X-ray scatter data for flat-panel detector CT

Physica Medica (2007) 23, 3e15

available at www.sciencedirect.com

journal homepage: http://intl.elsevierhealth.com/journals/ejmp

ORIGINAL PAPER

X-ray scatter data for flat-panel detector CT Yiannis Kyriakou, Willi A. Kalender* Institute of Medical Physics, University of Erlangen-Nuremberg, Henkestrasse 91, 91052 Erlangen, Germany Received 4 August 2006; received in revised form 29 September 2006; accepted 1 December 2006 Available online 28 March 2007

KEYWORDS Flat-panel detector CT; Scatter; Monte Carlo

Abstract In modern X-ray computed tomography (CT) a trend to increased volume coverage by using multi-row detectors is apparent. Flat-panel detector CT (FPD-CT) systems provide an even larger field of measurement which, however, results in an increased scatter fraction. We investigated the scatter intensities registered in the case of FPD-CT. A hybrid model for the simulation of scatter combining deterministic and Monte Carlo methods was used for the scatter calculations. The influence of imaging parameters on the registered scatter intensity was examined both in single projections and reconstructed images. Scatter-to-primary ratios (SPRs) are given for various values of object thickness, field size, object-to-detector distance, incident energy and projection angle. For the simulations, homogeneous water phantoms and realistic patient data sets were used to produce scatter data representative for clinical situations. The SPR increases with object size, collimation and z-extent resulting in SPR [ 1 and respective scatter artifacts in the reconstructed images. In contrary, the scatter intensity decreases non-linearly with the objectto-detector distance. The angular and spatial distributions of scatter form a flat function as compared to the distribution of the primary signal. Single scatter appears to determine the distribution and magnitude of the total-scatter intensity at the detector. ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica.

Introduction CT systems equipped with flat-panel detectors (FPDs) are currently employed in computed tomography (CT) measurements. Scatter has to be taken into account in the designing of these systems and for the optimization of the acquisition parameters. Flat-panel detector CT (FPD-CT) systems provide a large field of measurement due to the use of more

* Corresponding author. Tel.: þ49 91318522896; fax: þ49 91318522824. E-mail address: [email protected] (W.A. Kalender).

detector rows and an increased volume coverage which, however, results in an increased scatter fraction. A scatter-to-primary ratio in excess of 100% has been reported in Ref. [1] for cone-beam CT with a flat-panel imager. It is known from classical film radiography that scattered radiation reduces the contrast in the image by increasing the background film density. In the case of X-ray CT imaging the effect of scatter on the reconstructed images is more complex. Incident X-ray photons are scattered inside the object and if they reach the detector, result in an overestimation of the registered total intensity in each projection which is equivalent to an underestimation of attenuation. This may lead to image artifacts such as ‘‘cupping’’ in homogeneous objects or dark streaks between

1120-1797/$ - see front matter ª 2007 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. doi:10.1016/j.ejmp.2006.12.004

4 image regions of high attenuation [2,3]. As a result of the contamination of collected data with scattered photons, the low-contrast detectability of the system is decreased. Numerous methods for scatter suppression have been published or are already being used. Some methods involve the adjustment of the measurement parameters, e.g. increased air gap or decreased field size [4]. A scatter reduction technique used in projection radiography and currently in FPD-CT implies the use of anti-scatter grids [5e7]. Scatter correction algorithms may provide an elegant solution, but are still an area of development. Many correction approaches are based on scatter estimates or models, which can provide the necessary information in order to reduce scatter artifacts in CT imaging [8e11]. We here use a scatter calculation method, which combines Monte Carlo (MC) with analytical scatter computation methods for the estimation of the scatter-to-primary ratios (SPRs) for C-arm flat-panel CT [12]. Calculating the contribution of total scatter with a conventional MC simulation is usually accompanied with a large computational cost if a smooth signal is required [13]. Based on the predominance of single scatter regarding the spatial distribution of the scatter intensity, a method was pursued which combines a fast and precise analytical calculation of the singlescatter contribution and a coarse MC estimate of multiple scatter as reported in Ref. [12]. We employed this method to investigate scatter intensities relative to primary intensities for FPD-CT and provide scatter data which should help in the designing of FPD-CT systems and scatter correction schemes. Furthermore, the effects of the imaging parameters on scatter are examined in single projections and also in the reconstructed images. Results for scatter-to-primary intensity ratio and scatter fraction are given for various values of object thickness, field size, object-to-detector distance, primary energy and projection angle.

