- Email: [email protected]
Compton scattering spectrum as a source of information of normal and neoplastic breast tissues' composition
Applied Radiation and Isotopes 70 (2012) 1451–1455
Contents lists available at SciVerse ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Compton scattering spectrum as a source of information of normal and neoplastic breast tissues’ composition M. Antoniassi, A.L.C. Conceic- a~ o, M.E. Poletti n ~ Paulo, Ribeirao ~ Preto, 14040-901 Sa~ o Paulo, Brazil Departamento de Fı´sica—Faculdade de Filosofia Ciˆencias e Letras de Ribeira~ o Preto, Universidade de Sao
a r t i c l e i n f o
abstract
Available online 18 February 2012
In this work we measured X-ray scatter spectra from normal and neoplastic breast tissues using photon energy of 17.44 keV and a scattering angle of 901, in order to study the shape (FWHM) of the Compton peaks. The obtained results for FWHM were discussed in terms of composition and histological characteristics of each tissue type. The statistical analysis shows that the distribution of FWHM of normal adipose breast tissue clearly differs from all other investigated tissues. Comparison between experimental values of FWHM and effective atomic number revealed a strong correlation between them, showing that the FWHM values can be used to provide information about elemental composition of the tissues. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Compton scattering Compton profile Breast cancer Mammography
1. Introduction The study of Compton (inelastic) scattering has been reported as a source of information in the physical sciences being widely applied in the characterization of materials (Cesareo et al., 1992; Cooper, 1985; Harding, 1997). Specifically for medical purposes, it has been successfully used to characterize biological tissues (Antoniassi et al., 2010; Speller, 1999; Tartari et al., 1992; Theodorakou and Farquharson, 2008) and in imaging techniques (Harding, 1997). The techniques based on Compton scattering use the information present in the spectrum of scattered photons to obtain information about the tissue with which the primary radiation interacts. They can be separated in two groups of techniques: (i) techniques that explore the intensity (Sharaf, 2001) and (ii) techniques that explore the shape (profile) of the scattered photons’ spectrum. The latter is based on the fact that the shape of the energy distribution (spectrum) of Compton scattered photons is related to the momentum distribution of electrons of the elements which compose the scatterer material (Cooper, 1985; Ribberfors, 1975), particularly in the characterization of human tissues or materials of radiological interest. Holt et al. (1983) published results of a preliminary investigation which showed differences in the Compton spectrum shape between different samples of liver tissue. Gatti et al. (1986) suggested fitting experimentally measured Compton profiles as sums of free atom profiles to obtain the elemental composition of the scattering sample. Matscheko et al. (1989) analyzed the spectrum of four materials (beryllium, lucite, aluminum and polyethylene) highlighting that the differences between their shapes are due to the differences in electron
momentum distributions of the elements which compose the scattered materials. MacKenzie (1990) suggested that the high energy part of the Compton scattering profile in backscattering geometry could be used to evaluate bone mineral content. Tartari et al. (1994) reduced the Compton profile shape information to a single ratio between the count of two specific regions of the curve showing qualitatively a correlation between the mean atomic number of the sample and this ratio. More recently, Rao et al. (2004) calculated the Doppler broadening of Compton scattering for molecules, plastics, tissues and biological materials in the X-ray energy region. In the present work we have measured X-ray scatter spectra (Compton and Rayleigh) from normal (adipose and fibroglandular) and neoplastic (benign and malignant) breast tissues using a photon energy of 17.44 keV (Ka radiation of Mo) and a scattering angle of 901 (x¼0.99 A˚ 1). The selected parameter used to characterize the Compton spectrum shape was its full width at half maximum (FWHM). The results were discussed in terms of composition and histological characteristics of these tissues’ types. Statistical analyses were applied to the distributions of FWHM in order to verify the differences existing between normal and neoplastic tissues. The FWHM values of the breast tissues obtained were compared with experimental values of effective atomic number previously reported (Antoniassi et al., 2011) in order to verify the existence of the correlation between these quantities.
2. Materials and method 2.1. Experimental arrangement
n
Corresponding author. Tel.: þ55 16 3602 4442; fax: þ 55 16 3602 4887. E-mail address: [email protected] (M.E. Poletti).
0969-8043/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2012.02.008
The experimental set-up is shown in Fig. 1. The X-ray tube used was a Mo (Z¼ 42, Ka ¼17.44 keV and Kb ¼19.6 keV) operating at
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M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
can be written in the impulse approximation as (Cooper, 1997) 2 m0 r 20 E d s EE0 ð1cos yÞ Jðpz Þ ð1Þ 1 þ cos2 y þ 0 ¼ 0 2 2_K E m0 c dOdE where O is the solid angle, E is the incident photon energy, E’ is the scattered photon energy, r0 is the classical electron radius, K is the modulus of the X-ray scattering vector given as K ¼ 1=c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p E2 þE02 þ 2EE0 cos y, m0 is the mass of electron, _ is the reduced Planck constant, c is the speed of light, pz is the projection of the initial momentum p of the electron on the scattering vector direction (defined as z) and J(pz) is the Compton profile, which depends on the distribution of momenta n(p) of the atomic target electrons being defined as ZZ Jðpz Þ ¼ nðpÞdpx dpy ð2Þ Fig. 1. Experimental arrangement.
