An algorithm and program for data processing from Compton scatter imaging device a
Vladimir N. Vasilieva* and Ksenia V. Zaytsevab** Russian Sci. Center of Roentgenology & Radiology, 86, Profsoyuznaya, Moscow, 117997, Russia b Institute for Roentgen Optics, PMZR, 10, 1st Volokolamsky Pr., Moscow, 123060, Russia ABSTRACT
The VolumeScope, a prototype 3D X-ray scanner based on Compton backscatter detection, was designed for examination of a human body electron density distribution. An algorithm and computer program for 3D image reconstruction from the VolumeScope measured data are presented. The reconstruction includes corrections for photon attenuation and multiple scatter in surrounding tissues and postprocessing digital filtering. Properties of multiple scattered photons inside the object of examination were studied by Monte Carlo technique and a geometrical efficiency of the multiple scatter detection was calculated on the base of the collimator design. The contribution of multiple scattered photons in semi-infinite water medium was from 15 to 23% of maximum detector response. The VolumeScope program is described to perform data processing and display the electron density distribution of the object as 2D grayscale images and 3D surfaces of internal structures. Keywords: VolumeScope, Compton scatter tomography, attenuation correction, visualization, multiple scatter.
1. INTRODUCTION The VolumeScope is a prototype X-ray medical scanner for a human body examination based on detection of Compton scattered photons from the point of interest1. The device irradiates the object under examination by a narrow beam of Xrays and detects single scattered photons from the point of measurement by four scintillation detectors supplied with convergent lamellar collimators (Fig. 1). The intersection of the primary beam and the collimators’ focusing zone forms a volume of measurement. As the detector response is proportional to the electron density in this volume, the electron density distribution of the object under examination can be obtained by 3D scanning and some mathematical reconstruction.
Figure 1. Scatter detection by the VolumeScope. *
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**
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A block consisting of an X-ray tube, four detectors and four collimators moves over the object with speed 9 cm/s and scans row by row in a horizontal plane (Fig. 2). After finishing a horizontal slice, the block moves one voxel down and continues to scan next slice. The obtained response distribution is stored as a 3D rectangular grid of volume elements, voxels, of size 2 mm in each direction. Although the detector response is proportional to the electron density in the volume of measurement, some correction is required to obtain the density distribution on the base of measured data. Both primary and scattered beams pass through the object of examination and are attenuated inside it. The attenuation correction factor is significant and heavily depends on the density distribution in the slices between the entrance surface of the object and the volume of measurement. As the X-ray tube and the detectors are placed on the same side of the examined object, only slices over the point of measurement affect on the photon attenuation. A method of the attenuation correction used in the VolumeScope software is described below. Along with single scattered photons from the volume of measurement, a part of multiple scatter passes through the collimator and produces some signal irrespectively of measured electron density. For correct reconstruction, the multiple scattered (MS) fraction is to be evaluated and subtracted from the total detector response. In this study we present a calculation model of the MS contribution. Finally, we demonstrate a computer program to perform measured data reconstruction and electron density visualization as gray-scale images and 3D surfaces of the object. Some postprocessing of reconstructed data allows to improve the image quality and reduce the statistical noise.
Figure 2. VolumeScope collimator design. 1 – a primary beam diaphragm, 2 – lamellae, 3 – collimator frame, 4 – a scintillation detector.
2. DATA CORRECTION The object scanning and data reconstruction are being performed simultaneously slice by slice. As the X-ray tube and the detectors are on the same side of the object, just scanned and processed data can be immediately used for attenuation correction in the next slice. Cal
The attenuation correction was performed on the base of calibration response function N (t ) measured in semiinfinite water medium and parameterized vs. a total medium thickness along the primary and scattered beams. This
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dependence was very close to exponential except for surface buildup region (Fig. 3). The electron density in the volume of measurement was estimated as the responses ratio in actual and calibration conditions without MS contributions.