Y. Kyriakou, W.A. Kalender Table 1

Symbols and abbreviations

Nomenclature Symbols Total fan angle collimation at the center of Cf rotation Total collimation at the center of rotation in the Cz z-direction Object-to-detector distance (dod Z RD  rw) dod Ep Energy of primary photon Energy of scattered photon Es Primary intensity Ip Single-scatter intensity calculated Idet s;i deterministically Total-scatter intensity Is Total intensity (It Z Is þ Ip) It DSMC Multiple scatter simulated by Monte Carlo (DSMC Z Is  Is,1) Radius of given water phantom rw Distance rotation-axis to focus RF RD Distance rotation-axis to detector f Fan angle k Cone angle Abbreviations COR Center of rotation FPD Flat-panel detector FPD-CT FPD based CT FS Field size measured at the center of rotation (Cf  Cz) MC Monte Carlo simulation SPR Scatter-to-primary ratio Is/Ip SF Scatter fraction Is/(Ip þ Is)

Energy and spectra A point source of monoenergetic photons or spectra of photons corresponding to the X-ray tube voltages from 40 to 120 kV typical for diagnostic radiology was assumed. We will refer to monoenergetic spectra by stating the incident energy in keV. X-ray spectra were calculated via a semiempirical approach for tungsten targets [14]. In this paper an 80 kV and a 120 kV spectrum filtered with a total of 8 mm Al (inherent and additional filtration) were used as an example of typical FPD-CT spectra.

geometries provided that the source and the detector are given. Geometry definitions used by the simulation for the y/z-plane are shown in Fig. 1. The field size is given at the center of rotation (COR) which is defined by the respective fan angle f and cone angle k. Geometry definitions used by the simulation for the x/y- and the y/z-plane are shown in Fig. 1a, b, respectively. The simulation setup was based on a typical system geometry for a C-arm flat-panel detector CT system which was available to us for experimental verifications (see Table 2). The geometry of the simulated system was based on the Axiom Artis dTA (Siemens Medical Solutions, Forchheim, Germany) equipped with a large area detector of 40.0  30.0 cm2 with a detector layer of 0.6 mm CsI. The focusto-rotation center distance RF amounted to 785 mm and the detector-rotation-center distance RD was set to 415 mm. This geometry was kept as default for the simulations unless an explicit change was required (e.g. see ‘‘Dependence on the object-to-detector distance’’). The object-to-detector distance is defined as the smallest distance between the object and the detector (see Fig. 1). All simulations considered the given system without anti-scatter grid.

Geometry The simulation setup consisted of the source, the object and a detector array. The simulation concept is generalized such that it can be adapted for use with arbitrary

Phantoms For the simulations presented in this paper we used mathematical and voxel phantoms. A series of mathematical water cylinders were used as an example of

Materials and methods Symbols and abbreviations Symbols and abbreviations used throughout this paper are summarized in Table 1.

Materials and geometry

X-ray scatter data

5 Focus

Focus Bow-tie filter

Bow-tie filter

RF=785 mm

Collimator

Collimator κ

φ

z

x

3D Voxel volume

RF

3D Voxel volume

z

x

s1 Irradiated volume

υ

y

Irradiated volume

y

Cφ

υn

Cz

RD=415 mm

s2

Rotation axis

COR

RD Ip

dod

ΔS

dod

det

Is,1

Detector

Detector

(a)

(b)

Figure 1 Geometry definition for x/y-plane (a) and the y/z-plane (b). The field size at the center of rotation (COR) is determined by the respective fan and cone angle (darker regions in both schemes). Note: the example sketches show an FPD and a cylindrical phantom; the simulation can be trivially extended to a cylindrical or arbitrary CT detector shape.

homogeneous objects. The water phantoms ranged in radius from 20 mm to 160 mm and had a height (z-extent) of 240 mm. Only in the case of the investigation of the dependence of scatter on the z-extent of the phantom (see ‘‘Dependence on the z-extent’’), a change of the z-extent was performed. Additionally, voxel phantoms were constructed from clinical CT data sets (low-scatter conditions) and were employed in scatter simulations (see Fig. 2). Head, thorax and hip data sets were selected, representing typical scan regions for FPD-CT scans. For consistency, we restricted the height of the volume to a maximum of 240 mm (see Fig. 2); thus multiple scatter arising from body regions above and below the reconstructed volume was ignored. The investigation of the influence of the z-extent on the object is provided in ‘‘Dependence on the z-extent’’.

Table 2 Specifications of the simulation configurations corresponding to a system available for experimental verifications System

FPD-CTa

RF [mm] RD [mm] Scintillator Pixel size [mm2] Detector area [cm2] f [ ] k [ ] Cf [mm] Cz [mm] FS [mm2]

785 415 CsI 0.31  0.31 (at 2  2 binning) 30  40 19.0 14.25 261 196 Cf  Cz

a Axiom Artis dTA (Siemens Medical Solutions, Forchheim, Germany).

