9 1987 by The Humana Press Inc. All rights of anv nature, whatsoever, reserved. 0163-4984/87/1300-0209502.00
Prospects for MicrocomputerizedTomography Using Synchrotron Radiation CARL A. C A R L S S O N , * G E O R G M A T S C H E K O , AND
PER SPANNE Radiation Physics Department, University of Link6ping, the lVledical School, S-581 85 Link6ping, Sweden ABSTRACT A microversion of a computerized tomograph (CT) is described, in which the object is subjected to a successive series of translations with rotation by a small angle in between. The spatial resolution is determined by collimators and translation step lengths and is today, with clinical X-ray tubes, of the order of 100 ~m. The use of synchrotron radiation instead of X-ray tubes offers the advantages of much higher fluence rates, which can be used to diminish the exposure times from days to minutes or to increase the spatial resolution from 100 ~m to about 1 ~m. The possibility to receive monoenergetic photons of selectable energy makes it possible to avoid spectral hardening image artifacts, as well as to optimize the information sampling with regard to average absorbed dose or exposure time. Selectable photon energies are valuable also for tomochemistry applications. Index Entries: Microcomputerized tomography; high spatial resolution; synchrotron X-rays; optimal photon energy; tomochemistry.
DESIGN OF THE COMPUTERIZED TOMOGRAPH The t o m o g r a p h is described elsewhere (1). Here only the m a i n outlines are given. It is built on an optical b e n c h (Fig. 1) a n d is a c o m p u terized t o m o g r a p h (CT) m a c h i n e of the first generation, that is, it has a single detector a n d uses repeated scans with rotation by a small angle in between. The distances b e t w e e n the radiation source a n d the detector *Author to whom all correspondence and reprint requests should be addressed. Biological Trace Element Research
209
Vot 13, 1987
210
Carlsson, /Vlatscheko, a n d S p a n n e
can be varied from 2 m down to a few mm. During the tomography, the radiation source and detector are stationary while the object is moved (Fig. 1). The spatial resolution of the image is mainly determined by the collimators on both sides of the object. So far we have only used X-ray tubes designed for clinical diagnostic radiology (20-200 kV). A 32-bit minicomputer is used to control the movements and collect and store the signals from the detector, as well as to reconstruct the image. The reconstruction gives the average attenuation coefficients of the volume elements of the object that are represented as picture elements (pixels) in the image. Window technique is used for contrast enhancement of the displayed image. This means that only pixels within a chosen interval of attenuation coefficients are presented in the gray scale image. The rest of the pixels are either black or white.
OPTIMAL PHOTON ENERGY In digital radiography with ideal detectors (totally absorbing, unsaturable, and not producing noise), image processing makes it possible to display all information up to the limits of quantum noise. In the simple diagnostic problem shown in Fig. 2, with a small contrasting object of thickness x and linear attenuation coefficient bL2within a larger object with corresponding values L and ~1, a signal-to-noise ratio (SNR) can be expressed: S,T,-.
S Nip - N2p _ [ N o e -~'L ]1/2, I'qK - cs - X/NIp + N2p - k 2 J 1~,2 -
,t, P,1 I x
O)
scanning collim a f a r
collimator
,v- ~
~
~
Fig. 1. The principles of the tomograph.
Biological Trace Element Research
Vol. 13, 1987
Micro-CT with Synchrotron Radiation
211
I
li Nlp N2p Fig. 2. The model used for calculation of optimal energies. Where the signal, S, is the difference in the number of primary photons incident on two identical detector elements, N1, - N2t,. The last equality in Eq._l is valid only for small contrasts (1~2 - ~ l l x < < 1). The average dose D -- 6/ML in the object is for clinical diagnostic examinations used as the first step in calculating radiation risk (2,3). ~ stands for energy imparted to the object (patient) and ML for its mass, index L gives the thickness of the object (Fig. 2). If only primary monoenergetic photons are detected: -~ _ 2 A ( S N R t h ) 2
ML x2a2
IF hve ~'L (~1,2 --
(2)
~1) 2
Here, A is radiation field area; a2 the area of a picture element; IF the imparted fraction of the incident energy; Im the photon energy; and SNR,, a constant threshold value of the signal-to-noise ratio. Equation 2 is solved (Fig. 3) for L = 20, 2, and 0.2 mm; A = 100, 1, and 0.01 mm2; a = x = 0.1, 0.01, and 0.001 mm, that is, the phantoms are
Biological Trace Element Research
Vol. 13, 1987
10 s f / I
"
I
"
10 4
I
9
I
10 3 :
I
:
>,
10 z
~3
/ /
:
t/)
0 '10
I
: :
II
101
"0 JO b. 0 u} J~ (g
10 0
1 0-1 L_
>
,,r
i 10- z
~: :.l I 11
,.-"
i
i / i
10-4
9 ..
