- Email: [email protected]
Simulation of RBS spectra for quantitative mapping of inhomogeneous biological tissue
Nuclear Instruments and Methods in Physics Research B 104 (1995) 171-175
Beam Interactions with Materials & Atoms
Simulation of RBS spectra for quantitative mapping of inhomogeneous biological tissue Ph. Moretto”,
L. Razafindrabe
Centre d’Etudes Nucliaires de Bordeaux-Gradignan,
33175 Gradignan cedex, France
Abstract
A computational algorithm, capable to simulate RBS spectra recorded during scanning proton microprobe analysis of organic specimens with inhomogeneous thickness has been developed. This program is based on an enhancement of the RUMP source code. It allows us to normalize in terms of dry specimen mass the elemental concentrations obtained with simultaneous PIXE and RBS microanalysis. This code includes non-Rutherford cross sections for proton scattering from carbon, nitrogen and oxygen. It permits the computation of matrix correction factors for the analysis of low energy X-ray emitters. In this paper, the first version of the simulation algorithm is presented as also the application to the analysis of reference organic material.
1. Introduction
When applied in the biomedical field, the capability to extract accurate quantitative results, expressed in term of specimen mass, is certainly a strength of proton microprobes. However, the normalization of data obtained during beam scanning requires a perfect knowledge of the local mass in the irradiated area. This problem was solved using simultaneous PIXE and RBS analysis, allowing thus to determine carbon, nitrogen and oxygen, the main constituents of the organic matrix of living tissue. This procedure has been applied by numerous authors [l-3] but a difficulty that bears on the analytical accuracy was remaining. The inhomogeneous distribution of the thickness in the scanned area leads to a large spread in shapes of RBS spectra. This prevents the use of classical computational algorithms. In order to process these data, we developed a program based on an enhancement of the well-known RUMP source code [4]. The idea is to simulate the effect of an heterogeneous area1 mass density in the scanned region by means of a linear sum of theoretical spectra generated with a stepwise increasing thickness. The final contribution of each thickness class to this sum is then
*Corresponding (33) 56 75 11 80.
author. Tel.: (33) 56 89 18 00. Fax:
0168-583X/95/$9.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00444-0
adjusted to fit the shape of experimental data. The obtained weights are then employed for the calculation of the specimen average area1 mass density. This program, named RUMPIN, includes non-Rutherford cross sections for proton scattering from carbon, nitrogen and oxygen, at 135”, an angle which corresponds to the experimental configuration of the CENBG microprobe irradiation chamber [S]. The application of RUMPIN is thereby limited to the scattering of protons on organic matrices with thickness up to 1000 ug/cm’. Above this value, the slowing down of incident particles becomes too high and the low energy non-Rutherford scattering cross-sections ( < 500 keV) are not very well described leading to unreliable simulation values. When thin organic matrices are investigated, the collected charge can be accurately determined avoiding thus the use of a tedious, and sometimes inaccurate, experimental beam charge monitoring. This point is particularly useful when partial spectra are extracted from subregions of original maps. The related charge can be calculated in a simple way with RUMPIN and used in the calculation of absolute elemental concentrations which can then be expressed in terms of dry specimen mass. In addition, the knowledge of the distribution of the area1 mass density permits the calculation of matrix correction factors taking into account the slowing down of incident particles and the attenuation of low energy X-rays. The aim of this paper is to present the RUMPIN simulation algorithm and the certification procedure
IV. ANALYTICAL TECHNIQUES
172
Ph. Moretto, L. RazajindrabelNucl.