CT scan and reconstruction A rotation over 360 at an angular increment of 1.0 was used for the simulation of FPD-CT scans. The resulting raw data were reconstructed using a Feldkamp-algorithm [15]. We used SheppeLogan convolution kernel for all reconstructions. Scatter simulation We used a hybrid simulation model for the estimation of the scatter intensity: an analytical single-scatter model and a Monte Carlo simulation of multiple scatter [12]. Mathematical objects or patient data sets are voxelized and considered as a scatter source. For the single-scatter simulation every ray is traced from the focus to the voxels in the primarily irradiated field. The simulation procedure for the deterministic calculation of the single-scatter intensity Idet s;1;i for i e [Compton, Rayleigh], for a primary energy Ep can be expressed in a simplified form by: Z     en wiw wdet NEs 1  emdet ðEs Þddet dv Idet ð1Þ s;1;i Ep Z V

In Eq. (1), V is the irradiated volume, wiw is the interaction weight at an arbitrary voxel, wdet is the weight assigned for a photon to be detected, N is the number of incident quanta, and Es is the energy of the scattered photon and the last factor inside the integral describes the detection efficiency. The spatial distribution of scatter was shown in Ref. [12] to be predominantly determined by single scatter; the total-to-single scatter difference images show a low frequency distribution which can be estimated efficiently by a coarse Monte Carlo (MC) simulation of a multiple-scatter estimate DSMC. The simulation result is given by: Is Z

X i

MC Idet s;1;i þ DS

ð2Þ

6

Y. Kyriakou, W.A. Kalender

(a)

Head

90°

180 mm

162 mm

0°

200 mm Thorax

(b)

240 mm

355 mm

235 mm

Hip

(c)

240 mm

375 mm

x

z

245 mm y

Figure 2

y

Voxel phantoms used for the simulation representing typical head (a), thorax (b) and hip (c) regions.

where Is is the total-scatter intensity. The validation of the simulation tool was given in Ref. [12] in comparison to published measured data and Monte Carlo simulations.

Evaluation of scatter intensity and distribution The scatter-to-primary ratio (SPR) is a common way for describing the scatter influence in measured projections [3,16,17]. It is defined as: Is SPRZ Ip

ð3Þ

where Is is the total-scatter intensity and Ip is the primary intensity. Dependence on the primary energy Simulations of two water phantoms of 80 mm and 160 mm radius with a height of 240 mm were performed for energies of 40 keV, 60 keV, 80 keV, 100 keV, 120 keV and 140 keV, respectively. Additionally, the calculations were conducted for polyenergetic spectra of 80 kV and 120 kV as described in ‘‘Energy and spectra’’. The resulting SPR is given as a function of primary energy for two field sizes of 261 mm  196 mm and 130 mm  100 mm (approximately

X-ray scatter data

7

half of the original field dimensions to mimic a smaller detector setup). Dependence on the object-to-detector distance The same cylindrical water phantoms were employed for the assessment of the dependence of the SPR on the object-to-detector distance. Simulations were performed at 60 keV for both phantoms. The energy of 60 keV was chosen as representative for an estimate of the effective energy for typical FPD-CT spectra. For this investigation the default geometry of the system was changed by varying the object-to-detector distance. The dod varied from 100 mm to 600 mm in steps of 100 mm. The field size at the center of rotation and thus the exposed volume changed as we moved the detector by keeping the beam collimated on the detector area. Thereby, the center of the phantom remained at the same distance to focus (RF Z 785 mm). Dependence on object size Simulations were performed for cylindrical water phantoms of 40e200 mm radius and a height of 240 mm. Scatterto-primary ratio values for two field sizes were calculated: the first amounted to 261 mm  196 mm, the second was adjusted to 130 mm  100 mm, as above. The SPR was calculated for 60 keV. We have to mention here that all phantoms were placed such that the phantom center was placed at the COR since this is the common procedure for CT measurements. Thus the dod will vary for each phantom size given by dod Z RD  rw. For water phantoms of 40e 200 mm radius, dod values of 395e215 mm result. The influence of the dod is investigated in ‘‘Dependence of the SPR on the object-to-detector distance’’. Dependence on the collimation Firstly, the dependence of the SPR on the z-collimation only (the fan angle was kept constant) was examined with respect to the two water phantoms with a radius of 80 mm and 160 mm. We started at a z-collimation of 20 mm which

