Mathematical model for predicting malignant transformation of low-grade gliomas

INTRODUCTION. Low grade gliomas (LGG) steadily undergo anaplastic transformation with progression to a higher grade of malignancy. Currently in clinical practice, there is no accurate method that can be used in predicting the risk of progression of a resected tumor that takes into account not only the multifactorial nature of glioma transformation but also the unequal influence of various predictors.
AIM. To develop a mathematical model for predicting the risk of anaplastic transformation of low-grade malignant gliomas after surgical intervention.
MATERIALS AND METHODS. The study group consisted of 52 patients who underwent a second surgery for advanced LGG between 2019 and 2023. Inclusion criteria: age at the time of diagnosis older than 18 years; histologically and molecularly genetically verified LGG; no tumor accumulation of contrast according to MRI before the first surgery; radiopharmaceutical accumulation index according to PET-CT with methionine less than 1.7; Ki-67 expression level less than 6 %; no vascular proliferation and endothelial swelling. Radiological characteristics included localization, tumor size, extent of resection, and contrast accumulation after progression. More than 90 parameters were analyzed to identify factors influencing the progression of LGG. The distribution of all parameters and their comparison were performed using the Mann – Whitney and Kolmogorov – Smirnov criteria, median x2.
RESULTS. A model of probabilistic assessment of transformation risk with the following characteristics was built by means of logistic regression: sex; presence of seizures; tumor localization; histological data; postoperative treatment; time of progression. The role of the presented model is to obtain the characteristics of the logistic function Y for the standard equation, which makes it possible to calculate the probability of transformation depending on the factors and the degree of their influence on each other.
CONCLUSION. Integration of this mathematical model into the plan of dynamic follow-up of patients with LGG will allow to adjust the strategy of observation, diagnosis and treatment.

1. Louis D. N., Perry A., Wesseling P., Brat D. J., Cree I. A., Figarella-Branger D., Hawkins C., Ng H. K., Pfister S. M., Reifenberger G., Soffietti R., von Deimling A., Ellison D. W. The 2021 WHO Classification of Tumors of the Central Nervous System: a summary. Neuro Oncol. 2021;23(8):1231–1251. Doi: 10.1093/neuonc/noab106. PMID: 34185076; PMCID: PMC8328013.

2. Pouratian N., Schiff D. Management of low-grade glioma. Curr Neurol Neurosci Rep. 2010;10(3):224–231. Doi: 10.1007/s11910-010-0105-7. PMID: 20425038; PMCID: PMC2857752.

3. Jakola A. S., Myrmel K. S., Kloster R., Torp S. H., Lindal S., Unsgård G., Solheim O. Comparison of a strategy favoring early surgical resection vs a strategy favoring watchful waiting in low-grade gliomas. JAMA. 2012;308(18):1881–1888. Doi: 10.1001/jama.2012.12807. PMID: 23099483.

4. Smith J. S., Chang E. F., Lamborn K. R., Chang S. M., Prados M. D., Cha S., Tihan T., Vandenberg S., McDermott M. W., Berger M. S. Role of extent of resection in the long-term outcome of low-grade hemispheric gliomas. J Clin Oncol. 2008;26(8):1338–1345. Doi: 10.1200/JCO.2007.13.9337. PMID: 18323558.

5. Pignatti F., van den Bent M., Curran D., Debruyne C. et al. European Organization for Research and Treatment of Cancer Brain Tumor Cooperative Group; European Organization for Research and Treatment of Cancer Radiotherapy Cooperative Group. Prognostic factors for survival in adult patients with cerebral low-grade glioma. J Clin Oncol. 2002;20(8):2076–2084. Doi: 10.1200/JCO.2002.08.121. PMID: 11956268.

6. Pallud J., Varlet P., Devaux B., Geha S., Badoual M., Deroulers C., Page P., Dezamis E., Daumas-Duport C., Roux F. X. Diffuse low-grade oligodendrogliomas extend beyond MRI-defined abnormalities. Neurology. 2010;74(21):1724–1731. Doi: 10.1212/WNL.0b013e3181e04264. PMID: 20498440.

7. Garcia D. M., Fulling K. H., Marks J. E. The value of radiation therapy in addition to surgery for astrocytomas of the adult cerebrum. Cancer. 1985;55(5):919–927. Doi: 10.1002/1097-0142(19850301)55:5<919::aid-cncr2820550502>3.0.co;2-4. PMID: 3967199.

