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ESR dose estimation on fossil tooth enamel by fitting the natural spectrum into the irradiated spectra
Radiation Measurements 35 (2002) 87–93
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ESR dose estimation on fossil tooth enamel by $tting the natural spectrum into the irradiated spectra Rainer Gr(un ∗ Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia Received 26 November 2000; received in revised form 1 May 2001; accepted 22 May 2001
Abstract Fitting the natural, derivative ESR spectrum into the irradiated spectra has been tested as a method for the estimation of the dose value of powdered fossil tooth enamel, which is the basis of ESR dating. It was found that this method has signi$cant advantages over traditional peak-to-peak assessments, dose versus magnetic $eld plots as well as deconvolution of the absorption spectrum, because it is less dependent on a range of interferences. Furthermore, the $tting procedure is computationally trivial and the dose results are not dependent on random noise. It is concluded that $tting the natural spectrum ought to provide the most reliable dose estimations for most fossil teeth which have been exposed to doses of more than c 2002 Elsevier Science Ltd. All rights reserved. 5 –10 Gy.
1. Introduction The methods for ESR dose estimation on tooth enamel were recently reviewed by Gr(un (2000). The strategies for dose estimation can be grouped into peak-to-peak, dose versus magnetic $eld, and deconvolution (using Gaussian, Lorentzian or CO− 2 peak shapes or ESR spectra that show negligible interferences, e.g., Hayes and Haskell, 2000) methods. It is well known that the ESR spectrum of tooth enamel is generated by a range of radicals (e.g. Vanhaelewyn et al., 2000). It is, however, not so clear how the variable superposition of the ESR lines of these radicals a;ect the dose determination. The reason for this is that so far it was not possible to completely separate the ESR spectral components of the identi$ed radicals. 2. Methods for dose estimation Figs. 1A and B show absorption spectra of sample 1047, deconvoluted with the spectrum of the CO− 2 radical (as ∗ Corresponding author. Tel.: +61-2-6125-3122; fax: +61-26125-0315. E-mail address: [email protected] (R. Gr(un).
extracted from fossil teeth by maximum likelihood common factor analysis, Vanhaelewyn et al., 2000) plus a “wide” and two narrower (#1 and #2) Gaussian lines. The results of several studies (e.g. Jonas et al., 1994; Jonas, 1995; Gr(un, 1998) have shown that the “wide” line displays some dose sensitivity and usually yields much higher dose values than the central, apparently axial line, and that the Gaussian peaks #1 and #2 usually yield smaller dose values. Fitting the derivative spectrum with the spectrum of the CO− 2 radical (Figs. 1E and F) also shows that there is a series of relatively narrow peaks that are generated by a variety of radicals. The dose versus magnetic $eld plots con$rm that the central area is interfered with by a range of peaks each having considerably di;erent dose responses (see Gr(un and Jonas, 1996). The variable dose response of the radicals was the reason to prefer time intensive deconvolution over peak-to-peak methods. Table 1 lists the peaks observed in the residual spectra after the $tted spectrum of the CO− 2 radical was subtracted from the measured derivative spectrum. It is obvious that nearly all peaks have been observed in other studies, although the nature of some of the lines (e.g. at 2.0020 and 1.9972) is still unclear. The residuals of the low and high dosed samples (see Figs. 1G and H) do not align on the zero-line, clearly indicating the existence
c 2002 Elsevier Science Ltd. All rights reserved. 1350-4487/02/$ - see front matter PII: S 1 3 5 0 - 4 4 8 7 ( 0 1 ) 0 0 2 5 5 - 4
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R. Gr"un / Radiation Measurements 35 (2002) 87–93
R. Gr"un / Radiation Measurements 35 (2002) 87–93
89
Table 1 ESR lines observed in the residual spectra after $tting the experimental spectra with an idealised CO− 2 line (Figs. 1G and H) g-value
Width (mT) 0.26
Radical CO− 3
2.0115 2.0080 2.0056 2.0047 2.0032 2.0020
0.13 0.13 0.09 0.12
Rotating Peak #1? SO− 2 CO3− 3 ? Central dimethyl CO3− 3 ?
2.0006 1.9972
0.14 0.15
Tumbling CO− 2 ?