is a typical collimation value for clinical CT and enlarged the value up to 220 mm (typical for FPD-CT) in steps of 20 mm. Secondly, in order to visualize the effects of scatter in the case of an increasing collimation we performed simulations of CT scans for the head, thorax and hip voxel data sets described in ‘‘Phantoms’’. The detector was artificially enlarged to suffice a reconstruction without truncation artifacts. Dependence on the z-extent The ICRU (1962) [18] recommended that conditions for measuring scattered radiation in radiography include a 300 mm  300 mm water box of various thicknesses. The 300 mm represented the z-extent (or the height of the phantoms referring to the geometry definition in this paper as presented in Fig. 1). The investigation in this section aimed to clarify which z-extent of the phantom with respect to the scatter signal still accurately represents the patient, who is not limited in z-direction to 300 mm. Cylindrical water phantoms of 80 mm and 160 mm radius with a variable z-extent were used for the corresponding simulations using a field size of 261 mm  196 mm. The z-extent of the phantom was varied from 200 mm to 800 mm in steps of 100 mm. The choice of the starting zextent was based on the physical collimation of the system, such that the z-extent  Cz. All simulations were performed at 40 keV, 80 keV and 120 keV to cover the relevant energy range for diagnostic radiology and FPD-CT. We evaluated the SPR at the center pixel of the central detector row. Angular dependence of the scatter intensity For a demonstration of the angular dependence (projection angle) of the scatter intensity, the voxel data sets described in ‘‘Phantoms’’ were used, representing inhomogeneous and realistic cases. An FPD-CT scan simulation was performed to obtain two-dimensional projections of primary and scatter intensity for an angular range of 360 and a primary energy of 60 keV. Both primary and scatter

4.5 Monoenergetic Polyenergetic

4

FS [mm x mm] rw [mm]

3.5

260 x 196

160

1

130 x 100

160

0.5

260 x 196

80

130 x 100

80

SPR

3 2.5 2 1.5

0

40

60

80

100

120

140

Energy [keV] / U [kV] (monoenergetic / polyenergetic)

Figure 3 Scatter-to-primary ratios as a function of energy for the water phantoms of 80 mm and 160 mm radius conducted for monoenergetic and polyenergetic radiations. The results for the polyenergetic spectra of 80 kV and 120 kV are plotted at the 80 keV and 120 keV marks (horizontal axis), respectively, to simplify the visualization.

8

Y. Kyriakou, W.A. Kalender

Single-to-total scatter intensity In this section we address the question of which fraction of the total-scatter signal is provided by single scatter. The investigation considered the relation between single scatter and total scatter as a function of object size. The corresponding simulations were performed for cylindrical water phantoms of 20e160 mm radius and a z-extent of 240 mm. The field size was kept constant at 261 mm  196 mm.

SPR

(a)

4 3.5 3 2.5 2 1.5 1 0.5 0

0

100

150

200

Radius [mm]

Figure 5 SPR as a function of the object radius for two field sizes and an incident energy of 60 keV. The SPR increases with object radius for both field sizes.

Results and discussion

rw = 80 mm

Dependence of the SPR on primary energy 200

(b)

300

400

500

600

The dependence of the SPR on the primary energy is shown in Fig. 3 for the two water phantoms of 80 mm and 160 mm radius and for two different field sizes, respectively. Results are presented for both monoenergetic and polyenergetic simulations. The SPR for typical polyenergetic spectra of 80 kV and 120 kV can be considered in an

Relative scatter intensity 1

0.8

0.6

4 rw = 160 mm rw = 80 mm

3.5 0.4

rw = 160 mm

3 2.5

SPR

rw = 80 mm

0.2 1/(dod)2 0 100

50

rw = 160 mm

Object-to-detector distance / mm

Relative scatter intensity

FS = 260 mm x 196 mm FS = 130 mm x 100 mm

Then the ratio of single-to-total scatter intensity as a function of the collimation was determined. Simulations were carried out for Cz varying from 4 mm to 196 mm and a constant fan angle for the water phantom with 160 mm radius. The fraction of the single-to-total scatter intensity of the detector element of the central detector row served as evaluation parameter representing Is,1/Is. Both the investigation of the object size and the collimation used primary energies of 40 keV, 80 keV and 120 keV .

SPR 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 100

5 4.5

SPR

projections were normalized to the unattenuated primary intensity Ip,0. Typical scatter and primary intensity distributions were extracted for 0 (frontal projection), 45 (intermediate) and 90 (lateral projection) according to the notation in Fig. 2. Additionally, the maximum and mean scatter fractions SFmean and SFmax were evaluated as a function of projection angle for the complete rotation.

200

300

400

500

600

Object-to-detector distance / mm

Figure 4 Scatter-to-primary ratios as a function of objectto-detector distance for the water phantoms of 80 mm and 160 mm radius (a). The SPR decreases with object-to-detector distance. Relative scatter intensity as a function of object-todetector distance for the water phantoms of 80 mm and 160 mm radius (b). The scatter intensity falls non-linearly with the object-to-detector distance but does not obey exactly 2  law: Both figures were generated for an incident the 1=dod energy of 60 keV.

