A non-local diffusion magnetic resonance imaging tract density biomarker to stratify, predict, and interpret survival rates in human glioblastoma

Abstract

Background

Glioblastoma (GBM) is a lethal tumor, actively growing and invading neighboring neural tissue. GBMs appear functionally connected to distributed and spatially distant regions rather than representing an isolated and passive lesion disrupting the brain circuitry. Moreover, increasing evidence suggests that white matter serves as the morphological substrate for GBM to progress and migrate to distant areas in the human brain.

Methods

We hypothesized that the subset of white matter tracts intersecting the tumors depicts the physical substrate for large-scale neuron-glioma interactions and would therefore inform prognosis. Using normative models, we design, analyze, interpret, and test a Lesion-Tract Density Index (L -TDI) marker that considers the distributed white matter pathways interacting with the tumor in 2 independent cohorts of $N=367$ and $N=496$ patients, respectively.

Results

First, we show that the tract density within this white matter map robustly stratifies survival rates due to widespread white matter involvement. Second, we demonstrate why tract density-based markers offer critical and necessary insights into the morphology, location, and evolution of human GBM by proving how the proposed L -TDI implicitly considers tumor volume, white matter density, and location. We provide further evidence that the non-uniform distribution of GBMs and their differential prognosis emerge from white matter morphology. Third, we validate the L -TDI marker with multiple Cox survival models and analyze its contribution in relation to other covariates of interest (eg, MGMT promoter methylation). Lastly, by using a simple logistic model, we predict patient death at 12 months with balanced accuracies of 68% and 65%, and areas under the curve of 0.74 and 0.73 when training and testing in separate and independent cohorts.

Conclusions

Overall, we offer a concrete implementation of the emerging paradigm that views GBM not as a focal lesion, but as a network disease sh aped by its complex interactions with distant brain regions.

Key Points.

• Tractography describes interactions between glioblastomas and the brain’s white matter.

• A new Lesion-Tract Density Index (L -TDI) stratifies survival across independent cohorts.

• A robust and scalable neuroimaging framework to improve patient care and treatment.

Importance of the Study

Increasing evidence suggests that glioblastoma (GBM) growth and migration are shaped by neuronal activity and connectivity, rather than being confined to local structural disruption. Building on the call for a shift in understanding brain tumors through the lens of connectomics and distributed network theory, we propose and validate a novel biomarker. As opposed to earlier attempts, the Lesion-Tract Density Index (L -TDI) quantifies the intersection of GBM lesions with a normative white matter scaffold. We demonstrate that L -TDI robustly stratifies survival rates in 2 large and independent cohorts. This marker integrates key morphological variables and is predictive of patient outcomes beyond conventional clinical and molecular features. The L -TDI is validated through Cox and logistic regression models, achieving higher scores while maintaining interpretability and feasibility. These findings provide strong support for the concept of GBM as a network-based disease, one whose prognosis is informed by its embedding within brain-wide connectivity.

Recent discoveries in cancer neuroscience have revealed that gliomas, particularly glioblastomas (GBMs), exhibit dynamic interactions with neuronal circuits that go far beyond passive infiltration.^1,2 Unlike stroke or traumatic brain injury, which manifest as structural disconnections, gliomas appear to functionally integrate within existing brain networks.³ They leverage synaptic plasticity to reshape local and long-range circuitry,^4,5 evade detection, and recur in anatomically unpredictable locations, ultimately contributing to reduced overall survival rates.^6,7 Increasing evidence suggests the existence of a positive feedback loop between glioma-induced neuronal activity^8,9 and neuron-glioma connectivity,^10,11 which collectively promote tumor growth and invasion.¹² This active and adaptive behavior supports the view of gliomas as complex systems that interact with, and co-opt, the host brain’s own connectome. These features hinder the existence of 2 interdependent networks, the brain and neuron-glioma networks, both capable of functioning and evolving in relative isolation while influencing one another, thus giving rise to critical and seemingly random system behaviors.^13,14

In this conceptual framework, at least 3 central questions arise: (1) how does the whole-brain connectivity changes in the presence of GBM;15 (2) what are the properties of the neuron-glioma networks,¹⁶ and (3) to what extent does the tumor’s spatial embedding within the brain connectome, rather than its size or spatial location alone, determine its clinical impact, including survival? The answers to these questions remain largely unexplored in-vivo and the present study seeks to specifically address the latter.

We explore how these emerging insights can be translated into the neuroimaging domain. Unlike cancer neuroscience, which primarily relies on in-vitro, animal, or organoid models,^17,18 neuroimaging may offer rapid clinical applicability due to its non-invasive nature. Functional magnetic resonance imaging studies have mostly focused on the connectivity between the tumor and the rest of the brain,^19–21 and its potential association with survival and cognitive deficits.^22,23 In contrast, global alterations in functional connectivity profiles have shown less promising clinical implications.^24–27 Diffusion magnetic resonance imaging studies have primarily focused on structural alterations or impairments in whole-brain connectivity,^28,29 which appear more robustly associated with survival and cognitive outcomes.^29,30 Yet, these attempts often failed to conceptualize the tumor itself as a component of a broader network,¹⁶ ultimately determining disease progression.

To address this gap, we move towards a connectomics perspective,^31,32 modeling GBM as a node embedded in and interacting with a white matter scaffold, rather than a focal lesion. Building on recent work that used local tract density as a proxy for infiltration,³³ we introduce a novel approach, the Lesion-Tract Density Index (L -TDI), which incorporates both the lesion’s morphology and its spatial embedding within normative white matter tractograms. Herein, we apply this framework to 2 large, independent GBM cohorts, aiming at providing an imaging biomarker for GBM stratification and survival prediction.

Methods

In this study, 2 independent and publicly available GBM cohorts were employed. A comprehensive overview of the methodological framework is shown in Figure 1, while a more detailed description of the conceptual, theoretical, and computational steps performed is available in the Supplementary Material.

Figure 1.

The lesion-tract density index (L -TDI): a survival marker in human GBM. (A) For every subject, the data were normalized to a common template. The T2-weighted image was chosen as the reference modality, and the GBM was inversely masked to discard distorted tissue during the optimization. (B) The normalized tumor mask is used in combination with the whole brain normative tractogram to extract the set of streamlines that intersect the tumor in the same template space as in (A). (C) The lesion-tract density map (L -TDM) provides a unique white matter density map describing the tracts in (B) that interact with the GBM. (D) From the L -TDM, we can define the L -TDI marker by averaging the tract density within the L -TDM binary mask in (C). For a given cohort, the sample can be stratified according to a given percentile. (E) Once a stratification threshold has been set, we conduct thorough tests to assess the discovery of the biomarker. Additional survival analyses on multiple stratification thresholds help determine whether the potential biomarker holds prognostic value. The L -TDI can also be used to characterize both morphological and anatomical landscapes in GBMs, which can be used to understand differences in the survival rates. Once a robust effect has been identified, the L -TDI can be incorporated into standard risk analysis and predictive frameworks to improve patient care.

