The most likely path of an energetic charged particle through a uniform medium

Williams, D. C.

doi:10.1088/0031-9155/49/13/010

Cited by 143 publications

(173 citation statements)

References 15 publications

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“…Path estimation algorithms usually require the initial and final position (x) and direction (p) of the particles. The most widely used path reconstruction algorithm, the MLP, is a probabilistic method to estimate the particles lateral displacement and angular deflection at certain depth [4] [11]. Schulte et al [6] proposed a matrix based Bayesian MLP formalism, that derives the proton path solving the maximum likelihood problem based on Fermi-Eyges theory.…”

Section: The Most Likely Path Algorithmmentioning

confidence: 99%

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Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

Volz

Collins-Fekete

Piersimoni

et al. 2017

Current Directions in Biomedical Engineering

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A precise relative stopping power map of the patient is crucial for accurate particle therapy. Charged particle imaging determines the stopping power either tomographically -particle computed tomography (pCT) -or by combining prior knowledge from particle radiography (pRad) and x-ray CT. Generally, multiple Coulomb scattering limits the spatial resolution. Compared to protons, heavier particles scatter less due to their lower charge/mass ratio. A theoretical framework to predict the most likely trajectory of particles in matter was developed for light ions up to carbon and was found to be the most accurate for helium comparing for fixed initial velocity. To further investigate the potential of helium in particle imaging, helium computed tomography (HeCT) and radiography (HeRad) were studied at the Heidelberg Ion-Beam Therapy Centre (HIT) using a prototype pCT detector system registering individual particles, originally developed by the U.S. pCT collaboration. Several phantoms were investigated: modules of the Catphan QA phantom for analysis of spatial resolution and achievable stopping power accuracy, a paediatric head phantom (CIRS) and a custommade phantom comprised of animal meat enclosed in a 2 % agarose mixture representing human tissue. The pCT images were reconstructed applying the CARP iterative reconstruction algorithm. The MTF 10% was investigated using a sharp edge gradient technique. HeRad provides a spatial resolution above that of protons (MTF10 10% =6.07 lp/cm for HeRad versus MTF 10% =3.35 lp/cm for proton radiography). For HeCT, the spatial resolution was limited by the number of projections acquired (90 projections for a full scan). The RSP accuracy for all inserts of the Catphan CTP404 module was found to be 2.5% or better and is subject to further optimisation. In conclusion, helium imaging appears to offer higher spatial resolution compared to proton imaging. In future studies, the advantage of helium imaging compared to other imaging modalities in clinical applications will be further explored.

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Section: The Most Likely Path Algorithmmentioning

confidence: 99%

“…To overcome the problem of MCS, various path estimation algorithms have been proposed for protons, of which the most likely path (MLP) algorithm is the most widely used [4][5][6][7][8]. Compared to protons, heavier ions suffer less from MCS, due to on average smaller deflection angles per scattering.…”

Section: Introductionmentioning

confidence: 99%

Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

Volz

Collins-Fekete

Piersimoni

et al. 2017

Current Directions in Biomedical Engineering

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“…7 To simplify matters, we consider proton trajectories projected into the reconstruction plane (u-t plane in Figure 1). Given the position and direction of an incoming proton at point "A" (u 0 ,t 0 ,θ 0 = 0) and the exit position and direction at point "B" (u 1 ,t 1 ,θ 1 ), the MLP t(u) in a homogenous object is given by equation (14) in 7 :…”

Section: B Proton Path Estimatesmentioning

confidence: 99%

Reconstruction for proton computed tomography by tracing proton trajectories: A Monte Carlo study

et al. 2006

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Proton computed tomography (pCT) has been explored in the past decades because of its unique imaging characteristics, low radiation dose, and its possible use for treatment planning and on-line target localization in proton therapy. However, reconstruction of pCT images is challenging because the proton path within the object to be imaged is statistically affected by multiple Coulomb scattering. In this paper, we employ GEANT4-based Monte Carlo simulations of the two-dimensional pCT reconstruction of an elliptical phantom to investigate the possible use of the Algebraic Reconstruction Technique (ART) with three different path-estimation methods for pCT reconstruction. The first method assumes a straight-line path (SLP) connecting the proton entry and exit positions, the second method adapts the most-likely path (MLP) theoretically determined for a uniform medium, and the third method employs a cubic spline path (CSP). The ART reconstructions showed progressive improvement of spatial resolution when going from the SLP (2 line pairs (lp) cm -1 ) to the curved CSP and MLP path estimates (5 lp cm -1 ). The MLP-based ART algorithm had the fastest convergence and smallest residual error of all three estimates. This work demonstrates the advantage of tracking curved proton paths in conjunction with the ART algorithm and curved path estimates.

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“…A possible solution is to measure the trajectory parameters of each proton both upstream and downstream the target together with the residual proton kinetic energy. With this information the so called proton 'Most Likely Path' (MLP) could be estimated [3]. It has been shown that the one sigma envelope of a transverse coordinate of the MLP of a 200MeV kinetic energy proton in 20cm of water is of the order of 0.6mm [3].…”

Section: Introductionmentioning

confidence: 99%

“…With this information the so called proton 'Most Likely Path' (MLP) could be estimated [3]. It has been shown that the one sigma envelope of a transverse coordinate of the MLP of a 200MeV kinetic energy proton in 20cm of water is of the order of 0.6mm [3]. Assigning the proton energy loss to each MLP the 3-dimensional SP map can be constructed, using appropriate reconstructing algorithms [4].…”

Section: Introductionmentioning

confidence: 99%

Development of a Proton Computed Tomography system for pre-clinical tests

Civinini¹,

Brianzi²,

Bruzzi

et al. 2012

2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC)

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Abstract-Proton Computed Tomography (pCT) is an imaging method under investigation with the aim to improve the accuracy of treatment planning and patient positioning in hadron therapy. A pCT system should be capable to measure tissue electron density with an accuracy better than 1% and with a spatial resolution better than 1mm. A first apparatus based on a silicon tracker and a YAG:Ce crystal calorimeter, with a 5x5 cm 2 active area, has been already developed by the authors in the framework of the PRIMA (Proton Imaging) collaboration and tested with proton beams with promising results. A second prototype with larger area (5x20 cm 2 ) and improved data acquisition system is being designed. The details about this new prototype will be presented in this work.

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The most likely path of an energetic charged particle through a uniform medium

Cited by 143 publications

References 15 publications

Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

Reconstruction for proton computed tomography by tracing proton trajectories: A Monte Carlo study

Development of a Proton Computed Tomography system for pre-clinical tests

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