Technical note: The migration distance - a unidirectional distance metric for region-of-interest comparisons

The radiotherapy process relies on several metrics in determining a notion of "distance" from one three-dimensional region-of-interest (ROI) to another. The majority are symmetric (or commutative) and do not contain information pertaining to directionality. Growth versus regression, for example, is not inherently distinguished by these metrics.

The purpose of this work was to formalize a unidirectional distance metric, motivated by radiotherapy margin concepts, which we term the migration distance. Informally, the migration distance from ROI $$ to $$ is the minimum isotropic expansion of $$ such that $$ is completely encompassed by the expansion. If $$ is contained within $$ , the migration distance is negative with magnitude equal to the maximum isotropic contraction of $$ such that $$ remains contained within contraction. The metric is demonstrated by quantifying glioblastoma interfraction target changes.

An explicit mathematical formulation of the migration distance is presented and contrasted with the related Hausdorff distance. The results are demonstrated for the gross tumor volume (GTV) dynamics of a glioblastoma cohort consisting of 111 patients that underwent standard chemoradiotherapy with offline MR imaging at planning, fraction 10, fraction 20, and 1-month post radiotherapy.

The mean ± SD of the GTV migration distance relative to planning was 5.9 ± 3.9 mm at fraction 10, 6.2 ± 4.4 mm at fraction 20, and 7.9 ± 7.1 mm at 1-month post radiotherapy. The maximum GTV migration distance across all patients at the same timepoints was 20.4, 20.7, and 45.5 mm, respectively.

We have proposed and demonstrated a unidirectional distance metric. The migration distance may have applications in the quantification of anatomical changes, planning target volume designs, and dosimetric radiotherapy plan assessment.