CBCT Equivalent Source Generation Using HVL and Beam Profile Measurements. Johnny Little PSM - Medical Physics Graduate Student University of Arizona

Introduction CBCT has become a routine procedure for image guided radiation therapy in many clinics AAPM TG 75 suggests that: “The introduction of more intensive imaging procedures for IGRT now obligates the clinician to evaluate therapeutic and imaging doses in a more balanced manner” The purpose of this study is to develop a method of modeling the Varian OBI CBCT source for use in accurate Monte Carlo dosimetry simulations Note from Adam: you probably need an introduction/motivation slide here where you quickly make the point that the use of CBCT for IGRT has become very common and should lay out the purpose of your talk. This should be a quickly presented slide.

Overview of method Goal: model the energy spectrum and bowtie filtration using empirical and semi-empirical methods. Half Value Layer (HVL) will be used to characterize the energy spectrum. 2D dose profile measurements with a farmer chamber and Gafchromic film used to characterize the bowtie filter. Measurements will be used to generate an “equivalent source” Equivalent energy spectrum and equivalent bowtie filter 120 kVp was used for this work Note from Adam: This is a suggested slide to explain the goal of the equivalent source.

Varian Linac OBI Measurements for Source and Path Length Characterization

HVL 120 kVp, 4.77 mm Al

Equivalent Spectrum generation algorithm Kerma at a point directly downstream of a bowtie filter made of Al and the initial spectrum I0,E and a defined central thickness of t 0 . K 0 = E=0 kVp I 0,E E exp − μ E,Al t 0 μ tr ρ E,air Kerma at a point downstream of a bowtie filter made of some thickness, tAl , of aluminum is K Al = E=0 kVp I 𝟎,E E exp − μ E,Al t Al μ tr ρ E,air HVL obtained when K Al K 0 = 1 2 = E=0 kVp I 0,E E exp − μ E,Al HVL μ tr ρ E,air I 0,E E exp − μ E,Al t 0 μ tr ρ E,air

Generating equivalent spectra “soft” tungsten spectrum is iteratively hardened by an increasingly thick slab of hardening material The HVL of each hardened spectrum is calculated Equivalent spectrum is defined as the hardened spectrum with a calculated HVL equal to the measured HVL

Equivalent Spectrum

Ionization Chamber measurements Scandatronix/Wellhofer CC13 ionization chamber in air Sun Nuclear 1-D Scanner Exposure profile was sampled every 1 cm across the bowtie filter Source to measurement plane distance of 38 cm 120kVp, 100 mAs, 20 x 20 cm field Each measurement was normalized to the exposure at center

Bowtie Profile Measurements

Bowtie Profile Ion Chamber

Cubic Spline Interpolation Interpolation between data points with piecewise cubic polynomials Cubic spline has the following form over interval [ i, i+1 ]: x t = a x ∗ t 3 + b x ∗ t 2 + c x ∗t+ d x y t = a y ∗ t 3 + b y ∗ t 2 + c y ∗t+ d y Coefficients different for each interval Finds values at intermediate points of a F(x,y) that underlies data

Bowtie Profile w/ Spline Interpolated Ion Chamber Data

Ion Chamber vs Interpolated Ion Chamber

Photopolymerization Gafchromic XR opaque, active layer, laminated layer 0.1 – 20cGy One photochemical reaction can cause thousands of molecular monomer reactions to form a polymer At least ten hours to fully polymerize

Film Scans Films cut to fit dimensions of scan bed to standardize orientation Measurements taken with 20 x 20cm field Red channel extracted OD=ln PV bkg PV xposed Dose=ϕ∙ dT ρdx Since OD∝ϕ, OD ∝ Dose 2-D wiener used to reduce outliers

Bowtie Profile w/ Film The polarization effects and energy dependence effects can be see in the in the correction functions. At the gradient of the bowtie filter, were the energy change is the steepest there is an exaggerated response of the film. But the response does level out as bow tie filter levels off, i.e. energy gradient levels out

Film vs Ion Chamber

Equivalent bowtie filter generation Want dimensions of an equivalent bowtie that attenuates the equivalent spectrum in the same manner that the actual bowtie filter attenuates the actual cone beam spectrum Information needed: (a) the equivalent spectrum, (b) the beam profile measurements. NOTE FROM ADAM: This is a lot of words. Try to summarize this a little bit better and then you can explain the slide using words.

Equivalent bowtie filter generation algorithm Kerma at a point directly downstream of a bowtie filter made of Al and the equivalent spectrum IEq,E and a defined central thickness of t 0 . K 0 = E=0 kVp I Eq,E E exp − μ E,Al t 0 μ tr ρ E,air Kerma at a point downstream of a bowtie filter made of some thickness, tAl , of aluminum is K Al = E=0 kVp I Eq,E E exp − μ E,Al t Al μ tr ρ E,air Normalized Kerma K Al K 0 = E=0 kVp I Eq,E E exp − μ E,Al t Al μ tr ρ E,air I Eq,E E exp − μ E,Al t 0 μ tr ρ E,air

Equivalent bowtie filter generation algorithm (1) Using bowtie profile, the measured exposures are normalized. (2) The equivalent spectrum will be transmitted through the defined central ray thickness, the Kerma, K 0 , will be calculated. (3) The equivalent spectrum will then be transmitted through a very thin, uniform sheet of aluminum and the subsequent Kerma, K Al , in air will be calculated. (4) The ratio of the K Al from (3) to the K 0 from (2) will be calculated. (5) Steps (3)-(4) will be repeated iteratively, increasing the Al until the difference between the normalized bowtie profile and normalized equivalent bowtie are minimized. This minimization results in a Al thickness that is unique to the beam profile measurement data location from (1).

Equivalent FBT – Film Beam Profile

Equivalent FBT – Spline Interpolated Beam Profile Actual height dimension of bowtie is 2.7 cm

Conclusion A method has been described that produces an energy spectrum and bowtie filter model Will be used for Monte Carlo dosimetry simulations Method uses actual dose measurements and interpolated dose measurents on CBCT of interest Future work will be performed to evaluate accuracy of Monte Carlo simulations that use equivalent source models

References A. C. Turner and D. Zhang, “A method to generate equivalent energy spectra and filtration models based on measurement for multidetector CT Monte Carlo dosimetry simulations,” Med. Phys. 36, 2154-2164 2009. L. C. Ku, “IGRT with the Varian On-Board Imager” P. Alaei, “Review of the Doses from Cone Beam CT and Their Inclusion in the Treatment Planning” J. M. Boone, “Equivalent spectra as a measure of beam quality,” Med.Phys. 136, 861–868 1986. J. M. Boone and J. A. Seibert, “An accurate method for computer generating tungsten anode x-ray spectra from 30 to 140 kV,” Med. Phys. 2411, 1661–1670 1997. J. H. Siewerdsen, A. M. Waese, D. J. Moseley, S. Richard, and D. A. Jaffray, “Spektr: A computational tool for x-ray spectral analysis and imaging system optimization,” Med. Phys. 3111, 3057–3067 2004.