Computer simulations of the TRE in the LGP registration algorithm

Keywords: physics, Imaging, dose planning, gamma knife, technique

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     A prerequisite to fully benefit from the superior accuracy offered by the Leksell Gamma Knife® is that it is not limited by the quality of the images used when planning a treatment. 
     Computer simulations were used to investigate how simulated image imperfections affect the registration, and by extension the overall treatment accuracy.
     The LGP® registration algorithm was implemented in Matlab® and a simple graphical user interface (GUI) was set up, though witch it was possible to create virtual image stacks of adjustable slice thickness, d, and slice number, N. The points of intersection between the slices of such a stack and the fiducial rods of the indicator box, translated and rotated with respect to the scanner origin according to input, were calculated and simulated noise was added. The noise consisted of independent displacements of the points of intersection within the slice planes, normally distribtuted with standard deviation ? in two directions, giving an average displacement of . To evaluate the results, the target registration error (TRE), the distance between a point in the registered image volume and the corresponding point in physical space, was used. The average TRE in the ‘worst’ point inside a normal head ( , found at Leksell coordinate (100, 180, zmax)) over 1000 simulations was compared for > = 0.15, 0.3 and 0.6 mm, d = 0.5, 1, 2, and 4 mm, and stack height h=Nd ranging from 20 to 120 mm.
     In the examined range, the average TRE_w was described by (TRE) ?_w=30?N^(-1.17) d^(-0.67) (difference < 0.03 mm), with the 90th and 99th percentile TRE_w 1.7 – 2.1 and 2.6 – 3.4 times larger, respectively.
     Under the above conditions, the following conclusions are valid: (1) The expected TREs are proportional to the magnitude of the uncertainty in the images ?. (2) Halving d whilst keeping h constant, gives an improvement in expected the TREs by a factor of ?2. (3) 
     Registration of n>cd^(-0.57) slices in a stack, with cavg=15, c90=28 and c99=43, is required for the average, 90th and 99th percentile TRE_w in those slices to be lower than the expected point displacement, independent of ?.


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