35 kVp and 45 mA. A zirconium filter (Zr, Z¼40) filtered out the Mo Kb line and a graphite monochromator was used to select the fluorescence line (Ka). The beam size was limited by two slits S1 (0.5 0.5 mm2) and S2 (0.75 0.75 mm2), positioned in the entrance and exit of the monochromator, respectively. The flux rate on the sample was about 106 photons/s cm2. An additional set of circular (f ¼ 2 mm) slits (S3 and S4), separated by 15 mm, was placed in front of the detector in order to limit the range of accepted scattering angles, minimizing the angular broadening of Compton peak. The experimental geometry was in reflection mode with a scattering angle (y) of 901, corresponding to a momentum transfer value of x¼0.99 A˚ 1. The detection system consisted of a Si(Li) detector (Canberra SL30165) with energy resolution of 300 eV at 17.44 keV, coupled to a multichannel analyzer (MCA), which allows discriminating the peaks of elastic and inelastic scattering. The time for each measurement was 1000 s, in order to reduce the statistical uncertainties in the counts, for both elastic and inelastic peaks, to less than 1%.
2.2. Samples The breast tissue samples were obtained by the surgical removal of the entire breast (mastectomy) or plastic surgery for breast reduction (mastoplasty) at the Hospital das Clı´nicas da Faculdade de Medicina de Ribeira~ o Preto, Universidade de Sa~ o Paulo, Ribeira~ o Preto, Brazil, whose collection and handling of these fresh samples were performed in compliance with the requirements established by the local ethical committee. Upon removal, the samples were stored at room temperature in formalin (4% formaldehyde in water) in order to preserve the structures within the tissues such as cell walls and nuclei which are needed for accurate histopathological analysis. A total of 109 samples of breast tissues were analyzed, 65 of them histologically classified as normal (49 adipose and 16 fibroglandular), 10 as benign (fibroadenomas) and 34 as malignant (carcinomas) breast tissues. The sample thickness (6 mm) was chosen in order to provide sufficient single scattering events while minimizing the probability of multiple scattering (Kane et al., 1986).
The Compton profile J(pz) has been extensively tabulated by Biggs et al. (1975) according to the Hartree-Fock and relativistic Dirac–Hartree-Fock functions from the momentum distribution, n(p), for the electrons of all orbitals of all atoms. Fig. 2 shows the theoretical double differential cross section for atoms of hydrogen, carbon and oxygen (atoms of biological interest), obtained summing the contribution of each shell of the P atoms (Rao et al., 2004): d2s/dOdE0 ¼ Ni(d2s/dOdE0 )i, where Ni 2 0 and (d s/dOdE )i is the number of electrons and the double differential cross section of the ith shell, respectively. The effect of electron binding was introduced in the double differential cross section calculation constraining the Compton profile, J(pz), to values for which the energy transfer is larger than the ionization energy of the electron shell being excited. This effect is evidenced by the discontinuities in the curves. The Compton profile determines the shape and consequently the widths of the double differential cross sections. Moreover, we observe in Fig. 2 that the higher the atomic number the larger is the width of the curve. Following Cesareo et al. (1992) the width of the experimental energy distribution of Compton scattered photons is determined by (i) the Compton profile J(pz), where pz is dependent on both the excitation energy and the scattering angle, (ii) the energy resolution of detection system, (iii) the range of accepted scattering angles and (iv) the multiple scattering. Considering that the first factor is unique that can be used to obtain information about the composition of scatterer sample, it is desirable that other factors are minimized. In the present work the effect of the resolution of the detector was minimized using a detector with good energy resolution (300 eV) at the experimental energy (17.44 keV).
2.3. Basis of the experimental model The energy distribution (spectrum) of Compton scattered photons from a material at a scattering angle y, detected by the detector, is related to the double differential cross section, which
Fig. 2. Double differential cross section for hydrogen, carbon and oxygen for an incident energy of 17.44 keV and a scattering angle of 901.
M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
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The effects of the detector acceptance angle and multiple scattering on the width of the curve were minimized by the collimation system and the small thickness of sample used, respectively. 2.4. Determination of FWHM The FWHM of the Compton peaks were determined from the experimental spectra using a gaussian fitting procedure in which the width of the Rayleigh curve was kept constant, equal to the detector energy resolution (300 eV), permitting to exclude the contributions of the elastically scattered photons (Rayleigh) on Compton peak. The R2 values obtained were always better than 0.98.
3. Results and discussion Fig. 3 shows the normalized average spectra for the various histological classifications studied. The small peak (17.44 keV) of each spectrum corresponds to photons elastically (Rayleigh) scattered and its width is determined by the detector resolution (Cesareo et al., 1992). The high peak (16.86 keV) corresponds to photons that suffered loss of energy due to the inelastic (Compton) scattering in the breast sample. As shown in Fig. 3, there are differences between the widths of the inelastic peaks of each tissue type. The distributions of the FWHM values, displayed as box and whisker plots, are shown in Fig. 4. The thick line inside the boxes shows the median of each tissue type. The inter-quartile range is determined by the box and encloses the 25th–75th percentile. The whiskers contain all values within 1.5 box lengths. From Fig. 4 it is possible to observe variations in values of FWHM, for each tissue type, which can be attributed to external parameters (diet, medication and environment), individual parameters (age, hormonal status and genetics) or to micro-internal parameters associated to particular histological characteristic of each type of tissue. It was observed that FWHM values obtained with adipose breast tissues are smaller than those obtained with fibroglandular and neoplastic (benign and malignant) tissues. This fact was expected because the adipose tissue is composed mainly of specialized cells in storage lipids, called adipocytes, rich in carbon (Z¼6) (Woodard and White, 1986), while fibroglandular and neoplastic breast tissues are of conjunctive or epithelial origin
Fig. 3. Average normalized spectra of adipose, fibroglandular, fibroadenoma and carcinoma breast tissues.
