Research Article Circle Plus Partial Helical Scan Scheme for a Flat Panel Detector-Based Cone Beam Breast X-Ray CT

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1 Hinawi Publishing Corporation International Journal of Biomeical Imaging Volume 2009, Article ID , 11 pages oi: /2009/ Research Article Circle Plus Partial Helical Scan Scheme for a Flat Panel Detector-Base Cone Beam Breast X-Ray CT Dong Yang, Ruola Ning, an Weixing Cai Department of Imaging Sciences, University of Rochester Meical Center, 601 Elmwoo Avenue Rochester, NY 14642, USA Corresponence shoul be aresse to Dong Yang, xy8692@yahoo.com Receive 1 July 2009; Accepte 28 September 2009 Recommene by Seung Lee Flat panel etector-base cone beam breast CT (CBBCT) can provie 3D image of the scanne breast with 3D isotropic spatial resolution, overcoming the isavantage of the structure superimposition associate with X-ray projection mammography. It is very ifficult for Mammography to etect a small carcinoma (a few millimeters in size) when the tumor is occult or in ense breast. CBBCT feature with circular scan might be the most esirable moe in breast imaging ue to its simple geometrical configuration an potential applications in functional imaging. An inherite large cone angle in CBBCT, however, will yiel artifacts in the reconstruction images when only a single circular scan is employe. These artifacts usually manifest themselves as ensity rop an object geometrical istortion that are more noticeable in the reconstructe image areas that are further away from the circular scanning plane. In orer to combat this rawback, a circle plus partial helical scan scheme is propose. An exact circle plus straight line scan scheme is also conucte in computer simulation for the purpose of comparison. Computer simulations using a numerical breast phantom emonstrate the practical feasibility of this new scheme an correction to those artifacts to a certain egree. Copyright 2009 Dong Yang et al. This is an open access article istribute uner the Creative Commons Attribution License, which permits unrestricte use, istribution, an reprouction in any meium, provie the original work is properly cite. 1. Introuction Breast cancer imaging has improve over the last ecae with higher an more uniform quality stanars for mammography as well as through the increasing use of sonography an magnetic resonance imaging as the ajunct tools. Mammography is still the only screening tool to etect breast cancer for asymptomatic women. Due to the limitations associate with the aforementione techniques, such as imaging of the overlapping structure with mammography, technician epenent lack of ability to etect calcifications with ultrasoun, an low specificity an/or poor etection of the tiny calcium eposits with MRI, there remains an eneavor to explore new ways to better etect breast cancer. Recently one of the most exciting ways is cone beam breast CT (CBBCT) technology [1 4]. It is base on a flat panel etector, an with only one circular rotation or some other scanning path, it can provie the three-imensional ensity istribution of the breast, thus greatly eliminating the imaging problem of the structure overlapping seen in mammography to enhance the contrast resolution. It has been shown that the average glanular oses of CBBCT is equivalent to mammography [5, 6];so this technology might have the potential to replace mammography for breast cancer screening an iagnosis. Among all CBBCT technologies, FDK [7, 8] algorithmbase circular scan scheme possesses the following avantages: a stable an simple mechanical configuration, motion artifacts reuction, computation efficiency, an so forth. However, since a single circular source trajectory oes not satisfy the ata sufficient conition [9], the FDK algorithm will unavoiably inuce some artifacts such as an intensity rop along the rotation axis an object geometric istortion in the area further away from the circular scanning plane when cone angle becomes large. In orer to overcome these cone beam artifacts, we propose the circle plus partial helical (CH) scan scheme base on the iea that by partially filling the object support in the Raon omain (i.e., the well-known torus in 3D Raon omain) where the circular scan oes not touch through the aitional scanning trajectory (such as a partial helical orbit), we can acquire more information than from just a single circular scan. The iea behin

