A Monte Carlo based formalism to identify potential locations at high risk of tumor recurrence with a numerical model for glioblastoma multiforme

PURPOSE: The strategy currently used to treat glioblastoma multiforme (GBM) patients, which mostly relies on population-based failure patterns, does not consider the important variability in such patterns reported in the literature. As part of the multidisciplinary efforts being made to develop personalized therapeutic approaches, numerical models of tumor growth and treatment are increasingly being used by different groups around the world. In this study, a new formalism relying on the proliferation-invasion model is developed to identify potential locations of GBM recurrences. The authors assess the sensitivity of the location of potential tumor recurrences to the input parameter values predicted for a given patient by varying those values using a Monte-Carlo based approach. Our approach is designed to be prospective in the sense that it relies on patient-specific imaging data that can be gathered in one single preradiotherapy imaging session. METHODS: The authors modeled the infiltration paths of glial cells using patient-specific diffusion tensor imaging (DTI) data. Nine GBM patients with preradiotherapy DTI data are considered in this study. The possible locations of tumor recurrences are determined by randomly selecting many ensembles of values for each of the growth and radiobiological parameters in the GBM growth model. A novel concept, the occurrence probability (OP), is introduced to assess the sensitivity of potential tumor recurrence locations to the input parameter values. For a given patient, the OP map is derived from a superposition of all potential tumor recurrence locations obtained with all sets of parameter values. RESULTS: For eight out of nine of patients, the authors have identified a statistically significant region where the OP is above 50%. For two patients, these high risk regions are found to be located at a distance greater than 3.9 cm from the border of the gross tumor volume highlighting the inaccuracy of current margins for some patients. The exact location and size of these volumes with OP > 50 % are, however, sensitive to the number N of ensembles of parameter values for N ≲ 400. On the other hand, the authors have identified for each patient a threshold OP, the OP(T), which defines a volume that converges more rapidly with increasing N. The OP(T) for each patient varies between 20% and 40%. The volume defined by OP > OP(T) may be an adequate candidate to define a personalized margin for radiotherapy treatment planning of GBM patients. CONCLUSIONS: A new Monte-Carlo based formalism was described and used to assess the variability of sites of potential recurrence predicted by the proliferation-invasion model to input parameter values. The authors have shown that high risk areas could be consistently identified with a limited number of sets (N ≲ 400) of randomly chosen parameter values. A major strength of this formalism is its potential prospective nature. Although a validation of the accuracy of the model-predicted tumor recurrence location still remains to be done, our method is potentially applicable to orient patient-specific definition of margins.

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