- Email: [email protected]
On the limitations and optimisation of high-resolution 3D medical X-ray imaging systems
Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
On the limitations and optimisation of high-resolution 3D medical X-ray imaging systems Shu-Ang Zhou n, Anders Brahme Karolinska Institute, Department of Oncology–Pathology, P.O. Box 260, SE-171 76 Stockholm, Sweden
a r t i c l e i n f o
a b s t r a c t
Available online 19 November 2010
Based on a quantitative analysis of both attenuation and refractive properties of X-ray propagation in human body tissues and the introduction of a mathematical model for image quality analysis, some limitations and optimisation of high-resolution three-dimensional (3D) medical X-ray imaging techniques are studied. A comparison is made of conventional attenuation-based X-ray imaging methods with the phase-contrast X-ray imaging modalities that have been developed recently. The results indicate that it is theoretically possible through optimal design of the X-ray imaging system to achieve high spatial resolution (o 100 mm) in 3D medical X-ray imaging of the human body at a clinically acceptable dose level ( o 10 mGy) by introducing a phase-contrast X-ray imaging technique. & 2010 Elsevier B.V. All rights reserved.
Keywords: High resolution Optimisation Phase contrast X-ray
1. Introduction X-ray imaging has played an important role in medical imaging and diagnostics since its first introduction in the late 1800s. Despite the technology progresses during the past century, we are still limited in our ability to detect tumors in their earliest stages, monitor tumor phenotype, quantify invasion or metastasis and to visualize in vivo the effectiveness of anticancer treatments. Challenges remain in detecting early-stage solid tumors, especially for tumors of sizes less than 1 2 mm when significant angiogenesis has not yet been initiated [1]. If these early-stage tumors could be discovered, the risk of patients to get metastatic diseases can be minimized, and the cure rate would increase significantly since these tumors can be localized and eliminated by effective radiation and target-specific cancer therapies among others. At present, medical image resolution and diagnostic accuracy based on conventional attenuation-based X-ray imaging modalities are limited mainly due to their intrinsic limitations, such as low soft-tissue contrast and limited dose levels acceptable in clinical imaging practice. Recently, an increasing interest in the development of phasecontrast X-ray imaging techniques has been observed due to their potential advantageous applications in medical imaging [2–5]. The significance of phase contrast in X-ray imaging of soft tissues is understood in the classical framework of electromagnetic interactions in matter, where X-ray propagation properties of body tissues should be characterized by both their refractive indices and their attenuation coefficients. Within the diagnostic X-ray energy range,
n
Corresponding author. Tel.: + 46 8 6474753; fax: +46 8 343525. E-mail address: [email protected] (S.-A. Zhou).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.11.050
the refractive properties of soft tissues have been found to be able to play a significant role in X-ray imaging. As a result, phasecontrast X-ray imaging modalities may generate significantly greater image contrast compared to conventional attenuationbased radiography, especially for soft tissues and small objects. However, the optimal implementation of new phase-contrast X-ray imaging modalities for clinical applications requires further investigation in reducing radiation dose to the patient among others. Furthermore, we need to find an optimal solution to achieve good 3D and 4D (3D+ time) imaging, for example, to achieve accurate cancer diagnostics in a living body with moving organs. In the present paper, we investigated some limitations in achieving high-resolution 3D medical X-ray imaging techniques through quantitative analyses of X-ray propagation properties in typical body tissues and by studying image contrast, resolution and radiation dose relationships. Some issues related to the optimal design of X-ray imaging systems for early-stage cancer imaging are explored and the radiation dose limitation for human examination in clinical imaging practice is taken into consideration. In particular, we showed quantitatively the possibility of achieving highresolution 3D images for small objects of soft tissues embedded inside a thick body tissue at a clinically acceptable dose level.
