{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:45:51Z","timestamp":1760784351284},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s10957-017-1161-9","type":"journal-article","created":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T14:42:06Z","timestamp":1505486526000},"page":"218-235","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Optimization of Combined Leukemia Therapy by Finite-Dimensional Optimal Control Modeling"],"prefix":"10.1007","volume":"175","author":[{"given":"Svetlana","family":"Bunimovich-Mendrazitsky","sequence":"first","affiliation":[]},{"given":"Benzion","family":"Shklyar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,9,15]]},"reference":[{"key":"1161_CR1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1038\/nrc2808","volume":"10","author":"HM Byrne","year":"2010","unstructured":"Byrne, H.M.: Dissecting cancer through mathematics: from the cell to the animal model. Nat. Rev. Cancer 10, 221\u2013230 (2010)","journal-title":"Nat. Rev. Cancer"},{"issue":"3","key":"1161_CR2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1038\/nrc1295","volume":"4","author":"F Michor","year":"2004","unstructured":"Michor, F., Iwasa, Y., Nowak, M.: Dynamics of cancer progression. Nat. Rev. Cancer 4(3), 197\u2013205 (2004)","journal-title":"Nat. Rev. Cancer"},{"key":"1161_CR3","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02460644","volume":"56","author":"V Kuznetsov","year":"1994","unstructured":"Kuznetsov, V., Makalkin, I., Taylor, M., Perelson, A.: Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56, 295\u2013321 (1994)","journal-title":"Bull. Math. Biol."},{"issue":"3","key":"1161_CR4","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s002850050127","volume":"37","author":"D Kirschner","year":"1998","unstructured":"Kirschner, D., Panetta, J.: Modelling immunotherapy of the tumor\u2013immune interaction. J. Math. Biol. 37(3), 235\u2013252 (1998)","journal-title":"J. Math. Biol."},{"issue":"8","key":"1161_CR5","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1142\/S0218202506001571","volume":"16","author":"A d\u2019Onofrio","year":"2006","unstructured":"d\u2019Onofrio, A.: Tumor\u2013immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy. Math. Models Methods Appl. Sci. 16(8), 1375\u20131401 (2006)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"1161_CR6","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s00262-007-0387-z","volume":"57","author":"N Kronik","year":"2008","unstructured":"Kronik, N., Kogan, Y., Vainstein, V., Agur, Z.: Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics. Cancer Immunol. Immunother. 57, 425\u2013439 (2008)","journal-title":"Cancer Immunol. Immunother."},{"key":"1161_CR7","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/j.mcm.2009.11.005","volume":"51","author":"A d\u2019Onofrio","year":"2010","unstructured":"d\u2019Onofrio, A., Gatti, F., Cerrai, P., Freschi, L.: Delay-induced oscillatory dynamics of tumour\u2013immune system interaction. Math. Comput. Model. 51, 572\u2013591 (2010)","journal-title":"Math. Comput. Model."},{"key":"1161_CR8","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.jtbi.2003.09.004","volume":"226","author":"M Owen","year":"2004","unstructured":"Owen, M., Byrne, H., Lewis, C.: Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites. J. Theor. Biol. 226, 377\u2013391 (2004)","journal-title":"J. Theor. Biol."},{"key":"1161_CR9","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.compbiomed.2014.12.022","volume":"58","author":"S Bunimovich-Mendrazitsky","year":"2015","unstructured":"Bunimovich-Mendrazitsky, S., Pisarev, V., Kashdan, E.: Modeling and simulation of a low-grade urinary bladder carcinoma. Comput. Biol. Med. 58, 118\u2013129 (2015)","journal-title":"Comput. Biol. Med."},{"issue":"3","key":"1161_CR10","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1056\/NEJM199907153410306","volume":"341","author":"S Faderl","year":"1999","unstructured":"Faderl, S., Talpaz, M., Estrov, Z., O\u2019Brien, S., Kurzrock, R., Kantarjian, H.: The biology of chronic myeloid leukemia. N. Engl. J. Med. 341(3), 164\u2013172 (1999)","journal-title":"N. Engl. J. Med."