2 1.5 1 0.5 0

0

40

80

120

160

200

z-Collimation [mm]

Figure 6 Scatter-to-primary ratios as a function of the collimation in the z-direction for the water phantoms of 80 mm and 160 mm radius at 60 keV. As shown for both phantoms, the SPR increases almost linearly with collimation.

X-ray scatter data

9 Nevertheless, the SPR for FPD-CT is much higher than the SPR for comparable phantoms and energy spectra for clinical single-slice CT [17].

Dependence of the SPR on the object-to-detector distance

6 HU

-24 HU

Cz = 100 mm

Primary only

Scatter-to-primary ratios decreased rapidly as the objectto-detector distance increased. As shown in Fig. 4(a) for a primary energy of 60 keV, the SPR decreased for both phantoms with increasing dod. For a small dod of 100 mm, high scatter-to-primary ratios of 6.9 and 0.98 were registered for the water phantom with 80 mm and 160 mm

Cz = 20 mm

acceptable agreement with monoenergetic simulations between 60 keV and 120 keV. Thus Fig. 3 can be considered as adequate proof that respective monoenergetic simulations can give an acceptable approximation of the SPR as compared to polyenergetic spectra. The dependence of the SPR on primary energy in the range of energies which are relevant for FPD-CT appears to be a slowly varying function. At a primary energy of 40 keV the highest SPR of up to 3.80 was registered for the water phantom and the large field size, which then drops slowly with energy. The water phantom with 80 mm radius and the smaller field size of 130 mm  100 mm provided the lowest SPR of around 0.3 for the two polyenergetic spectra of 80 kV and 120 kV or when averaged over all energies.

Cz = 200 mm

-96 HU

-146 HU

C 0/W 1000

C 0/W 1000

C 0/ W 800

Figure 7 Reconstructions of the central slice of the head, thorax and hip data sets after superimposing the corresponding simulated scatter intensities on the primary signal (upper row) for increasing z-collimation from 20 mm (2nd row) to 100 mm (3rd row) and 200 mm (4th row) for a primary energy of 60 keV. The scatter artifact content increases with collimation, as expected. Note: some bright streak artifacts are due to inadequate sampling and not due to scatter.

10 radius, respectively. A typical FPD-CT scanner with a dod of 250e350 mm offers a strongly reduced SPR. Firstly, the rate of decrease depends on the field size which changes when the detector is moved, because we kept the radiation beam focused on the detector. This means that with increasing dod the field size at the center of rotation decreases. Secondly, the intensity of the scatter 2 radiation also obeys the 1=dod -law at least in a first order approximation which is shown in Fig. 4(b), which is a further reason for the fall-off.

Dependence of the SPR on object radius Fig. 5 shows the SPR results for cylindrical water phantoms of 40e200 mm radius and two field sizes at 60 keV. The SPR increased non-linearly with water phantom radius for both field sizes. For smaller cross-sections the SPR values decreased, whereas in the case of the larger field size a stronger increase rate was registered. The SPR increased more than 40 times when the radius increased from 40 mm to 200 mm. When considering the same situation for the smaller field size of 130 mm  100 mm an increase by a factor of 23.0 was registered. This corresponds approximately to the relative difference of the small field size to the larger field size which provides twice the irradiated area at the COR.

Dependence of the SPR on the z-collimation It was reported in previous studies that scatter-to-primary ratios increase with field size [1,19]. In this section only the z-collimation of the system was varied which is a typical procedure for CT scanners. As shown in Fig. 6 the SPR increased almost linearly with collimation. Some discrepancies are expected due to the limited z-extent of the phantom with 240 mm for the case of the larger collimations. This will be discussed in ‘‘Dependence of the of the SPR on the z-extent’’. Furthermore, when increasing the collimation from 20 mm to 220 mm we registered an increase of the SPR by a factor 7.5 and 8.6 for the water phantoms of 80 mm and 160 mm radius, respectively. Fig. 7 visualizes the effects of scatter in the reconstructed images for increasing z-collimation. As this is a monoenergetic simulation, no beam hardening effects are included in the reconstructed images. Fig. 7 shows the central slice for head, thorax and hip voxel data sets, respectively. The scatter artifact content increases in the images with increasing collimation. For Cz Z 20 mm which corresponds to a typical clinical CT setup, a relative small corruption of the images is observed as compared to Cz Z 100 mm and Cz Z 200 mm which correspond to typical FPD-CT geometries. For consistency it must be mentioned here that Cf is much smaller in the case of FPD-CT scanners. Scatter artifacts are characterized by a ‘‘cupping’’ in the images as clearly shown for the head data and directed dark streaks between bony structures as in the case of the hip. According to Fig. 5, the head is expected to be less prone to scatter artifacts than the hip region. Even though, we register a drop of the CT values in a central region of interest from 6 HU to 24 HU, 96 HU and 146 HU for

Y. Kyriakou, W.A. Kalender Cz Z 20, 100 and 200 mm, respectively, which is a major concern for the evaluation of FPD-CT images.