2 2 International Journal of Biomeical Imaging the partial helical scan is to improve the image quality by correcting the aforementione artifacts to a certain egree while not exposing the patient with too much raiation exposure. In orer to maintain computation efficiency, a filtere backprojection (FBP) metho is employe for the reconstruction part associate with partial helical scan. Recently, Katsevich an Kapralov [10] propose a circle plus general curve scan algorithm for exact reconstruction, which is also of FBP type; moreover, it is an exact shiftinvariant algorithm an very computationally efficient. The requirements for this aitional scan are that, first, this aitional general curve has to be a piecewise smooth curve (i.e., a straight line or helix); secon, uring this aitional scan the circle trajectory must fin its projection on the etector as it is seen from the X-ray source. General CT scanner an C-arm can easily meet this requirements an exact ROI reconstruction can be achieve by employing this algorithm. In case of CBBCT prototype, however, it is better to keep the X-ray collimation fixe (i.e., half cone illumination) uring aitional noncircular scan to reuce the system complexity since the scanner possesses a half cone geometry covering the whole etector. So the secon requirement with respect to the aforementione Katsevich algorithm is har to meet. Base on this special geometric requirement of CBBCT, the propose partial helical scan part will be reconstructe using a shift-variant filtere-backprojection [11]. When variable size collimation is available, Katsevich type reconstruction can be conucte along a straight line scan in numerical simulation. The hybri reconstruction metho is aopte for both cases. For the propose CH scheme, the reconstruction is compose of three parts: FDK term for circle [7], Hui s term for circle [12], an a shift-variant FBP term for partial helical scan, whereas for circle plus straight line (CL) scheme, the reconstruction is compose of two terms, circle an straight line reconstructions [13]. Instea of using Hilbert reconstruction for circle part presente by original algorithm, FDK was use ue to the better computational efficiency an spatial resolution [14]. Results from both cases are compare an iscusse. Overall, computer simulations base on the numerical breast phantom verifie that the propose CH scheme outperforms the FDK-base single circular scan scheme. 2. Methos an Materials 2.1. Data Acquisition Analysis in Terms of Raon Domain. It is well known that a single circular cone beam scan oes not provie complete information for an exact reconstruction. This can be appreciate by the 3-D Raon transform of the object function f ( r), which is mathematically shown as Rf ( ρ ε ) = f ( r ) δ ( r ε ρ ) r. (1) The equation above represents a 3-D Raon transform of f ( r) along the plane efine by r ε = ρ. One of the properties of 3D Raon transform is that an object with a spherical support in object space has the same size of spherical support in Raon space. In cone beam projection, the istance between the X-ray source an the rotation center X C 1 Virtual etector Circle scan trajectory O Y Z N θ ρ ε ϕ D o C 2 Raon shell Figure 1: Illustration of 3-D Raon transform an Raon shell in object space. is the iameter that etermines a spherical Raon shell where the points on this Raon shell are Raon points in Raon space. Their values are represente by the integral of the plane that is efine by r ε = ρ in the object space. Figure 1 illustrates the 3-D Raon transform an concept of the spherical Raon shell. XOY efines a scanning plane, an the point C represents one X-ray source on the circle scan trajectory; O is the rotation center; OC is the iameter by which a Raon shell is efine; D o is a point on the Raon shell; N is a point where the line CD o intersects the virtual etector. C 1 C 2 is a line that crosses the point N an is perpenicular to the line ON, CC 1 C 2 efines a plane (i.e., Raon plane) where its normal is ε, an the istance from the rotation center O to this plane which is also the length of the line OD o is ρ. The corresponing Raon point D r in Raon omain that is efine by the Raon plane CC 1 C 2 in the object space is illustrate in Figure 2. During a circular scan, this spherical Raon shell sweeps aroun the rotation axis (Z axis) to constitute a torus in a 3-D Raon omain. In the CBBCT scanning geometry, the