Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

B cell chronic lymphocytic leukemia - A model with immune response

Pages: 1053 - 1076, Volume 18, Issue 4, June 2013      doi:10.3934/dcdsb.2013.18.1053

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Seema Nanda - Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore 560065, India (email)
Lisette dePillis - Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States (email)
Ami Radunskaya - Department of Mathematics, Pomona College, Claremont, CA, 91711, United States (email)

Abstract: B cell chronic lymphocytic leukemia (B-CLL) is known to have substantial clinical heterogeneity. There is no cure, but treatments allow for disease management. However, the wide range of clinical courses experienced by B-CLL patients makes prognosis and hence treatment a significant challenge. In an attempt to study disease progression across different patients via a unified yet flexible approach, we present a mathematical model of B-CLL with immune response, that can capture both rapid and slow disease progression. This model includes four different cell populations in the peripheral blood of humans: B-CLL cells, NK cells, cytotoxic T cells and helper T cells. We analyze existing data in the medical literature, determine ranges of values for parameters of the model, and compare our model outcomes to clinical patient data. The goal of this work is to provide a tool that may shed light on factors affecting the course of disease progression in patients. This modeling tool can serve as a foundation upon which future treatments can be based.

Keywords:  B-CLL, chronic lymphocytic leukemia, mathematical model, NK cell, T cell.
Mathematics Subject Classification:  Primary: 92C550, 92B05; Secondary: 37N25, 62H99.

Received: August 2012;      Revised: October 2012;      Available Online: February 2013.