},{"issue":"Suppl 2","key":"1161_CR11","doi-asserted-by":"crossref","first-page":"S64","DOI":"10.3816\/CLM.2007.s.004","volume":"7","author":"F Guilhot","year":"2007","unstructured":"Guilhot, F., Roy, L., Martineua, G., Guilhot, J., Millot, F.: Immunotherapy in chronic myelogenous leukemia. Clin. Lymph. Myeloma 7(Suppl 2), S64\u201370 (2007)","journal-title":"Clin. Lymph. Myeloma"},{"issue":"2","key":"1161_CR12","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/10428190400012029","volume":"46","author":"A Burchert","year":"2005","unstructured":"Burchert, A., Neubauer, A.: Interferon alpha and T-cell responses in chronic myeloid leukemia. Leuk. Lymph. 46(2), 167\u201375 (2005)","journal-title":"Leuk. Lymph."},{"key":"1161_CR13","doi-asserted-by":"crossref","first-page":"3263","DOI":"10.1182\/blood.V99.9.3263","volume":"99","author":"M Montoya","year":"2002","unstructured":"Montoya, M., Schiavoni, G., Mattei, F., Gresser, I., Belardelli, F., Borrow, P., Tough, D.F.: Type I interferons produced by dendritic cells promote their phenotypic and functional activation. Blood 99, 3263\u20133271 (2002)","journal-title":"Blood"},{"key":"1161_CR14","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1056\/NEJM200104053441401","volume":"344","author":"BJ Druker","year":"2001","unstructured":"Druker, B.J., Talpaz, M., et al.: Efficacy and safety of a specific inhibitor of the BCR-ABL tyrosine kinase in chronic myeloid leukemia. N. Engl. J. Med. 344, 1031\u20131037 (2001)","journal-title":"N. Engl. J. Med."},{"key":"1161_CR15","doi-asserted-by":"crossref","first-page":"2640","DOI":"10.1182\/blood-2004-08-3097","volume":"105","author":"MWN Deininger","year":"2005","unstructured":"Deininger, M.W.N., Buchdunger, E., Druker, B.J.: The development of imatinib as a therapeutic agent for chronic myeloid leukemia. Blood 105, 2640\u20132653 (2005)","journal-title":"Blood"},{"issue":"6","key":"1161_CR16","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1038\/leu.2015.45","volume":"29","author":"A Burchert","year":"2015","unstructured":"Burchert, A., Saussele, S., Eigendorff, E., et al.: Interferon alpha 2 maintenance therapy may enable high rates of treatment discontinuation in chronic myeloid leukemia. Leukemia 29(6), 1331\u20135 (2015)","journal-title":"Leukemia"},{"issue":"2","key":"1161_CR17","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.cyto.2011.11.018","volume":"57","author":"I Hardan","year":"2012","unstructured":"Hardan, I., Stanevsky, A., Volchek, Y., et al.: Treatment with interferon alpha prior to discontinuation of imatinib in patients with chronic myeloid leukemia. Cytokine 57(2), 290\u20133 (2012)","journal-title":"Cytokine"},{"issue":"26","key":"1161_CR18","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1056\/NEJMoa1004095","volume":"363","author":"C Preudhomme","year":"2010","unstructured":"Preudhomme, C., Guilhot, J., Nicolini, F.E., et al.: Imatinib plus peginterferon alfa-2a in chronic myeloid leukemia. N. Engl. J. Med. 363(26), 2511\u20132521 (2010)","journal-title":"N. Engl. J. Med."},{"issue":"12","key":"1161_CR19","doi-asserted-by":"crossref","first-page":"3228","DOI":"10.1182\/blood-2011-02-336685","volume":"118","author":"B Simonsson","year":"2011","unstructured":"Simonsson, B., Gedde-Dahl, T., Markevarn, B., et al.: Combination of pegylated IFN-alpha2b with imatinib increases molecular response rates in patients with low- or intermediate-risk chronic myeloid leukemia. Blood 118(12), 3228\u201335 (2011)","journal-title":"Blood"},{"key":"1161_CR20","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.jtbi.2007.05.015","volume":"248","author":"A Cappuccio","year":"2007","unstructured":"Cappuccio, A., Elishmereni, M., Agur, Z.: Optimization of interleukin-21 immunotherapeutic strategies. J. Theor. Biol. 248, 259\u2013266 (2007)","journal-title":"J. Theor. Biol."},{"key":"1161_CR21","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.mbs.2004.06.003","volume":"191","author":"A d\u2019Onofrio","year":"2004","unstructured":"d\u2019Onofrio, A., Gandolfi, A.: Tumor eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. Math. Biosci. 191, 159\u2013184 (2004)","journal-title":"Math. Biosci."