Monte Carlo evaluation of the Filtered Back Projection method for image reconstruction in proton computed tomography

Nuclear Instruments and Methods in Physics Research A 658 (2011) 78–83

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Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

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journal homepage: www.elsevier.com/locate/nima

Monte Carlo evaluation of the Filtered Back Projection method for imagereconstruction in proton computed tomography

G.A.P. Cirrone a,�, M. Bucciolini e, M. Bruzzi g, G. Candiano b, C. Civinini h, G. Cuttone a, P. Guarino c,a,D. Lo Presti f, S.E. Mazzaglia a, S. Pallotta e, N. Randazzo d, V. Sipala d,f, C. Stancampiano d, C. Talamonti e

a Laboratori Nazionali del Sud – National Instiute for Nuclear Physics INFN (INFN-LNS), Via S.Sofia 64, 95100 Catania, Italyb Laboratorio di Tecnologie Oncologiche HSR, Giglio Contrada, Pietrapollastra-Pisciotto, 90015 Cefalu, Palermo, Italyc Nuclear Engineering Department, University of Palermo, Via... Palermo, Italyd National Institute for Nuclear Physics INFN, Section of Catania, Via S.Sofia 64, 95123 Catania, Italye Department of ‘Fisiopatologia Clinica’, University of Florence, V.le Morgagni 85, I-50134 Florence, Italyf Physics Department, University of Catania, Via S. Sofia 64, I-95123, Catania, Italyg Energetic Department, University of Florence, Via S. Marta 3, I-50139 Florence, Italyh National Institute for Nuclear Physics INFN, Section of Florence, Via G. Sansone 1, Sesto Fiorentino, I-50019 Florence, Italy

a r t i c l e i n f o

Available online 12 June 2011

Keywords:

Proton tomography

Monte Carlo simulation

Geant4

Reconstruction algorithm

02/$ - see front matter & 2011 Elsevier B.V. A

016/j.nima.2011.05.061

esponding author.

ail address: [email protected] (G.A.P. Cirrone

a b s t r a c t

In this paper the use of the Filtered Back Projection (FBP) Algorithm, in order to reconstruct tomographic

images using the high energy (200–250 MeV) proton beams, is investigated. The algorithm has been

studied in detail with a Monte Carlo approach and image quality has been analysed and compared with

the total absorbed dose. A proton Computed Tomography (pCT) apparatus, developed by our group, has

been fully simulated to exploit the power of the Geant4 Monte Carlo toolkit. From the simulation of the

apparatus, a set of tomographic images of a test phantom has been reconstructed using the FBP at

different absorbed dose values. The images have been evaluated in terms of homogeneity, noise, contrast,

spatial and density resolution.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

An Italian Collaboration (the INFN PRIMA project and thePRIN2006 funded by the Italian Ministry of Education, Universityand Research) [1] is developing a prototype system for tomo-graphic image reconstruction with high energy (200–250 MeV)proton beams [2–5]. The use of protons, instead of X-rays, hasmany potential advantages. Nowadays, dose calculation in protontreatments is based on a knowledge of the tissue attenuationcoefficients (ms) distribution obtained from X-ray CT data. Theattenuation coefficients are then converted to stopping powermaps to calculate proton dose deposition. Several studies [6–9]have already demonstrated that this conversion leads to errors ofup to 10% in proton range evaluations. The use of protons,permitting the direct derivation of proton stopping powers, woulddecrease the intrinsic errors. Present knowledge of image recon-structions with protons is still limited. The main difficulties comefrom the statistical, non-deterministic, nature of Multiple CoulombScattering (MCS) processes which affect protons in matter. Theapproach adopted for a conventional xCT needs to be revised for

ll rights reserved.

).

protons. The application of the conventional image reconstructionalgorithms normally used in xCT is in fact no longer suitable. Themostly used algorithm is the Filtered Back Projection (FBP), basedon the assumption that the paths of the particles are rectilinear andparallel. When protons are considered it is necessary to determinetheir intrinsic uncertainty through a deeper knowledge of theproton path in the traversed medium. This can be obtained usinga device able to track each proton individually and then usinga formalism [10,11] able to determine the proton path L, alsoreferred to as the Most Likely Path (or MLP) [10,12,14]. The spatialand density resolutions of the reconstructed image increase with aknowledge of L as shown in [12]. In this paper the capabilities ofthe Monte Carlo Geant4 toolkit [17,18] are exploited to simulate apCT apparatus and to generate the projections needed to recon-struct of tomographic images. The Monte Carlo method was alsoused to evaluate the spatial and density resolution variationsobtained with the absorbed dose. The paper is organized as follows.In Section 2 the basic principles of proton imaging are introduced.In Section 3 our improvements in employing FBP for proton imagereconstruction, including a brief introduction to Geant4 physicsmodels and the description of simulated apparatus and phantom,are presented. Finally, Section 3.2 shows and discusses the recon-structed images, and the corresponding noise, in terms of spatialand density resolution.

