Decoding Patient Heterogeneity Influencing Radiation-Induced Brain Necrosis

Abstract

Purpose:

In radiotherapy (RT) for brain tumors, patient heterogeneity masks treatment effects, complicating the prediction and mitigation of radiation-induced brain necrosis. Therefore, understanding this heterogeneity is essential for improving outcome assessments and reducing toxicity.

Experimental Design:

We developed a clinically practical pipeline to clarify the relationship between dosimetric features and outcomes by identifying key variables. We processed data from a cohort of 130 patients treated with proton therapy for brain and head and neck tumors, utilizing an expert-augmented Bayesian network to understand variable interdependencies and assess structural dependencies. Critical evaluation involved a 3-level grading system for each network connection and a Markov blanket analysis to identify variables directly impacting necrosis risk. Statistical assessments included log-likelihood ratio (LLR), integrated discrimination index (IDI), net reclassification index (NRI), and receiver operating characteristic (ROC).

Results:

The analysis highlighted tumor location and proximity to critical structures like white matter and ventricles as major determinants of necrosis risk. The majority of network connections were clinically supported, with quantitative measures confirming the significance of these variables in patient stratification (LLR=12.17, p=0.016; IDI=0.15; NRI=0.74). The ROC curve area was 0.66, emphasizing the discriminative value of non-dosimetric variables.

Conclusions:

Key patient variables critical to understanding brain necrosis post-RT were identified, aiding the study of dosimetric impacts and providing treatment confounders and moderators. This pipeline aims to enhance outcome assessments by revealing at-risk patients, offering a versatile tool for broader applications in RT to improve treatment personalization in different disease sites.

INTRODUCTION

Radiation-induced brain necrosis (RN) is a radiotherapy (RT) complication that can arise in the treatment of central nervous system (CNS), base of skull (BOS), or head and neck (H&N) tumors. Proton therapy, known for its precise dose delivery given its unique dosimetric characteristics, has been increasingly utilized for these tumor locations due to the anatomical complexity and proximity to organs-at-risk. While proton therapy offers distinct advantages, the literature reports mixed findings regarding its association with brain necrosis (1). In recent studies, the incidence of RN in patients treated with proton therapy varies widely, ranging between 0.5% to 31%, depending on factors such as the volume and dose of irradiated tissue (2–12). The expected advantage of proton therapy is based on a reduced volume exposure and radiation dose to the healthy brain, i.e., lower total integral dose.

Dose in the normal tissue is a causal factor for toxicity. Despite sparing more healthy tissue, proton therapy can have an elevated damage within the irradiated region due to its high linear energy transfer (LET), which measures the energy released by radiation along the proton beam path in the tissue. While some research indicated a potential link between increased LET and radiographic changes (13), other studies and meta-analyses found no significant correlation (14–16). These findings suggest that the relationship between the treatment variables and RN is complex and masked by patient heterogeneity, highlighting the importance of studying this heterogeneity to better understand and predict RN.

Previous studies have identified a significant role of tumor location in the risk of necrosis (17–19), with high radiation sensitivity of the white matter (9,20–22), tissue next to ventricles (23–25), and specifically the periventricular white matter (26–28). While these studies have highlighted the impact of tumor location, there remains a need to study more comprehensive variables, understand their interactions, and measure their contribution to patient stratification. To achieve this, we developed a Bayesian network model that incorporates patient demographics, tumor characteristics, and treatment parameters. We deliberately excluded comprehensive dose and LET distributions in our analysis to focus on the effect of patient heterogeneity.

During the model design, we focus on clinical integrability, specifically the augmentation of expert knowledge to exclude clinically irrelevant correlations and assess the role of established risk factors during the exploration of new predictors. Additionally, we focused not only on identifying predictors, but also on determining intra-predictor relationships, which are necessary to examine variables interactions and confounders that are needed to improve risk assessment and trial design. Importantly, our study provides a quantitative assessment of how patient heterogeneity impacts outcome variation and measures how much the identified variables can be used to stratify patients. The findings are particularly relevant to proton therapy as they offer a basis for future research into the role of LET while accounting for patient heterogeneity. Additionally, the identified variables and their interactions help us develop advanced predictive scoring models that can be used to identify at-risk patients and personalize treatment selection in CNS, BOS, and H&N.

MATERIAS AND METHODS

Our study introduces a framework for examining patient heterogeneity and its effect on outcome variability (Figure 1). Initially, we collect and process data, then establish rules based on expert knowledge and statistical metrics to construct a Bayesian network aimed at exploring correlations between patient-specific factors and the treatment outcome. After the network was learned, we conducted a qualitative assessment of the model’s clinical feasibility, followed by an analysis of the Markov blanket (MB) to identify critical risk factors associated with the outcome. A quantitative analysis of these factors then assesses their capacity to capture variations in patient outcomes. This method elucidates the influence of diverse factors on treatment response variability and may extend to other outcomes affected by patient variability.

Figure 1: Systematic Framework for Analyzing Patient Heterogeneity via Bayesian Networks.

