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Probabilistic Definition of the Clinical Target Volume -- Implications for Tumor Control Probability Modeling

D Craft*, T Bortfeld, Massachusetts General Hospital, Boston, MA

Presentations

(Sunday, 7/12/2020)   [Eastern Time (GMT-4)]

Room: AAPM ePoster Library

Purpose: Evidence has been presented that moving beyond the binary definition of the Clinical Target Volume (CTV) towards a probabilistic CTV can result in better treatment plans. The probabilistic CTV takes the likelihood of disease spread outside of the gross tumor volume into account. An open question is: how to optimize tumor control probability (TCP) based on the probabilistic CTV if we go beyond the assumption of voxel independence.

Methods: We derive expressions for TCP under the assumptions of voxel independence and dependence. For the dependent case, me make the assumption that tumors grow outward from the gross tumor volume; in 1D voxel model, we term this the no-tunneling assumption (the set of tumorous voxels is contiguous). In a 2D generative model, we see connected tumorous regions.

Results: For small numbers of voxels, we demonstrate by brute-force search and constrained nonlinear optimization that the optimal dose distribution (under total dose constraint) is different for the two models, even though the probabilities of each voxel being tumorous are set to the same in both cases. For larger number of voxels we rely on global optimization techniques and come to the same conclusion. We observe and justify phase transitions, where a voxel is either dosed to a high level or effectively ‘sacrificed’. From this observation, we derive a heuristic consisting of an iterative sequence of convex optimizations which yields solutions within 10% of the optimal solutions for both cases.

Conclusion: Both independent and correlated voxels assumption result in non-convex TCP functions. For 3D geometries, although correlated voxels is a more reasonable assumption, the correlation function is in general unknown. We numerically demonstrate that optimizing under the independent voxel assumption yields solutions that are within 10% of the optimal solution for correlated voxels, and demonstrate a numerically tractable heuristic approach for the optimization.




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