Fig. 1. Layout of the phantom for density and spatial resolution. For density

evaluation, 45 cylinders are simulated. Each cylinder is identified in the picture

with an order number: the first 23 cylinders (cylinder 0–22) have a density value

lower than background; the cylinders from number 23 to 44 have a density value

higher than background.

G.A.P. Cirrone et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 78–83 79

2. Image reconstruction principles for proton beams

The reconstruction of a pCT image presents additional com-plications as compared to a conventional xCT. The FBP Projectionalgorithm allows the attenuation coefficients map of the object toobtained from a set of measurements of the x-ray attenuationsalong several different directions. Each projection represents theline integral of the attenuation coefficients of the traversedtissues, and the whole projection set is the Radon transform ofthe attenuation coefficient distribution.

For pCT, energy losses in various directions are used to derivethe electronic density map. In this case the starting data are themeasured particle energy losses inside the object. These representthe new projections set along the defined directions. From these,making use of the Bethe-Bloch formula, a relationship betweenthe reciprocal of the stopping power and the electron densitiesalong the proton path L, can be derived:Z Eout

Ein

dE

SðImat ,EÞ¼

ZLreðrÞ dl ð1Þ

where re is the relative electron density with respect to water,Imat is the mean excitation potential of the material, consideredthe same as in water (Imat ¼ I¼ 75 eV [19]), E and S are the protonenergy and proton stopping power in water, respectively.

In this case the projection data set is made up of set of lineintegrals of the electron density along the proton path L. Eq (1)can be expressed in terms of Radon transform in the straight lineapproximation. It therefore represents the basis of FBP applic-ability for image reconstruction in pCT [12].

In order to solve Eq. (1), the residual energy must be experi-mentally measured and the proton path L should be known. Asprotons undergo MCS, their paths L have been estimated using ananalytical formulation [10] which made it possible to derive Lfrom a knowledge of the initial and final energies of protons, aswell as from their position and direction. Once L has beenestimated, the FBP algorithm can be applied, as previously stated,only if the proton paths are assumed to be parallel and coplanar.This can be done by rejecting protons with paths that are far fromthis assumption. In the following section two different exclusioncriteria, adopted for image reconstruction, will be described.

3. Monte Carlo simulations

The main purpose of this work is to test the applicability of theFBP algorithm in the specific case of proton computed tomogra-phy using the Monte Carlo Geant4 toolkit, version 9.3 [17,18] forprojection generation. The Geant4 ‘Standard’ electromagneticpackage coupled with the inelastic ‘Binary cascade’ models hasbeen used for the simulation of the electromagnetic and hadronicprocesses, respectively.

3.1. pCT device and phantom device

In our simulation a cylindrical water phantom with a diameterof 20 cm was reconstructed.

The mathematical phantom, whose scheme is reported inFig. 1, is provided with two different kinds of inserts for densityand spatial resolution evaluations.

To investigate the density resolution (Section 4.2), a set of 45cylinders close to the side surface of the phantom were simulated.These cylinders were filled with water having different physicaldensities, covering the 0.9–1.1 g cm�3 range with a 0:0045 g cm�3

steps. The background density (i.e. the homogeneous part of thephantom) has the exact value of 1 g cm�3. A well-defined holepattern was also simulated, to quantitatively evaluate the image

spatial resolution (Section 4.3). The pattern was made up of 10groups of three cylinders, filled with air and with diametersdecreasing from 8 to 0.5 mm. Also the center-to-center distanceof each hole progressively decreased its value being twice thecorresponding hole diameter (see Fig. 1).

