8437
2008, 112, 8437–8442 Published on Web 06/28/2008
Visualizing the Dose Distribution and Linear Energy Transfer by 1D and 2D ESR Imaging: A Potassium Dithionate Dosimeter Irradiated with C6+ and N7+ Ions Håkan Gustafsson,† Krzysztof Kruczala,‡,§ Eva Lund,*,† and Shulamith Schlick*,§ Department of Medical and Health Sciences, Radiation Physics, Faculty of Health Sciences, Linkoping UniVersity, S-58185 Linkoping, Sweden, On leaVe from Faculty of Chemistry, Jagiellonian UniVersity, Ingardena 3, 30-060 Cracow, Poland, and Department of Chemistry and Biochemistry, UniVersity of Detroit Mercy, 4001 West McNichols Road, Detroit, Michigan 48221-3038 ReceiVed: April 28, 2008
We report the application of one- and two-dimensional (1D and 2D) spectral-spatial electron spin resonance imaging (ESRI) for visualizing the dose distribution and linear energy transfer (LET) in a potassium dithionate, K2S2O6 (PDT), dosimeter irradiated with the heavy ions C6+ and N7+. The ESR spectrum in the irradiated PDT consists of a superposition of two isotropic signals assigned to two •SO3- radicals, R1 and R2, with no hyperfine splittings and slightly different g values. The 1D ESRI profiles clearly indicate the spatial penetration of the beams and the location of the sharp maximum dose, the “Bragg peak”, detected for each beam. The depth penetrations are different: ≈2.3 mm for C6+ and ≈1.8 mm for N7+ beams, (0.1 mm; beyond these limits, no radicals were detected. 2D spectral-spatial ESRI images reflect both the dose distribution and the spatial dependence of the relative intensities of radicals R1 and R2, an effect that is assigned to the depth variation of the LET. This study has demonstrated that ESRI is a promising new method for dose and LET determination. Of particular interest are applications in the field of radiotherapy with heavy ions, because in this case the Bragg peak is pronounced and the dose can be focused at specific depths while the surrounding areas are protected. Introduction Detailed information on dose distributions in systems exposed to radiation is essential in numerous and diverse fields, including radiation damage in materials, food sterilization by irradiation, and a wide range of medical applications. In radiation therapy, the main goal is to expose the target volume to a high dose, while protecting the surrounding healthy tissue. Therefore, irradiations with steep dose gradients outside the target volume are preferable, and high spatial resolution in dose mapping is necessary. Dose distributions can be determined with high spatial resolution using dye films stacked along the beam track, small thermoluminescent dosimeters (1 × 1 × 1 mm3), or detectors based on optically stimulated luminescence (OSL). Because ionizing radiation usually leads to the formation of radicals, electron spin resonance (ESR) spectroscopy is an important tool in dosimetry because of its high sensitivity and selectivity for the presence of species with unpaired electron spins.1 An important advantage of ESR is the ability to study cumulative effects of radiation, which are unaltered in ESR measurements but destroyed in other methods; moreover, the dose response is in most cases linear in a broad range, up to 104 Gy. ESR dosimetry based on alanine has emerged as an important method for dose measurements.1–3 Alanine dosimeters have been studied as extruded films, dispersed in agarose gels, and as * Authors to whom correspondence should be addressed. E-mail:
[email protected] (E.L.) and
[email protected] (S.S.). † Linkoping University. ‡ Jagiellonian University. § University of Detroit Mercy.