The University of California San Francisco Glioblastoma (UCSF) Cohort

From the original 501 samples available in the University of California San Francisco dataset,³⁴ we included the $N=367$ patients with recorded survival data and confirmed grade 4 GBM IDH-wildtype diagnosis as per the WHO 2021 classification.³⁵ The original sample also contained high-grade IDH-mutant and low-grade IDH-wildtype entries with significantly better prognosis (Figure S1A). These patients were discarded from all subsequent analyses. Additionally, 6 follow-up entries from the original 501 were discarded. All the selected patients had available high-quality multimodal imaging data and tumor multi-tissue segmentations obtained from automated deep learning models and manually corrected if necessary.³⁴

Clinical data (Table S1) included biological sex, age at the time of the MRI scan, MGMT (O⁶-methylguanine-DNA methyltransferase) promoter status, MGMT index, and the extent of resection (EOR) based on the surgical and/or postoperative MRI reports. Overall survival (OS) was measured in days from the initial diagnosis to the date of death (status = 1) or the last clinical follow-up (status = 0). For this cohort, 39.24% of the patients were right-censored (ie, lost to follow-up). Additionally, 41 patients did not undergo a full surgical procedure.

The University of Pennsylvania Glioblastoma (UPENN) Cohort

From the original 671 samples available in the University of Pennsylvania dataset,³⁶ we included the $N=496$ patients with recorded survival data and confirmed GBM grade 4 IDH-wildtype diagnosis as per the WHO 2021 classification.³⁵ The original sample also contained high grade IDH-mutant and not otherwise specified (NOS/NEC) entries with significantly better prognosis (Figure S2A). These patients were discarded from all subsequent analyses. Additionally, 60 follow-up entries from the original 671 were discarded. All the selected patients had available high-quality multimodal imaging data and tumor multi-tissue segmentations obtained from automated deep learning models and manually corrected if necessary.³⁶

Clinical data (Table S1) included biological sex, age at the time of the MRI scan, MGMT (O⁶-methylguanine-DNA methyltransferase) promoter status, MGMT index, and the extent of resection (EOR) representing excision of more or less than 90% of the tumor. Karnofsky performance status (KPS) scores were available for $N=53$ patients. OS was measured in days from the first surgical intervention until the date of death (status = 1) or the last clinical follow-up (status = 0). For this cohort, 2.82% of the patients were right-censored (ie, lost to follow-up).

Image Normalization to the Montreal Neurological Institute (MNI) Template

Image acquisition protocols and details can be found in the original publications. Briefly, for the discovery cohort,³⁴ preoperative imaging was performed with a 3T scanner (GE Healthcare) and included 3D T2-weighted, T2-weighted FLAIR, and pre-/post-contrast T1-weighted sequences. For the replication cohort,³⁶ preoperative imaging was performed with 1.5-3T scanners and included 2D-3D T2-weighted, T2-weighted FLAIR, and pre-/post-contrast T1-weighted sequences.

For both cohorts, already included multimodal tumor segmentations consisted of enhancing tumor, necrotic core (ie, non-enhancing tissue), and surrounding FLAIR hyperintensity (often interpreted as peritumoral edema or infiltrated tissue). Whole-tumor masks included all the above. The structural and multi-label lesion segmentations were already co-registered (ie, aligned in subject space). We nonlinearly normalized all the necessary images to a common anatomical template (0.5 mm³ isotropic resolution) in the Montreal Neurological Institute standard space³⁷ (MNI ICBM 2009b NLIN Asymmetric; hereafter referred to as “MNI template”). Before normalizing, for both cohorts, we binarized and inverted the multi-label lesion, ensuring that no pathological tissue was used during the registration process. Then, we nonlinearly mapped the T2 images to the T2 MNI template³⁸ and applied the transformation to the tumor masks. The normalized images were overlaid onto the MNI template to visually assess the alignment of anatomical landmarks (eg, sulci and gyri). As a last step, the volume of the tumors was computed in cubic centimeters in MNI space from the whole-tumor masks (Figure 1A).

Normative Tractograms, Tract Density Maps, and Indices

To evaluate the white matter pathways interacting with the tumor lesion, we sought to employ a publicly available normative structural tractogram constructed from 985 healthy subjects and 11,820,000 streamlines.³⁷ To compute a patient-specific lesion-tract density map (L -TDM) and index (L -TDI), we selected the streamlines that intersected a given tumor mask (Figure 1B and C) and obtained the corresponding L -TDM by counting the number of streamlines passing through every voxel.³⁹ The L -TDI was the tract density within the L -TDM (Figure 1D), thus encompassing the total white matter density of the whole brain-lesion normative circuit. For completeness, we also obtained the tract density map (TDM) and index (TDI) of every patient.³³ For that, from the normative tractogram, we generated a voxel -wise density map, overlaid each tumor mask to create patient-specific TDMs, and computed the TDI as the average density within each tumor.

In summary, the L -TDI serves as an indirect measure of the extent and complexity of the white matter circuits affected by GBM beyond its visible boundaries. This supports a model of GBM as a distributed network disease rather than a purely localized structural disruption. In contrast, the TDI reflects the local density of white matter tracts within the tumor mask, such that tumors located in regions with a higher number of streamlines yield higher TDI values. While higher TDI reflects a greater number of fibers likely exposed to tumor-related alterations, its direct relationship with histopathological tumor infiltration remains to be conclusively established. Importantly, the TDI cannot distinguish edema from tumor infiltration, misinterpreting true tract density. The L -TDI, while subject to the same limitation, provides a complementary perspective by mapping the broader spatial relationship between white matter pathways and tumor-affected regions.

Survival Analysis and Statistical Procedures

We treated UCSF as the discovery and UPENN as the replication cohort to avoid dataset-specific bias. In the UCSF, we stratified patients into “Low” and “High” L -TDI groups using percentiles ranging from 20 to 50 (in steps of 5). Kaplan-Meier curves were compared using 2-sided log-rank tests, with P-values False Discovery Rate (FDR)-corrected across several percentiles. We then assessed median OS for deceased patients using 2-sided Mann-Whitney U-tests, also FDR-corrected. This confirmed robust, threshold-independent survival differences based on tract density-based stratification. We compared average L -TDI and TDI between patients who died or survived past specific timepoints (6-48 months) using 2-sided Mann-Whitney U-tests, FDR-corrected. We also computed Pearson correlations (ρ) between (L -)TDIs and survival times within subgroups of patients who died before each threshold. Significance was assessed via 2-sided permutation tests ($n=2500$ resamples), with FDR correction applied across thresholds.

Lastly, we computed ROC curves using raw L -TDI values to classify survival at 12 and 24 months, reporting balanced accuracy via Youden’s J index.⁴⁰ Additionally, we assessed the time-dependent discriminative power of tract density markers using cumulative and dynamic AUCs.⁴¹ A repeated K-fold cross-validation (50 runs) estimated the censoring distribution, with time sampled from 6 to 36 months and K set to 2, 6, and 8. Dynamic AUCs were trained on (K–1) folds and tested on the held-out split. All the previous analyses were then repeated in the same way for the replicative cohort.

