Functional Relationship between the Volume of a Near-Target Peripheral Isodose Line and Its Isodose Value for Gamma Knife® Radiosurgery

Aims: To study how the volume of a peripheral isodose line would relate to its isodose value for Gamma Knife® (GK) radiosurgery. Method: A theoretical model was developed to derive the relationship between the volume of a near-target peripheral isodose line and its isodose value. The formula was tested based on cases with uniformly matched target volumes as well as random target volumes ranging from 0.1 to 37 cc. Results: To the second order approximation, the volume of a near-target peripheral isodose line (V) relates to its dose value (D) by the following formula: V/V₀ = (D/D₀)–3/2, where D₀ is the prescription dose and V₀ is the prescription isodose volume. Applied to patient data, we found V/V₀ = (D/D₀)Γ, where Γ = ––1.50 ± 0.16 at the 95% of the confidence level, and showed excellent agreement with the theoretical prediction. Conclusion: For GK radiosurgery, the near-target peripheral isodose volume relates to its isodose value in a similar fashion as to the way in which the volume of a sphere relates to the inverse of its surface area. Such a predictable relationship justifies the use of a single near-target peripheral isodose volume, as a sufficient measure of the dose to the normal brain.