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An inverse-geometry volumetric CT system with a large-area scanned

source: A feasibility study

Taly Gilat Schmidt,a)Rebecca Fahrig, and Norbert J. Pelc

Department of Radiology, Stanford University, Stanford, California 94305

Edward G. Solomon

NexRay Inc., Los Gatos, California 95032

?Received 26 November 2003; revised 23 April 2004; accepted for publication 7 July 2004;

published 26 August 2004?

We propose an inverse-geometry volumetric CT system for acquiring a 15-cm volume in one

rotation with negligible cone-beam artifacts. The system uses a large-area scanned source and a

smaller detector array. This note describes two feasibility investigations. The first examines data

sufficiency in the transverse planes. The second predicts the signal-to-noise ratio ?SNR? compared

to a conventional scanner. Results showed sufficient sampling of the full volume in less than 0.5 s

and, when compared to a conventional scanner operating at 24 kW with a 0.5-s voxel illumination

time ?e.g., 0.5-s gantry rotation and pitch of one?, predicted a relative SNR of 76%.

American Association of Physicists in Medicine. ?DOI: 10.1118/1.1786171?

© 2004

I. INTRODUCTION

Volumetric CT imaging was advanced significantly by the

development of multiple-detector computed tomography

?MDCT? systems. These systems provide faster scan times,

thinner slices, and reduced motion artifacts compared to

single-slice scanners.

The volume thickness covered in a single rotation by cur-

rent MDCT scanners is still relatively small; for example

these systems require many gantry rotations to image an en-

tire organ such as the liver. In order to acquire a thicker

volume per rotation, the detector extent in the axial direction

?i.e., in the direction of the axis of rotation? must be in-

creased, leading to a larger cone-beam angle. For a single

rotation cone-beam acquisition ?that is, a point x-ray source

and an area detector rotated in a circle about the patient? an

exact reconstruction is not possible because the acquired data

set is insufficient.1Approximate reconstruction algorithms

are available and generally used.2For small cone angles the

resulting artifacts are negligible, but as the cone angle in-

creases, so do the artifacts. A separate problem with this

approach is that the detector array for such a system is nec-

essarily very large. In order to support short scan times, the

sampling rate for each element needs to be comparable to

that of current clinical CT systems, raising concerns about

cost.

This paper proposes an inverse-geometry volumetric CT

system ?IGCT? for acquiring a sufficient data set of a thick

volume, on the order of several centimeters, in one subsec-

ond gantry rotation. The proposed system uses a large-area

scanned source array and a smaller array of fast detectors. In

the transverse direction the sampling is fanlike, and in the

axial direction the source and detector have the same extent,

in principle providing a sufficient data set for accurate recon-

struction.

We are proposing the IGCT system to achieve volumetric

coverage in a single rotation while avoiding cone-beam arti-

facts. Another approach for achieving this is to use a 1D

scanned source ?scanned in the axial direction? with a large-

area detector array. While both approaches avoid data insuf-

ficiency problems, the IGCT system achieves this using a

smaller detector array, which may provide significant scatter

reduction and cost advantages.

The purpose of this technical note is to introduce the

IGCT concept and to describe two feasibility investigations.

The first examined whether sufficient sampling can be

achieved in a scan time of 0.5 s or less. The second investi-

gation determined whether enough photons are available to

achieve a signal-to-noise ratio ?SNR? comparable to that of a

conventional MDCT scanner.

II. SYSTEM DESCRIPTION

The basic system geometry is illustrated in Fig. 1.

The proposed x-ray source has an electron beam that is

electromagnetically steered across a transmission target,

dwelling at a series of source locations. An array of collima-

tor holes limits the x-ray beam produced at each location so

that the beam illuminates only the detector. The detector is

comprised of a smaller array of fast photon-counting detec-

tors. For each source position, the entire detector array is

read out producing a 2D divergent projection covering a

fraction of the field of view ?FOV?. This is repeated for all

source positions and for all gantry rotation angles. The scan-

ning of the entire source is rapid compared to the rotation

rate.