Dimensionality Reduction and Clustering of Macroscopic Features in GBMs

To understand the relationship between tract density indices and tumor volume, we performed linear principal component (PC) analyses with the TDI, L -TDI, and volume as features of interest. The first and second PCs accounted for more than 99% of the variance, indicating that the L -TDI was linearly predictable from them. Then, we performed automatic K-means clustering of patients based on the TDI and tumor volume. We calculated the Kaplan-Meier curves of each of the 3 found groups and obtained the average overlap of every brain lobe delineated in the USCLobes brain atlas⁴² with the tumor masks. Similarly, to move beyond traditional lesion-symptom mappings, we computed the average overlap between the white matter tracts defined in the XTRACT atlas⁴³ and the L -TDMs. The resulting overlaps were then sorted in descending order and compared between clusters using both Spearman correlation and Kendall’s $\tau$ coefficients.

Cox Proportional Hazard Modeling

To evaluate the added clinical value of tract density-based markers, we fitted 4 Cox proportional hazard models per cohort:

1. A naïve model with classical covariates (sex, age, MGMT status, EOR),

2. An L -TDI model (naïve + L -TDI),

3. A TDI model (naïve + TDI),

4. A TDI+Volume model (naïve + TDI + lesion volume).

Models were compared using log-likelihood ratio tests. Hazard ratios were assessed via 2-sided Wald tests with associated Z-distributions, and 95% CIs were reported.

To improve the estimates of the hazard rates, we also joined the survival data from the 2 cohorts, effectively doubling the sample size (see Supplementary Materials). However, since the survival was measured from days of diagnosis and from days of surgery in the UCSF and UPENN cohorts, respectively, we accounted for measurement-related site differences in survival rates. For each patient, we obtained the site-corrected OS,

$$\begin{array}{c}{\stackrel{\sim }{t}}_p=t_p\cdot e^{{\beta }_s\cdot S_p},\end{array}$$ (1)

where ${\beta }_s$ is estimated from a Cox model incorporating a variable $S_p=\left\{\mathrm{0,1}\right\}$ for the UCSF and UPENN cohorts, respectively. After applying the transformation in eqn (1) to all the survival times, we fitted a second Cox multivariate model to evaluate the hazard ratios associated with each covariate. When comparing survival rates across different strata, the time must be measured using the same reference units. Crucially, changing the measurement units introduces a proportional shift in the underlying hazard rates (eg, $365$ days $=12$ months). Since the covariate $S_p$ complies with the assumption of proportional hazards (see Figure S3), the transformation in eqn (1) and the procedure described here can be reliably used to estimate the conversion factor between “days from diagnosis” and “days from surgery.” See the Supplementary Materials for details on the effects that this transformation causes on the survival and hazard rates.

Lastly, we computed Harrell’s concordance index $\left(C^H\right)$ to evaluate the discriminative power of a given feature.⁴⁴ For each feature (eg, MGMT promoter status), we fitted a simple Cox model and computed the associated $C^H$ score. The significance was assessed through non-parametric permutation tests ($n=1000$resamples). All the procedures described here were carried out after discarding the samples with missing data.

Logistic Regression Modeling of Survival and Death Predictions

We fitted logistic regression models to assess the contribution of each feature to survival at a given time point (1 died, 0 survived). Mirroring the Cox analyses, we tested 4 models to evaluate the tract density-based markers, recording each covariate’s significance, CI, and model log-likelihood. The different models were compared using log-likelihood ratio tests. We fitted models to each cohort independently and after merging the survival data.

To predict whether a patient would die before a specified time point, we trained a logistic classifier using repeated stratified cross-validation. A grid search varied the number of splits (2-12) and repeats (5-25), with performance evaluated using both AUC and balanced accuracy (bACC). We selected the parameter set that minimized the average of the 2 scores to balance class separability and true positive rates. The final model was retrained on the full training cohort and tested on the independent cohort. This process was repeated for 6, 12, and 18-month predictions, alternating training and testing cohorts. Survival times were pre-corrected for site effects as described earlier. All the procedures described here were carried out after discarding the samples with missing data. Additionally, we trained a complement naïve Bayes classifier to perform the same task. The training procedure was identical to the one used to train the logistic classifiers. A complement naïve Bayes classifier is particularly well -suited for imbalanced datasets; such is the case in survival predictions when considering early and late thresholds.

Results

Demographic and Classical Clinical Covariates

In both cohorts, GBMs were more frequent in males than in females, with a ratio of 60/40% (Figures S1B, S2B). However, no significant sex-related differences in prognosis were observed (${\mathrm{\chi }}^2=1.0057$, $P=0.3159$ for the UCSF cohort; ${\mathrm{\chi }}^2=0.0674$, $P=0.7952$ for the UPENN cohort; 2-sided log-rank test). Importantly, positive MGMT promoter methylation and gross total resection (GTR), as opposed to subtotal resection (STR), were associated with increased survival in both datasets (Figures S1C-E, S2C-D). Additionally, in the UPENN cohort, a high Karnofsky Performance Status (KPS) score further contributed to improved prognosis (Figure S2E).

The Lesion-Tract Density Index (L -TDI) is Robustly Associated with Survival in GBM

We investigated whether the set of streamlines intersecting the tumor was associated with overall survival (OS). Prior work postulated that the normative white matter tract density index (TDI) within the tumor significantly modulated OS when stratifying the population into 2 groups based on the first and third quartiles of the density distribution.³³ Building on this approach, we instead computed the normative white matter density of the entire lesion-intersecting tractogram rather than limiting the analysis to the tumor mask alone (see Methods). In both the discovery (ie, UCSF) and replicative (ie, UPENN) cohorts, higher values of L -TDI were significantly associated with worse prognosis (Figure 2A-B). To measure the robustness of this marker, we also evaluated multiple stratification thresholds (Figure 2C). In the UCSF cohort, Kaplan-Meier curves consistently showed significant survival differences between low and high L -TDI groups across all thresholds. Similarly, in the UPENN cohort, patients with high L -TDI exhibited significantly worse survival in 5 out of 7 stratifications, with the remaining 2 thresholds approaching statistical significance. As a result, median survival times were also significantly reduced in patients with high L -TDIs in both the discovery (High L -TDI $9.58\pm \left[4.15, 13.74\right]$ and Low L -TDI: $17.88\pm [11.14, 21.06]$ months after diagnosis; stratified at 25/75-th percentiles) and replicative (High L -TDI $15.74\pm \left[4.96, 19.00\right]$ and Low L -TDI: $19.89\pm [11.21, 24.39]$ months after surgery; stratified at 25/75-th percentiles) cohorts (Figure 2D-E; Figure S4B-5B).

Figure 2.