Fig. 4. Box plots of the FWHM for each tissue type.
(rich in collagen fiber and water), presenting a higher oxygen composition (Z ¼8) (Poletti et al., 2002a, b) and consequently a larger FWHM. Thus the observed differences in the FWHM values are mainly related to the amount of carbon and oxygen present in each tissue type, since the hydrogen composition is relatively minor and approximately equal for all tissues types, as can be seen in Table 1, which compares the mass percentage of hydrogen, carbon and oxygen, the major constituents of the tissues, obtained by Hammerstein et al. (1979), Poletti et al. (2002a, b) and Woodard and White (1986). Although there is no previously published data of composition of fibroadenoma, the obtained values of FWHM for this tissue type permit to infer that its composition is similar to the composition of fibroglandular or carcinoma tissues presented in Table 1. In order to verify the experimental results, the double differential cross section (Rao et al., 2004) for each tissue type was calculated using the elemental composition summarized in Table 1 (Poletti et al., 2002a, b), which is shown in Fig. 5. From Fig. 5 it is possible to observe that adipose breast tissue present the smallest FWHM value, whereas normal fibroglandular and carcinoma tissues present similar values (in accordance with the experimental spectrum). Moreover, the theoretical calculation from the double differential cross sections predicts an absolute difference, between the FWHM of adipose tissue and the other tissues (fibroglandular and neoplastic), about 0.026 keV, which is in good agreement with that obtained experimentally (around 0.02 keV). The statistical comparisons took the form of a one-way analysis of variance (ANOVA) with the Bonferroni test applied as a post-hoc test, showing that FWHM values from normal adipose tissue are significantly different from all the other investigated tissue types (p o0.01), while the other comparisons are not statistically significant. Finally, the correlation degree between FWHM and composition of tissue was verified comparing the experimental FWHM of each tissue with its correspondent value of effective atomic number (Zeff) previously reported (Antoniassi et al., 2011), as can be seen in Fig. 6, which shows the distribution of FWHM versus Zeff of the samples. Pearson’s correlation test was applied and found a statistically significant correlation (r ¼0.954; po0.0001) between these two quantities, showing that the FWHM of Compton scattering can provide similar information to that obtained with the effective atomic number.
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M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
Table 1 Mass density and chemical composition (mass percentage) of hydrogen, carbon and oxygen of breast tissues in literature. Hammerstein et al. (1979)
Poletti et al. (2002a, b)
Woodard and White (1986)
Tissue type
Density (g/cm 3)
H (Z¼ 1) (mass%)
C (Z¼ 6) (mass%)
O (Z ¼8) (mass%)
Density (g/cm 3)
H (Z ¼1) (mass%)
C (Z¼6) (mass%)
O (Z ¼8) (mass%)
Density (g/cm 3)
H (Z ¼1) (mass%)
C (Z ¼6) (mass%)
O (Z¼ 8) (mass%)
Adipose Fibroglandular Carcinoma
0.93 1.04 NM
11.2 10.2 NM
61.9 18.4 NM
25.1 67.7 NM
0.92 1.04 NM
12.4 7 0.1b 9.3 7 0.5b 9.92a
76.5 71.1b 18.4 70.9b 19.36a
10.7 71.3b 67.9 7 2.0b 65.98a
0.95 1.02 NM
11.4 10.6 NM
59.8 33.2 NM
27.8 52.7 NM
NM: not measured. a b
Mean percentage of carcinomas presented by Poletti et al. (2002a). Mass percentage presented by Poletti et al. (2002b).
Fig. 5. Double differential cross sections for adipose, fibroglandular and carcinoma breast tissues.
compositions of the histological constituent of each type of tissue. Statistical comparisons were made using the obtained distributions, showing that normal adipose breast tissue clearly differs from all other types of tissues. The FWHM values of the breast tissues obtained were compared with experimental values of effective atomic number (Antoniassi et al., 2011). A strong correlation between them was verified which permitted to show that the differences in FWHM values of each tissue type are related to differences in the composition of the tissues. Considering that the technique based on the FWHM of the Compton scattering peak showed to be sensitive to the variation of composition of the tissues, the next step of this work is to analyze the potentialities of imaging techniques (Gatti et al., 1986) to add spatial information of the tissue in the breast (boundaries, infiltration, shape, position and extension) to the contrast information obtained by FWHM, increasing the potential of the technique to differentiate tissues according their histological classifications.