10- s ........
, ........... 10 100
Photon keV
energy
Fig. 3. Average absorbed dose in a water phantom containing a thin contrasting object of aluminum ( . . . ) , air (--), or polyethylene (---). The detectability is the same on all points of all curves. The minima give the optimal p h o t o n energies. The thickness of the water phantoms are, from left to right, 0.2, 2, and 20 mm. Biological Trace E l e m e n t Research
VoL 13, 1987
/Vlicro-CT with Synchrotron Radiation
213
similar in shape, but all linear dimensions are changed in steps of 10. The mass of the three phantoms are 70 g, 70 mg, and 70 I*g. All points on all curves in Fig. 3 have the same SNR,, = 5, that is, the same image quality or information content. The minima show the optimal energy. Equation 2 is also solved for three different materials of the contrasting object, aluminum (comparable to bone), air, and polyethylene (comparable to fat). Figure 3 shows that the optimal energy is approximately the same for the three contrast materials at these phantom thicknesses. For higher thicknesses one needs a higher optimal energy for detecting air than for detecting fat or bone (2,3). For equally thick contrasting objects of aluminum, air, and polyethylene, aluminum is much easier to detect. The optimal energy increases with phantom thickness and is about 4 keV for 1 tzm spatial resolution for a 200-I,m thick water phantom. The average dose in the object at the optimal energy increases with decreases of phantom thickness. The average dose variation with phantom thickness is similar to that reported by Grodzins (4,5). If smaller differences in linear attenuation coefficients are to be detected it can only be made at the expense of a higher average absorbed dose. Figure 3 is calculated for scatter-free transmission radiography, but the variations of the average absorbed dose with photon energy and attenuation coefficients are valid also for CT-applications, although the absolute value may be different (4,5). The large variation of/~ with photon energy makes it favorable to work with X-ray tubes of different anode materials. For 20 and 2 mm thick objects, anodes of Mo and Cu, respectively, are suitable.
PROBLEMS WITH A MICRO-CT As has been discussed earlier, a main problem with a micro-CT is the long exposure times needed. If, with an X-ray tube, one tries to use photon energies around the optimal energy, the exposure time is further increased because of low yield of X-rays at low tube potentials. It is probably advantageous to choose the anode material so that the characteristic X-rays dominate the radiation spectrum. The thermal expansion of the anode during an examination is a problem appearing also in high-resolution clinical CT, but is more important in micro-CT (1). The emission rate within the focal spot area of a clinical X-ray tube varies heavily. With small collimators, only a small part of the focal area is used, and thermal expansion of the anode may cause large fluctuations in emission (see Fig. 4).
