Fractal dimension as a predictive biomarker for tumor grade and cerebellar mutism syndrome in pediatric posterior fossa tumors

Introduction

Posterior fossa tumors represent the most prevalent type of central nervous system (CNS) tumor in the pediatric population, accounting for 45–60% of all pediatric brain tumors (1). These tumors are classified by the World Health Organization (WHO) into low-grade (WHO grades 1 and 2) and high-grade (WHO grades 3 and 4) categories, based on molecular testing that distinguishes benign from malignant characteristics (2). The pathological features and tumor grades are critical factors in determining appropriate treatment strategies (3). At present, tumor grading largely depends on biopsy or post-surgical histopathological examination. The magnetic resonance imaging (MRI) tumor interface often exhibits a complex and irregular geometry due to the dynamic processes of tumor growth, which include cell proliferation and invasion into adjacent tissues (4). Consequently, quantifying the complexity of tumor boundaries may provide valuable insights into the malignancy of the tumor.

In addition to the tumor’s malignancy, it is equally important to consider postoperative complications. Cerebellar mutism syndrome (CMS) is one of the most frequent and significant complications following the surgical resection of posterior fossa tumors in pediatric patients, underscoring the urgent need for strategies to predict and mitigate its occurrence. Although the duration of cerebellar motor dysfunction and cognitive-emotional impairment associated with CMS is generally transient, long-term sequelae can severely impact the patient’s quality of life (5). To predict and prevent CMS, multiple presurgical MRI studies have sought to identify potential imaging markers, including tumor location, internal radiomic features, and tumor size (6-9). However, the complexity of the tumor boundary has yet to be fully explored in these studies.

Fractal dimension (FD) is a quantitative measure of structural complexity that has garnered significant attention in medical imaging, particularly for characterizing irregular and intricate anatomical structures (10-14). FD computation methods include box-counting (most prevalent in medical imaging), differential box-counting, fractional Brownian motion, and triangular prism approaches (15). As a ratio of logarithms, FD is highly sensitive to subtle variations in complexity—even minor changes in tissue architecture can be reflected (16). Pathological conditions often induce localized distortions in tissue structure, and FD’s ability to detect these small-scale changes highlights it as a promising biomarker for early tumor characterization and the prediction of potential complications (17). In this study, we investigate the application of FD in evaluating posterior fossa tumors across different grades and assess its potential as a biomarker for predicting the risk of CMS. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-620/rc).

Methods

Patients

The study included 247 patients diagnosed with posterior fossa tumors who underwent surgical treatment at Beijing Children’s Hospital between June 2013 and December 2023. The inclusion criteria were as follows: (I) age range: 0–18 years; (II) availability of both preoperative MRI and postoperative pathological evaluation performed at our institution; (III) confirmed diagnosis of posterior fossa tumor established at our center; (IV) surgical resection of the tumor; (V) definitive postoperative diagnosis of CMS or non-CMS, agreed upon by two senior neurosurgeons. The exclusion criteria were as follows: (I) incomplete clinical data; (II) missing MRI data or pathological examination data; (3) unsatisfactory normalization upon visual inspection.

The specific pathological types of the lesions and their corresponding WHO grades were carefully documented. Clinical variables, including gender, age, tumor size, tumor location, tumor consistency, presurgical ventriculoperitoneal (VP) shunt and paraventricular edema, were retrieved from medical records. Tumor consistency was assessed on preoperative MRI, with lesions classified as solid when cystic components comprised less than 50% of the total tumor volume. CMS status was recorded at 3- to 6-month follow-up intervals, either by phone or in-person at our outpatient center. CMS was diagnosed based on postoperative mutism or severe speech reduction, with possible associated symptoms including hypotonia, dysphagia, irritability, and involuntary movements. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Beijing Children’s Hospital (No. 2019-k-344) and informed consent was provided by guardians of the patients.

MRI and imaging procedures

All patients from our study were scanned on a 3.0 T Discovery 750 scanner (GE Healthcare, Milwaukee, WI, USA) with an 8-channel head coil (voxel size, 0.6×0.6×5 mm³) or a 3.0 T Ingenia CX scanner (Philips Healthcare, Best, the Netherlands) with a 32-channel head coil (voxel size, 1×1×1 mm³). Tumor masks, excluding the peritumoral edema area, were meticulously delineated on standard T1-weighted images through ITK-SNAP (https://www.itksnap.org) by a senior neurosurgeon. These masks were subsequently reviewed in a double-blind manner by a senior radiologist. Any discrepancies identified during this review were resolved through discussion and consultation. T2-weighted and fluid-attenuated inversion recovery (FLAIR) images were referenced to ensure accuracy during the tumor delineation procedure.

