2.3. Data processing
The database of coordinates for each set of anatomical
landmarks were read into an in-house developed iterative
optimization computer program that was specifically written
to evaluate translation of target isocenter in any control CT
data set, relative to the reference/planning data set. The
optimization algorithm iteratively varied the x, y and
z-translation and the rotation about the x, y and z-axes of
the control data set until the root mean square (RMS)
variation between control and reference data point positions
was minimized. The values reported here as the translation
of target isocenter of the control data set relative to the
reference data set are the values output by the program
based on rigid body mechanics calculation of target
movement due to the determined translations and rotations
of the patient. All values reported are rounded to two
decimals to stay consistent with the way the original
landmark coordinates were acquired in the treatment
planning software, although the program outputs data in
higher resolution. This iterative fit technique is necessary, as
opposed to a direct calculation method, because the small,
but non-zero errors inherent to the process of visually
identifying discrete anatomical points make it impossible to
perfectly overlay the two sets of data points. The objective
function output (i.e. the RMS goodness of fit parameter) was
verified to be at or below values consistent with the
previously mentioned 0.25 mm SD for identification of
individual bony anatomical landmarks. The mean target
isocenter dislocation is reported in the present study as both
the average position (derived from positive and negative
numerical positional data) and as the absolute value of
isocenter translation. Additionally, the SD of the mean