2. Analysis of image resolution and contrast in relation with radiation dose We start with the investigation of quality of medical images that can be characterised by its image resolution and contrast. For clinical applications of X-ray imaging modalities, the image quality will depend on the radiation dose applied in the medical imaging
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
practice for human examination. Since the study of low-dose highresolution digital imaging techniques is our major concern here, in which the quantum noise is one of the major limiting factors, it is reasonable to make use of the well-known Rose model for the radiographic study [6,7]. Neither noise sources other than quantum noise nor contrast reduction due to Compton scattering is considered here. According to the Rose model, in order to resolve the smallest feature of a radiographic image, the minimum number of X-ray photons Nmin required to be incident on an image area of interest on the image plane is given by Nmin ¼NpS2N/C2, where Np denotes the total number of pixels in the projected image area of interest provided that the smallest feature has the size of a single pixel. If however the smallest feature is an irradiance distribution area Af that covers several pixels, one has then Np ¼A/Af with A being the full area of the image of interest. The parameter C denotes the image contrast of the irradiation distribution, and SN is the differential signal-to-noise ratio. The value of SN depends on the acceptable false probability and is normally in the range 4–6 according to the Rose criterion. As an example, we consider a breast tissue with a thickness of L¼10 cm (along X-ray beam direction) that is examined with two different photon energies of 30 and 60 keV. The question is then how high image (spatial) resolution we could achieve at a given dose level. Here, the dose level is usually limited by clinical specifications in medical X-ray imaging (normally below 10 mGy or rather 10 mSv). On the image resolution, an image with a spatial resolution of about 100 mm may be considered as high resolution in human body imaging, but it may not be the case for small animal imaging. Mathematically, according to the Rose model, an equation has been found to relate the entrance surface dose De and the achievable image resolution rs (the smallest feature size observable), depending on the size of the object, its attenuation property, image contrast as well as X-ray photon energy applied [5,8]. Numerically, shown in Fig. 1 is a quantitative relationship between the image resolution and the dose level for a variety of image contrast values at X-ray photon energies of 30 and 60 keV, respectively. It can be seen that to image objects with low contrast, a reduced image resolution can be expected to keep a specific dose level. Since the phase contrast in X-ray imaging may improve softtissue contrast, it is therefore possible to improve the image resolution while maintaining an acceptable dose level. It is also possible to reduce the dose to patients for cases where moderate
104 C = 0 001
image resolution is sufficient and/or by selecting proper photon energy.
3. Limitations of 3D image resolution in attenuation-based X-ray imaging systems To investigate possible limitations of 3D image resolution in the conventional (attenuation-based) imaging systems, let us consider a case in which a small tissue object is embedded inside a surrounding tissue, as shown in Fig. 2. Since we have noticed from the above section that the achievable image resolution is closely related to the image contrast of the tissue object to be resolved in the medical X-ray image system, we shall first give an analysis on the image contrast of a 3D tissue object that depends not only on its tissue property, but also on its size as well as the transmission direction of X-rays inside the body. In the case shown in Fig. 2, the radiographic image (attenuation) contrast value may be characterized by Ca ¼9I2–I19/I1, where I2 denotes the image intensity of X-ray passing through the region of the tissue object of interest, and I1 is the image intensity of X-ray passing through the background tissue surrounding the object tissue. In Fig. 3(a), the dependence of the attenuation contrast Ca on the size (Lo) of the tissue object is shown for some object tissues at the X-ray photon energy of 30 keV. Here, the surrounding tissue taken is the adipose tissue and its thickness is L¼L1 + Lo + L2 ¼10 cm. X-ray attenuation properties of these tissues can be found in literature [9,10]. It can be seen that the attenuation contrast generally increases with increase in size of the object. The cortical bone has a much higher image contrast than soft tissues, such as the blood and breast (mammary gland). It is shown that at the object size of Lo ¼100 mm, the attenuation contrast of the cortical bone relative to the adipose tissue has a value of about 1%, while the attenuation contrast of soft tissues has a value of around 0.1% or lower at photon energy of around 30 keV or higher. With such a low soft-tissue contrast, it is hardly possible to achieve a spatial resolution less than 100 mm in 3D medical X-ray imaging of thick body tissues (unless some external contrast agents are used) at clinically acceptable dose levels by the conventional (attenuationbased) X-ray method (see Fig. 1). On the other hand, due to much increase in the image contrast for soft tissues in phase-contrast X-ray imaging practice, it is possible to achieve low-dose 3D medical X-ray imaging with a spatial resolution below 100 mm, as discussed in the following section.
