title: An angle-dependent estimation of CT x-ray spectrum from rotational transmission measurements.
abstract: OBJECTIVE
  Computed tomography (CT) performance as well as dose and image quality is directly affected by the x-ray spectrum. However, the current assessment approaches of the CT x-ray spectrum require costly measurement equipment and complicated operational procedures, and are often limited to the spectrum corresponding to the center of rotation. In order to address these limitations, the authors propose an angle-dependent estimation technique, where the incident spectra across a wide range of angular trajectories can be estimated accurately with only a single phantom and a single axial scan in the absence of the knowledge of the bowtie filter.
  
  
  METHODS
  The proposed technique uses a uniform cylindrical phantom, made of ultra-high-molecular-weight polyethylene and positioned in an off-centered geometry. The projection data acquired with an axial scan have a twofold purpose. First, they serve as a reflection of the transmission measurements across different angular trajectories. Second, they are used to reconstruct the cross sectional image of the phantom, which is then utilized to compute the intersection length of each transmission measurement. With each CT detector element recording a range of transmission measurements for a single angular trajectory, the spectrum is estimated for that trajectory. A data conditioning procedure is used to combine information from hundreds of collected transmission measurements to accelerate the estimation speed, to reduce noise, and to improve estimation stability. The proposed spectral estimation technique was validated experimentally using a clinical scanner (Somatom Definition Flash, Siemens Healthcare, Germany) with spectra provided by the manufacturer serving as the comparison standard. Results obtained with the proposed technique were compared against those obtained from a second conventional transmission measurement technique with two materials (i.e., Cu and Al). After validation, the proposed technique was applied to measure spectra from the clinical system across a range of angular trajectories [-15°, 15°] and spectrum settings (80, 100, 120, 140 kVp).
  
  
  RESULTS
  At 140 kVp, the proposed technique was comparable to the conventional technique in terms of the mean energy difference (MED, -0.29 keV) and the normalized root mean square difference (NRMSD, 0.84%) from the comparison standard compared to 0.64 keV and 1.56%, respectively, with the conventional technique. The average absolute MEDs and NRMSDs across kVp settings and angular trajectories were less than 0.61 keV and 3.41%, respectively, which indicates a high level of estimation accuracy and stability.
  
  
  CONCLUSIONS
  An angle-dependent estimation technique of CT x-ray spectra from rotational transmission measurements was proposed. Compared with the conventional technique, the proposed method simplifies the measurement procedures and enables incident spectral estimation for a wide range of angular trajectories. The proposed technique is suitable for rigorous research objectives as well as routine clinical quality control procedures.
authors.affiliation: Carl E. Ravin Advanced Imaging Laboratories, Duke University Medical Center, Durham, North Carolina 27705 and Physics Department, Duke University, Durham, North Carolina 27708.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Lin
authors.affiliation: Siemens Medical Solutions, Malvern, Pennsylvania 19355.
authors.forename: Juan Carlos
authors.initials: JC
authors.lastname: Ramirez-Giraldo
authors.affiliation: Physics Department, Duke University, Durham, North Carolina 27708.
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Gauthier
authors.affiliation: Siemens Healthcare, Forchheim 91301, Germany.
authors.forename: Karl
authors.initials: K
authors.lastname: Stierstorfer
authors.affiliation: Carl E. Ravin Advanced Imaging Laboratories, Duke University Medical Center, Durham, North Carolina 27705 and Physics Department, Duke University, Durham, North Carolina 27708.
authors.forename: Ehsan
authors.initials: E
authors.lastname: Samei
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D012399:Rotation; D014057:Tomography, X-Ray Computed / Q000295:instrumentation / Q000379:methods*; D014965:X-Rays