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Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 7081 (http://iopscience.iop.org/0031-9155/59/22/7081) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.83.63.20 This content was downloaded on 26/08/2017 at 16:06 Please note that terms and conditions apply.
You may also be interested in: Dual-energy CT imaging for measuring proton stopping ratios M Yang, G Virshup, J Clayton et al. Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Nora Hünemohr, Bernhard Krauss, Christoph Tremmel et al. Reply to ‘Comment on “Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates”’ Nora Hünemohr, Nina Niebuhr and Steffen Greilich A stoichiometric calibration method for dual energy computed tomography Alexandra E Bourque, Jean-François Carrier and Hugo Bouchard Comprehensive analysis of proton range uncertainties related to patient stopping-power-ratio estimation using the stoichiometric calibration Ming Yang, X Ronald Zhu, Peter C Park et al. Comprehensive analysis of proton range uncertainties related to stopping-power-ratio estimation using dual-energy CT imaging B Li, H C Lee, X Duan et al.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 7081–7084
Physics in Medicine & Biology doi:10.1088/0031-9155/59/22/7081
Comment
Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Paolo Farace Proton therapy Unit, APSS, Trento, Italy Email: [email protected] Received 31 December 2013 Accepted for publication 19 August 2014 Published 31 October 2014 Abstract
A two-steps procedure is presented to convert dual-energy CT data to stopping power ratio (SPR), relative to water. In the first step the relative electron density (RED) is calculated from dual-energy CT-numbers by means of a bi-linear relationship: RED = a HUscH + b HUscL + c, where HUscH and HUscL are scaled units (HUsc = HU + 1000) acquired at high and low energy respectively, and the three parameters a, b and c has to be determined for each CT scanner. In the second step the RED values were converted into SPR by means of published poly-line functions, which are invariant as they do not depend on a specific CT scanner. The comparison with other methods provides encouraging results, with residual SPR error on human tissue within 1%. The distinctive features of the proposed method are its simplicity and the generality of the conversion functions. Keywords: CT calibration, stopping power ratio, proton therapy (Some figures may appear in colour only in the online journal) The calculation of the particles range, which has a profound effect on particles treatments, is determined with the knowledge of the stopping power of the tissues along the beam path. Computer tomographic (CT) images of the patient are used to account for the effect of tissue inhomogeneity by applying an appropriate calibration of CT-Hounsfield units (HU) into stopping power ratio (SPR), relative to water. Recently, Hünemohr et al (2014) presented an interesting method to predict SPR from dual-energy CT data. The calculation of relative electron density (RED) and effective atomic number (EAN) from dual CT data was performed by a procedure requiring the determination of two linear and an exponential coefficients, instead of using iterative approaches (as in Torikoshi et al 2003). Then the mean excitation energy (Im) was estimated from EAN by an empirical linear relationship between the logarithm of Im and the EAN, as originally proposed 0031-9155/14/227081+4$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA
7081
P Farace
Phys. Med. Biol. 59 (2014) 7081
Figure 1. Individual residual RED (top) and SPR (bottom) of 18 tissue surrogates
(at 80 and 140 kV). The residuals estimated by Hünemohr et al (2014) are reported by black bars for comparison; the residuals obtained by the two-steps procedure by white bars. The following values were obtained by equation (1): a = 1.421 × 10−3; b = −0.428 × 10−3; c = 4.5 × 10−6.
by Yang et al (2010). Finally the SPR was calculated by applying the estimated RED and Im into Bethe equation. Herein, the following two-steps procedure to convert dual-energy CT data to SPR was analysed: (a) calculation of RED from dual CT-numbers by means of the following bi-linear relationship H L RED = a HUsc + b HUsc +c H HUsc
(1)
L HUsc
where and are scaled units (HUsc = HU + 1000) acquired at high and low energy respectively, and the three parameters a, b and c has to be determined for each CT scanner; (b) conversion of RED into SPR by the poly-line functions proposed by Kanematsu et al (2012). In step (a) the application of equation (1), is equivalent to the method proposed by Saito (2012), who introduced a dual-energy subtracted quantity that was converted into RED via a single linear relationship with three parameters. The advantage of equation (1) is that it can be solved by a simple linear regression, avoiding the numerical approach required in the original method. Equation (1) can be simplified (by assigning c = 0) if it is assumed that HU of air is −1000. Then it can be exactly converted to the equation proposed by Hünemohr et al (equation (14) in their manuscript), with only one parameter to be calculated, if it is also assumed than the HU of water is zero. This last equation with only one parameter corresponds to the ideal case in the original study of Saito (2012). However, this author continued to apply a three parameters equation in a successive study (Tsukihara et al 2013), despite values close to the ideal case have been always found. The optimal number of parameters to be used in these 7082
P Farace
Phys. Med. Biol. 59 (2014) 7081
Figure 2. Histogram of relative errors in SPR of 34 human tissues at 80 and 140 kVp (from Yang et al 2010) estimated by the two-steps procedure. The root-mean-square error was 0.31%. The greatest errors were −0.79% (for cell nucleus), +0.75% (for skeleton yellow marrow), −0.68% (for skeleton red marrow) and 0.52% (for breast mammary gland) respectively. All the other errors were below 0.5%.