10.1021/jp803695p CCC: $40.75
pressed pellets in paraffin or polymeric matrices. Alanine-based dosimetry is well-established in transfer dosimetry and is recommended by the International Atomic Energy Agency (IAEA) for measurements of high radiation doses.4 However, adequate precision at the dose levels administrated in radiation therapy is difficult to achieve, because of the relatively low sensitivity of alanine ESR dosimeters. The ESR spectrum of irradiated alanine is broad and consists of a superposition of several components; the signal intensity is usually estimated from the peak-to-peak height of the central, most intense, line. The ideal ESR dosimeter is a material with a high G value (the G value is the number of radicals generated by the absorbed radiation per 100 eV of energy that reaches the sample) and an ESR signal with narrow lines. The material should also be tissue equivalent with respect to mass energy absorption and scattering properties, have a high radical stability, and be robust against environmental disturbances. The quest for new materials for ESR dosimetry led to the study of various formates.5,6 The dominant radical in irradiated formates is •CO2-. The corresponding ESR signal is narrow (much narrower than for alanine), and its line shape and line width depend on the neutralizing cation in the formate. Lithium formate monohydrate, HCO2Li · H2O, is suitable for doses in the range 0.1-1000 Gy and is about 5 times more sensitive compared with alanine, if the microwave power is optimized for both materials.6 In recent years, ESR dosimetry based on dithionates ((NH4)2S2O6, BaS2O6, Li2S2O6, and K2S2O6) has emerged as an attractive alternative to L-alanine ESR dosimetry when deviations from tissue-equivalence can be tolerated.7–12 2008 American Chemical Society
8438 J. Phys. Chem. B, Vol. 112, No. 29, 2008 The ESR spectrum in the irradiated dithionates consists of a superposition of two isotropic signals with no hyperfine splittings and slightly different g values. The signals were assigned to two •SO3- radicals in different local environments in terms of spin-lattice interactions, thus leading to different g values and relaxation times.8,13 Radiotherapy is currently based mostly on irradiation with photons and electrons. However, irradiation by protons and heavy ions is studied with great interest and is expected to be more frequently used in the future, because of its ability to locally confine the radiation and to protect the surrounding tissue. The radiation field in a volume irradiated with heavy charged particles consists of primary ions and secondary particles such as recoiling target atoms and secondary electrons.14 The energy loss per unit path of the absorber irradiated by heavy charged particles increases with decreasing particle velocity and gives rise to a sharp maximum in ionization, which is known as the Bragg peak, near the end of the spatial range.15 The spatial variation of ionizations along a particle track can be described by the linear energy transfer (LET). The products of chemical reactions induced by irradiation depend on the beam LET.15 The specific biological effect of the radiation depends therefore not only on the absorbed dose, but also on the beam quality, which is reflected in the beam LET. The LET variation over the sample depth is especially evident when the ESR spectrum consists of two or more spectral components with different microwave saturation properties.2 While ESR dosimetry can detect and identify the presence and intensity of radicals as average properties in whole samples, the dose distribution of radicals along one, two, or three dimensions in the dosimeter can be obtained by ESR imaging (ESRI). The method is nondestructive and is capable of high spatial resolution, typically ≈80 µm, in X-band ESRI experiments for narrow signals and a high gradient, ≈200 G/cm.16 The radical profile along sample depth can be determined by 1D ESRI; the ESR spectrum as a function of sample depth can be deduced from 2D spectral-spatial ESRI measurements. ESRI offers therefore the unique possibility to map the line shape and intensity changes in ESR spectra as a function of penetration depth in samples irradiated with different beams, including charged particles. The first attempt to use ESRI in dosimetry was applied to alanine irradiated with electrons from a 4 MeV linear accelerator. The one-dimensional (1D) profile and the two-dimensional (2D) spectral-spatial image were presented, but without further analysis.17,18 More recently, commercial alanine dosimeters irradiated with beta particles to a maximum dose of 6 kGy were examined by ESRI.19 Although 1D profiles as well as 2D spatialspatial plots were published, the conclusion was that ESRI cannot be used to advantage in the case of alanine dosimeters. The reason is clear: with a total spectral width >100 G, the ESR spectrum (no gradient) of irradiated alanine and the 1D image (ESR spectrum in the presence of a gradient of ≈ 50 G/cm) are essentially identical (Figure 2, ref 19). The major objective of the present study was to use the ESRI methods developed in the Detroit laboratory16,20–25 in order to visualize spectral changes in potassium dithionate (PDT) irradiated with the heavy ions C6+ and N7+ as a function of sample depth. As shown below, this study has demonstrated that the spatial variation of the line shapes and relative intensities of the ESR signals from the two types of •SO3- radicals reflect both the dose distribution and the beam LET.
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Figure 1. ESR spectra of irradiated PDT measured with 0.02 mW (black line) and 63 mW (blue line) microwave power: (A) irradiation by C6+ ions, (B) irradiation by N7+ ions. The calculated contribution from signal R1 is given in A and B. (C) Calculated (blue line, 25% R2) and experimental ESR spectra (black line) of a sample irradiated with C6+ and registered at 160 K and 0.02 mW. (D) Increase in the relative intensity of the R2 component in ESR spectra at different microwave power for samples irradiated by C6+ (black line, triangles) and N7+ (blue line, circles).
