Application of Boolean Algebra for Definition of Myeloid Neoplasms

Main Article Content

Gerhard Zugmaier Sophie Kerkmann Franco Locatelli

Abstract

The definition of disease has become increasingly complex in the last 20 years. Especially the definition of tumors of hematopoietic and lymphoid tissues includes multiple parameters such as cytology, histology, immune phenotyping, cytogenetics and molecular genetics. Myeloid neoplasms include an especially high number of permutations of these parameters, requiring a mathematical approach. Mathematical concepts have the merit to show what can be proven and what can be calculated. Boolean algebra also sometimes called “mathematical logic” has been shown to be a useful tool of the definition of acute leukemias. This tool was also applied in this study for the definition of the more complex myeloid neoplasms. The binary number system was used that only includes the sequence of 0 and 1. Presence of a diagnostic parameter was coded by 1, absence by 0. Disease was defined not only by an algorithm but also by symbolic calculation. This way, myeloid neoplasms could successfully be defined by an algebraic system.

Keywords: Boolean Algebra, Application of Boolean Algebra, Boolean Algebra for Definition of Myeloid Neoplasms, Myeloid Neoplasms, Definition of Myeloid Neoplasms, Application of Boolean Algebra for Definition of Myeloid Neoplasms

Article Details

How to Cite
ZUGMAIER, Gerhard; KERKMANN, Sophie; LOCATELLI, Franco. Application of Boolean Algebra for Definition of Myeloid Neoplasms. Medical Research Archives, [S.l.], v. 11, n. 1, jan. 2023. ISSN 2375-1924. Available at: <https://esmed.org/MRA/mra/article/view/3456>. Date accessed: 23 feb. 2024. doi: https://doi.org/10.18103/mra.v11i1.3456.
Section
Research Articles

References

1. Swerdlow, SH et al. WHO Classification of Tumours of Haematopoietic and Lymphoid Tissues, World Health Organization Classification of Tumours. 4th ed. Lyon: International Agency for Research on Cancer; 2008.

2. Swerdlow SH et al. WHO Classification of Tumours of Haematopoietic and Lymphoid Tissues. Revised 4th ed. Lyon: International Agency for Research on Cancer; 2017.

3. Zugmaier G, Locatelli F. Application of Mathematical Logic for Immunophenotyping of B-Cell Precursor Acute Lymphoblastic Leukemia (BCP-ALL). Biomedical Genetics and Genomics. 2019;4: 1-3. doi:10.15761/bgg.1000148

4. Zugmaier G, Locatelli F. Application of Mathematical Logic for Cytogenetic Definition and Risk Stratification of B-Cell Precursor Acute Lymphoblastic Leukemia (BCP-ALL). Medical Research Archives. 2021;9(2):1-8. doi:10.18103/mra.v9i2.2328

5. Brown FM. Boolean Reasoning: The Logic of Boolean Equations. 2nd ed. Mineola, New York: Dover; 2003.

6. Takeuti G. Proof Theory. 2nd ed. Amsterdam, North Holland: Dover Publications; 1987.

7. Hoffmann DW. Grundlagen der technischen Informatik. 5. Auflage. München: Carl Hanser Verlag; 2016

8. Matthäus F, Matthäus S, Harris S, Hillen T. The Art of Theoretical Biology. Springer; 2020.

9. Albert R, Robeva R. Signaling Networks: Asynchronous Boolean Models. Algebraic and Discrete Mathematical Methods for Modern Biology. 2015:65-91. doi:10.1016/b978-0-12-801213-0.00004-6

10. He Q, Macauley M, Davies R. Dynamics of Complex Boolean Networks. Algebraic and Discrete Mathematical Methods for Modern Biology. 2015:93-119. doi:10.1016/b978-0-12-801213-0.00005-8

11. Lin P-CK, Khatri SP. Logic Synthesis for Genetic Diseases: Modeling Disease Behavior Using Boolean Networks. New York, New York: Springer; 2014.

12. Macauley M, Youngs N. The Case for Algebraic Biology: From Research to Education. Bulletin of Mathematical Biology. 2020;82(9):115. doi:10.1007/s11538-020-00789-w

13. Varadan V, Anastassiou D. Inference of Disease-Related Molecular Logic from Systems-Based Microarray Analysis. PLoS Computational Biology. 2006;2(6): 585-597. doi:10.1371/journal.pcbi.0020068.eor

14. DiAndreth B, Hamburger AE, Xu H, Kamb A. The TMOD Cellular Logic Gate as a Solution for Tumor-Selective Immunotherapy. Clinical Immunology. 2022;241: 1-8. doi:10.1016/j.clim.2022.109030

15. Riede U, Moore GW, Williams MB. Quantitative Pathology by Means of Symbolic Logic. CRC Critical Reviews in Toxicology. 1983;11(4):279-332. doi:10.3109/10408448309037457

16. Palma A, Iannuccelli M, Rozzo I, et al. Integrating Patient-Specific Information into Logic Models of Complex Diseases: Application to Acute Myeloid Leukemia. Journal of Personalized Medicine. 2021;11(2):117. doi:10.3390/jpm11020117

17. Grattan-Guinness I. Mathematics and Symbolic Logics: Some Notes on an Uneasy Relationship. History and Philosophy of Logic. 1999;20(3-4):159-167. doi:10.1080/01445349950044116

18. Leitgeb H. Hype: A System of Hyperintensional Logic (With an Application to Semantic Paradoxes). Journal of Philosophical Logic. 2019;48(2):305-405. doi:10.1007/s10992-018-9467-0

19. Steffens HJ, Muehlmann K, Zoellner C. Mathematik für Informatiker für Dummies. Weinheim: Wiley – VCH; 2020

20. Hua H, Hovestadt L. P-adic Numbers Encode Complex Networks. Nature. 2021;11(17). doi:10.1038/s41598-020-79507-4