Acknowledgments The authors would like to acknowledge the support by the Brazilian agencies Fundac- a~ o de Amparo a Pesquisa do Estado de Sa~ o Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq). In addition, we also would like to thank the Departamento de Patologia do Hospital das Clı´nicas de Ribeira~ o Preto, Brazil, for allowing the collection of the human breast samples and for the histopathological classification of the tissues. References
Fig. 6. Distribution of FWHM versus effective atomic number.
4. Conclusion In this work we measured X-ray scatter spectra (Compton and Rayleigh) from normal (adipose and fibroglandular) and neoplastic (benign and malignant) breast tissues using a photon energy of 17.44 keV (Ka radiation of Mo) and a scattering angle of 901 (x¼0.99 A˚ 1), in order to obtain the FWHM of the Compton peaks. The results showed that adipose breast tissue has smaller FWHM than fibroglandular and neoplastic breast tissues (fibroadenoma and carcinoma), fact related to the carbon and oxygen
Antoniassi, M., Conceic- a~ o, A.L.C., Poletti, M.E., 2010. Characterization of breast tissues using Compton scattering. Nucl. Instrum. Methods Phys. Res. A 619, 375–378. Antoniassi, M., Conceic- a~ o, A.L.C., Poletti, M.E., 2011. Study of effective atomic number of breast tissues determined using the elastic to inelastic scattering ratio. Nucl. Instrum. Methods Phys. Res. A 652, 739–743. Biggs, F., Mendelsohn, L.B., Mann, J.B., 1975. Hartree-Fock Compton profiles for the elements. At. Data Nucl. Data Tables 16, 201–309. Cesareo, R., Hanson, A.L., Gigante, G.E., Pedraza, L.J., Mathaboally, S.Q.G., 1992. Interaction of keV photons with matter and new applications. Phys. Rep. 213, 117–178. Cooper, M.J., 1985. Compton scattering and electron momentum determination. Rep. Prog. Phys. 48, 415–481. Cooper, M.J., 1997. Compton scattering and the study of electron momentum density distributions. Radiat. Phys. Chem. 50, 63–76. Gatti, E., Rehak, P., Kemmer, J., 1986. Proposal for a New Tomographic Device Providing Information on the Chemical Properties of a Body Section. IEEE Trans. Med. Imag. 5, 207–221. Hammerstein, G.R., Miller, D.W., White, D.R., Masterson, M.E., Woodard, H.Q., Laughlin, J.S., 1979. Absorbed radiation dose in mammography. Radiology 130, 485–491. Harding, G., 1997. Inelastic photon scattering: effects and applications in biomedical science and industry. Radiat. Phys. Chem. 50, 91–111.
M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
Holt, R.S., Kouris, K., Cooper, M.J., Jackson, D.F., 1983. Assessment of gamma ray scattering for the characterisation of biological material. Phys. Med. Biol. 28, 1435–1440. Kane, P.P., Kissel, L., Pratt, R.H., Roy, S.C., 1986. Elastic scattering of [gamma]-rays and X-rays by atoms. Phys. Rep. 140, 75–159. MacKenzie, I.K., 1990. An axially symmetric gamma-ray backscatter system for DuMond spectrometry. Nucl. Instrum. Methods Phys. Res. A 299, 377–381. Matscheko, G., Carlsson, G.A., Ribberfors, R., 1989. Compton spectroscopy in the diagnostic X-ray energy range: II effects of scattering material and energy resolution. Phys. Med. Biol. 34, 199–208. Poletti, M.E., Gonc- alves, O.D., Mazzaro, I., 2002a. Coherent and incoherent scattering of 17.44 and 6.93 keV X-ray photons scattered from biological and biological-equivalent samples: characterization of tissues. X-Ray Spectrom. 31, 57–61. Poletti, M.E., Gonc- alves, O.D., Mazzaro, I., 2002b. X-ray scattering from human breast tissues and breast-equivalent materials. Phys. Med. Biol. 47, 47–63. Rao, D.V., Cesareo, R., Brunetti, A., Gigante, G.E., Akatsuka, T., Takeda, T., Itai, Y., 2004. Doppler broadening calculations of Compton scattering for molecules, plastics, tissues, and few biological materials in the X-ray region: an analysis
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in terms of Compton broadening and geometrical energy broadening. J. Phys. Chem. Ref. Data 33, 627–712. Ribberfors, R., 1975. Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. Phys. Rev. B 12, 2067–2074. Sharaf, J.M., 2001. Practical aspects of Compton scatter densitometry. Appl. Radiat. Isot. 54, 801–809. Speller, R.D., 1999. Tissue analysis using X-ray scattering. X-Ray Spectrom. 28, 224–250. Tartari, A., Casnati, E., Felsteiner, J., Baraldi, C., Singh, B., 1992. Feasibility of in vivo tissue characterisation by Compton scattering profile measurements. Nucl. Instrum. Methods Phys. Res. B 71, 209–213. Tartari, A., Casnati, E., Fernandez, J.E., Felsteiner, J., Baraldi, C., 1994. Photon backscattering tissue characterization by energy dispersive spectroscopy evaluations. Phys. Med. Biol. 39, 219. Theodorakou, C., Farquharson, M.J., 2008. Human soft tissue analysis using X-ray or gamma-ray techniques. Phys. Med. Biol. 53, R111–R149. Woodard, H.Q., White, D.R., 1986. The composition of body tissues. Br. J. Radiol. 59, 1209–1218.
