A generalized model for the conversion from CT numbers to linear attenuation coefficients

We have developed a generalized model for accurate conversion from CT numbers to linear attenuation coefficients (LACs) by introducing a material-dependent conversion factor (CF). Using this model and assuming that a material x is a uniform mixture of water and another material A (denoted as "water-A assumption" in this paper), we show that the conversion from CT number of x (HU_x) to LAC is linear. The slope of the linear function is determined by the attenuation property of material A. This generalized model can be applied to the conversion from CT images to attenuation maps for combined CT/PET and CT/SPECT imaging. When HU_x is less than zero, we use "water-air assumption", otherwise, we use "water-cortical-bone assumption". This leads to different slopes for the linear conversion for CT numbers below and above zero. In practice, for each CT system, a cylindrical phantom with a small cortical bone cylinder in the center is filled with water and scanned once for each operational kVp. The CT number of the cortical bone (HU_CB) at each kVp is then measured and used for the conversion. Experiments show that the conversion using this technique is accurate. In addition, the proposed technique can be used to characterize CT systems by obtaining the effective CT energy at each kVp. This allows for absolute attenuation measurement using CT systems instead of the relative measurement given by CT-numbers.