SU-F-I-39: In Search of Infinity: Finding the Limiting Dose for An Infinite CT Scan On a Cylinder of Finite Length




The ICRU/TG200 phantom is a cylinder of polyethylene, 30 cm in diameter and 60 cm long. The dose h(L) in the central plane of the phantom resulting from a scan of length L increases asymptotically with increasing L to a limiting value Deq. However, even after scanning the entire length of this phantom, it is clear that the resultant dose h(60 cm) is still somewhat below the limiting value. The known behavior of h(L) provides a means for estimating the true limit.


h(L) approaches its limiting but unknown value Deq exponentially. By estimating Deq as Deq* and plotting Deq* − h(L) as a function of L on a semi-log scale, a straight line will result only if Deq* = Deq. If not, there will be significant curvature at the end of the plotted data. Adjusting Deq* by trial-and-error or by an iterative scheme will, if done correctly, accurately determine Deq.


The log of Deq* − h(L) was plotted as a function of L using Microsoft Excel. The coefficient of determination (R-squared) was displayed and Deq* was adjusted until R-squared equaled 1. Alternatively, iteration using the Solver tool in Excel can automatically find the best estimate of Deq. The resultant values for Deq was were an increase of around 1.5% above h(60 cm) for the center and 0.8% at the periphery.


The experiments show that a 60 cm phantom is long enough for the central dose to be within a couple of percentage points of what would be achieved with an infinite phantom. Though this small underestimation of Deq is of little consequence for dose estimates, an accurate determination of Deq allows for a better parameterization of continuous functions representing h(L).