30 keV
I0
Image resolution (microon)
60 k V
103 C = 0.01
S285
I0
C = 0.001
L1 102 C=01
101
100 10-3
C = 0.01
C = 0.1
10-2 Dose (Gy)
Object tissue
Lo
Surrounding tissue
L2
10-1
Fig. 1. Image resolution versus absorbed dose at two X-ray photon energies for a breast tissue with a variety of contrasts. Here, the differential signal-to-noise ratio SN is chosen to be SN ¼ 4.
I1
I2
Fig. 2. Transmission of X-ray through a body tissue, in which a small tissue object is embedded in its surrounding tissue.
S286
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
object. Both j1 and j2 are supposed to be in the range from p to + p in the numerical example. Some numerical results for the dependence of the phase contrast Cp on the size (Lo) of the tissue object at the X-ray photon energy of 30 keV can be shown in Fig. 3(b). Here, the numerical data of tissue refractive properties are derived using d ¼4.484 10 16l2re with d being the refractive index decrement, l the X-ray wavelength and re the electron density of the tissue [9,10]. It is shown in Fig. 3(b) that the phase contrast increases with increase in size of the object. The cortical bone has a much higher phase contrast than soft tissues, such as the blood and breast (mammary gland) as we may expect. It can be seen that even at the object size of Lo ¼30 mm, the phase contrast of these soft tissues relative to the adipose tissue has a value above 1% at the photon energy of 30 keV. The much increased image contrast for soft tissues in phase-contrast X-ray imaging makes it therefore possible to achieve high-resolution 3D medical X-ray imaging at clinically acceptable dose levels.
100 30 keV Cortical bone
Attenuation-contrast Ca
10-1
10-2
Blood
Cartilage
Brain ((grey/white) / hi )
10-3 GI tract (intenstine)
10-4 Breast (mammary gland)
10-5 101
102
104
103
Object size Lo (micron) Image resolution (micron)
*
100 30 keV C ti l bone Cortical b
Phase contrast Cp
10-1 Blood
10-2
10
-3
Breast (mammary gland)
L = 10 cm
GI tract (intenstine)
L = 500 µm
Brain (grey/white)
D = 10 mGy
Blood Cartilage
103
Brain (grey/white)
Cartilage g
102
GI tract (intenstine) ( )
20
30
40 50 60 70 80 X-ray photon energy (keV) X
90
100
B Breast ((mammary gland) l d)
104
101 Object size Lo (micron)
102
Fig. 3. Dependence of (a) the attenuation contrast Ca and (b) the phase contrast Cp on the object size Lo for some object tissues at the X-ray photon energy of 30 keV. Here, the surrounding tissue is assumed to be adipose tissue with thickness L¼ 10 cm.
4. Analysis of X-ray phase contrast for high-resolution 3D medical imaging To study quantitatively the phase-contrast imaging, let us consider the example in which a small tissue object is embedded inside an adipose tissue as shown in Fig. 2. When the X-ray wave propagates through the body tissue, there will be a phase shift of the X-ray wave across the small tissue object relative to the wave passing through its surrounding tissue [2–4]. Here, we study the case in which monochromatic X-rays are used and introduce the phase contrast by Cp ¼9j2–j19/(2p) in the projected phase map on the image plane, where j2 denotes the phase of the X-ray wave passing through the small object of interest and j1 is the phase of the X-ray wave across the background tissue surrounding the
* Image resolution (micron)
10-4 100
Breast (mammary gland)
L = 10 cm
GI tract (intenstine)
L = 100 µm
Brain (grey/white)
D = 1 mGy
Blood
103
Cartilage
102
101 20
30
40
50
60
70
80
90
100
X ray photon energy (keV) XFig. 4. Dependence of image resolution on X-ray photon energy for some object tissues: (a) attenuation-contrast imaging method and (b) phase-contrast imaging method. Here, the surrounding tissue is assumed to be adipose tissue with thickness L¼10 cm.