3.2. Physical models

All the possible physical processes for protons and secondaryparticles were activated in the simulation. It is beyond the scopeof this paper to present the details of the Geant4 physics models.We will only emphasise that proton energy losses were calculatedon the basis of the ICRU49 tables [20]. We used the Option 30 ofthe Urban MSC approach. Details of the MCS model can be foundin the Geant4 Physics Reference Manual [21] and in V NIvanchenko [22]. Hadronic processes were also activated in thesimulation, to take account of the contribution of elastic andinelastic nuclear reactions in the total dose calculation.

3.3. Simulation of the whole pCT apparatus

In order to proceed with image reconstruction and with theuse of the two discussed approximations for the FBP application,a realistic pCT system was simulated using the Monte Carloapproach.

The Monte Carlo simulation is used here to retrieve informa-tion on the position, direction and energy of each proton (beforeand after the object) as in realistic experimental conditions. Theproton path inside the object, necessary for the application ofEq. (1), is then calculated using these quantities and employingthe analytical approach described in [10]. Our simulation repro-duces the prototype developed by the PRIMA Collaboration[1,2,4]. It consists of four pairs of silicon microstrip detectors(each with a spatial resolution of about 60 mm in units of r.m.s.)and a final calorimeter. Proton positions and directions aremeasured before and after the phantom with the silicon micro-strip detectors, the final proton energy is measured using ascintillator as the calorimeter. Fig. 2 shows the simulated pCTapparatus with the cylindrical water phantom located after thefirst two detector couples.

A 200 MeV rectangular 1�200 mm2 proton beam was gener-ated with its axis exactly entering the phantom in its center. Inthis configuration, as the beam dimension entirely covers thephantom section, it is possible to reconstruct the image of itscentral slice.

Fig. 2. Layout of the simulated proton Computed Tomography: protons positions

and directions are measured before and after the phantom with two sets of pairs

of microstrip silicon detectors. Final proton energy is measured using a scintillator

as the calorimeter.

Fig. 3. Schematic representation of the central phantom slice divided in channels.

Two possible proton paths are also shown.

Fig. 4. Reconstructed central slice of the phantom at three different dose levels:

1.5 mGy (first column), 6.2 mGy (second column) and 62 mGy (third column).

Images are reconstructed with both Methods A (first row) and B (second row).

G.A.P. Cirrone et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 78–8380

To reconstruct the phantom slices, a number of primaryincident protons from 12 K up to 1.25 M were used. The corre-sponding absorbed doses were estimated using the concept ofComputed Tomography Dose Index (CTDI) [23], simulating atypical cylindrical ionisation chamber positioned along the axisof the phantom and measuring the dose deposited in it.

3.4. Proposed approaches to apply the FBP

The image slices were derived applying the FBP algorithm withsome approximations. The possibility of applying the FBP requiresrectilinear and parallel beams. This condition is satisfied forphotons, but not for protons that are deflected by the nuclei ofthe traversed medium. In order to respect the geometricalrequirements imposed by the FBP algorithm, it was necessaryto select those protons whose trajectory could be consideredrectilinear.

To achieve this the phantom was ideally subdivided intochannels perpendicular to the phantom axis. The channels per-mitted the application of two different exclusion criteria so theFBP algorithm could be applied. These approximations can beseen as two different ways to accept protons for the reconstruc-tion. The first method (hereafter, Method A) selects protonsentering and exiting the same channel without any check ontheir path inside the phantom; the second one (Method B)considers an additional constraint: the proton trajectory L mustnever exceed the given channel at any point. The first caserequires only a knowledge of the initial and final positions, whilein the second case the calculation of the proton path is alsonecessary: this is performed by means of the MLP approach [10].

Fig. 3 shows schematically the two methods used to filterprotons.

The channel thickness was fixed to 1 mm in our studies. This isa compromise between the achievable spatial resolution of thefinal image (the thinner the channels, the better the resolution),the total number of particles that can be considered for the

reconstruction (strictly related to the total dose) and, finally, thetotal computation time required for the reconstruction. Eachimage was realized with 360 contiguous projections obtained byrotating the phantom in an angular range from 01 to 3591. Foreach phantom rotation, the entrance and exit energy, position anddirection of each proton were registered, in the same way as ispossible with our real pCT prototype. These values permitted theprojection data to be derived by numerical calculation of theintegral on the left in Eq. (1).

The projection data were finally arranged in a matrix (sino-gram) and the application of the FBP to this matrix produced thereconstructed tomographic slice.

