278.

    PubMed Central  PubMed  Google Scholar 

  18. Atari MI, Chappell MJ, Errington RJ, Smith PJ, Evans ND. Kinetic modelling of the role of the aldehyde dehydrogenase enzyme and the breast cancer resistance protein in drug resistance and transport. Comput Methods Programs Biomed. 2011;104:93–103. doi:10.1016/j.cmpb.2010.06.008.

    Article  CAS  PubMed  Google Scholar 

  19. Lavi O, Gottesman MM, Levy D. The dynamics of drug resistance: a mathematical perspective. Drug Resist Updat Rev Comment Antimicrob Anticancer Chemother. 2012;15:90–7. doi:10.1016/j.drup.2012.01.003.

    Article  Google Scholar 

  20. Faratian D, Goltsov A, Lebedeva G, Sorokin A, Moodie S, Mullen P, et al. Systems biology reveals new strategies for personalizing cancer medicine and confirms the role of PTEN in resistance to trastuzumab. Cancer Res. 2009;69:6713–20. doi:10.1158/0008-5472.can-09-0777.

    Article  CAS  PubMed  Google Scholar 

  21. Kirouac DC, Du JY, Lahdenranta J, Overland R, Yarar D, Paragas V, et al. Computational modeling of ERBB2-amplified breast cancer identifies combined ErbB2/3 blockade as superior to the combination of MEK and AKT inhibitors. Sci Signal. 2013;6:ra68. doi:10.1126/scisignal.2004008.

    PubMed  Google Scholar 

  22. Niepel M, Hafner M, Pace EA, Chung M, Chai DH, Zhou L, et al. Profiles of basal and stimulated receptor signaling networks predict drug response in breast cancer lines. Sci Signal. 2013;6:ra84. doi:10.1126/scisignal.2004379.

    PubMed  Google Scholar 

  23. Engel R, Kaklamani V. HER2-Positive Breast Cancer. Drugs. 2007;67:1329–41. doi:10.2165/00003495-200767090-00006.

    Article  CAS  PubMed  Google Scholar 

  24. Romond EH, Perez EA, Bryant J, Suman VJ, Geyer CE, Davidson NE, et al. Trastuzumab plus adjuvant chemotherapy for operable HER2-positive breast cancer. N Engl J Med. 2005;353(16):1673–84. doi:10.1056/NEJMoa052122.

    Article  CAS  PubMed  Google Scholar 

  25. Vera J, Schmitz U, Lai X, Engelmann D, Khan FM, Wolkenhauer O, et al. Kinetic modeling-based detection of genetic signatures that provide chemoresistance via the E2F1-p73/DNp73-miR-205 network. Cancer Res. 2013;73:3511–24. doi:10.1158/0008-5472.can-12-4095.

    Article  CAS  PubMed  Google Scholar 

  26. Roe-Dale R, Isaacson D, Kupferschmid M. A mathematical model of breast cancer treatment with CMF and doxorubicin. Bull Math Biol. 2011;73:585–608. doi:10.1007/s11538-010-9549-9.

    Article  CAS  PubMed  Google Scholar 

  27. Tannock IF. Tumor physiology and drug resistance. Cancer Metastasis Rev. 2001;20:123–32.

    Article  CAS  PubMed  Google Scholar 

  28. Whiteside TL. The tumor microenvironment and its role in promoting tumor growth. Oncogene. 2008;27:5904–12.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  29. Koumoutsakos P, Pivkin I, Milde F. The fluid mechanics of cancer and its therapy. Annu Rev Fluid Mech. 2013;45:325.

    Article  Google Scholar 

  30. Sanga S, Sinek JP, Frieboes HB, Ferrari M, Fruehauf JP, Cristini V. Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev Anticancer Ther. 2006;6:1361–76.

    Google Scholar 

  31. Stylianopoulos T, Martin JD, Chauhan VP, Jain SR, Diop-Frimpong B, Bardeesy N, et al. Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proc Natl Acad Sci. 2012;109:15101–8.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  32. Padera TP, Stoll BR, Tooredman JB, Capen D, di Tomaso E, Jain RK. Cancer cells compress intra-tumour vessels. Nature. 2004;427:695.

    Article  CAS  PubMed  Google Scholar 

  33. Torchilin VP. Drug targeting. Eur J Pharmaceut Sci. 2000;11:S81–91.

    Article  CAS  Google Scholar 

  34. Heldin C-H, Rubin K, Pietras K, Östman A. High interstitial fluid pressure—an obstacle in cancer therapy. Nat Rev Cancer. 2004;4:806–13.

