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Molière maximum likelihood proton path estimation approximated by cubic Bézier curve for scatter corrected proton CT reconstruction

Lazos, Dimitrios, Collins-Fekete, Charles-Antoine, Evans, Philip M. and Dikaios, Nikolaos (2020) Molière maximum likelihood proton path estimation approximated by cubic Bézier curve for scatter corrected proton CT reconstruction Physics in Medicine & Biology.

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Abstract

A maximum likelihood approach to the problem of calculating the proton paths inside the scanned object in proton computed tomography is presented. Molière theory is used for first time to derive a physical model that describes proton multiple Coulomb scattering, avoiding the need for the Gaussian approximation currently used. To enable this, the proposed method approximates proton paths with cubic Bézier curves and subsequently maximizes the path likelihood through parametric optimization, based on the Molière model. Results from the Highland formula-based Gaussian approximation are also presented for comparison. The simplex method is utilized for optimisation. The scattering properties of the material(s) of the scanned object are taken into account by appropriately calculating the scattering parameters from the stopping power map that is calculated/updated at every iteration of the algebraic reconstruction process. Proton track length constraint imposed by the proton energy loss is also accounted for. The method is also applied in the case that no exit angle data are measured. Geant4 Monte Carlo simulations were performed for model validation. Our results show that use of Molière probability density function for modelling the multiple Coulomb scattering presents a modest 2% accuracy improvement over the Gaussian approximation and most-likely-path method. Simulations of voxelized phantom showed no essential benefit from the inclusion of the material information into the optimization, while path optimization with energy constraint slightly increased path resolution in a bone/water interface phantom. Method error was found to depend on energy, proton track-length within the medium, and proportion of data filtering.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
NameEmailORCID
Lazos, Dimitrios
Collins-Fekete, Charles-Antoine
Evans, Philip M.p.evans@surrey.ac.uk
Dikaios, Nikolaos
Date : 18 May 2020
Funders : EPSRC, Natural Sciences and Engineering Research Council of Canada
DOI : 10.1088/1361-6560/ab9413
Grant Title : EPSRC Grant
Copyright Disclaimer : © 2020 Institute of Physics and Engineering in Medicine
Uncontrolled Keywords : proton computed tomography, multiple Coulomb scattering, Geant4 Monte Carlo, proton stopping power, proton path reconstruction, Bézier curve, scatter correction
Additional Information : Embargo OK Metadata Pending Accepted manuscript online; awaiting final version
Depositing User : James Marshall
Date Deposited : 24 Aug 2020 15:31
Last Modified : 24 Aug 2020 15:31
URI: http://epubs.surrey.ac.uk/id/eprint/858483

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