of a wider line or complex similar to peak #1 in Figs. 1A and B. When comparing the results from the deconvolution of the absorption spectrum with those of matching the spectrum of the CO− 2 radical with the derivative spectrum, it is evident that the latter is preferable. Firstly, the $tting process using only one single CO− 2 spectrum is much easier to carry out than the simultaneous optimisation of this spectrum plus three independent Gaussian peaks. Secondly, the residuals in the derivative spectra (compare Figs. 1C and D with F and E) are signi$cantly smaller. Thirdly, the deconvolution process on the absorption spectra is Kawed in several respects and it is not certain that the centrally $tted CO− 2 line yields the least interfered dose values. For example, the so-called wide line is most probably largely due to a spectrometer response function (Robertson and Gr(un, 2000). Thus, it ought not be radiation sensitive. However, the observed apparent dose sensitivity implies that the $tting procedure incorporates a range of other radicals into this “wide” line. In turn, the $tted height of the CO− 2 radical is critically dependent on the height of the wide line in the centre of the ESR spectrum, particularly in low dosed samples. The contribution of the wide line to the total signal is signi$cantly smaller in the higher dosed sample (compare the relative size of the ‘wide’ line in Figs. 1B and A). Fitting the derivative spectrum with the CO− 2 line shows that the positions which are often used for peak-to-peak dose ←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Fig. 1. Deconvolution methods. Left column: sample 1047 irradiated with 7:8 Gy; right column, irradiated with 661 Gy. (A,B) Deconvolution of the absorption spectrum using an ideal CO− 2 spectrum plus 3 Gaussian lines. Residuals are o;set for clarity. (C,D) Derivatives of the spectra, best $t and residuals of the above $gures. Residuals are o;set for clarity. T1, B1 and B2 denote the positions used for peak-to-peak $tting; (*) Dimethyl radical; (#) − SO− 2 ; ($) tumbling CO2 ; (?) as yet unidenti$ed radical with an isotropic line at g = 1:9972. (E,F) Fitting the derivative spectra using an ideal CO− 2 spectrum. Residuals are o;set for clarity. (G,H) central area of the residuals.
Symbol
Reference
+
Callens et al. (1989)
#
Bouchez et al. (1988) Callens et al. (1987) Bouchez et al. (1988) Callens et al. (1987) See also Doi et al. (1979) Bouchez et al. (1988) Callens et al. (1987), Bouchez et al. (1988), Scherbina and Brik (2000)
*
$ ?
estimation, T1, B1, and B2 (as marked in Fig. 1C) seem all interfered with several narrow lines. T1 is overlapped by the central line of the methyl radical (central ∗ ) as well as the trough of peak #1 and=or possibly a CO3− line (Van3 haelewyn et al., 2000), B1 by the line of the tumbling CO− 2 radical ($) and possibly CO3− 3 as well, and B2 by a thus far unidenti$ed peak ((?) in Figs. 1E and F), an isotropic line was also observed by Callens et al. (1987), Bouchez et al. (1988) as well as Scherbina and Brik (2000). Peak-to-peak measurements are critically dependent on the occurrence of narrow lines and their dose response, whereas $tting the derivative spectrum with the relatively broad spectrum of the CO− 2 radical has the advantage that the “wide” line has no inKuence on the results, and the $tting results are not inKuenced by narrow, symmetrical lines. 3. Natural spectrum tting The underlying question of the various $tting methods is: what are the qualitative and quantitative di;erences between natural and irradiated spectra? This becomes particularly important when analysing the dose response of tooth enamel fragments, where it is not possible to $t the ESR spectra with the CO− un, 2000; 2 radical spectrum (see Robertson and Gr( Gr(un et al., in press). In order to investigate this question the natural spectrum was $tted into the irradiated spectra, because it was thought that the residuals would reveal the ESR peaks with di;erent dose response. The $tting procedure is straight forward. The natural and irradiated spectra were aligned onto the central zero-passing and subsequently, the natural spectrum is linearly scaled into the irradiated spectrum by minimising the sum of squares of the di;erences between the scaled natural and irradiated spectra, respectively. The sum of squares was calculated only for the central region (between “S” and “E” marked in Fig. 2A). Alignment was checked by shifting the optimised natural spectrum up and down $eld, but it turned out that this is in the range of 6 2 channels (out of 2048). No consideration of eventual peak-widening was made. Dose
90
R. Gr"un / Radiation Measurements 35 (2002) 87–93
Fig. 2. Natural $tting. Left column: sample 1047 irradiated with 7:8 Gy; right column, irradiated with 661 Gy. (A,B) Spectra, $tting results and residuals (which are o;set for clarity). S, T2 and E denote positions for the de$nition of regions of interest. Natural spectrum $tting in these $gures was carried out by optimising the region between S and E. (C,D) central area of the residuals.