The acquired scan images and corresponding tumor masks were subsequently normalized to the Montreal Neurological Institute (MNI) space using the Clinical Toolbox (https://www.nitrc.org/projects/clinicaltbx) within statistical parametric mapping (SPM12, Welcome Department of Neuroscience, London, UK; https://www.fl.ion.ucl.ac.uk/spm/software/spm12/). The normalized images underwent visual quality assessment, with poorly aligned cases excluded from subsequent analysis. Normalized tumor masks [binary region of interest (ROI): tumor =1, background =0] were directly used for tumor mask area (mFD) analysis without grayscale thresholding.

This study additionally utilized the lesion map derived from our prior study for calculating significant region FD (sFD) (18). The lesion map was generated using the sparse canonical correlation analysis (SCCAN) method implemented in R Lesion to Symptom Mapping (LESYMAP). This approach utilizes a multivariate methodology to conduct lesion-symptom mapping (LSM) analysis. Specifically, the normalized tumor masks and CMS classification data were input into LESYMAP to produce a lesion probability map, which displays both the spatial distribution of voxels correlated with CMS and the statistical strength of these voxel-wise associations. The generated lesion map was used to represent the regions significant to CMS in this study. Details of the lesion map are provided in Table S1 and Figure S1.

FD analysis

Following image preprocessing, the gradient method was used to extract the tumor interface boundaries from the three-dimensional (3D) masks. Subsequently, mFD and sFD (theoretical range: 2.0–3.0) were calculated using the box-counting algorithm. Specifically, mFD was determined based on the boundary of the normalized tumor masks. For sFD, calculations were performed using the significant tumor boundary determined by the common border between the tumor mask and the lesion map.

Statistical analysis

Following the measurement of mFD and sFD, Kruskal-Wallis test with Dunn’s multiple comparisons was utilized to investigate the relationship between tumor’s mFD and WHO grading. A P value <0.05 was considered significantly different.

The t-test (for continuous variables) and chi square test (for category variables) were used to assess the difference in sFD and clinical variables between CMS and non-CMS patients, with P<0.05 considered significant. Receiver operating characteristic (ROC) curve analysis was subsequently conducted to determine the diagnostic accuracy of sFD in differentiating CMS and non-CMS patients. Subgroup analyses were conducted based on significantly different clinical variables.

All analyses were conducted using MATLAB (R2017b, MathWorks, Natick, MA, USA), R (version 4.3.3, R Foundation for Statistical Computing, Vienna, Austria), and Python (version 3.7, Python Software Foundation, Wilmington, DE, USA).

Results

A total of 247 patients were enrolled in this study, comprising 140 males and 107 females. The cohort included 71 patients with WHO grade 1 tumors, 26 with WHO grade 2 tumors, 41 with WHO grade 3 tumors, and 109 with WHO grade 4 tumors. The basic demographic characteristics across the different WHO groups are summarized in Table 1. There were no significant differences in gender or age among the four WHO groups (P>0.05). Post-hoc power analysis indicated that our study achieved approximately 92% statistical power to detect differences among tumor grades at a medium effect size (Cohen’s f =0.25) and a significance level of 0.05, suggesting sufficient sensitivity to identify meaningful group differences.

The mFD demonstrated good differentiation between high- and low-grade posterior fossa tumors according to the WHO classification, with an area under the curve (AUC) of 0.80, sensitivity of 78%, and specificity of 75%. Statistically significant differences in mFD were observed between the four WHO groups (Figure 1A). When analyzing each WHO grade cohort separately (Table 2), mFD was significantly higher in WHO grade 4 patients [0.88 (0.82–0.94)] compared to WHO grade 3 [0.79 (0.68–0.89)], WHO grade 2 [0.68 (0.48–0.76)], and WHO grade 1 patients [0.71 (0.41–0.79)] (P=0.03, <0.01, and <0.01, respectively). Additionally, mFD was significantly higher in WHO grade 3 patients [0.79 (0.68–0.89)] compared to WHO grade 2 patients [0.68 (0.48–0.76)] (P=0.008). However, no significant difference was observed between WHO Grade 2 and WHO Grade 1 patients (P=1.00).

Figure 1 mFD analysis of posterior fossa tumors stratified by WHO grade and pathology groups. (A) Boxplot of mFD grouped by WHO grades. (B) Boxplot of mFD grouped by pathology groups. AE, anaplastic ependymoma; ATRT, atypical teratoid rhabdoid tumor; DA, diffuse astrocytoma; DIPG, diffuse intrinsic pontine glioma; GG, ganglioglioma; MB, medulloblastoma; mFD, mask fractal dimension; PA, pilocytic astrocytoma; PMA, pilomyxoid astrocytomaWHO, World Health Organization.