},{"key":"1161_CR22","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.physd.2005.06.032","volume":"208","author":"A d\u2019Onofrio","year":"2005","unstructured":"d\u2019Onofrio, A.: A general framework for modelling tumour immune system and immunotherapy: mathematical analysis and medical inferences. Physica D 208, 220\u2013235 (2005)","journal-title":"Physica D"},{"key":"1161_CR23","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1111\/j.1365-2184.2009.00595.x","volume":"42","author":"A d\u2019Onofrio","year":"2009","unstructured":"d\u2019Onofrio, A., Gandolfi, A., Rocca, A.: The dynamics of tumour vasculature interaction suggests low dose, time-dense antiangiogenic scheduling. Cell Prolif. 42, 317\u2013329 (2009)","journal-title":"Cell Prolif."},{"issue":"1","key":"1161_CR24","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.mbs.2006.05.003","volume":"209","author":"LG Pillis de","year":"2007","unstructured":"de Pillis, L.G., Gu, W., Fister, K.R., Head, T., Maples, K., Murugan, A., Neal, T., Yoshida, K.: Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209(1), 292\u2013315 (2007)","journal-title":"Math. Biosci."},{"key":"1161_CR25","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/10273660008833062","volume":"3","author":"J Smieja","year":"2001","unstructured":"Smieja, J., Swierniak, A., Duda, Z.: Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy. J. Theor. Med. 3, 25\u201336 (2001)","journal-title":"J. Theor. Med."},{"key":"1161_CR26","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1002\/oca.704","volume":"23","author":"RF Stengel","year":"2002","unstructured":"Stengel, R.F., Ghigliazza, R., Kulkarni, N., Laplace, O.: Optimal control of innate immune response. Optim. Control Appl. Methods 23, 91\u2013104 (2002)","journal-title":"Optim. Control Appl. Methods"},{"key":"1161_CR27","first-page":"135","volume":"4","author":"T Burden","year":"2004","unstructured":"Burden, T., Ernstberger, J., Fister, K.R.: Optimal control applied to immunotherapy. Discrete Contin. Dyn. Syst. Ser. B 4, 135\u2013146 (2004)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"1161_CR28","doi-asserted-by":"crossref","first-page":"499","DOI":"10.3934\/mbe.2005.2.499","volume":"2","author":"KR Fister","year":"2005","unstructured":"Fister, K.R., Donnelly, J.H.: Immunotherapy: an optimal control approach. Math. Biosci. Eng. (MBE) 2, 499\u2013510 (2005)","journal-title":"Math. Biosci. Eng. (MBE)"},{"key":"1161_CR29","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.mbs.2009.08.004","volume":"222","author":"A d\u2019Onofrio","year":"2009","unstructured":"d\u2019Onofrio, A., Ledzewicz, U., Maurer, H., Schattler, H.: On optimal delivery of combination therapy for tumors. Math. Biosci. 222, 13\u201326 (2009)","journal-title":"Math. Biosci."},{"key":"1161_CR30","doi-asserted-by":"crossref","first-page":"E24265","DOI":"10.1371\/journal.pone.0024265","volume":"6","author":"E Jager","year":"2011","unstructured":"Jager, E., van der Velden, V.H.J., te Marvelde, J.G., Walter, R.B., Agur, Z., et al.: Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization. PLoS ONE 6, E24265 (2011)","journal-title":"PLoS ONE"},{"key":"1161_CR31","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.jtbi.2003.11.024","volume":"227","author":"H Moore","year":"2004","unstructured":"Moore, H., Li, N.K.: A mathematical model of chronic myelogenous leukemia (CML) and T cell interaction. J. Theor. Biol. 227, 513 (2004)","journal-title":"J. Theor. Biol."},{"key":"1161_CR32","doi-asserted-by":"crossref","first-page":"e1000095","DOI":"10.1371\/journal.pcbi.1000095","volume":"4","author":"P Kim","year":"2008","unstructured":"Kim, P., Lee, P., Levy, D.: Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput. Biol. 4, e1000095 (2008)","journal-title":"PLoS Comput. Biol."},{"key":"1161_CR33","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1038\/nature03669","volume":"435","author":"F Michor","year":"2005","unstructured":"Michor, F., Hughes, T., Iwasa, Y., Branford, S., Shah, N., Sawyers, C., Nowak, M.: Dynamics of chronic myeloid leukemia. Nature 435, 1267\u20131270 (2005)","journal-title":"Nature"},{"key":"1161_CR34","doi-asserted-by":"crossref","first-page":"14931","DOI":"10.1073\/pnas.0607006103","volume":"103","author":"F Michor","year":"2006","unstructured":"Michor, F., Iwasa, Y., Nowak, M.: The age incidence of chronic myeloid leukemia can be explained by a one-mutation model. Proc. Natl. Acad. Sci. U. S. A. 103, 14931\u201314934 (2006)","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"1161_CR35","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.mbs.2007.05.003","volume":"210","author":"S Nanda","year":"2007","unstructured":"Nanda, S., Moore, H., Lenhart, S.: Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci. 210, 143 (2007)","journal-title":"Math. Biosci."