equations and the optimal number and composition of tissue surrogates to be used for their determination deserve deeper investigation. In step (b) the relationship suggested by Kanematsu et al (2012) were obtained by applying the Bethe formula to calculate SPR on human-tissues of known elemental composition, and then by using poly-line functions to convert RED into SPR. Since the energy-dependent variation of SPR is within 1% under therapeutic condition (Kanematsu et al 2003), the suggested poly-line functions do not depend on energy, but energy dependent functions might be also calculated. These function do not need the calculation of EAN from dual-energy voxel data since they were based on RED only. In particular, in Yang et al (2010) and Hünemohr et al the human tissues and the tissue surrogates were subdivided into two categories: soft tissues and bony tissues. Within each group, the logarithm of Im had a good linear relationship with EAN except for the thyroid tissue which contains iodine. The authors decided to exclude the thyroid tissue and to keep two separated relationships for soft and bone tissues respectively. As a consequence, it is not completely clear which Im has to be assigned to the voxels resulting characterized by EAN intermediate between soft and bone tissues. The above two-steps procedure was applied to the same data reported by Hünemohr et al (figure 1). The relative RED errors (figure 1(a)) were smaller than 1%. Since they were similar to those obtained by Hünemohr et al, the use of one or three parameters in equation (1) did not markedly affect the results on this data set. The residual SPR were greater (figure 1(b)), as tissue surrogates have a different composition compared to the real tissues. In fact, both Hünemohr et al and Kanematsu et al (2012) used human tissue to estimate Im versus EAN and SPR versus RED respectively. Accordingly, by applying the two-steps approach to the human-tissue data reported by Yang et al (2010), the residual errors were always smaller than 1% (figure 2). These results seem only slightly different than those obtained by the Yang et al (2010), who reported a maximum error = 1.00% and a root-mean-square error = 0.26%. Interestingly, the error on the thyroid tissues resulted −0.39%, which is thus included in the 7083
P Farace
Phys. Med. Biol. 59 (2014) 7081
calibration, confirming that by the two-steps procedure it can be possible to predict the SPR of any combination of HUs. A distinctive feature of the proposed method is the simplicity and the generality of the conversion functions. In practice, CT calibration needs only the calculation of three (or less) scanner-specific parameters in equation (1), which can be obtained by a simple linear fitting of the data acquired on tissue surrogates. As in Hünemohr et al, the available tissue surrogates would not be a source of error in the calibration procedure despite their limitation in mimicking radiation characteristics of real tissues. In fact, in step (a) the scanner-specific parameters are expected to be the same both for tissue surrogates and real tissues, and the relationship applied in step (b), which was calculated on human tissues, is generally valid as it does not depend on a specific CT scanner. References Hünemohr N, Krauss B, Tremmel C, Ackermann B, Jäkel O and Greilich S 2014 Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Phys Med Biol. 59 83–96 Kanematsu N, Inaniwa T and Koba Y 2012 Relationship between electron density and effective densities of body tissues for stopping, scattering, and nuclear interactions of proton and ion beams Med Phys. 39 1016–20 Kanematsu N, Matsufuji N, Kohno R, Minohara S and Kanai T 2003 A CT calibration method based on the polybinary tissue model for radiotherapy treatment planning Phys Med Biol. 48 1053–64 Saito M 2012 Potential of dual-energy subtraction for converting CT numbers to electron density based on a single linear relationship Med Phys. 39 2021–30 Torikoshi M, Tsunoo T, Sasaki M, Endo M, Noda Y, Ohno Y, Kohno T, Hyodo K, Uesugi K and Yagi N 2003 Electron density measurement with dual-energy x-ray CT using synchrotron radiation Phys Med Biol. 48 673–85 Tsukihara M, Noto Y, Hayakawa T and Saito M 2013 Conversion of the energy-subtracted CT number to electron density based on a single linear relationship: an experimental verification using a clinical dual-source CT scanner Phys Med Biol. 58 N135–44 Yang M, Virshup G, Clayton J, Zhu XR, Mohan R and Dong L 2010 Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues Phys Med Biol. 55 1343–62
7084
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My IOPscience
Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 7081 (http://iopscience.iop.org/0031-9155/59/22/7081) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.83.63.20 This content was downloaded on 26/08/2017 at 16:06 Please note that terms and conditions apply.
You may also be interested in: Dual-energy CT imaging for measuring proton stopping ratios M Yang, G Virshup, J Clayton et al. Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Nora Hünemohr, Bernhard Krauss, Christoph Tremmel et al. Reply to ‘Comment on “Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates”’ Nora Hünemohr, Nina Niebuhr and Steffen Greilich A stoichiometric calibration method for dual energy computed tomography Alexandra E Bourque, Jean-François Carrier and Hugo Bouchard Comprehensive analysis of proton range uncertainties related to patient stopping-power-ratio estimation using the stoichiometric calibration Ming Yang, X Ronald Zhu, Peter C Park et al. Comprehensive analysis of proton range uncertainties related to stopping-power-ratio estimation using dual-energy CT imaging B Li, H C Lee, X Duan et al.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 7081–7084
Physics in Medicine & Biology doi:10.1088/0031-9155/59/22/7081
Comment
Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Paolo Farace Proton therapy Unit, APSS, Trento, Italy Email: [email protected] Received 31 December 2013 Accepted for publication 19 August 2014 Published 31 October 2014 Abstract
A two-steps procedure is presented to convert dual-energy CT data to stopping power ratio (SPR), relative to water. In the first step the relative electron density (RED) is calculated from dual-energy CT-numbers by means of a bi-linear relationship: RED = a HUscH + b HUscL + c, where HUscH and HUscL are scaled units (HUsc = HU + 1000) acquired at high and low energy respectively, and the three parameters a, b and c has to be determined for each CT scanner. In the second step the RED values were converted into SPR by means of published poly-line functions, which are invariant as they do not depend on a specific CT scanner. The comparison with other methods provides encouraging results, with residual SPR error on human tissue within 1%. The distinctive features of the proposed method are its simplicity and the generality of the conversion functions. Keywords: CT calibration, stopping power ratio, proton therapy (Some figures may appear in colour only in the online journal) The calculation of the particles range, which has a profound effect on particles treatments, is determined with the knowledge of the stopping power of the tissues along the beam path. Computer tomographic (CT) images of the patient are used to account for the effect of tissue inhomogeneity by applying an appropriate calibration of CT-Hounsfield units (HU) into stopping power ratio (SPR), relative to water. Recently, Hünemohr et al (2014) presented an interesting method to predict SPR from dual-energy CT data. The calculation of relative electron density (RED) and effective atomic number (EAN) from dual CT data was performed by a procedure requiring the determination of two linear and an exponential coefficients, instead of using iterative approaches (as in Torikoshi et al 2003). Then the mean excitation energy (Im) was estimated from EAN by an empirical linear relationship between the logarithm of Im and the EAN, as originally proposed 0031-9155/14/227081+4$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA
7081
P Farace
Phys. Med. Biol. 59 (2014) 7081
Figure 1. Individual residual RED (top) and SPR (bottom) of 18 tissue surrogates
(at 80 and 140 kV). The residuals estimated by Hünemohr et al (2014) are reported by black bars for comparison; the residuals obtained by the two-steps procedure by white bars. The following values were obtained by equation (1): a = 1.421 × 10−3; b = −0.428 × 10−3; c = 4.5 × 10−6.