Dependence of the SPR on the z-extent Table 3 shows the results for the SPR as a function of the object’s z-extent relative to the z-collimation (Dz Z ‘‘zextent’’  Cz) and the energy at a constant z- and f-collimation. The SPR is illustrated for water phantoms of 80 mm and 160 mm radius for the middle pixel of the central detector row. For the FPD-CT geometry and a field size of 261 mm  196 mm it is shown that the SPR increases with the z-extent of the object. The SPR value convergence depends on the phantom size and the energy. At a z-extent of 300 mm which is the z-extent recommended by the ICRU an underestimation of the total scatter intensity is still to be expected. The increase of the SPR with the z-extent is energy dependent especially for the larger phantom where the attenuation paths are longer. Regarding the 160 mm water cylinder radius, an increase of the SPR of 15%, 21% and 27% was registered for 40 keV, 80 keV and 120 keV, respectively, when increasing the z-extent from 200 mm to 800 mm. The impact of the z-extent increase for the water phantom with 80 mm radius was smaller, as shown by the respective SPR increase of 7.4%, 7.6% and 8.3% for 40 keV, 80 keV and 120 keV, respectively. The bold values in Table 3 mark the values of Dz which deviate by less than 2% from the SPR values provided by a z-extent of 800 mm, corresponding to a Dz of 600 mm. For a more practical representation we can also express Dz in terms of half-value layers (HVLs) for water. For a typical body scan a Dz of 3.9, 7.9 and 9.3 HVL of water

Table 3 SPR as a function of Dz Z ‘‘z-extent’’  Cz and energy for water phantoms with radius rw Z 80 mm and 160 mm Dz [mm]

Ep Z 40 keV

Ep Z 80 keV

Ep Z 120 keV

rw Z 80 mm 0 100 200 300 400 500 600

0.74 0.80 0.81 0.81 0.81 0.81 0.81

0.48 0.51 0.52 0.53 0.53 0.53 0.53

0.44 0.47 0.48 0.49 0.49 0.49 0.49

rw Z 160 mm 0 3.48 100 4.05 200 4.07 300 4.08 400 4.09 500 4.09 600 4.09

2.86 3.40 3.59 3.65 3.67 3.67 3.67

2.80 3.40 3.69 3.75 3.81 3.83 3.84

For better representation we rounded up the z-collimation from 196 mm to 200 mm and marked the values bold for which an agreement of <2% is given for the given phantom and energy as compared to the value provided by Dz Z 600 mm.

X-ray scatter data

11

(a)

(b)

(c) 0.14 0.12 0.1 0.08 0.06 0.04 0.02

(d)

(f)

(e)

0.025 0.02 0.015 0.01 0.005

(g)

(h)

100

100

Scatter Primary

(i) 100

Scatter Primary

10-1

10-1

10-1

10-2

10-2

10-2

10-3

0

100

200

300

Detector position [mm]

400

10-3

0

100

200

300

Detector position [mm]

400

10-3

Scatter Primary

I Ip,0

0

100

200

300

400

Detector position [mm]

Figure 8 Two-dimensional primary (aec) and scatter (def) intensity distributions for the head data set for frontal (0 ), intermediate (45 ) and lateral (90 ) views, respectively, for a primary energy of 60 keV. The signals were normalized to the unattenuated primary intensity Ip,0. Figures (gei) show the relative intensity profiles along the central detector row.

corresponding to 100 mm, 300 mm, and 400 mm for 40 keV, 80 keV and 120 keV, respectively, would be necessary to achieve a sufficient convergence. In the case of the head scan this would yield a Dz of 3.9, 5.3 and 7.0 HVL corresponding to 100 mm, 200 mm and 300 mm for 40 keV, 80 keV and 120 keV, respectively. This can be applied well for the case of FPD-CT body scans by continuing the image volume by Dz/2 on each side to get a realistic scatter signal contribution. It is more difficult to draw respective conclusions for a head scan due to the anatomical z-extent limitation. The same holds for paediatric scans which also invoke a limited z-extent, which results in a lower SPR.