4. Results

Phantom images were reconstructed using the above mentionedapproaches (Methods A and B) and varying the total absorbed dosefrom 1.5 mGy (corresponding to an overall number of incidentprotons 12.5 K) to a maximum of 155 mGy (obtained for 1.25 Mincident protons). Fig. 4 regroups the reconstructed images of thecentral slice of the phantom for three different values of the absorbeddose: 1.5 mGy (first column), 6.2 mGy (second column) and 62 mGy(third column). For each dose level the image is reconstructed bothwith both Methods A (first row) and B (second row). We observe animprovement of image quality as the adsorbed dose increases andwhen Method B is used as the filtering technique.

4.1. Homogeneity and noise

Image homogeneity was evaluated using a standard proce-dure adopted in medical diagnostic quality assurance. Four ROIs(Regions Of Interest) were acquired in different homogeneousregions of the phantom and the corresponding mean pixel valueshave been calculated for each of them. Homogeneity were thenestimated as the percentage difference between the maximumand minimum of the ROIs mean pixel values. Table 2 reportshomogeneities calculated for all the considered values of dose andfor the two methods.

Image noise can be expressed as the relative standard devia-tion of the value of the pixels calculated in an ROI of thehomogeneous section of the phantom. For each reconstructedimage, an ROI containing about 3000 pixels was chosen. The noisevalues calculated in this way are reported in Fig. 5 versus the totalabsorbed dose and for both Method A and B.

Table 1Correspondence between each hole group, holes diameter and spatial resolution.

The last visible group determines the best spatial resolution achievable.

Holes’ Holes’ Corresponding

group diameter (mm) spatial resolution (Lp/cm)

1 8.0 0.6

2 6.0 0.8

3 4.0 1.2

4 3.0 1.6

5 2.0 2.5

6 1.5 3.3

7 1.0 5.0

8 0.75 6.6

9 0.5 10.0

Table 2Homogeneity values obtained for all the considered dose values with recon-

structed methods A and B.

Dose (mGy) Homogeneity

Method A (%) Method B (%)

1.5 0.24 0.34

3.1 0.31 0.47

6.2 0.10 0.25

15.5 0.08 0.15

31.0 0.05 0.04

62.0 0.18 0.08

155.0 0.10 0.08

Fig. 5. Noise trend for images reconstructed with method A and B at different

dose levels.

Table 3Calculated density resolutions for different dose values and reconstruction

Methods A and B.

Dose (mGy) Density resolution

Method A (%) Method B (%)

1.5 8.6 6.4

3.1 5.6 4.2

6.2 3.3 4.2

15.5 1.1 1.1

31 1.1 1.1

62 1.0 0.6

155 0.6 0.6

Table 4Spatial resolution in terms of visible line-pairs per centimeters as a function of

dose for Methods A and B.

Dose (mGy) Spatial resolution

Method A (Lp cm�1) Method B (Lp cm�1)

1.5 1.2 2.5

3.1 1.6 2.5

6.2 1.6 3.3

15.5 2.5 3.3

31 2.5 3.3

62 3.3 3.3

155 3.3 3.3

G.A.P. Cirrone et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 78–83 81

4.2. Density resolution

A quantitative evaluation of the obtained image resolution interms of density contrast was performed using the Contrast toNoise Ratio (CNR) concept. CNR is analytically defined by thefollowing analytical expression [24]:

CNR¼PVin�PVoutffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s2inþs

2out

q ð2Þ

where PVin is the mean pixel value in an ROI inside a single cylinder,PVout is the mean pixel value measured in an ROI in the neighboringwater medium; sin and sout are the standard deviations of themeasured ROIs.

The CNR hence expresses the difference between pixels valuesin two different regions of the image scaled to the image noise.Higher CNR values hence correspond to a higher image qualityand, in our specific case, CNR permitted the visibility of thecylinders to be quantified with variable densities inside the waterphantom (see Fig. 1).

Similar values of the CNR were obtained by Eq. (2) for the first23 cylinders of the upper side of the phantom (see Fig. 1), i.e. forthe set of cylinders with a density value lower than background.

Following the approach described in [24], the density resolu-tion, or contrast resolution of the image, was evaluated bycalculating the percent density difference between inside andoutside for the last cylinder with a CNR value different from zero.This method was applied to evaluate the contrast resolution foreach absorbed dose level. The results obtained are summarised inTable 3, where the calculated resolution is reported along withthe corresponding total absorbed dose.