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
Quantitatively, shown in Fig. 4 are the dependence of image resolution on X-ray photon energies at a given entrance surface dose level for some body tissues when the attenuation-contrast imaging (see Fig. 4(a)) and the phase-contrast imaging method (see Fig. 4(b)) are used, respectively. The numerical results shown here are based on the Rose model with the differential signal-to-noise ratio of SN ¼4 [5]. It is shown in Fig. 4(a) that at an entrance surface dose level below 10 mGy, it is hardly possible to achieve a spatial image resolution less than 100 mm in 3D medical X-ray imaging of thick soft body tissues by applying the conventional attenuation-based X-ray methods unless some external contrast agents are used. Using the phase-contrast method, as shown in Fig. 4(b), it is theoretically possible to achieve an isotropic spatial resolution of about 100 mm in 3D images for some typical soft tissues in a relatively thick body tissue at a dose level of around 1 mGy, depending on the number of projected images required for a specific 3D imaging modality. In particular, it is shown that there exists an optimal range of X-ray photon energies (50–60 keV for the case studied) at which the relatively high spatial resolution can be achieved. Furthermore, the numerical result indicates that the achievable image resolution can be much reduced at lower X-ray photon energies (o30 keV), despite the fact that the image contrast for soft tissues is higher at lower X-ray energy. This is mainly due to the fact that the number of low-energy photons reaching the detector is much reduced for the thick sample of the body tissue. Consequently the image resolution is reduced according to the Rose model. Thus, to achieve optimal imaging results, proper system parameters have to be chosen in medical imaging practice for human body imaging, which can be quite different for small animal imaging. Besides, it should be pointed out that the numerical analyses given here are based on ideal cases. In practice, imaging results will also depend on the imaging system setup with respect to specific requirements of absorption and phase contrast as well as phase-retrieval techniques that deserve further research efforts. Since the radiation dose increases rapidly with increase in spatial resolution in 3D imaging, it is hardly possible for conventional X-ray computed tomography (CT) techniques to achieve 3D medical imaging at a spatial resolution less than 100 mm for human examination at a clinically acceptable dose level. One way of reducing the radiation dose to a patient is to reduce the number of X-ray exposures of the patient in imaging examination. In such a case, stereoscopic imaging that requires only a few X-ray exposures (at least two) might have an advantage in comparison with CT techniques that may require several hundreds of X-ray exposures in order to get sufficient numbers of projected images for reasonable 3D image reconstruction, besides its short imaging time as well as its possibility of avoiding unnecessary exposure of important organs that are not under examination.
S287
5. Conclusions Possible limitations and optimisation of high-resolution 3D medical X-ray imaging systems are investigated by analysing quantitatively the image contrast, spatial resolution, radiation doses and their relationships for some typical body tissues. It is shown that while it is hardly possible to achieve an image resolution less than 100 mm in 3D medical X-ray imaging of human body at clinically acceptable dose levels by conventional attenuation-based X-ray CT methods (unless certain external contrast agents are used), it is theoretically possible to achieve high image resolution ( o100 mm) in an optimized phase-contrast stereoscopic X-ray imaging system at clinically acceptable dose levels ( o10 mGy). Such a high-resolution 3D medical imaging modality may open a new way of differentiating early-stage tumors of sizes around a few millimeters, resolve their geometrical shapes and improve significantly our diagnostic capability, and therefore, reduce the risk of patients to get metastatic diseases if these early-stage tumors could be identified and eliminated.
Conflict of interest statement There are no actual or potential conflicts of interest regarding this paper.
Acknowledgement Kind supports from the Cancer Society in Stockholm and the EU FP7 ULICE project are gratefully acknowledged.