Change
RtJMP simulation
Instr. and Meth. in Phys. Res. B 104 (1995) 171-I 75
ich. KS
Fig. 1. The RUMPIN algorithm.
using original reference samples of spiked polyacrylamide gels.
obtained
by cryosection
2. Simulation algorithm This program is based on the three following observations: (a) When an organic matrix is scanned with a proton microbeam, the total RBS spectrum is constituted by a finite sum of basic spectra, each of them being recorded on a region of different area1 mass density. The resulting total energy spectrum of backscattered particles has a smoothed shape, more especially at the low energy edge. (b) On the energy spectrum of particles scattered by organic materials mainly made of carbon, hydrogen, nitrogen and oxygen, the front edge of each peak or each step is not really affected by the sample heterogeneity. Approximate values of collected charge and stoichiometry for C, N and 0 can thus be determined and set as initial conditions to begin a more complex simulation. This is particularly true when the proton energy exceeds 2 MeV and if modern particle detectors with convenable energy resolution (- 15 keV for a 20 mm’ solid detector) are employed. (c) The variation of the main components stoichiometry in living tissues (C, N, 0), and more especially
in the analysed specimen, is generally limited. The consequence is that all basic theoretical spectra will be generated with the same composition. The algorithm is constructed in an iterative manner and based upon the conventional two steps procedure: simulation/fit with experimental data. Using classical RUMP simulation, the stoichiometry and the total collected charge are first adjusted in order to fit the front edge of each step on the experimental spectrum. This stage permits to fix initial values for the total collected charge Qr and an approximate stoichiometry which will be used to generate the first serial basic spectra. At the same time, the maximum range of the area1 mass density of the sample is assessed. Fourteen basic spectra are then simulated using the RUMP code and the previous parameters. Each spectrum is generated with a stepwise increasing thickness, in such a manner that the whole range of the previously set mass density is covered. At the starting point of the calculation, all spectra are simulated with the same basic charge Qi = Qr/14. Resulting spectra are stored in 14 vectors Ni(c) (c is the channel number). The theoretical total spectrum is calculated as a linear sum NT(c) = Z(Qi/QT). Ni(c) with statistical weights equally distributed (Qi/QT = A) . This vector is then compared with the experimental spectrum using graphic overlay on the computer screen (Fig. 2). The distribution of the area1 mass density in the irradiated region of the sample (i.e. the statistical weights QJQr) is displayed under the form of an histogram (Fig. 2). A graphic user interface allows us to act directly on this histogram, by means of a mouse button, in order to modify the statistical contribution Qi/QT of each basic spectrum. In that case, the sum C Qi/QT is automatically normalized to 1. The linear sum NT(c) is recalculated and the spectrum is plotted again. From this point, the user can also modify one of the initial parameters, stoichiometry, charge, maximum mass density and start again the whole previous procedure. This iterative process is interrupted when a good agreement between theoretical and experimental spectra is achieved. The average mass density is then calculated with a simple linear sum using Qi/QT weights.
3. Matrix correction factors When necessary, matrix correction factors (M.C.F.) for micro-PIXE analysis taking into account the attenuation of low energy X-rays and the slowing down of incident particles can be calculated. The description of the sample previously provided by RUMPIN with respect to the distribution of its mass density and its global composition is employed. A basic multiplicative factor (M.C.F.)i is evaluated for each one of the 14 defined thickness values and a linear sum is computed as follows: M.C.F. = C (Qi/Q& (M.C.F.)i. In this approach, the resulting M.C.F. can be directly applied to the elemental
173
Ph. Moretto, L. Ra.zajindrabe/Nucl. Instr. and Meth. in Phys. Res. B 104 (1995) 17/- 17.~ Thickness distribution (%)
Thickness ditribution
(9%)
7.5
A.M.
A.M.
