title: Dose equations for shift-variant CT acquisition modes using variable pitch, tube current, and aperture, and the meaning of their associated CTDI(vol).
abstract: OBJECTIVE
  With the increasing clinical use of shift-variant CT protocols involving tube current modulation (TCM), variable pitch or pitch modulation (PM), and variable aperture a(t), the interpretation of the scanner-reported CTDI(vol) is called into question. This was addressed for TCM in their previous paper published by Dixon and Boone [Med. Phys. 40, 111920 (14pp.) (2013)] and is extended to PM and concurrent TCM/PM as well as variable aperture in this work.
  
  
  METHODS
  Rigorous convolution equations are derived to describe the accumulated dose distributions for TCM, PM, and concurrent TCM/PM. A comparison with scanner-reported CTDI(vol) formulae clearly identifies the source of their differences with the traditional CTDI(vol). Dose distribution simulations using the convolution are provided for a variety of TCM and PM scenarios including a helical shuttle used for perfusion studies (as well as constant mA)-all having the same scanner-reported CTDI(vol). These new convolution simulations for TCM are validated by comparison with their previous discrete summations.
  
  
  RESULTS
  These equations show that PM is equivalent to TCM if the pitch variation p(z) is proportional to 1/i(z), where i(z) is the local tube current. The simulations show that the local dose at z depends only weakly on the local tube current i(z) or local pitch p(z) due to scatter from all other locations along z, and that the "local CTDI(vol)(z)" or "CTDI(vol) per slice" do not represent a local dose but rather only a relative i(z) or p(z). The CTDI-paradigm does not apply to shift-variant techniques and the scanner-reported CTDI(vol) for the same lacks physical significance and relevance.
  
  
  CONCLUSIONS
  While the traditional CTDI(vol) at constant tube current and pitch conveys useful information (the peak dose at the center of the scan length), CTDI(vol) for shift-variant techniques (TCM or PM) conveys no useful information about the associated dose distribution it purportedly represents. On the other hand, the total energy absorbed E ("integral dose") as well as its surrogate DLP remain robust (invariant) with respect to shift-variance, depending only on the total mAs = 〈i〉t0 accumulated during the total beam-on time t0 and aperture a, where 〈i〉 is the average current.
authors.affiliation: Department of Radiology, Wake Forest University School of Medicine, Winston-Salem, North Carolina 27157.
authors.forename: Robert L
authors.initials: RL
authors.lastname: Dixon
authors.affiliation: Departments of Radiology and Biomedical Engineering, University of California Davis, Sacramento, California 95817.
authors.forename: John M
authors.initials: JM
authors.lastname: Boone
authors.affiliation: Department of Biomedical Engineering, Wake Forest University School of Medicine, Winston-Salem, North Carolina 27157.
authors.forename: Robert A
authors.initials: RA
authors.lastname: Kraft
mesh_terms: D065638:Absorption, Radiation; D007091:Image Processing, Computer-Assisted; D019047:Phantoms, Imaging; D011829:Radiation Dosage; D014057:Tomography, X-Ray Computed / Q000379:methods*