title: Comparison of simple models of periodic protocols for combined anticancer therapy.
abstract: Several simple ordinary differential equation (ODE) models of tumor growth taking into account the development of its vascular network are discussed. Different biological aspects are considered from the simplest model of Hahnfeldt et al. proposed in 1999 to a model which includes drug resistance of cancer cells to chemotherapy. Some of these models can be used in clinical oncology to optimize antiangiogenic and cytostatic drugs delivery so as to ensure maximum efficacy. Simple models of continuous and periodic protocols of combined therapy are implemented. Discussion on the dynamics of the models and their complexity is presented.
authors: Department of Automatic Control, Silesian University of Technology, ul. Akademicka 2A, 44-100 Gliwice, Poland. marzena.dolbniak@polsl.pl
authors: Marzena
authors: M
authors: Dołbniak
authors: Andrzej
authors: A
authors: Swierniak
mesh_terms: D020533:Angiogenesis Inhibitors / Q000008:administration & dosage; D000970:Antineoplastic Agents / Q000008:administration & dosage; D000971:Antineoplastic Combined Chemotherapy Protocols; D019295:Computational Biology; D004334:Drug Administration Schedule; D019008:Drug Resistance, Neoplasm; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply / Q000188:drug therapy / Q000473:pathology; D009389:Neovascularization, Pathologic / Q000188:drug therapy
chemical_list: D020533:Angiogenesis Inhibitors; D000970:Antineoplastic Agents
references: Bull Math Biol. 1998 Sep;60(5):857-99
references: 9739618
references: Cell. 2011 Mar 4;144(5):646-74
references: 21376230
references: Math Med Biol. 2009 Mar;26(1):63-95
references: 19033598
references: CA Cancer J Clin. 2011 Mar-Apr;61(2):69-90
references: 21296855
references: Nat Rev Cancer. 2008 Aug;8(8):592-603
references: 18650835
references: Nanomedicine (Lond). 2012 Apr;7(4):597-615
references: 22471722
references: J Theor Biol. 2010 May 21;264(2):253-65
references: 20100496
references: Nat Rev Clin Oncol. 2011 Mar 01;8(4):210-21
references: 21364524
references: Math Med Biol. 2003 Jun;20(2):135-81
references: 14636027
references: Math Biosci. 2004 Oct;191(2):159-84
references: 15363652
references: Angiogenesis. 2002;5(3):203-14
references: 12831061
references: J Theor Biol. 1991 Oct 7;152(3):377-403
references: 1721100
references: Nat Med. 2003 Jun;9(6):685-93
references: 12778167
references: J Clin Oncol. 2005 Feb 20;23(6):1295-311
references: 15718328
references: Bull Math Biol. 2002 Jul;64(4):673-702
references: 12216417
references: Postepy Hig Med Dosw (Online). 2011 Jul 04;65:437-46
references: 21734328
references: Math Med Biol. 2010 Jun;27(2):157-79
references: 20513667
references: Math Biosci. 2011 Jan;229(1):123-34
references: 21129386
references: Bull Math Biol. 2010 May;72(4):830-68
references: 20052558
references: Cancer Res. 1999 Oct 1;59(19):4770-5
references: 10519381
references: N Engl J Med. 1971 Nov 18;285(21):1182-6
references: 4938153
references: Math Biosci Eng. 2011 Apr;8(2):307-23
references: 21631132
references: Curr Pharm Biotechnol. 2011 Feb 1;12(2):231-42
references: 21044002
references: Bull Math Biol. 2003 May;65(3):407-24
references: 12749532
references: J Chin Med Assoc. 2010 Jun;73(6):281-8
references: 20603084
references: PLoS Med. 2006 Nov;3(11):e442
references: 17132052
references: PLoS One. 2011;6(5):e19989
references: 21637756
references: Math Biosci Eng. 2005 Jul;2(3):511-25
references: 20369937
references: Mol Cancer Ther. 2008 Dec;7(12):3670-84
references: 19074844