Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models

We optimize radiotherapy (RT) administration strategies for treating low-grade gliomas. Specifically, we consider different tumour growth laws, both with and without spatial effects. In each scenario, we find the optimal treatment in the sense of maximizing the overall survival time of a virtual low-grade glioma patient, whose tumour progresses according to the examined growth laws. We discover that an extreme protraction therapeutic strategy, which amounts to substantially extending the time interval between RT sessions, may lead to better tumour control. The clinical implications of our results are also presented.

[1]  J. G. Skellam.  Random dispersal in theoretical populations , 1951, Biometrika.

[2]  Juan Belmonte-Beitia,et al.  Bright solitary waves in malignant gliomas. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  P Schucht,et al.  A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications. , 2017, Mathematical biosciences.

[4]  H Duffau,et al.  Improving the time‐machine: estimating date of birth of grade II gliomas , 2012, Cell proliferation.

[5]  P K Maini,et al.  Modelling biological invasions: Individual to population scales at interfaces. , 2013, Journal of theoretical biology.

[6]  R. Guillevin,et al.  Velocity of tumor spontaneous expansion predicts long-term outcomes for diffuse low-grade gliomas. , 2013, Neuro-oncology.

[7]  I. Spiteri,et al.  Current Challenges in Glioblastoma: Intratumour Heterogeneity, Residual Disease, and Models to Predict Disease Recurrence , 2015, Front. Oncol..

[8]  A. Karim,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. , 1996, International journal of radiation oncology, biology, physics.

[9]  K Hendrickson,et al.  Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach , 2010, Physics in medicine and biology.

[10]  Paul Kinahan,et al.  A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18F-FMISO-PET , 2015, Journal of The Royal Society Interface.

[11]  E. Jung,et al.  Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery , 2015, Journal of The Royal Society Interface.

[12]  John M. L. Ebos,et al.  Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth , 2014, PLoS Comput. Biol..

[13]  Kevin J. Harrington,et al.  The tumour microenvironment after radiotherapy: mechanisms of resistance and recurrence , 2015, Nature Reviews Cancer.

[14]  G. Reifenberger,et al.  The 2016 World Health Organization Classification of Tumors of the Central Nervous System: a summary , 2016, Acta Neuropathologica.

[15]  Johan Pallud,et al.  A Tumor Growth Inhibition Model for Low-Grade Glioma Treated with Chemotherapy or Radiotherapy , 2012, Clinical Cancer Research.

[16]  Marek Bodnar,et al.  A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications , 2017, PloS one.

[17]  Andreas Raabe,et al.  Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas , 2019, PLoS computational biology.

[18]  J. Thijssen,et al.  Mathematical Methods for Physics and Engineering: A Comprehensive Guide , 1998 .

[19]  Luc Taillandier,et al.  Computational modeling of the WHO grade II glioma dynamics: principles and applications to management paradigm , 2008, Neurosurgical Review.

[20]  V. Tombolini,et al.  Radiation Tolerance of Normal Brain: QUANTEC 2010 and Beyond , 2016 .

[21]  R. Guillevin,et al.  Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging , 2005, Magnetic resonance in medicine.

[22]  Changes in the retreatment radiation tolerance of the spinal cord with time after the initial treatment , 2018, International journal of radiation biology.

[23]  Peter Canoll,et al.  Glial progenitor cell recruitment drives aggressive glioma growth: mathematical and experimental modelling , 2012, Journal of The Royal Society Interface.

[24]  Alicia Martínez-González,et al.  Delay effects in the response of low-grade gliomas to radiotherapy: a mathematical model and its therapeutical implications. , 2014, Mathematical medicine and biology : a journal of the IMA.

[25]  Norman F. Kirkby,et al.  A mathematical model of brain tumour response to radiotherapy and chemotherapy considering radiobiological aspects. , 2010, Journal of theoretical biology.

[26]  Ignacio Ramis-Conde,et al.  Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas , 2017, Commun. Nonlinear Sci. Numer. Simul..

[27]  Walter J. Curran,et al.  Radiation plus Procarbazine, CCNU, and Vincristine in Low-Grade Glioma. , 2016, The New England journal of medicine.

[28]  R Grant,et al.  Guidelines on management of low‐grade gliomas: report of an EFNS–EANO * Task Force , 2010, European journal of neurology.