= 88 fig/cm*
= 143 &ml~ -B-
-A-
Channel number
Chanoel ouxnber
Fig. 2. An example of RUMPIN treatment of 2 MeV proton backscattering data after the analysis of a human polynuclear cancer cell [19]. Dimension of the scan 130 x 130 pm’. The total three-dimensional carbon map is displayed on the left. On rhe right map, one can see the subregions employed for the extraction of the three partial spectra. For each subregion (B, C or D) and for the whole scan (A), the experimental and theoretical spectra are overlaid. The histogram represents the distribution of the area1 mass density within the related region. The average mass density (A.M.) is also given.
concentration normalized with the previous RUMPIN average area1 mass density. Basic (M.C.F.)j are computed using a conventional numerical integration of the X-ray yields calculated at each point of the path, within the matrix, of the decelerating particle. FORTRAN routines are taken from [2,6]. The stopping powers are extracted from [7]. The photon cross-sections of Viegele [S] are used in the calculation of X-ray attenuation. The semi-empirical cross-sections for X-ray production are taken from [9]. At the present time, M.C.F. for the correction of K, lines from Na to Ca are available.
4. Non-Rutherford
cross sections
The cross section for proton scattering from light nuclei (2 < 12) may be significantly greater than pure Rutherford. It is especially true for carbon, the main constituent of the organic matrix. The enhancement is seven times that of the Rutherford value for 2 MeV protons. Unfortunately the carbon, nitrogen and oxygen cross sections are not accurately known in the whole energy range necessary for the RUMPIN simulation, more particularly at low energy ( < 1 MeV). We used consequently numerical approximation on the basis of
IV. ANALYTICAL
TECHNIQUES
174
Ph. Moretto, L. Razajindrabe/Nucl.
Instr. and Meth. in Phys. Res. 5 IO4 (1995) 171-I 75
(cl 0
IO 20 30 40 THICKNESS (pm)
Go
Fig. 4. RBS and PIXE microanalysis of polyacrylamide gel sections spiked with NaCl. The sodium concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 5 to 40 urn Mean f SD = 2322 i 275 (12% deviation) (n = 16)
MAGNESIUM I I I I I
,I 0000
\ Energy
(MeV)
Fig. 3. The estimated resonant cross sections for the scattering of protons from rZC, r4N and I60 at 135”. The Rutherford cross section is displayed for comparison (dashed line). See text for details.
experimental data extracted from different authors. We sometimes interpolated data derived from different scattering angles in order to estimate values at 135”. The ‘2C(p,p)‘2C cross section was estimated in the range 1500/3000 keV with the natural carbon cross section of Amirikas et al. [ 111. Values at 150” and 110” were interpolated to provide values at 135” and the 1% contribution of 13C to natural carbon was neglected. In the range 500/1500 keV, Jackson’s’ experimental data for 12C at 127.8” in the centre-of-mass system were fitted using a third order polynomial function [12]. Complementary information was obtained from [13]. The 160(p,p)‘60 cross section was estimated in the range 600/2000 keV using the experimental values at 135” from [14] which were fitted with a fourth order polynomial function. In the range 2000/3000 keV, the experimental data from [ll] at 110” and 150” were interpolated. Values were cross-checked using several points from angular dependence in [15]. The 14N(p,p)i4N cross section in the range 800/2000 keV was obtained using results of the Knox’s fitting procedure [13] of data from [16,17]. Above 2000 keV, the program RESS included in the RUMP package was employed. This program, based on the
M
2
8000
g !fi
6000
2 E Z 8
4000 2000 0
I
1, , , , , ,fj 0
5
10
15
20
25
30
35
THICKNESS (pm) Fig. 5. RBS and PIXE microanalysis of polyacrylamide gel sections spiked with MgSO,. The magnesium concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 2 to 30 urn. Mean k SD = 6693 f 344 (5% deviation) (n = 13) nuclear shell model, describes the resonances in [18] terms. Amplitudes were adjusted in order to reproduce the data of Bashkin et al. [16]. Fig. 3 shows the estimated resonance cross section for the setting of “C, 14N and I60 at 135”. All these cross sections were injected in RUMP simulation.
