Technical Note: On the accuracy of parametric two‐parameter photon cross‐section models in dual‐energy CT applications

Purpose To evaluate and compare the theoretically achievable accuracy of two families of two‐parameter photon cross‐section models: basis vector model (BVM) and modified parametric fit model (mPFM). Method The modified PFM assumes that photoelectric absorption and scattering cross‐sections can be accurately represented by power functions in effective atomic number and/or energy plus the Klein‐Nishina cross‐section, along with empirical corrections that enforce exact prediction of elemental cross‐sections. Two mPFM variants were investigated: the widely used Torikoshi model (tPFM) and a more complex “VCU” variant (vPFM). For 43 standard soft and bony tissues and phantom materials, all consisting of elements with atomic number less than 20 (except iodine), we evaluated the theoretically achievable accuracy of tPFM and vPFM for predicting linear attenuation, photoelectric absorption, and energy‐absorption coefficients, and we compared it to a previously investigated separable, linear two‐parameter model, BVM. Results For an idealized dual‐energy computed tomography (DECT) imaging scenario, the cross‐section mapping process demonstrates that BVM more accurately predicts photon cross‐sections of biological mixtures than either tPFM or vPFM. Maximum linear attenuation coefficient prediction errors were 15% and 5% for tPFM and BVM, respectively. The root‐mean‐square (RMS) prediction errors of total linear attenuation over the 20 keV to 1000 keV energy range of tPFM and BVM were 0.93% (tPFM) and 0.1% (BVM) for adipose tissue, 0.8% (tPFM) and 0.2% (BVM) for muscle tissue, and 1.6% (tPFM) and 0.2% (BVM) for cortical bone tissue. With exception of the thyroid and Teflon, the RMS error for photoelectric absorption and scattering coefficient was within 4% for the tPFM and 2% for the BVM. Neither model predicts the photon cross‐sections of thyroid tissue accurately, exhibiting relative errors as large as 20%. For the energy‐absorption coefficients prediction error, RMS errors for the BVM were less than 1.5%, while for the tPFM, the RMS errors were as large as 16%. Conclusion Compared to modified PFMs, BVM shows superior potential to support dual‐energy CT cross‐section mapping. In addition, the linear, separable BVM can be more efficiently deployed by iterative model‐based DECT image‐reconstruction algorithms.