Lesion-tract density index (L -TDI) and overall survival in GBM patients. (A-B) Kaplan-Meier curves for the two strata at the $p=25$-th percentile of the L -TDI distribution for (A) the UCSF and (B) the UPENN cohorts. The group with low L -TDI (blue) is significantly associated with longer survival times than the high L -TDI (red) group (${\mathrm{\chi }}^2=10.2820$, $P=.0012$, two-sided log-rank test). The shaded areas correspond to the 95% CI. Small vertical dashes indicate right-censored entries. (C) Natural logarithm of the two-sided log-rank p-value (black solid lines) as a function of the stratification thresholds in the UCSF (top) and UPENN (bottom) cohorts. The blue circles are the FDR significance values. Values below the significance level (red dashed horizontal lines; $\mathrm{\alpha }=0.05$) correspond to strata with significant differences in survival rates. The Kaplan-Meier curves for the lowest P-value in the discovery cohort (ie, $P=25/75$-th percentiles) are plotted in (A-B). (D-E) In patients known to have died, the median survival times for the two cohorts and strata shown in (A-B) were significantly higher in the low L -TDI group ($P<.001$, two-sided Mann-Whitney U-tests); both in the UCSF (D) and UPENN (E) cohorts. (F) L -TDI distributions of dead (orange) and alive (green) patients across multiple survival thresholds in the UCSF (Left) and UPENN (Right) cohorts. Black squares and lines show the median and third quartiles, respectively. In black text, the P-values of each comparison (‘***’ $P\le .001,$ ‘**’ $P\le .01,$ ‘*’ $P\le .05,$ ‘n.s.’ $P\ge .05,$ two-sided Mann-Whitney U-tests). In blue text the FDR corrected significance values. (G) Pearson correlation between survival times and L -TDIs in patients known to have died in the UCSF (Left) and UPENN (Right) cohorts (see Methods). The correlation stabilized around $\rho =-0.2$ after 18 months. (H-I) Receiver operating characteristic (ROC) curves and balanced accuracies (bACC) obtained from the same strata as (A-B) in the (H) UCSF and (I) UPENN cohorts. Separability was assessed at 12 (light blue) and 24 (orange) months. The corresponding bACCs were obtained using Youden’s J index (gray dashed vertical lines and colored circles). (J) For both discovery (gray solid line) and replicative (dark red line) cohorts, the time-dependent AUC was stable up to 18 months, after which it started to decay. The months in which the dynamic AUC was calculated were automatically selected depending on the cross-validation scheme (see “Methods” section).

To move beyond the use of arbitrary thresholds, we assessed whether patients who had died by specific time points had lower L -TDIs (Figure 2F). Noteworthy, alive patients at 6, 12, and 18 months consistently exhibited lower indices. In fact, the Pearson correlation between the OS and L -TDI progressively decreased and settled around $\rho =-0.2$ when considering patients surviving 1.5-2 years from the date of diagnosis or surgery (Figure 2G). These 2 findings revealed a natural survival cutoff situated close to the median survival times where the L -TDI showed stable behavior. Specifically, patients with low-L -TDI had increased probabilities of living more than 18 months compared to patients whose GBMs resulted in higher indices (Figures S4D and S5D). To test this cutoff in a more quantitative way, we measured the separability of the 2 strata defined from the first and third quartiles (Figure 2H-I). Similar results were observed when using an alternative 50/50 stratification, though the balanced accuracy for predicting survival at 12 and 24 months showed a slight decline (Figure S6D-H; Figure S7D-H). Lastly, the cumulative dynamic area under the curve (see Methods), was stable until the 18-month point, after which it started to decrease in both the UCSF and UPENN cohorts (Figure 2J).

In summary, the proposed L -TDI consistently stratifies survival times in patients with GBM (Figure 2A-C). To better contextualize this finding, we also computed the corresponding TDI and conducted parallel analyses in both cohorts (Figure S4-7). Most notably, higher TDIs were associated with reduced survival times only in the replicative cohort (ie, UPENN), suggesting its potential, despite limited, prognostic role. However, our results did not favor this local tumor description over the distributed model provided by the L -TDI. Indeed, in the discovery cohort, TDI showed no significant association with survival across multiple stratification thresholds (Figure S6A-C), failing to distinguish survival outcomes at 6, 12, or 18 months (Figure S4C; Figure S6D-I). Nonetheless, we do not consider TDI and L -TDI as competing metrics, but rather as complementary descriptors of GBM white matter involvement. We therefore sought to further investigate potential redundancies and synergies between these 2 density-based indices.

The L -TDI Provides a Morpho-Anatomical Model of Patient Survival

A key concern when introducing new biomarkers is determining whether they offer genuinely novel insights or merely reflect existing information, particularly in clinical settings, where interpretability is essential for informing therapies and targets. To this end, we examined the relationship between tumor volume, the proposed L -TDI, and the TDI. While both tract density-based markers were moderately correlated with each other, their association appeared limited to lower index values, indicating that they capture similar information only in a limited subset of cases (Figure 3A and B). Additionally, the L -TDI showed a strong positive correlation with tumor volume (UCSF: $P=0.85$, $P<0.001$; UPENN: $P=0.81$, $P<0.001$; 2-sided exact tests), whereas TDI was only weakly related to the tumor volume (UCSF: $P=0.06$, $P<0.155$; UPENN: $P=0.10$, $P<0.048$; 2-sided exact tests). Since the same normative tractogram was used for both cohorts, we pooled the data into a unified set of markers. Interestingly, while tumor volume and TDI differed slightly between cohorts, the L -TDI exhibited highly consistent distributions, hinting at an increased generalizability across independent samples (Figure S8).

Figure 3.

Tract density markers, morphology, and anatomy of GBM. (A-B) Scatter plots of the tract-density markers and the corresponding tumor volumes in (A) UCSF and (B) UPENN cohorts. Tumor volume increased somewhat linearly with the L -TDI but not with the TDI. The red text shows the Pearson correlation and the corresponding two-sided exact tests. (C) Principal component (PC) analysis of the 3 features in (A-B). More than 99.9% of the explained variance can be attributed to the first and second PCs. The first and second PCs largely account for the variance in the tumor volumes (left; tumor volume increasing from left to right) and TDIs (right; TDI increasing from bottom to top). (D) Observed and predicted L -TDI values obtained from the linear combination of the first two PCs. The $R^2$ depicts the determination coefficient of the linear fit. (E) Scatter plot of the first and second PCs together with the corresponding L -TDIs. The diagonal lines depict areas of constant L -TDI, and the black arrow indicates the direction along which the L -TDI increases. Because of the orthogonality of the first two PCs in (D-E), the L -TDI contains unique and non-redundant information of both tumor volume and indirect white matter infiltration. (F) Automatic K-means clustering from the tumor volumes and TDIs revealed 3 distinct groups. (G) Kaplan-Meier curves of each group in (F) revealed decreased hazard rates for small tumors with reduced TDI (purple—cluster 2) when compared with small tumors with increased TDI as well as large tumors (${\mathrm{\chi }}^2=6.1977$, $P=.0451$, two-sided log-rank test). Post hoc comparisons revealed equivalent survival rates for small tumors and high TDI (orange—cluster 1) and large tumors with medium TDI (green—cluster 0; ${\mathrm{\chi }}^2=0.6158$, $P=.4326$, two-sided log-rank test; $p=0.4326$, FDR corrected). Survival rates were adjusted for site effects (see “Methods” section). (H) Average [mean $\pm$ SEM] age in years for each cluster in (F). At least one cluster had a significantly different age ($F=6.6746$, $P=.0013$; one-way ANOVA). Follow-up analyses revealed that small tumors with low TDIs occurred in significantly younger patients (post hoc Tukey’s HSD). (I) Maximum intensity projection of the lesion group maps for the 3 distinct clusters in (F). The colorbars show the number of subjects with a GBM in each point of the brain. (J) Average percentage of the lesion that overlaps with each brain lobe defined in the USCLobes atlas for each cluster in (F). Percentages were calculated by averaging the overlap in each patient belonging to every distinct cluster. (K) Average percentage of overlap between the major white matter tracts defined in the XTRACT atlas and the L -TDM of every subject belonging to each cluster in (F). The white matter tracts appear sorted in decreasing order, and only the first 5 are shown (Figure S11C-E).

