Article no.5

Theoretical Basis of Optimal Therapy for Individual Patients in Chronic Myeloid Leukemia: A Mathematical ApproachResearch Paper, July 6, 2020 / Lorand Gabriel Parajdi

Published in Taylor & Francis Online, Journal of Interdisciplinary Mathematics 23(3), 669-690, DOI: 10.1080/09720502.2019.1681699,  2020.

  Paper is available on the Taylor & Francis Online, Journal of Interdisciplinary Mathematics website: https://www.tandfonline.com/doi/abs/10.1080/09720502.2019.1681699

Authors: Lorand Gabriel Parajdi1, Radu Precup1, Delia Dima3, Vlad Moisoiu2,3 and Ciprian Tomuleasa31 Department of Mathematics, “Babeş–Bolyai” University, Cluj-Napoca, Romania2 IMOGEN Research Institute County Clinical Emergency Hospital, Cluj-Napoca, Romania3 Department of Hematology, “Ion Chiricuţă” Clinical Cancer Center, Cluj-Napoca, Romania

Abstract: Even if the successful pharmacological therapy for chronic myeloid leukemia has reached today a near normal life expectancy in a patient diagnosed with this malignancy, almost one in four patients will change the line of tyrosin-kinase inhibitors during therapy, may it be due to poor response of due to intolerance to therapy. In this paper, starting from a mathematical characterization of the chronic phase in myeloid leukemia, a theoretical investigation of optimal therapy is undertaken as base for further pharmaceutical research and personalized treatment protocols.

Subject Classification: 92B05, 92D25, 92C50

Keywords: Mathematical model; Chronic myeloid leukemia; Dynamic system; Optimization problem.

Cite As: Lorand Gabriel Parajdi, Radu Precup, Delia Dima, Vlad Moisoiu & Ciprian Tomuleasa (2020) Theoretical basis of optimal therapy for individual patients in chronic myeloid leukemia: A mathematical approach, Journal of Interdisciplinary Mathematics, 23:3, 669-690,  DOI: 10.1080/09720502.2019.1681699.

References:
1. Tomuleasa, C., D. Dima, I. Frinc, et al . BCR-ABL1 T315I mutation, a negative prognostic factor for the terminal phase of chronic myelogenous leukemia treated with first- and second-line tyrosine kinase inhibitors, might be an indicator of allogeneic stem cell transplant as the treatment of choice. Leuk Lymphoma, (2014) 56: 546-7.  [Taylor & Francis Online][Google Scholar]

2. Hochhaus, A. , S. Saussele, G. Rosti, et al . Chronic myeloid leukaemia: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up. Annals of Oncology. (2017) 28(suppl 4): iv41-iv51. [Article]

3. Timis, T. , C. Berce, A. Duarte-Garcia, et al . Paraneoplastic syndromes with connective tissue involvement. “It’s not always lupus!”, J. BUON. (2012) 17: 417-21. [Google Scholar]

4. Frinc, I. , M.S. Muresan, F. Zaharie, et al . Cancer stem-like cells: the dark knights of clinical hematology and oncology. J. BUON. (2014) 19(2): 328-35. [Google Scholar]

5. Adimy, M. , F. Crauste and S. Ruan . A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. (2005) 65: 1328–1352.  [Article]

6. Dale, D.C. and M.C. Mackey . Understanding, treating and avoiding hematological disease: Better medicine through mathematics? Bull. Math. Biol. (2015) 77: 739–757.  [Article]

7. Foley, C. and M.C. Mackey . Dynamic hematological disease: a review. J. Math. Biol. (2009) 58: 285–322.  [Article]

8. He, Q. , J. Zhu, D. Dingli, et al . Optimized treatment schedules for chronic myeloid leukemia. PLoS Comput. Biol. (2016) 12(10): e1005129. [Article]

9. Jayachandran, D. , A.E. Rundell, R.E. Hannemann, et al . Optimal chemotherapy for leukemia: a model-based strategy for individualized treatment. PLoS ONE (2014) 9(10): e109623. [Article]

10. Kaplan, D. and L. Glass . Understanding Nonlinear Dynamics . New York : Springer (1995). [Book]

11. Mac Lean, A.L. , C. Lo Celso and M.P.H. Stumpf . Population dynamics of normal and leukaemia stem cells in the haematopoietic stem cell niche show distinct regimes where leukaemia will be controlled. J. R. Soc. Interface  (2013) 10: 20120968. [Article]

12. Sbeity, H. and R. Younes. Review of optimization methods for cancer chemotherapy treatment planning. J. Comput. Sci. Syst. Biol. (2015) 8: 74–95. [Article]

13. Mackey, M.C. and L. Glass . Oscillation and chaos in physiological control systems. Science (1977) 197: 287–289. [Article]

14. Dingli, D. and F. Michor . Successful therapy must eradicate cancer stem cells. Stem Cells (2006) 24: 2603–2610. [Article]

15. Cucuianu, A. and R. Precup . A hypothetical-mathematical model of acute myeloid leukemia pathogenesis. Comput. Math. Methods Med. (2010) 11: 49–65. [Taylor & Francis Online], [Google Scholar]

16. Parajdi, L. Modeling the treatment of tumor cells in a solid tumor. J. Nonlinear Sci. Appl. (2014) 7(3): 188–195. [Article]

17. Michor, F. , T.P. Hughes, Y. Iwasa, et al . Dynamics of chronic myeloid leukaemia. Nature (2005) 435: 1267–1270. [Article]

18. Precup, R. , S. Arghirescu, A. Cucuianu, et al . Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation in acute myeloid leukemia. Int. J. Biomath. (2012) 5: 1250026 [18 pages]. [Article]

19. Precup, R. , M.A. Serban, D. Trif, et al . A planning algorithm for correction therapies after allogeneic stem cell transplantation. J. Math. Model. Algor. (2012) 11: 309–323. [Article]

20. Precup, R. Mathematical understanding of the autologous stem cell transplantation. Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity (2012) 10: 155-167. [Google Scholar]

21. Parajdi, L.G. , R. Precup, E.A. Bonci and C. Tomuleasa . A mathematical model of the transition from the normal hematopoiesis to the chronic and acceleration-acute stages in myeloid leukemia. Mathematics (2020) 8(3):376.  [Article]

22. Hideo, E. , M. Yohei and S. Toshio . Heterogeneity and hierarchy of hematopoietic stem cells. Exp. Hematol. (2014) 42(2): 74-82.  [Article]

23. Herzenberg, L.A. , D. Parks, B. Sahaf, et al . The History and Future of the Fluorescence Activated Cell Sorter and Flow Cytometry: A View from Stanford. Clin. Chem. (2002) 48(10): 1819-1827. [Article]

24. Dayneka, N.L. , V. Garg and W.L. Jusko . Comparison of four basic models of indirect pharmacodynamic responses. J. Pharmacokinet. Pharmacodyn. (1993) 21(4): 457-478.  [Article]

25. Karmanov, V.G. Mathematical Programming . Moscow : Mir Publishers  (1989).  [Google Scholar]

26. LuptáČik, M. Mathematical Optimization and Economic Analysis . New York : Springer (2010).  [Book]

27. Heck, A. Introduction to Maple, 3rd edn. New York : Springer (2003). [Book]

28. Parajdi, L.G. Mathematical modeling of cell dynamics and optimization problems in chronic myeloid leukemia therapy (Abstract). 11th European Conference on Mathematical and Theoretical Biology (ECMTB 2018) – Book of Abstracts . Ed. MairaAguiar . Lisbon: Portuguese Mathematical Society. pp. 252-253. [Book of Abstracts] (2018). [Google Scholar]