5. Application of reference material In order to check the mass normalization procedure and the evaluation of the M.C.F., we developed reference specimens with physical and chemical properties as close
Ph. Moretto, L. Razafindrabe / Nucl. Instr. and Meth. in Phys. Res. I3 104 (1995) 171-l 75
3
I
5000
7. Conclusion
PLATINUM I I I I
\ .Fj 4000 z El 3000 2 E
2000
z g
1000
u
1 0 5
10
15
20
25
THICKNESS
30 35 (Km)
40
175
45
Fig. 6. RBS and PIXE microanalysis of poiyacrylamide gel sections spiked with cisplatin. The platinum concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 10 to 40 t.tm. Mean + SD = 3120 + 110 (3.5% deviation) (n = 10).
as possible from that of living tissue. A polyacrylamide gel, generally used for electrophoresis purpose was prepared according to the following scheme: different mineral salts (NaCI, MgS04) and cisplatin, an organometallic compound, were added to solutions .of acrylamide/bis-acrylamide (37.5 : 1 ratio) (SIGMA reagents). Temed and ammonium persulfate (SIGMA reagents) were then added as catalysts of acrylamide polymerization. When the gel had set, it was cryofixed in isopentane chilled with liquid nitrogen. Serial sections with a thickness ranging from 2 to 40 pm were obtained using a cryomicrotome. The slides were mounted on thin formvar foils (20 pg/cm’) and freeze-dried in the cryostat for 2 h. All slides were analysed using the CENBG microprobe. PIXE and RBS analysis were simultaneously carried out and RBS data were treated with the RUMPIN program whereas PIXE spectra were fitted using GUPIX software [IO]. The Na, Mg and Pt concentrations expressed in terms of the dry organic mass are presented in Figs. 4-6 for gels respectively spiked with NaCl, MgSO.+ and cisplatin. For Na and Mg the values were corrected with the RUMPIN M.C.F. For these three elements, one can verify that the concentrations expressed in unit of ngjg are independent of the section thickness.
6. Software RUMPIN runs on an IBM-PC or compatible computer. It has been implemented in MicrosoftR FORTRAN 5.1 and the graphic library has been taken from an IBMR Graphics Development Toolkit version 1.1.
The achievement of accurate absolute concentrations is certainly one of the main advantages of simultaneous micro-PIXE and micro-RBS analysis when compared to other micro-analytical techniques generally applied in the biomedical field, such as secondary ion mass spectrometry (SIMS) or Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICPMS). The accuracy of the given absolute concentrations is difficult to assess because of the lack of reference material which can be used at the micrometer scale and more especially because their matrix composition is very far from that of living tissue. Nevertheless, the polyacrylamide gel approach is an interesting advance, even though problems in the homogeneity of included elements are still remaining. First values obtained with RUMPIN in the microanalysis of individual human tumours cells were cross-checked with bulk PIXE analysis [19]. A good agreement was observed. This is certainly one of the best proofs.
References [l] N.E. Whitehead, Nucl. Instr. and Meth. 164 (1979) 381. [2] D. Heck and E. Rokita, Nucl. Instr. and Meth. B 3 (1984) 259. [3] K. Themner and K.G. Malmqvist, Nucl. Instr. and Meth. B 15 (1986) 404. [4] L.R. Doolittle, Nucl. Instr. and Meth. B 9 (1985) 344. [S] Y. Llabador, D. Bertault, J.C. Gouillaud and Ph. Moretto, Nucl. Instr. and Meth. B 49 (1990) 435. [6] D. Heck, E. Rokita, Report KfK 3909 (1985). [7] L.C. Northcliffe and R.F. &hilling, Nucl. Data Tables A 7 (1970) 233. [S] Wm.J. Veigele, At. Data Tables 5 (1973) 51. [9] S.A.E. Johansson and T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 473. [lo] J.A. Maxwell, J.L. Campbell and W.J. Teesdale, Nucl. Instr. and Meth. B 43 (1989) 218. [11] R. Amirikas, D.N. Jamieson and S.P. Dooley, Nucl. Instr. and Meth. B 77 (1993) 110. [12] H.L. Jackson, A.I. Galonsky, F.J. Eppling, R.W. Hill, E. Goldberg and J.R. Cameron, Phys. Rev. 89 (2) (1953) 365. [13] J.M. Knox, R.J. M&sod, D.R. Mayo and X. Qian, Nucl. Instr. and Meth. B 45 (1990) 26. [14] M. Braun and T. Freid, Z. Phys. A 311 (1983) 173. [15] M. Luomajlrvi, E. Rauhala and M. Hautala, Nucl. Instr. and Meth. B 9 (1985) 255. [16] S. Bashkin, R.R. Carlson and R.A. Douglas, Phys. Rev. 114 (1959) 1552. Cl77 J.W. Olness, J. Vorona and H.W. Lewis, Phys. Rev. 112 (2) (1958) 475. [18] J.R. Cameron, Phys. Rev. 90 (1953) 839. [19] Ph. Moretto, R. Ortega, Y. Llabador, M. Simonoff, J. Bbnard, these Proceedings (ICNMTA’94) Nucl. Instr. and Meth. B 104 (1995) 292. 1203 K. Themner, Nucl. Instr. and Meth. B 54 (1991) 115.
