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 allenuation coefficients (LAC) by introducing a material-dependent conversion factor (CF). When assuming that a material x is a uniform mixture of water and another material A (we call this the "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, namely, its CT number (HU_A) at a given kVp and density (ρ_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 us "water-cortical bone assumption.\´ These assumptions lead to different slopes for the linear conversion when CT number is below and above 0. 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 kVp. The CT number of the cortical bone (HU_CB) at each kVp is then measured and used for the conversion. Experiments performed on a Philips CT AURA system show that, for a spongiosa bone sample with known LAC, the errors in LAC\´s converted from CT images at all the kVp\´s are 0% for PET and less than 1.5% for SPECT. Conclusions: The proposed model illustrates the linearity for the conversion from CT numbers to LAC at energy of interest under the water-A assumption. Its application to the conversion from CT images to PET/SPECT attenuation maps is accurate and convenient. In addition, the proposed technique can be used to characterize CT systems by obtaining the effective CT energy at each operating kVp. This allows for absolute attenuation measurement using CT systems instead of the relative measurement given by CT-numbers.