Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Cancer and Tumor Development: Biomedical Background Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

8. Optimal Control for Mathematical Models of Tumor Immune System Interactions

verfasst von : Heinz Schättler, Urszula Ledzewicz

Erschienen in: Optimal Control for Mathematical Models of Cancer Therapies

Verlag: Springer New York

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, we consider the second major feature of the tumor microenvironment: interactions between the tumor and the immune system. Fundamental principles that have already been outlined in the introduction (see Section 1.3.4) will be expanded upon in this chapter. As a vehicle for the analysis we use the classical model by Stepanova [303] and some of its modifications that have been developed in the literature. This model captures the main features that we want to discuss here—immune surveillance and tumor dormancy—and, at the same time, being low-dimensional and minimally parameterized, has the advantage of allowing us to easily visualize associated geometric features (regions of attractions, stability boundaries, etc.). We formulate an optimal control problem whose objective to be minimized is tailored to the inherent multi-stable structure that these systems have. These problems are considered under chemotherapy and under combinations of chemotherapy with a rudimentary form of an immune boost.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Combination Therapies with Antiangiogenic Treatments
Nächstes Kapitel Concluding Remarks
Fußnoten
1
The reader may find the short fragment “On Exactitude in Science” by Jorge Luis Borges [33] of interest.
 
2
The numerical computations were carried out by our former graduate students Mohammad Naghneian and Mozhdeh Moselman Faraji Sadat.
 