8. Karim A. B., Maat B., Hatlevoll R., Menten J, Rutten EH, et al. A randomized trial on dose-response in radiation therapy of low-grade cerebral glioma: European Organization for Research and Treatment of Cancer (EORTC) Study 22844. Int J Radiat Oncol Biol Phys. 1996;36(3):549–556. Doi: 10.1016/s0360-3016(96)00352-5. PMID: 8948338.

9. Buckner J. C., Shaw E. G., Pugh S. L., Chakravarti A., Gilbert M. R. et al. Radiation plus Procarbazine, CCNU, and Vincristine in Low-Grade Glioma. N Engl J Med. 2016;374(14):1344–1355. Doi: 10.1056/NEJMoa1500925. PMID: 27050206; PMCID: PMC5170873.

10. van den Bent M. J., Taphoorn M. J., Brandes A. A., Menten J., Stupp R., Frenay M., Chinot O., Kros J. M., van der Rijt C. C., Vecht Ch. J., Allgeier A., Gorlia T. European Organization for Research and Treatment of Cancer Brain Tumor Group. Phase II study of first-line chemotherapy with temozolomide in recurrent oligodendroglial tumors: the European Organization for Research and Treatment of Cancer Brain Tumor Group Study 26971. J Clin Oncol. 2003;21(13):2525–2528. Doi: 10.1200/JCO.2003.12.015. PMID: 12829671.

11. Cairncross J. G., Ueki K., Zlatescu M. C., Lisle D. K., Finkelstein D. M., Hammond R. R., Silver J. S., Stark P. C., Macdonald D. R., Ino Y., Ramsay D. A., Louis D. N. Specific genetic predictors of chemotherapeutic response and survival in patients with anaplastic oligodendrogliomas. J Natl Cancer Inst. 1998;90(19):1473–1479. Doi: 10.1093/jnci/90.19.1473. PMID: 9776413.

12. Fisher B. J., Pugh S. L., Macdonald D. R., Chakravatri A., Lesser G. J. et al. Phase 2 Study of a Temozolomide-Based Chemoradiation Therapy Regimen for High-Risk, LowGrade Gliomas: Long-Term Results of Radiation Therapy Oncology Group 0424. Int J Radiat Oncol Biol Phys. 2020;107(4):720–725. Doi: 10.1016/j.ijrobp.2020.03.027. PMID: 32251755; PMCID: PMC7456814.

13. Yan H., Parsons D. W., Jin G., McLendon R., Rasheed B. A., Yuan W., Kos I., Batinic-Haberle I., Jones S., Riggins G. J., Friedman H., Friedman A., Reardon D., Herndon J., Kinzler K. W., Velculescu V. E., Vogelstein B., Bigner D. D. IDH1 and IDH2 mutations in gliomas. N Engl J Med. 2009;360(8):765–773. Doi: 10.1056/NEJMoa0808710. PMID: 19228619; PMCID: PMC2820383.

14. Ohgaki H., Kleihues P. Genetic profile of astrocytic and oligodendroglial gliomas. Brain Tumor Pathol. 2011;28(3):177–183. Doi: 10.1007/s10014-011-0029-1. PMID: 21442241.

15. Balss J., Meyer J., Mueller W., Korshunov A., Hartmann C., von Deimling A. Analysis of the IDH1 codon 132 mutation in brain tumors. Acta Neuropathol. 2008;116(6):597–602. Doi: 10.1007/s00401-008-0455-2. PMID: 18985363.

16. Ramensky V. V., Ulitin A. Yu., Kalmens V. Ya. et al. Sign “non-conformities; T2/FLAIR as a neuroimaging marker of the genetic profile of low-grade gliomas. Russian neurosurgical journal named after professor A. L. Polenov. 2023;15(2):81–87. (In Russ.). Doi: 10.56618/2071-2693_2023_15_2_81. EDN; WWQNOW.

17. Johnson B. E., Mazor T., Hong C., Barnes M., Aihara K., McLean C. Y. et al. Mutational analysis reveals the origin and therapy-driven evolution of recurrent glioma. Science. 2014;343(6167):189–193. Doi: 10.1126/science.1239947. PMID: 24336570; PMCID: PMC3998672.