To disentangle the contributions of these 3 features, we performed linear dimensionality reduction and observed that more than 99% of the variance was captured by the first 2 principal components. Further inspections revealed that the first and second PCs corresponded to the tumor volume ($P=0.9992$, $P<0.0001$; 2-sided exact test) and TDI ($P=0.3969$, $P<0.0001$; 2-sided exact test), respectively. In other words, tumor volume increased from left to right in the first PC, and TDI from bottom to top in the second PC, confirming their linear independence (Figure 3C). Crucially, this implied that the L -TDI should be linearly predictable from the linear combination of the first 2 PCs (Figure 3D; $R^2=0.87$). In other words, the L -TDI contained both information about the tumor volume and the normative local white matter density, linearly and monotonously increasing with both size and density of white matter (Figure 3E).

It is worth noting that the computation of the L -TDI does not explicitly consider the size of the tumor, but, given that larger tumors intersect more normative tracts, higher L -TDI values were naturally expected for larger lesions. In contrast, the TDI presented a more complex, non-linear relationship with the morphology of the tumor. However, linear independence need not imply the absence of any relationship. Indeed, when applying unsupervised clustering to the 2-dimensional space defined by tumor volume and TDI, 3 distinct GBM subtypes emerged (Figure 3F): (1) small tumors with low TDI, (2) small tumors with high TDI, and (3) large tumors with intermediate TDI. These 3 groups had significantly different survival rates (${\mathrm{\chi }}^2=6.1977$, $P=0.0451$, 2-sided log-rank test; Figure 3G). Post hoc comparisons revealed that patients with small tumors and low TDI had significantly longer survival compared to those with small tumors and high TDI (${\mathrm{\chi }}^2=6.3676$, $P=0.0116$, 2-sided log-rank test, $P=0.0349$, FDR corrected). This subset of patients was also significantly younger than the rest (Figure 3H). While both TDI and L -TDI were only weakly correlated with age at diagnosis ($P=0.10$, $P=0.15$, $P<0.01$; 2-sided exact test), age is a known prognostic factor of OS, and this pattern would suggest that distinct mechanisms may underlie GBM development across different age groups. Similar results were observed when clustering into 4 groups instead of 3 (Figure S8F-H; Table S2) and were replicated in both the UCSF and UPENN cohorts independently (Figure S9-10).

These 3 tumor subgroups also showed distinct anatomical distribution within the brain (Figure 3I-J), aligning with prior findings,^33,45,46 and offered a white-matter description of the non-uniform anatomical distribution of human gliomas. While 2 of the 3 clusters had statistically similar survival rates, their anatomical and morphological configuration differed markedly.

Specifically, small tumors with high TDIs were predominantly located in the left parietal lobe, while large tumors with medium TDIs were primarily found in the right frontal lobe (Figure 3I). The percentage of affected brain lobes was significantly lower for the small tumor and high TDI (Figure S11A), yet this anatomical sparing did not translate into improved prognosis (clusters 0 and 1 in Figure 3G; ${\mathrm{\chi }}^2=0.6158$, $P=0.4326$, 2-sided log-rank test). However, the corresponding L -TDMs of these 2 groups of tumors were largely equivalent (Kendall’s $\tau =0.2049$, $P=0.0592$, 2-sided exact test), showing substantial overlap with key eloquent white matter pathways such as the corticospinal tract and superior longitudinal fasciculus (Figure 3K; Figure S11B-E).

In summary, the L -TDI and its spatial counterpart, the L -TDM, integrate information about tumor morphology, white matter density, and anatomical localization into a unified marker. This integrative approach also explained why tumors of different sizes resulted in similar survival outcomes, particularly when they involve similar white matter pathways despite differing in local tract densities (ie, TDIs). These findings challenge conventional lesion-symptom mapping models and underscore the need to conceptualize GBM as a disorder of distributed white matter network involvement.

Multivariate Cox Proportional Hazard Models of Survival Rates in Human GBMs

We wanted to assess whether tract density-based markers significantly improved the prediction of survival rates compared to the habitual clinical variables, that is, sex, age, MGMT status, EOR, and KPS. Initially, we computed Harrell’s concordance index $\left(C^H\right)$ of each clinical covariate, as well as tract-density indices and the tumor volume (Figure 4A-B; Table S3). The L -TDI was associated with significant discriminative power in the UCSF ($C^H=0.5829$, $P<0.0001$, one-sided permutation tests; $n=1000$ resamples) and UPENN ($C^H=0.5492$, $P=0.002$, one-sided permutation tests; $n=1000$ resamples) cohorts. In contrast, the TDI retained statistical significance only in the UPENN cohort ($C^H=0.5677$, $P<0.0001$, one-sided permutation tests; $n=1000$ resamples). Upon joining the 2 cohorts and stratifying the combined sample according to the $P=50$th percentile (eg, the most conservative stratification threshold) of the L -TDI and TDI distributions, respectively, we confirmed the superior robustness of the L -TDI in (Figure 4C-D).

Figure 4.

Predictive models of GBM survival using tract density-based biomarkers. (A-B) Harrell concordance index $\left(C^H\right)$ associated with every clinical covariate for the (A) UCSF and (B) UPENN cohorts. The dotted black lines show no discriminative power (ie, expected at random). Blue and gray bars correspond to covariates with significant and non-significant indices, respectively (“***” $P\le .001,$ “**” $P\le .01,$ “*” $P\le .05,$ “n.s.” $P\ge .05$; one-sided permutation tests; $n=1000$ resamples). Features were sorted in descending order of importance (Table S2). (C-D) Kaplan-Meier curves for the two strata at the $p=50$-th percentile of the (C) L -TDI and (D) TDI distributions. The group with low L -TDI (blue) is significantly more associated with longer survival times than the low TDI (red) group (${\mathrm{\chi }}^2=7.4882$, $P=.0062$; ${\chi }^2=4.8820$, $P=.0271$, two-sided log-rank test). The shaded areas correspond to the 95% CI. Small vertical dashes indicate right-censored entries. (E) Forest plot showing the hazard ratios for all the corresponding Cox models in Table 1. Error bars depict the 95% CIs. The magenta inset shows the “TDI” and “volume” hazard ratios in greater detail. CIs not crossing the $HR=1$ vertical dark line carry statistical significance ($P\le .05$; two-sided Wald’s t-test). (F, Left) One-sided log-likelihood ratio tests comparing the Cox models with added covariates with respect to the naive ($C^H=0.668$). (F, Right) L -TDI Cox model compared to the model with TDI and TDI+volume as added covariates of interest. All tests were done with 1 degree of freedom except when comparing the TDI+Volume and Naive models ($df=2$). The colors are shared with those in panel (E). (G, Left) One-sided log-likelihood ratio tests comparing the logistic regression with added covariates with respect to the naive. (G, Right) L -TDI logistic regression compared to the model with TDI and TDI+volume as added covariates of interest. The positive class corresponded to the number of dead patients before 6, 12, and 18 months, respectively. (H) Schematic representation of the training and testing procedure used to validate a binary logistic classifier of deaths occurring 12 months after the initial diagnosis. All the survival curves and models were fit using the joint cohorts after accounting for site-related effects (see “Methods” section).

