ACCURATE EXTRACTION OF TISSUE PARAMETERS FOR MONTE CARLO SIMULATIONS USING MULTI-ENERGY CT Arthur Lalonde and Hugo Bouchard Département de physique, Université de Montréal

THE IMPORTANCE OF MC IN RT Monte Carlo (MC) simulations offer many advantages over conventional algorithms for dose calculation: • In brachytherapy , dose deposition depends strongly on Z due to the dominance of 183 MeV protons photoelectric effect at low photon energies. 100 max ] 80 • In particle therapy , accurate beam range Relative dose [%D Muscle 60 Adipose calculation is critical for optimal planning and 40 patient safety. 20 0 0 50 100 150 200 Depth [mm] 2

PATIENT GEOMETRY TO MC INPUTS • One of the key steps in the preparation of a MC simulation is the creation of the patient geometry, including the assignment of material composition in each voxel. • Complete elemental composition and mass density is necessary to calculate the exact cross sections for all interactions considered. • Great attention must be paid to this step as it influences all results generated by the simulation: « Rubbish in, Rubbish out ». 3

THE SCHNEIDER METHOD To extract MC inputs from single energy CT (SECT) data, the gold standard is the method of Schneider et al. (2000). The CT is calibrated to construct a segmented look-up table (LUT) that links every possible HU Composition 23 to a certain set of MC inputs. Composition 1 Composition 2 Composition 3 Composition 4 … 1.8 1.6 1.4 Reference 1.2 SPR dataset ALLO ALLO ALLO ALLO ASTRO 1 0.8 0.6 0.4 0.2 -1000 -500 0 500 1000 1500 2000 2500 3000 HU 4

THE SCHNEIDER METHOD To extract MC inputs from single energy CT (SECT) data, the gold standard is the method of Schneider et al. (2000). The CT is calibrated to construct a segmented look-up table (LUT) that links every possible HU Composition 23 to a certain set of MC inputs. Composition 1 Composition 2 Composition 3 Composition 4 … 2 Connectivetissue .1 1.8 Skin2 8 Skin1 Skin3 Liver3 6 Eyelens 1.6 Mammarygland3 Trachea Liver2 Spleen 4 Redmarrow Pancreas Thyroid 1.4 Kidney1 Adrenalgland Lymph Prostate Mammarygland2 2 Gallbladderbile Smallintestinewall Reference Urine Yellowmarrow 1.2 BrainCerebrospinalfluid 1 Mammarygland1 SPR dataset ALLO ALLO ALLO ALLO ASTRO 1 8 Adiposetissue1 Adiposetissue2 Up to 4.4% 6 0.8 Adiposetissue3 4 errors 0.6 0.4 0.2 -1000 -500 0 500 1000 1500 2000 2500 3000 HU 5

DUAL AND MULTI-ENERGY CT • With dual- or multi-energy CT, HU 1 { empirical LUT are obsolete, as more information can be extracted directly from MECT data { http://www.healthcare.siemens.com/. HU 2 6

DUAL AND MULTI-ENERGY CT • With dual- or multi-energy CT, HU 1 { empirical LUT are obsolete, as more information can be extracted directly from MECT data • Still not enough information to derive directly MC inputs { • How can we use optimally the http://www.healthcare.siemens.com/. HU 2 added information to improve the quality of MC inputs? 7

CT DATA TO MONTE CARLO INPUTS • We want to extract full atomic composition and mass density, but we have only limited information (# of energies) per voxel. • Tissue characterization for Monte Carlo dose calculation from CT data is an underdetermined problem • We propose to use principal component analysis (PCA) on reference dataset to extract a new basis of variables that can describe human tissues composition more ef ficient ly by reducing the dimensionality of the problem. • We call these variables Eigentissues (ET) 8

CT DATA TO MONTE CARLO INPUTS • We want to extract full atomic composition and mass density, but we have only limited information (# of energies) per voxel. • Tissue characterization for Monte Carlo dose calculation from CT data is an underdetermined problem • We propose to use principal component analysis (PCA) on reference dataset to extract a new basis of variables that can describe human tissues composition more ef ficient ly by reducing the dimensionality of the problem. • We call these variables Eigentissues (ET) 9

EIGENTISSUE REPRESENTATION OF HUMAN BODY • All information relevant for dose calculation can be stocked in a vector of partial electron densities: Density of electrons Fraction of electrons of element M in the tissue x = ⇢ e [ λ 1 λ 2 ... λ M ] = [ x 1 x 2 ... x M ] • The ET representation consists of a linear transformation of x: x = y 1 · ET 1 + y 2 · ET 2 + ... + y M · ET M Vector of the partial densities in the M th eigentissue 10

