The impact of dose matrix and voxel dimensions to dose calculation for stereotactic radiosurgery.

The purpose of the present study was the optimization of dose calculation for intracranial stereotactic radiosurgery.We evaluated the Singular Value Decomposition (SVD) analysis as a novel optimization technique. Our approach to dose distribution optimization was to recover estimates of minibeams weights from well-defined provisional dose matrices. The dose delivered by a set of minibeams is formulated as a matrix equation. We studied the influence of dose matrix and voxel dimensions on the conditioning of stereotactic radiotherapy inverse problem. Dose matrix dimensions varied from 16 to 96 mm3, while voxel dimension was kept constant at 2 mm3. In the assessment of voxel dimension, matrix dimension was kept constant at 80 mm3 while voxel dimensions varied from 1 to 8 mm3. The reconstruction of dose distributions was studied using a truncated SVD expansion in the calculation of approximation to the generalised matrix inverse.The conditioning was deteriorated by either the decreasing of dose matrix dimensions or by the increasing of voxel size. The condition number was equal to 89×103 and 7×103 for the 16 mm3 and 96 mm3 dose matrix dimensions, respectively. The condition number was equal to 9.9×103 and to 2.7×106 for 1 mm3 and 8 mm3 voxel size, respectively. The reconstruction of dose distributions revealed that an ill-conditioned problem yields poor quality reconstruction.We considered that a good compromise between quality of dose distribution, time calculation and hard disk memory would be the use of a 64 mm3 matrix dimension with a 2 mm3 voxel size.