Methodology to reduce 6D patient positional shifts into a 3D linear shift and its verification in frameless stereotactic radiotherapy

The aim of this article is to derive and verify a mathematical formulation for the reduction of the six-dimensional (6D) positional inaccuracies of patients (lateral, longitudinal, vertical, pitch, roll and yaw) to three-dimensional (3D) linear shifts.

The formulation was mathematically and experimentally tested and verified for 169 stereotactic radiotherapy patients. The mathematical verification involves the comparison of any (one) of the calculated rotational coordinates with the corresponding value from the 6D shifts obtained by cone beam computed tomography (CBCT). The experimental verification involves three sets of measurements using an ArcCHECK phantom, when (i) the phantom was not moved (neutral position: 0MES), (ii) the position of the phantom shifted by 6D shifts obtained from CBCT (6DMES) from neutral position and (iii) the phantom shifted from its neutral position by 3D shifts reduced from 6D shifts (3DMES). Dose volume histogram and statistical comparisons were made between $⟨TPSCAL\text{-}0MES⟩$ and $⟨3DMES\text{-}6DMES⟩$.

The mathematical verification was performed by a comparison of the calculated and measured yaw (γ°) rotation values, which gave a straight line, Y  =  1X with a goodness of fit as R ²  =  0.9982. The verification, based on measurements, gave a planning target volume receiving 100% of the dose (V100%) as 99.1  ±  1.9%, 96.3  ±  1.8%, 74.3  ±  1.9% and 72.6  ±  2.8% for the calculated treatment planning system values TPSCAL, 0MES, 3DMES and 6DMES, respectively. The statistical significance (p-values: paired sample t-test) of V100% were found to be 0.03 for the paired sample $⟨3DMES\text{-}6DMES⟩$ and 0.01 for $⟨0MES\text{-}TPSCAL⟩$.

In this paper, a mathematical method to reduce 6D shifts to 3D shifts is presented. The mathematical method is verified by using well-matched values between the measured and calculated γ°. Measurements done on the ArcCHECK phantom also proved that the proposed methodology is correct. The post-correction of the table position condition introduces a minimal spatial dose delivery error in the frameless stereotactic system, using a 6D motion enabled robotic couch.

This formulation enables the reduction of 6D positional inaccuracies to 3D linear shifts, and hence allows the treatment of patients with frameless stereotactic radiosurgery by using only a 3D linear motion enabled couch. (paper)