aforementione Raon shell becomes a half Raon shell on the scanning plane; so only a half Raon ball is shown. The light gray volume insie the half Raon ball support is what is calle the missing volume, meaning that no Raon points in this volume can be acquire through circular scan. In the spherical coorinates, this missing Raon volume is expresse as ρ > OC sin θ. We can make two claims by observing this missing Raon volume. (1) When the sampling rate is fixe, more Raon points are neee to fill this missing volume in the part further away from the scanning plane than in the part closer to the scanning plane. This actually inicates that the reconstruction base on the circular scan has more artifacts in the reconstructe slices that further away from the scanning plane than those closer to the scanning plane. (2) The ratio of the raius of the object support an the iameter of the spherical Raon shell etermines the size of the misse Raon ata volume, which results in the reconstructe object that is closer to or farther away from the exact reconstruction. With a fixe iameter (i.e., the istance between the X-ray source an the rotation C

3 International Journal of Biomeical Imaging 3 X O Y Z θ ϕ Missing Raon volume ρ ε D r Object half Raon ball support Figure 2: Illustration of the raon point in the raon omain within object Raon support. center) of the Raon shell, it is evient that the smaller the breast, the better the reconstructe image; the bigger the breast, the worse the reconstructe image in terms of artifacts. Accoring to Chen an Ning [1], when the scanning half cone angle spanne by the breast is within 8 egrees, the circular-base moifie FDK (MFDK) [12] (whichis the aition of first two terms in CH scheme) still provies clinically acceptable reconstructe images. However, as the half cone angle gets bigger than 8 egrees, artifacts such as ensity rop an geometrical istortion are more noticeable in the reconstructe images base on a single circular scan. An aitional scanning trajectory shoul be ae to fill the missing Raon ata volume in orer to prouce clinically acceptable images. Base on the claims mae in the previous paragraphs, the filling of the missing Raon volume probably oes not nee to be complete. In other wors, only part of the missing Raon volume nee to be fille so as to correct to a certain egree of the artifacts associate with a single circle scan. Also note that in practical CBBCT imaging this misse volume is actually a small portion in the half ball Raon support of the object. The sampling rate of Raon ata within this volume oes not nee to be as high as it oes in the volume acquire through a circular scan. These realizations can help us give the patient not too much extra X-ray exposure by introucing an auxiliary scanning trajectory an improve image quality to a certain egree as well. There are a couple of propose circle plus trajectories [11, 13, 15 18]. Due to the special geometrical configuration of the CBBCT, the circle plus arc is not applicable; however the CL seems to be applicable. For ease of operation an in orer to avoi unnecessary extra X-ray exposure, the X-ray half cone collimation associate with the circle scan must be kept for line scan trajectory. If the line-scan trajectory is escribe as φ L (l) = (0, m, l), where m is a constant in the Y-axis, an l is a variable along the Z-axis, representing the line scan X-ray shot position, base on the illustration from Figure 1, we can see that only a half Raon shell associate with each X-ray position uring line scan can be efine an it is tangential to the XOZ plane. In Figure 2, the filling of the Raon ata from this line-scan can only be ae in half of the missing Raon volume separate by the XOZ plane. Since the missing Raon volume is symmetrical aroun the rotation axis (Z axis), then this unsymmetrical filling of the Raon ata in terms of projection angle in the missing Raon volume may not achieve the best reconstruction result. By taking avantage of the circular scanning feature of CBBCT, one way to combat this unsymmetrical filling is to lower own the X-ray tube an etector while simultaneously rotating them aroun the breast to achieve an approximate symmetrical filling of the Raon ata in the missing Raon volume. It is like the helical scan but with sparse X-ray shots at positions escribe as φ HL (β i, l i ) = (D cos β i, D sin β i, l i ), where D is the istance from the X-ray tube to