Experimental Section Preparation of the Dosimeter. PDT was prepared in two steps: MnS2O6 was first prepared by the reaction of MnO2 with SO2, and then reacted with KOH. The resulting PDT was sieved to grain size in the range 180-500 µm using an Endecotts
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J. Phys. Chem. B, Vol. 112, No. 29, 2008 8439 gradient along the irradiation direction. Experiments were performed using a cylindrical resonator ER 4108 TMH, and the gradient, 200 G/cm, was generated by two Lewis coils powered by two regulated direct current (DC) power supplies. In these experiments, the concentration profile is deduced from two spectra, one in the presence and one in the absence of the field gradient. The 1D image is a convolution of the ESR spectrum (no gradient) with the radical profile. The process starts by assuming an initial distribution, followed by optimization methods that use the convolution of this initial distribution function with the ESR spectrum in order to calculate the 1D image; the deviation between calculated and experimental spectra is then minimized by the genetic algorithm (GA), which allows the best fit to be chosen automatically.25 A typical GA consists of several steps: creation of the initial population, calculation of the fit to experimental data, and selection of the couples, crossover (reproduction), and mutation. The approach and terminology are adopted from biology and resemble fundamental steps in evolution. 2D spectral-spatial ESRI experiments provide the ESR spectrum as a function of sample depth. Data collection consisted of projections at angles R in the H (spectral) and L (spatial) coordinate system, where R is the angle between the L coordinate and the direction of a given projection. The maximum attainable angle, Rmax, is (L/∆H)Gmax, where L is the sample length, ∆H is the spectral width, and Gmax is the maximum gradient. Each 2D image was reconstructed from a complete set of 256 projections collected as a function of the magnetic field gradient, using a convoluted back-projection algorithm.20 In the complete set, 179 projections were accessible, and the rest were projections at the “missing angles”. Initially the projections at the missing angles were assumed to be identical to the projection measured at the largest available angle. In the second stage, projections at the missing angles were obtained by the projection slice algorithm (PSA) with 10 iterations.21–24
Figure 2. (A) Typical ESR spectrum of irradiated PDT measured at a microwave power of 0.02 mW. Arrows indicate the height that was considered proportional to the signal intensity (black for R1 and red for R2). (B,C) Saturation curves of the R1 and R2 signals in PDT irradiated by C6+ and N7+ ions, respectively.
MINOR sieve shaker, mixed with 10 wt % paraffin as the binder, heated in an oven until the paraffin melted, and cooled to room temperature. The melting and mixing steps were repeated three times in order to produce a homogeneous mixture. By using a press, tablets of diameter 4.5 mm and length 4-5 mm were prepared using ≈170 mg of PDT and paraffin mixture. Irradiation of the Dosimeters. Irradiations were performed with C6+ or N7+ ions accelerated to a surface energy of 34.5 (C6+) and 33.5 (N7+) MeV/amu at the Gustaf Werner Cyclotron located at The Svedberg Laboratory, Uppsala University, Sweden. Tablets were irradiated with one flat side facing the beam. The calculated energy and LET at the surface of the dosimeters and the estimated range in water for the two beams are given in Supporting Information. ESR Measurements. ESR spectra were collected with Bruker X-band EMX spectrometers operating at 9.7 GHz and 100 kHz magnetic field modulation. The modulation amplitude was varied in the range 1 G (for ESR and 2D ESRI experiments) and up to 5 G (for 1D ESRI experiments). The power saturation experiments were performed at 160 K in the microwave power range 20 µW-63 mW with the standard Bruker resonator ER 4102ST. ESR Imaging Experiments. The intensity profile was obtained from 1D ESRI experiments, with the magnetic field
Results and Discussion ESR spectra of PDT irradiated by C6+ and N7+ beams were studied in the temperature range 100-300 K in order to characterize the ESR signals and to determine their microwave power saturation properties. All ESR spectra consist of a superposition of two signals. The g values for the two radicals, 2.0030 for R1 and 2.0020 for R2, ( 0.0005, do not vary with temperature. The different g values for the two •SO3- radicals are assigned to the different environments of the two types of radicals.8 A similar situation was reported for the radical •O3in X-irradiated KClO3 single crystals: three radical sites for the radical were detected, with different orientations in the single crystal, and slightly different g and 17O hyperfine tensors.26 The behavior of radicals R1 and R2 in terms of relative intensities and microwave saturation properties are presented in Figures 1 and 2. The variation of the ESR signal with microwave power, and the relative intensities of signals R1 and R2 at 160 K are presented in Figure 1. This temperature was chosen because the saturation behavior is more clearly detected than that at ambient temperature. Figure 1A,B presents ESR spectra of PDT irradiated by C6+ and N7+ ions, respectively, and shows the relative intensity of radical R1 in percent (%) for low and high microwave power, 0.02 mW (black line) and 63 mW (blue line) respectively. The relative contributions of signals R1 and R2 were calculated by fitting the ESR signal with the Winsim2002 software,27 as shown in Figure 1C for the signal obtained by C6+ irradiation and measured at 160 K with 0.02 mW. Figure
