2013, 10(3): 565-578. doi: 10.3934/mbe.2013.10.565

Mathematical modeling of glioma therapy using oncolytic viruses

1. 

Laboratoire Interdisciplinaire des Environnements Continentaux, Université de Lorraine, CNRS UMR 7360, 8 rue du Général Delestraint, 57070 METZ, France

2. 

Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, UMR 6085 CNRS, Avenue de l'Université, 76801 Saint Etienne du Rouvray, France

3. 

Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, United States

Received  June 2012 Revised  February 2013 Published  April 2013

Diffuse infiltrative gliomas are adjudged to be the most common primary brain tumors in adults and they tend to blend in extensively in the brain micro-environment. This makes it difficult for medical practitioners to successfully plan effective treatments. In attempts to prolong the lengths of survival times for patients with malignant brain tumors, novel therapeutic alternatives such as gene therapy with oncolytic viruses are currently being explored. Based on such approaches and existing work, a spatio-temporal model that describes interaction between tumor cells and oncolytic viruses is developed. Conditions that lead to optimal therapy in minimizing cancer cell proliferation and otherwise are analytically demonstrated. Numerical simulations are conducted with the aim of showing the impact of virotherapy on proliferation or invasion of cancer cells and of estimating survival times.
Citation: Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565
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show all references

References:
[1]

in "The Pathology of the Aging Human Nervous System" (ed. S. Duckett), Lea and Fabiger, Philadelphia, (1991), 210-286. Google Scholar

[2]

Virology, 156 (1987), 107-121. doi: 10.1016/0042-6822(87)90441-7.  Google Scholar

[3]

PLoS Comput. Biol., 7 (2011), e1001085. doi: 10.1371/journal.pcbi.1001085.  Google Scholar

[4]

AJNR Am. J. Neuroradiol, 16 (1995), 1001-1012. Google Scholar

[5]

J. Neurosurg, 68 (1988), 698-704. doi: 10.3171/jns.1988.68.5.0698.  Google Scholar

[6]

Abstract and Applied Analysis, (ID 590326), (2012), 1-13. doi: 10.1155/2012/590326.  Google Scholar

[7]

Cell Cycle, 5 (2006), 2244-2252. Google Scholar

[8]

Acta Neuropathol, 114 (2007), 443-458. doi: 10.1007/s00401-007-0293-7.  Google Scholar

[9]

Am. J. Roentgenol. Radium Ther. Nucl. Med., 84 (1960), 99-107. Google Scholar

[10]

J. Neurooncol, 67 (2004), 83-93. doi: 10.1023/B:NEON.0000021735.85511.05.  Google Scholar

[11]

Am. J. Respir. Cell Mol. Biol., 32 (2005), 498-503. doi: 10.1165/rcmb.2005-0031OC.  Google Scholar

[12]

Phys. Lett. A, 277 (2000), 212-218. doi: 10.1016/S0375-9601(00)00725-8.  Google Scholar

[13]

J. Math. Biol., 47 (2003), 391-423. doi: 10.1007/s00285-003-0199-5.  Google Scholar

[14]

American Control Conference, (2009), 2904-2909. doi: 10.1109/ACC.2009.5160022.  Google Scholar

[15]

J. Neuropathol. Exp. Neurol., 66 (2007), 1-9. doi: 10.1097/nen.0b013e31802d9000.  Google Scholar

[16]

Hum. Gene. Ther., 12 (2001), 1323-1332. doi: 10.1089/104303401750270977.  Google Scholar

[17]

J. Neurosurg., 66 (1987), 865-874. doi: 10.3171/jns.1987.66.6.0865.  Google Scholar

[18]

Curr. Opin. Mol. Ther., 5 (2003), 618-624. Google Scholar

[19]

Clin. Cancer Res., 9 (2003), 693-702. Google Scholar

[20]

Ann. Neurol., 53 (2003), 524-528. Google Scholar

[21]

3rd edition, Springer-Verlag, New York, 2003.  Google Scholar

[22]

Biology Direct, 1 (2006), 1-18. Google Scholar

[23]

Neurol. Res., 28 (2006), 518-522. Google Scholar

[24]

Ann. Neurol., 60 (2006), 380-383. Google Scholar

[25]

Brain Pathol., 9 (1999), 241-245. Google Scholar

[26]

Phys. Med. Biol., 55 (2010), 3271-3285. Google Scholar

[27]

Neurosurgery, 36 (1995), 275-282. Google Scholar

[28]

J. Neurosurg., 86 (1997), 525-531. Google Scholar

[29]

J. Neurolog. Sci., 216 (2003), 1-10. Google Scholar

[30]

Br. J. Cancer, 98 (2008), 113-119. Google Scholar

[31]

Microbiol. Immunol., 45 (2001), 709-715. Google Scholar

[32]

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[33]

J. Math. Analysis and Applications, 254 (2001), 138-153. doi: 10.1006/jmaa.2000.7220.  Google Scholar

[34]

World Scientific Publishing Company, Singapore, 2005. Google Scholar

[35]

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[36]

PLoS ONE, 4 (2009), e4271. doi: 10.1371/journal.pone.0004271.  Google Scholar

[37]

Bull. Math. Biol., 63 (2001), 731-768. Google Scholar

[38]

Bull. Math. Biol., 66 (2004), 605-625. doi: 10.1016/j.bulm.2003.08.016.  Google Scholar

[39]

J. Theor. Biol., 245 (2007), 1-8. doi: 10.1016/j.jtbi.2006.09.029.  Google Scholar

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