the rotation center, an l i is the position along the Z axis, an can be escribe as l i = l 0 +(i 1)Δl,wherel 0 is the starting position along the Z axis for this partial helical scan, i is inex of X- ray shot, Δl is the line increment along the Z axis, an β is the projection angle, an also can be escribe as β i = (i 1)Δβ, where Δβ is the projection angle increment in the unit of raians. The Raon ata acquire through this scanning trajectory can fill the part of this missing Raon volume. Thus the result is not an exact reconstruction. The key point here is to introuce the aitional scanning trajectory so as to correct to a certain egree the reconstruction artifacts associate with a single circular scan. For comparison, a CL scanning is also conucte in numerical simulation base on Katsevich s concept uner the less restrictive conitions. During the line scanning, the etector is always fixe at the position where circle scan is conucte, an the X-ray collimation size varie to make sure that X-ray illumination always covers the whole etector as it moves along the line trajectory. In this way, the missing raon volume is fille completely an an exact reconstruction can be achieve through CL scan Scan Design for the Partial Helical Scan an Straight Line Scan Trajectory. Base on the geometric parameters of current CBBCT, we esigne a new scan scheme. The position of the X-ray source is at z = 0 cm uring the circular scan. After the circular scan, the X-ray source an etector lower own simultaneously while they are still rotating. When the X-ray source gets to the point where z = l 0 (we will talk later how we choose the l 0 ), it starts to shoot at positions escribe as φ HL (β i, l i ) = (D cos β i, D sin β i, l i )(i = 0ton), an the X-ray source maintains the same half cone illumination for each shooting as it is with circular scan; so part of the breast in each helical shot between z = 0an z = l i (i = 0ton, n is total number of X-ray shots uring partial helical scan) can avoi being expose by the X-ray. The projection angles associate with partial helical scans are uniformly istribute within 2π range. There are32 an 64 X-ray shots uring partial helical scans that uniformly cover the angular range of 2π, an the movement in the Z irection is from 49 mm to 121 mm with the increment

4 4 International Journal of Biomeical Imaging Detector Breast W Line scan trajectory the whole etector, an the length of this scanning line is 2W. The circle trajectory can always be projecte onto the etector as it is seen from the X-ray source uring the straight line scan, thus enabling us to use Katsevich s algorithm to o the reconstruction for this line scan part. 2W 2.3. FBP Reconstruction Algorithm Associate with DifferentScanSchemes Figure 3: Illustration of the straight line scan to achieve exact reconstruction. Z Algorithm for CH Scan Scheme. Composite reconstruction framework is probably the most preferable algorithm for the CBBCT. The reconstructe object is f ( r) ancanbe mathematically escribe by the following equation: f ( r ) = f cir ( r ) + fhui ( r ) + fhl ( r ), (2) T X Virtual etector O β (t, z) r where f cir ( r) is the reconstructe object from a single circular scan; f Hui ( r) isthereconstructeobjectfromhui sterm base on a single circular scan; f HL ( r) is the reconstructe object from a partial helical scan; Figure 4 escribes circular scan geometry. The mathematic equation of f cir ( r) an f Hui ( r) canbe expresse by (3)an(5), respectively, as follows. (i) FDK algorithm: Y Figure 4: The geometric illustration of a circular scan. S ( ) 1 f cir r = 4 π 2 2 ( + r s ) 2 P 1 (t, z)β, (3) where interval of 2.34 an 1.15 mm base on the size of the simulate breast phantom. The reason we chose the starting position at Z = 49 mm for partial helical scan is because we foun that base on our simulate scanning geometrical parameter the attenuation coefficient rop in the regular circular scan starte approximately at Z = 49 mm. Some of the Raon ata points acquire from this aitional scanning trajectory still can be acquire through a circular scan. This is what is calle reunant sampling points in the Raon omain an can be efficiently eliminate by a winow function. The geometric setup of the collimation uring the partial helical scan is maintaine as it is with the circle scan, that is, the half cone illumination geometry. This can avoi the reunant sampling in the missing volume