response data were $tted by linearisation and the Monte Carlo error simulation (see Gr(un and Brumby, 1994), the previously used simplex optimisation is unfortunately prone to in$nite solution matrices. 4. Results and discussion Figs. 2A and B show the $tting results of two spectra from samples irradiated with 7.8 and 661 Gy, respectively. It can be seen that the residual of the smaller dose step does not contain any identi$able signals (Fig. 2C). The residual of the higher dosed spectrum (Fig. 2D) contains a series of narrow peaks. It shows that the methyl radical (∗ ) and SO− 2 (#) are less radiation sensitive than the over-all spectrum (as expressed by negative line shape particularly clear for the two outer methyl lines in Fig. 2D). The isotropic lines at g = 2:0006 ($) and g = 2:0115 (+) show a higher sensitivity. The residual does not contain any component that resembles the Gaussian peak #1 which was thought to be the main culprit for dose underestimation (Jonas et al., 1994; Jonas, 1995). This may either be due to the fact that sig-
nals with a very similar shape have a closely similar dose response to the main ESR spectrum or that peak #1 is an artefact of the deconvolution procedure (the latter is not likely, see residuals in Figs. 1G and H). After running a series of other, powdered samples, it can be concluded that the ESR spectra of irradiated powdered fossil tooth enamel can be well $tted with the natural spectrum and that the residual spectrum only contains a series of narrow peaks. These, however, may occur in the exact positions of T1, B1 and B2, which are usually used for peak-to-peak measurements (see above). Particularly, the region immediately left of the central peak (between about the second methyl peak and T1), where peaks #1 and #2 are placed in the deconvolution procedure of the absorption spectra (Figs. 1A and B), is well $tted with the scaled natural spectrum (apart, of course, from the narrower lines of the SO− 2 (#) and rotating CO3− (+) radicals). This indicates that the overall 3 dose response of this region is very similar to the main peak area. Note that the above observations do not apply to recent or very young teeth where the natural spectrum does not contain the central peak of the CO− 2 radical which is typical
R. Gr"un / Radiation Measurements 35 (2002) 87–93
91
Table 2 Results of dose estimation on sample 1047 using di;erent strategies (see also Gr(un, 2000) Method
Aliquot 1 (10 measurements)
Aliquots 1– 40
Peak-to peak T1 B1 B2 T1-B1 T1-B2 Integral maximum
76.1±2.3 68.0±2.7 69.7±2.6 72.5±2.3 73.5±0.9 78.9±2.6
74.3±3.0 66.0±3.1 73.2±2.9 70.7±2.9 73.5±2.4 77.9±3.4
Dose versus magnetic $eld plot Absorption Derivative
76.9±2.3 to 81.2±2.1 62.3±2.2 to 70.6±3.6
76.1±3.9 to 81.9±4.1 63.8±3.9 to 71.9±3.4
Gaussian deconvolution (absorption spectrum) 4 peaks: G3 G4 G3+G4 7 Peaks: G3 G4 G3+G4
78.7±2.1 82.7±1.9 80.3±2.0 75.3±2.6 82.2±2.5 77.6±2.5
Lorentzian deconvolution (absorption spectrum) 4 peaks: L2 L3 L4 L2-L4
78.7±2.2 73.1±3.4 114±11.0 82.5±5.0
CO− 2 $tting Absorption Derivative
73.6±1.7 75.2±1.2
75.1±3.0 76.1±3.1
Natural spectrum $tting Whole spectrum T1-region B1-region B2-region T1-B1 region T1-B2 regions T1-B2 width Peak width
74.6±1.6 76.9±2.1 69.6±3.7 68.7±2.6 75.7±2.4 75.1±1.5 75.9±1.5 72.7±4.9
75.1±4.5 76.8±4.7 66.7±4.8 74.2±4.1 75.1±4.8 76.4±4.4 77.6±4.4 78.2±4.2
for fossil samples that were exposed to sizable natural doses (& 1 Gy) (see e.g. Chumak et al., 1996a, b). A few fossil samples which may have been exposed to higher doses show similar e;ects (Gr(un, unpublished data). Rather than $tting the whole central peak region, one can de$ne narrower regions of interest in which the $tting is optimised. Thus, di;erent parts of the spectra, such as the T1, B1 and B2 regions, their combinations, or indeed any other occurring feature can be analysed. The following regions of interest were analysed (for positions see markings
in Figs. 1C and 2A): “whole spectrum” (S to E); T1-region (half height zero=T1 to zero passing), B1-region (zero passing to half height B1=T2); B2-region (half height T2=B2 to half height B2=zero); T1-B1 and T1-B2 are combinations of previously de$ned regions; T1-B2 width (S to T1 and B1 to E) and peak width (S to half height of T1 region and half height B2 to E). The latter two regions were tested to allow a $tting that is somewhat independent of interferences in the central peak region. To evaluate the dose results from natural spectrum $tting, the spectra of sample 1047 were
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R. Gr"un / Radiation Measurements 35 (2002) 87–93
supports the results of Vanhaelewyn et al. (2000), who estimated that more than 99% of the central ESR signal has the same dose response. Tests on very noisy spectra which were $tted raw as well as after removing the noise using the Fourier transformation (see Gr(un and Clapp, 1996) show that the dose values and errors are independent of random, white noise. Therefore, one can also conclude that narrow, symmetrical lines also have no inKuence on the dose response curve when the data are derived from natural spectrum $tting. 5. Conclusions
Fig. 3. Comparison of 10 repeated dose estimations of the $rst aliquot of sample 1047 (all methods, except natural spectrum $tting, were described by Gr(un (2000)). Dotted line: average of the T1-B2 peak-to-peak result. This has been the routine method for the vast majority of dose estimations in ESR dating.