EXAMPLES OF IMAGES Figure 5 shows a CT image of a lead pencil; 57 x 57 picture elements, circular collimators 300 t*m wide, and angular increments of 3.1 ~ Biological Trace Element Research
VoL 13, 1987
214
Day
Carlsson, Matscheko, and Spanne
I
Day 2
Day 3
a
b
Fig. 4. Sinogram of a freeze-dried mouse brain. 27.5 kV, Mo-anode and Mo-filter, collimator 100 p.m, 103 • 103 matrix. (a) Original sinogram; and (b) corrected sinogram. were used. An X-ray tube with an Mo-anode and Mo-filter was used at a potential difference of 25 kV. Figure 5 reveals the coating, the graphite, and the wood. Details, such as annular rings, are seen in the wood. Only the highest linear attenuation coefficients are displayed in Fig. 5b. Here the graphite looks inhomogeneous. This is an artifact, the spectral hardening effect, caused by violating the basic linearity conditions of CT [the radon transform (6)] when polyenergetic photons are used. Figure 4 shows a so called sinogram (7) of the profiles obtained during an examination of a freeze-dried mouse brain. Variations along a horizontal line show variations in the projections p = ILpodLduring a scan (profile). Between two successive scans the object was rotated 1.2 ~ If, as in Fig. 4, the profiles are arranged successively below each other, a sinogram, each point in the object describes a sine curve. Those sine curves differ in phase and amplitude, but have the same frequency. This investigation lasted 30 h, divided between 3 d. The thermal expansion of the anode caused heavy fluctuations in the emission rate. In the beginning of d 2 the emission almost disappeared. The different profiles were normalized (Fig. 4b) to constant values of ILIIL ~ dL dL• a quantity that provided that spectral hardening can be neglected, and is constant in CT (8). L and L• are two orthogonal lengths embracing the object. Figure 6a and b shows the reconstructed images, using the original and normalized raw data, respectively. Figure 7 shows a tomogram of a mouse leg (thigh), obtained with low quantum noise, but a somewhat unfavorable spectrum (40 kV, W-anode) and moderate spatial resolution (200 ~,m collimators). Biological Trace Element Research
VoL 13, 1987
~icro-CT with Synchrotron Radiation
215
Fig. 5. Tomogram of a pencil. 25 kV, Mo-anode and Mo-filter, collimator diameter 300 i~m, 57 • 57 matrix. (Top) Original image; (Bottom) contrastenhanced image, showing only the graphite.
EXPECTATIONS FROM CT WITH SYNCHROTRON RADIATION Synchrotron radiation seems to solve most problems of micro-CT. The high fluence rates open the way to tomograms of high spatial resolution (-1 i~m) without the extremely long exposure times. Synchrotron Biological Trace Element Research
VoL 13, 1987
216
Carlsson, /Vlatscheko, and Spanne
Fig. 6. Tomograms reconstructed from the digital sinograms (a) and (b) in Fig. 4, respectively. radiation can, by means of mirrors and Bragg diffraction crystals, be focused and produced continuously selectable in energy. With this nearly monoenergetic radiation, the problem with spectral hardening artifacts is avoided, and the optimal energy for each imaging task can be chosen. With big unmovable radiation sources, moving the object is the only CTmethod that can be used. The use of CT with synchrotron radiation is nearly ideal for imaging. We are building a CT-machine based on a microcomputer for controlling the movements as well as for collecting and storing the information from the radiation detector. The image re-
Fig. 7. Tomogram of a mouse leg (thigh). 40 kV, W-anode collimator 200 izm, step length 100 Bm, 171 x 171 matrix, angular increment 0.67~ Biological TraceElementResearch
Vol. 13, 1987
,~licro-CT with Synchrotron Radiation
217
construction has to be made on a more powerful computer. This CTmachine is planned to be installed at one of the synchrotron radiation ports at Brookhaven National Laboratory for studying the capabilities of CT in imaging small objects, as well as for use in biological applications with biopsies, insects, rodents, and, perhaps, h u m a n beings. The selectable energy combined with subtraction techniques makes quantitative analyses of spatial distributions of bone mineral in the skeleton or heavy elements in tissues (tomochemistry) attractive (9,10).
ACKNOWLEDGMENTS This work has been supported by the Swedish Cancer Society (project No 1407-B81-02, B80-01T) and the Swedish Medical Research Council (project No B82-17X-5722-03).
REFERENCES 1. C. A. Carlsson, G. Matscheko, and P. Spanne, submitted for publication (1985). 2. C. A. Carlsson, in Medical Physics, J. R. Greening, ed., North Holland, Amsterdam, 1981, pp. 481-490. 3. C. A. Carlsson, in Teknisk Sgkerhet i Sjukv&den P. Ask and P. A. Oberg, eds., Almqvist & Wiksell, Stockholm, 1984 (in Swedish). 4. L. Grodzins, Nucl. Instr. Meth. 206, 541 (1983). 5. L. Grodzins, Nucl. Instr. Meth. 206, 546 (1983). 6. J. Radon, Ber. Verh. Sfichs. Akad. 69, 262 (1917). 7. P. Edholm, Phys. Med. Biol. 23, 90 (1978). 8. P. Edholm, unpublished. 9. S. J. Riederer and C. A. Mistretta, Med. Phys. 4, 474 (1977). 10. B. K. Rutt, I. A. Cunningham, and A. Fenster, Med. Phys. 10, 801 (1983).
