Date: Thu, 18 July 2024 21:41:00 +00:00
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{img fileId="3389" width="400" align="center" desc = "Figure 52."}
!!!Center of Rotation (COR) correction:
The gamma camera moves on a circular orbit, while the axis of rotation is intersected always at the same point (center of camera) by the line perpendicular to the camera’s surface. During a round many projections of the sections are prepared.
In practice, the circular orbit of the movement is not so regular due to the really large weight of the camera, so the projections are distorted. In order to reduce this distortion, a correction for center migration is applied.
{img fileId="3390" width="400" align="center" desc = "Figure 53."}
For the correction of center migration, a point source is placed near to the axis of rotation, since the accurate position of the axis of rotation cannot be identified. Projection images are taken from this point source.
{img fileId="3391" width="400" align="center" desc = "Figure 54."}
The y coordinate of the projection must not change, if the plane of the camera’s surface is parallel with the axis of rotation all along. The measure of the center migration in the y direction can be determined in the case of a projection with a {HTML()}θ{HTML} angle by averaging the y coordinates. Then the measure of the migration is calculated as the difference of the current y from this constant.
{img fileId="3401" width="400" align="center" desc = "Figure 55."}
The x coordinate shows a changing forming a sine, because the point source usually is not precisely on the axis of rotation. According to this, a a*sin({HTML()}θ{HTML} - {HTML()}φ{HTML}) function can be fitted to the x coordinates, where a and φ are free parameters.
{IMG(fileId="484",width="400",align="center" desc = "Figure 56.")}{IMG}
In the case of a specific tomography examination, the projection with {HTML()}θ{HTML} angle has to be moved before the reconstruction corresponding to the correction calculated as above.
!!!Homogeneity correction
The inhomogeneity of the camera causes artifacts on the sections similar to a ring. Avoiding this, homogeneity correction is accomplished on the sections: the projection is multiplied by the homogeneity image and the reciprocal of the homogeneity image’s average at each pixel.
!!!Attenuation correction
The distribution of the radiopharmacon is required on the sections derived from SPECT examinations, but it is disturbed by the partial attenuation of the radiation following the radioactive decay in the body before the preparation of the projections. Thus there is no sufficient information for the application of the projection’s correction.
The sections reconstructed from the projections without correction show lower activity at the middle than in reality. Chang offered the following method for the attenuation correction of the sections:
The contour line of the body has to be determined in the section! After that lines are drawn to the contour line from an arbitrary point.
{img fileId="3392",width="400",align="center" desc = "Figure 57.")}{IMG}
Assume that the linear attenuation coefficient is a constant μ value inside the whole body. Of course, it is true only approximately. Then the attenuation on the R{SUB()}i{SUB} ray can be written as e{SUP()}-{HTML()}μ{HTML}Ri{SUP}. If the number of the lines is M, then the average attenuation is {EQUATION(size="75")}(\sum{e^{-\mu R_{i}}})/M{EQUATION}.
Based on the method described above, the C corrected image inside the contour line is {EQUATION(size="75")}C=M(\sum{e^{-\mu R_{i}}})^{-1}{EQUATION}. The correction has to be executed by the multiplication of the original image with the C image pixel by pixel (not by matrix multiplication).
{IMG(fileId="461",width="400",align="center" desc = "Figure 58.")}{IMG}
{IMG(fileId="459",width="400",align="center" desc = "Figure 59.")}{IMG}