analysed (the ten repeated measurements of aliquot 1 as well as the $rst run of all 40 aliquots, see Gr(un and Clapp, 1996). This sample has been repeatedly used for the comparison of dose evaluation methods and reproducibility tests (Gr(un, 1998, 2000). Table 2 and Fig. 3 show the results of the natural spectrum $tting in comparison with the alternative methods. Natural spectrum $tting yielded very robust results. The results of the “whole spectrum” are identical with those of the CO− 2 $tting (this was also observed on a range of other samples). It is remarkable that the T1-B2 peak-to-peak analysis yields also a good agreement (indeed it has the smallest overall error) although one could think of at least four interfering signals which should render dose assessment using this method completely useless. Natural spectrum $tting of the smaller regions shows good agreement with the respective peak-to-peak results which implied that the dose value derived from T1 is somewhat larger and those from B1; doses derived from B2 are smaller than the values from the T1-B2, respectively. The $tting routines can of course be used for very narrow regions, thus, peak-to-peak $tting (T1-B1, T1-B2 etc) can be carried out at the same time. It is interesting to note that the two procedures, which are mainly based on the width of the central line (T1-B2 width and “peak width”), yielded agreeing results with those methods using the whole peak or regions within the central line. This
By de$ning the smaller regions of interest, natural spectrum $tting can be carried out to study a range of e;ects simultaneously. Some samples show clear interferences, particularly in the B1 region. Separate $tting of this region allows the assessment of these interferences on the dose value. Altogether, the residuals from natural spectrum $tting procedure are signi$cantly smaller than those of the other deconvolution=$tting methods which implies that the bulk of the central ESR signal has a similar dose response. Interferences from narrow lines have negligible impact on the $tting procedure, particularly, if these lines are symmetric. Apart from the computational ease of the procedures, CO− 2 and natural spectrum $tting of the derivative spectra are preferred over the Gaussian and Lorentzian deconvolution of the absorption spectra, because the results of the latter procedure are critically dependent on the position and magnitude of the “wide” line. Considering all observed and possible interferences, natural spectrum $tting ought to provide the most reliable dose estimations on fossil teeth. Note that this does not apply to retrospective dosimetry which is usually in the range of less than 5 –10 Gy. Fitting the spectrum of the CO− 2 radical into the measured derivative spectrum provides residuals which can be used for the qualitative and semi-quantitative assessments of interferences. This will be of particular importance when measuring enamel fragments where the ESR spectra as well as the derived dose values show angular dependencies (Gr(un and Robertson, 2000; Brik et al., 2000; Gr(un et al., in press). Acknowledgements I thank Mr. S. Robertson, RSES, for comments.
References Bouchez, R., Cox, R., Herve, A., Lopez-Carranza, E., Ma, J.L., Piboule, M., Poupeau, G., Rey, P., 1988. Q-band ESR studies of fossil teeth, consequences for ESR dating. Quat. Sci. Rev. 7, 497–501.
R. Gr"un / Radiation Measurements 35 (2002) 87–93 Brik, A., Haskell, E., Brik, V., Scherbina, O., Atamanenko, O., 2000. Anisotropy e;ects of EPR signals and mechanisms of mass transfer in tooth enamel and bones. Appl. Radiat. Isotopes 52, 1077–1083. Callens, F.J., Verbeeck, R.M.H., Matthys, P.F.A., Martens, L.C., Boesman, E.R., 1987. The contribution of CO3− and CO− 3 2 to the ESR spectrum near g = 2 of powdered human tooth enamel. Calcif. Tissue Int. 41, 124–129. Callens, F.J., Verbeeck, R.M.H., Naessens, D.E., Matthys, P.F.A., Boesman, E.R., 1989. E;ect of carbonate content on the ESR spectrum near g = 2 of carbonated calciumapatites synthesized from aqueous media. Calcif. Tissue Int. 44, 114–124. Chumak, V., Baili;, I., Baran, N., Bugai, A., Dubrovsky, S., Fedosov, I., Finin, V., Haskell, E., Hayes, R., Ivannikov, A., Kenner, G., Kirilov, V., Khamidova, L., Kolesnik, S., Liidja, G., Likhtarev, I., Lippmaa, E., Maksimenko, V., Meijer, A., Minenko, V., Pasalskaya, L., Past, J., Puskar, J., Radchuk, V., Sholom, S., Skvortsov, V., Stepanenko, V., Vaher, U., Wieser, A., 1996a. The $rst international intercomparison of EPR-dosimetry with teeth: $rst results. Appl. Radiat. Isotopes 47, 1281–1286. Chumak, V., Pavlenko, J., Sholom, S., 1996b. An approach to the assessment of overall uncertainty of determination of dose using an ESR technique. Appl. Radiat. Isotopes 47, 1287–1291. Doi, Y., Aoba, T., Okazaki, M., Takahashi, J., Moriwaki, Y., 1979. Analysis of paramagnetic centers in X-ray-irradiated enamel, bone and carbonate-containing hydroxyapatite by electron spin resonance spectroscopy. Calcif. Tissue Int. 28, 107–112. Gr(un, R., 1998. Reproducibility measurements for ESR signal intensity and dose determination: high precision but doubtful accuracy. Radiat. Meas. 29, 177–193.
