A polynomial approximation to an exponential growth function for calculating equilibrium dose in CT

We propose a polynomial approach to approximate equilibrium dose A_eq reported in AAPM TG111 method of wide beam CT dosimetry. A formula for Aeq was derived by expanding the exponential growth function in a Taylor series and comparing the resulting function to a polynomial. The formula incorporates coefficients of polynomial fits up to 3rd order. The polynomial coefficients were obtained as fits of the point dose data and used to calculate the length constant β and A_eq. The length constant could also be made available to users by the v endors of various makes and models of CT scanners. We evaluated our polynomial approximation formula for A_eq by comparing with A_eq obtained from measured data in a 256 slice GE revolution CT scanner. To that end, point dose data was collected in 600 mm body and head phantoms with a Farmer chamber for beam widths from 40 to 160 mm. A table of A_eq and length constants β, and plots of fits for various filters (pediatric head, adult head, large body, medium body and small body bowtie filters) were presented. For the 256 slice GE revolution CT scanner, a length constant of β∼= 65 mm can be used for pediatric head, adult head, body (large filter), body (medium filter), and body (small filter) at 120 kV when growth function fit is used. The estimated A_eq using the proposed polynomial based method is within 86.79% (83.14%-90.38%) of A_eq obtained from fitting the growth function for beam widths from 40 to 160 mm. The proposed polynomial based estimation to the equilibrium dose, A_eq, can be readily implemented in practice for point dose measurements of wide beam CT scanners.