Further analysis was performed on mFD values stratified by pathological tumor types. The following pathological types were considered: ganglioglioma (GG, WHO grade 1), pilocytic astrocytoma (PA, WHO grade 1), pilomyxoid astrocytoma (PMA, WHO grade 1), diffuse astrocytoma (DA, WHO grade 2), anaplastic ependymoma (AE, WHO grade 3), atypical teratoid rhabdoid tumor (ATRT, WHO grade 4), diffuse intrinsic pontine glioma (DIPG, WHO grade 4), and medulloblastoma (MB, WHO grade 4). Pathological types with fewer than five cases were excluded to ensure statistical robustness (Table 3, Figure 1B). Based on mFD values, tumors of WHO Grades 3 and 4 were generally well-differentiated from low-grade tumors (P<0.05). However, no statistically significant distinctions were found between AE and ATRT (P=0.51) or AE and DIPG (P=0.34). Furthermore, the differentiation between WHO grade 1 and grade 2 pathological types was less clear (P>0.05) (Table S2).

Baseline analysis was conducted comparing the CMS cohort (n=74) with the non-CMS cohort (n=173). Age, tumor size, tumor consistency, paraventricular edema, and presurgical VP shunt status did not differ significantly between the two groups (P>0.05). However, significant differences were observed in gender (P=0.016), tumor location (P=0.009), and sFD (P<0.001) (Table 4).

The ROC curve analysis for using sFD to predict CMS yielded a sensitivity of 67%, specificity of 61%, and an AUC of 66%. After adjusting for gender and tumor location, a higher level of FD was still significantly associated with an increased risk of CMS [odds ratio (OR): 11.70, 95% confidence interval (CI): 3.10–43.90, P<0.001]. Subgroup analyses were performed based on gender and tumor location to explore potential differences within these categories. The female cohort exhibited higher sensitivity (83%) compared to the male cohort (60%), although with slightly lower specificity (59% vs. 64%). The AUC values were 73% for females and 63% for males, respectively. For the midline cohort, sensitivity was 47% and specificity was 77%, with an AUC of 62%, whereas the non-midline cohort demonstrated 62% sensitivity and 80% specificity, with an AUC of 72% (Figure 2A-2E).

Figure 2 Predictive performance of sFD for CMS. (A) ROC cure for predicting CMS from sFD. (B) ROC cure for predicting CMS from sFD in the male cohort. (C) ROC cure for predicting CMS from sFD in the female cohort. (D) ROC cure for predicting CMS from sFD in the tumor midline location cohort. (E) ROC cure for predicting CMS from sFD in the tumor non-midline location cohort. AUC, area under the curve; CMS, cerebellar mutism syndrome; ROC, receiver operating characteristic; sFD, significant region fractal dimension.

Discussion

Differentiating between low- and high-grade tumors holds significant clinical value, as tumor grade directly influences survival trends and treatment strategies (19). Although biopsy remains the standard procedure for tumor diagnosis, it carries inherent risks, such as complications and potential for metastasis, which have prompted increased interest in non-invasive radiological alternatives (20). FD exhibits relative stability and is less influenced by imaging noise compared to other texture features, making it particularly promising for tumor grade characterization (21). FD, a concept derived from fractal geometry, quantifies the irregularity of objects and has been successfully applied in tumor studies (22,23). In this study, we employed the box-counting algorithm to extract the FD from T1-weighted magnetic resonance (MR) images, a technique that involves overlaying boxes of decreasing sizes onto a 3D ROI at various grid orientations (24). From the results of our study, it is clear that FD is a potentially useful biomarker for differentiating grades in posterior fossa tumors.

We observed that mFD was significantly higher in high-grade posterior fossa tumors compared to low-grade tumors, with an increasing trend in mFD corresponding to higher WHO grades. This suggests that high-grade tumors exhibit more complex borders on MRI. Although limited studies have focused on FD in posterior fossa tumors, our results align with previous studies indicating that FD increases with the grade of gliomas (14). FD has been shown to describe tumor growth patterns (25,26). Malignant brain tumors, which invade surrounding tissue, often exhibit branching and structural alterations that can be captured by FD (27). Additionally, study have reported that tumor spread to adjacent brain regions via axons may alter the tumor’s boundary and its surrounding tissues (15). Di Ieva’s research further supports our findings, showing that lower FD values are associated with microvasculature in low-grade tumors, whereas higher FD values correlate with microbleeds and necrosis in high-grade tumors (28). These morphological changes are well-reflected by FD, positioning it as a valuable biomarker for tumor grading. However, our study also highlights the limitations of mFD in differentiating between grade 1 and grade 2 tumors. Specifically, among grade 1 tumors, only PA exhibited higher mFD values compared to grade 2 tumors, but the large number of PAs in the cohort may have skewed the results, complicating reliable differentiation. Further studies should explore the relationship between the pathological characteristics of PA and its relatively higher mFD values, which could improve the accuracy of tumor grading.