This flow chart outlines a systematic approach to developing a Bayesian network for decoding patient heterogeneity in outcome variation. It begins with the collection and preprocessing of patient data, ensuring quality and consistency. The process then involves defining expert and statistical rules to guide the construction of the BN, ensuring that it is both clinically relevant and statistically robust. Structural learning techniques are employed to develop the network, followed by a qualitative assessment to validate its clinical feasibility. The identification of key risk factors is conducted through Markov Blanket analysis, isolating the most influential variables. Finally, a quantitative assessment of these variables is performed to understand their contribution to explaining outcome variation. This comprehensive approach ensures the creation of a data-driven, clinically applicable model that aids in understanding patient-specific factors influencing health outcomes.

Data

Retrospective data from patients treated with passive scattering proton therapy at Massachusetts General Hospital (MGH, 2004-2016) for CNS, BOS, and H&N tumors was used (Figure 1, block A). The study was approved by MGH’s Institutional Review Board committee (protocol number 2016P001950). The cohort consisted of 179 patients who were previously analyzed for dose response to RN post-proton therapy and LET correlation (14,29). Patients with <6 months follow-up or incomplete imaging were excluded, resulting in 130 patients for analysis.

Post-treatment MRIs utilized T1-weighted with and without gadolinium contrast, T2-weighted-fluid-attenuated inversion recovery, and diffusion-weighted imaging protocols, with imaging frequency tailored to patient diagnosis and clinical concerns. Glioma patients received scans 4 to 6 weeks post-radiation, then every 3 months for the first 1 to 2 years, with intervals extending to 4 to 6 months, while extracranial diagnoses had baseline scans at 6 to 12 weeks, followed by scans every 3 to 6 months in the first year, then annually. The classification of RN involved initial MRI interpretation by neuroradiologists, a review of all cases by two neuro-oncology specialists and relied on serial imaging to observe the evolution of necrosis over time. Surgical confirmation was obtained for 6 CNS and 1 H&N case, all in the frontal lobe (29). Regions of necrosis were contoured and graded using the Common Terminology Criteria for Adverse Events (CTCAE) v4.03. Patients who developed necrosis before death or their last follow-up were classified as having necrosis. Those without signs of necrosis until their last follow-up or death were considered not to have developed necrosis and censored. Following this evaluation, 50 out of the 130 patients were confirmed to have developed radiographic changes indicative of grade 1 or more radionecrosis. Using grade 1+ as a primary endpoint reflects its utility as an early indicator of radiation damage, reflecting radiation sensitivity and its impact on outcome. Additionally, it broadens the scope of our analysis as it includes grade 2+, enhancing statistical power and improving sensitivity to the early manifestations of necrosis.

Candidate variables

We focused on patient-specific variables such as biometric variables (sex and race) and comorbidities (diabetes and hypertension). Tumor-related variables included clinical target volume (CTV), tumor lateralization, location (intracranial vs. extracranial), and the ‘cerebral lobe at greatest risk’ (highest radiation dose). Grouping tumors as intra or extracranial helped consolidate diverse diagnoses, potentially enhancing statistical power given our sample size despite less granular tumor data. Treatment variables included prior surgery, chemotherapy status, RT type (definitive/adjuvant), and the mean and maximum radiation dose in the brain, converted to 2 Gy equivalent to account for differences in fractionation schemes among patients.

Additional variables that could affect sensitivity were obtained by contouring brain ventricles and white matter using SynthSeg (30). This included the volume of the whole ventricular system and ‘distance to ventricles’ based on its correlation with RN (23), calculated from the maximum dose to the nearest ventricle boundary. We also added a binary variable that indicates whether the maximum dose is in the white matter or not. The combination distance to ventricles and maximum dose location in relation to white matter served as a surrogate for the sensitivity of the deep white matter tracks that are known to be prone to necrosis (31).

Processing of variables

To prepare the variables for the Bayesian network modeling, continuous variables were normalized to zero mean and unit standard deviation to ensure scale comparability, then discretized to improve model stability and minimize outlier effects (32). The Akaike Information Criterion (AIC) (33) guided the number of discretization levels, balancing data graduality and fit. Given AIC’s normal distribution assumption, we verified and transformed variable distributions as needed: skewed distributions underwent Yeo-Johnson transformations (34), while bimodal distributions were addressed using Gaussian mixture models. We tested 2+ categories for skewed and 3+ for bimodal data, selecting the count with the lowest AIC up to 10 categories.

Structural Learning and Bayesian Network Development

During structural learning, we eliminated clinically infeasible connections (Figure 1, block B). Variables were grouped by patient, tumor, and treatment categories, with constraints imposed against clinically implausible upward connections (e.g., tumor influencing patient variables). Specifically, constraints ensured tumor properties did not affect patient biometrics or comorbidities and that treatments were determined by, but did not determine tumor and patient characteristics. Additionally, we used mutual information (MI) theory (35) to further guide the structural learning process (Figure 1, block B). MI was calculated for variable pairs and analyzed, particularly at the lower distribution, to pinpoint weak correlations. A threshold at the low 25th percentile was chosen to eliminate the least statistically relevant connections. Following the setup of constraints, the structural learning proceeded (Figure 1, block C). While we imposed manual constraints to prevent a clinically implausible network, the connections that resulted in the network were derived from the data with no manual addition of edges, aiming to reflect the statistical relationships present in our dataset.