APPLYING PCA TO HUMAN TISSUES • Human tissues are composed of a limited number of elements. Including trace elements, only 13 different chemical components are reported in the literature. • Also, the weight fraction of these elements is often strongly correlated (ex: P & Ca) or anticorrelated (ex: C & O). • The eigentissues allow to characterize human tissues with less than 13 variables without losing much accuracy. 14 14 14

ADAPTATION TO CT DATA • Using a suitable stoichiometric calibration, the photon attenuation of each ET can be estimated for any spectrum or imaging protocol. µ ( E i , ET 1 ) ˆ ⇣ ⌘ µ ( E i , ET 2 ) ˆ k ( i ) 1 ,k ( i ) µ ( E i , x) ⇡ f 2 ,... . ALLO ALLO ASTRO ALLO ALLO . . µ ( E i , ET M ) ˆ 15 15

ADAPTATION TO CT DATA • Once their attenuation coefficient is estimated, the ETs are treated as virtual materials. • If K information is available (i.e. K energies), decomposition is performed to extract the fraction of the K more meaningful ETs in each voxel. 0 1 0 1 − 1 0 1 ˆ µ ( E 1 , ET 1 ) ˆ µ ( E K , ET 1 ) ˆ µ ( E 1 ) y 1 ... B C B C B C . . . . ... A ⌘ . . . . @ @ A @ A . . . . ˆ µ ( E 1 , ET K ) ˆ µ ( E K , ET K ) ˆ µ ( E K ) y k ... 16 16 16

APPLICATION TO DECT: BENCHMARKING WITH OTHER METHODS • Comparison with two recently published methods for the characterization of 43 3 WLP reference soft tissues using DECT: Parametrization 2.5 PCA ETD RMS error [p.p.] • Water-Lipid-Protein (WLP) 2 decomposition (Malusek et al. 2013) 1.5 • Parameterization (Hünemohr et al. 2014) 1 0.5 • Simulated HU for 80 kVp and 140/Sn kVp 0 spectra of the SOMATOM Definition Flash EAC SPR DSCT 17 17

POTENTIAL EXTENSION TO MECT • Separating a 140 kVp 20 1 Energy bin spectrum in five 2 Energy bins energy bins, the 3 Energy bins 15 4 Energy bins RMS error [p.p.] method shows 5 Energy bins improvement in 10 extracting elemental weights with more 5 than two information. 0 H C N O P Ca Element 18 18 18

VALIDATION OF ETD ON PATIENT GEOMETRY Bladde r • A virtual patient generated from real anatomical S mall inte s tinewall Re d marro w data is used as ground truth for MC dose calculation Pros tate Mus cle • A reference tissue with known composition is Fe m ur conical troc hante r Fe m ur s phe rical he ad assign to each voxel, while the density is allowed to Calci fi cations Air vary. Adipos e 3 • SECT and DECT images are simulated using 1.4 Matlab − 3 ) ity (g.cm 1.3 • Dose calculation is performed using the EGSnrc 1.2 ns sde user-code BrachyDose for Brachytherapy and 1.1 Mas TOPAS for proton therapy 1 0.9 19 19

ETD FOR BRACHYTHERAPY: RESULTS SECT - Schneider DECT - ETD Relative error on dose See Poster #144 - Remy et al. 20 20

ETD FOR PROTON THERAPY: RESULTS GT GT ETD SECT 21

ETD FOR PROTON THERAPY: RESULTS GT GT ETD SECT Range error up to 1.5 mm using SECT 22

CONCLUSION • Eigentissues representation of human body composition minimizes the number of parameters needed for accurate characterization • Adapting this representation to material decomposition of CT data allows extracting high quality Monte Carlo inputs from only few measurements • The method is accurate and versatile: • Not limited to only two parameters (EAN and ED) • Valid through the whole range of X-ray energies (e.g. kV and MV) • More accurate dose calculation for both low-kV photons and protons than the gold-standard SECT approach • Associated Publications: • A. Lalonde and H. Bouchard (2016), A general method to derive tissue parameters for Monte Carlo dose calculation with dual- and multi-energy CT , Phys. Med. Biol. • A. Lalonde, E. Bär and H. Bouchar d (2017). A Bayesian approach to solve proton stopping powers from noisy multi-energy CT data, Med. Phys. 23 23

THANK YOU FOR YOUR ATTENTION Acknowledgements: • Charlotte Remy • Est her Bär • Jean-François Carrier • Dominic Bél iveau- Nadeau • Mikaël Simar d 24 24

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