Lacunarity and fractal dimension as prognostic biomarkers in glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a median survival of only 15 months with standard of care treatment. Typically, these tumors present with regions of necrosis, contrast enhancement and edema, visible on standard clinical magnetic resonance imaging (MRI). The prognostic impact of the shape of these regions has not been fully explored. Lacunarity and fractal dimension are two quantitative morphological measures that describe how shapes fill space and their complexity at varying spatial scales. Both of these measures have been shown to distinguish overall survival (OS) and progression free survival (PFS) when applied to regions of necrosis. In our cohort of patients with first-diagnosis GBM (n=400), we sought to validate these previously published results and extend this work to other tumor-induced imaging abnormalities. We calculated median lacunarity and fractal dimension values of necrosis (n=390), necrosis with contrast enhancement (n=400), and edema (n=257) on a per patient basis and searched for cutoffs that significantly distinguished survival. In our cohort, we found that lacunarity can significantly distinguish PFS when applied to necrosis and can significantly distinguish OS when applied to necrosis with contrast enhancement, or edema. We find that fractal dimension can also significantly distinguish OS when applied to edema. We believe that morphological measures such as lacunarity and fractal dimension may play an important prognosticating role in GBM presentation. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location, or microenvironmental factors that should be further explored.