in the Raon omain within the X-ray shots in a helical trajectory. Since the collimation uring partial helical scan unavoiably encounters the longituinal truncation, a geometric epenent truncation winow function has to be use to hanle this case to remove the incorrect Raon ata. In line scan case, as Figure 3 shows, the virtual etector length along the circular rotation axis is W. Those little black ots represent the X-ray source at ifferent positions in line scan. During the line scan, the etector is fixe an the collimation of the X-ray is aaptively change to cover P 1 (t, z) = 2 + t 2 + z 2 P β(t, z)h(t t )t, t = r T + r S, z = r Z + r S, (4) where h(t) is the impulse response of the regularize ramp filter; P β (t, Z) is the cone beam projection ata. (ii) Hui s term: where ( ) 1 f Hui r = 4π 2 P 2 (z) = z z ( + r s ) 2 P 2 (z) β, (5) 2 + t 2 + z 2 P β(t, z) t, z = r Z + r S. (6)

5 International Journal of Biomeical Imaging 5 Z c 2 Truncate breast projection image X Virtual etector N l ϕ θ ρ O D D c 1 T X Ω Z i φ β θ ρ O φ φ Zi (β) S Y Helical scan trajectory Y Figure 5: The Geometrical illustration of the same Raon value efine in object coorinates an reconstruction coorinates associate with the partial helical scan. Helical scan term: ( ) 1 Zn π/2 f HL r = 4π 2( + r s ) ( ) Z H Zi l, ϕ ϕ, Z 0 π/2 ( ) H Zi l, ϕ = cos ϕ ( ) ( ) w Zi l, ϕ wtrzi l, ϕ ( ( ) 2l Z i l, ϕ 2 l ( ) l, ϕ = Z i l t 2 + Z 2 + P Z i (t, Z) δ ( t sin ϕ + Z cos ϕ l ) t Z, ( ) ) Z i l, ϕ l 2 ( ) 1, 2lZ i cos ϕ + Zi 2 cos 2 ϕ 2 sin 2 ϕ>0, w Zi l, ϕ = 0, otherwise, ( ) 1, line c 1 c 2 oes not cross the region of Ω, w trzi l, ϕ = 0, line c 1 c 2 crosses the region of Ω. (7) Base on Figure 5, the reconstruction term for partial helical scan can be formatte as a type of filtere backprojection (FBP) base on the 3-D Raon inversion formula [11]. The mathematic equation of f HL ( r) is expresse as (7). As was state in Section 2.1, a reunant winow function w Zi (l, ϕ) is use to remove Raon points that are acquire through partial helical scan but have alreay been, touche by previous circular scan uring the reconstruction. As Figure 5 shows, Raon plane SC 1 C 2 efine in the reconstruction coorinates uring partial helical scan correspons to a Raon point expresse as (ρ, φ, θ)interms of spherical coorinates. This Raon point must be mappe to the Raon omain efine by the object coorinates expresse as (ρ, φ, θ) in orer to construct the winow function w Zi (l, ϕ). P Zi (t, Z) is the projection ata associate with each X-ray position uring partial helical scan. This helical reconstruction formula is actually similar to what was presente by Hu [11], except that a partial longituinal truncation winow function w trzi (l, ϕ) is inclue in this paper. Base on the scanning esign, the partial helical scan will unavoiably encounter the longituinal truncation uring the scan. Some Raon points it acquires o not reflect the actual Raon ata an shoul be remove uring the back-projection [19]. Winow function w trzi (l, ϕ) is use to achieve this purpose Algorithm for CL Scan Scheme. The final reconstruction is compose of two parts, first one is from circular scan, the secon one is from straight line scan, an can be mathematically escribe by the following equation: f ( r ) = f cir ( r ) + fline ( r ). (8) f cir ( r) isescribeby(3), an f line ( r) willbereconstructe using Katsevich s algorithm. Figure 6 geometrically illustrates the straight line scan. The curve escribe by z(x) on the virtual etector is the projection of circle

6 6 International Journal of Biomeical Imaging Z Virtual etector Truncate breast projection image Line scan trajectory z(x) X-ray source O H X Y Figure 6: Illustration of straight line scanning. (a) FDK (b) Hui term (c) MFDK () Helix recon (32 shots) (e) MFDK + Helix (32 shots) (f) Helix recon (64 shots) (g) MFDK + Helix (64 shots) (h) Phantom image Figure 7: Central sagittal image comparison between MFDK, phantom, an circle plus partial helical term with ifferent sampling intervals. (a) Circular FDK reconstruction; (b) circular Hui s term; (c) MFDK reconstruction (circle FDK + Hui term); () partial helical reconstruction (32 X-ray shots uring helix scan); (e) MFDK + Helix reconstruction (32 shots for helical scan); (f) partial helical reconstruction (64 X-ray shots uring helix scan); (g) MFDK + Helix reconstruction (64 shots for helical scan); (h) phantom image of the same sagittal slice.

