Dose equations for tube current modulation in CT scanning and the interpretation of the associated CTDI_vol

Purpose: The scanner-reported CTDI_vol for automatic tube current modulation (TCM) has a different physical meaning from the traditional CTDI_vol at constant mA, resulting in the dichotomy "CTDI _vol of the first and second kinds" for which a physical interpretation is sought in hopes of establishing some commonality between the two. Methods: Rigorous equations are derived to describe the accumulated dose distributions for TCM. A comparison with formulae for scanner-reported CTDI _vol 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_vol. Results: These convolution equations and simulations show that the local dose at z depends only weakly on the local tube current i(z) due to the strong influence of scatter from all other locations along z, and that the "local CTDI_vol(z)" does not represent a local dose but rather only a relative i(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_vol of the second kind which lacks relevance. Conclusions: While the traditional CTDI_vol at constant mA conveys useful information (the peak dose at the center of the scan length), CTDI_vol 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 E ("integral dose") as well as its surrogate DLP remain robust between variable i(z) TCM and constant current i₀ techniques, both depending only on the total mAs = it₀ = i₀ t₀ during the beam-on time t₀.