18. Touat M., Li Y. Y., Boynton A. N., Spurr L. F., Iorgulescu J. B., Bohrson C. L. et al. Mechanisms and therapeutic implications of hypermutation in gliomas. Nature. 2020;580(7804):517–523. Doi: 10.1038/s41586-020-2209-9. PMID: 32322066; PMCID: PMC8235024.

19. Murphy E. S., Leyrer C. M., Parsons M., Suh J. H., Chao S. T. et al. Risk Factors for Malignant Transformation of Low-Grade Glioma. Int J Radiat Oncol Biol Phys. 2018;100(4):965–971. Doi: 10.1016/j.ijrobp.2017.12.258. PMID: 29485076.

20. Michor F., Beal K. Improving Cancer Treatment via Mathematical Modeling: Surmounting the Challenges Is Worth the Effort. Cell. 2015;163(5):1059–1063. doi: 10.1016/j.cell.2015.11.002. PMID: 26590416; PMCID: PMC4676401.

21. Altrock P. M., Liu L. L., Michor F. The mathematics of cancer: integrating quantitative models. Nat Rev Cancer. 2015;15(12):730–745. doi: 10.1038/nrc4029. PMID: 26597528.

22. Maley C. C., Aktipis A., Graham T. A., Sottoriva A., Boddy A. M., Janiszewska M., Silva A. S., Gerlinger M., Yuan Y. et al. Classifying the evolutionary and ecological features of neoplasms. Nat Rev Cancer. 2017;17(10):605–619. doi: 10.1038/nrc.2017.69. PMID: 28912577; PMCID: PMC5811185.

23. Gallaher J. A., Massey S. C., Hawkins-Daarud A., Noticewala S. S. et al. From cells to tissue: How cell scale heterogeneity impacts glioblastoma growth and treatment response. PLoS Comput Biol. 2020;16(2):e1007672. doi: 10.1371/journal.pcbi.1007672. PMID: 32101537; PMCID: PMC7062288.

24. Leder K., Pitter K., LaPlant Q., Hambardzumyan D., Ross B. D., Chan T. A., Holland E. C., Michor F. Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules. Cell. 2014;156(3):603–616. doi: 10.1016/j.cell.2013.12.029. PMID: 24485463; PMCID: PMC3923371.

25. Tom M. C., Park D. Y. J., Yang K., Leyrer C. M. et al. Malignant Transformation of Molecularly Classified Adult Low-Grade Glioma. Int J Radiat Oncol Biol Phys. 2019;105(5):1106–1112. doi: 10.1016/j.ijrobp.2019.08.025. PMID: 31461674.

26. Chaichana K. L., McGirt M. J., Laterra J., Olivi A., Quiñones-Hinojosa A. Recurrence and malignant degeneration after resection of adult hemispheric lowgrade gliomas. J Neurosurg. 2010;112(1):10–17. doi: 10.3171/2008.10.JNS08608. PMID: 19361270.

27. Toh C. H., Castillo M., Wei K. C., Chen P. Y. MRS as an Aid to Diagnose Malignant Transformation in Low-Grade Gliomas with Increasing Contrast Enhancement. AJNR Am J Neuroradiol. 2020;41(9):1592–1598. doi: 10.3174/ajnr.A6688. PMID: 32732270; PMCID: PMC7583095.

28. Satar Z., Hotton G., Samandouras G. Systematic review-Time to malignant transformation in low-grade gliomas: Predicting a catastrophic event with clinical, neuroimaging, and molecular markers. Neurooncol Adv. 2021;3(1):vdab101. doi: 10.1093/noajnl/vdab101. PMID: 34466805; PMCID: PMC8403481.

29. Nakasu S., Nakasu Y. Malignant Progression of Diffuse Low-grade Gliomas: A Systematic Review and Meta-analysis on Incidence and Related Factors. Neurol Med Chir (Tokyo). 2022;62(4):177–185. Doi: 10.2176/jns-nmc.2021-0313. PMID: 35197400; PMCID: PMC9093671.

30. Swanson K. R., Rockne R. C., Claridge J., Chaplain M. A., Alvord E. C. Jr., Anderson A. R. Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res. 2011;71(24):7366–7375. Doi: 10.1158/0008-5472.CAN-11-1399. PMID: 21900399; PMCID: PMC3398690.