The source and detector arrays for the proposed system

are conceptually similar to those used by NexRay, Inc., for

their interventional cardiology C-arm system.3In the IGCT

system, the source and detector would be mounted on a gan-

try and rotated rapidly around the patient.

III. MATERIALS AND METHODS

A. Sampling

Since the source and detector of the IGCT system have

the same axial extent, and assuming the spacing of source

points and detectors in this direction is adequate, the sam-

2623 2623Med. Phys. 31 „9…, September 20040094-2405Õ2004Õ31„9…Õ2623Õ5Õ$22.00 © 2004 Am. Assoc. Phys. Med.

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pling in the slice direction is sufficient. The rays connecting

each source with the row of detectors directly opposing it

ensures this, and any additional oblique rays provide addi-

tional sampling, much as in 3D positron emission tomogra-

phy ?PET? imaging. The feasibility question being investi-

gated is whether sufficient sampling in the transverse ?or

in-plane? direction can be acquired in a scan time of 0.5 s or

less.

To answer this question it is helpful to consider the ac-

quired data in Radon space. For a single-slice CT system,

each ray can be described by two parameters, the rotation

angle about the axis of rotation, ?, and the perpendicular

distance to the center of rotation, ?. The 1D projections can

be represented in a 2D Radon space, with coordinates ? and

?.Aparallel-ray projection acquires a range of ? values all at

the same ? value, i.e., a horizontal line in Radon space. A

single-slice fan-beam projection acquires a range of ? values

over a modest range of ? values ?e.g., ?20°?. The samples

form a curve in Radon space that for modest fan-beam angles

is visually similar to a slanted line. A sufficient data set re-

quires adequate sampling of all needed ? values, based on

the FOV and spatial resolution, and a range of ? values

spanning at least ? radians.

For the IGCT system, one ‘‘view’’ of in-plane samples

can be defined as the rays connecting all source locations in

a source row to all detectors in the opposed detector row. We

define ? to be the rotation angle of a ray in the absence of

gantry rotation, as illustrated in Fig. 2. The ray connecting a

source location s to a detector location d is defined by

??arctan?

??d•cos????DID•sin???,

?????g,

where SID is the source-to-iso-center distance, DID is the

detector-to-iso-center distance, and ?gis the rotation angle

of the gantry.

The rays connecting the entire source row with a single

detector element form a fan, so the total sampling from a full

view is a set of fans shifted in ? and ? from each other,

thereby forming a slanted swath in Radon space, as illus-

trated in Fig. 3. The fan formed by the upper detector ele-

s?d

SID?DID?,

?1?

?2?

?3?

ment ?A in Fig. 3?, contains the rays with largest positive ?

and most negative ? ?with clockwise being the positive ro-

tation direction?. Moving towards the lower detector ele-

ment, the fans shift in the negative ? and positive ? direc-

tions.

As the gantry rotates, the next scan of the same source

row generates a new swath in Radon space. In order to have

a sufficient data set, enough views must be acquired so that

there are no gaps between swaths. For a desired scan time,

the number of views is limited by the time needed to scan the

source which includes the dwell time at each source location

and the beam steering time. The detector read out is over-

lapped with the beam steering and therefore does not impact

the total scan time. We examined this sampling using the

timing parameters of the NexRay source3and also consid-

ered the impact of sequential versus nonsequential sampling

of the source rows.

B. Photon flux and signal-to-noise ratio

The SNR in a CT image depends on the number of pho-

tons that passed through a resolution element and were de-

FIG. 1. Proposed IGCT geometry shown with the x-ray beam at one position

in the source array.

FIG. 2. The in-plane IGCT geometry with one source row and one detector

row at a gantry rotation of ?g. The ray connecting source location s and

detector location d has an inherent rotation angle ?, a total rotation angle ?,

and is at a distance ? from the isocenter.