References [1] [2] [3] [4] [5] [6]
[7] [8]
[9]
[10]
G.N. Naumov, L.A. Akslen, J. Folkman, Cell Cycle 5 (2006) 1779. P. Suortti, W. Thomlinson, Phys. Med. Biol. 48 (2003) R1. R.A. Lewis, Phys. Med. Biol. 49 (2004) 3573. S.-A. Zhou, A. Brahme, Med. Phys. Euro. J. Med. Phys. 24 (2008) 129. S.-A. Zhou, A. Brahme, Radiat. Prot. Dosim. 139 (2010) 334. A. Rose, Television pickup tubes and problem of vision, in: Marston (Ed.), Advances in Electronics and Electron Physics, Academic Press, New York, 1948, pp. 131–166. A.E. Burgess, J. Opt. Soc. Am. A 16 (3)(1999) 633. ¨ H. Aichinger, J. Dierker, S. Joite-Barfub, M. Sabel, Radiation Exposure and Image Quality in X-Ray Diagnostic Radiology: Physical Principles and Clinical Applications, Springer-Verlag, Berlin, 2004. ICRU Report 44, Tissue substitutes in radiation dosimetry and measurement, International Commission on Radiation Units and Measurements, Maryland, USA, 1989. B.L. Henke, E.M. Gullikson, J.C. Davis, At. Data Nucl. Data Tables 54 (1993) 181.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
On the limitations and optimisation of high-resolution 3D medical X-ray imaging systems Shu-Ang Zhou n, Anders Brahme Karolinska Institute, Department of Oncology–Pathology, P.O. Box 260, SE-171 76 Stockholm, Sweden
a r t i c l e i n f o
a b s t r a c t
Available online 19 November 2010
Based on a quantitative analysis of both attenuation and refractive properties of X-ray propagation in human body tissues and the introduction of a mathematical model for image quality analysis, some limitations and optimisation of high-resolution three-dimensional (3D) medical X-ray imaging techniques are studied. A comparison is made of conventional attenuation-based X-ray imaging methods with the phase-contrast X-ray imaging modalities that have been developed recently. The results indicate that it is theoretically possible through optimal design of the X-ray imaging system to achieve high spatial resolution (o 100 mm) in 3D medical X-ray imaging of the human body at a clinically acceptable dose level ( o 10 mGy) by introducing a phase-contrast X-ray imaging technique. & 2010 Elsevier B.V. All rights reserved.
Keywords: High resolution Optimisation Phase contrast X-ray
1. Introduction X-ray imaging has played an important role in medical imaging and diagnostics since its first introduction in the late 1800s. Despite the technology progresses during the past century, we are still limited in our ability to detect tumors in their earliest stages, monitor tumor phenotype, quantify invasion or metastasis and to visualize in vivo the effectiveness of anticancer treatments. Challenges remain in detecting early-stage solid tumors, especially for tumors of sizes less than 1 2 mm when significant angiogenesis has not yet been initiated [1]. If these early-stage tumors could be discovered, the risk of patients to get metastatic diseases can be minimized, and the cure rate would increase significantly since these tumors can be localized and eliminated by effective radiation and target-specific cancer therapies among others. At present, medical image resolution and diagnostic accuracy based on conventional attenuation-based X-ray imaging modalities are limited mainly due to their intrinsic limitations, such as low soft-tissue contrast and limited dose levels acceptable in clinical imaging practice. Recently, an increasing interest in the development of phasecontrast X-ray imaging techniques has been observed due to their potential advantageous applications in medical imaging [2–5]. The significance of phase contrast in X-ray imaging of soft tissues is understood in the classical framework of electromagnetic interactions in matter, where X-ray propagation properties of body tissues should be characterized by both their refractive indices and their attenuation coefficients. Within the diagnostic X-ray energy range,
n
Corresponding author. Tel.: + 46 8 6474753; fax: +46 8 343525. E-mail address: [email protected] (S.-A. Zhou).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.11.050
the refractive properties of soft tissues have been found to be able to play a significant role in X-ray imaging. As a result, phasecontrast X-ray imaging modalities may generate significantly greater image contrast compared to conventional attenuationbased radiography, especially for soft tissues and small objects. However, the optimal implementation of new phase-contrast X-ray imaging modalities for clinical applications requires further investigation in reducing radiation dose to the patient among others. Furthermore, we need to find an optimal solution to achieve good 3D and 4D (3D+ time) imaging, for example, to achieve accurate cancer diagnostics in a living body with moving organs. In the present paper, we investigated some limitations in achieving high-resolution 3D medical X-ray imaging techniques through quantitative analyses of X-ray propagation properties in typical body tissues and by studying image contrast, resolution and radiation dose relationships. Some issues related to the optimal design of X-ray imaging systems for early-stage cancer imaging are explored and the radiation dose limitation for human examination in clinical imaging practice is taken into consideration. In particular, we showed quantitatively the possibility of achieving highresolution 3D images for small objects of soft tissues embedded inside a thick body tissue at a clinically acceptable dose level.