[29]  P. Varlet,et al.  Oedema‐based model for diffuse low‐grade gliomas: application to clinical cases under radiotherapy , 2014, Cell proliferation.

[30]  Gabriel F. Calvo,et al.  Effective particle methods for Fisher-Kolmogorov equations: Theory and applications to brain tumor dynamics , 2014, Commun. Nonlinear Sci. Numer. Simul..

[31]  G. Reifenberger,et al.  Advances in the molecular genetics of gliomas — implications for classification and therapy , 2017, Nature Reviews Clinical Oncology.

[32]  Brigitta G. Baumert,et al.  Temozolomide chemotherapy versus radiotherapy in high-risk low-grade glioma , 2016, The Lancet. Oncology.

[33]  Hervé Delingette,et al.  Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins , 2010, Medical Image Anal..

[34]  S. Disney,et al.  On the Lambert W function: EOQ applications and pedagogical considerations , 2010 .

[35]  D. Indelicato,et al.  Late Effects After Radiotherapy for Childhood Low-grade Glioma , 2016, American journal of clinical oncology.

[36]  G. F. Calvo,et al.  Interplay of Darwinian Selection, Lamarckian Induction and Microvesicle Transfer on Drug Resistance in Cancer , 2019, Scientific Reports.

[37]  J. Murray,et al.  Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion , 2003, Journal of the Neurological Sciences.

[38]  E. Jung,et al.  Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy , 2019, PloS one.

[39]  Víctor M. Pérez-García,et al.  Hypoxic Cell Waves Around Necrotic Cores in Glioblastoma: A Biomathematical Model and Its Therapeutic Implications , 2012, Bulletin of Mathematical Biology.

[40]  K. Painter,et al.  Mathematical modelling of glioma growth: the use of Diffusion Tensor Imaging (DTI) data to predict the anisotropic pathways of cancer invasion. , 2013, Journal of theoretical biology.

[41]  Víctor M. Pérez-García,et al.  Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas , 2019, bioRxiv.

[42]  Marek Bodnar,et al.  Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy , 2019, Commun. Nonlinear Sci. Numer. Simul..

[43]  A. Michalowski.  Effects of radiation on normal tissues: Hypothetical mechanisms and limitations of in situ assays of clonogenicity , 1981, Radiation and environmental biophysics.

[44]  G Powathil,et al.  Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy , 2007, Physics in medicine and biology.

[45]  E. Kostelich,et al.  Virtual glioblastoma: growth, migration and treatment in a three‐dimensional mathematical model , 2009, Cell proliferation.

[46]  H. Frieboes,et al.  Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method. , 2008, Journal of theoretical biology.

[47]  Geirmund Unsgård,et al.  Comparison of a strategy favoring early surgical resection vs a strategy favoring watchful waiting in low-grade gliomas. , 2012, JAMA.

[48]  M. Williams,et al.  Basic clinical radiobiology , 1994, British Journal of Cancer.

[49]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[50]  K. Swanson,et al.  A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle , 2007, British Journal of Cancer.

[51]  Jennifer S. Yu,et al.  Risk Factors for Malignant Transformation of Low-Grade Glioma. , 2017, International journal of radiation oncology, biology, physics.

[52]  E. Yorke,et al.  Use of normal tissue complication probability models in the clinic. , 2010, International journal of radiation oncology, biology, physics.

[53]  C Norman Coleman,et al.  Effects of radiation on normal tissue: consequences and mechanisms. , 2003, The Lancet. Oncology.

[54]  B. Ross,et al.  Mathematical Modeling of PDGF-Driven Glioblastoma Reveals Optimized Radiation Dosing Schedules , 2014, Cell.

[55]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[56]  Philip Gerlee,et al.  The model muddle: in search of tumor growth laws. , 2012, Cancer research.

[57]  Olivier Clatz,et al.  Biocomputing: numerical simulation of glioblastoma growth and comparison with conventional irradiation margins. , 2011, Physica medica : PM : an international journal devoted to the applications of physics to medicine and biology : official journal of the Italian Association of Biomedical Physics.

[58]  V. Pérez-García,et al.  Extreme protraction for low grade gliomas: Theoretical proof of concept of a novel therapeutical strategy , 2014, 1407.2228.