FIG. 3. The fans formed by ?a? connecting a detector element in the detector

row to the entire source row and ?b? the corresponding sampling in Radon

space. The fans from all detector elements sample a slanted swath of Radon

space.

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Medical Physics, Vol. 31, No. 9, September 2004

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tected, and the spatial resolution of the system. For this pre-

liminary investigation, the question of SNR was studied by

determining whether the proposed system can provide

enough photon flux as compared to a conventional MDCT

scanner.

We first analyzed the relative usable x-ray flux of the

IGCT system compared to a conventional scanner. We define

this as the number of photons per mA that illuminate a voxel.

In this analysis we assume that the voxel is at isocenter, and

we expect the results to be similar throughout the FOV. In a

conventional scanner, each voxel in the FOV is illuminated

by the source continuously as long as the voxel is within the

axial coverage of the x-ray beam, while in the IGCT system,

the voxel is only illuminated by a fraction of the source

locations, for example when the source is in the area illus-

trated as A? in Fig. 4. This effective area, A?, which is the

detector area, Ad, magnified onto the source, depends on the

SID and the DID,

A??Ad•SID2

DID2.

?4?

Therefore, in the IGCT geometry, a voxel is illuminated

for a fraction of the scan time equal to the ratio of A? to As,

and the relative usable x-ray flux is proportional to this ratio.

Also in the IGCT system, the x-ray beam is turned off while

the beam is moved from one location to another, which can

be accounted for by fduty, the fraction of the time the

scanned source produces x rays ?i.e., one minus the fraction

of the time spent moving the source from one location to

another?. Conventional x-ray tubes use ‘‘reflection’’ targets

while the proposed system uses a transmission target, and

there are differences in the Brehmsstrahlung emissions for

these two approaches.3The relative efficiency of the Brems-

strahlung emission of the transmission target compared to a

reflection target can be expressed using the factor fx. In both

systems, the number of photons at the object is inversely

proportional to SID2. Combining these parameters, the rela-

tive usable x-ray flux of the IGCT system compared to a

conventional MDCT scanner, Frel, is

Frel?A?

As?

SIDconv

SID?

2

•fx•fduty.

?5?

In the IGCT system, the FOV in the transverse direction,

FOVt, depends on the transverse source extent and the mag-

nification, while in the axial direction, since the source and

detector have the same extent, the field of view, FOVa, is

equivalent to the axial source extent. The source area, As,

can be expressed in terms of the total FOV,

As?FOVt•FOVa•?SID?DID?

DID

.

?6?

Equations ?4?–?6? can be used to calculate the relative

usable x-ray flux of the IGCT system compared to a MDCT

system. We now assume that the two geometries have the

same magnification and source-to-detector distance. Because

of the inverted geometry, this implies that the SID of the

IGCT system is equivalent to the DID of the conventional

system. Using this relationship along with Eqs. ?4? and ?6?,

Eq. ?5? can be written as

Ad•DID

FOVt•FOVa•?SID?DID?•fx•fduty.

Frel?

?7?

The relative SNR is proportional to the square root of the

total number of photons, which depends on the relative us-

able x-ray flux, the relative detective quantum efficiency,

DQErel, the relative power, Prel, and the relative exposure

times, Trel, of the two systems

SNRrel??Frel•DQErel•Prel•Trel.

?8?

Note that for determining Trel, the exposure time for a

MDCT system scanning in helical mode is the time during

which a resolution element is irradiated, which is a fraction

of the total scan time.

Together, Eqs. ?7? and ?8? provide an analytical method

for examining the SNR feasibility of the IGCT system.

C. Investigated geometry

The specifications of the analyzed IGCT system are given

in Table I. The values are based on the current NexRay com-

ponents, with some reasonable modifications to support a CT

application. The source and detector dimensions have been

FIG. 4. The effective area of the source, A?, for a voxel in the object, where

Asand Adare the areas of the source and detector, respectively.

TABLE I. Specifications for preliminary investigated IGCT geometry.

Source dimensions ?transverse?axial?

Number of source locations

Detector dimensions ?transverse?axial?