2. Analysis of image resolution and contrast in relation with radiation dose We start with the investigation of quality of medical images that can be characterised by its image resolution and contrast. For clinical applications of X-ray imaging modalities, the image quality will depend on the radiation dose applied in the medical imaging
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
practice for human examination. Since the study of low-dose highresolution digital imaging techniques is our major concern here, in which the quantum noise is one of the major limiting factors, it is reasonable to make use of the well-known Rose model for the radiographic study [6,7]. Neither noise sources other than quantum noise nor contrast reduction due to Compton scattering is considered here. According to the Rose model, in order to resolve the smallest feature of a radiographic image, the minimum number of X-ray photons Nmin required to be incident on an image area of interest on the image plane is given by Nmin ¼NpS2N/C2, where Np denotes the total number of pixels in the projected image area of interest provided that the smallest feature has the size of a single pixel. If however the smallest feature is an irradiance distribution area Af that covers several pixels, one has then Np ¼A/Af with A being the full area of the image of interest. The parameter C denotes the image contrast of the irradiation distribution, and SN is the differential signal-to-noise ratio. The value of SN depends on the acceptable false probability and is normally in the range 4–6 according to the Rose criterion. As an example, we consider a breast tissue with a thickness of L¼10 cm (along X-ray beam direction) that is examined with two different photon energies of 30 and 60 keV. The question is then how high image (spatial) resolution we could achieve at a given dose level. Here, the dose level is usually limited by clinical specifications in medical X-ray imaging (normally below 10 mGy or rather 10 mSv). On the image resolution, an image with a spatial resolution of about 100 mm may be considered as high resolution in human body imaging, but it may not be the case for small animal imaging. Mathematically, according to the Rose model, an equation has been found to relate the entrance surface dose De and the achievable image resolution rs (the smallest feature size observable), depending on the size of the object, its attenuation property, image contrast as well as X-ray photon energy applied [5,8]. Numerically, shown in Fig. 1 is a quantitative relationship between the image resolution and the dose level for a variety of image contrast values at X-ray photon energies of 30 and 60 keV, respectively. It can be seen that to image objects with low contrast, a reduced image resolution can be expected to keep a specific dose level. Since the phase contrast in X-ray imaging may improve softtissue contrast, it is therefore possible to improve the image resolution while maintaining an acceptable dose level. It is also possible to reduce the dose to patients for cases where moderate
104 C = 0 001
image resolution is sufficient and/or by selecting proper photon energy.
3. Limitations of 3D image resolution in attenuation-based X-ray imaging systems To investigate possible limitations of 3D image resolution in the conventional (attenuation-based) imaging systems, let us consider a case in which a small tissue object is embedded inside a surrounding tissue, as shown in Fig. 2. Since we have noticed from the above section that the achievable image resolution is closely related to the image contrast of the tissue object to be resolved in the medical X-ray image system, we shall first give an analysis on the image contrast of a 3D tissue object that depends not only on its tissue property, but also on its size as well as the transmission direction of X-rays inside the body. In the case shown in Fig. 2, the radiographic image (attenuation) contrast value may be characterized by Ca ¼9I2–I19/I1, where I2 denotes the image intensity of X-ray passing through the region of the tissue object of interest, and I1 is the image intensity of X-ray passing through the background tissue surrounding the object tissue. In Fig. 3(a), the dependence of the attenuation contrast Ca on the size (Lo) of the tissue object is shown for some object tissues at the X-ray photon energy of 30 keV. Here, the surrounding tissue taken is the adipose tissue and its thickness is L¼L1 + Lo + L2 ¼10 cm. X-ray attenuation properties of these tissues can be found in literature [9,10]. It can be seen that the attenuation contrast generally increases with increase in size of the object. The cortical bone has a much higher image contrast than soft tissues, such as the blood and breast (mammary gland). It is shown that at the object size of Lo ¼100 mm, the attenuation contrast of the cortical bone relative to the adipose tissue has a value of about 1%, while the attenuation contrast of soft tissues has a value of around 0.1% or lower at photon energy of around 30 keV or higher. With such a low soft-tissue contrast, it is hardly possible to achieve a spatial resolution less than 100 mm in 3D medical X-ray imaging of thick body tissues (unless some external contrast agents are used) at clinically acceptable dose levels by the conventional (attenuationbased) X-ray method (see Fig. 1). On the other hand, due to much increase in the image contrast for soft tissues in phase-contrast X-ray imaging practice, it is possible to achieve low-dose 3D medical X-ray imaging with a spatial resolution below 100 mm, as discussed in the following section.
