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An analytical expression for R50% dependent on PTV surface area and volume: A cranial SRS comparison.

Dharmin D Desai¹, E L Johnson², Ivan L Cordrey¹

¹Department of Radiation Oncology, CHI Memorial Hospital, Chattanooga, TN, USA.

Journal of Applied Clinical Medical Physics

|January 25, 2021

Summary

A new analytical expression for R50% in stereotactic radiosurgery (SRS) planning was derived. This formula, based on physical principles, may represent a theoretical lower limit for dose spill in SRS treatments.

Keywords:

PTV surface area R50%R50%Analytic cranial SRS/SRT dose drop-off distance

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Area of Science:

Medical Physics
Radiation Oncology
Radiosurgery

Background:

Quantifying intermediate dose spill is crucial in stereotactic radiosurgery (SRS).
The R50% metric, defined as the 50% isodose cloud volume (V_IDC50%) divided by the planning target volume (PTV) volume, is used for this quantification.

Purpose of the Study:

To derive an analytical expression for R50% for a spherical PTV.
To compare the derived analytical R50% values with clinical SRS data.

Main Methods:

Developed an analytical expression for R50% using physical principles.
The expression incorporates PTV surface area, PTV volume, and dose fall-off distance (Δr).
Compared analytical R50% (R50%_Analytic) with clinical R50% (R50%_Clinical) from existing SRS data.

Main Results:

R50%_Analytic was consistently lower than R50%_Clinical by an average of 15% ± 7%.
The trend of R50%_Clinical versus PTV volume was mirrored by the trend of R50%_Analytic.
The derived analytical expression showed potential as a theoretical lower limit for clinical SRS R50% values.

Conclusions:

The analytical R50% expression provides a potential theoretical lower bound for clinical SRS dose spill.
Further research is needed to validate R50%_Analytic as a definitive lower limit.
R50%_Analytic may offer valuable insights for optimizing SRS treatment planning.