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Dose equations for tube current modulation in CT scanning and the interpretation of the associated CTDIvol
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1. R. L. Dixon, and A. C. Ballard, “Experimental validation of a versatile system of CT dosimetry using a conventional ion chamber: Beyond CTDI100,” Med. Phys. 34(8), 33993413 (2007).
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Image of FIG. 1.

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FIG. 1.

A traveling in the phantom reference frame is created when an axial dose profile () is translated along the phantom central axis by table translation at velocity , where is the gantry rotation period (in s), which has the familiar form of a traveling wave.

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FIG. 2.

Accumulated dose at constant mA for a superposition (summation) of the 11 dose profiles () depicted, where assumes integral values between (−5 ≤ ≤ 5), each profile having an aperture of = 26 mm and spaced at like intervals using a table increment = = 26 mm (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 (0) due to scatter. In such a scan series with multiple adjacent profiles, the scatter contribution at = 0 is built up by the scatter tails of the entire ensemble of profiles reaching back to z = 0.

Image of FIG. 3.

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FIG. 3.

Realistic example of a clinical auto TCM () profile, including chest and abdomen.

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FIG. 4.

(a) Accumulated dose obtained from the summation of the = 11 individual mA-weighted dose profiles (), individually depicted in the figure, based on the (z) profile mA3 (also plotted), having the common average ⟨ = 3.73⟩ of the entire family of four mA profiles. The same scan interval = = 26 mm used in Fig. 2 applies here (and in all other examples). (b) A logarithmic plot of the data depicted in the linear plot of Fig. 4(a) 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() for the three 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.

Image of FIG. 5.

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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 = 286 mm, namely, ⟨mA = 3.73⟩, where the constant mA value is likewise mA = 3.73, such that the scanner will report the same value of “CTDI” for all family members [without making any distinction between for those using TCM with variable mA(z) and the bona fide CTDI at constant mA in profile mA].

Image of FIG. 6.

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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 . The actual constant mA used is likewise equal to 3.73, hence all have the same , and identical scanner-reported values of “CTDI.” The common number of rotations = 11 additionally confers the same integral dose and DLP.

Image of FIG. 7.

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FIG. 7.

The average dose over the entire scan length = 286 mm, for the family of mA profiles all having the same average mA, the same , and the same scan length = 286 mm and thence the same integral dose and DLP (note that the value of CTDI is above this average as expected).

Image of FIG. 8.

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FIG. 8.

Match between the theoretical analytical dose profiles of Dixon and Boone (Ref. 2 ) and the experimental data of Mori (Ref. 14 ) normalized to unity for = 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 the experimental data or the physics is wrong (or vice versa); fortunately the match is good.


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Various accumulated dose and energy deposition fractions for the central axis of the body phantom at 120 kV and constant mA (aperture ) for which = 117 mm and the S/P ratio = 13, as calculated from Eqs. (14)–(17) above. The bold line = 286 mm refers to our previous simulatioms.


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The scanner-reported CTDI for automatic tube current modulation (TCM) has a different physical meaning from the traditional CTDI at constant mA, resulting in the dichotomy “CTDI of the first and second kinds” for which a physical interpretation is sought in hopes of establishing some commonality between the two.

Rigorous equations are derived to describe the accumulated dose distributions for TCM. A comparison with formulae for scanner-reported CTDI clearly identifies the source of their differences. Graphical dose simulations are also provided for a variety of TCM tube current distributions (including constant mA), all having the same scanner-reported CTDI .

These convolution equations and simulations show that the local dose at z depends only weakly on the local tube current(z) due to the strong influence of scatter from all other locations along , and that the “local CTDI (z)” does not represent a local dose but rather only a relative (z) ≡ mA(z). TCM is a shift-variant technique to which the CTDI-paradigm does not apply and its application to TCM leads to a CTDI of the second kind which lacks relevance.

While the traditional CTDI at constant mA conveys useful information (the peak dose at the center of the scan length), CTDI of the second kind conveys no useful information about the associated TCM dose distribution it purportedly represents and its physical interpretation remains elusive. On the other hand, the total energy absorbed (“integral dose”) as well as its surrogate DLP remain robust between variable () TCM and constant current techniques, both depending only on the total mAs = ⟨ = during the beam-on time .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dose equations for tube current modulation in CT scanning and the interpretation of the associated CTDIvol