Number of detector elements

Dwell time per source location

Move time between successive source locations

Source power

Gantry rotation time

SID

DID

FOV ?transverse?axial?

50?15 cm

200?60

5?15 cm

48?144

1 ?s

0.28 ?s

96 kW

0.5 s

41 cm

54 cm

30 cm?15 cm

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modified in the proposed system to provide the desired FOV.

The source power has also been increased by assuming a

0.6-mm source focal spot as opposed to the current 0.3-mm

focal spot. The relevant MDCT specifications which factor

into Eqs. ?7? and ?8? are listed in Table II. The MDCT de-

tector size, scanning mode, and gantry rotation time deter-

mine the voxel illumination time but otherwise do not affect

the SNR calculation.

IV. RESULTS

A. Sampling

Using the parameters in Table I, 0.256 ms is needed to

scan each source row, and 15.4 ms is needed to scan the

entire source array. Therefore the complete source array can

be scanned a total of 32 times during a 0.5 s scan.

Figure 5?a? shows the in-plane sampling of Radon space

from one row in one view, calculated using Eqs. ?1?–?3? and

Table I. This calculation assumes that the gantry is being

continuously rotated at a speed of 4? radians/second.

During an acquisition, the remaining source rows in the

array are scanned before this particular row is rescanned 15.4

ms later. During this time, the gantry rotates 0.19 radians.

Figure 5?b? shows the Radon space coverage from the initial

scan of the source row, and from the same source row 15.4

ms later. This sampling scheme is insufficient, as a gap exists

between the swaths. This problem is not due to an insuffi-

cient number of measurements but rather a poor distribution.

In fact, each swath in Radon space is oversampled.

The sequential scanning of source rows as simulated

above is inefficient because the information acquired by two

adjacent source rows is very similar. That is, a resolution

element in the scanned volume is sampled through very simi-

lar ray paths by the two adjacent source rows. Therefore,

scanning these two rows consecutively in time yields nearly

redundant data. A better method for scanning the source is to

interleave the source row order, for example scanning first

the odd source rows, followed by the even source rows. Fig-

ure 5?c? shows the Radon space coverage of the first source

and detector rows, and the sampling of the adjacent source

and detector rows after all the odd rows have been scanned.

The gap in Radon space has been removed, and in fact the

swaths overlap suggesting that the scan time can be short-

ened. Therefore, by using interlaced source scanning, suffi-

cient data can be acquired for the 15-cm volume in less than

0.5 s.

B. Photon flux and signal-to-noise ratio

Using a transmission x-ray target improves photon gen-

eration by a factor of 1.7 compared to a reflection target.3

Assuming the specifications in Tables I and II, Eq. ?7? yields

a relative usable x-ray flux of 0.12, meaning that the pro-

posed system has approximately one tenth of the flux of a

conventional system, within the volume that each is illumi-

nating during a single rotation. Note that when scanning a

large volume, the MDCT system does not illuminate the en-

tire volume during the full scan time.

To understand the implications of this photon flux on im-

age quality, the relative SNR can be calculated using Eq. ?8?.

We assume that the comparison MDCT system operates at 24

kW with each voxel in the volume illuminated for 0.5 s, for

example a MDCT system with a 0.5 s gantry rotation and a

helical pitch of one. The assumed DQE of the photon-

counting detector used in the IGCT system was 1.2 times

that of a conventional detector.4Using the relative usable

x-ray flux, the relative DQE, and the scan time, power level,

and other specifications listed in Tables I and II, the SNR of

the IGCT system is predicted to be 76% of the SNR of a

conventional MDCT system.

This analysis shows that the SNR of the proposed system

is of the same order as that of a MDCT system. Note that the

IGCT system achieves this performance in a single rotation

while the MDCT system needs multiple rotations to cover

the same volume. As can be seen from Eqs. ?7? and ?8?, this

comparison depends strongly on the design parameters. For

example, increasing the detector size in the transverse direc-

tion can quickly improve the relative flux and SNR by in-

creasing the solid angle subtended by each source location.