31. Bogdańska M. U., Bodnar M., Piotrowska M. J., Murek M., Schucht P., Beck J., Martínez-González A., Pérez-García V. M. A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications. PLoS One. 2017;12(8):e0179999. Doi: 10.1371/journal.pone.0179999. PMID: 28763450; PMCID: PMC5538650.

32. Wong A. M., Siow T. Y., Wei K. C., Chen P. Y., Toh C. H., Castillo M. Prediction of Malignant Transformation of WHO II Astrocytoma Using Mathematical Models Incorporating Apparent Diffusion Coefficient and Contrast Enhancement. Front Oncol. 2021;11:744827. Doi: 10.3389/fonc.2021.744827. PMID: 34660309; PMCID: PMC8511697.

33. Aoki K., Suzuki H., Yamamoto T., Yamamoto K. N., Maeda S., Okuno Y., Ranjit M., Motomura K., Ohka F. et al. Mathematical Modeling and Mutational Analysis Reveal Optimal Therapy to Prevent Malignant Transformation in Grade II IDH-Mutant Gliomas. Cancer Res. 2021;81(18):4861–4873. Doi: 10.1158/0008-5472.CAN-21-0985. PMID: 34333454; PMCID: PMC9635454.

34. Colman H., Giannini C., Huang L., Gonzalez J., Hess K., Bruner J., Fuller G., Langford L., Pelloski C., Aaron J., Burger P., Aldape K. Assessment and prognostic significance of mitotic index using the mitosis marker phospho-histone H3 in low and intermediate-grade infiltrating astrocytomas. Am J Surg Pathol. 2006;30(5):657–664. Doi: 10.1097/01.pas.0000202048.28203.25. PMID: 16699322.

35. Vera E., Christ A., Grajkowska E., Briceno N., Choi A., Crandon S. K., Wall K., Lindsley M., Leeper H. E., Levine J., Reyes J. et al. Relationship between RANO-PRO Working Group standardised priority constructs and disease progression among malignant glioma patients: A retrospective cohort study. EClinicalMedicine. 2022;55:101718. Doi: 10.1016/j.eclinm.2022.101718. PMID: 36386035; PMCID: PMC9661442.

36. Pallud J., Audureau E., Blonski M., Sanai N., Bauchet L. et al. Epileptic seizures in diffuse low-grade gliomas in adults. Brain. 2014;137(Pt 2):449–462. Doi: 10.1093/brain/awt345. PMID: 24374407.

37. Capelle L., Fontaine D., Mandonnet E., Taillandier L., Golmard J. L. et al. Spontaneous and therapeutic prognostic factors in adult hemispheric World Health Organization Grade II gliomas: a series of 1097 cases: clinical article. J Neurosurg. 2013;118(6):1157–1168. Doi: 10.3171/2013.1.JNS121. PMID: 23495881.

38. Wen B., Fu F., Hu L., Cai Q., Xie J. Subventricular zone predicts high velocity of tumor expansion and poor clinical outcome in patients with low grade astrocytoma. Clin Neurol Neurosurg. 2018;168:12–17. Doi: 10.1016/j.clineuro.2018.02.036. PMID: 29500965.

39. Cancer Genome Atlas Research Network; Brat D. J.; Verhaak R. G.; Aldape K. D.; Yung W. K.; Salama S. R.; Cooper L. A.; Rheinbay E.; Miller C. R.; Vitucci M. et al. Comprehensive, Integrative Genomic Analysis of Diffuse Lower-Grade Gliomas. N. Engl. J. Med. 2015;(372):2481–2498. Doi: 10.1056/NEJMoa1402121. PMID: 26061751; PMCID: PMC4530011.

40. Choi S., Yu Y., Grimmer M. R., Wahl M., Chang S. M., Costello J. F. Temozolomide-associated hypermutation in gliomas. Neuro Oncol. 2018;20(10):1300–1309. Doi: 10.1093/neuonc/noy016. PMID: 29452419; PMCID: PMC6120358.

41. Sokolov I. A., Ulitin A. Yu., Vasilenko A. V., Bulaeva M. A. Results of surgical treatment of patients with epilepsy associated with primary neuroepithelial brain tumors of supratentorial localization in adults. Russian neurosurgical journal named after professor A. L. Polenov. 2023;15(3):122–127. (In Russ.). Doi: 10.56618/2071-2693_2023_15_3_122. EDN; VFYXRD.