Test of the centre of rotation offset and alignment of axes

4.3.6. Test of the centre of rotation offset and alignment of axes

Purpose of test To test the centre of rotation offset, alignment of the camera Y axis and

head tilt with respect to the axis of rotation. This is considered a test to be performed if an error is observed with the test for resolution in air (see Section 4.3.4). This is an extended version of a test that should be described in the manufacturer’s SPECT system manual.

Materials

A small 99m Tc point source is used, together with some method of suspending it in air within the field of view, for example, by attaching the source to a long ruler, or a purpose-made supporting device. The computer system should be set up as specified by the supplier as indicated in step (3) below, noting the comments given previously in Section 4.1.3.

Procedure (1) Using a spirit level, ensure that the camera is accurately aligned so that

the head is parallel with the axis of rotation, i.e. that the head is not tilted (but see observations below).

(2) Suspend the point source in air within about 2 cm of the axis of rotation and within about 2 cm of the centre of the field of view. (3) Perform a normal tomographic acquisition using the finest digital matrix size available, collecting about 10 000 counts at every angular position. An acquisition consisting of 32 angles over 360° is adequate for this test.

(4) Repeat steps (2) and (3) with the point source placed about 10 cm radial distance away from the centre of rotation. (5) Repeat steps (1)–(4), placing the point source along the axis of rotation, but as far as possible away from the central slice, for example, within 5 cm of the edge of the field of view in the positive Y direction. It is important to ensure that the point source is always within the field of view of the camera throughout the tomographic acquisition.

(6) Repeat step (5) with the point source close to the edge of the field of view in the opposite direction. Note that, alternatively, if suitable software is available, three point sources may be used and a single set of measurements performed for the central point (steps (2), (5) and (6)).

(7) Perform steps (1)–(6) for rotation in the opposite direction (if the system

can acquire data in both the clockwise and anticlockwise directions).

Data analysis Most manufacturers’ systems provide software to calculate and

incorporate the correction required into the normal tomographic acquisition and reconstruction process. The test and the methods used vary considerably from system to system. The centre of rotation correction accuracy can be checked by using the resolution test in air (Section 4.3.4), or the raw values checked using the method given below. The method suggested does not depend on the special software provided by the manufacturer for this purpose.

The aim of this test is to estimate the centre of gravity of the image of the point source, angle by angle, and hence to estimate the position of the centre of rotation. Most software packages treat the centre of rotation, as used in the reconstruction, as being at N/2 + 0.5 (where the pixel on one edge is designated

1 and the pixel on the other edge, N). If this is not true, the calculations given below should be converted into the frame of reference used by the software provided. (For example, an alternative convention is to refer to the pixel on one edge as 0 and on the other edge as N – 1. In this case, the centre of rotation would simply be (N – 1)/2 + 0.5.)

Calculate the centre of gravity of the point source for each image, using the method given in the data analysis part of Section 4.3.2. The values COGX and COGY should be estimated to a fraction of a pixel. Two methods of analysing the results exist; both methods may require special purpose software to implement. Most tomographic systems provide a program to perform one or the other of the calculations given below.

Method A (1) The offset from the centre of rotation should be calculated as follows. If

X 0 is the value of COGX at 0° and X 180 is the value at 180° degrees, then, if N is the number of pixels across the image (e.g. 256 if the data were collected in 256  256), the offset from the centre of rotation, R, is given by:

(20) (2) This value should be calculated for each pair of angles, q, separated by

R 0 = (N + 1 – X 0 –X 180 )/2

180° to generate a set of values R(q).

Method B (1) The COGX may be plotted as a function of angle over the total angle of

rotation, here 360°. (2) A sine function A + B sin(q + f) can be fitted to this curve, where q is the angle of rotation and A, B and f are fitting constants. (3) The value of A should be compared with the expected centre of the matrix (normally (N + 1)/2, as stated above). The difference between the constant A and the centre of rotation is the mean offset. Mathematically, this value should be identical to that calculated by method A.

(g) The fitted sine function should be subtracted from the observed curve to show the residuals. This indicates the variation in the centre of rotation as

a function of angle of rotation; R(q) is given by these residuals plotted against angle q.

For both methods (1) The value of R(q) should be plotted as a function of angle.