Biological Trace Element Research
Vol. 13, 1987
Prospects for MicrocomputerizedTomography Using Synchrotron Radiation CARL A. C A R L S S O N , * G E O R G M A T S C H E K O , AND
PER SPANNE Radiation Physics Department, University of Link6ping, the lVledical School, S-581 85 Link6ping, Sweden ABSTRACT A microversion of a computerized tomograph (CT) is described, in which the object is subjected to a successive series of translations with rotation by a small angle in between. The spatial resolution is determined by collimators and translation step lengths and is today, with clinical X-ray tubes, of the order of 100 ~m. The use of synchrotron radiation instead of X-ray tubes offers the advantages of much higher fluence rates, which can be used to diminish the exposure times from days to minutes or to increase the spatial resolution from 100 ~m to about 1 ~m. The possibility to receive monoenergetic photons of selectable energy makes it possible to avoid spectral hardening image artifacts, as well as to optimize the information sampling with regard to average absorbed dose or exposure time. Selectable photon energies are valuable also for tomochemistry applications. Index Entries: Microcomputerized tomography; high spatial resolution; synchrotron X-rays; optimal photon energy; tomochemistry.
DESIGN OF THE COMPUTERIZED TOMOGRAPH The t o m o g r a p h is described elsewhere (1). Here only the m a i n outlines are given. It is built on an optical b e n c h (Fig. 1) a n d is a c o m p u terized t o m o g r a p h (CT) m a c h i n e of the first generation, that is, it has a single detector a n d uses repeated scans with rotation by a small angle in between. The distances b e t w e e n the radiation source a n d the detector *Author to whom all correspondence and reprint requests should be addressed. Biological Trace Element Research
209
Vot 13, 1987
210
Carlsson, /Vlatscheko, a n d S p a n n e
can be varied from 2 m down to a few mm. During the tomography, the radiation source and detector are stationary while the object is moved (Fig. 1). The spatial resolution of the image is mainly determined by the collimators on both sides of the object. So far we have only used X-ray tubes designed for clinical diagnostic radiology (20-200 kV). A 32-bit minicomputer is used to control the movements and collect and store the signals from the detector, as well as to reconstruct the image. The reconstruction gives the average attenuation coefficients of the volume elements of the object that are represented as picture elements (pixels) in the image. Window technique is used for contrast enhancement of the displayed image. This means that only pixels within a chosen interval of attenuation coefficients are presented in the gray scale image. The rest of the pixels are either black or white.
OPTIMAL PHOTON ENERGY In digital radiography with ideal detectors (totally absorbing, unsaturable, and not producing noise), image processing makes it possible to display all information up to the limits of quantum noise. In the simple diagnostic problem shown in Fig. 2, with a small contrasting object of thickness x and linear attenuation coefficient bL2within a larger object with corresponding values L and ~1, a signal-to-noise ratio (SNR) can be expressed: S,T,-.
S Nip - N2p _ [ N o e -~'L ]1/2, I'qK - cs - X/NIp + N2p - k 2 J 1~,2 -
,t, P,1 I x
O)
scanning collim a f a r
collimator
,v- ~
~
~
Fig. 1. The principles of the tomograph.
Biological Trace Element Research
Vol. 13, 1987
Micro-CT with Synchrotron Radiation
211
I
li Nlp N2p Fig. 2. The model used for calculation of optimal energies. Where the signal, S, is the difference in the number of primary photons incident on two identical detector elements, N1, - N2t,. The last equality in Eq._l is valid only for small contrasts (1~2 - ~ l l x < < 1). The average dose D -- 6/ML in the object is for clinical diagnostic examinations used as the first step in calculating radiation risk (2,3). ~ stands for energy imparted to the object (patient) and ML for its mass, index L gives the thickness of the object (Fig. 2). If only primary monoenergetic photons are detected: -~ _ 2 A ( S N R t h ) 2
ML x2a2
IF hve ~'L (~1,2 --
(2)
~1) 2
Here, A is radiation field area; a2 the area of a picture element; IF the imparted fraction of the incident energy; Im the photon energy; and SNR,, a constant threshold value of the signal-to-noise ratio. Equation 2 is solved (Fig. 3) for L = 20, 2, and 0.2 mm; A = 100, 1, and 0.01 mm2; a = x = 0.1, 0.01, and 0.001 mm, that is, the phantoms are
Biological Trace Element Research
Vol. 13, 1987
10 s f / I
"
I
"
10 4
I
9
I
10 3 :
I
:
>,
10 z
~3
/ /
:
t/)
0 '10
I
: :
II
101
"0 JO b. 0 u} J~ (g
10 0
1 0-1 L_
>
,,r
i 10- z
~: :.l I 11
,.-"
i
i / i
10-4
9 ..