Qualitative Evaluating of the Model Clinical Feasibility

We applied constraints based on known causality impossibilities and weak MI during the structural learning phase. The network emerged from a standard structural learning process directly derived from data while respecting the set constraints. Yet, before analysis, we thoroughly evaluated the network’s connections post-structural learning (Figure 1, block D). Connections were categorized as ‘valid’ (clinically established), ‘conceivable’ (clinically rational without strong evidence), or ‘incidental’ (lacking clinical links). We aimed from this assessment to ensure that the network was clinically feasible, minimizing spurious or irrelevant findings.

Identification of Clinical Risk Factors for RN through Markov Blanket Analysis

Post model construction and feasibility assessment, the RN node’s Markov Blanket (MB) was identified (Figure 1, block E). The MB contains variables directly influencing the RN node: parents, children, and spouses (other parents of these children). Identifying the MB delineates direct RN risk factors, excluding less influential peripheral variables.

Quantitative Evaluation of Identified Variables in Explaining Patient Heterogeneity

We quantified the clinical significance of MB-identified variables through a set of statistical tests (Figure 1, block F), hypothesizing they capture patient heterogeneity regarding RN. Our null model, including only the intercept with no predictors, served as a benchmark, representing a standard dosimetric-focused approach.

We used the log-likelihood ratio (LLR) test (36) to quantify how MB variables explain patient outcome variance, yielding a p-value to assess significance against the null model. We also calculated the Integrated Discrimination Improvement (IDI) (37), measuring changes in discrimination slope upon adding MB variables. An IDI greater than zero suggests that including the MB variables enhances the ability to differentiate between patients at risk for RN versus those not at risk.

In addition, we used the Net Reclassification Index (NRI) (37) to evaluate the improvement in risk stratification offered by the MB variables compared to the null model. NRI assesses whether patients categorized into incorrect risk tiers under the null model are more accurately classified when the MB variables are included. We used five risk groups for this analysis. Mathematically, it is represented as: $\mathrm{NRI}=\left[\mathrm{P}\left(\mathrm{up}|\mathrm{RN}\right)-\mathrm{P}\left(\mathrm{down}|\mathrm{RN}\right)\right]+[\mathrm{P}\left(\mathrm{down}|\mathrm{no\; RN}\right)-\mathrm{P}\left(\mathrm{up}|\mathrm{no\; RN}\right)]$, where “up” means placing a patient into a higher risk group than the null model and “down” means placing the patient into lower risk group. For instance, $\mathrm{P}\left(\mathrm{up}|\mathrm{RN}\right)$ is the probability of correct upward movement for patients who did experience RN and $\mathrm{P}\left(\mathrm{down}|\mathrm{RN}\right)$ is the probability of incorrect downward movement for the same type of patients. A positive NRI indicates better patient stratification using the MB.

We verified the robustness of MB variables with logistic regression over 5-fold cross-validation. Model performance was evaluated using the area under (AUC) the receiver operating characteristic curve (ROC) (38). It is important to note our objective was not to construct a predictive model, but to critically evaluate the incremental value of the MB variables in the discrimination between patients likely and unlikely to develop RN. Therefore, the logistic regression model was intentionally simplistic and excluded dosimetric variables to single out the influence of MB variables on RN differentiation. We compared the model to both the null model and a model without MB variables to demonstrate the rigor of using the MB variables when analyzing RN. These comparisons quantify the distinctive contribution of MB variables in capturing the variance in the outcome.

Data Availability

The code used in this study and the results of statistical analyses will be available upon request. Due to privacy, patient data are not publicly available and will be stored in a secure repository which has restricted access, requiring Institutional Review Board-approval for data queries. For data inquiries, please contact the corresponding author.

RESULTS

Patient Characteristics and Treatment Variables

Our cohort was 56% male and 44% female but included mostly white patients (92%, n=120). Among the patients, 28% (n=37) had hypertension and 7% (n=9) had diabetes. The median whole ventricular volume was 27.10 cc, with an interquartile range (IQR) of 20.36 to 37.10 cc. Tumors were nearly split between extracranial (46%, n=60) and intracranial (54%, n=70) locations: 60 H&N, 65 CNS, 5 BOS. 25% (n=33) had bilateral treatment targets, with most at-risk lobes being frontal or temporal (42% each, n=54), and 17% (n=22) other lobes. Median distance from the maximum dose to the ventricles was 62 mm (IQR: 37-95 mm), with 10% (n=13) receiving the maximum dose in white matter.