(2) The mean value of R(q), its standard deviation and maximum deviation from the mean value should be calculated. (3) The centre of gravity of the point source along the Y axis should be calculated using the same method (for each detector head) and should be recorded for each angular position. A manipulation which may be used with some software to obtain the plot of the variations in the Y axis is to rotate the raw data by 90° and use the same software as that used for estimating the X axis variation.

(4) Convert the values thus determined into millimetres by using the known pixel size for the camera, as determined in Section 4.3.2, for the corresponding matrix size.

In particular, step (3) must be performed for each head separately for multiple head systems, since it is very important to check that the Y axis gains and offsets of each of the heads match. All of these calculations are identical for both the normal acquisition performed with the well centred sources, for the clockwise and anticlockwise acquisition, and for the various other positions of the point source away from the central slice.

Observations This test is intended to be performed as a reference test and at weekly or

quarterly intervals, depending on the stability of the system.

A SPECT system must be accurately centred if resolution is not to be degraded and this test is designed to ensure that the reconstructed image does not suffer from degradation resulting from this cause. Every millimetre loss of accuracy in centring, whether mechanical, electronic, within the camera head or in the interface, will degrade the resolution by a greater amount in the reconstructed image. While the two methods of analysis give the same value for the mean offset averaged over opposite views, the second method gives a better indication of variations in offset as a function of angle of rotation.

When problems are observed with multiple head systems, a good tactic to use in order to identify the source of such problems is to treat each head separately as a single headed system. For example, with a dual headed system, acquire data for each head over 360° and apply the data analysis separately for each head.

As previously stated (see Section 4.1.1), the centre of rotation offset may not be constant with respect to angle. These second order effects may be observed on the plot of variations with angle, which should be small. They may, however, be ignored if they are taken into account by the reconstruction software, provided that they are reproducible. In this case, the centring test should be repeated in order to confirm reproducibility.

Interpretation of results The interpretation of the results will depend on the extent to which the

hardware and software of the tomographic system correct for errors in centring and therefore on the results of Section 4.3.4: Testing tomographic resolution in air. If the results of this test are unsatisfactory, the most likely explanation is the inaccuracy of the centring of the system. The interpretation of these two tests should be considered as a pair.

If the centre of rotation offset in X used by the system is accessible, this should be compared with that calculated using this test. For those systems that do not perform a centre of rotation offset correction, the value estimated by this test should tend to zero.

The curve of the offsets should be reasonably smooth and flat. The offset at the start and end angles should be very close. If considerable fluctuations exist, as measured by the standard deviation of the offset, in particular, if they are not reproducible, the system is likely to give poor clinical performance.

The plot of the centre of gravity along the Y axis for a source radially distant from the central axis gives a good indication of the tilt of the head or possible collimator hole angulation. If the head is not tilted, this Y axis offset should be independent of angle (the plot should be flat). It is important to realize that if the gantry supporting the head(s) is not accurately vertical, then The plot of the centre of gravity along the Y axis for a source radially distant from the central axis gives a good indication of the tilt of the head or possible collimator hole angulation. If the head is not tilted, this Y axis offset should be independent of angle (the plot should be flat). It is important to realize that if the gantry supporting the head(s) is not accurately vertical, then

With multiple heads, it is important that the values of the X axis offsets measured for each head are the same, unless the reconstruction software specifically takes this into account. In addition, the values for the COGY should be the same for each head at each angular position. Thus, the plots for each head should be compared, or, if the results for one head are plotted as a continuation of those for another head, the data should be continuous. For example, the plot of the Y centre of rotation should be flat over the range of all head angles considered.

The centre of rotation offset should be independent of the position of the point source within the field of view. If this is not the case it may be an indication that the Y axis is not aligned with the axis of rotation.

Caution must be taken if the method for correction of circular rotation error is included in the reconstruction and is inaccessible to the user. In such a case, the raw acquired projection images may indicate a centring error that is, in fact, corrected for in the ensuing reconstruction.

Limits of acceptability The mean value of the centre of rotation offset should be less than 2 mm,

or it must otherwise be corrected. The centre of rotation offset estimated at the centre and for the edges of the field of view should all be within 2 mm of each other. For multiple head systems, the position of the Y = 0 axis, as well as the Y gain, should be the same for both heads.

Conclusion Record whether or not the results confirm acceptable performance. If

not, indicate the follow-up action taken.