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

Abstract

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 PFM 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.

Impact of joint statistical dual‐energy CT reconstruction of proton stopping power images: Comparison to image‐ and sinogram‐domain material decomposition approaches

“…The electron-density estimation errors are within 0.2% for all tissues with the exception of thyroid tissue. The relatively high modeling error for thyroid is mainly due to the existence of iodine ( Z = 53), which lies outside the range of typical elements of biological tissues [40].…”

“…Recently, our group has investigated an alternative tissue property parameterization: a linear basis vector model (BVM) for photon cross-section and proton SPR approximation [39, 40]. This linear model not only exhibits theoretical accuracy comparable to more complex nonlinear ρ e - Z eff models, but enables an efficient DECT joint statistical image reconstruction (JSIR) algorithm called dual-energy alternating minimization (DEAM) algorithm [41–43].…”

Experimental implementation of a joint statistical image reconstruction method for proton stopping power mapping from dual‐energy CT data

“…To link the proton SPR values and DECT measurements, the BVM parameterizes both the photon linear attenuation coefficients and the proton stopping power as a combination of two dissimilar reference materials . Images of two BVM weights are first reconstructed from the measured data via the DEAM algorithm.…”

“…As alternative to the – parameterization, we have investigated a linear basis vector model (BVM) for tissue property parameterization, which exhibits high accuracy for approximating both monoenergetic photon cross‐sections and proton SPRs. This linear model enables an efficient model‐based joint statistical image reconstruction (JSIR) algorithm: the dual‐energy alternating minimization (DEAM) algorithm .…”

Preliminary X-ray CT investigation to link Hounsfield unit measurements with the International System of Units (SI)

“…Absolute differences between the experimental and theoretical values are given in S4 and S5 Tables in the Supporting Information. In our approach, the vector is related to tube voltages, which differs from earlier presentations of the Basis-Vector Model (BVM) [10, 12, 27] in which the independent variable is the photon energy.…”