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Objective: The overarching objective is to make the definition of theclinical target volume (CTV) in radiation oncology less subjective and morescientifically based. The specific objective of this study is to investigatesimilarities and differences between two methods that model tumor spread beyondthe visible gross tumor volume (GTV): 1. The shortest path model, which is thestandard method of adding a geometric GTV-CTV margin, and 2. Thereaction-diffusion model.  Approach: These two models to capture the invisible tumor "fire front" aredefined and compared in mathematical terms. The models are applied to examplecases that represent tumor spread in non-uniform and anisotropic media withanatomical barriers.  Main Results: The two seemingly disparate models bring forth traveling wavesthat can be associated with the front of tumor growth outward from the GTV. Theshape of the fronts is similar for both models. Differences are seen in caseswhere the diffusive flow is reduced due to anatomical barriers, and in complexspatially non-uniform cases. The diffusion model generally leads to smootherfronts. The smoothness can be controlled with a parameter defined by the ratioof the diffusion coefficient and the proliferation rate.  Significance: Defining the CTV has been described as the weakest link of theradiotherapy chain. There are many similarities in the mathematical descriptionand the behavior of the common geometric GTV-CTV expansion method, and thedefinition of the CTV tumor front via the reaction-diffusion model. Itsmechanistic basis and the controllable smoothness make the diffusion model anattractive alternative to the standard GTV-CTV margin model.

Modeling the propagation of tumor fronts with shortest path and diffusion models -- implications for the definition of the clinical target volume