Radiosurgery Dose Distributions: Theoretical Impact of Inhomogeneities on Lesion Control

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Abstract
Objective: To develop a mathematical model to predict the impact of dose heterogeneities on tumor/lesion control during radiosurgery. It is necessary to be able to estimate these effects in order to quantitatively and objectively assess competing treatment plans. Methods: Target cells are assumed to be uniformly distributed throughout the lesion. The control rate for the entire lesion is assumed to be the product of the control probabilities for each subregion within the target volume. The lesion control probability (LCP) for each region is assumed to equal EXP (the number of surviving target cells within the subregion), as predicted by Poisson statistics. Subregions of variable size are assumed to receive variable doses, and the impact of this dose heterogeneity on the LCP is calculated based on the single-fraction radiation cell survival curve predicted by the single-hit multitarget model. Results: The impact of a dose heterogeneity on LCP is related to three variables: the LCP predicted with uniform irradiation, the volume of the lesion that is irradiated to a new dose, and the magnitude of the dose change relative to the slope of the single- fraction radiation cell survival curve of (ΔD/D0). The calculations predict that the detrimental effect of underdosing regions of the lesion can, in some instances, be offset by escalating the dose to other subregions within the target volume. In this regard, the “average” dose delivered to the lesion rather than the minimum dose may be most predictive of the lesion control probability. In some situations, escalating the dose to part of the lesion may improve the lesion control rate. Conclusion: These calculations quantify the theoretical impact of dose heterogeneities on lesion control rate and may be very useful when comparing competing treatment plans.

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