1.0 Detector #0 Detector #1
Response, arb. units
Detector #2 Detector #3
0.1 0.0
5.0
10.0
15.0
20.0
Total thickness, cm Figure 3. Detector response in semi-infinite water.
Using the calibration data, the electron density at the point r can be calculated as
ε (r ) = where
N (r ) − N MS (r ) , Cal (t (r ) ) N (t (r ) ) − N MS
(1)
Cal
Cal N (r ) is the measured response from the point r , N MS (r ) and N MS are the estimated contribution of multiple
Cal
is the detector response in calibration scattered photons in actual and calibration conditions respectively, N conditions, t (r ) is the total actual thickness (a line integral of electron density) along the primary and scattered beams. In fact, the use of Eq. (1) is based on the t (r ) and N MS (r ) calculation algorithms presented in Sections 3 and 4 respectively.
3. TOTAL THICKNESS CALCULATION Total thickness t (r ) is a sum of the medium thickness along the primary beam and along the scattered beam in the collimator viewing cone t (r ) = t pr (r ) + tsc (r ) . As the primary beam of the VolumeScope is narrow and vertical, the thickness along it can be calculated by summing the electron density in vertical column of voxels from the point r to the entrance surface, i.e.
t pr (r ) =
k max
∑ ε (i , j , k )∆z , r
k = kr
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r
(2)
ir , jr , kr are voxel indexes at the point r , ε (i, j, k ) is the electron density in the voxel of indexes i, j, k , k max is the value of the index at the entrance surface, and ∆z is voxel size along the axis Z. Here and below the electron density ε is relative to water.
where
Calculation of the thickness along the scattered beam is more sophisticated problem, as the beam intersects numerous voxels in the collimator viewing cone (Fig. 4). We used the average thickness in the cone weighted on the scattered photons’ angular distribution and calculated as following.
Figure 4. Thickness calculation in the viewing cone (not in scale).
A number of rays from the point of measurement to the detector were sampled using the differential Klein-Nishina formula (Fig. 4). The thickness along each ray was calculated on regular 3D voxel grid by the Siddon algorithm2 and represented as a sum of ray segments intersecting each voxel weighted on its electron density, i.e. N
ti = ∑ lijε j ,
(3)
j =0
where
ti is the thickness along i-th ray, ε j is the electron density in j-th voxel, lij is the segment length of i-th ray
lij is zero if i-th ray doesn’t intersect j-th
intersecting j-th voxel, N is the total number of voxels. The segment length voxel. Thus, average thickness in the cone is
t=
1 M
M
∑ ti = i =1
1 M
M
N
∑∑ l ε ij
j
,
(4)
i =1 j =1
where M is the number of sampled rays. After some reorganizing the calculation order, we can sum the ray segments intersecting results as voxel weights gi N 1 t = ∑ε j j =1 M
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M
∑l
ij
i =1
N = ∑ε j g j . j =1
i -th voxel and express the
(5)
As the VolumeScope tube/detector block moves along the voxel grid with a step equal to the voxel size, a timeconsuming procedure of the rays generation and segments calculation can be performed once. All intersection points and line segment lengths will be valid after that translation; only voxel indexes are to be changed according to the volume of measurement position. The voxel specific weights gi were generated during the detector data initializing, saved in a configuration file and used in data reconstruction process. Thus, the presented algorithm is in fact a Monte Carlo integration of the response with cashing intermediate geometric data. According our tests, such approach increases the calculation performance about 1600 times in comparison with direct integration by the Siddon algorithm.
