Meningiomas are the most common primary central nervous system tumors, accounting for 39.7% of cases [13]. Preoperative knowledge of the WHO grade can significantly influence the therapeutic plan for meningiomas, as their treatment ranges from close monitoring to radical tumor resection with or without postsurgical radiation therapy. A commonly employed strategy is surgical resection of tumors that show growth, edematous tissue reaction, or cause neurological symptoms [14]. The prognosis of meningiomas classified as CNS WHO grade 1 (low-grade) is significantly better than that of WHO grade 2/3 (high-grade) tumors [15], allowing for less aggressive treatment strategies. In contrast, patients with high-grade meningiomas may benefit from radical surgery (including dura and skull bone removal, combined with dura-skull reconstructive measures). With the recent spread of radiomic methods, significant research is being directed toward the non-invasive determination of the histological classification of meningiomas.

Traditional radiomics approaches predominantly analyze texture features at fixed spatial scales or examine local pixel neighborhoods to extract statistical measures of intensity distributions, whereas fractal geometry analysis provides a fundamentally different approach by capturing geometric complexity across multiple scales simultaneously. While conventional texture features primarily describe statistical relationships between neighboring pixels within predefined regions, fractal parameters provide a global characterization of the entire tumor’s structural complexity. Fractal dimension quantifies how irregular structures fill three-dimensional space and characterizes the self-similar, hierarchical patterns inherent in biological tissues, while lacunarity index measures the spatial distribution of gaps or heterogeneity within the tumor volume [6, 7]. This multi-scale geometric approach may be particularly relevant for pediatric brain tumors, where architectural complexity often reflects underlying biological processes such as cellular organization, vascular patterns, and growth dynamics that manifest at various spatial scales throughout the tumor volume.

The first research study investigating the relationship between fractal parameters determined from MRI images and the WHO grade of the tumor was published in 2016. Czyz et al. [16] determined FD values on different MRI slices, i.e., in 2 dimensions (2D), which showed a significant difference between low- and high-grade meningiomas. Their model considered several clinical and radiological parameters (absence of peritumoral edema, male sex, skull base location, age over 75, capsular contrast enhancement, non-homogeneous contrast enhancement) alongside FD, resulting in an AUC value of 0.83 in their cut-off point analysis for effectiveness determination. In their study, Park et al. [17] correlated the 3D FD and LI values of tumors with the WHO grade. Their model also included clinical and radiological parameters in addition to fractal properties (AUC = 0.82). These findings raise the question of whether 2D or 3D fractal parameters provide a more accurate WHO grade determination for meningiomas. Kim et al. [18] compared the usefulness of 2D and 3D fractal parameters. Their research showed that the model using 2D parameters (AUC = 0.690) significantly underperformed compared to the model using 3D parameters (AUC = 0.813). This outcome is consistent with the findings of Friconnet et al. [19], who used the 2D FD parameter to distinguish between WHO grade 1 and WHO grade 2/3 tumors with an AUC efficiency of 0.690. Fractal analysis according to the work of Won et al. [20] may also be suitable for distinguishing between WHO grade 2 tumors with wild-type and mutant TERT promoter regions, thus enabling not only the preoperative identification of histopathological results but also molecular markers.

Another significant factor influencing the complexity of surgery, and the extent of resection is tumor consistency [21]. Soft tumors can be removed by cutting and suction techniques, while more solid tumors, particularly skull base meningiomas, are more challenging. In such cases, additional surgical tools such as ultrasonic aspirators, electrophysiological monitoring, and intraoperative navigation are required [22]. Therefore, the development of a noninvasive preoperative method to predict tumor consistency is crucial. In the past, predictions were based on signal intensity from T2-weighted images or FLAIR images, but these methods had limited accuracy [23]. Radiomics has emerged as a promising approach for noninvasive, high-throughput analysis of tumor characteristics and has been applied to a variety of tumors, including pituitary adenomas and gliomas [24, 25]. However, there has been limited research on the use of radiomic features to predict meningioma consistency. Zhai et al. [2] aimed to develop a radiomics model for preoperative prediction of meningioma consistency in their latest paper. Their nomogram showed good sensitivity and specificity with AUC values of 0.861 and 0.960 in train and test cohorts, respectively, in predicting meningioma consistency.

In our study, we aimed to differentiate between soft and hard meningiomas and to predict the histological type based on fractal characteristics. To the best of our knowledge, studies exploring the use of fractal geometry analysis in predicting meningioma consistency have not yet been reported. When only fractal parameters were used for prediction, it was found that LI was able to separate the two subgroups (soft vs. hard). The AUC value was 0.745 (95% CI: 0.538–0.958) for consistency. When tumor homogeneity was added, these values changed to 0.763 (95% CI: 0.518–1.000). Using the same tools, we found that WHO grade could be predicted with an AUC value of 0.697 (95% CI: 0.490–0.952) using fractal dimension only. When we add more parameters such as age, tumor homogeneity and volume, this value increases to 0.841 (95% CI: 0.625–1.000).

The main limitation in evaluating predictions is the small sample size, which can result in substantial variability across individual bootstrap samples or cross-validation folds, making it easier for outliers to distort the metrics. Furthermore, excessive optimization for a particular random split may cause overfitting, leading to an overestimation of performance.

Fractal measurement with subsampling takes approximately 20 min per patient (system configuration: 2x Intel(R) Xeon(R) Platinum 8268 CP @2.90 GHz, 900 GB RAM), creating a significant bottleneck. Without subsampling, it would take about two weeks to achieve accurate measurements on the current hardware. This slowdown is mainly caused by the “curse of dimensionality,” where the number of boxes to evaluate increases polynomially with higher-dimensional objects, requiring a correspondingly larger number of CPU cores to sustain processing speed.

In conclusion, our results demonstrate that fractal dimension and lacunarity measurements are powerful predictors of noninvasive histopathological and tissue consistency information. When combined with structural imaging data, the multimodal feature set serves as an effective decision-support tool.