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

Abstract

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.

Figure 1

Computing lacunarity and fractal dimension (FD) and testing the statistical significance of these against patient survival data. (A) As an example, lacunarity and FD are computed on each slice of T1Gd necrosis segmentations. The median of these values is stored, giving one value of lacunarity and FD for each patient. We do the same for T1Gd enhancement with necrosis, and T2/FLAIR edematous regions. (B) Individual median values are collated into a cohort analysis. Each median value that does not split the cohort into groups of less than 10% of the cohort size is then tested as a cutoff to distinguish either overall survival or progression free survival. A log-rank test provides a significance value for each potential cutoff and a log-rank statistic is calculated alongside a separate significance threshold that accounts for multiple comparisons. The maximal log-rank statistic is chosen as this maximally distinguishes the two groups. This is carried out for lacunarity and FD, across necrosis, enhancement with necrosis, and edema regions.

Figure 2

Results amongst all patients that remained significant with adjustment (A) The group of lower median lacunarity values of enhancement with necrosis (Lac ≤ 0.3074) were associated with prolonged overall survival. (B) The group of lower median lacunarity values of edema were associated with longer overall survival (Lac ≤ 0.4817). (C) The group of higher median fractal dimension values of edema were associated with longer overall survival (FD > 1.6543). (D) An example patient with lower overall survival of 193 days who consistently fell into the short overall survival groups of subpanels A-C. Example MRI slices shown with translucent segmentation overlays. (E) An example patient with longer overall survival of 900 days, who consistently fell into the longer overall survival groups of subpanels A-C. Example MRI slices shown with translucent segmentation overlays.

Figure 3

Fractal dimension and lacunarity cutoffs that significantly distinguish survival amongst patients confirmed to have received the current standard of care. (A) Fractal dimension of necrosis regions significantly distinguished OS. (B) Fractal dimension of necrosis regions significantly distinguished PFS. (C) Lacunarity significantly distinguished PFS. All three results remained significant with adjustment. Adjusted p values shown in bold.

Figure 4

Univariate Cox proportional hazard models for age at diagnosis, fractal dimension, lacunarity and tumor radius, across all three regions (necrosis n = 390, enhancement with necrosis n = 402, edema n = 257). Both fractal dimension and lacunarity of edema-related abnormalities are significant prognostic indicators of overall survival. Age at diagnosis was significant for all three regions, while radius was significant for both necrosis and enhancement with necrosis. Values of these tests can be found in Supplement 4.

Figure 5

(Left) Multivariate CPH models of lacunarity, age at diagnosis, and abnormality radius for necrosis (n = 390), enhancement with necrosis (n = 402), and edema regions (n = 257). Lacunarity of both edema and enhancement with necrosis were significant predictors of overall survival in their respective models (p = 0.0007 and p = 0.042, respectively). Age at diagnosis, as expected, was consistently significant for survival. Radius was a significant predictor for regions of necrosis and enhancement with necrosis (p = 0.036). (Right) Corresponding Cox proportional hazard model of fractal dimension, age at diagnosis, and abnormality radii for necrosis, enhancement with necrosis, and edematous regions. Fractal dimension values of both edema and enhancement with necrosis were significant predictors of overall survival in their respective CPH models (p < 0.0001 and p = 0.0003, respectively). Age at diagnosis was consistently significant across all CPH models, while only enhancement with necrosis, and necrosis radii were significant (p = 0.0018 and p = 0.028, respectively). For a complete table including confidence intervals and significance values, see Supplement 4.

Figure 6

Significant differences in lacunarity and fractal dimension between regions of interest. (Left) We note significant differences in lacunarity values across all three regions of interest, with necrosis the highest, followed by edema, followed by enhancement with necrosis (all comparisons p < 0.001). (Right) Fractal dimension values are significantly higher in edema and enhancement with necrosis when compared with necrosis (p < 0.001), but we did not observe significant differences in fractal dimension between edema and enhancement with necrosis (p = 0.49).

Figure 7

Significant relationships between morphology and age reversed between enhancement with necrosis and edematous regions. (Top row) We see a weak significantly negative correlation between lacunarity and age at diagnosis in enhancement with necrosis ROIs (p = 0.0217, R = − 0.11) and a weak significantly positive correlation within edema ROIs (p = 0.0035, R = 0.18). (Bottom row) We see weak significant relationships between fractal dimension and age at diagnosis within enhancement with necrosis (p < 0.001, R = 0.19) and edema ROIs (p < 0.001, R = − 0.21), respectively. Fractal dimension of enhancement with necrosis is positively correlated with age at diagnosis whereas the fractal dimension of edema ROIs has a negative correlation. Trend lines are shown for significant correlations.