10- s ........
, ........... 10 100
Photon keV
energy
Fig. 3. Average absorbed dose in a water phantom containing a thin contrasting object of aluminum ( . . . ) , air (--), or polyethylene (---). The detectability is the same on all points of all curves. The minima give the optimal p h o t o n energies. The thickness of the water phantoms are, from left to right, 0.2, 2, and 20 mm. Biological Trace E l e m e n t Research
VoL 13, 1987
/Vlicro-CT with Synchrotron Radiation
213
similar in shape, but all linear dimensions are changed in steps of 10. The mass of the three phantoms are 70 g, 70 mg, and 70 I*g. All points on all curves in Fig. 3 have the same SNR,, = 5, that is, the same image quality or information content. The minima show the optimal energy. Equation 2 is also solved for three different materials of the contrasting object, aluminum (comparable to bone), air, and polyethylene (comparable to fat). Figure 3 shows that the optimal energy is approximately the same for the three contrast materials at these phantom thicknesses. For higher thicknesses one needs a higher optimal energy for detecting air than for detecting fat or bone (2,3). For equally thick contrasting objects of aluminum, air, and polyethylene, aluminum is much easier to detect. The optimal energy increases with phantom thickness and is about 4 keV for 1 tzm spatial resolution for a 200-I,m thick water phantom. The average dose in the object at the optimal energy increases with decreases of phantom thickness. The average dose variation with phantom thickness is similar to that reported by Grodzins (4,5). If smaller differences in linear attenuation coefficients are to be detected it can only be made at the expense of a higher average absorbed dose. Figure 3 is calculated for scatter-free transmission radiography, but the variations of the average absorbed dose with photon energy and attenuation coefficients are valid also for CT-applications, although the absolute value may be different (4,5). The large variation of/~ with photon energy makes it favorable to work with X-ray tubes of different anode materials. For 20 and 2 mm thick objects, anodes of Mo and Cu, respectively, are suitable.
PROBLEMS WITH A MICRO-CT As has been discussed earlier, a main problem with a micro-CT is the long exposure times needed. If, with an X-ray tube, one tries to use photon energies around the optimal energy, the exposure time is further increased because of low yield of X-rays at low tube potentials. It is probably advantageous to choose the anode material so that the characteristic X-rays dominate the radiation spectrum. The thermal expansion of the anode during an examination is a problem appearing also in high-resolution clinical CT, but is more important in micro-CT (1). The emission rate within the focal spot area of a clinical X-ray tube varies heavily. With small collimators, only a small part of the focal area is used, and thermal expansion of the anode may cause large fluctuations in emission (see Fig. 4).
