American Institute of Mathematical Sciences

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

Mathematical modeling of glioma therapy using oncolytic viruses

Baba Issa Camara 1, , Houda Mokrani 2, and  Evans K. Afenya 3,

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.
Keywords: Cancer gene therapy, mathematical model., oncolytic viruses.
Mathematics Subject Classification: Primary: 92C37, 35B35; Secondary: 35B4.
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
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]

Science in China Series A: Mathematics, 51 (2008), 2315-2329. doi: 10.1007/s11425-008-0070-7.  Google Scholar

[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]

Cancer Res., 61 (2001), 3501-3507. Google Scholar

[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

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]

Science in China Series A: Mathematics, 51 (2008), 2315-2329. doi: 10.1007/s11425-008-0070-7.  Google Scholar

[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]

Cancer Res., 61 (2001), 3501-3507. Google Scholar

[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

[1]

Reihaneh Mostolizadeh, Zahra Afsharnezhad, Anna Marciniak-Czochra. Mathematical model of Chimeric Anti-gene Receptor (CAR) T cell therapy with presence of cytokine. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 63-80. doi: 10.3934/naco.2018004
[2]

Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences & Engineering, 2015, 12 (1) : 163-183. doi: 10.3934/mbe.2015.12.163
[3]

Zizi Wang, Zhiming Guo, Huaqin Peng. Dynamical behavior of a new oncolytic virotherapy model based on gene variation. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1079-1093. doi: 10.3934/dcdss.2017058
[4]

Dominik Wodarz. Computational modeling approaches to studying the dynamics of oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 939-957. doi: 10.3934/mbe.2013.10.939
[5]

Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immuno-therapy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1037-1053. doi: 10.3934/mbe.2015.12.1037
[6]

Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279
[7]

J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263
[8]

Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891
[9]

Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040
[10]

Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White. Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1435-1463. doi: 10.3934/mbe.2018066
[11]

Avner Friedman, Xiulan Lai. Free boundary problems associated with cancer treatment by combination therapy. Discrete & Continuous Dynamical Systems, 2019, 39 (12) : 6825-6842. doi: 10.3934/dcds.2019233
[12]

Avner Friedman, Xiulan Lai. Antagonism and negative side-effects in combination therapy for cancer. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2237-2250. doi: 10.3934/dcdsb.2019093
[13]

Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945
[14]

Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147
[15]

Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479
[16]

Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707
[17]

Svetlana Bunimovich-Mendrazitsky, Yakov Goltser. Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529-547. doi: 10.3934/mbe.2011.8.529
[18]

Yangjin Kim, Avner Friedman, Eugene Kashdan, Urszula Ledzewicz, Chae-Ok Yun. Application of ecological and mathematical theory to cancer: New challenges. Mathematical Biosciences & Engineering, 2015, 12 (6) : i-iv. doi: 10.3934/mbe.2015.12.6i
[19]

Urszula Ledzewicz, Heinz Schättler. On the role of pharmacometrics in mathematical models for cancer treatments. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 483-499. doi: 10.3934/dcdsb.2020213
[20]

M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks & Heterogeneous Media, 2006, 1 (3) : 399-439. doi: 10.3934/nhm.2006.1.399

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (37)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences