Use of recovery coefficients as a test of system linearity of response in positron emission tomography (PET).

Quantitative determination of activity concentration has always been regarded as a goal of PET scanner design. Therefore, a linear response with respect to activity concentration is essential. To prove system linearity of response a test is proposed based on the determination of recovery coefficients (RC) for different object geometries. If all degrading effects, especially scatter and attenuation, are corrected to a sufficient degree of accuracy, the system behaves linearly resulting in a theoretical relationship between hot (HSRC) and cold spot recovery coefficients (CSRC). Therefore this relationship, applied to appropriate phantom data containing hot or cold spheres, combined with the constraints on asymptotic behaviour of RC can be used as a test of system linearity of response. After applying the system's standard corrections RC were determined using both 2D and 3D data acquisition modes. For both 2D and 3D data, HSRC directly measured showed an excellent agreement with the HSRC calculated from the CSRC. The analysis was extended to radionuclides of different positron ranges, to the effect of data smoothing, and to that of iterative reconstruction. The agreement between the RC determined under varying border conditions demonstrates the effectiveness of the corrections used in constituting system linearity. Therefore, the method proposed is used as a test of system linearity of response.