30 keV
I0
Image resolution (microon)
60 k V
103 C = 0.01
S285
I0
C = 0.001
L1 102 C=01
101
100 10-3
C = 0.01
C = 0.1
10-2 Dose (Gy)
Object tissue
Lo
Surrounding tissue
L2
10-1
Fig. 1. Image resolution versus absorbed dose at two X-ray photon energies for a breast tissue with a variety of contrasts. Here, the differential signal-to-noise ratio SN is chosen to be SN ¼ 4.
I1
I2
Fig. 2. Transmission of X-ray through a body tissue, in which a small tissue object is embedded in its surrounding tissue.
S286
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
object. Both j1 and j2 are supposed to be in the range from p to + p in the numerical example. Some numerical results for the dependence of the phase contrast Cp on the size (Lo) of the tissue object at the X-ray photon energy of 30 keV can be shown in Fig. 3(b). Here, the numerical data of tissue refractive properties are derived using d ¼4.484 10 16l2re with d being the refractive index decrement, l the X-ray wavelength and re the electron density of the tissue [9,10]. It is shown in Fig. 3(b) that the phase contrast increases with increase in size of the object. The cortical bone has a much higher phase contrast than soft tissues, such as the blood and breast (mammary gland) as we may expect. It can be seen that even at the object size of Lo ¼30 mm, the phase contrast of these soft tissues relative to the adipose tissue has a value above 1% at the photon energy of 30 keV. The much increased image contrast for soft tissues in phase-contrast X-ray imaging makes it therefore possible to achieve high-resolution 3D medical X-ray imaging at clinically acceptable dose levels.
100 30 keV Cortical bone
Attenuation-contrast Ca
10-1
10-2
Blood
Cartilage
Brain ((grey/white) / hi )
10-3 GI tract (intenstine)
10-4 Breast (mammary gland)
10-5 101
102
104
103
Object size Lo (micron) Image resolution (micron)
*
100 30 keV C ti l bone Cortical b
Phase contrast Cp
10-1 Blood
10-2
10
-3
Breast (mammary gland)
L = 10 cm
GI tract (intenstine)
L = 500 µm
Brain (grey/white)
D = 10 mGy
Blood Cartilage
103
Brain (grey/white)
Cartilage g
102
GI tract (intenstine) ( )
20
30
40 50 60 70 80 X-ray photon energy (keV) X
90
100
B Breast ((mammary gland) l d)
104
101 Object size Lo (micron)
102
Fig. 3. Dependence of (a) the attenuation contrast Ca and (b) the phase contrast Cp on the object size Lo for some object tissues at the X-ray photon energy of 30 keV. Here, the surrounding tissue is assumed to be adipose tissue with thickness L¼ 10 cm.
4. Analysis of X-ray phase contrast for high-resolution 3D medical imaging To study quantitatively the phase-contrast imaging, let us consider the example in which a small tissue object is embedded inside an adipose tissue as shown in Fig. 2. When the X-ray wave propagates through the body tissue, there will be a phase shift of the X-ray wave across the small tissue object relative to the wave passing through its surrounding tissue [2–4]. Here, we study the case in which monochromatic X-rays are used and introduce the phase contrast by Cp ¼9j2–j19/(2p) in the projected phase map on the image plane, where j2 denotes the phase of the X-ray wave passing through the small object of interest and j1 is the phase of the X-ray wave across the background tissue surrounding the
* Image resolution (micron)
10-4 100
Breast (mammary gland)
L = 10 cm
GI tract (intenstine)
L = 100 µm
Brain (grey/white)
D = 1 mGy
Blood
103
Cartilage
102
101 20
30
40
50
60
70
80
90
100
X ray photon energy (keV) XFig. 4. Dependence of image resolution on X-ray photon energy for some object tissues: (a) attenuation-contrast imaging method and (b) phase-contrast imaging method. Here, the surrounding tissue is assumed to be adipose tissue with thickness L¼10 cm.