4. MULTIPLE SCATTER CALCULATION 4.1. Multiple scatter model In general, the flux of multiple scattered (MS) photons passed through the collimator can be calculated as
Φ MS (r ) = ∫ ϕ MS (r ′)ε (r ′)g (r ′ − r )catt (r ′) dV ,
(6)
V
g (r ′ − r ) is a geometric efficiency of the collimator determined by the lamellae positions, ϕ MS (r ′) is MS photon flux distribution inside the object, ε (r ′) is the electron density distribution of the object, catt (r ′) is an attenuation correction factor between the last scatter point r ′ and the detection point, and V is the volume of the object under examination. Angular distribution of MS photons before last scattering at the point r′ was considered to be
where
isotropic.
g (r ′ − r ) can be calculated from the collimator geometrical parameters as g (r ′ − r ) = ∆Ω(r ′ − r ) / 4π , where ∆Ω(r ′ − r ) is the solid angle of viewing the open part of the detector from the
The geometrical efficiency
point r through the collimator. In most cases except for the collimator focusing zone, only single strip of the detector is visible from the point of last scattering r′ through a single slit between one pair of lamellae. An example of g (r ′ − r ) distribution in the plane orthogonal to the lamellae is shown in Fig. 5. The efficiency peak is in the collimator focusing zone.
Figure 5. Distribution of the collimator geometrical efficiency in vertical plane.
The attenuation correction
catt (r ′) from the last scattering point r ′ to the detector was calculated as
catt (r ′) = exp( − µ eff t eff ) , where µeff is an effective attenuation coefficient calculated on the base of energy spectrum
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of MS photons (see Section 3.3) and
teff is a linear density integral from the point r′ to the detector. The thickness teff
was calculated by the Siddon algorithm with caching the intermediate geometrical data as described in Section 3. 4.2. Monte Carlo simulation Multiple scattered radiation transport inside the object of examination was simulated by the FASTER Monte Carlo code. The code designed for photon and neutron transport simulation was originally developed by Jordan3 and then ported to PC platform. The geometrical parameters of the task were similar to real VolumeScope examination. A primary X-ray beam of 2 mm in diameter was directed into the object of examination and a scattered photon flux was counted in 80 point detectors placed on the rectangular grid with the step 1 cm up to the radius 9 cm from the beam axis and to the depth 7 cm from the entrance surface. Photons of various scatter order were counted separately. An energy spectrum of primary photons was used from the handbook4 for the X-ray tube voltage 160 kV and total beam filtration 0.5 mm Cu and 1 mm Al according to the used VolumeScope parameters. Photon interaction cross sections in water and air were tabulated from the XCOM database5. The photon transport simulation was carried out in homogeneous semi-infinite water phantom and a water horizontal cylinder of 8 cm in diameter simulating a human forearm to estimate the boundary effect. 4.3. Simulation results The results of the calculation are shown in Fig. 6. Radial dependence of multiple scattered photon flux is most pronounced due to cylindrical symmetry of the task. Some scatter buildup with further decrease is noticeable only in the vicinity of the primary beam. The calculation in the cylinder demonstrated a statistically significant difference only near the boundary (within 1-2 cm) due to escape of scattered photons outside. Otherwise both data sets were close to each other. The comparison of the calculation results allowed to separate the boundary effect and fit the correction factor as
k ( r ) = 1 − 0.4871 ⋅ exp( −0.8331r ) , where r is the distance to the nearest boundary.
Figure 6. Distribution of multiple scattered photon flux density around the primary beam in semi-infinite water.
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(7)
Along with the MS flux distribution stability, a stability of scattered photon energy spectrum was found. Fig. 7a shows the spectra of MS photons in nine detectors covering the investigated area. Fig. 7b demonstrates that after normalization all spectra are similar each other. 0.20
0.40
Detectors
Detectors Det #12
N(E), arb. units
N(E), arb. units
Det #12 Det #16 Det #20 Det #42
0.10
Det #46 Det #50 Det #72 Det #76
Det #16 Det #20 Det #42
0.20
Det #46 Det #50 Det #72 Det #76
Det #80
Det #80
0.00 0
50
100
Energy, keV
0.00
150
0
a)
50
100
Energy, keV
150
b)
Figure 7. The spectra of multiple scattered photons in nine detectors, a – as calculated, b – normalized to equal integral.