Regarding treatment variables, surgery prior to RT was performed for most of the intracranial tumor patients (79%, 55 out 70) and for a lower percentage of the extracranial tumor patients (62%, 37 out of 60). Nearly half of the patients (47%, n=61) received concomitant chemotherapy. The majority of patients (59%, n=77) received definitive RT, while the rest (41%, n=53) received adjuvant RT. Median mean and maximum brain doses were 5.4 Gy (IQR: 3.3-10.6 Gy) and 67.1 Gy (IQR: 63.5-72.1 Gy), respectively. RN (grade 1+) was observed in 38% (n=50), with no signs in 62% (n=80). There is a notable difference in the frequency of RN among various tumor subtypes. Gliomas had a necrosis rate of 33% (14 out of 42), while meningiomas had a lower rate of 26% (5 out of 19). Head and neck tumors showed a higher overall grade 1+ necrosis rate of 50% (30 out of 60), highlighting the variability in RN incidence across different tumor types. Detailed distributions of these variables are provided in Table 1.

Table 1: Distribution of Variables (n=130).

Continuous variables are presented as median (interquartile range) and categorical variables are presented as count (percentage).

Variable		Value
Patient-level
Biometric	Sex
	Male	73 (56%)
	Female	57 (44%)
	Race
	White	120 (92%)
	Other	10 (8%)
Comorbidities	Hypertension
	Yes	37 (28%)
	No	93 (72%)
	Diabetes
	Yes	9 (7%)
	No	121 (93%)
Brain characteristics	Whole ventricular volume (cc)	27.10 (20.36-37.10)
Tumor-level
Tumor characteristics	Type
	H&N	60 (46%)
	CNS	65 (50%)
	BOS	5 (6%)
	Location
	Extracranial	60 (46%)
	Intracranial	70 (54%)
	Bilateral radiation target
	Yes	33 (25%)
	No	97 (75%)
	Clinical target volume (cc)	118.16 (60.06-266.49)
Tumor location variables	Cerebral lobe at risk
	Frontal	54 (42%)
	Temporal	54 (42%)
	Other	22 (17%)
	Distance from maximum dose to ventricles (mm)	62 (37-95)
	Maximum dose in white matter
	Yes	13 (10%)
	No	117 (90%)
Treatment-level
Other therapies	Prior surgery
	Gross total resection	36 (28%)
	Near total resection	18 (14%)
	Subtotal resection	38 (29%)
	None	38 (29%)
	Concurrent chemotherapy
	Yes	61 (47%)
	No	69 (53%)
Radiotherapy variables	Radiotherapy indication
	Definitive	77 (59%)
	Adjuvant	53 (41%)
	Mean brain dose (Gy)	5.4 (3.3-10.6)
	Maximum brain dose (Gy)	67.1 (63.5-72.1)
Radiation Necrosis
Overall		50 (38%)
Central Nervous System		19 out of 65
	Glioma	14 out of 42
	Meningioma	5 out of 19
	Ependymomas	0 out of 1
	Hemangiopericytomas	0 out of 2
	Other	0 out of 1
Head and Neck		30 out of 60
	Nasopharyngeal carcinomas	21 out of 47
	Salivary gland tumors	6 out of 10
	Other 3 out of 3
Base of Skull		1 out of 5
	Chordomas	0 out of 5
	Chondrosarcomas	1 out of 2
	Other	0 out of 1

Categorization of Continuous Variables

Analysis of continuous variables showed skewed distributions for ventricular volume and minimum distance to ventricles, and bimodal distributions for CTV, mean, and maximum brain dose (Figure S1). After transformation, skewed variables normalized (central tendency around 0), and peaks of bimodal variables were brought closer, centering around 0. AIC minimization helped identify optimal categorizations: two categories for skewed and three for bimodal distributions. Post-discretization, categories in bi-category distributions were balanced, while in tri-category distributions, the middle level was most frequent.

Mutual Information Threshold

Figures S2–S3 show the pairwise MI values between variables as well as the overall distribution. We observed a range of connection strengths, and we imposed a threshold, excluding connections with an MI value of less than 0.0029, corresponding to the 25^th percentile of the MI distribution, to eliminate statistically insignificant connections and facilitate network learning.

Bayesian Network Model and Qualitative Assessment of Clinical Feasibility

The resulting Bayesian network, shown in Figure 2, included a total of 24 connections, with clinical evaluation detailed in Table 2. Of the 24 connections, 12 were classified as valid, aligning with established medical knowledge; 10 as conceivable, showing potential relevance and rational basis; and 2 as incidental, likely reflecting sample biases or non-causal links. None of the incidental connections were directly related to the outcome node. All the variables were conditionally independent of the race, and RN was conditionally independent of the maximum brain dose and CTV.

Figure 2: Bayesian Network Centered on Radiation Necrosis.

This graphical representation positions radiation necrosis at the heart of the network, with its Markov blanket distinctly shaded in gray. The diagram underscores the intricate interplay of variables in close proximity to our focal node, capturing both direct influences and reciprocations, essential for understanding radiation treatment outcomes.