4.3. Spatial resolution

A quantitative evaluation of the spatial resolution was per-formed simulating a pattern resolution object, as described inSection 3.1. The object was reconstructed with all the considereddose values and for both Method A and B. The pattern approachfor evaluating the resolution consists in identifying, for eachimage, the last visible group of holes corresponding to a well-defined spatial resolution (Table 1). To improve the detection ofthe visible hole triplet, a line profile is calculated along the centerof the holes, thus permitting the density variations produced bythe holes to be identified. Spatial resolution values obtainedfor both Method A and B and for all dose values are reportedin Table 4.

4.4. The first experimental tomography

Exploiting the capabilities of the apparatus described in [2,26],we realized a first experimental tomography using a clinical

Fig. 6. The phantom used for the first experimental tomography.

Fig. 7. The phantom central slice reconstruction with the FBP method.

G.A.P. Cirrone et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 78–8382

62 MeV proton beam available at the INFN-LNS CATANA [27,28]proton therapy facility. A specific PMMA (PoliMetilMetAcrilato)phantom was developed for this application. The phantom (Fig. 6)was cylindrical in shape (diameter¼20 mm, height¼40 mm) andprovided with two cylindrical air inserts of different diameters(6 and 4 mm). Experimental data were acquired irradiating thephantom at angles from 01 to 1801 in steps of 101, using 105

particles per projection. The previously discussed limitations ofthe FBP and the limited total number of particles used for thereconstruction, produced a relatively low quality image.

Nonetheless, Fig. 7 shows that the air inserts are clearlydiscernible in the image obtained using the FBP method. We arethus motivated to improve the reconstruction algorithm in orderto obtain better results in terms of image resolution.

5. Conclusion

In this work the possibility of applying the well-known FBPalgorithm to the image reconstruction of proton beams has beeninvestigated. Our results demonstrate that a pCT experimentaldevice based on the single tracking approach (see Fig. 2) coupledwith the FBP algorithm permits images with good quality in termsof density and spatial resolution to be reconstructed. At a doselevel of about 15 mGy a density resolution of about 1.1% wasobtained, i.e. about the value needed for a pCT image, with no

differences in the statistical errors between the filtering methods(A and B). Our results compare well with the density resolutionsof about 1% obtained by Schulte [25] (see Fig. 5 in their paper) at adose level of 15 mGy. On the other hand, spatial resolution is theonly image parameter that does not reach the requested value fora good pCT image (1 mm). The best value obtained was 3.3 Lp/cm,corresponding to 3 mm in absolute terms. This value can beachieved with both methods, Method B needing relatively lowdoses (6.2 mGy) to reach this resolution. We conclude thatMethod B allows qualitatively better images to be obtained ascompared to Method A at the same dose level. By comparing ourresults with those obtained by Li et al. in [14] we observe that theapplication of the ART algorithm in a straight line approximationgives analogous results to our FBP application at about the samedose level. In fact, for a dose value of 3.5 mGy, the application ofthe ART algorithm in a straight line approximation producesimages with a spatial resolution between 2 and 2.5 Lp/cm, similarto those obtained at 3.1 mGy with Method B. On the other hand,unlike the FBP, the application of ART allows to overcome thestraight line approximation and to use the best approximation forthe proton path inside the object to be used, i.e. the MLP [10]. Thisadvantage leads to a spatial resolution of 5 Lp/cm, but thismethod requires longer calculation times [13,14]. With advancesin computing speed and algorithms, the reconstruction time maybe substantially reduced by improvements in both hardware andsoftware: for example large-scale parallel computing or optimised(GPU) hardware architectures in consumer, personal computergraphics cards [15,16]. The application of FBP, even imposing thestraight path condition, is still advantageous, with respect toother techniques based on algebraic reconstruction, in terms ofcomputation simplicity and, hence, of the overall limited compu-tation time. The best obtained value, 3.3 Lp/cm, is still notsatisfactory, a result due both to intrinsic MCS processes, causinga proton path which is far from being straight, and to the binthickness chosen to select particles in Methods A and B. In fact, athickness of 1 mm causes further intrinsic indetermination in theproton path inside the object. Improvements in spatial resolutioncould probably be obtained by reducing the thickness of the bin tomake a more stricter selection of the particles to be considered forimage reconstruction. In conclusion, both FBP application, testedin this work, and ART applications [14] need further elaborationand optimisation to achieve the spatial resolution required forproton imaging. Forthcoming works will focus on investigatingfurther this fundamental limitation to the final implementation ofthe pCT technique.

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