Angular dependence of the scatter intensity The simulated projections for the primary and scatter signals for the 0 (frontal projection), 45 (intermediate) and 90 (lateral projection) are shown in Figs. 8e10. The relative two-dimensional scatter intensity distributions (in all three figures noted as def) are dominated by rather

low-frequency components as compared to the corresponding primary distributions (aec). The scatter intensity decreases with the distance to the center of the radiation field both in row and in column directions when observing the intensity fall-off along outer regions of the detector. The scatter intensity is maximal behind regions of low primary attenuation. Accordingly the highest amount of detected scatter in each shown projection is found near the boundary of the object shadow. Nevertheless, the SPR is the highest in the regions of high attenuation as is easily extracted from Figs. 8(gei), 9 (gei) and 10 (gei). Scatter intensity profiles for the central detector row confirm the lowfrequency dominance in the scatter intensity. As far as the primary component is concerned, more high frequency components are seen and a stronger dependence on the projection angle is illustrated in the respective plots for different views. As shown in Figs. 9 and 10, where the objects are obviously not rotationally symmetric, the scatter signal intensity and distribution vary much less than the corresponding primary signal with the spatial and angular positions. As expected, for the case of the head data set in Fig. 8 the angular

12

Y. Kyriakou, W.A. Kalender

(a)

(c)

(b)

0.14 0.12 0.1 0.08 0.06 0.04 0.02

(d)

(e)

(f) 0.025 0.02 0.015 0.01 0.005

(g)

(h)

100

100

Scatter Primary

(i) 100

Scatter Primary

Scatter Primary

10-1 10-1

10-1

I Ip,0

10-2 10-2

10-2

10-3

0

100

200

300

Detector position [mm]

400

10-3

10-3

0

100

200

300

Detector position [mm]

400

10-4

0

100

200

300

400

Detector position [mm]

Figure 9 Two-dimensional primary (aec) and scatter (def) intensity distributions for the thorax data set for frontal (0 ), intermediate (45 ) and lateral (90 ) views, respectively, for a primary energy of 60 keV. The signals were normalized to the unattenuated primary intensity Ip,0. Figures (gei) show the relative intensity profiles along the central detector row.

and spatial variations of the primary signal are lower, but still not comparable to the scatter signal. Furthermore, we investigated the distribution of the scatter fraction (SF) as a function of the projection angle. As shown in Fig. 11 for head, thorax and hip data sets an evaluation of the mean and maximum SF values is provided. For the head phantom in Fig. 11(a) the SFmean and SFmax as a function of the projection angle (0 as shown in Fig. 2) show small oscillations around the values of 0.15 and 0.75, respectively. For the thorax, SFmean and SFmax are higher than for the head phantom as expected (see Fig. 11(b)). SFmean amounts in average to 0.42, whereas SFmax slowly oscillates around the value of 0.91. Analogous, as the results for the hip data set with an average SFmean and SFmax of 0.52 and 0.92, respectively, depict a slightly larger projection angle dependence of the SF than for the head phantom as expected. For both the thorax and the hip regions, an explicit increase of the scatter fraction is observed for intermediate and lateral views as compared to the a.p. or p.a. views.

Single-to-total scatter intensity In this section we look at the quantitative relation between single scatter and total scatter for variable object crosssections. Fig. 12(a) shows the relative fraction of singleto-total scatter as a function of the water phantom radius size for cylindrical water phantoms of 20e160 mm radius at 40 keV, 80 keV and 120 keV. A polynomial fit was applied to the simulated points to provide better visualization. For the FPD-CT geometry and the field size of 261 mm  196 mm, the relative fraction of single scatter to total scatter was found to decrease with phantom size as shown in Fig. 12. Still Is,1 determines a significant part of the total-scatter intensity. The ratio Is,1/Is for the case of the largest cylindrical water phantom of 160 mm radius was found to be about 0.40, 0.29 and 0.24 for 40 keV, 80 keV and 120 keV, respectively. For smaller objects the ratio of Is,1/Is increases because multiple-scatter events are less probable to occur. Because

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Figure 10 Two-dimensional primary (aec) and scatter (def) intensity distributions for the hip data set for frontal (0 ), intermediate (45 ) and lateral (90 ) views, respectively, for a primary energy of 60 keV. The signals were normalized to the unattenuated primary intensity Ip,0. Figures (gei) show the relative intensity profiles along the central detector row.