Table 2: Clinical Evaluation of the Bayesian Network Connections.

This table presents a clinical interpretation of the associations derived from the Bayesian network structural learning. Connections are categorized as ‘Incidental,’ ‘Valid,’ or ‘Conceivable’ to reflect their clinical plausibility and potential impact on outcome prediction in radiotherapy.

Connection	Clinical sensibility	Clinical meaning
Sex → distance to ventricles	Conceivable	The patient sex may affect brain size, which affects the distances measured within it.
Sex → hypertension	Valid	Sex differences in hypertension risk are established, with different susceptibilities in males (39).
Sex → ventricular volume	Conceivable	The patient sex may affect the size of brain ventricles due to differences in brain size, and aging rates among other factors.
Diabetes → distance to ventricles	Incidental	Diabetes is not clinically related to the distance of tumors from the ventricles; if observed, likely represents sample bias.
Diabetes → hypertension	Valid	Diabetes and hypertension co-existence is well-documented in clinical literature (40).
Hypertension → Whole ventricular volume	Conceivable	Previous research suggests that hypertension is associated with larger mean lateral and third ventricle volumes, indicating a possible link between hypertension and changes in certain brain structures, including ventricular size (41).
Whole ventricular volume → Risk to frontal lobe	Incidental	A larger ventricular volume does not clearly correlate to increased risk to the frontal lobe; correlations may be due to sample bias.
Tumor location → concurrent chemotherapy	Conceivable	The use of chemotherapy varies depending on the diagnosis.
Tumor location → risk to temporal lobe	Conceivable	Intracranial tumors could pose a higher risk to the temporal lobe due to their location within the brain.
Target location → bilateral target	Conceivable	The necessity of bilateral target treatment is influenced by the tumor’s location, with bilateral treatment being more likely in cases where disease patterns or risk areas span both sides of the targeted region.
Bilateral target → mean brain dose	Conceivable	Whether the tumor is bilateral or not may affect dose distribution and thus the mean dose in the brain.
Distance to ventricles → tumor group	Valid	Intracranial tumors are inherently closer to the ventricles due to their location.
Distance to ventricles → risk to white matter	Valid	Proximity to the ventricles may inherently imply that the maximum dose lies in the white matter.
Risk to white matter → radiation necrosis	Valid	Increased sensitivity of white matter to radiation can lead to a higher likelihood of radiation necrosis (9,20).
Risk to frontal lobe → radiation necrosis	Conceivable	The association between risk to the frontal lobe and radiation necrosis might exist but is not definitively established.
Risk to frontal lobe → Risk to temporal lobe	Valid	If radiation is centered in the frontal lobe, the risk to the temporal lobe decreases compared to the frontal lobe.
Risk to frontal lobe → Risk to other lobes	Valid	A similar principle applies as above. If radiation is centered in the frontal lobe, the other lobes are relatively at lower risk.
Risk to frontal lobe → bilateral intracranial radiation target	Conceivable	The presence of a frontal lobe tumor may correlate with bilateral irradiation in the brain.
Risk to frontal lobe → surgery type	Conceivable	This correlation depends on diagnosis, histology, stage.
Risk to temporal lobe → Risk to other lobes	Valid	If radiation is centered in the temporal lobe, the other lobes are relatively at lower risk.
Surgery type → definitive RT	Valid	The application of definitive RT is influenced by whether surgery was performed.
Maximum brain dose → CTV	Valid	This size of the clinical target directly affects dose distribution and may be correlated with the maximum dose in the brain.
Mean brain dose → maximum brain dose	Valid	Mean and maximum brain dose are depended.
Radiation necrosis → tumor group	Valid	Extracranial tumors have a higher normal tissue complication probability curve than intracranial tumors (29).

Risk Factors of Radiation Necrosis: Markov Blanket Analysis

At the core of our Bayesian network is the RN node (Figure 2), with its enveloping MB defining key determinants of patient response heterogeneity. Parent nodes—‘Risk to White Matter’ and ‘Frontal Lobe at Risk’— underscore the regions’ varying susceptibility to radiation damage and its impact on necrosis. The ‘Tumor Location’ child node differentiates between intracranial and extracranial tumors, reflecting the varied necrosis risks based on location. Additionally, the spouse node ‘Distance to Ventricles’ relates to tumor location and implies that the proximity of maximal radiation dose to ventricles is a critical spatial risk determinant, influencing individual necrosis patterns. Additionally, the spouse node ‘Distance to Ventricles’ relates to tumor location and implies that the proximity of maximal radiation dose to ventricles is a critical spatial risk determinant, influencing individual necrosis patterns.

