Shape matters: morphological metrics of glioblastoma imaging abnormalities as biomarkers of prognosis

Lacunarity, a quantitative morphological measure of how shapes fill space, and fractal dimension, a morphological measure of the complexity of pixel arrangement, have shown relationships with outcome across a variety of cancers. However, the application of these metrics to glioblastoma (GBM), a very aggressive primary brain tumor, has not been fully explored. In this project, we computed lacunarity and fractal dimension values for GBM-induced abnormalities on clinically standard magnetic resonance imaging (MRI). In our patient cohort (n = 402), we connect these morphological metrics calculated on pretreatment MRI with the survival of patients with GBM. We calculated lacunarity and fractal dimension on necrotic regions (n = 390), all abnormalities present on T1Gd MRI (n = 402), and abnormalities present on T2/FLAIR MRI (n = 257). We also explored the relationship between these metrics and age at diagnosis, as well as abnormality volume. We found statistically significant relationships to outcome for all three imaging regions that we tested, with the shape of T2/FLAIR abnormalities that are typically associated with edema showing the strongest relationship with overall survival. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location or microenvironmental factors that should be further explored.


Cohort numbers for patients with known overall survival (OS) and progression free survival (PFS).
This table shows the patients with known OS and PFS, including the subsets known to have received the current standard of care (SOC). We also present how these cohorts are split by patient sex. The discrepancy between patients with necrosis ROIs and T1Gd enhancing is due to 10 patients with negligible necrosis that did not meet our criteria to be included in this retrospective study. Mean fractal dimension tests that showed at least one significant cutoff that distinguishes survival. We show both overall survival (OS) and progression free survival (PFS) with those that were significant in light gray. The results that remained significant while adjusting for multiple comparisons are shown in dark gray.

Supplement 3: Intraclass Coefficients of Lacunarity and Fractal Dimension Values
On a subset of images with multiple segmentations available (most had two, some with three or four), we tested the intraclass coefficients (ICCs) of lacunarity and fractal dimension across the three imaging abnormalities presented in the main text. This was carried out using the two-way case with multiple raters in the irrNA package in R (1).
We present the

Multivariate CPH for Progression-Free Survival
Multivariate Cox proportional hazard model for progression-free survival. Separate analyses for necrosis (n=125), enhancement with necrosis (n=130) and edema (n=78) are all presented here. (Left) No significance was found for any variables. (Right) Lacunarity of enhancement with necrosis showed significant influence for overall survival. The only other variable to show significance was necrosis radius. 9

Multivariate CPH for Overall Survival
Multivariate Cox proportional hazard model for overall survival. Extent of resection coded with biopsy as control, STR=Subtotal resection, GTR=Gross total resection. Separate analyses for necrosis (n=263), enhancement with necrosis (n=274) and edema (n=155) are all presented here. (Left) Fractal dimension of edema was significantly associated with overall survival, along with most variables included. (Right) Lacunarity of edema showed significant influence for overall survival alongside many other variables presented here.

Image Resolution against Lacunarity and Fractal Dimension Values
We ran Kruskal-Wallis tests to determine the existence of a relationship between image resolution and lacunarity/fractal dimension values. We present the outcome of these 6 tests here: We see lacunarity is significantly associated with resolution in all three imaging abnormalities. Image count presented above each boxplot.  We observe significant relationships between fractal dimension and image resolution in enhancement with necrosis and edema regions, but not in necrosis. Image count presented above each boxplot

Multivariate CPH Overall Survival Plots Including Image Resolution
Multivariate CPH plots showing (left) image resolution (divided by 100 for visual scale), radius (cm), age (decades) and lacunarity (right) image resolution (divided by 100 for visual scale), radius (cm), age (decades) and fractal dimension. Comparing this result to Figure 5 in the main manuscript, we see that significant lacunarity and fractal dimension results persisted through the inclusion of image resolution. Interestingly, we see T2/FLAIR resolution was significantly associated with survival in the left panel, this is in opposition to the lacunarity result (which was more significant as a result), and may point to an increase in image resolution over time alongside slight improvements in overall survival. This suggests that the relationships between resolution and imaging metrics are not the drivers of the prognostic signal we observe in the main text.