    Article  CAS  PubMed  Google Scholar 

  35. Jain RK, Stylianopoulos T. Delivering nanomedicine to solid tumors. Nat Rev Clin Oncol. 2010;7:653–64.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  36. Stylianopoulos T, Martin JD, Snuderl M, Mpekris F, Jain SR, Jain RK. Co-evolution of solid stress and interstitial fluid pressure in tumors during progression: implications for vascular collapse. Cancer Res. 2013;73:3833–41.

    Google Scholar 

  37. Tunggal JK, Cowan DSM, Shaikh H, Tannock IF. Penetration of anticancer drugs through solid tissue: a factor that limits the effectiveness of chemotherapy for solid tumors. Clin Cancer Res. 1999;5:1583–6.

    CAS  PubMed  Google Scholar 

  38. Grantab R, Sivananthan S, Tannock IF. The penetration of anticancer drugs through tumor tissue as a function of cellular adhesion and packing density of tumor cells. Cancer Res. 2006;66:1033–9.

    Article  CAS  PubMed  Google Scholar 

  39. Jain RK. Transport of molecules in the tumor interstitium: a review. Cancer Res. 1987;47:3039–51.

    CAS  PubMed  Google Scholar 

  40. Eisbruch A, Shewach DS, Bradford CR, Littles JF, Teknos TN, Chepeha DB, et al. Radiation concurrent with gemcitabine for locally advanced head and neck cancer: a phase I trial and intracellular drug incorporation study. J Clin Oncol. 2001;19:792–9.

    CAS  PubMed  Google Scholar 

  41. Taghian AG, Abi-Raad R, Assaad SI, Casty A, Ancukiewicz M, Yeh E, et al. Paclitaxel decreases the interstitial fluid pressure and improves oxygenation in breast cancers in patients treated with neoadjuvant chemotherapy: clinical implications. J Clin Oncol. 2005;23:1951–61. doi:10.1200/JCO.2005.08.119.

    Article  CAS  PubMed  Google Scholar 

  42. Lankelma J, Dekker H, Luque RF, Luykx S, Hoekman K, van der Valk P, et al. Doxorubicin gradients in human breast cancer. Clin Cancer Res. 1999;5:1703–7.

    CAS  PubMed  Google Scholar 

  43. Primeau AJ, Rendon A, Hedley D, Lilge L, Tannock IF. The distribution of the anticancer drug Doxorubicin in relation to blood vessels in solid tumors. Clin Cancer Res. 2005;11:8782–8.

    Article  CAS  PubMed  Google Scholar 

  44. Transport properties of pancreatic adenocarcinoma describe gemcitabine delivery and response. J Clin Invest. 2014. doi:10.1172/JCI73455. This study presents a modeling-aided approach to describe changes in tumor density during routine contrast-enhanced CT imaging of pancreatic cancer patients. The pre-therapy CT-derived transport properties were found to significantly correlate with the drug delivery and also with pathologic response and survival in pancreatic cancer patients who received gemcitabine-based therapy.

  45. Farrell JJ, Elsaleh H, Garcia M, Lai R, Ammar A, Regine WF, et al. Human equilibrative nucleoside transporter 1 levels predict response to gemcitabine in patients with pancreatic cancer. Gastroenterology. 2009;136:187–95. doi:10.1053/j.gastro.2008.09.067.

    Article  PubMed  Google Scholar 

  46. Sinek JP, Sanga S, Zheng X, Frieboes HB, Ferrari M, Cristini V. Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation. J Math Biol. 2009;58:485–510.

    Article  PubMed Central  PubMed  Google Scholar 

  47. Zheng X, Wise SM, Cristini V. Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull Math Biol. 2005;67:211–59.

    Article  CAS  PubMed  Google Scholar 

  48. Cristini V, Bławzdziewicz J, Loewenberg M. An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. J Comput Phys. 2001;168:445–63.

    Article  CAS  Google Scholar 

  49. Baish JW, Stylianopoulos T, Lanning RM, Kamoun WS, Fukumura D, Munn LL, et al. Scaling rules for diffusive drug delivery in tumor and normal tissues. Proc Natl Acad Sci. 2011;108:1799–803.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  50. Jain RK. Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. Science. 2005;307:58–62.