Contents lists available at SciVerse ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Compton scattering spectrum as a source of information of normal and neoplastic breast tissues’ composition M. Antoniassi, A.L.C. Conceic- a~ o, M.E. Poletti n ~ Paulo, Ribeirao ~ Preto, 14040-901 Sa~ o Paulo, Brazil Departamento de Fı´sica—Faculdade de Filosofia Ciˆencias e Letras de Ribeira~ o Preto, Universidade de Sao
a r t i c l e i n f o
abstract
Available online 18 February 2012
In this work we measured X-ray scatter spectra from normal and neoplastic breast tissues using photon energy of 17.44 keV and a scattering angle of 901, in order to study the shape (FWHM) of the Compton peaks. The obtained results for FWHM were discussed in terms of composition and histological characteristics of each tissue type. The statistical analysis shows that the distribution of FWHM of normal adipose breast tissue clearly differs from all other investigated tissues. Comparison between experimental values of FWHM and effective atomic number revealed a strong correlation between them, showing that the FWHM values can be used to provide information about elemental composition of the tissues. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Compton scattering Compton profile Breast cancer Mammography
1. Introduction The study of Compton (inelastic) scattering has been reported as a source of information in the physical sciences being widely applied in the characterization of materials (Cesareo et al., 1992; Cooper, 1985; Harding, 1997). Specifically for medical purposes, it has been successfully used to characterize biological tissues (Antoniassi et al., 2010; Speller, 1999; Tartari et al., 1992; Theodorakou and Farquharson, 2008) and in imaging techniques (Harding, 1997). The techniques based on Compton scattering use the information present in the spectrum of scattered photons to obtain information about the tissue with which the primary radiation interacts. They can be separated in two groups of techniques: (i) techniques that explore the intensity (Sharaf, 2001) and (ii) techniques that explore the shape (profile) of the scattered photons’ spectrum. The latter is based on the fact that the shape of the energy distribution (spectrum) of Compton scattered photons is related to the momentum distribution of electrons of the elements which compose the scatterer material (Cooper, 1985; Ribberfors, 1975), particularly in the characterization of human tissues or materials of radiological interest. Holt et al. (1983) published results of a preliminary investigation which showed differences in the Compton spectrum shape between different samples of liver tissue. Gatti et al. (1986) suggested fitting experimentally measured Compton profiles as sums of free atom profiles to obtain the elemental composition of the scattering sample. Matscheko et al. (1989) analyzed the spectrum of four materials (beryllium, lucite, aluminum and polyethylene) highlighting that the differences between their shapes are due to the differences in electron
momentum distributions of the elements which compose the scattered materials. MacKenzie (1990) suggested that the high energy part of the Compton scattering profile in backscattering geometry could be used to evaluate bone mineral content. Tartari et al. (1994) reduced the Compton profile shape information to a single ratio between the count of two specific regions of the curve showing qualitatively a correlation between the mean atomic number of the sample and this ratio. More recently, Rao et al. (2004) calculated the Doppler broadening of Compton scattering for molecules, plastics, tissues and biological materials in the X-ray energy region. In the present work we have measured X-ray scatter spectra (Compton and Rayleigh) from normal (adipose and fibroglandular) and neoplastic (benign and malignant) breast tissues using a photon energy of 17.44 keV (Ka radiation of Mo) and a scattering angle of 901 (x¼0.99 A˚ 1). The selected parameter used to characterize the Compton spectrum shape was its full width at half maximum (FWHM). The results were discussed in terms of composition and histological characteristics of these tissues’ types. Statistical analyses were applied to the distributions of FWHM in order to verify the differences existing between normal and neoplastic tissues. The FWHM values of the breast tissues obtained were compared with experimental values of effective atomic number previously reported (Antoniassi et al., 2011) in order to verify the existence of the correlation between these quantities.
2. Materials and method 2.1. Experimental arrangement
n
Corresponding author. Tel.: þ55 16 3602 4442; fax: þ 55 16 3602 4887. E-mail address: [email protected] (M.E. Poletti).
0969-8043/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2012.02.008
The experimental set-up is shown in Fig. 1. The X-ray tube used was a Mo (Z¼ 42, Ka ¼17.44 keV and Kb ¼19.6 keV) operating at
1452
M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
can be written in the impulse approximation as (Cooper, 1997) 2 m0 r 20 E d s EE0 ð1cos yÞ Jðpz Þ ð1Þ 1 þ cos2 y þ 0 ¼ 0 2 2_K E m0 c dOdE where O is the solid angle, E is the incident photon energy, E’ is the scattered photon energy, r0 is the classical electron radius, K is the modulus of the X-ray scattering vector given as K ¼ 1=c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p E2 þE02 þ 2EE0 cos y, m0 is the mass of electron, _ is the reduced Planck constant, c is the speed of light, pz is the projection of the initial momentum p of the electron on the scattering vector direction (defined as z) and J(pz) is the Compton profile, which depends on the distribution of momenta n(p) of the atomic target electrons being defined as ZZ Jðpz Þ ¼ nðpÞdpx dpy ð2Þ Fig. 1. Experimental arrangement.
