Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte la política de Acceso Abierto del editor

Abstract:

The Wheldon model (1975) of a chronic myelogenous leukemia (CML) dynamics is modified and enriched by introduction of a time-varying microenvironment and time-dependent drug efficacies. The resulting model is a special class of nonautonomous nonlinear system of differential equations with delays. Via topological methods, the existence of positive periodic solutions is proven. We introduce our main insight and formulate some relevant open problems and conjectures. © 2013 Texas State University - San Marcos.

Registro:

Documento: Artículo
Título:Existence of periodic solutions in the modified wheldon model of CML
Autor:Amster, P.; Balderrama, R.; Idels, L.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
Department of Mathematics, Vancouver Island University (VIU), 900 Fith St., Nanaimo BC, Canada
Palabras clave:Chronic myelogenous leukemia; Leray-Schauder degree; Model with pharmacokinetics; Nonlinear nonautonomous delay differential equation; Positive periodic solution
Año:2013
Volumen:2013
Título revista:Electronic Journal of Differential Equations
Título revista abreviado:Electron. J. Differ. Equ.
ISSN:10726691
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2013_n_p_Amster

Referencias:

  • Batzel, J., Kappel, F., Time delay in physiological systems: Analyzing and modeling its impact (2011) Mathematical Biosciences, 234, pp. 61-74
  • Bellomo, N., Bellouquid, A., Nieto, J., Soler, J., Complexity and mathematical tools toward the modelling of multicellular growing systems (2010) Math. Comput. Modelling, 51, pp. 441-551
  • Bellomo, N., Knopoff, D., Soler, J., On the dificult interplay between life, "complexity", and mathematical sciences (2013) Math. Models Methods Appl. Sci, 23 (10), pp. 1861-1913
  • Bellouquid, A., De Angelis, E., Knopoff, D., From the modeling of the immune hallmarks of cancer to a black swan in biology (2013) Math. Models Methods Appl. Sci., 23, pp. 949-978
  • Castorina, P., Deisboeck, T., Gabriele, P., Guiot, C., Growth Laws in Cancer: Implications for Radiotherapy (2007) Radiat. Res., 168, pp. 349-356
  • Colijn, C., McKey, M., A mathematical model of hematopoiesis I. Periodic chronic myeloge-nous leukemia (2005) Journal of Theoretical Biology, 237, pp. 117-132
  • Eftimie, R., Bramson, J., Earn, D., Interactions between the immune system and cancer: A brief review of non-spatial mathematical models (2011) Bull. Math. Biol., 73, pp. 2-32
  • Fessler, E., Dijkgraaf, F., De Sousa, F., Melo, E., Medema, J., Cancer stem cell dynamics in tumor progression and metastasis: Is the microenvironment to blame? (2012) Cancer Letters, , In Press, Corrected Proof, Available online 22 October
  • Goldman, J., Melo, J., Chronic Myeloid Leukemia (2003) Advances in Biology and New Approaches to Treatment, N Engl J Med, 349, pp. 1451-1464
  • Horn, M., Loeffer, M., Roeder, I., Mathematical modeling of genesis and treatment of chronic myeloid leukemia (2008) Cells Tissues Organs, 188, pp. 236-247
  • Lloyd, N., (1978) Degree Theory, , Cambridge University. Press, Cambridge
  • McKlina, P., Lowengrub, J., Nonlinear simulation of the effect of microenvironment on tumor growth (2007) Journal of Theoretical Biology, 245, pp. 677-704
  • Mayani, H., Flores-Figueroa, E., Chavez-Gonzalez, A., In vitro biology of human myeloid leukemia (2009) Leukemia Research, 33, pp. 624-637
  • Mawhin, J., (1979) Topological degree methods in nonlinear boundary value problems, volume 40 of CBMS Regional Conference Series in Mathematics, , American Mathematical Society, Prov-idence, RI, Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 9-15, 1977
  • Perrotti, D., Jamieson, C., Goldman, J., Skorski, T., Chronic myeloid leukemia: Mechanisms of blastic transformation (2010) J. Clin Invest., 120, pp. 2254-2264
  • Roeder, I., d'Inverno, M., New experimental and theoretical investigations of hematopoi-etic stem cells and chronic myeloid leukemia (2009) Blood Cells, Molecules, and Diseases, 43, pp. 88-97
  • Swierniak, A., Kimmel, M., Smieja, J., Mathematical modeling as a tool for planning anticancer therapy (2009) European Journal of Pharmacology, 625, pp. 108-121
  • Vaupel, P., Tumor microenvironmental physiology and its implications for radiation oncology (2004) Seminars in Radiation Oncology, 14, pp. 198-206
  • Wheldon, E., Lindsay, K., Wheldon, T., The dose-response relationship for cancer incidence in a two-stage radiation carcinogenesis model incorporating cellular repopulation (2000) International Journal of Radiation Biology, 76, pp. 699-710
  • Wheldon, T., (1988) Mathematical Models in Cancer Research, , Bristol and Philadelphia, PA: Adam Hilger
  • Wheldon, T., Mathematical models of oscillatory blood cell production (1975) Mathematical Bio-sciences, 24, pp. 289-305
  • Wheldon, T., Kirk, J., Finlay, H., Cyclical granulopoiesis in chronic granulocytic leukemia: A simulation study (1974) Blood, 43, pp. 379-387

Citas:

---------- APA ----------
Amster, P., Balderrama, R. & Idels, L. (2013) . Existence of periodic solutions in the modified wheldon model of CML. Electronic Journal of Differential Equations, 2013.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2013_n_p_Amster [ ]
---------- CHICAGO ----------
Amster, P., Balderrama, R., Idels, L. "Existence of periodic solutions in the modified wheldon model of CML" . Electronic Journal of Differential Equations 2013 (2013).
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2013_n_p_Amster [ ]
---------- MLA ----------
Amster, P., Balderrama, R., Idels, L. "Existence of periodic solutions in the modified wheldon model of CML" . Electronic Journal of Differential Equations, vol. 2013, 2013.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2013_n_p_Amster [ ]
---------- VANCOUVER ----------
Amster, P., Balderrama, R., Idels, L. Existence of periodic solutions in the modified wheldon model of CML. Electron. J. Differ. Equ. 2013;2013.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2013_n_p_Amster [ ]