Figure Captions
Fig. 1 A traveling dose rate profile f ( z  vt )   1 f ( z  vt ) in the phantom reference
frame is created when an axial dose profile f (z ) is translated along the phantom central
axis z by table translation at velocity υ, where τ is the gantry rotation period (in sec),
which has the familiar form of a traveling wave.
Fig. 2 Accumulated dose at constant mA for a superposition (summation) of the 11
dose profiles f(z – kb) depicted, where k assumes integral values between (-5 ≤ k ≤ 5),
each profile having an aperture of a = 26 mm and spaced at like intervals using a table
increment b = a = 26mm (no primary beam overlap). The peak accumulated dose at z = 0
contributed by the 11 adjacent profiles shown in Fig. 2 exhibits a fourfold increase over
the peak dose of a single axial profile f(0) due to scatter. In such a scan series with
multiple adjacent profiles, the scatter contribution at z = 0 is built up by the scatter tails of
the entire ensemble of profiles reaching back to z = 0.
Fig. 3 Realistic example of a clinical auto TCM mA(z) profile, including chest and
abdomen.
Fig. 4a Accumulated dose obtained from the summation of the N = 11 individual mAweighted dose profiles f (z), individually depicted in the Figure, based on the mA(z)
profile mA3 (also plotted), having the common average mA = 3.73 of the entire family
of four mA profiles. The same scan interval b = a = 26 mm used in Fig. 2 applies here
(and in all other examples).
~
Figure 4b A logarithmic plot log 10[ DL ( z )] of the data depicted in the linear plot of Fig.
4a in order to better visualize the “lateral throw” of the scatter tails which bolster the dose
in the center. Thus despite the fact that the local mA(z) for the 3 central profiles drops by
a factor of 6, these scatter tails prop up the central dose and limit its drop at the center to
a modest factor of 5/3 = 1.7.
Fig. 5 The other members of the family of mA profiles used in this paper (mA3 is not reshown here for clarity), each profile having the same average mA value over L = 286
mm, namely mA = 3.73, where the constant mA value is likewise mA0 = 3.73, such
that the scanner will report the same value of “CTDIvol” for all family members (without
TCM
making any distinction between CTDI vol
for those using TCM with variable mA(z) and
the bona-fide CTDIvol at constant mA in profile mA0).
Fig. 6 Accumulated dose distributions for the complete set of auto mA distributions from
Fig. 5 – all having the same average mA value mA = 3.73 taken over the scan length L.
TCM
The actual constant mA used is likewise equal to 3.73, hence all have the same CTDI vol
= CTDIvol = 5.0, and identical scanner-reported values of “CΤDIvol”. The common
number of rotations N = 11 additionally confers the same integral dose E and DLP.
Fig. 7 The average dose over the entire scan length L = 286 mm, for the family of mA
TCM
profiles all having the same average mA, the same CTDI vol
= CTDIvol = 5.0, and the
same scan length L = 286 mm and thence the same integral dose E and DLP (note that the
value of CTDIvol is above this average as expected).
Fig. A1 Match between the theoretical analytical dose profiles of Dixon and Boone5 and
the experimental data of Mori et al.12 normalized to unity for a = 138 mm. There are no
empirical parameters in the theory which is based on fundamental physics, nor is any
curve-fitting involved (there are no adjustable parameters), so the theoretical curves
either match the experimental data or the physics is wrong (or vice–versa); fortunately
the match is good.