IV. ANALYTICAL TECHNIQUES
Beam Interactions with Materials & Atoms
Simulation of RBS spectra for quantitative mapping of inhomogeneous biological tissue Ph. Moretto”,
L. Razafindrabe
Centre d’Etudes Nucliaires de Bordeaux-Gradignan,
33175 Gradignan cedex, France
Abstract
A computational algorithm, capable to simulate RBS spectra recorded during scanning proton microprobe analysis of organic specimens with inhomogeneous thickness has been developed. This program is based on an enhancement of the RUMP source code. It allows us to normalize in terms of dry specimen mass the elemental concentrations obtained with simultaneous PIXE and RBS microanalysis. This code includes non-Rutherford cross sections for proton scattering from carbon, nitrogen and oxygen. It permits the computation of matrix correction factors for the analysis of low energy X-ray emitters. In this paper, the first version of the simulation algorithm is presented as also the application to the analysis of reference organic material.
1. Introduction
When applied in the biomedical field, the capability to extract accurate quantitative results, expressed in term of specimen mass, is certainly a strength of proton microprobes. However, the normalization of data obtained during beam scanning requires a perfect knowledge of the local mass in the irradiated area. This problem was solved using simultaneous PIXE and RBS analysis, allowing thus to determine carbon, nitrogen and oxygen, the main constituents of the organic matrix of living tissue. This procedure has been applied by numerous authors [l-3] but a difficulty that bears on the analytical accuracy was remaining. The inhomogeneous distribution of the thickness in the scanned area leads to a large spread in shapes of RBS spectra. This prevents the use of classical computational algorithms. In order to process these data, we developed a program based on an enhancement of the well-known RUMP source code [4]. The idea is to simulate the effect of an heterogeneous area1 mass density in the scanned region by means of a linear sum of theoretical spectra generated with a stepwise increasing thickness. The final contribution of each thickness class to this sum is then
*Corresponding (33) 56 75 11 80.
author. Tel.: (33) 56 89 18 00. Fax:
0168-583X/95/$9.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00444-0
adjusted to fit the shape of experimental data. The obtained weights are then employed for the calculation of the specimen average area1 mass density. This program, named RUMPIN, includes non-Rutherford cross sections for proton scattering from carbon, nitrogen and oxygen, at 135”, an angle which corresponds to the experimental configuration of the CENBG microprobe irradiation chamber [S]. The application of RUMPIN is thereby limited to the scattering of protons on organic matrices with thickness up to 1000 ug/cm’. Above this value, the slowing down of incident particles becomes too high and the low energy non-Rutherford scattering cross-sections ( < 500 keV) are not very well described leading to unreliable simulation values. When thin organic matrices are investigated, the collected charge can be accurately determined avoiding thus the use of a tedious, and sometimes inaccurate, experimental beam charge monitoring. This point is particularly useful when partial spectra are extracted from subregions of original maps. The related charge can be calculated in a simple way with RUMPIN and used in the calculation of absolute elemental concentrations which can then be expressed in terms of dry specimen mass. In addition, the knowledge of the distribution of the area1 mass density permits the calculation of matrix correction factors taking into account the slowing down of incident particles and the attenuation of low energy X-rays. The aim of this paper is to present the RUMPIN simulation algorithm and the certification procedure
IV. ANALYTICAL TECHNIQUES
172
Ph. Moretto, L. RazajindrabelNucl.