    Article  CAS  PubMed  Google Scholar 

  51. Thurber GM, Yang KS, Reiner T, Kohler RH, Sorger P, Mitchison T, et al. Single-cell and subcellular pharmacokinetic imaging allows insight into drug action in vivo. Nat Comm. 2013;4:1504.

    Article  Google Scholar 

  52. Stapleton S, Milosevic M, Allen C, Zheng J, Dunne M, Yeung I, et al. A mathematical model of the enhanced permeability and retention effect for liposome transport in solid tumors. PloS One. 2013;8:e81157.

    Article  PubMed Central  PubMed  Google Scholar 

  53. Maeda H, Wu J, Sawa T, Matsumura Y, Hori K. Tumor vascular permeability and the EPR effect in macromolecular therapeutics: a review. J Control Rel. 2000;65:271–84.

    Article  CAS  Google Scholar 

  54. Wu M, Frieboes HB, McDougall SR, Chaplain MAJ, Cristini V, Lowengrub J. The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. J Theor Biol. 2013;320:131–51.

    Article  PubMed Central  PubMed  Google Scholar 

  55. Macklin P, McDougall S, Anderson ARA, Chaplain MAJ, Cristini V, Lowengrub J. Multiscale modelling and nonlinear simulation of vascular tumour growth. J Math Biol. 2009;58:765–98.

    Article  PubMed Central  PubMed  Google Scholar 

  56. Stylianopoulos T, Soteriou K, Fukumura D, Jain RK. Cationic nanoparticles have superior transvascular flux into solid tumors: insights from a mathematical model. Ann Biomed Eng. 2013;41:68–77.

    Article  PubMed  Google Scholar 

  57. Stylianopoulos T, Diop-Frimpong B, Munn LL, Jain RK. Diffusion anisotropy in collagen gels and tumors: the effect of fiber network orientation. Biophys J. 2010;99:3119–28.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  58. Stylianopoulos T, Poh M-Z, Insin N, Bawendi MG, Fukumura D, Munn LL, et al. Diffusion of particles in the extracellular matrix: the effect of repulsive electrostatic interactions. Biophys J. 2010;99:1342–9.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  59. 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.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  60. Frieboes HB, Edgerton ME, Fruehauf JP, Rose FR, Worrall LK, Gatenby RA, et al. Prediction of drug response in breast cancer using integrative experimental/computational modeling. Cancer Res. 2009;69:4484–92. doi:10.1158/0008-5472.can-08-3740.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  61. Das H, Wang Z, Niazi MKK, Aggarwal R, Lu J, Kanji S, et al. Impact of diffusion barriers to small cytotoxic molecules on the efficacy of immunotherapy in breast cancer. PloS One. 2013;8:e61398.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  62. Pascal J, Bearer EL, Wang Z, Koay EJ, Curley SA, Cristini V. Mechanistic patient-specific predictive correlation of tumor drug response with microenvironment and perfusion measurements. Proc Natl Acad Sci. 2013;110:14266–71. This study presents a diffusion-based mathematical model by treating the tumor as a physical entity. As a result, the model explained how physical properties of the microenvironment influence penetration of chemotherapy drugs into the tumor and successfully predicted how much of a tumor an individual’s treatment regimen will kill. Information to build the model can be directly assessed from CT scans, patient tissue analyses, and other noninvasive or minimally-invasive procedures that the patient would normally receive.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  63. Gillies RJ, Schornack PA, Secomb TW, Raghunand N. Causes and effects of heterogeneous perfusion in tumors. Neoplasia. 1999;1:197.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  64. Vaupel P. Tumor microenvironmental physiology and its implications for radiation oncology. Semin Radiat Oncol. 2004;14:198–206.

    Google Scholar 

  65. Gerweck LE, Vijayappa S, Kozin S. Tumor pH controls the in vivo efficacy of weak acid and base chemotherapeutics. Mol Cancer Therapeut. 2006;5:1275–9.

    Article  CAS  Google Scholar 

  66. Tannock IF, Rotin D. Acid pH in tumors and its potential for therapeutic exploitation. Cancer Res. 1989;49:4373–84.

    CAS  PubMed  Google Scholar 

  67. Shah MA, Schwartz GK. Cell Cycle-mediated drug resistance an emerging concept in cancer therapy. Clin Cancer Res. 2001;7:2168–81.

    CAS  PubMed  Google Scholar 

  68. Venkatasubramanian R, Henson MA, Forbes NS. Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J Theor Biol. 2006;242:440–53.

