Probabilistic clinical target definition with nearest neighbor correlation

<i>Objective.</i>The delineation of the clinical target volume (CTV) in radiotherapy is fundamentally uncertain due to the invisibility of microscopic disease on medical images. The ICRU 83 report acknowledges this by proposing a probabilistic interpretation of the CTV, but it does not define how to compute the probability of microscopic tumor presence (MTP) in tissue. This work addresses this gap by introducing a novel stochastic model that estimates the probability of MTP at the voxel level based on local spatial correlations in the voxels' neighborhood.<i>Approach.</i>We developed two first-principles stochastic models to simulate MTP under different assumptions, incorporating spatial correlation between neighboring voxels. The constant marginal probability (CMP) model assumes spatially uniform MTP and is suited for tumors without radial dependence on the distance from the gross tumor volume (GTV). The variable marginal probability (VMP) model introduces radial dependence, modeling decreasing MTP with distance from the GTV. The CMP model was evaluated on prostate cancer data, while the VMP model was assessed using breast and lung cancer data.<i>Results.</i>Both models accurately reproduced the fraction of times that MTP is present. In the prostate case, the CMP model estimated a marginal probability of MTP of 0.03, consistent with a literature report that indicates an average total microscopic tumor volume of approximately583mm3across patients. The VMP model successfully replicated the radial distribution of tumor islets, achieving mean absolute errors of 0.01 mm and 0.011 mm for breast and lung cancer distance distributions, respectively. However, not all MTP characteristics could be fully captured by the models, and in some cases discrepancies with population based tumor characteristics remain.<i>Significance.</i>This work introduces a statistically consistent framework that enables a probabilistic definition of the CTV. The proposed models provide a new way to capture key aspects of microscopic disease spread by introducing local voxel correlations.