},{"key":"1161_CR36","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1038\/nm1487","volume":"12","author":"I Roeder","year":"2006","unstructured":"Roeder, I., Horn, M., Glauche, I., et al.: Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat. Med. 12, 1181\u20131184 (2006)","journal-title":"Nat. Med."},{"key":"1161_CR37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.matcom.2015.03.002","volume":"121","author":"IR Radulescu","year":"2016","unstructured":"Radulescu, I.R., Candea, D., Halanay, A.: Optimal control analysis of a leukemia model under imatinib treatment. Math. Comput. Simul. 121, 1\u201311 (2016)","journal-title":"Math. Comput. Simul."},{"key":"1161_CR38","unstructured":"Swierniak, A.: Optimal treatment protocols in leukemia\u2014modelling the proliferation cycle. In: Proceedings of the 12th IMACS World Congress, Paris, vol. 4, pp. 170\u2013172 (1988)"},{"key":"1161_CR39","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.semcancer.2005.07.002","volume":"15","author":"D Wodarz","year":"2005","unstructured":"Wodarz, D., Komarova, N.: Emergence and prevention of resistance against small molecule inhibitors. Semin. Cancer Biol. 15, 506\u2013514 (2005)","journal-title":"Semin. Cancer Biol."},{"key":"1161_CR40","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1137\/S0036139998338509","volume":"60","author":"KR Fister","year":"2000","unstructured":"Fister, K.R., Panetta, J.C.: Optimal control applied to cell-cycle specific cancer chemotherapy. SIAM J. Appl. Math. 60, 1059\u20131072 (2000)","journal-title":"SIAM J. Appl. Math."},{"key":"1161_CR41","first-page":"257","volume":"217","author":"L Berezansky","year":"2013","unstructured":"Berezansky, L., Bunimovich-Mendrazitsky, S., Domoshnitsky, A.: A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia. Adv. Differ. Equ. 217, 257\u2013266 (2013)","journal-title":"Adv. Differ. Equ."},{"issue":"1","key":"1161_CR42","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1007\/s10957-015-0717-9","volume":"167","author":"L Berezansky","year":"2015","unstructured":"Berezansky, L., Bunimovich-Mendrazitsky, S., Shklyar, B.: Stability and controllability issues in mathematical modeling of the intensive treatment of leukemia. J. Optim. Theory Appl. 167(1), 326\u2013341 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"1161_CR43","first-page":"7067","volume":"48","author":"L Norton","year":"1988","unstructured":"Norton, L.: A Gompertzian model of human breast cancer growth. Cancer Res. 48, 7067\u20137071 (1988)","journal-title":"Cancer Res."},{"key":"1161_CR44","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1038\/bjc.1964.55","volume":"18","author":"AK Laird","year":"1964","unstructured":"Laird, A.K.: Dynamics of tumor growth. Br. J. Cancer 18, 490\u2013502 (1964)","journal-title":"Br. J. Cancer"},{"key":"1161_CR45","unstructured":"Pontryagin, L., Boltyanskii, V., Gamkrelidze, R., Mishchenko, E.: The Mathematical Theory of Optimal Processes. Interscience, New York. ISBN 2-88124-077-1 (1962)"},{"key":"1161_CR46","volume-title":"Linear Operators","author":"N Dunford","year":"1958","unstructured":"Dunford, N., Schwartz, J.T.: Linear Operators, vol. 1. Wiley-Interscience, New York (1958)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-017-1161-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1161-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1161-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,2]],"date-time":"2017-10-02T11:39:22Z","timestamp":1506944362000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-017-1161-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,15]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["1161"],"URL":"https:\/\/doi.org\/10.1007\/s10957-017-1161-9","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,15]]}}}