由于整个神经胶质瘤块及其子成分——增强区域（肿瘤的恶性部分）、非增强区域（侵袭性较小的肿瘤细胞）、坏死核心（死亡细胞）和水肿（水沉积）——是复杂且不规则的结构，因此-需要欧几里得几何度量，例如分形维数（FD或“分形”）和空隙度来量化其结构复杂性。分形性衡量结构不规则的程度，而空隙性衡量空间分布或间隙。神经胶质瘤亚成分的复杂几何图案可能与级别和分子景观密切相关。因此，我们测量了神经胶质瘤亚成分中的 FD 和腔隙性，并开发了机器学习模型来区分肿瘤分级和异柠檬酸脱氢酶 (IDH) 基因状态。使用从癌症基因组图谱 (TCGA) 和加州大学旧金山分校获得的术前结构 MRI 测量增强、非增强加坏死核心和水肿子成分的 3D 分形维数 (FD3D) 和腔隙性 (Lac3D)弥漫性神经胶质瘤 MRI (UCSF-PDGM) 神经胶质瘤队列。然后比较肿瘤亚成分的 FD3D 和 Lac3D 测量值（HGG：高级别神经胶质瘤与 LGG：低级别神经胶质瘤）和 IDH 状态（突变型与野生型）。利用这些措施，开发了区分神经胶质瘤级别和 IDH 状态的机器学习平台。 Kaplan-Meier 生存分析用于评估 FD3D 和 Lac3D 测量的预后意义。与 LGG 相比，HGG 在增强子组件中表现出显着更高的分形性和更低的空隙性，并且在非增强子组件中表现出更低的分形性。这表明增强子组件中高度不规则且复杂的几何形状是 HGG 的一个特征。 IDH 野生型和 IDH 突变型神经胶质瘤之间 FD3D 和 Lac3D 的比较显示，突变型神经胶质瘤在增强子成分中 FD3D 降低约 2.5 倍，在非增强子成分中 FD3D 较高，而 Lac3D 较低，这表明突变神经胶质瘤的复杂性较低，且在非增强子成分中具有较低的 Lac3D。 IDH 突变神经胶质瘤的特征是平滑增强子成分和更连续的非增强子成分。使用来自增强子组件和非增强子组件的 FD3D 的监督 ML 模型在区分神经胶质瘤等级 (~97.9%) 和 IDH 状态 (~94.4%) 方面表现出高灵敏度。使用 MR 图像对增强和非增强子成分进行组合分形估计可以作为区分神经胶质瘤分级和 IDH 状态的非侵入性、精确和定量测量。 2-羟基戊二酸-磁共振波谱 (2HG-MRS) 与 FD3D 和 Lac3D 定量相结合，可以作为神经胶质瘤亚型分型的可靠成像特征。© 2024 John Wiley

Since the overall glioma mass and its subcomponents-enhancing region (malignant part of the tumor), non-enhancing (less aggressive tumor cells), necrotic core (dead cells), and edema (water deposition)-are complex and irregular structures, non-Euclidean geometric measures such as fractal dimension (FD or "fractality") and lacunarity are needed to quantify their structural complexity. Fractality measures the extent of structural irregularity, while lacunarity measures the spatial distribution or gaps. The complex geometric patterns of the glioma subcomponents may be closely associated with the grade and molecular landscape. Therefore, we measured FD and lacunarity in the glioma subcomponents and developed machine learning models to discriminate between tumor grades and isocitrate dehydrogenase (IDH) gene status. 3D fractal dimension (FD3D) and lacunarity (Lac3D) were measured for the enhancing, non-enhancing plus necrotic core, and edema-subcomponents using preoperative structural-MRI obtained from the The Cancer Genome Atlas (TCGA) and University of California San Francisco Preoperative Diffuse Glioma MRI (UCSF-PDGM) glioma cohorts. The FD3D and Lac3D measures of the tumor-subcomponents were then compared across glioma grades (HGGs: high-grade gliomas vs. LGGs: low-grade gliomas) and IDH status (mutant vs. wild type). Using these measures, machine learning platforms discriminative of glioma grade and IDH status were developed. Kaplan-Meier survival analysis was used to assess the prognostic significance of FD3D and Lac3D measurements. HGG exhibited significantly higher fractality and lower lacunarity in the enhancing subcomponent, along with lower fractality in the non-enhancing subcomponent compared to LGG. This suggests that a highly irregular and complex geometry in the enhancing-subcomponent is a characteristic feature of HGGs. A comparison of FD3D and Lac3D between IDH-wild type and IDH-mutant gliomas revealed that mutant gliomas had ~2.5-fold lower FD3D in the enhancing-subcomponent and higher FD3D with lower Lac3D in the non-enhancing subcomponent, indicating a less complex and smooth enhancing subcomponent, and a more continuous non-enhancing subcomponent as features of IDH-mutant gliomas. Supervised ML models using FD3D from both the enhancing and non-enhancing subcomponents together demonstrated high-sensitivity in discriminating glioma grades (~97.9%) and IDH status (~94.4%). A combined fractal estimation of the enhancing and non-enhancing subcomponents using MR images could serve as a non-invasive, precise, and quantitative measure for discriminating glioma grade and IDH status. The combination of 2-hydroxyglutarate-magnetic resonance spectroscopy (2HG-MRS) with FD3D and Lac3D quantification may be established as a robust imaging signature for glioma subtyping.© 2024 John Wiley & Sons Ltd.