7 International Journal of Biomeical Imaging 7 Iso istance Magnification factor Detector pixel pitch Table 1: Partial helical scan parameters. Number of projections Detector size Scanning starting position Scanning ening position Sampling interval along scanning axis 650 mm mm Z = 49 mm Z = 121 mm Δl = 2.34 mm (64) (Δl = 1.15 mm) Iso istance Magnification factor Detector pixel pitch Table 2: Straight line scan parameters. Number of projection Detector size Scanning starting position Scanning ening position Sampling interval along scanning axis 650 mm mm Z = 0mm Z = 510 mm Δl = mm (210) (Δl = mm) (64) (Δl = mm) trajectory seen from the current X-ray source. f line ( r) is mathematically escribe as ( ) 1 1 f line r = 2π 2 y ( ) l r 2π 0 l P( y ( ) ( )) (9) l, Θ l, r, y γ sin y l. The implementation of the f line ( r)canbereferreto[20, 21]. Please note that uner the current CBBCT geometry, the curve z(x) is escribe mathematically as z(x) = H [ ( ) ] x 2 1. (10) 2 Apparently, this is a parabola with its vertex at (0, H/2), where z an x are the vertical an horizontal coorinates on the etector, an H is the istance of X-ray source to the circular scanning plane. The filtering lines (on which the Hilbert filtering are conucte) are etermine by the intersection of the flat panel etector with the planes tangent to the curve z(x). On the etector this line can be escribe as z l (x) = Kx+b,whereb>H/2. By inserting this line equation into (10), the tangent filtering lines can be escribe as 2Hb H 2 z l (x) =± x + b, (11) where b is actually the intersection of those lines with the Z axis an can be use as an inex parameter. Note from (11) that there are two sets of filtering lines that can provie the ouble coverage of the etector area above the curve z(x). Hilbert filtering on these two sets of lines shoul be carefully treate since Hilbert filtering is sensitive to the filtering irection. In the current simulation, contributions from these two sets of filtering lines are ae. 3. Computer Simulation 3.1. Description of the Mathematic Breast Phantom an Scanning Parameter Settings. Computer simulations are carrie out on a mathematic breast phantom that was create for this stuy. This breast phantom is a half-ellipsoi with three half-axes of 8.8, 8.8, an 16 cm, a large phantom, specifically esigne to aress the artifacts resulting from the single circular scan. The phantom is wrappe by simulate skin with a thickness of 2 mm. Within the simulate skin, the base material is a compoun of aipose an glanular tissues (e.g., 50% aipose an 50% glanular). There are three groups of objects insie the breast phantom. Within first two groups are two sets of spheres: one set of carcinoma spheres with iameters of 1, 2, 4, 6, an 8 mm, respectively, locate at the positions where Z = 10, 70, 130 mm from the chest wall, an one set of glanular spheres with iameters of 1, 2, 4, 6, an 8 mm, respectively, locate at the same position as the group of carcinoma spheres. The thir group is compose of two low contrast isk-type objects specifically constructe to aress the geometrical istortion of the reconstructe objects aroun the nipple area locate at the position where Z = 148 mm from the chest wall. The isc length along the X-, Y-, an Z-axis is 10, 10, an 2.5 mm, respectively. The linear attenuation coefficients with respect to skin, base material, carcinoma, glanular, an isk-type object are 0.22, 0.19, 0.23, 0.24, an 0.21, respectively, in unit of 1/cm. The istance between the X-ray source an the rotation center is 650 mm an the etector pixel size is mm; the magnification factor is 1.43; the etector size is 661 by 661. The value of the reconstructe images is converte to CT number by using the 0.25 as the linear attenuation coefficient of water. Tables 1 an 2 summarize scanning parameters associate with two auxiliary scan schemes Results Performance with a Different Sampling Interval uring Partial Helical Scan. The simulation was conucte in severalsettings asiscusse in Section2.1. Figure 7 illustrates the comparison of the central sagittal images from CH scheme with ifferent sampling intervals in the helical scan an phantom. The angular scanning range is 2π within a partial helical scan. The objects at ifferent layers within the