Quantitative Assessment of the Identified Variables in Patient Heterogeneity

The log-likelihood ratio test comparing MB variables to the null model resulted in an LLR of 12.17 and a p-value of 0.016. The IDI after adding the MB variables was positive (0.15), and the net reclassification analysis improved risk stratification with an NRI of 0.74. Figure 3 illustrates the cohort’s segmentation before and after MB-based stratification, ranging from <20% risk score in Group 1 (G1) to >80% in Group 5 (G5). The reclassification table shows 50 patients with RN moving to higher risk categories, while 80 without RN moved to lower ones, reflecting MB variables’ predictive impact. Post-reclassification, patient distribution was: G1 (17), G2 (41), G3 (33), G4 (23), G5 (16). RN incidence was 18% in G1 and gradually increased to 63% in G5, highlighting the stratification’s effectiveness of the MB variables. ROC analysis (Figure 4) showed the null model’s AUC at 0.5 (Panel A), indicating no predictive power. Including MB variables raised the AUC to 0.66 (Panel B), while excluding them reduced it to 0.49 (Panel C). This comparison demonstrates that the MB variables are particularly needed among other variables to capture the variance in outcomes, confirming their contribution even before dosimetric variables are included.

Figure 3: Patient Stratification and Reclassification with Markov Blanket Variables.

Top panel: Initial unstratified patient cohort with individuals who developed radiation necrosis (RN) marked in red and those without in black. Bottom panel: Patient cohort following stratification based on Markov blanket (MB) variables into five risk groups (G1-G5) with corresponding RN percentages. Arrows indicate the direction of patient movement between risk groups after MB stratification. The table below details the distribution of all patients (n=130), positive patient movement (n=50), and negative patient movement (n=80) across the risk groups, highlighting the reclassification impact of the MB variables on risk assessment for RN.

Figure 4: Comparative ROC Curves for Predictive Models.

The figure illustrates three Receiver Operating Characteristic (ROC) curves for different logistic regression models used to predict clinical outcomes. Panel A represents a null model with no predictive features, resulting in an AUC of 0.5, indicating no better than random prediction. Panel B shows the ROC curve for a model that includes MB variables, with an AUC of 0.66 without including treatment variables. Panel C displays the ROC for a model where MB variables are excluded, yielding an AUC of 0.49, which is consistent with chance-level prediction. The shaded areas around each curve in Panels B and C represent the standard deviation of the 5-fold cross-validation.

Variables Influencing Markov Blanket Predictors

Besides the MB variables, the Bayesian network showed that certain variables, not part of the MB, directly influence variables within the MB. Specifically, patient sex and the presence of diabetes were found to affect the distance to ventricles, while the whole ventricular volume influenced the risk of radiation to the frontal lobe. Furthermore, the tumor’s extracranial location was connected to concurrent chemotherapy, maximum radiation to the temporal lobe, and whether the tumor was bilateral. A subgroup analysis (see Supplementary Data Figures S4–S7) revealed that for extracranial tumors, concurrent chemotherapy and temporal lobe irradiation moved into the MB, becoming predictors of necrosis.

DISCUSSION

RN is a delayed, progressive, and sometimes irreversible form of radiation-induced injury to normal brain tissue, primarily involving glial and endothelial cell damage (26). The exact mechanisms are multifactorial and not fully understood. Brain injury is caused by both vascular damage and damage to glial cells (particularly oligodendrocytes and neurons), as well as interactions between the two (42–44). Vascular damage leads to endothelial cell death, increased vascular permeability, and blood-brain barrier disruption, resulting in hypoxia and edema. Damage to glial cells disrupts myelin production and impairs neuronal function. There is evidence that vascular damage is the main driver, e.g., indirect evidence from the treatment of necrosis with Bevacizumab, which targets VEGF to reduce vascular permeability and edema (45).

RN remains a significant complication in various forms of RT, including proton therapy, which is increasingly used in the treatment of brain tumors. However, despite its precision, proton therapy carries a risk to normal issue that is potentially exacerbated by LET effects, indicating a higher relative biological effectiveness (RBE) than the standard 1.1 (13), which necessitates caution. Research shows mixed results on LET’s impact on RN (1), with significant associations reported in some studies (46–48), and negligible ones in others (14–16). These studies attempted to analyze the effects of dose and LET on RN as direct causes; however, they have consistently shown that the relationship is masked by patient heterogeneity. This motivated our study to decode patient heterogeneity to facilitate our understanding of RN in CNS, BOS, and H&N patients.

While the effect of tumor location and sensitivity of the periventricular white matter is well documented in the literature, there is a need to integrate more detailed patient variables, study their interaction, and, importantly, quantify the ability of a family of identified predictors to capture the heterogenous RT effect on necrosis. To address this problem, we developed a systematic framework for creating clinically relevant Bayesian networks to analyze patient heterogeneity. This framework, characterized by its structured data collection approach, preprocessing, and expert-guided network construction, may offer a robust method for capturing the intricate interplay of various patient-specific factors. Our analysis showed critical factors within the MB, including disease location and proximity to vital brain structures (white matter, ventricles, frontal lobe).

