A Review of Mathematical Models for Leukemia and Lymphoma.

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy.

[1]  Tom Lenaerts,et al.  Dynamics of chronic myeloid leukemia under nilotinib therapy , 2010 .

[2]  Ching-Hon Pui,et al.  Modeling Mechanisms of In Vivo Variability in Methotrexate Accumulation and Folate Pathway Inhibition in Acute Lymphoblastic Leukemia Cells , 2010, PLoS Comput. Biol..

[3]  Mithat Gönen,et al.  Selection pressure exerted by imatinib therapy leads to disparate outcomes of imatinib discontinuation trials , 2012, Haematologica.

[4]  D Grillot,et al.  Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through Bcl-XL and Bcl-2. , 1996, Blood.

[5]  Franziska Michor,et al.  Successful Therapy Must Eradicate Cancer Stem Cells , 2006, Stem cells.

[6]  Willi Jäger,et al.  Modeling of asymmetric cell division in hematopoietic stem cells--regulation of self-renewal is essential for efficient repopulation. , 2009, Stem cells and development.

[7]  Stefan Fruehauf,et al.  Effect of CD34+ cell dose on hematopoietic reconstitution and outcome in 508 patients with multiple myeloma undergoing autologous peripheral blood stem cell transplantation , 2007, European journal of haematology.

[8]  Holden T Maecker,et al.  Development and dynamics of robust T-cell responses to CML under imatinib treatment. , 2008, Blood.

[9]  Ingo Roeder,et al.  An “Age” Structured Model of Hematopoietic Stem Cell Organization with Application to Chronic Myeloid Leukemia , 2009, Bulletin of mathematical biology.

[10]  Bob Löwenberg,et al.  Review Articles (434 articles) , 2008 .

[11]  Dominik Wodarz,et al.  Drug resistance in cancer: principles of emergence and prevention. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[12]  F. Crauste,et al.  Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling , 2012 .

[13]  C. Tomasetti.  A new hypothesis: imatinib affects leukemic stem cells in the same way it affects all other leukemic cells , 2011, Blood cancer journal.

[14]  Doron Levy,et al.  Dynamics and Potential Impact of the Immune Response to Chronic Myelogenous Leukemia , 2008, PLoS Comput. Biol..

[15]  D. Levy,et al.  Role of symmetric and asymmetric division of stem cells in developing drug resistance , 2010, Proceedings of the National Academy of Sciences.

[16]  Karen M Page,et al.  Mathematical models of the fate of lymphoma B cells after antigen receptor ligation with specific antibodies. , 2006, Journal of theoretical biology.

[17]  Ignacio A. Rodriguez-Brenes,et al.  Evolutionary dynamics of feedback escape and the development of stem-cell–driven cancers , 2011, Proceedings of the National Academy of Sciences.

[18]  Martin C. Müller,et al.  Model-based decision rules reduce the risk of molecular relapse after cessation of tyrosine kinase inhibitor therapy in chronic myeloid leukemia. , 2013, Blood.

[19]  Ching-Hon Pui,et al.  A mathematical model of in vivo methotrexate accumulation in acute lymphoblastic leukemia , 2002, Cancer Chemotherapy and Pharmacology.

[20]  A. Marciniak-Czochra,et al.  Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics , 2012 .

[21]  M. Matasar,et al.  Advances in the diagnosis and management of lymphoma , 2012 .

[22]  Fabien Crauste,et al.  DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA , 2008 .

[23]  A. Traulsen,et al.  Tyrosine kinase inhibitor therapy can cure chronic myeloid leukemia without hitting leukemic stem cells , 2009, Haematologica.

[24]  P. Ding,et al.  BCR-ABL tyrosine kinase inhibitors in the treatment of Philadelphia chromosome positive chronic myeloid leukemia: a review. , 2010, Leukemia research.

[25]  D. Wodarz,et al.  Combination of Two but Not Three Current Targeted Drugs Can Improve Therapy of Chronic Myeloid Leukemia , 2009, PloS one.

[26]  M. Mackey,et al.  Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia. , 2011, Journal of theoretical biology.

[27]  Ingo Roeder,et al.  Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications , 2006, Nature Medicine.

[28]  Doron Levy,et al.  Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models , 2008, Bulletin of mathematical biology.

[29]  Philippe Rousselot,et al.  Discontinuation of imatinib in patients with chronic myeloid leukaemia who have maintained complete molecular remission for at least 2 years: the prospective, multicentre Stop Imatinib (STIM) trial. , 2010, The Lancet. Oncology.

[30]  M. Bodnar,et al.  About a generalized model of lymphoma , 2012 .

[31]  G. Núñez,et al.  Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through Bcl-XL and Bcl-2 , 1996 .

[32]  Michael C Mackey,et al.  A mathematical model of hematopoiesis--I. Periodic chronic myelogenous leukemia. , 2005, Journal of theoretical biology.

[33]  A. Trumpp,et al.  Therapy of chronic myeloid leukaemia can benefit from the activation of stem cells: simulation studies of different treatment combinations , 2012, British Journal of Cancer.

[34]  J. Radich,et al.  Six-year follow-up of patients receiving imatinib for the first-line treatment of chronic myeloid leukemia , 2010, Leukemia.

[35]  Doron Levy,et al.  A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia , 2008, Bulletin of mathematical biology.

[36]  G. Chatta,et al.  Effect of recombinant granulocyte colony-stimulating factor on neutrophil kinetics in normal young and elderly humans. , 1996, Blood.

[37]  Franziska Michor,et al.  Fitness Conferred by BCR-ABL Kinase Domain Mutations Determines the Risk of Pre-Existing Resistance in Chronic Myeloid Leukemia , 2011, PloS one.

[38]  W. Evans,et al.  Mechanistic mathematical modelling of mercaptopurine effects on cell cycle of human acute lymphoblastic leukaemia cells , 2005, British Journal of Cancer.