35 kVp and 45 mA. A zirconium filter (Zr, Z¼40) filtered out the Mo Kb line and a graphite monochromator was used to select the fluorescence line (Ka). The beam size was limited by two slits S1 (0.5 0.5 mm2) and S2 (0.75 0.75 mm2), positioned in the entrance and exit of the monochromator, respectively. The flux rate on the sample was about 106 photons/s cm2. An additional set of circular (f ¼ 2 mm) slits (S3 and S4), separated by 15 mm, was placed in front of the detector in order to limit the range of accepted scattering angles, minimizing the angular broadening of Compton peak. The experimental geometry was in reflection mode with a scattering angle (y) of 901, corresponding to a momentum transfer value of x¼0.99 A˚ 1. The detection system consisted of a Si(Li) detector (Canberra SL30165) with energy resolution of 300 eV at 17.44 keV, coupled to a multichannel analyzer (MCA), which allows discriminating the peaks of elastic and inelastic scattering. The time for each measurement was 1000 s, in order to reduce the statistical uncertainties in the counts, for both elastic and inelastic peaks, to less than 1%.
2.2. Samples The breast tissue samples were obtained by the surgical removal of the entire breast (mastectomy) or plastic surgery for breast reduction (mastoplasty) at the Hospital das Clı´nicas da Faculdade de Medicina de Ribeira~ o Preto, Universidade de Sa~ o Paulo, Ribeira~ o Preto, Brazil, whose collection and handling of these fresh samples were performed in compliance with the requirements established by the local ethical committee. Upon removal, the samples were stored at room temperature in formalin (4% formaldehyde in water) in order to preserve the structures within the tissues such as cell walls and nuclei which are needed for accurate histopathological analysis. A total of 109 samples of breast tissues were analyzed, 65 of them histologically classified as normal (49 adipose and 16 fibroglandular), 10 as benign (fibroadenomas) and 34 as malignant (carcinomas) breast tissues. The sample thickness (6 mm) was chosen in order to provide sufficient single scattering events while minimizing the probability of multiple scattering (Kane et al., 1986).
The Compton profile J(pz) has been extensively tabulated by Biggs et al. (1975) according to the Hartree-Fock and relativistic Dirac–Hartree-Fock functions from the momentum distribution, n(p), for the electrons of all orbitals of all atoms. Fig. 2 shows the theoretical double differential cross section for atoms of hydrogen, carbon and oxygen (atoms of biological interest), obtained summing the contribution of each shell of the P atoms (Rao et al., 2004): d2s/dOdE0 ¼ Ni(d2s/dOdE0 )i, where Ni 2 0 and (d s/dOdE )i is the number of electrons and the double differential cross section of the ith shell, respectively. The effect of electron binding was introduced in the double differential cross section calculation constraining the Compton profile, J(pz), to values for which the energy transfer is larger than the ionization energy of the electron shell being excited. This effect is evidenced by the discontinuities in the curves. The Compton profile determines the shape and consequently the widths of the double differential cross sections. Moreover, we observe in Fig. 2 that the higher the atomic number the larger is the width of the curve. Following Cesareo et al. (1992) the width of the experimental energy distribution of Compton scattered photons is determined by (i) the Compton profile J(pz), where pz is dependent on both the excitation energy and the scattering angle, (ii) the energy resolution of detection system, (iii) the range of accepted scattering angles and (iv) the multiple scattering. Considering that the first factor is unique that can be used to obtain information about the composition of scatterer sample, it is desirable that other factors are minimized. In the present work the effect of the resolution of the detector was minimized using a detector with good energy resolution (300 eV) at the experimental energy (17.44 keV).
2.3. Basis of the experimental model The energy distribution (spectrum) of Compton scattered photons from a material at a scattering angle y, detected by the detector, is related to the double differential cross section, which
Fig. 2. Double differential cross section for hydrogen, carbon and oxygen for an incident energy of 17.44 keV and a scattering angle of 901.
M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
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The effects of the detector acceptance angle and multiple scattering on the width of the curve were minimized by the collimation system and the small thickness of sample used, respectively. 2.4. Determination of FWHM The FWHM of the Compton peaks were determined from the experimental spectra using a gaussian fitting procedure in which the width of the Rayleigh curve was kept constant, equal to the detector energy resolution (300 eV), permitting to exclude the contributions of the elastically scattered photons (Rayleigh) on Compton peak. The R2 values obtained were always better than 0.98.
3. Results and discussion Fig. 3 shows the normalized average spectra for the various histological classifications studied. The small peak (17.44 keV) of each spectrum corresponds to photons elastically (Rayleigh) scattered and its width is determined by the detector resolution (Cesareo et al., 1992). The high peak (16.86 keV) corresponds to photons that suffered loss of energy due to the inelastic (Compton) scattering in the breast sample. As shown in Fig. 3, there are differences between the widths of the inelastic peaks of each tissue type. The distributions of the FWHM values, displayed as box and whisker plots, are shown in Fig. 4. The thick line inside the boxes shows the median of each tissue type. The inter-quartile range is determined by the box and encloses the 25th–75th percentile. The whiskers contain all values within 1.5 box lengths. From Fig. 4 it is possible to observe variations in values of FWHM, for each tissue type, which can be attributed to external parameters (diet, medication and environment), individual parameters (age, hormonal status and genetics) or to micro-internal parameters associated to particular histological characteristic of each type of tissue. It was observed that FWHM values obtained with adipose breast tissues are smaller than those obtained with fibroglandular and neoplastic (benign and malignant) tissues. This fact was expected because the adipose tissue is composed mainly of specialized cells in storage lipids, called adipocytes, rich in carbon (Z¼6) (Woodard and White, 1986), while fibroglandular and neoplastic breast tissues are of conjunctive or epithelial origin
Fig. 3. Average normalized spectra of adipose, fibroglandular, fibroadenoma and carcinoma breast tissues.