Categorizing continuous variables and guiding the Bayesian network’s structural learning were crucial to suit our cohort size and ensure clinical relevance. We ensured that the network structure was informed by clinical knowledge, minimizing connections that lacked plausible clinical meaning. This was important to strengthen the validity of the key variables identified within the MB of RN. Most network connections were clinically sensible; however, the absence of direct correlations between maximum brain dose, CTV, and brain necrosis was unexpected. The relation between dose and volume is complex. On one hand, high doses might safely be delivered to smaller volumes in the brain; on the other hand, the localized impact of such doses, particularly in terms of vascular damage and subsequent hypoxia, may increase the risk of RN. The complex dose-volume interplay may explain the lack of direct correlation. Additionally, the homogeneity of our cohort, a limitation, might have masked expected connections, like those related to race.

MB analysis highlighted the white matter’s critical role as a parent node in RN, emphasizing its susceptibility to radiation-induced damage. This vulnerability is likely due to the radiosensitivity of oligodendrocytes (49), vital for myelin production, and glial cells (50), essential for brain homeostasis. Supporting studies, such as Bojaxhiu et al. (9) and Lin et al. (20), affirm white matter irradiation as an indicator for RN. The presence of both proximity of treatment areas to ventricular systems and white matter in the MB of the model suggested a surrogate marker for deep white matter tract sensitivity. This is particularly relevant for structures like the corpus callosum, known for their vulnerability to radiation-induced damage (51). These insights underscore the importance of considering anatomical proximity in RT planning, especially in relation to sensitive structures.

Additionally, the frontal lobe was another vulnerable parent node to RN, highlighting its complex neural and vascular architecture’s susceptibility, calling for additional investigations specific to the frontal lobe since previous studies focused on the temporal lobe. For example, OuYang et al. (52), identified the need for risk-based follow-up for early detection of temporal lobe injury, a specific type of RN, in patients with nasopharyngeal carcinoma.

The distinction between intracranial and extracranial tumors as a child node in our MB underscores its relevance to RN development. This differentiation supports existing data, such as findings by Niyazi et al. (29), indicating that extracranial tumors may exhibit a higher normal tissue complication probability (NTCP) than intracranial ones. Potential explanations for this discrepancy could involve variations in vascular response (53), the tumor microenvironment (54), immunological factors (55), and inherent radiobiological characteristics of the tissue (56). Each hypothesis warrants additional studies to delineate the effect of these factors on RN.

The distance to ventricles, a spouse node in the MB, aligns with the spatial correlation between RN and white matter risk, echoing studies that link ventricular proximity to increased sensitivity (23,24). It also resonates with the findings of Winter et al. (25), who reported in their study that necrotic lesions are more present in the periventricular region compared to other regions. This proximity indicates a biological gradient of risk, likely due to the vascular network near the ventricles, which is highly susceptible to radiation damage, reinforcing the need to consider these anatomical and biological factors in treatment planning. Additionally, the ventricles are surrounded by glial cells that are known to be radiosensitive (50), further explaining the increased risk when tumors are nearby.

To quantitatively evaluate the effectiveness of the MB variables in capturing the patient heterogeneity, we conducted a series of statistical evaluations. The likelihood ratio test indicated significant improvement in model explanatory power with MB variables (p<0.05), confirming their crucial role in delineating the biological and clinical factors influencing RN risk. A positive IDI further reinforced the enhancement of model discrimination, broadening the discriminative distance between patient risk profiles. Additionally, the NRI value of 0.74 underscored substantial improvements in patient stratification into risk categories accurately reflecting RN risk.

This enhanced stratification capability highlights MB variables as critical for identifying patients needing intensive monitoring and tailored therapies. The transition from a homogeneous risk distribution in the unstratified cohort to a well-defined risk gradient in the MB-stratified cohort reinforces the potential clinical utility of these variables. The considerable patient movement into different risk categories emphasizes the need for incorporating patient-specific variables beyond traditional dosimetric factors in risk assessment. The positive reclassification of patients with necrosis into higher risk groups suggests that the MB variables can capture the underlying risk factors.

In the ROC analysis, the null model’s AUC was around 0.5, indicating no predictive power. Integration of MB variables improved the AUC to 0.66 even without including dosimetric variables such as dose distribution and LET. This increase in the AUC suggests that these variables carry substantial weight in evaluating individual risk. Model performance dropped to an AUC of 0.49 when MB variables were omitted, underlining their critical function in the predictive equation and the potential void their absence creates.

The Bayesian network analysis not only identified direct predictors of necrosis but also determined intra-variable relationships that impact these predictors. It revealed a direct influence of the patient sex, diabetes status, and whole ventricular volume on MB predictors, underscoring a potential confounding role of these non-treatment variables that may need to be considered to refine outcome analysis and prospective trial design. Additionally, the association between extracranial tumor location and factors such as concurrent chemotherapy, tumor bilaterality, and temporal lobe irradiation offers new potential reasons why extracranial tumors have a higher risk of necrosis.