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Gr(un, R., 2000. Methods of dose determination using ESR spectra of tooth enamel. Radiat. Meas. 32, 767–772. Gr(un, R., Brumby, S., 1994. The assessment of errors in the past radiation doses extrapolated from ESR=TL dose response data. Radiat. Meas. 23, 307–315. Gr(un, R., Clapp, R., 1996. An automated sample changer for Bruker ESR spectrometers. Ancient TL 14, 1–5. Gr(un, R., Jonas, M., 1996. Plateau tests and spectrum de-convolution for ESR dose determination. Radiat. Meas. 26, 621–629. Gr(un, R., Robertson, S., Gordon, M. Dose evaluation on a fossil tooth using an enamel fragment as well as multiple and single powder aliquots. Ancient TL, in press. Hayes, R.B., Haskell, E.H., 2000. A method for the identi$cation of interfering signals in EPR dating of tooth enamel. Radiat. Meas. 32, 781–785. Jonas, M., 1995. Spectral deconvolution of the ESR dating signal in fossil tooth enamel. Quat. Geochronol. (QSR) 14, 431–438. Jonas, M., Zhou, L.P., Marseglia, E., Mellars, P., 1994. New analysis of ESR spectra of fossil tooth enamel. Cambridge Arch. J. 4, 139–146. Robertson, S., Gr(un, R., 2000. Dose determination on tooth enamel fragments from two human fossils. Radiat. Meas. 32, 773–779. Scherbina, O.I., Brik, A.B., 2000. Temperature stability of carbonate groups in tooth enamel. Appl. Radiat. Isotopes 52, 1071–1075. Vanhaelewyn, G., Callens, F., Gr(un, R., 2000. EPR spectrum deconvolution and dose assessment of fossil tooth enamel using maximum likelihood common factor analysis. Appl. Radiat. Isotopes 52, 1317–1326.
www.elsevier.com/locate/radmeas
ESR dose estimation on fossil tooth enamel by $tting the natural spectrum into the irradiated spectra Rainer Gr(un ∗ Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia Received 26 November 2000; received in revised form 1 May 2001; accepted 22 May 2001
Abstract Fitting the natural, derivative ESR spectrum into the irradiated spectra has been tested as a method for the estimation of the dose value of powdered fossil tooth enamel, which is the basis of ESR dating. It was found that this method has signi$cant advantages over traditional peak-to-peak assessments, dose versus magnetic $eld plots as well as deconvolution of the absorption spectrum, because it is less dependent on a range of interferences. Furthermore, the $tting procedure is computationally trivial and the dose results are not dependent on random noise. It is concluded that $tting the natural spectrum ought to provide the most reliable dose estimations for most fossil teeth which have been exposed to doses of more than c 2002 Elsevier Science Ltd. All rights reserved. 5 –10 Gy.
1. Introduction The methods for ESR dose estimation on tooth enamel were recently reviewed by Gr(un (2000). The strategies for dose estimation can be grouped into peak-to-peak, dose versus magnetic $eld, and deconvolution (using Gaussian, Lorentzian or CO− 2 peak shapes or ESR spectra that show negligible interferences, e.g., Hayes and Haskell, 2000) methods. It is well known that the ESR spectrum of tooth enamel is generated by a range of radicals (e.g. Vanhaelewyn et al., 2000). It is, however, not so clear how the variable superposition of the ESR lines of these radicals a;ect the dose determination. The reason for this is that so far it was not possible to completely separate the ESR spectral components of the identi$ed radicals. 2. Methods for dose estimation Figs. 1A and B show absorption spectra of sample 1047, deconvoluted with the spectrum of the CO− 2 radical (as ∗ Corresponding author. Tel.: +61-2-6125-3122; fax: +61-26125-0315. E-mail address: [email protected] (R. Gr(un).
extracted from fossil teeth by maximum likelihood common factor analysis, Vanhaelewyn et al., 2000) plus a “wide” and two narrower (#1 and #2) Gaussian lines. The results of several studies (e.g. Jonas et al., 1994; Jonas, 1995; Gr(un, 1998) have shown that the “wide” line displays some dose sensitivity and usually yields much higher dose values than the central, apparently axial line, and that the Gaussian peaks #1 and #2 usually yield smaller dose values. Fitting the derivative spectrum with the spectrum of the CO− 2 radical (Figs. 1E and F) also shows that there is a series of relatively narrow peaks that are generated by a variety of radicals. The dose versus magnetic $eld plots con$rm that the central area is interfered with by a range of peaks each having considerably di;erent dose responses (see Gr(un and Jonas, 1996). The variable dose response of the radicals was the reason to prefer time intensive deconvolution over peak-to-peak methods. Table 1 lists the peaks observed in the residual spectra after the $tted spectrum of the CO− 2 radical was subtracted from the measured derivative spectrum. It is obvious that nearly all peaks have been observed in other studies, although the nature of some of the lines (e.g. at 2.0020 and 1.9972) is still unclear. The residuals of the low and high dosed samples (see Figs. 1G and H) do not align on the zero-line, clearly indicating the existence
c 2002 Elsevier Science Ltd. All rights reserved. 1350-4487/02/$ - see front matter PII: S 1 3 5 0 - 4 4 8 7 ( 0 1 ) 0 0 2 5 5 - 4
88
R. Gr"un / Radiation Measurements 35 (2002) 87–93
R. Gr"un / Radiation Measurements 35 (2002) 87–93
89
Table 1 ESR lines observed in the residual spectra after $tting the experimental spectra with an idealised CO− 2 line (Figs. 1G and H) g-value
Width (mT) 0.26
Radical CO− 3
2.0115 2.0080 2.0056 2.0047 2.0032 2.0020
0.13 0.13 0.09 0.12
Rotating Peak #1? SO− 2 CO3− 3 ? Central dimethyl CO3− 3 ?