Change
RtJMP simulation
Instr. and Meth. in Phys. Res. B 104 (1995) 171-I 75
ich. KS
Fig. 1. The RUMPIN algorithm.
using original reference samples of spiked polyacrylamide gels.
obtained
by cryosection
2. Simulation algorithm This program is based on the three following observations: (a) When an organic matrix is scanned with a proton microbeam, the total RBS spectrum is constituted by a finite sum of basic spectra, each of them being recorded on a region of different area1 mass density. The resulting total energy spectrum of backscattered particles has a smoothed shape, more especially at the low energy edge. (b) On the energy spectrum of particles scattered by organic materials mainly made of carbon, hydrogen, nitrogen and oxygen, the front edge of each peak or each step is not really affected by the sample heterogeneity. Approximate values of collected charge and stoichiometry for C, N and 0 can thus be determined and set as initial conditions to begin a more complex simulation. This is particularly true when the proton energy exceeds 2 MeV and if modern particle detectors with convenable energy resolution (- 15 keV for a 20 mm’ solid detector) are employed. (c) The variation of the main components stoichiometry in living tissues (C, N, 0), and more especially
in the analysed specimen, is generally limited. The consequence is that all basic theoretical spectra will be generated with the same composition. The algorithm is constructed in an iterative manner and based upon the conventional two steps procedure: simulation/fit with experimental data. Using classical RUMP simulation, the stoichiometry and the total collected charge are first adjusted in order to fit the front edge of each step on the experimental spectrum. This stage permits to fix initial values for the total collected charge Qr and an approximate stoichiometry which will be used to generate the first serial basic spectra. At the same time, the maximum range of the area1 mass density of the sample is assessed. Fourteen basic spectra are then simulated using the RUMP code and the previous parameters. Each spectrum is generated with a stepwise increasing thickness, in such a manner that the whole range of the previously set mass density is covered. At the starting point of the calculation, all spectra are simulated with the same basic charge Qi = Qr/14. Resulting spectra are stored in 14 vectors Ni(c) (c is the channel number). The theoretical total spectrum is calculated as a linear sum NT(c) = Z(Qi/QT). Ni(c) with statistical weights equally distributed (Qi/QT = A) . This vector is then compared with the experimental spectrum using graphic overlay on the computer screen (Fig. 2). The distribution of the area1 mass density in the irradiated region of the sample (i.e. the statistical weights QJQr) is displayed under the form of an histogram (Fig. 2). A graphic user interface allows us to act directly on this histogram, by means of a mouse button, in order to modify the statistical contribution Qi/QT of each basic spectrum. In that case, the sum C Qi/QT is automatically normalized to 1. The linear sum NT(c) is recalculated and the spectrum is plotted again. From this point, the user can also modify one of the initial parameters, stoichiometry, charge, maximum mass density and start again the whole previous procedure. This iterative process is interrupted when a good agreement between theoretical and experimental spectra is achieved. The average mass density is then calculated with a simple linear sum using Qi/QT weights.
