Abstract

Doses to small spinal cord isodose volume (such as those ranging from Dmax 0.0 cc to 0.5 cc) as well as to large volumes (such as those ranging from 0.5 cc to 3.0 cc) are critical parameters to guide safe practice of spine SBRT. We here report a mathematical formula that links the most probable dose volume limits together for common spine SBRT cases.Methods and materials: A dose ripple formula parameterized with equivalent dose radius (EDR) was derived to model spinal cord small-volume doses for a spine SBRT treatment. A cohort of spine SBRT cases (n=68), treated with either a robotic x-band linac or a conventional S-band linac, was selected to verify the model predictions. The mean prescription dose was 22± 4 Gy (range, 12-40 Gy) delivered in 2±1 fractions. The mean and median target volume was 39.4±42.5 cc and 30.3 cc (range, 0.24-264.2 cc), respectively. Direct correlations between the spinal cord Dmax and variable spinal cord doses of increasing isodose volumes (ranging from 0.0 cc to 3.0 cc) of different planning organ-at-risk volumes (PRVs) were investigated. The PRV structures for the study included the true cord, thecal sac and the true cord plus variable margins ranging from 1.0 mm to 3.0 mm.No direct linear correlation was observed amongst the small volume doses to the spinal cord PRVs. However, strong linear correlations (R2 > 0.96) for all the studied PRVs were observed when correlating EDRs amongst isodose volumes ranging from 0.0 cc to 3.0 cc. In particular, EDR dependence was found to differ significantly for the thecal sac versus the spinal cord with or without 1-3 millimeter margins. With strong EDR correlation, the most probable relationship among the small-volume dose limits was derived for the spinal cord PRVs.An analytical formula linked the most probable pin-point/small isodose volume doses with relatively large isodose volume doses of the spinal cord for spine SBRT. As a result, a small number of dose limits such as Dmax or D(0.35cc) are likely sufficient to surrogate the spinal cord dose tolerance for consistent treatment planning optimization and outcome analysis.

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