8 8 International Journal of Biomeical Imaging (a) FDK (b) Line scan (556 shots) (c) FDK + Line scan (556 shots) () Line scan (210 shots) (e) FDK + Line scan (210 shots) (f) Line scan (64 shots) (g) FDK + Line scan (64 shots) (h) Phantom Figure 8: The central sagittal image comparison between phantom an CL scan scheme with ifferent sampling intervals along straight line trajectory. (a) Circular FDK reconstruction; (b) straight line scan reconstruction (556 shots); (c) FDK + Line reconstruction (556 shots for line scan); () straight line scan reconstruction (210 shots); (e) FDK + Line reconstruction (210 shots for line scan); (f) straight line scan reconstruction (64 shots); (g) FDK + Line reconstruction (64 shots for line scan); (h) phantom image of the same sagittal slice. breast are simulate tumors with ifferent sizes. The isplay winow is [ ] except Figures 7(b), 7(), an7(f) Performance with a Different Sampling Interval uring Straight Line Scan. The contribution from straight line scan was reconstructe using Katsevich s algorithm. Figure 8 shows the central sagittal image comparison between phantom an CL scan scheme with ifferent sampling interval along the line scan trajectory. The isplay winow is [ ] except Figures 8(b), 8(),an8(f) Profile Comparison between Phantom, MFDK, CH an CL Scan Schemes Figure 9 shows profile comparison between phantom, MFDK, MFDK plus helical scan, an FDK plus straight line scan schemes Performance Comparison between MFDK, CH, an CL, in Terms of Reconstruction Error. A quantitative Table 3: RE (%) of the numerical breast phantom among MFDK, CH, an CL. Scan scheme MFDK (circle) CH (64 shots in Helix scan) CL (556 shots in Line scan) RE (%) measurement of reconstruction error (RE) is conucte accoring to the following formula: N 1 i=0 I r (i) I p (i) RE(%) = N 1, (12) I p (i) where N is the total pixel number of the central sagittal image; I r (i) is the CT number of the ith pixel in the reconstructe central sagittal image; I p (i) is the CT number of the same pixel in the central sagittal phantom image. Table 3 summarizes the RE from ifferent scan schemes Performance over Simulate X-Ray Quantum Noise. In orer to test the performance of this new scheme i=0

9 International Journal of Biomeical Imaging Intensity (CTS) (a) Phantom image with three profile lines Position (pixels) (b) Profile comparison along the mile vertical line in (a) Intensity (CTS) Intensity (CTS) Position (pixels) Phantom MFDK + helix (64 shots) FDK + line (556 shots) MFDK (c) Profile comparison along the left vertical line in (a) Position (pixels) Phantom MFDK + helix (64 shots) FDK + line (556 shots) MFDK () Profile comparison along the horizontal line in (a) Figure 9: Profile comparison between phantom, MFDK, MFDK plus helical scan, an FDK plus straight line scan schemes. (a) Phantom image with three profile lines; (b) profile comparison along the mile vertical line in (a); (c) profile comparison along the left vertical line in (a); () profile comparison along the horizontal line in (a). over the quantum noise that is commonly encountere in practical CBBCT ata acquisition, we generate quantum noise contaminate ata. An X-ray with 60 kvp was selecte which correspons to an effective photon fluence of photons/cm 2 mr [22].Theexposurelevelperprojection was set to 4 mr; so the total exposure level for a circular scan is 1200 mr, for CH in which helix scan has 64 points is 1456 mr an for CL in which line scan has 556 points is 3424 mr. Figure 10 shows the central sagittal image from ifferent scanning schemes when projection is contaminate by quantum noise. The isplay winow is [ ]. 4. Conclusion an Discussion The new scanning scheme of CH scan works better than a single circular scan in terms of image uniformity an geometrical correctness base on the computer simulations of a mathematic breast phantom an a simulate breast phantom on CBBCT prototype stuy. Partial helical scan with ifferent sampling intervals showe that the number of X-ray shootings between 32 an 64 coul provie acceptable reconstructe images in terms of correction to the intensity rop along the scanning axis an geometrical istortion