We conducted separate analyses for intracranial and extracranial tumors to investigate potential differences in factors contributing to brain necrosis. The results of these subgroup analyses, detailed in the Supplementary Data (Figures S4–S7), indicate that the smaller sample sizes pose a risk of overfitting and thus limit the strength of the conclusions. However, these analyses provided valuable insights. For intracranial tumors, our Bayesian network did not identify significant predictors, demonstrating the model’s robustness against overfitting. For extracranial tumors, chemotherapy and radiation risk to the temporal lobe emerged as significant predictors after incorporating priors. These findings, though preliminary, highlight the need for further research with larger datasets to validate and expand upon these insights.

Consider grade 1+ necrosis, rather than limiting our analysis to more severe grades, enhanced our statistical power. This approach acknowledges that even mild radiation-induced necrosis (grade 1) has significant clinical implications, including early symptomatology, impact on patient management, and insights into treatment sensitivity. We aim to reinforce the clinical relevance of detecting and addressing all grades of necrosis, highlighting the role of asymptomatic grades as a precursor to more severe injury and their influence on therapeutic strategies.

While our study offers new insights into RN-associated variables, it has limitations. The complexity of analyzing tumor size, location, and applied dose introduces biases that we have attempted to address, but these factors inherently limit the generalizability of our findings. Our sample size, although sufficient for initial exploration, may not fully represent the heterogeneity. This limitation makes it challenging to generalize our results to a wider demographic. Prospective validation is required to confirm our findings and ensure their predictive value across diverse patient groups. Additionally, our study did not account for the ‘recall effect’ of pre- or post-radiation drugs on necrosis or the prevalent use of pencil beam scanning techniques, both of which could significantly impact outcomes.

Future research will explore the effects of dose and LET distributions on brain necrosis, accounting for identified effect moderators. Investigating how LET and patient-specific factors interact could illuminate mechanisms of necrosis and optimize proton therapy. Furthermore, predictive modeling efforts, such as through NTCP or machine learning modeling, could be enhanced by incorporating the patient-specific variables identified in this study. Additionally, we plan to conduct a multicenter study to expand our patient population, which will allow us to develop and validate a comprehensive risk scoring system. This multicenter approach will help to eliminate biases, increase the reliability and generalizability of our findings, and facilitate the creation of a robust scoring system that can be widely applied in clinical practice.

This research underscores the hypothesis that patient heterogeneity can be effectively captured and distilled into a quantifiable, clinically meaningful risk profile. These insights highlight the value of MB variables and advocate for their integration into clinical decision-making to identify high-risk patients and reduce RN incidence. Lastly, the framework developed in this study can be used beyond RN, applicable across medical research domains where patient heterogeneity significantly influences outcomes. By allowing researchers to dissect and understand patient variability, it holds the potential to improve predictive models, and ultimately contribute to more individualized patient care strategies.

Overall, this study identified critical patient-specific factors influencing the risk of radiation-induced brain necrosis in patients undergoing proton therapy. By employing a Bayesian network model, we determined that tumor location and its proximity to sensitive brain structures, such as white matter, ventricles, and the frontal lobe, are major determinants of necrosis risk. While aligning with previous evidence on the importance of the periventricular white matter, our findings highlight the frontal lobe as a new significant variable. We quantified the extent to which these variables contribute to outcome heterogeneity, revealing complex interactions and intra-predictor correlations. The Bayesian network showed a potential influence of patient characteristics (sex, diabetes status and ventricular volume) on the predictors of necrosis, which could help refine prospective trial designs. Subgroup analysis by tumor location indicated a potential role for chemotherapy temporal lobe irradiation in increasing sensitivity in treating extracranial tumors, which needs confirmation with a larger dataset. This study underscores the necessity of integrating these factors when evaluating the dose effect of RT and considering patient heterogeneity to enhance personalized treatment strategies.

Translational Relevance.

This study elucidates the critical risk factors for radiation-induced brain necrosis in patients undergoing proton therapy for brain-related cancers. By deploying a Bayesian network model, we isolate key variables—specifically, tumor location and its proximity to sensitive brain structures such as the frontal lobe, white matter, and ventricles—that significantly influence patient susceptibility to necrosis. The findings reveal that considering these patient-specific factors, in addition to traditional dosimetric parameters, can enhance the precision of treatment toxicity assessments. This approach not only supports clinicians in tailoring radiation therapy plans more effectively but also lays the groundwork for developing predictive models that can accurately assess individual risk. The methodology and insights presented have direct applications in refining clinical protocols to minimize the occurrence of brain necrosis, thereby improving patient outcomes and quality of life post-therapy.

Abbreviations List:

AIC

Akaike information criterion

AUC

area under the receiver operating characteristic curve

BOS

base of skull

CNS

central nervous system

CTCAE

common terminology criteria for adverse events

G1

group 1

G2

group 2

G3

group 3

G4

group 4

G5

group 5

H&N

head and neck

IDI

integrated discrimination index

IQR

interquartile range

LET

linear energy transfer

LLR

log-likelihood ratio

MB

Markov blanket

MI

mutual information

MGH

Massachusetts General Hospital

NRI

net reclassification index

RBE

relative biological effectiveness

RN

radiation-induced brain necrosis

ROC

receiver operating characteristic

RT

radiotherapy