Geodesic
Up and Down Estimate of Therapy Quality in Non-Linear Distributed Mathematical Glioma Model
Matematičeskaâ biologiâ i bioinformatika, Tome 9 (2014) no. 1, pp. 20-32.

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We consider the distributed mathematical model for brain tumor growth dynamics. The task of search optimal strategy in terms of the specified optimal functional is very hard to analytical solving. We construct the analytical down-estimation for the functional and the up-estimation by using numerical methods. In case of both estimates pass not far from each other results could be useful for ill-prognosis and the selection of the convenient therapy strategy. 
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     title = {Up and {Down} {Estimate} of {Therapy} {Quality} in {Non-Linear} {Distributed} {Mathematical} {Glioma} {Model}},
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S. Yu. Kovalenko; A. S. Bratus'. Up and Down Estimate of Therapy Quality in Non-Linear Distributed Mathematical Glioma Model. Matematičeskaâ biologiâ i bioinformatika, Tome 9 (2014) no. 1, pp. 20-32. http://geodesic.mathdoc.fr/item/MBB_2014_9_1_a4/

[1] Murray D., Mathematical Biology, v. 2, Spatial Models and Biomedical Applications, Springer, 2003 | MR

[2] Shilbergeld D. L., Chicoine M. R., “Isolation and Characterization of human malignant glioma cells from histologically normal brain”, J. Neuwsurg., 86 (1997), 525–531 | DOI

[3] Swanson K. R., Alvord E. C. (Jr.), Murray J. D., “Virtual Resection of Gliomas: Effect of Extent of Resection on Recurrence”, Mathematical and Computer Modelling, 37:11 (2003), 1177–1190 | DOI | Zbl

[4] Matsukado Y., McCarthy C. S., Kernohan J. W., “The Growth of glioblastoma multiforme (asytrocytomas, grades 3 and 4) in neurosurgical practice”, J. Neuwsurg., 18 (1961), 636–644 | DOI

[5] Jbabdi S., Mandonnet E., Du au H., Capelle L., Swanson K. R., Pelegrini-Issac M., Guillevin R., Benali H., “Simulation of Anisotropic Growth of Low-Grade Gliomas Using Di usion Tensor Imaging”, Magnetic Resonance in Medicine, 54 (2005), 616–624 | DOI

[6] Tracqui P., “From passive diffusion to active cellular migration in mathematical models of tumour invasion”, Acta Biotheoretica, 43 (1995), 443–464 | DOI

[7] Bratus A. S., Chumerina E. S., “Cintez optimalnogo upravleniya v zadache vybora lekarstvennogo vozdeistviya na rastuschuyu opukhol”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 48:6 (2008), 946–966 | MR | Zbl

[8] Butkovskii A. G., Teoriya optimalnogo upravlenie sistemami s raspredelennymi parametrami, Nauka, M., 1965 | MR

[9] Melikyan A. A., “Singular characteristics of HJBI equation in state constraint optimal control problems”, Preprints of IFAC Symposium Modeling and control of economic system (Klagenfert, 2001), 155–156 | MR

[10] Vasilev F. P., Metody optimizatsi, v. 2, MTsNMO, M., 2011

[11] Avvakumov S. N., Kiselev Yu. N., “Nekotorye algoritmy optimalnogo upravleniya”, Trudy Instituta matematiki i mekhaniki UrO RAN, 12, no. 2, 2006, 3–17 | Zbl