10 10 International Journal of Biomeical Imaging (a) FDK (b) MFDK + Helix (64 shots) (c) FDK + Line (556 shots) Figure 10: The Central sagittal image comparison between ifferent scanning schemes base on simulate quantum noise in the projection ata. (a) Circular FDK; (b) MFDK + Helix reconstruction (64 shots for helical scan); (c) FDK + Line reconstruction (556 shots for line scan). aroun the nipple area base on the scanning geometrical parameters an breast size. This is encouraging, since the quality of reconstructe images coul improve without too much aitional raiation exposure to the patient. Also note that the smaller the sampling interval (the larger the number of projections) in helical scan, the less the streak artifacts in the correcte area. However, these streak artifacts are faintly visible. In practical situation, the image quality shoul be balance with the sampling interval in helical scan. This new scanning scheme is not intene to conuct an exact reconstruction. Theoretically, when the missing volume in Raon omain is completely fille an at least as ensely sample as those accesse by circle scan, the combine reconstruction is exact. By sparsely sampling the missing volume through a propose scanning scheme, it suffices to correct the artifacts occurring in a single circular scan. On the other han, the new scanning scheme is easy to operate in practice without complicate mechanical moification on the current prototype CBBCT system. As was mentione in Section 2.3.2, an exact FBP type reconstruction was also conucte in numerical breast phantom simulation base on the concept propose by Katsevich about circle plus general trajectory scanning [10]. Three sampling intervals were simulate in the line scanning reconstruction, the first is one an a half times the size of an actual pixel pitch, the secon is four times bigger, an the thir is thirteen an three quarters times bigger. Katsevich s algorithm [13] was use for reconstruction. The results shown in Figure 8 inicate that the bigger the sampling interval, the more blur the eges of the reconstructe objects, an when sampling interval was increase to the point that only 64 X-ray shots require to cover the scanning length, some geometrical istortions were still observe in the combine image (Figure 8(g)). In Katsevich s algorithm, the Hilbert filtration is conucte on the ifferentiate projection ata which was approximate by the ifference of two ajacent projections ivie by sampling interval, an X-ray source corresponing to the Hilbert filtere ifference projection ata was assume to be at the position that is in the mile of these two ajacent corresponing X-ray source positions. Since ifference of two ajacent projection ata can be thought as filtering, so the bigger the sampling interval, the poorer the spatial resolution, an the subtracte ata may not correctly reflect the actual projection geometrical position when the X-ray shots at the assume corresponing position. This is the reason why the aforementione phenomena were observe when the sampling interval gets bigger. This actually states that when Katsevich s algorithm is employe for reconstruction, sampling interval between each projection ata must be taken into careful consieration so as to minimize the reconstruction error as much as possible. Visually, the reconstruction from CL scheme looks smoother than that from CH scheme; all the streak artifacts notice in CH are gone in CL. This can also be appreciate from the profile comparison. The profile comparison in Figure 9 shows that the CL compensates ensity rop artifacts a little better than CH while behave the similar geometrical correction effect as CH oes. This actually confirms our conjecture that by partially filling the missing Raon volume through the propose CH, the reconstructe image quality in terms of correction to those artifacts is close to exact reconstruction; moreover, the qualitative error measurement conucte in Section confirme our conjecture. However the number of X-ray shots is quite ifferent for these two auxiliary trajectories, 64 for CH an 556 for CL, which is a big issue consiering the extra X-ray exposure level to the patient. Furthermore, the practical operation of CH is much easier than CL in which aaptively changing of X-ray collimation poses an impossible mechanical realization. Simulate quantum noise stuy conucte in Section base on mathematic breast phantom showe that the propose CH scheme works as goo as CL scheme. In conclusion, by incorporating a sparse partial helical scanning trajectory into an FDK-base single circular scanning scheme, a new circle plus partial helical scanning scheme was propose to compensate for the artifacts inherite by a single circular scan for CBBCT prototype system. The numerical simulation stuy has emonstrate its feasibility. Acknowlegments This project was supporte in part by NIH Grants 8 R01 EB , R01 9 HL078181, 4 R33 CA94300, an

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