8440 J. Phys. Chem. B, Vol. 112, No. 29, 2008
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Figure 3. (A) Configuration of the PDT dosimeters used in the ESRI experiments. Black downward arrow shows the direction of heavy ions irradiation, and red arrows point to the sample depth. The magnetic field gradient, 200 G/cm, is parallel to the irradiation direction. (B,D) 1D images at 300 K for samples irradiated by C6+ and N7+, respectively, are shown as black traces. Blue lines represent the convolution of the ESR spectrum with the concentration profiles shown in C for the C6+ beam and shown in E for the N7+ beam. Note the increase of the radical concentration from the irradiated side and into the dosimeter depth, the clearly visible Bragg peak, and the penetration of the C6+ beam to ≈2.3 mm and of the N7+ beam to ≈1.8 mm.
1D presents % R2 in ESR spectra measured at different microwave power for samples irradiated by C6+ ions (black line, triangle) and N7+ ions (blue line, circle). The relative contribution from signal R2 increased with increasing microwave power for both samples, but the increase depends on the irradiating beam. Because the radicals represent the same chemical species, •SO3-, the different saturation properties presented above suggest that the ESR properties represent the specific effect of the heavy ions in modifying the local environment of the radicals. The saturation properties of radicals R1 and R2 are shown in Figure 2. Figure 2A presents the measured spectrum shown in Figure 1C, for C6+-irradiated PDT measured at 160 K and microwave power 0.02 mW, and the method used to estimate the intensities of radicals R1 and R2. Because the line widths do not change measurably with microwave power, we have used the heights indicated by blue and red arrows to represent the signal intensity for radicals R1 and R2, respectively. Figure 2B,C shows the variation of the ESR intensity of the two radicals, for C6+ and N7+ irradiation, respectively. The saturation curves shown in Figure 2B,C provide additional support for the idea that the nature of the beam is reflected in the variation of intensity of the two signals R1 and R2 with microwave power. For both beams, the •SO3- radicals of type R2 have shorter T1 values, as they saturate at higher microwave power compared with radicals R1. Small differences are also detected in the behavior of R2 radicals for the two radiation sources: the maximum intensity is detected for a higher microwave power
for C6+ irradiation. The general conclusion from Figures 1 and 2 is that the relative intensity of •SO3- radicals R1 and R2 and the corresponding saturation properties are sensitive to the irradiation source. The ESRI experiments of PDT irradiated by C6+ and N7+ were initiated in order to obtain spatially resolved information on the dose distribution and the variation of the LET along the dosimeter depth. Results of the 1D ESRI experiments are shown in Figure 3. Figure 3A indicates the irradiation direction of the dosimeter and the parallel magnetic field gradient (200 G/cm). This configuration allows the determination of the radical profiles along the sample depth. Figure 3B,D presents the 1D images measured at 300 K for samples irradiated by C6+ and N7+, respectively (black traces). Blue lines represent the convolution of the ESR spectrum with the corresponding concentration profiles of the radicals shown in Figure 3C,E. The 1D profiles, Figure 3C for C6+ and Figure 3E for N7+ irradiation, clearly indicate the depth penetration of the beams and the sharp Bragg peak detected in each case. The depth penetrations are different: ≈2.3 mm for C6+ and ≈1.8 mm for N7+ beams, (0.1 mm; beyond these limits no radicals were detected. It seems reasonable to assume that the deeper penetration of C6+ ions in the dosimeter is due to their lower mass, compared with that of the N7+ ions. In addition, the penetration depths deduced from Figure 3C,E are lower than those calculated for water, 2.3 versus 3.8 mm for the C6+ beam and 1.8 versus 3.0 mm for the N7+ beam; see Supporting Information. The lower penetration
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J. Phys. Chem. B, Vol. 112, No. 29, 2008 8441
Figure 4. 2D spectral-spatial ESRI perspective images of PDT dosimeters irradiated by C6+ and N7+ ions (left) and the corresponding spectral slices at the indicated depths (right). Arrows show the positions of the ESR lines due to radicals R1 and R2. The calculated relative intensities (in %) of radical R1 in the ESR signals for each slice is also given. The 2D images were measured at 300 K. (A,B) The dosimeters were irradiated by C6+ ions and the perspective 2D images were measured at a microwave power of 0.2 mW and 5 mW, respectively. (C,D) Corresponding perspective images for dosimeters irradiated by N7+ ions.