Fig. 4. Box plots of the FWHM for each tissue type.
(rich in collagen fiber and water), presenting a higher oxygen composition (Z ¼8) (Poletti et al., 2002a, b) and consequently a larger FWHM. Thus the observed differences in the FWHM values are mainly related to the amount of carbon and oxygen present in each tissue type, since the hydrogen composition is relatively minor and approximately equal for all tissues types, as can be seen in Table 1, which compares the mass percentage of hydrogen, carbon and oxygen, the major constituents of the tissues, obtained by Hammerstein et al. (1979), Poletti et al. (2002a, b) and Woodard and White (1986). Although there is no previously published data of composition of fibroadenoma, the obtained values of FWHM for this tissue type permit to infer that its composition is similar to the composition of fibroglandular or carcinoma tissues presented in Table 1. In order to verify the experimental results, the double differential cross section (Rao et al., 2004) for each tissue type was calculated using the elemental composition summarized in Table 1 (Poletti et al., 2002a, b), which is shown in Fig. 5. From Fig. 5 it is possible to observe that adipose breast tissue present the smallest FWHM value, whereas normal fibroglandular and carcinoma tissues present similar values (in accordance with the experimental spectrum). Moreover, the theoretical calculation from the double differential cross sections predicts an absolute difference, between the FWHM of adipose tissue and the other tissues (fibroglandular and neoplastic), about 0.026 keV, which is in good agreement with that obtained experimentally (around 0.02 keV). The statistical comparisons took the form of a one-way analysis of variance (ANOVA) with the Bonferroni test applied as a post-hoc test, showing that FWHM values from normal adipose tissue are significantly different from all the other investigated tissue types (p o0.01), while the other comparisons are not statistically significant. Finally, the correlation degree between FWHM and composition of tissue was verified comparing the experimental FWHM of each tissue with its correspondent value of effective atomic number (Zeff) previously reported (Antoniassi et al., 2011), as can be seen in Fig. 6, which shows the distribution of FWHM versus Zeff of the samples. Pearson’s correlation test was applied and found a statistically significant correlation (r ¼0.954; po0.0001) between these two quantities, showing that the FWHM of Compton scattering can provide similar information to that obtained with the effective atomic number.
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Table 1 Mass density and chemical composition (mass percentage) of hydrogen, carbon and oxygen of breast tissues in literature. Hammerstein et al. (1979)
Poletti et al. (2002a, b)
Woodard and White (1986)
Tissue type
Density (g/cm 3)
H (Z¼ 1) (mass%)
C (Z¼ 6) (mass%)
O (Z ¼8) (mass%)
Density (g/cm 3)
H (Z ¼1) (mass%)
C (Z¼6) (mass%)
O (Z ¼8) (mass%)
Density (g/cm 3)
H (Z ¼1) (mass%)
C (Z ¼6) (mass%)
O (Z¼ 8) (mass%)
Adipose Fibroglandular Carcinoma
0.93 1.04 NM
11.2 10.2 NM
61.9 18.4 NM
25.1 67.7 NM
0.92 1.04 NM
12.4 7 0.1b 9.3 7 0.5b 9.92a
76.5 71.1b 18.4 70.9b 19.36a
10.7 71.3b 67.9 7 2.0b 65.98a
0.95 1.02 NM
11.4 10.6 NM
59.8 33.2 NM
27.8 52.7 NM
NM: not measured. a b
Mean percentage of carcinomas presented by Poletti et al. (2002a). Mass percentage presented by Poletti et al. (2002b).
Fig. 5. Double differential cross sections for adipose, fibroglandular and carcinoma breast tissues.
compositions of the histological constituent of each type of tissue. Statistical comparisons were made using the obtained distributions, showing that normal adipose breast tissue clearly differs from all other types of tissues. The FWHM values of the breast tissues obtained were compared with experimental values of effective atomic number (Antoniassi et al., 2011). A strong correlation between them was verified which permitted to show that the differences in FWHM values of each tissue type are related to differences in the composition of the tissues. Considering that the technique based on the FWHM of the Compton scattering peak showed to be sensitive to the variation of composition of the tissues, the next step of this work is to analyze the potentialities of imaging techniques (Gatti et al., 1986) to add spatial information of the tissue in the breast (boundaries, infiltration, shape, position and extension) to the contrast information obtained by FWHM, increasing the potential of the technique to differentiate tissues according their histological classifications.
Acknowledgments The authors would like to acknowledge the support by the Brazilian agencies Fundac- a~ o de Amparo a Pesquisa do Estado de Sa~ o Paulo (FAPESP) and Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq). In addition, we also would like to thank the Departamento de Patologia do Hospital das Clı´nicas de Ribeira~ o Preto, Brazil, for allowing the collection of the human breast samples and for the histopathological classification of the tissues. References
Fig. 6. Distribution of FWHM versus effective atomic number.