To further quantify the prognostic value of tract density-based markers, we also fitted multiple Cox models to measure the respective hazard ratios ($HR$) in a multivariate context (Figure 4E, see also Table 1). After pooling together the 2 cohorts and correcting for site-related differences (see “Methods” section), both markers retained statistical significance. Notably, the L -TDI provided a considerably higher contribution to survival ($HR=1.0742$, $P=0.0050$, 2-sided Wald’s t-test), exerting a considerably larger effect than the TDI ($HR=1.0026$, $P=0.0250$, 2-sided Wald’s t-test). These results highlight the predominant role of tract density-based markers, and particularly of L -TDI, in driving worse survival outcomes. These results were confirmed after fitting the same Cox models to each cohort independently (Table S4). Amongst the classical clinical predictors, both the EOR and MGMT promoter status were associated with the largest $\mathit{HRs}$, confirming their positive prognostic value. Age, despite having relatively weaker $\mathit{HRs}$, proved to be the most robust indicator of decreased survival rates (Table S4-S8), that is, it significantly participated in all the models and cohorts. Log-likelihood ratio ($\mathit{LLR}$) tests emphasized the added prognostic value of tract density-based imaging biomarkers (Figure 4F; Figure S12). Crucially, the L -TDI model ($C^H=0.675$) was more plausible than the TDI one ($P=0.0296$, one-sided $\mathit{LLR}$ test; $C^H=0.671$), but not than the model that contained both TDI and volume as added features ($P=0.1674$, one-sided $\mathit{LLR}$ test; $C^H=0.673$). This could be understood because the L -TDI implicitly accounts for both local white matter density and lesion morphology (Figure 3). These findings remained consistent after discarding (1) subjects without proper surgical resections and (2) the EOR as a primary covariate (Figure S13A-C; Tables S5-S7).

Table 1.

Multivariate Cox survival models and logistic regressions to estimate the probability of dying before 12 months

Multivariate cox survival models
Model	Hazard ratio				P-value
	L -TDI	TDI	TDI+Volume	Naive	L -TDI	TDI	TDI+Volume	Naive
Sexn.s.	0.9501	0.9614	0.9570	0.9770	.595	.682	.648	.8084
Age **	1.0276	1.0271	1.0273	1.0281	<.001	<.001	<.001	<.001
MGMT **	0.7270	0.7224	0.7241	0.7262	<.001	<.001	<.001	<.001
EOR **	0.5709	0.5644	0.5652	0.5472	<.001	<.001	<.001	<.001
L -TDI **	1.0742	N.A.	N.A.	N.A.	.005	N.A.	N.A.	N.A.
TDI **	N.A.	1.0026	1.0025	N.A.	N.A.	.025	.039	N.A.
volume n.s.	N.A.	N.A.	1.0009	N.A.	N.A.	N.A.	.188	N.A.

Multivariate logistic regressions
Model	Coefficient for 12 months				P-value
	L -TDI	TDI	TDI+Volume	Naive	L -TDI	TDI	TDI+Volume	Naive
Constant *	−1.5277	−1.1045	−1.6310	−0.6189	.048	.156	.043	.392
Sex n.s.	−0.1230	−0.1225	−0.1088	−0.0948	.550	0.546	.597	.638
Age **	0.0546	0.0545	0.0548	0.0563	<.001	<.001	<.001	<.001
MGMT **	−0.2976	−0.2905	−0.2997	−0.2926	.004	.004	.003	.004
EOR **	−0.967	−1.0188	−1.027	−1.0696	<.001	<.001	<.001	<.001
L -TDI **	0.2185	N.A.	N.A.	N.A.	<.001	N.A.	N.A.	N.A.
TDI n.s.	N.A.	0.0044	0.0043	N.A.	N.A.	0.077	0.093	N.A.
Volume n.s.	N.A.	N.A.	0.0044	N.A.	N.A.	N.A.	.003	N.A.

The Cox survival models were fitted for the joint cohort ($N=617$) after correcting for site effects and discarding missing values. Hazard ratios ($e^{{\beta }_i}$) and the corresponding p-values (two-sided Wald’s t-test; $df=N-\#\mathit{covariates}$). The logistic regressions were fitted to predict the probability of dying (status = 1) before 12 months. Patients who were lost to follow-up (status = 0) before 12 months were discarded. For the joint cohort ($N=546$), after correcting for site effects and discarding missing values, the coefficients and the corresponding P-values (two-sided Wald’s z-test; $df=N-\#\mathit{covariates}$). Bold numbers indicate significant hazard ratios and coefficients (P$<.05$). The asterisks mark whether the $i$-th feature statistically contributes to 0, at least 1, or all the models (“n.s.”, “*”, and “**” respectively). N.A. stands for “not applicable” due to the specifics of the regressions fitted (see “Methods” section). Table S3 includes the 95% CIs and the results of each independent cohort. Table S8 includes the 95% CIs and the results of each independent cohort and multiple time horizons.

We fitted a last multivariate Cox survival model on the subset of patients with available KPS in the UPENN cohort ($N=53$; Figure S13D; Table S8). Across all 4 models, age and MGMT covariates retained statistical significance in all 4 models. In contrast, the EOR remained borderline significant. In this subset, the L -TDI emerged as the strongest predictor of survival, showing the highest hazard ratio ($HR=1.3519$, $P=0.005$, 2-sided Wald’s t-test). The KPS score was only significant in the 3 models where the L -TDI was not used. The TDI index did not provide significant predictive value in the 2 models where it was included, and the tumor volume’s hazard ratio was also not significant. Consistent with previous analyses, log-likelihood ratio tests showed that the L -TDI model significantly outperformed the Naive ($P=0.0050$, one-sided $\mathit{LLR}$ test), and TDI ($P=0.0292$, one-sided $\mathit{LLR}$ test), but not the TDI+Volume ($P=1.000$, one-sided $\mathit{LLR}$ test) models.

The L -TDI Improves the Prediction of Survival Probability

To estimate the probability of death within a specific timeframe, we used a logistic model suited for this binary classification task. First, using the entire joint cohort, we fitted a logistic model to predict the probability of a patient dying before 12 months from the date of diagnosis (Table 1). This approach provided insight into the predictive value of each feature. In line with the results obtained from the multivariate Cox models, the L -TDI significantly contributed to the prediction ($\mathit{coef}=0.2185$, $P<0.001$, 2-sided Wald’s z-test), along with the traditional clinical features (ie, age, MGMT status, and EOR). In contrast, the TDI remained borderline non-significant ($\mathit{coef}=0.0044$, $P=0.077$, 2-sided Wald’s z-test). Tumor volume significantly added to the fit ($\mathit{coef}=0.0044$, $P<0.003$, 2-sided Wald’s z-test). These results were consistent when considering each cohort independently (Table S9). Precisely, the L -TDI retained statistical significance in both cohorts, while the TDI only appeared significant in the UPENN cohort.