The SNR can also be increased by lengthening the scan time.

TABLE II. Specifications for comparison MDCT geometry.

Source power

Voxel illumination time

Gantry rotation time

Helical pitch

SID

DID

24 kW

0.5 s

0.5 s

1

54 cm

41 cm

FIG. 5. For all plots, the gantry is rotating continuously at 4? radians per

second. ?a? The swath in Radon space representing the in-plane samples of

the IGCT system, that is, all rays connecting each position in one source row

to all the elements in the opposing detector row. ?b? The first swath and the

additional swath sampled by the same source and detector rows after the

entire source array has been scanned. ?c? The first swath and the swath

sampled by the adjacent source and detector rows after half of the source

rows have been scanned.

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Medical Physics, Vol. 31, No. 9, September 2004

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V. DISCUSSION AND CONCLUSIONS

This paper proposes an inverse-geometry volumetric CT

system that uses a large-area scanned source. The proposed

system can acquire a 15-cm volume thickness in one circular

scan. Although more work is needed to understand the per-

formance of the system, the preliminary investigations de-

scribed in this note demonstrate feasibility in two areas. The

sampling investigation establishes that sufficient sampling is

possible at scan times of less than 0.5 s. The SNR calculation

predicts noise performance comparable to a conventional

MDCT scanner. Of note, this SNR is achieved for a volumet-

ric scan in a single rotation, while the MDCT system needs

multiple rotations for the same volumetric coverage and

SNR.

One important aspect that was not discussed above is an

appropriate reconstruction method to use for the acquired

data set. This is beyond the scope of the present paper. How-

ever, it should be noted that the data set from the IGCT

system is very similar to that from a multiring PET system,

and therefore a PET reconstruction algorithm could be used

for the IGCT system.5,6We are exploring the use of a recon-

struction method using rebinning to 2D parallel-ray projec-

tions.

The results of this preliminary investigation are very en-

couraging, but significant challenges remain. In addition to

the algorithm work, the sampling and SNR predictions of the

present analysis need to be confirmed with simulations and

experimental measurements on a bench top system. Because

of the relationship between the source size and the FOV,

achieving a large in-plane FOV with an IGCT system while

maintaining a fast scan time will be challenging. Finally,

construction of a prototype will require significant engineer-

ing work, including design solutions for mounting the com-

ponents on the gantry and for transferring the large data set

from the rotating gantry. Nonetheless, the IGCT concept is

promising, and offers the possibility of high-speed volumet-

ric imaging with freedom from cone-beam artifacts.

a?Also at Department of Electrical Engineering, Stanford University, Stan-

ford, California 94305.

1B. D. Smith, ‘‘Cone-beam tomography: Recent advances and a tutorial

review,’’ Opt. Eng. 29, 524–534 ?1990?.

2L. A. Feldkamp, L. C. Davis, and J. W. Kress, ‘‘Practical cone-beam

algorithm,’’ J. Opt. Soc. Am. A 1, 612–619 ?1984?.

3E. G. Solomon, B. P. Wilfley, M. S. Van Lysel, A. W. Joseph, and J. A.

Heanue, ‘‘Scanning-beam digital x-ray ?SBDX? system for cardiac an-

giography,’’ in Medical Imaging 1999: Physics of Medical Imaging

?SPIE, New York, 1999?, Vol. 3659, pp. 246–257.

4M. J. Tapiovaara and R. F. Wagner, ‘‘SNR and DQE analysis of broad

spectrum x-ray imaging,’’ Phys. Med. Biol. 30, 519–529 ?1985?.

5M. Defrise, D. W. Townsend, and R. Clack, ‘‘Three-dimensional image

reconstruction from complete projections,’’ Phys. Med. Biol. 34, 573–

587 ?1989?.

6N. J. Pelc, ‘‘A generalized filtered backprojection algorithm for three

dimensional reconstruction,’’ Ph.D. thesis, Harvard University, 1979.

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