of the smaller volume size, the photons are more likely to exit the object before undergoing multiple interactions. Especially in the case of smaller objects with a radius of 20e30 mm, a relative fraction of single scatter of about 75e85% was determined. The multiple-scatter fraction increased with increasing energy since photons of higher energy have a larger probability to get involved in multiple interactions without getting absorbed in the volume. The evaluation of the dependence of Is,1/Is on the z-collimation was performed for varying z-collimations of 4 mm up to 196 mm and the water phantom of 160 mm radius. The results in Fig. 12(b) show a relatively weak dependence on the collimation. The ratio Is,1/Is decreases with energy as already mentioned previously. There is a slow drop of the Is,1/Is ratio as a function of collimation for all three energies. The first reason explaining this slow fall-off (as compared to the relation between size and Is,1/Is) is the fact that the z-extent of the phantom was kept constant at 240 mm. In the case of larger z-collimations, a larger z-extent of the phantom indicated to reflect a more realistic relation between single and multiple

scatter with respect to the patient (considering the case of a body section). The second reason for the slow fall-off is that we only modified the collimation, i.e. the cone angle, whilst keeping the fan angle constant. A change in both directions would lead to a larger influence of the field size on Is,1/Is as also reported in Ref. [19]. The investigation of the ratio Is,1/Is can be used for the development of scatter correction algorithms based on a hybrid simulation for scatter. Single scatter was shown to be the most important component of the distribution of scatter in the projections [12]. The fact that its intensity is also significant implies that an exact calculation of single scatter provides a major part of the scatter intensity distribution necessary for a correction algorithm [20].

Summary and conclusions The hybrid simulation method used in this paper is a powerful tool for the investigation of scatter intensities in FPDCT. In combination with a simulation of primary radiation,

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Figure 12 Ratio of single-scatter intensity to total-scatter intensity for the center pixel as a function of water phantom radius (a) shows that the contribution from single scatter decreases with increasing radius. The single-scatter intensity to total-scatter intensity ratio (b) decreases with increasing energy and z-collimation (results are given for the water phantom with 160 mm radius).

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the hybrid simulation can be used for the optimization of imaging parameters and equipment. Furthermore, the method provided a fast assessment of the scatter intensity and low-noise distributions, which can be used as basis for scatter correction models. Parametric scatter models [8] or scatter convolution kernels can therefore be efficiently evaluated.

The investigations of the SPR as a function of several imaging parameters provide an extensive overview of the scatter intensities and distributions in FPD-CT. As expected, the SPR increases with object radius, field size and linearly with collimation. Furthermore, the investigation of the energy dependence yielded a more complex relation between the primary energy and the SPR. There is a weak energy dependence which appears to result from a combination of several complementary reasons. First, an increased photoelectric cross-section regarding primary attenuation and an increased relative Rayleigh cross-section at low energies. Second, at higher energies the primary rays are less attenuated due to the photo-effect but the scatter intensity also increases due to an increased Compton-scatter cross-section. And finally, the attenuation of scatter becomes larger than that of the primary radiation because of the lower energy of Compton-scattered photons and the longer paths of scattered radiation in the object. Using the air-gap technique it is expected that the scatter intensity decreases faster than the primary intensity behind the object because of the shorter distance

X-ray scatter data to the source. The decrease of the relative scatter intensity 2 for realistic field sizes does not fulfill the 1=dod  law which is only approximated when approaching a point source for very small fields, as shown in Fig. 4. The scatter intensity increases with the z-extent of the phantom or patient but converges to a maximum value as shown in Table 3. The Dz required for an adequate convergence depends on the energy and the phantom size. For example, for a bodysection scan with a primary energy of 120 keV an additional z-extent of up to 9.3 HVL of water (4.65 HVL on each side if the object is centered) should be considered. Simulations using realistic patient data sets showed that the necessity of scatter suppression becomes larger with the increased collimation provided by FPD-CT systems. SPR values [ 1 result in severe scatter artifact content in the images as shown in Fig. 7. Nevertheless, the scatter intensity generally showed low-frequency angular and spatial distributions even in the case of strong inhomogeneities like in the case of the hip data set (see Fig. 10). This was confirmed in ‘‘Angular dependence of the scatter intensity’’, where the dependence of the scatter signal on the projection angle is by far lower than the corresponding dependence of the primary signal. Consequently, simulations or measurements of scatter for FPD-CT scans can be carried out with very sparse angular and spatial samplings. The missing projection data can be gained by interpolation [9]. We provided scatter intensity data as a function of the most important measurement parameters in FPD-CT including the impact of geometry, energy and object. Taking into account the difficulties in interpreting measurement results by several scatter measurement techniques, our data compared well with measurements from other investigators [12]. Consequently, the simulation provided realistic and reliable data which are based on existing and already deployed measurement setups (e.g. C-arm units equipped with FPD detectors). The presented data can be used for the optimization of scatter correction techniques or as basis data for design considerations of FPD-CT systems which have to adequately consider the influence of scatter.

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