compared with that of water is assigned to the higher density in the PDT dosimeter; the different penetration of the two beams can be related to the different atomic numbers of the ions. The variation of the ESR spectra as a function of sample depth was deduced from the 2D spectral-spatial ESRI experiments presented in Figure 4. Figure 4A,B presents 2D spectralspatial perspective images at 300 K of the PDT dosimeter irradiated by C6+ ions for microwave powers of 0.2 mW (A) and 5 mW (B). Spectral slices at the indicated depths are shown to the right of each perspective plot, and arrows point to the signals from radicals R1 and R2. The spectral slices were averaged from 0.4 mm layers, and the indicated depth is at the center of each slice; for example, a depth marked 2.1 mm represents the 1.9 to 2.3 mm layer. The calculated percentages of the radical R1 in the complex ESR signals are also given. Corresponding results for irradiation with N7+ ions are shown in Figure 4C,D. All perspective images show the increase in the signal intensity from the irradiated side of the sample to the Bragg peak, as also seen in the 1D ESRI profiles, Figure 3. The additional information obtained from Figure 4 is the evolution of the ESR spectra with sample depth. Radical R1 is dominant for both irradiating beams, but the relative intensity of this spectral component decreases from the irradiated side to the Bragg peak; the decrease is more pronounced in Figure 4B,D, at the higher microwave power. The images obtained for a microwave power of 0.2 mW, Figure 4A,C, represent the variation of the LET with sample depth for the two beams, without complications from the saturation properties of the ESR signals. Results obtained for a microwave power of 5 mW, Figure 4B,D, reflect the combination of LET variation with sample depth and saturation properties of the two radical types; these results must be considered in view of the possibility that
ESR spectra may in general be measured under conditions that maximize the signal intensity. The results presented above represent the first experiments that visualize both the dose distribution and the variation of the ionization density along the radiation track following irradiation with heavy charged particles. The relative dose distribution as a function of tablet depth can be estimated from the 1D profiles, Figure 3. The 2D ESRI results illustrate the change in the spectral shape with increasing sample depth and thus the increasing LET. Together with additional calibration data of the intensity of R1 and R2 radicals for known values of LET and comparison with data from tablets irradiated to known absorbed doses, the approach described in this study is expected to lead to an elegant method, based on ESR and ESRI methods, for accurate determination of both the LET and the absorbed dose distribution. Knowledge of the microwave power saturation properties of the two radicals, presented in Figures 1 and 2, is essential for these determinations. Acknowledgment. Development of ESRI methods in the Detroit laboratory is continuously and generously supported by the Polymers Program of NSF, with additional support from the Founders Fellowship of AAUW to S.S., and the University Research Program (URP) of Ford Motor Company. Research in Linko¨ping, Sweden is supported by grants from the Swedish Cancer Society no. 4276-B05-07XBC. Research in Poland is supported by MNiI Project No. 3T0 9A 051 28. We thank B. Stenerlo¨w and H. Karlsson (Gustav Werner Cyclotron, The Svedberg Laboratory, Uppsala University) for information about the beam characteristics and valuable help with irradiation, and for the gift of PDT. We are grateful to A. Lund (Linko¨ping University) for illuminating discussions on PDT dosimetry.