4. Conclusion In this work we measured X-ray scatter spectra (Compton and Rayleigh) from normal (adipose and fibroglandular) and neoplastic (benign and malignant) breast tissues using a photon energy of 17.44 keV (Ka radiation of Mo) and a scattering angle of 901 (x¼0.99 A˚ 1), in order to obtain the FWHM of the Compton peaks. The results showed that adipose breast tissue has smaller FWHM than fibroglandular and neoplastic breast tissues (fibroadenoma and carcinoma), fact related to the carbon and oxygen
Antoniassi, M., Conceic- a~ o, A.L.C., Poletti, M.E., 2010. Characterization of breast tissues using Compton scattering. Nucl. Instrum. Methods Phys. Res. A 619, 375–378. Antoniassi, M., Conceic- a~ o, A.L.C., Poletti, M.E., 2011. Study of effective atomic number of breast tissues determined using the elastic to inelastic scattering ratio. Nucl. Instrum. Methods Phys. Res. A 652, 739–743. Biggs, F., Mendelsohn, L.B., Mann, J.B., 1975. Hartree-Fock Compton profiles for the elements. At. Data Nucl. Data Tables 16, 201–309. Cesareo, R., Hanson, A.L., Gigante, G.E., Pedraza, L.J., Mathaboally, S.Q.G., 1992. Interaction of keV photons with matter and new applications. Phys. Rep. 213, 117–178. Cooper, M.J., 1985. Compton scattering and electron momentum determination. Rep. Prog. Phys. 48, 415–481. Cooper, M.J., 1997. Compton scattering and the study of electron momentum density distributions. Radiat. Phys. Chem. 50, 63–76. Gatti, E., Rehak, P., Kemmer, J., 1986. Proposal for a New Tomographic Device Providing Information on the Chemical Properties of a Body Section. IEEE Trans. Med. Imag. 5, 207–221. Hammerstein, G.R., Miller, D.W., White, D.R., Masterson, M.E., Woodard, H.Q., Laughlin, J.S., 1979. Absorbed radiation dose in mammography. Radiology 130, 485–491. Harding, G., 1997. Inelastic photon scattering: effects and applications in biomedical science and industry. Radiat. Phys. Chem. 50, 91–111.
M. Antoniassi et al. / Applied Radiation and Isotopes 70 (2012) 1451–1455
Holt, R.S., Kouris, K., Cooper, M.J., Jackson, D.F., 1983. Assessment of gamma ray scattering for the characterisation of biological material. Phys. Med. Biol. 28, 1435–1440. Kane, P.P., Kissel, L., Pratt, R.H., Roy, S.C., 1986. Elastic scattering of [gamma]-rays and X-rays by atoms. Phys. Rep. 140, 75–159. MacKenzie, I.K., 1990. An axially symmetric gamma-ray backscatter system for DuMond spectrometry. Nucl. Instrum. Methods Phys. Res. A 299, 377–381. Matscheko, G., Carlsson, G.A., Ribberfors, R., 1989. Compton spectroscopy in the diagnostic X-ray energy range: II effects of scattering material and energy resolution. Phys. Med. Biol. 34, 199–208. Poletti, M.E., Gonc- alves, O.D., Mazzaro, I., 2002a. Coherent and incoherent scattering of 17.44 and 6.93 keV X-ray photons scattered from biological and biological-equivalent samples: characterization of tissues. X-Ray Spectrom. 31, 57–61. Poletti, M.E., Gonc- alves, O.D., Mazzaro, I., 2002b. X-ray scattering from human breast tissues and breast-equivalent materials. Phys. Med. Biol. 47, 47–63. Rao, D.V., Cesareo, R., Brunetti, A., Gigante, G.E., Akatsuka, T., Takeda, T., Itai, Y., 2004. Doppler broadening calculations of Compton scattering for molecules, plastics, tissues, and few biological materials in the X-ray region: an analysis
1455
in terms of Compton broadening and geometrical energy broadening. J. Phys. Chem. Ref. Data 33, 627–712. Ribberfors, R., 1975. Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. Phys. Rev. B 12, 2067–2074. Sharaf, J.M., 2001. Practical aspects of Compton scatter densitometry. Appl. Radiat. Isot. 54, 801–809. Speller, R.D., 1999. Tissue analysis using X-ray scattering. X-Ray Spectrom. 28, 224–250. Tartari, A., Casnati, E., Felsteiner, J., Baraldi, C., Singh, B., 1992. Feasibility of in vivo tissue characterisation by Compton scattering profile measurements. Nucl. Instrum. Methods Phys. Res. B 71, 209–213. Tartari, A., Casnati, E., Fernandez, J.E., Felsteiner, J., Baraldi, C., 1994. Photon backscattering tissue characterization by energy dispersive spectroscopy evaluations. Phys. Med. Biol. 39, 219. Theodorakou, C., Farquharson, M.J., 2008. Human soft tissue analysis using X-ray or gamma-ray techniques. Phys. Med. Biol. 53, R111–R149. Woodard, H.Q., White, D.R., 1986. The composition of body tissues. Br. J. Radiol. 59, 1209–1218.