2.0006 1.9972
0.14 0.15
Tumbling CO− 2 ?
of a wider line or complex similar to peak #1 in Figs. 1A and B. When comparing the results from the deconvolution of the absorption spectrum with those of matching the spectrum of the CO− 2 radical with the derivative spectrum, it is evident that the latter is preferable. Firstly, the $tting process using only one single CO− 2 spectrum is much easier to carry out than the simultaneous optimisation of this spectrum plus three independent Gaussian peaks. Secondly, the residuals in the derivative spectra (compare Figs. 1C and D with F and E) are signi$cantly smaller. Thirdly, the deconvolution process on the absorption spectra is Kawed in several respects and it is not certain that the centrally $tted CO− 2 line yields the least interfered dose values. For example, the so-called wide line is most probably largely due to a spectrometer response function (Robertson and Gr(un, 2000). Thus, it ought not be radiation sensitive. However, the observed apparent dose sensitivity implies that the $tting procedure incorporates a range of other radicals into this “wide” line. In turn, the $tted height of the CO− 2 radical is critically dependent on the height of the wide line in the centre of the ESR spectrum, particularly in low dosed samples. The contribution of the wide line to the total signal is signi$cantly smaller in the higher dosed sample (compare the relative size of the ‘wide’ line in Figs. 1B and A). Fitting the derivative spectrum with the CO− 2 line shows that the positions which are often used for peak-to-peak dose ←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Fig. 1. Deconvolution methods. Left column: sample 1047 irradiated with 7:8 Gy; right column, irradiated with 661 Gy. (A,B) Deconvolution of the absorption spectrum using an ideal CO− 2 spectrum plus 3 Gaussian lines. Residuals are o;set for clarity. (C,D) Derivatives of the spectra, best $t and residuals of the above $gures. Residuals are o;set for clarity. T1, B1 and B2 denote the positions used for peak-to-peak $tting; (*) Dimethyl radical; (#) − SO− 2 ; ($) tumbling CO2 ; (?) as yet unidenti$ed radical with an isotropic line at g = 1:9972. (E,F) Fitting the derivative spectra using an ideal CO− 2 spectrum. Residuals are o;set for clarity. (G,H) central area of the residuals.
Symbol
Reference
+
Callens et al. (1989)
#
Bouchez et al. (1988) Callens et al. (1987) Bouchez et al. (1988) Callens et al. (1987) See also Doi et al. (1979) Bouchez et al. (1988) Callens et al. (1987), Bouchez et al. (1988), Scherbina and Brik (2000)
*
$ ?
estimation, T1, B1, and B2 (as marked in Fig. 1C) seem all interfered with several narrow lines. T1 is overlapped by the central line of the methyl radical (central ∗ ) as well as the trough of peak #1 and=or possibly a CO3− line (Van3 haelewyn et al., 2000), B1 by the line of the tumbling CO− 2 radical ($) and possibly CO3− 3 as well, and B2 by a thus far unidenti$ed peak ((?) in Figs. 1E and F), an isotropic line was also observed by Callens et al. (1987), Bouchez et al. (1988) as well as Scherbina and Brik (2000). Peak-to-peak measurements are critically dependent on the occurrence of narrow lines and their dose response, whereas $tting the derivative spectrum with the relatively broad spectrum of the CO− 2 radical has the advantage that the “wide” line has no inKuence on the results, and the $tting results are not inKuenced by narrow, symmetrical lines. 3. Natural spectrum tting The underlying question of the various $tting methods is: what are the qualitative and quantitative di;erences between natural and irradiated spectra? This becomes particularly important when analysing the dose response of tooth enamel fragments, where it is not possible to $t the ESR spectra with the CO− un, 2000; 2 radical spectrum (see Robertson and Gr( Gr(un et al., in press). In order to investigate this question the natural spectrum was $tted into the irradiated spectra, because it was thought that the residuals would reveal the ESR peaks with di;erent dose response. The $tting procedure is straight forward. The natural and irradiated spectra were aligned onto the central zero-passing and subsequently, the natural spectrum is linearly scaled into the irradiated spectrum by minimising the sum of squares of the di;erences between the scaled natural and irradiated spectra, respectively. The sum of squares was calculated only for the central region (between “S” and “E” marked in Fig. 2A). Alignment was checked by shifting the optimised natural spectrum up and down $eld, but it turned out that this is in the range of 6 2 channels (out of 2048). No consideration of eventual peak-widening was made. Dose
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R. Gr"un / Radiation Measurements 35 (2002) 87–93
Fig. 2. Natural $tting. Left column: sample 1047 irradiated with 7:8 Gy; right column, irradiated with 661 Gy. (A,B) Spectra, $tting results and residuals (which are o;set for clarity). S, T2 and E denote positions for the de$nition of regions of interest. Natural spectrum $tting in these $gures was carried out by optimising the region between S and E. (C,D) central area of the residuals.