We extended this framework to account for potential differences in the time courses of survival rates by predicting the probability of dying before 6 and 18 months, respectively (Table S9). The corresponding $\mathit{LLR}$s tests confirmed that logistic fits were statistically more plausible when incorporating explicitly the L -TDI jointly with the habitual clinical markers (Figure 4G). Importantly, models based on the TDI did not outperform the naïve baseline, whereas those including the L -TDI consistently showed superior predictive performance across all time windows. Additionally, it offered a considerably better fit than the TDI model at 12 months ($P=0.0004$, one-sided $\mathit{LLR}$ test). As before, the combination of TDI and lesion volume approximated the performance of the L -TDI model (Figure 4G, Right), further reinforcing that the L -TDI captures both features in a compact representation.

Finally, to assess the reaL -world applicability and generalizability of the L -TDI, we leveraged the 2 independent cohorts to construct cross-site predictive models. Among several modeling options, we intentionally opted for a simple logistic classifier to test the robustness of the proposed marker explicitly. We trained and tested models across the UCSF and UPENN cohorts, then repeated the procedure by swapping their roles (Figure 4H), automatically readjusting cross-validation parameters to optimize training (“Methods” section; Figure S10). Since survival prediction is inherently imbalanced (ie, the number of deceased subjects increases over time), we used the area under the curve (AUC) and balanced accuracy (bACC) as evaluation metrics. The performance of the models was stable when considering the different combinations of training and testing cohorts, with the L -TDI model consistently outperforming the TDI and Naive models, albeit modestly ($\sim 65\%-68\%$ bACC at 12 months; see Table 2). Results were comparable when predicting death at 18 months (Figure S9; Table S11), suggesting that including L -TDI enhances model performance as a relevant imaging feature. A Bayes classifier using the L -TDI improved the classification accuracy, especially considering survival after 6 months. Such prediction of early deaths is challenging due to an imbalanced fraction of dead patients. Notably, the accuracy reached $\sim 66$% for predicting early deaths, slightly improved and remained stable across survival thresholds ($68\%-70\%$ bACC), and showed a significant improvement compared to the models augmented with the TDI biomarker (Tables S12 and S13).

Table 2.

Classification metrics for the logistic classifier trained to predict mortality within 12 months

AREA UNDER THE CURVE (AUC)
		Train (12 months)			Train (12 months)
	Model	L-TDI	TDI	Naive	L-TDI	TDI	Naive
Test (12 months)	UCSF	N.A.			0.7433	0.7088	0.7220
	UPENN	0.7327	0.7039	0.7077	N.A.
BALANCED ACCURACY (BACC)
		Train (12 months)			Train (12 months)
	Model	L-TDI	TDI	Naive	L-TDI	TDI	Naive
Test (12 months)	UCSF	N.A.			0.6498	0.6463	0.6418
	UPENN	0.6753	0.656	0.6661	N.A.

Area under the curve (AUC) and balanced accuracy (bACC) of the models tested on each independent cohort. N.A. stands for not applicable, since we did not perform testing on the cohort used for training. Bold numbers indicate the best model on the testing cohort.

Discussion

In this work, we provide a robust and reproducible stratification of GBM survival outcomes by leveraging a novel L -TDI marker, thus presenting compelling evidence that GBM prognosis is fundamentally influenced by the underlying architecture of the brain’s white matter. Crucially, a newly emerging paradigm suggests that GBM interferes with the brain’s circuitry,¹⁶ consequently altering various critical functions.^1,30,31 In agreement with it, our findings reinforce the view that GBM is not solely a focal pathology, but a disease of large-scale structural involvement, whose clinical impact is governed by its interaction with the brain’s network infrastructure. Prior studies have shown that tumor volume alone does not reliably predict survival.^47–49 Our findings challenge the conventional focus on tumor size or gray matter location and instead highlight the critical importance of the underlying white matter network. As such, GBMs should not be viewed merely as a localized mass disconnecting distant regions, but rather as a network-level disease, involving large-scale white matter organization and, consequently, impacting global brain communication.^4,15

A major contribution of this study lies, therefore, in establishing the L -TDI as a marker that simultaneously captures multiple critical GBM dimensions, its volume, spatial distribution, and potential pathways of infiltration, therefore offering a white matter-informed perspective on glioma localization. In line with prior work, our findings reinforce that GBMs are not randomly distributed across the brain but preferentially arise in regions of distinct white matter density.⁴⁶ Yet, unlike traditional volumetric or anatomical metrics, the L -TDI encodes how the tumor is embedded within the broader scaffold of white matter tracts, fundamentally moving beyond lesion-symptom associations. The morpho-anatomical model of the current study highlights tumor topography as an emergent property of the structural connectivity architecture of the brain. Indeed, although small tumors with high TDI affected a smaller portion of the brain in terms of lobe involvement compared to large GBMs with an intermediate TDI (Figure 3; Figure S11A), this anatomical sparing did not translate into improved prognosis. This underscores a critical point: the clinical impact of a GBM is not solely determined by its size or anatomical topography but by the interaction between the tumor and surrounding white matter pathways. Accordingly, the spatial patterns of white matter involvement of these 2 subgroups were remarkably similar, indicating that both tumor groups converged on key white matter structures. Hence, our findings suggest that clinical evolution might benefit from augmenting therapeutic strategies with non-local targets.

In addition to clarifying the non-trivial relationship between the tract density markers, morphology, and anatomy in GBM, we validated the prognostic value of L -TDI using multivariate Cox regression models, demonstrating that its contribution to OS prediction remains significant even after accounting for welL -established clinical and molecular variables, including MGMT promoter methylation status. The additive power of L -TDI in these models underscores its utility as a non-redundant biomarker that complements, rather than replaces, current prognostic tools. Moreover, L -TDI offers a mechanistic bridge between macroscopic lesion burden and microscale tumor invasiveness, reflecting the involvement of long-range communication pathways critical to brain function and resilience. Ultimately, radiotherapy planning might benefit from targeting this glioma-neuron scaffold.^16,31

Importantly, the L -TDI possessed predictive value. A simple logistic regression achieved competitive accuracies in predicting 12-month mortality (Table 2; see also Table S11), both within the original sample and when applied to an independent validation cohort. A more sophisticated classifier demonstrated improved performance in predicting early deaths while generalizing across thresholds and cohorts (Table S13). This cross-site generalizability is essential for clinical translation and suggests that the L -TDI framework could be readily deployed within existing neuroimaging pipelines. Furthermore, the present retrospective study draws on one of the largest cohorts reported in recent literature, strengthening the statistical power and generalizabi­lity of the results. Such large-scale efforts are key to fostering open clinical collaboration and establishing multi-center networks that can improve the reliability and translational potential of findings in GBM management.⁵⁰ However, a reduced set of clinical covariates may limit scalability for highly individualized medicine insights. In contrast, AI-based approaches capitalize on big data consortia to deliver accurate prognostics at the expense of reduced interpretability and increased computational demands. For these reasons, studying the interaction between tractography markers, treatment variables, and radiomics or imaging-based features remains an essential step forward.

FET-PET features have shown utility in assessing re-irradiation responses.⁵¹ Radiomics and machine learning-based subgrouping systems hold promise for accurate GBM survival predictions by integrating multiparametric MRI features, clinical, and molecular data in large, multi-institutional cohorts.^52,53 Interestingly, reported accuracies and concordance indices have reached 74.27% and 0.68, respectively, which are comparable to our results (ie, 69.56% and 0.675), albeit we are relying on a simpler and more tractable framework. Hence, while these models excel at handling large-scale heterogeneity and high-dimensional radiomic signatures to identify statistical patterns of survival, the L -TDI provides a mechanistically grounded and anatomically interpretable biomarker, grounding meaningful survival predictions in network-level disease mechanisms. Ultimately, these approaches may converge in integrative nomograms combining clinical, molecular, imaging, and white matter–informed features to optimize patient-level prognostication.

