Analytical equations for CT dose profiles derived using a scatter kernel of Monte Carlo parentage with broad applicability to CT dosimetry problems.

Purpose: Knowledge of the complete axial dose profile f(z), including its long scatter tails, provides the most complete (and flexible) description of the accumulated dose in CT scanning. The CTDI paradigm (including CTDIvol) requires shift-invariance along z (identical dose profiles spaced Sat equal intervals), and is therefore inapplicable to many of the new and complex shift-variant scan protocols, e.g., high dose perfusion studies using variable (or zero) pitch. In this work, a convolustion-based beam model developed by Dixon et al. [Med. Phys. 32, 3712-3728, (2005)] updated with a scatter LSF kernel (or DSF) derived from a Monte Carlo simulation by Boone [Med. Phys. 36, 4547-4554 (2009)] is used to create an analytical equation for the axial dose profile f(z) in a cylindrical phantom. Using f(z), equations are derived which provide the analytical description of Sconventional (axial and helical) dose, demonstrating its physical underpinnings; and likewise for the peak axial dose f(0) appropriate to stationary phantom cone beam CT, (SCBCT). The methodology can also be applied to dose calculations in shift-variant scan protocols. This paper is an extension of our recent work Dixon and Boone [Med. Phys. 37, 2703-2718 (2010)], which dealt only with the properties of the peak dose f(0), its relationship to CTDI, and its appropriateness to SCBCT.

Methods: The experimental beam profile data f(z) of Mori et al. [Med. Phys. 32, 1061-1069 (2005)] from a 256 channel prototype cone beam scanner for beam widths (apertures) ranging from a = 28 to 138 mm are used to corroborate the theoretical axial profiles in a 32 cm PMMA body phantom.

Results: The theoretical functions f(z) closely-matched the central axis experimental profile data for all apertures (a = 28 -138 mm). Integration of f(z) likewise yields analytical equations for all the (CTDI-based) dosimetric quantities of conventional CT (including CTDIL itself) in addition to the peak dose f(0) relevant to SCBCT (allowing direct cross-comparison between CT scan modes and mathematical proofs of several hypotheses of practical utility in CT dosimetry). A fast, analytical dose simulator6 is also demonstrated-successfully matching complex dose distributions measured using OSL and film dosimetry.

Conclusions: The model described allows one to obtain analytical functions describing both the primary and scatter components of the axial dose profile. This model (using no empirical functions or adjustable fit parameters) provides a good match to the experimental data, as well as a complete analytical description of dose for both conventional (axial and helical) CT and cone beam CT. An efficient method whereby the complete data set for both modalities can be obtained from a single measurement of either CTDI100 or f(0) is illustrated. This method is also flexible--allowing calculation of heretofore unattainable doses for recently-introduced shift-variant protocols [e.g., variable pitch (irregular scan spacing), variable aperture, shuttle mode acquisition, and mA modulation schemes].