response data were $tted by linearisation and the Monte Carlo error simulation (see Gr(un and Brumby, 1994), the previously used simplex optimisation is unfortunately prone to in$nite solution matrices. 4. Results and discussion Figs. 2A and B show the $tting results of two spectra from samples irradiated with 7.8 and 661 Gy, respectively. It can be seen that the residual of the smaller dose step does not contain any identi$able signals (Fig. 2C). The residual of the higher dosed spectrum (Fig. 2D) contains a series of narrow peaks. It shows that the methyl radical (∗ ) and SO− 2 (#) are less radiation sensitive than the over-all spectrum (as expressed by negative line shape particularly clear for the two outer methyl lines in Fig. 2D). The isotropic lines at g = 2:0006 ($) and g = 2:0115 (+) show a higher sensitivity. The residual does not contain any component that resembles the Gaussian peak #1 which was thought to be the main culprit for dose underestimation (Jonas et al., 1994; Jonas, 1995). This may either be due to the fact that sig-
nals with a very similar shape have a closely similar dose response to the main ESR spectrum or that peak #1 is an artefact of the deconvolution procedure (the latter is not likely, see residuals in Figs. 1G and H). After running a series of other, powdered samples, it can be concluded that the ESR spectra of irradiated powdered fossil tooth enamel can be well $tted with the natural spectrum and that the residual spectrum only contains a series of narrow peaks. These, however, may occur in the exact positions of T1, B1 and B2, which are usually used for peak-to-peak measurements (see above). Particularly, the region immediately left of the central peak (between about the second methyl peak and T1), where peaks #1 and #2 are placed in the deconvolution procedure of the absorption spectra (Figs. 1A and B), is well $tted with the scaled natural spectrum (apart, of course, from the narrower lines of the SO− 2 (#) and rotating CO3− (+) radicals). This indicates that the overall 3 dose response of this region is very similar to the main peak area. Note that the above observations do not apply to recent or very young teeth where the natural spectrum does not contain the central peak of the CO− 2 radical which is typical
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Table 2 Results of dose estimation on sample 1047 using di;erent strategies (see also Gr(un, 2000) Method
Aliquot 1 (10 measurements)
Aliquots 1– 40
Peak-to peak T1 B1 B2 T1-B1 T1-B2 Integral maximum
76.1±2.3 68.0±2.7 69.7±2.6 72.5±2.3 73.5±0.9 78.9±2.6
74.3±3.0 66.0±3.1 73.2±2.9 70.7±2.9 73.5±2.4 77.9±3.4
Dose versus magnetic $eld plot Absorption Derivative
76.9±2.3 to 81.2±2.1 62.3±2.2 to 70.6±3.6
76.1±3.9 to 81.9±4.1 63.8±3.9 to 71.9±3.4
Gaussian deconvolution (absorption spectrum) 4 peaks: G3 G4 G3+G4 7 Peaks: G3 G4 G3+G4
78.7±2.1 82.7±1.9 80.3±2.0 75.3±2.6 82.2±2.5 77.6±2.5
Lorentzian deconvolution (absorption spectrum) 4 peaks: L2 L3 L4 L2-L4
78.7±2.2 73.1±3.4 114±11.0 82.5±5.0
CO− 2 $tting Absorption Derivative
73.6±1.7 75.2±1.2
75.1±3.0 76.1±3.1
Natural spectrum $tting Whole spectrum T1-region B1-region B2-region T1-B1 region T1-B2 regions T1-B2 width Peak width
74.6±1.6 76.9±2.1 69.6±3.7 68.7±2.6 75.7±2.4 75.1±1.5 75.9±1.5 72.7±4.9
75.1±4.5 76.8±4.7 66.7±4.8 74.2±4.1 75.1±4.8 76.4±4.4 77.6±4.4 78.2±4.2
for fossil samples that were exposed to sizable natural doses (& 1 Gy) (see e.g. Chumak et al., 1996a, b). A few fossil samples which may have been exposed to higher doses show similar e;ects (Gr(un, unpublished data). Rather than $tting the whole central peak region, one can de$ne narrower regions of interest in which the $tting is optimised. Thus, di;erent parts of the spectra, such as the T1, B1 and B2 regions, their combinations, or indeed any other occurring feature can be analysed. The following regions of interest were analysed (for positions see markings
in Figs. 1C and 2A): “whole spectrum” (S to E); T1-region (half height zero=T1 to zero passing), B1-region (zero passing to half height B1=T2); B2-region (half height T2=B2 to half height B2=zero); T1-B1 and T1-B2 are combinations of previously de$ned regions; T1-B2 width (S to T1 and B1 to E) and peak width (S to half height of T1 region and half height B2 to E). The latter two regions were tested to allow a $tting that is somewhat independent of interferences in the central peak region. To evaluate the dose results from natural spectrum $tting, the spectra of sample 1047 were
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supports the results of Vanhaelewyn et al. (2000), who estimated that more than 99% of the central ESR signal has the same dose response. Tests on very noisy spectra which were $tted raw as well as after removing the noise using the Fourier transformation (see Gr(un and Clapp, 1996) show that the dose values and errors are independent of random, white noise. Therefore, one can also conclude that narrow, symmetrical lines also have no inKuence on the dose response curve when the data are derived from natural spectrum $tting. 5. Conclusions
Fig. 3. Comparison of 10 repeated dose estimations of the $rst aliquot of sample 1047 (all methods, except natural spectrum $tting, were described by Gr(un (2000)). Dotted line: average of the T1-B2 peak-to-peak result. This has been the routine method for the vast majority of dose estimations in ESR dating.