The obtained stability of MS photon flux distribution around the beam in the VolumeScope allows to fit the data in Fig. 6 by simple analytical function and use it as an universal estimate of ϕ MS (r ′) in Eq. (6). Combining with calculation of
g (r ′ − r ) and catt (r ′) as shown above, these data allows to evaluate the MS detector response from any object of examination with actual electron density distribution ε (r ′) . 5. A STATISTICAL NOISE AND DIGITAL FILTERING A reconstructed VolumeScope image contains a statistical noise of approximately Gaussian distribution and the standard deviation 3.6% as measured in a homogeneous water sample. To reduce the noise, a 2D low-pass digital filter was used. A number of filters with various frequency characteristics were tested with the VolumeScope sample images and a filter with the passband edge 0.3 cycles per voxel was selected for further use. Such filter saves high-frequency details of the image and effectively reduces the statistical noise down to standard deviation 1.6%, i.e. to the level of CT scanners. The filter was constructed on the base of the approach proposed in Ref. 6. The effect of filtering is demonstrated in Fig. 8 with a skull surface reconstructed from measured head data of the ATOM anthropomorphic phantom (CIRS Inc., USA)7. As the figure shows, bone-equivalent cylindrical TLD-inserts were placed in the phantom in front of the eyesockets and in the middle of forehead. The filter coefficients are presented in Table 1. Table 1. The coefficients of used 2D 7 x 7 filter (a quarter is presented, other quarters are symmetrical).
Indexes on Y
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0 0.232276 0.138312 0.0362372 -0.0292847
Indexes on X ±1 ±2 0.138312 0.0362372 0.0940693 0.0219109 0.0219109 -0.0204361 -0.0249658 -0.0104287
238
±3 -0.0292847 -0.0249658 -0.0104287 0
a)
b)
Figure 8. The skull surface before (a) and after (b) low-pass digital filtering.
6. THE VOLUMESCOPE SOFTWARE Currently, the VolumeScope Software consists of two parts: the Scat program controls the primary X-Ray beam, voltage, movements and other device settings; and the VolumeScope Viewer displays the acquired data, reconstructs the electron density distribution and shows the result. Two programs could be connected through the network and allow slice by slice scanning and continuous reconstruction of obtained data. The main window of VolumeScope viewer consists of four areas to display a 3D image, transversal, frontal, and saggital sections of the object (Fig. 9a). Each area has a toolbar to navigate and control (Fig. 9b).
a) Figure 9. Main window of VolumeScope viewer (a) and the toolbar for iso-surface view (b).
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b)
A 3D internal structure of the object is displayed in the 3D View as a set of iso-surfaces calculated from the reconstructed data for user selectable electron density values. The program allows to switch between the surfaces, set the transparency and color of each surface, rotate, translate and scale the image. Sectional views display the data sections slice by slice along any coordinate axis. The slice number and the display mode are user selectable. The data can be displayed as a gray-scale image similar to a CT slice, a set of iso-contours, and a set of flat iso-surfaces (Fig. 10).
a) b) c) Figure 10. VolumeScope Software sectional views: Gray-Scale mode (a), Iso-Contour mode (b), and Flat Iso-Surface mode (c).
The electron density value at the point under mouse cursor can be displayed both in absolute units and as a percentage of maximum density value. A number of auxiliary tools such as angle and distance markers and regions of interest can be used and a statistical information about the region can be calculated including the area, mean value, variance, etc. (Fig. 11).
Figure 11. Gray-scale image with markers and statistical data of the selected region of interest.
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Another useful tool of the data analysis is the density distribution map (Fig. 12) to display the electron density histogram and control the density interval for visualization.
Figure 12. The density distribution map.
The reconstructed data can be exported both in own and DICOM formats. Examples of obtained images of various anthropomorphic phantoms are presented in Ref. 8.
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