3. Matrix correction factors When necessary, matrix correction factors (M.C.F.) for micro-PIXE analysis taking into account the attenuation of low energy X-rays and the slowing down of incident particles can be calculated. The description of the sample previously provided by RUMPIN with respect to the distribution of its mass density and its global composition is employed. A basic multiplicative factor (M.C.F.)i is evaluated for each one of the 14 defined thickness values and a linear sum is computed as follows: M.C.F. = C (Qi/Q& (M.C.F.)i. In this approach, the resulting M.C.F. can be directly applied to the elemental
173
Ph. Moretto, L. Ra.zajindrabe/Nucl. Instr. and Meth. in Phys. Res. B 104 (1995) 17/- 17.~ Thickness distribution (%)
Thickness ditribution
(9%)
7.5
A.M.
A.M.
= 88 fig/cm*
= 143 &ml~ -B-
-A-
Channel number
Chanoel ouxnber
Fig. 2. An example of RUMPIN treatment of 2 MeV proton backscattering data after the analysis of a human polynuclear cancer cell [19]. Dimension of the scan 130 x 130 pm’. The total three-dimensional carbon map is displayed on the left. On rhe right map, one can see the subregions employed for the extraction of the three partial spectra. For each subregion (B, C or D) and for the whole scan (A), the experimental and theoretical spectra are overlaid. The histogram represents the distribution of the area1 mass density within the related region. The average mass density (A.M.) is also given.
concentration normalized with the previous RUMPIN average area1 mass density. Basic (M.C.F.)j are computed using a conventional numerical integration of the X-ray yields calculated at each point of the path, within the matrix, of the decelerating particle. FORTRAN routines are taken from [2,6]. The stopping powers are extracted from [7]. The photon cross-sections of Viegele [S] are used in the calculation of X-ray attenuation. The semi-empirical cross-sections for X-ray production are taken from [9]. At the present time, M.C.F. for the correction of K, lines from Na to Ca are available.
4. Non-Rutherford
cross sections
The cross section for proton scattering from light nuclei (2 < 12) may be significantly greater than pure Rutherford. It is especially true for carbon, the main constituent of the organic matrix. The enhancement is seven times that of the Rutherford value for 2 MeV protons. Unfortunately the carbon, nitrogen and oxygen cross sections are not accurately known in the whole energy range necessary for the RUMPIN simulation, more particularly at low energy ( < 1 MeV). We used consequently numerical approximation on the basis of
IV. ANALYTICAL
TECHNIQUES
174
Ph. Moretto, L. Razajindrabe/Nucl.
Instr. and Meth. in Phys. Res. 5 IO4 (1995) 171-I 75
(cl 0
IO 20 30 40 THICKNESS (pm)
Go
Fig. 4. RBS and PIXE microanalysis of polyacrylamide gel sections spiked with NaCl. The sodium concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 5 to 40 urn Mean f SD = 2322 i 275 (12% deviation) (n = 16)
MAGNESIUM I I I I I
,I 0000
\ Energy
(MeV)
Fig. 3. The estimated resonant cross sections for the scattering of protons from rZC, r4N and I60 at 135”. The Rutherford cross section is displayed for comparison (dashed line). See text for details.
experimental data extracted from different authors. We sometimes interpolated data derived from different scattering angles in order to estimate values at 135”. The ‘2C(p,p)‘2C cross section was estimated in the range 1500/3000 keV with the natural carbon cross section of Amirikas et al. [ 111. Values at 150” and 110” were interpolated to provide values at 135” and the 1% contribution of 13C to natural carbon was neglected. In the range 500/1500 keV, Jackson’s’ experimental data for 12C at 127.8” in the centre-of-mass system were fitted using a third order polynomial function [12]. Complementary information was obtained from [13]. The 160(p,p)‘60 cross section was estimated in the range 600/2000 keV using the experimental values at 135” from [14] which were fitted with a fourth order polynomial function. In the range 2000/3000 keV, the experimental data from [ll] at 110” and 150” were interpolated. Values were cross-checked using several points from angular dependence in [15]. The 14N(p,p)i4N cross section in the range 800/2000 keV was obtained using results of the Knox’s fitting procedure [13] of data from [16,17]. Above 2000 keV, the program RESS included in the RUMP package was employed. This program, based on the
M
2
8000
g !fi
6000
2 E Z 8
4000 2000 0
I
1, , , , , ,fj 0
5
10
15
20
25
30
35
THICKNESS (pm) Fig. 5. RBS and PIXE microanalysis of polyacrylamide gel sections spiked with MgSO,. The magnesium concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 2 to 30 urn. Mean k SD = 6693 f 344 (5% deviation) (n = 13) nuclear shell model, describes the resonances in [18] terms. Amplitudes were adjusted in order to reproduce the data of Bashkin et al. [16]. Fig. 3 shows the estimated resonance cross section for the setting of “C, 14N and I60 at 135”. All these cross sections were injected in RUMP simulation.