CMS remains one of the most significant challenges for children with CNS tumors (5,29). We observed a significant difference in sFD between the CMS and non-CMS cohorts, suggesting its potential as an early predictor of post-surgical CMS. Therefore, sFD may facilitate timely interventions, which are crucial for patients’ rehabilitation (3,30). We calculated sFD in the common border between the tumor mask and the significant region, a brain area identified as being strongly associated with CMS in our prior research (18). Given its ability to reflect the complexity of critical CMS-related regions, sFD may serve as an important biomarker for predicting CMS. The compression and distortion at the interface between the tumor and surrounding brain regions can be quantified by sFD. Previous studies have utilized sFD of tumor-segregation boundaries as an effective metric to estimate compression forces between cells (31). Our findings are consistent with the widely accepted theory that CMS is caused by damage to the dentato-thalamo-cortical (DTC) pathway (32-35), which connects the cerebellum to cortical regions involved in motor and language processing (36). Injury to this pathway, especially to fibers in the right superior cerebellar peduncle and brainstem, could impair higher cognitive functions, resulting in CMS-related symptoms (37-39). Notably, McAfee et al. have proposed an alternative hypothesis implicating disruption of the fastigial nucleus in CMS pathogenesis, suggesting that the DTC pathway represents one of several potential mechanisms (40). Therefore, assessing the compression and distortion effects in these regions is crucial for CMS prediction.

As observed in previous studies, we identified gender and tumor location as significant risk factors for CMS (41,42), which should be considered when interpreting the predictive value of sFD. Our subgroup analysis revealed that sFD was more effective in predicting CMS in females, with an AUC of 0.73, compared to males, who showed lower predictive efficacy. This gender difference in prediction performance may be attributed to underlying biological mechanisms that remain poorly understood. Hormonal or neurological differences between males and females could influence language development and functional differences in language processing. Some studies have shown that during early childhood, girls typically develop superior expressive language skills compared to boys (43), and functional differences in language-related brain activity between genders have been well-documented (44). Additionally, location-based subgroup analysis revealed better predictive performance for non-midline tumors, likely due to their greater compressive effects on the dentate nucleus and superior cerebellar peduncle, regions critical for the DTC pathway. However, given the small sample size in the non-midline cohort, further studies with larger cohorts are necessary to confirm these findings.

In this study, we employed two distinct FD metrics, mFD and sFD, to evaluate the boundary complexity of different tumor regions. mFD measures the FD of the entire tumor boundary, making it suitable for assessing overall tumor grade and aggressiveness. Meanwhile, sFD focuses on the FD of CMS-related regions, providing insights into structural complexities that may predict CMS development. Given the focus on different regions—overall versus specific areas—FD addressed two clinical questions related to posterior fossa tumors. By employing more tailored FD metrics, we believe that a wider array of clinical questions related to tumor assessment and management can be effectively addressed.

Our study has several limitations that should be considered. First, this study was conducted at a single center with a relatively small patient population, and larger multicenter studies are needed to validate our results. Second, the fractal analysis algorithm used in this study—box-counting—lacks standardization, which may limit the reproducibility of findings. Nevertheless, box-counting remains one of the most used methods in medical research and provides a robust framework for assessing FD in tumor studies. In the future, artificial intelligence-based imaging recognition and analysis are anticipated to significantly enhance the ability to recommend non-invasive diagnostic techniques.

Conclusions

This study demonstrates that FD analysis of preoperative MRI scans provides clinically valuable biomarkers for pediatric posterior fossa tumors. mFD effectively differentiated tumor grades, whereas sFD independently predicted CMS risk, particularly in specific patient subgroups. These findings suggest that FD metrics could serve as a comprehensive preoperative assessment tool, potentially guiding clinical decision-making for tumor management and surgical risk stratification through a single MRI acquisition. Further multicenter validation is warranted to establish standardized implementation protocols.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-620/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-620/dss

Funding: This study was funded by Beijing Hospital’s Authority Clinical Medicine Development of Special Funding (No. XMLX202144).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-620/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Beijing Children’s Hospital (No. 2019-k-344) and informed consent was provided by guardians of the patients.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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