Estimation of complications for linear accelerator radiosurgery with the integrated logistic formula

Radiosurgery techniques permit high doses of single fraction irradiation to be administered to small volumes of tumor with relative sparing of surrounding brain tissue. The tolerance of surrounding normal brain tissue to dose distributions from linear accelerator radiosurgery with different collimator sizes is an important factor that must be estimated by anyone using these treatment techniques. The exponential and linear quadratic versions of the integrated logistic formula were used to estimate the probability of brain necrosis at different doses for radiosurgical dose distributions administered by a 6 MV linear accelerator with a 5 arc technique for collimator sizes from 12.5 to 30 mm in diameter. Dose-volume isoeffect curves for a 3% risk of brain necrosis from linear accelerator radiosurgery were then calculated. These curves approximate those calculated for gamma knife radiosurgery and a published 1% dose-volume isoeffect line predicted for proton beam irradiation. Similar dose-volume isoeffect curves were calculated for single fraction radiosurgery boosts administered after 30 Gy of whole brain irradiation in 12 fractions. The integrated logistic formula appears to be a useful tool for estimating tolerance and providing guidelines for prescribing radiation doses for linear accelerator radiosurgery.