Monitoring Frequency of Intra‐Fraction Patient Motion Using the ExacTrac System for LINAC‐based SRS Treatments

Purpose: The aim of this study was to investigate the intra‐fractional patient motion using the ExacTrac system in LINAC‐based stereotactic radiosurgery (SRS). Method: A retrospective analysis of 104 SRS patients with kilovoltage image‐guided setup (Brainlab ExacTrac) data was performed. Each patient was imaged pre‐treatment, and at two time points during treatment (1st and 2nd mid‐treatment), and bony anatomy of the skull was used to establish setup error at each time point. The datasets included the translational and rotational setup error, as well as the time period between image acquisitions. After each image acquisition, the patient was repositioned using the calculated shift to correct the setup error. Only translational errors were corrected due to the absence of a 6D treatment table. Setup time and directional shift values were analyzed to determine correlation between shift magnitudes as well as time between acquisitions. Results: The average magnitude translation was 0.64 ± 0.59 mm, 0.79 ± 0.45 mm, and 0.65 ± 0.35 mm for the pre‐treatment, 1st mid‐treatment, and 2nd mid‐treatment imaging time points. The average time from pre‐treatment image acquisition to 1st mid‐treatment image acquisition was 7.98 ± 0.45 min, from 1st to 2nd mid‐treatment image was 4.87 ± 1.96 min. The greatest translation was 3.64 mm, occurring in the pre‐treatment image. No patient had a 1st or 2nd mid‐treatment image with greater than 2 mm magnitude shifts. Conclusion: There was no correlation between patient motion over time, in direction or magnitude, and duration of treatment. The imaging frequency could be reduced to decrease imaging dose and treatment time without significant changes in patient position

The Gorenstein and complete intersection properties of associated graded rings

Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F(I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I, we observe that: (i) G(I) is Cohen-Macaulay iff F(I) is Cohen- Macaulay, (ii) G(I) is Gorenstein iff both F(I) and R/I are Gorenstein, and (iii) G(I) is a relative complete intersection iff F(I) is a relative complete intersection. In case R/I is Gorenstein, we give a necessary and sufficient condition for G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with \mu(J) = dim R and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein iff J:I^{r-i} = J + I^{i+1}, for i = 0, ...,r-1. If (R,m) is a Gorenstein local ring and I \subseteq m is an ideal having a reduction J with reduction number r such that \mu(J) = ht(I) = g > 0, we prove that the extended Rees algebra R[It, t^-1}] is quasi-Gorenstein with \a-invariant a if and only if J^n:I^r = I^{n+a-r+g-1} for every integer n