    Article  CAS  PubMed  Google Scholar 

  69. Venkatasubramanian R, Henson MA, Forbes NS. Integrating cell-cycle progression, drug penetration and energy metabolism to identify improved cancer therapeutic strategies. J Theor Biol. 2008;253:98–117.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  70. Blanco E, Ferrari M. Emerging nanotherapeutic strategies in breast cancer. Breast. 2013;23:10–8.

    Google Scholar 

  71. Frieboes HB, Wu M, Lowengrub J, Decuzzi P, Cristini V. A computational model for predicting nanoparticle accumulation in tumor vasculature. PloS One. 2013;8:e56876.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  72. Pascal J, Ashley CE, Wang Z, Brocato TA, Butner JD, Carnes EC, et al. Mechanistic modeling identifies drug-uptake history as predictor of tumor drug resistance and nano-carrier-mediated response. ACS Nano. 2013;11174–82. doi:10.1021/nn4048974.

  73. van de Ven AL, Wu M, Lowengrub J, McDougall SR, Chaplain MAJ, Cristini V, et al. Integrated intravital microscopy and mathematical modeling to optimize nanotherapeutics delivery to tumors. AIP Adv. 2012;7:011208.

    Google Scholar 

  74. Susa M, Iyer AK, Ryu K, Hornicek FJ, Mankin H, Amiji MM, et al. Doxorubicin loaded polymeric nanoparticulate delivery system to overcome drug resistance in osteosarcoma. BMC Cancer. 2009;9:399.

    Article  PubMed Central  PubMed  Google Scholar 

  75. Wang Z, Bordas V, Deisboeck TS. Discovering molecular targets in cancer with multiscale modeling. Drug Dev Res. 2011;72:45–52. doi:10.1002/ddr.20401.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  76. Wang Z, Deisboeck TS. Mathematical modeling in cancer drug discovery. Drug Discov Today. 20137:145–50. doi:10.1016/j.drudis.2013.06.015.

  77. Wang Z, Bordas V, Deisboeck TS. Identification of critical molecular components in a multiscale cancer model based on the integration of Monte Carlo, resampling, and ANOVA. Front Physiol. 2011;2:35. doi:10.3389/fphys.2011.00035.

    Google Scholar 

  78. Silverman EK, Loscalzo J. Developing new drug treatments in the era of network medicine. Clin Pharmacol Therapeut. 2013;93:26–8. doi:10.1038/clpt.2012.207.

    Article  CAS  Google Scholar 

  79. Edgerton ME, Chuang YL, Macklin P, Yang W, Bearer EL, Cristini V. A novel, patient-specific mathematical pathology approach for assessment of surgical volume: application to ductal carcinoma in situ of the breast. Anal Cell Pathol. 2011;34:247–63. doi:10.3233/ACP-2011-0019.

    Google Scholar 

  80. Diamandis M, White NM, Yousef GM. Personalized medicine: marking a new epoch in cancer patient management. Mol Cancer Res. 2010;8:1175–87. doi:10.1158/1541-7786.MCR-10-0264.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

This work has been supported in part by the National Science Foundation (NSF) Grant DMS-1263742 (Z.W., V.C.), NSF SBIR 1315372 (V.C.), the National Institutes of Health (NIH) Grant 1U54CA149196 (V.C.), 1U54CA143837 (E.K., V.C.), 1U54CA151668 (V.C.), and 1U54CA143907 (V.C.), the University of New Mexico Cancer Center Victor and Ruby Hansen Surface Professorship in Molecular Modeling of Cancer (V.C.), the Houston Methodist Research Institute (E.K., V.C.), and the Anne Eastland Spears Fellowship for GI Cancer Research (E.K.).

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Terisse Brocato, Prashant Dogra, Eugene J. Koay, Armin Day, Yao-Li Chuang, Zhihui Wang, and Vittorio Cristini all declare that they have no conflict of interest.

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This article does not contain any studies with human or animal subjects performed by any of the authors.

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Correspondence to Zhihui Wang or Vittorio Cristini.

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T. Brocato, P. Dogra, and E.J. Koay contributed equally to this work.

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Brocato, T., Dogra, P., Koay, E.J. et al. Understanding Drug Resistance in Breast Cancer with Mathematical Oncology. Curr Breast Cancer Rep 6, 110–120 (2014). https://doi.org/10.1007/s12609-014-0143-2

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