3
The numerical calculations were carried out by Behrooz Amini.
 
Literatur
9.
N. André, L. Padovani, E. Pasquier, Metronomic scheduling of anticancer treatment: the next generation of multitarget therapy? Future Oncology, 7(3), (2011), pp. 385–394.CrossRef
15.
D.J. Bell and D.H. Jacobson, Singular Optimal Control Problems, Academic Press, New York, 1975.MATH
16.
J. Bellmunt, J.M. Trigo, E. Calvo, J. Carles, J.L. Pérez-Garcia, J.A. Virizuela, R. Lopez, M. Lázaro and J. Albanell, Activity of a multi-targeted chemo-switch regimen (sorafenib, gemcitabine, and metronomic capecitabine) in metastatic renal-cell carcinoma: a phase-2 study (SOGUG-02-06), Lancet Oncology, 2010.
19.
D.A. Benson, A Gauss pseudospectral transcription for optimal control, Ph.D. dissertation, Dept. of Aeronautics and Astronautics, MIT, November 2004.
20.
D.A. Benson, G.T. Huntington, T.P. Thorvaldsen, and A.V. Rao, Direct trajectory optimization and costate estimation via an orthogonal collocation method, Journal of Guidance, Control, and Dynamics, 29 (6), (2006), pp. 1435–1440.CrossRef
21.
S. Benzekry, N. André, A. Benabdallah, J. Ciccolini, C. Faivre, F. Hubert and D. Barbolosi, Modeling the impact of anticancer agents on metastatic spreading, Mathematical Modeling of Natural Phenomena, 7(1), 2012, pp. 306–336, doi: 10.1051/mmnp/20127114.MATHCrossRef
23.
S. Benzekry and P. Hahnfeldt, Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers, J. Theoretical Biology, 335, (2013), pp. 235—244.CrossRef
24.
G. Bocci, K. Nicolaou and R.S. Kerbel, Protracted low-dose effects on human endothelial cell proliferation and survival in vitro reveal a selective antiangiogenic window for various chemotherapeutic drugs, Cancer Research, 62, (2002), pp. 6938–6943.
33.
J. Borges, On rigor in science, in: Dreamtigers, University of Texas Press, Austin, 1964.
39.
T. Browder, C.E. Butterfield, B.M. Kräling, B. Shi, B. Marshall, M.S. O’Reilly and J. Folkman, Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer, Cancer Research, 60, (2000), pp. 1878–1886.
111.
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Verlag, New York, 1983.MATHCrossRef
114.
116.
P. Hahnfeldt, D. Panigrahy, J. Folkman and L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Research, 59, (1999), pp. 4770–4775.
117.
P. Hahnfeldt, J. Folkman and L. Hlatky, Minimizing long-term burden: the logic for metronomic chemotherapeutic dosing and its angiogenic basis, J. of Theoretical Biology, 220, (2003), pp. 545–554.CrossRef
118.
D. Hanahan, G. Bergers and E. Bergsland, Less is more, regularly: metronomic dosing of cytotoxic drugs can target tumor angiogenesis in mice, J. Clinical Investigations, 105(8), (2000), pp. 1045–1047.CrossRef
129.
G.T. Huntington, Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control, Ph.D. dissertation, Dept. of Aeronautics and Astronautics, MIT, May 2007.
136.
B. Kamen, E. Rubin, J. Aisner, and E. Glatstein, High-time chemotherapy or high time for low dose? J. Clinical Oncology, 18, (2000), editorial, pp. 2935–2937.
145.
H.K. Khalil, Nonlinear Systems, 3rd. ed. Prentice Hall, 2002.
158.
D. Kirschner and J.C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. of Mathematical Biology, 37, (1998), pp. 235–252.MATHCrossRef
162.
G. Klement, S. Baruchel, J. Rak, S. Man, K. Clark, D.J. Hicklin, P. Bohlen and R.S. Kerbel, Continuous low-dose therapy with vinblastine and VEGF receptor-2 antibody induces sustained tumor regression without overt toxicity, J. Clinical Investigations, 105(8), (2000), R15–R24.CrossRef
171.
V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor and A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology, 56, (1994), pp. 295–321.MATHCrossRef
176.
U. Ledzewicz, M.S. Faraji Mosalman, and H. Schättler, On optimal protocols for combinations of chemo- and immunotherapy, Proc. 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA (2012), pp. 7492–7497.
187.
U. Ledzewicz, O. Olumoye and H. Schättler, On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth, Mathematical Biosciences and Engineering - MBE, 10(3), (2012), pp. 787–802, doi:10.3934/mbe.2013.10.787.CrossRef
211.
U. Ledzewicz and H. Schättler, A review of optimal chemotherapy protocols: from MTD towards metronomic therapy, Mathematical Modeling of Natural Phenomena, 9(4), 2014, pp. 131-152, doi: 10.1051/mmnp/20149409.MATHCrossRef
212.
U. Ledzewicz and H. Schättler, Tumor microenvironment and anticancer therapies: an optimal control approach, in: Mathematical Oncology (A. d’Onofrio and A. Gandolfi, Eds.,), Springer, (2014), pp. 295–334.
248.
A. d’Onofrio, A general framework for modelling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedial inferences, Physica D, 208, (2005), pp. 202–235.MathSciNet
249.
A. d’Onofrio, Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy, Mathematical Models and Methods in Applied Sciences, 16, (2006), pp. 1375–1401.MATHMathSciNetCrossRef
250.
A. d’Onofrio, Tumor evasion from immune control: strategies of a MISS to become a MASS, Chaos, Solitons and Fractals, 31, (2007), pp. 261–268.
254.
A. d’Onofrio, Fractal growth of tumors and other cellular populations: Linking the mechanistic to the phenomenological modeling and vice versa, Chaos, Solitons and Fractals, 41, (2009), pp. 875–880.
263.
A. d’Onofrio, A. Gandolfi and A. Rocca, The dynamics of tumour-vasculature interaction suggests low-dose, time-dense antiangiogenic schedulings, Cell Proliferation, 42, (2009), pp. 317–329.CrossRef
272.
E. Pasquier, M. Kavallaris and N. André, Metronomic chemotherapy: new rationale for new directions, Nature Reviews|Clinical Oncology, 7, (2010), pp. 455–465.
273.
E. Pasquier, and U. Ledzewicz, Perspective on “More is not necessarily better”: Metronomic Chemotherapy, Newsletter of the Society for Mathematical Biology, 26(2), (2013), pp. 9–10.
277.
K. Pietras and D. Hanahan, A multi-targeted, metronomic and maximum tolerated dose “chemo-switch” regimen is antiangiogenic, producing objective responses and survival benefit in a mouse model of cancer, J. of Clinical Oncology, 23, (2005), pp. 939–952.CrossRef
284.
A.V. Rao, D.A. Benson, G.T. Huntington, C. Francolin, C.L. Darby, and M.A. Patterson, User’s Manual for GPOPS: A MATLAB Package for Dynamic Optimization Using the Gauss Pseudospectral Method, University of Florida Report, 2008.
298.
H.E. Skipper, On mathematical modeling of critical variables in cancer treatment (goals: better understanding of the past and better planning in the future), Bulletin of Mathematical Biology, 48, (1986), pp. 253–278.MathSciNetCrossRef
303.
N.V. Stepanova, Course of the immune reaction during the development of a malignant tumour, Biophysics, 24, (1980), pp. 917–923.
334.
H.P. de Vladar and J.A. González, Dynamic response of cancer under the influence of immunological activity and therapy, J. of Theoretical Biology, 227, (2004), pp. 335–348.CrossRef
341.
S.D. Weitman, E. Glatstein and B.A. Kamen, Back to the basics: the importance of concentration × time in oncology, J. of Clinical Oncology, 11, (1993), pp. 820–821.
343.
T.E. Wheldon, Mathematical Models in Cancer Research, Boston-Philadelphia: Hilger Publishing, 1988.MATH
Metadaten
Titel
Optimal Control for Mathematical Models of Tumor Immune System Interactions
verfasst von
Heinz Schättler
Urszula Ledzewicz
Copyright-Jahr
2015
Verlag
Springer New York
Buch
Optimal Control for Mathematical Models of Cancer Therapies

Print ISBN: 978-1-4939-2971-9

Electronic ISBN: 978-1-4939-2972-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-1-4939-2972-6_8

Premium Partner

    Bildnachweise