A theoretical investigation of optimal target-dose conformity in gamma knife radiosurgery

The purpose of this paper is to suggest guidelines for target-dose conformity in gamma knife stereotactic radiosurgery (GKSRS) by taking into account factors that have been linked to GKSRS complications. We also suggest an explanation for the failure of previous studies to find a correlation between improved conformity index and reduced risk of GKSRS toxicity, where the conformity index, C(S), is defined as the ratio of the prescription volume, V(P), to the target volume, V(T).

Previous investigations have shown that symptomatic toxicity in GKSRS is correlated with the volume of nontarget tissue receiving the prescription dose, D(P). In this study, we formulated the volume of nontarget tissue, V(NTD), receiving dose D < or = D(P) as a function of the target volume, prescription volume, and prescription dose. We verified the model for D = 12-15 Gy by comparing VNTD calculated from the model versus VNTD calculated directly for 114 tumors in 63 consecutive patients treated at our institution. Once verified, we used this formulation of V(NTD) to calculate the volume of nontarget tissue receiving doses between 12 and 15 Gy from published data reported for patients experiencing varying degrees of GKSRS toxicity. Next, assuming that the VNTD values calculated for those patients who had either no toxicity or mild neurological symptoms in the published study represented safe levels of normal tissue irradiated to the dose in question, we substituted these V(NTD) values into an equation expressing C(S) in terms of V(NTD), V(T), and D(P), and examined how C(S) varied as a function of V(T) and D(P).

The R2 value for the correlation between VNTD calculated directly or calculated with the proposed formula for VNTD ranged from 0.98 to 0.99, indicating that the formula accurately models the behavior of the nontarget volume receiving dose D. Applying this formulation of VNTD to historical data suggested that the requirements V(NT15) < or = 2.2 cm3, V(NT14) < or = 2.6 cm3, V(NT13) < or = 3.1 cm3 and V(NT12) < or = 3.8 cm3 minimize the risk of severe complications following GKSRS. Imposing these criteria imply that as the target size increases, delivering a given prescription dose requires increasing target-dose conformity. For tumor sizes >5 cm3 C(S) must be < or = 1.2 to restrict V(NTD) to the values listed above. For very small targets, on the other hand, nearly any reasonable conformity index will lead to acceptable values of V(NTD). These observations may explain why previous investigations failed to show a correlation between improved conformity and decreased toxicity in GKSRS, because in these earlier studies the range of conformity indices represented was not wide enough, in particular C(S) values <1.3 were not represented for large tumors.

Our model suggests that for target volumes > or = 3 cm3, high levels of target-dose conformity (C(S) < 1.3) are required for typical GKSRS prescription doses in order to limit VNTD to levels associated with either no toxicity or mild neurological symptoms in a previous investigation.