Purpose: High-grade glioma (HGG) is a common form of malignant primary brain cancer with poor prognosis. The diffusive nature of HGGs implies that tumor cell invasion of normal tissue extends several centimeters away from the visible gross tumor volume (GTV). The standard methodology for clinical volume target (CTV) delineation is to apply a 2- to 3-cm margin around the GTV. However, tumor recurrence is extremely frequent. The purpose of this paper was to introduce a framework and computational model for the prediction of normal tissue HGG cell invasion and to investigate the agreement of the conventional CTV delineation with respect to the predicted tumor invasion.

Methods and Materials: A model for HGG cell diffusion and proliferation was implemented and used to assess the tumor invasion patterns for 112 cases of HGGs. Normal brain structures and tissues as well as the GTVs visible on diagnostic images were delineated using automated methods. The volumes encompassed by different tumor cell concentration isolines calculated using the model for invasion were compared with the conventionally delineated CTVs, and the differences were analyzed. The 3-dimensional-Hausdorff distance between the CTV and the volumes encompassed by various isolines was also calculated.

Results: In 50% of cases, the CTV failed to encompass regions containing tumor cell concentrations of 614 cells/mm³ or greater. In 84% of cases, the lowest cell concentration completely encompassed by the CTV was ≥1 cell/mm³. In the remaining 16%, the CTV overextended into normal tissue. The Hausdorff distance was on average comparable to the CTV margin.

Conclusions: The standard methodology for CTV delineation appears to be inconsistent with HGG invasion patterns in terms of size and shape. Tumor invasion modeling could therefore be useful in assisting in the CTV delineation for HGGs.

Purpose: This study aimed at applying a mathematical framework for the prediction of high-grade gliomas (HGGs) cell invasion into normal tissues for guiding the clinical target delineation, and at investigating the possibility of using tumor infiltration maps for patient overall survival (OS) prediction.

Material & methods: A model describing tumor infiltration into normal tissue was applied to 93 HGG cases. Tumor infiltration maps and corresponding isocontours with different cell densities were produced. ROC curves were used to seek correlations between the patient OS and the volume encompassed by a particular isocontour. Area-Under-the-Curve (AUC) values were used to determine the isocontour having the highest predictive ability. The optimal cut-off volume, having the highest sensitivity and specificity, for each isocontour was used to divide the patients in two groups for a Kaplan-Meier survival analysis.

Results: The highest AUC value was obtained for the isocontour of cell densities 1000 cells/mm³ and 2000 cells/mm³, equal to 0.77 (p < 0.05). Correlation with the GTV yielded an AUC of 0.73 (p < 0.05). The Kaplan-Meier survival analysis using the 1000 cells/mm³ isocontour and the ROC optimal cut-off volume for patient group selection rendered a hazard ratio (HR) of 2.7 (p < 0.05), while the GTV rendered a HR = 1.6 (p < 0.05).

Conclusion: The simulated tumor cell invasion is a stronger predictor of overall survival than the segmented GTV, indicating the importance of using mathematical models for cell invasion to assist in the definition of the target for HGG patients.

Objective: Glioblastoma (GBM) prognosis remains poor despite progress in radiotherapy and imaging techniques. Tumor recurrence has been attributed to the widespread tumor invasion of normal tissue. Since the complete extension of invasion is undetectable on imaging, it is not deliberately treated. To improve the treatment outcome,  models have been developed to predict tumor invasion based standard imaging data. This study aimed to investigate whether a tumor invasion model, together with the predicted number of surviving cells after radiotherapy, could predict tumor progression post-treatment.

Approach: A tumor invasion model was applied to 56 cases of GBMs treated with radiotherapy. The invasion was quantified as the volume encompassed by the 100 cells/mm3 isocontour (V100). A new metric, cell-volume-product, was defined as the product of the volume with cell density greater than a threshold value (in cells/mm3), and the number of surviving cells within that volume, post-treatment. Tumor progression was assessed at 20±10 days and 90±20 days after treatment. Correlation between progression and the gross tumor volume (GTV), V100, and cell-volume-product, was determined using Receiver Operating Characteristic curves.

Main results: For the early follow-up time, the correlation between GTV and tumor progression was not statistically significant (p = 0.684). However, statistically significant correlations with progression were found between V100 and cell-volume-product with a cell threshold of 10-6 cells/mm3 with areas-under-the-curve of 0.69 (p = 0.023) and 0.66 (p = 0.045), respectively. No significant correlations were found for the late follow-up time.

Significance: Modeling of tumor spread otherwise undetectable on conventional imaging, as well as radiobiological model predictions of cell survival after treatment, may provide useful information regarding the likelihood of tumor progression at an early follow-up time point, which could potentially lead to improved treatment decisions for patients with GBMs.

Introduction: Glioblastoma (GBM) is the most common primary malignant brain tumor in adults, but treatment outcome is poor, and tumor recurrence is often unavoidable. Evidence suggests that regions with tumor cell densities below the medical imaging visibility threshold are more prevalent than the current treatment methodologies account for. Consequently, tumor spread models have been developed to predict the direction and magnitude of GBM cell invasion. This study aimed to explore different treatment planning strategies that take into account the microscopic tumor cell distribution, as determined through mathematical modeling.

Material & Methods: The treatment planning considering the extent of the distribution of the tumor cells beyond the observable borders of the target was made for three patients with GBMs presenting different degrees of complexity for planning depending on the size and location of the target. A diffusion-proliferation model was used to predict the tumor spread. The extent of the spread was quantified as the invasion volume V_x, defined as the volume encompassed by a cell density isocontour x (cells/mm³). Dose plans were created using targets defined by V₁₀₀₀, V₁₀₀, and V₁₀. Doses prescribed were 60 Gy over 30 fractions. Dose plans were evaluated according to recommended clinical goals. Additionally, radiobiological modeling was used to predict the optimal dose per voxel needed to achieve a tumor control probability of 0.95 and treatment plans were made by mimicking the optimal dose distributions as reference. The plans were evaluated with respect to dose homogeneity in the target, conformity index, and the constraints for the organs at risks. The difference between the reference dose distributions and mimicked dose plans was quantified as the  percentage of voxels in the mimicked plan receiving a dose within 95% and 107% of prescribed dose (quality index, Q0.95̶ 1.07).

Results: All of the dose plans produced with the first methodology were clinically acceptable with regards to tumor coverage and sparing of OARs. Homogeneity at 98% volume ranged from 0.88 to 0.94. Conformity at 60 Gy isodose ranged from 0.85 to 0.96. The quality index of the GTV ranged from a maximum of Q_{0.95̶ 1.07} = 95.0% to a minimum of Q_{0.95̶ 1.07} = 76.0%, showing a tendency to decrease as the target volume increased. 

Conclusion: Incorporating tumor spread models into treatment planning is feasible and may be considered for further investigation to potentially enhance treatment outcomes for GBMs. While dose planning strategies based on modifying the CTV with respect to predicted tumor invasion showed clinical feasibility, dose mimicking approaches based on reference dose distribution require careful planning and become particularly challenging for large, complex targets.