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10 results

  • Stability Analysis of Cell Dynamics in Leukemia

  • H. Özbay, C. Bonnet, H. Benjelloun, J. Clairambault
  • Journal:
    Mathematical Modelling of Natural Phenomena / Volume 7 / Issue 1 / 2012
    Published online by Cambridge University Press:
    25 January 2012, pp. 203-234
    Print publication:
    2012

  • In order to better understand the dynamics of acute leukemia, and in particular to findtheoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia,we investigate stability of a system modeling its cell dynamics.

    The overall system is a cascade connection of sub-systems consisting of distributeddelays and static nonlinear feedbacks. Earlier results on local asymptotic stability areimproved by the analysis of the linearized system around the positive equilibrium. For thenonlinear system, we derive stability conditions by using Popov, circle and nonlinearsmall gain criteria. The results are illustrated with numerical examples andsimulations.

  • Chapter 26 - ART and oocyte donation in cancer survivors

  • from Section 6 - Fertility preservation strategies in the female: ART
  • Edited by Jacques Donnez, Université Catholique de Louvain, Belgium, S. Samuel Kim, University of Kansas
  • Book:
    Principles and Practice of Fertility Preservation
    Published online:
    04 February 2011
    Print publication:
    03 February 2011, pp 310-327

  • Summary

    Over the last several decades, survival rates for childhood cancer have steadily increased. Spermatogonial stem cells are responsible for the continual production of spermatozoa throughout adult life. Autotransplantation is considered more acceptable than allotransplantation or xenotransplantation, although both of the latter have been used successfully in mouse models. Spermatogenesis in vitro from biopsied germ cells is considered to be an excellent alternative for pre-pubertal boys with malignancies, particularly of hematopoietic origin, who carry a risk of relapse after transplantation. Despite significant advances in spermatogonial cell biology and subsequent fertility management, malignant contamination remains one of the main concerns surrounding autologous transplantation. The potential for transferring tumor cells within cryopreserved and subsequently cultured and/or expanded testicular tissue back into the patient is of paramount concern. Children most at risk of transmitting cancer cells include those with a haematological malignancy such as acute leukemia.