Beyond delivering accurate survival predictions, this framework has the potential to inform several aspects of clinical decision-making in neuro-oncology. In radiotherapy planning, L -TDMs may serve as surrogate descriptors of white matter pathway involvement. This would enable refinement of clinical target volumes by identifying potential routes of microscopic tumor spread while also supporting clinical target volume reduction in regions of low connectomic relevance.⁵⁴ For clinical trial design, L -TDIs offer anatomically grounded biomarkers that may improve patient selection, especially in studies prioritizing preservation of cognitive or motor function, where treatment-related toxicity may depend on tract involvement and network vulnerability. In resource-limited settings, normative connectivity models could approximate tumor-tract relationships in the absence of patient-specific diffusion imaging, eventually guiding supra-total resection strategies.

Despite these advantages, clinical reproducibility and translation rely on 2 crucial steps: accurate tumor segmentation and image registration. These require multi-modal MRI acquisitions, preferably, with high spatial resolution (ie, ≤1.5 mm³ isotropic, with ≤1.5 mm slice thickness) or 3D sequences to minimize partial volume effects. Brain lesions may impair image registration, but resampling and co-registering all modalities before normalization provides a robust pipeline suitable for clinical use. Additionally, masking pathological tissue during normalization may help reduce distortion artifacts and improve alignment for L -TDI computation (see Supplementary Material).

Lastly, we acknowledge that using normative templates may be perceived as a limitation. Given the known tendency of gliomas to infiltrate, displace, and degrade surrounding tissue, normative atlases might under- or overestimate local white matter involvement. However, relying on normative rather than subject-specific tractograms offers important advantages, particularly in the context of standardized analysis, reproducibility, and computational tractability. In clinical environments, where patient-specific diffusion imaging is often noisy or unavailable, normative L -TDI provides a viable and informative proxy. That said, a crucial direction for future research will be validating L -TDI within a patient-specific tractography framework. This would allow us to assess how accurately the normative-based L -TDI reflects individual white matter anatomy in the presence of tumor-induced distortion. Nevertheless, performing diffusion tractography in the presence of brain tumors is a technically challenging task,^21,28,55 and any potential gains must be weighed against the cost and complexity of acquiring high-quality diffusion data in a clinical context.

Conclusions

Our findings establish a new L -TDI as a robust and clinically meaningful biomarker that captures the complex interplay between tumor morphology and white matter architecture. By integrating tumor volume, spatial distribution, and normative tract density into a single index, this L -TDI offers a biologically grounded explanation for survival differences that are not accounted for by traditional metrics. Unlike purely local features, the L -TDI reflects the extent to which a tumor interacts with critical white matter circuitry, providing insights into disease prognosis. It consistently outperformed or matched alternative models across multiple statistical frameworks and independent cohorts, while maintaining interpretability and feasibility using normative connectomes. As such, this work represents a step forward toward connectomics-guided neuro-oncology, with the potential to inform individualized risk stratification, clinical decision-making, therapeutic planning, and ultimately, patient outcomes.

Supplementary material

Supplementary material is available online at Neuro-Oncology (https://academic.oup.com/neuro-oncology).

Author Contributions

Conceptualization: J.F.-R. and A.C. Methodology: J.F.-R. and A.C. Software: J.F.-R. Validation: J.F.-R., G.A.B., A.J., S. L., L.S.P., and A.C. Formal analysis: J.F.-R. and A.C. Investigation: J.F.-R. Resources: J.F.-R., J.K.A., and A.C. Data Curation: J.F.-R. and A.C. Writing—Original Draft: J.F.-R. and A.C. Writing—Review & Editing: J.F.-R., G.A.P, A.J., S.L., L.S.P, J.K.A., and A.C. Visualization: J.F.-R., G.A.P., A.J., and A.C. Supervision: A.C. Project administration: J.F.-R., J.K.A., and A.C. Funding acquisition: J.F.-R., J.K.A., and A.C.

Conflict of Interest Statement

None declared.

Funding

This research was funded in part by the National Science Centre, Poland No UMO-2024/53/N/NZ4/03513 (J.F.-R., A.C.). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 857533 and from the International Research Agendas Programme of the Foundation for Polish Science No MAB PLUS/2019/13 (J.F.-R., A.J., J.K.A.). The publication was created within the project of the Minister of Science and Higher Education “Support for the activity of Centers of Excellence established in Poland under Horizon 2020” on the basis of the contract number MEiN/2023/DIR/3796 (J.F.-R., A.J., J.K.A.). We gratefully acknowledge Polish high-performance computing infrastructure PLGrid (HPC Center: ACK Cyfronet AGH) for providing computer facilities and support within computational grant no. PLG/2025/018289 (J.F.-R., A.J., J.K.A.). A.C. and L.S.P. were also supported by the National Plan for NRRP Complementary Investments (PNC, established with the decree-law May 6 2021, n. 59, converted by law n. 101 of 2021) in the call for the funding of research initiatives for technologies and innovative trajectories in the health and care sectors (Directorial Decree n. 931 of 06-06-2022)—project n. PNC0000003 - AdvaNced Technologies for Human-centrEd Medicine (project acronym: ANTHEM). This work reflects only the authors’ views and opinions, neither the Ministry for University and Research nor the European Commission can be considered responsible for them.

Role of the Funding Source

The funder had no role in the design, data collection, data analysis, and reporting of this study. The authors declare no competing interests.

Ethics Statement

Data collection was performed in accordance with relevant guidelines and regulations and was approved by the UCSF institutional review board with a waiver for consent. Collection, analysis, and release of the UPenn-GBM data has happened in compliance with all relevant ethical regulations. The protocol was approved by the Institutional Review Board at the UPHS, and informed consent was obtained from all participants.

Data Availability

The discovery dataset was retrieved from The University of California San Francisco Preoperative Diffuse Glioma MRI repository in The Cancer Imaging Archive.⁵⁶ The replicative dataset was retrieved from the Multi-parametric magnetic resonance imaging (mpMRI) scans for de novo GBM patients from the University of Pennsylvania Health System collection in The Cancer Imaging Archive.⁵⁷ The normative connectome employed in the present work is also freely available.³⁷ The USCLobes brain atlas can be downloaded from: https://brainsuite.org/usclobesatlas/, and the XTRACT white matter atlas is openly accessible in FSL. We previously registered both parcellations to the same MNI template used in this study, following the same steps outlined in the Methods.

Code Availability

The codes to perform the normalization to MNI, computation of the tract density indices, and the statistical analyses are publicly available in Open Science Framework (https://doi.org/10.17605/OSF.IO/P8XGH) and/or can be requested from the corresponding authors. A combination of custom codes and software packages was used. Specifically, survival analyses were carried out within the statsmodels,⁵⁸ Scikit-survival,⁵⁹ and lifelines⁶⁰ Python packages. All the figures in the main and supplementary text were generated with custom Python codes, saved as scalable vector graphics (SVG) files, and assembled in Inkscape.