5. Application of reference material In order to check the mass normalization procedure and the evaluation of the M.C.F., we developed reference specimens with physical and chemical properties as close
Ph. Moretto, L. Razafindrabe / Nucl. Instr. and Meth. in Phys. Res. I3 104 (1995) 171-l 75
3
I
5000
7. Conclusion
PLATINUM I I I I
\ .Fj 4000 z El 3000 2 E
2000
z g
1000
u
1 0 5
10
15
20
25
THICKNESS
30 35 (Km)
40
175
45
Fig. 6. RBS and PIXE microanalysis of poiyacrylamide gel sections spiked with cisplatin. The platinum concentrations are expressed in unit of organic dry mass following the RUMPIN normalization and for a thickness ranging from 10 to 40 t.tm. Mean + SD = 3120 + 110 (3.5% deviation) (n = 10).
as possible from that of living tissue. A polyacrylamide gel, generally used for electrophoresis purpose was prepared according to the following scheme: different mineral salts (NaCI, MgS04) and cisplatin, an organometallic compound, were added to solutions .of acrylamide/bis-acrylamide (37.5 : 1 ratio) (SIGMA reagents). Temed and ammonium persulfate (SIGMA reagents) were then added as catalysts of acrylamide polymerization. When the gel had set, it was cryofixed in isopentane chilled with liquid nitrogen. Serial sections with a thickness ranging from 2 to 40 pm were obtained using a cryomicrotome. The slides were mounted on thin formvar foils (20 pg/cm’) and freeze-dried in the cryostat for 2 h. All slides were analysed using the CENBG microprobe. PIXE and RBS analysis were simultaneously carried out and RBS data were treated with the RUMPIN program whereas PIXE spectra were fitted using GUPIX software [IO]. The Na, Mg and Pt concentrations expressed in terms of the dry organic mass are presented in Figs. 4-6 for gels respectively spiked with NaCl, MgSO.+ and cisplatin. For Na and Mg the values were corrected with the RUMPIN M.C.F. For these three elements, one can verify that the concentrations expressed in unit of ngjg are independent of the section thickness.
6. Software RUMPIN runs on an IBM-PC or compatible computer. It has been implemented in MicrosoftR FORTRAN 5.1 and the graphic library has been taken from an IBMR Graphics Development Toolkit version 1.1.
The achievement of accurate absolute concentrations is certainly one of the main advantages of simultaneous micro-PIXE and micro-RBS analysis when compared to other micro-analytical techniques generally applied in the biomedical field, such as secondary ion mass spectrometry (SIMS) or Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICPMS). The accuracy of the given absolute concentrations is difficult to assess because of the lack of reference material which can be used at the micrometer scale and more especially because their matrix composition is very far from that of living tissue. Nevertheless, the polyacrylamide gel approach is an interesting advance, even though problems in the homogeneity of included elements are still remaining. First values obtained with RUMPIN in the microanalysis of individual human tumours cells were cross-checked with bulk PIXE analysis [19]. A good agreement was observed. This is certainly one of the best proofs.
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IV. ANALYTICAL TECHNIQUES