8442 J. Phys. Chem. B, Vol. 112, No. 29, 2008 Supporting Information Available: The calculated energy and LET at the surface of the dosimeters, and the estimated range in water. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Ikeya, M. New Applications of Electron Spin Resonance, World Scientific Publishing: Singapore, 1993; Chapter 13, pp 395-426. (2) Ciesielski, B.; Wielopolski, L. Radiat. Res. 1994, 140, 105. (3) Malinen, E.; Heydari, M. Z.; Sagstuen, E.; Hole, E. O. Radiat. Res. 2003, 159, 23. (4) Metha, K.; Girzikowsky, R. Appl. Radiat. Isot. 1996, 47, 1189. (5) Gustafsson, H.; Olsson, S.; Lund, A.; Lund, E. Radiat. Res. 2004, 161, 464. (6) Malinen, E.; Waldeland, E.; Hole, E. O.; Sagstuen, E. Spectrochim. Acta Part A - Molec. Biomolec. Spectr. 2006, 63, 861. (7) Lund, A.; Olsson, S.; Bonora, M.; Lund, E.; Gustafsson, H. Spectrochim. Acta Part A - Molec. Biomolec. Spectr. 2002, 58, 1301. (8) Gustafsson, H.; M.; Danilczuk, M.; Sastry, M. D.; Lund, A.; Lund, E. Spectrochim. Acta Part A - Molec. Biomolec. Spectr. 2005, 62, 614. (9) M. Danilczuk, M.; Gustafsson, H.; Sastry, M. D.; Lund, E.; Lund, A. Spectrochim. Acta Part A - Molec. Biomolec. Spectr. 2008, 69, 18. (10) Bogushevich, S. E.; Ugolev, I. I. Appl. Radiat. Isot. 2000, 52, 1217. (11) Baran, M. P.; Bugay, O. A.; Kolesnik, S. P.; Maksimenko, V. M.; Teslenko, V. V.; Petrenko, T. L.; Desrosiers, M. F. Radiat. Prot. Dosim. 2006, 120, 202. (12) Chantry, G. W.; Horsfield, A.; Morton, J. R.; Rowlands, J. R.; Whiffen, D. H. Mol. Phys. 1962, 5, 233. (13) Gomes, E. M.; Ortega, J.; Etxebarria, J.; Zuniga, F. J.; Breczewski, T. J. Phys.: Condens. Matter 1996, 8, 2063.
Letters (14) ICRU, Stopping of Ions HeaVier than Helium, Report 73; International Commission on Radiation Units and Measurements: Bethesda, MD, 2005. (15) Chu, W. T.; Ludewigt, B. A.; Renner, T. R. ReV. Scd. Instrum. 1993, 64, 2055. (16) Schlick, S.; Motyakin, M. V. In Specialist Periodical Reports Electron Paramagnetic Resonance; Gilbert, B. C., Davies, M. J., Murphy, D. M., Eds; Royal Society of Chemistry: Cambridge, 2007; Vol. 20, pp 1-28. (17) Morita, Y.; Ohno, K.; Ohashi, K.; Sohma, J. Appl. Radiat. Isot. 1989, 40, 1237. (18) Ohno, K. In EPR Imaging and In ViVo EPR; Eaton, G. R., Eaton, S. S., Ohno, K., Eds.: CRC Press, Inc.: Boca Raton, FL, 1989; Chapter 18, p 183. (19) Anton, M.; Selbach, H.-J. Bruker Report 2006, 157/158, 48. (20) Kruczala, K.; Motyakin, M. V.; Schlick, S. J. Phys. Chem. B 2000, 104, 3387. (21) Motyakin, M. V.; Schlick, S. Macromolecules 2002, 35, 3984. (22) Kruczala, K.; Bokria, J. G.; Schlick, S. Macromolecules 2003, 36, 1909. (23) Kruczala, K.; Aris, W.; Schlick, S. Macromolecules 2005, 38, 6979. (24) Schlick, S.; Kruczala, K. In AdVanced ESR Methods in Polymer Research, Schlick, S., Ed.; Wiley: Hoboken, NJ, 2006; Chapter 8, pp 229254. (25) Spalek, T.; Kruczala, K.; Sojka, Z.; Schlick, S. J. Magn. Reson. 2007, 189, 139. (26) Schlick, S. J. Chem. Phys. 1972, 56, 654. (27) The WinSim software can be accessed at http://www.niehs.nih.gov/research/resources/software/tools/index.cfm.
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