S.-A. Zhou, A. Brahme / Nuclear Instruments and Methods in Physics Research A 648 (2011) S284–S287
Quantitatively, shown in Fig. 4 are the dependence of image resolution on X-ray photon energies at a given entrance surface dose level for some body tissues when the attenuation-contrast imaging (see Fig. 4(a)) and the phase-contrast imaging method (see Fig. 4(b)) are used, respectively. The numerical results shown here are based on the Rose model with the differential signal-to-noise ratio of SN ¼4 [5]. It is shown in Fig. 4(a) that at an entrance surface dose level below 10 mGy, it is hardly possible to achieve a spatial image resolution less than 100 mm in 3D medical X-ray imaging of thick soft body tissues by applying the conventional attenuation-based X-ray methods unless some external contrast agents are used. Using the phase-contrast method, as shown in Fig. 4(b), it is theoretically possible to achieve an isotropic spatial resolution of about 100 mm in 3D images for some typical soft tissues in a relatively thick body tissue at a dose level of around 1 mGy, depending on the number of projected images required for a specific 3D imaging modality. In particular, it is shown that there exists an optimal range of X-ray photon energies (50–60 keV for the case studied) at which the relatively high spatial resolution can be achieved. Furthermore, the numerical result indicates that the achievable image resolution can be much reduced at lower X-ray photon energies (o30 keV), despite the fact that the image contrast for soft tissues is higher at lower X-ray energy. This is mainly due to the fact that the number of low-energy photons reaching the detector is much reduced for the thick sample of the body tissue. Consequently the image resolution is reduced according to the Rose model. Thus, to achieve optimal imaging results, proper system parameters have to be chosen in medical imaging practice for human body imaging, which can be quite different for small animal imaging. Besides, it should be pointed out that the numerical analyses given here are based on ideal cases. In practice, imaging results will also depend on the imaging system setup with respect to specific requirements of absorption and phase contrast as well as phase-retrieval techniques that deserve further research efforts. Since the radiation dose increases rapidly with increase in spatial resolution in 3D imaging, it is hardly possible for conventional X-ray computed tomography (CT) techniques to achieve 3D medical imaging at a spatial resolution less than 100 mm for human examination at a clinically acceptable dose level. One way of reducing the radiation dose to a patient is to reduce the number of X-ray exposures of the patient in imaging examination. In such a case, stereoscopic imaging that requires only a few X-ray exposures (at least two) might have an advantage in comparison with CT techniques that may require several hundreds of X-ray exposures in order to get sufficient numbers of projected images for reasonable 3D image reconstruction, besides its short imaging time as well as its possibility of avoiding unnecessary exposure of important organs that are not under examination.
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5. Conclusions Possible limitations and optimisation of high-resolution 3D medical X-ray imaging systems are investigated by analysing quantitatively the image contrast, spatial resolution, radiation doses and their relationships for some typical body tissues. It is shown that while it is hardly possible to achieve an image resolution less than 100 mm in 3D medical X-ray imaging of human body at clinically acceptable dose levels by conventional attenuation-based X-ray CT methods (unless certain external contrast agents are used), it is theoretically possible to achieve high image resolution ( o100 mm) in an optimized phase-contrast stereoscopic X-ray imaging system at clinically acceptable dose levels ( o10 mGy). Such a high-resolution 3D medical imaging modality may open a new way of differentiating early-stage tumors of sizes around a few millimeters, resolve their geometrical shapes and improve significantly our diagnostic capability, and therefore, reduce the risk of patients to get metastatic diseases if these early-stage tumors could be identified and eliminated.
Conflict of interest statement There are no actual or potential conflicts of interest regarding this paper.
Acknowledgement Kind supports from the Cancer Society in Stockholm and the EU FP7 ULICE project are gratefully acknowledged.
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