analysed (the ten repeated measurements of aliquot 1 as well as the $rst run of all 40 aliquots, see Gr(un and Clapp, 1996). This sample has been repeatedly used for the comparison of dose evaluation methods and reproducibility tests (Gr(un, 1998, 2000). Table 2 and Fig. 3 show the results of the natural spectrum $tting in comparison with the alternative methods. Natural spectrum $tting yielded very robust results. The results of the “whole spectrum” are identical with those of the CO− 2 $tting (this was also observed on a range of other samples). It is remarkable that the T1-B2 peak-to-peak analysis yields also a good agreement (indeed it has the smallest overall error) although one could think of at least four interfering signals which should render dose assessment using this method completely useless. Natural spectrum $tting of the smaller regions shows good agreement with the respective peak-to-peak results which implied that the dose value derived from T1 is somewhat larger and those from B1; doses derived from B2 are smaller than the values from the T1-B2, respectively. The $tting routines can of course be used for very narrow regions, thus, peak-to-peak $tting (T1-B1, T1-B2 etc) can be carried out at the same time. It is interesting to note that the two procedures, which are mainly based on the width of the central line (T1-B2 width and “peak width”), yielded agreeing results with those methods using the whole peak or regions within the central line. This
By de$ning the smaller regions of interest, natural spectrum $tting can be carried out to study a range of e;ects simultaneously. Some samples show clear interferences, particularly in the B1 region. Separate $tting of this region allows the assessment of these interferences on the dose value. Altogether, the residuals from natural spectrum $tting procedure are signi$cantly smaller than those of the other deconvolution=$tting methods which implies that the bulk of the central ESR signal has a similar dose response. Interferences from narrow lines have negligible impact on the $tting procedure, particularly, if these lines are symmetric. Apart from the computational ease of the procedures, CO− 2 and natural spectrum $tting of the derivative spectra are preferred over the Gaussian and Lorentzian deconvolution of the absorption spectra, because the results of the latter procedure are critically dependent on the position and magnitude of the “wide” line. Considering all observed and possible interferences, natural spectrum $tting ought to provide the most reliable dose estimations on fossil teeth. Note that this does not apply to retrospective dosimetry which is usually in the range of less than 5 –10 Gy. Fitting the spectrum of the CO− 2 radical into the measured derivative spectrum provides residuals which can be used for the qualitative and semi-quantitative assessments of interferences. This will be of particular importance when measuring enamel fragments where the ESR spectra as well as the derived dose values show angular dependencies (Gr(un and Robertson, 2000; Brik et al., 2000; Gr(un et al., in press). Acknowledgements I thank Mr. S. Robertson, RSES, for comments.
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R. Gr"un / Radiation Measurements 35 (2002) 87–93 Brik, A., Haskell, E., Brik, V., Scherbina, O., Atamanenko, O., 2000. Anisotropy e;ects of EPR signals and mechanisms of mass transfer in tooth enamel and bones. Appl. Radiat. Isotopes 52, 1077–1083. Callens, F.J., Verbeeck, R.M.H., Matthys, P.F.A., Martens, L.C., Boesman, E.R., 1987. The contribution of CO3− and CO− 3 2 to the ESR spectrum near g = 2 of powdered human tooth enamel. Calcif. Tissue Int. 41, 124–129. Callens, F.J., Verbeeck, R.M.H., Naessens, D.E., Matthys, P.F.A., Boesman, E.R., 1989. E;ect of carbonate content on the ESR spectrum near g = 2 of carbonated calciumapatites synthesized from aqueous media. Calcif. Tissue Int. 44, 114–124. Chumak, V., Baili;, I., Baran, N., Bugai, A., Dubrovsky, S., Fedosov, I., Finin, V., Haskell, E., Hayes, R., Ivannikov, A., Kenner, G., Kirilov, V., Khamidova, L., Kolesnik, S., Liidja, G., Likhtarev, I., Lippmaa, E., Maksimenko, V., Meijer, A., Minenko, V., Pasalskaya, L., Past, J., Puskar, J., Radchuk, V., Sholom, S., Skvortsov, V., Stepanenko, V., Vaher, U., Wieser, A., 1996a. The $rst international intercomparison of EPR-dosimetry with teeth: $rst results. Appl. Radiat. Isotopes 47, 1281–1286. Chumak, V., Pavlenko, J., Sholom, S., 1996b. An approach to the assessment of overall uncertainty of determination of dose using an ESR technique. Appl. Radiat. Isotopes 47, 1287–1291. Doi, Y., Aoba, T., Okazaki, M., Takahashi, J., Moriwaki, Y., 1979. Analysis of paramagnetic centers in X-ray-irradiated enamel, bone and carbonate-containing hydroxyapatite by electron spin resonance spectroscopy. Calcif. Tissue Int. 28, 107–112. Gr(un, R., 1998. Reproducibility measurements for ESR signal intensity and dose determination: high precision but doubtful accuracy. Radiat. Meas. 29, 177–193.
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