EXAMPLES OF IMAGES Figure 5 shows a CT image of a lead pencil; 57 x 57 picture elements, circular collimators 300 t*m wide, and angular increments of 3.1 ~ Biological Trace Element Research
VoL 13, 1987
214
Day
Carlsson, Matscheko, and Spanne
I
Day 2
Day 3
a
b
Fig. 4. Sinogram of a freeze-dried mouse brain. 27.5 kV, Mo-anode and Mo-filter, collimator 100 p.m, 103 • 103 matrix. (a) Original sinogram; and (b) corrected sinogram. were used. An X-ray tube with an Mo-anode and Mo-filter was used at a potential difference of 25 kV. Figure 5 reveals the coating, the graphite, and the wood. Details, such as annular rings, are seen in the wood. Only the highest linear attenuation coefficients are displayed in Fig. 5b. Here the graphite looks inhomogeneous. This is an artifact, the spectral hardening effect, caused by violating the basic linearity conditions of CT [the radon transform (6)] when polyenergetic photons are used. Figure 4 shows a so called sinogram (7) of the profiles obtained during an examination of a freeze-dried mouse brain. Variations along a horizontal line show variations in the projections p = ILpodLduring a scan (profile). Between two successive scans the object was rotated 1.2 ~ If, as in Fig. 4, the profiles are arranged successively below each other, a sinogram, each point in the object describes a sine curve. Those sine curves differ in phase and amplitude, but have the same frequency. This investigation lasted 30 h, divided between 3 d. The thermal expansion of the anode caused heavy fluctuations in the emission rate. In the beginning of d 2 the emission almost disappeared. The different profiles were normalized (Fig. 4b) to constant values of ILIIL ~ dL dL• a quantity that provided that spectral hardening can be neglected, and is constant in CT (8). L and L• are two orthogonal lengths embracing the object. Figure 6a and b shows the reconstructed images, using the original and normalized raw data, respectively. Figure 7 shows a tomogram of a mouse leg (thigh), obtained with low quantum noise, but a somewhat unfavorable spectrum (40 kV, W-anode) and moderate spatial resolution (200 ~,m collimators). Biological Trace Element Research
VoL 13, 1987
~icro-CT with Synchrotron Radiation
215
Fig. 5. Tomogram of a pencil. 25 kV, Mo-anode and Mo-filter, collimator diameter 300 i~m, 57 • 57 matrix. (Top) Original image; (Bottom) contrastenhanced image, showing only the graphite.
EXPECTATIONS FROM CT WITH SYNCHROTRON RADIATION Synchrotron radiation seems to solve most problems of micro-CT. The high fluence rates open the way to tomograms of high spatial resolution (-1 i~m) without the extremely long exposure times. Synchrotron Biological Trace Element Research
VoL 13, 1987
216
Carlsson, /Vlatscheko, and Spanne
Fig. 6. Tomograms reconstructed from the digital sinograms (a) and (b) in Fig. 4, respectively. radiation can, by means of mirrors and Bragg diffraction crystals, be focused and produced continuously selectable in energy. With this nearly monoenergetic radiation, the problem with spectral hardening artifacts is avoided, and the optimal energy for each imaging task can be chosen. With big unmovable radiation sources, moving the object is the only CTmethod that can be used. The use of CT with synchrotron radiation is nearly ideal for imaging. We are building a CT-machine based on a microcomputer for controlling the movements as well as for collecting and storing the information from the radiation detector. The image re-
Fig. 7. Tomogram of a mouse leg (thigh). 40 kV, W-anode collimator 200 izm, step length 100 Bm, 171 x 171 matrix, angular increment 0.67~ Biological TraceElementResearch
Vol. 13, 1987
,~licro-CT with Synchrotron Radiation
217
construction has to be made on a more powerful computer. This CTmachine is planned to be installed at one of the synchrotron radiation ports at Brookhaven National Laboratory for studying the capabilities of CT in imaging small objects, as well as for use in biological applications with biopsies, insects, rodents, and, perhaps, h u m a n beings. The selectable energy combined with subtraction techniques makes quantitative analyses of spatial distributions of bone mineral in the skeleton or heavy elements in tissues (tomochemistry) attractive (9,10).
ACKNOWLEDGMENTS This work has been supported by the Swedish Cancer Society (project No 1407-B81-02, B80-01T) and the Swedish Medical Research Council (project No B82-17X-5722-03).
REFERENCES 1. C. A. Carlsson, G. Matscheko, and P. Spanne, submitted for publication (1985). 2. C. A. Carlsson, in Medical Physics, J. R. Greening, ed., North Holland, Amsterdam, 1981, pp. 481-490. 3. C. A. Carlsson, in Teknisk Sgkerhet i Sjukv&den P. Ask and P. A. Oberg, eds., Almqvist & Wiksell, Stockholm, 1984 (in Swedish). 4. L. Grodzins, Nucl. Instr. Meth. 206, 541 (1983). 5. L. Grodzins, Nucl. Instr. Meth. 206, 546 (1983). 6. J. Radon, Ber. Verh. Sfichs. Akad. 69, 262 (1917). 7. P. Edholm, Phys. Med. Biol. 23, 90 (1978). 8. P. Edholm, unpublished. 9. S. J. Riederer and C. A. Mistretta, Med. Phys. 4, 474 (1977). 10. B. K. Rutt, I. A. Cunningham, and A. Fenster, Med. Phys. 10, 801 (1983).
Biological Trace Element Research
Vol. 13, 1987