by Yang et al (2010). Finally the SPR was calculated by applying the estimated RED and Im into Bethe equation. Herein, the following two-steps procedure to convert dual-energy CT data to SPR was analysed: (a) calculation of RED from dual CT-numbers by means of the following bi-linear relationship H L RED = a HUsc + b HUsc +c H HUsc
(1)
L HUsc
where and are scaled units (HUsc = HU + 1000) acquired at high and low energy respectively, and the three parameters a, b and c has to be determined for each CT scanner; (b) conversion of RED into SPR by the poly-line functions proposed by Kanematsu et al (2012). In step (a) the application of equation (1), is equivalent to the method proposed by Saito (2012), who introduced a dual-energy subtracted quantity that was converted into RED via a single linear relationship with three parameters. The advantage of equation (1) is that it can be solved by a simple linear regression, avoiding the numerical approach required in the original method. Equation (1) can be simplified (by assigning c = 0) if it is assumed that HU of air is −1000. Then it can be exactly converted to the equation proposed by Hünemohr et al (equation (14) in their manuscript), with only one parameter to be calculated, if it is also assumed than the HU of water is zero. This last equation with only one parameter corresponds to the ideal case in the original study of Saito (2012). However, this author continued to apply a three parameters equation in a successive study (Tsukihara et al 2013), despite values close to the ideal case have been always found. The optimal number of parameters to be used in these 7082
P Farace
Phys. Med. Biol. 59 (2014) 7081
Figure 2. Histogram of relative errors in SPR of 34 human tissues at 80 and 140 kVp (from Yang et al 2010) estimated by the two-steps procedure. The root-mean-square error was 0.31%. The greatest errors were −0.79% (for cell nucleus), +0.75% (for skeleton yellow marrow), −0.68% (for skeleton red marrow) and 0.52% (for breast mammary gland) respectively. All the other errors were below 0.5%.
equations and the optimal number and composition of tissue surrogates to be used for their determination deserve deeper investigation. In step (b) the relationship suggested by Kanematsu et al (2012) were obtained by applying the Bethe formula to calculate SPR on human-tissues of known elemental composition, and then by using poly-line functions to convert RED into SPR. Since the energy-dependent variation of SPR is within 1% under therapeutic condition (Kanematsu et al 2003), the suggested poly-line functions do not depend on energy, but energy dependent functions might be also calculated. These function do not need the calculation of EAN from dual-energy voxel data since they were based on RED only. In particular, in Yang et al (2010) and Hünemohr et al the human tissues and the tissue surrogates were subdivided into two categories: soft tissues and bony tissues. Within each group, the logarithm of Im had a good linear relationship with EAN except for the thyroid tissue which contains iodine. The authors decided to exclude the thyroid tissue and to keep two separated relationships for soft and bone tissues respectively. As a consequence, it is not completely clear which Im has to be assigned to the voxels resulting characterized by EAN intermediate between soft and bone tissues. The above two-steps procedure was applied to the same data reported by Hünemohr et al (figure 1). The relative RED errors (figure 1(a)) were smaller than 1%. Since they were similar to those obtained by Hünemohr et al, the use of one or three parameters in equation (1) did not markedly affect the results on this data set. The residual SPR were greater (figure 1(b)), as tissue surrogates have a different composition compared to the real tissues. In fact, both Hünemohr et al and Kanematsu et al (2012) used human tissue to estimate Im versus EAN and SPR versus RED respectively. Accordingly, by applying the two-steps approach to the human-tissue data reported by Yang et al (2010), the residual errors were always smaller than 1% (figure 2). These results seem only slightly different than those obtained by the Yang et al (2010), who reported a maximum error = 1.00% and a root-mean-square error = 0.26%. Interestingly, the error on the thyroid tissues resulted −0.39%, which is thus included in the 7083
P Farace
Phys. Med. Biol. 59 (2014) 7081
calibration, confirming that by the two-steps procedure it can be possible to predict the SPR of any combination of HUs. A distinctive feature of the proposed method is the simplicity and the generality of the conversion functions. In practice, CT calibration needs only the calculation of three (or less) scanner-specific parameters in equation (1), which can be obtained by a simple linear fitting of the data acquired on tissue surrogates. As in Hünemohr et al, the available tissue surrogates would not be a source of error in the calibration procedure despite their limitation in mimicking radiation characteristics of real tissues. In fact, in step (a) the scanner-specific parameters are expected to be the same both for tissue surrogates and real tissues, and the relationship applied in step (b), which was calculated on human tissues, is generally valid as it does not depend on a specific CT scanner. References Hünemohr N, Krauss B, Tremmel C, Ackermann B, Jäkel O and Greilich S 2014 Experimental verification of ion stopping power prediction from dual energy CT data in tissue surrogates Phys Med Biol. 59 83–96 Kanematsu N, Inaniwa T and Koba Y 2012 Relationship between electron density and effective densities of body tissues for stopping, scattering, and nuclear interactions of proton and ion beams Med Phys. 39 1016–20 Kanematsu N, Matsufuji N, Kohno R, Minohara S and Kanai T 2003 A CT calibration method based on the polybinary tissue model for radiotherapy treatment planning Phys Med Biol. 48 1053–64 Saito M 2012 Potential of dual-energy subtraction for converting CT numbers to electron density based on a single linear relationship Med Phys. 39 2021–30 Torikoshi M, Tsunoo T, Sasaki M, Endo M, Noda Y, Ohno Y, Kohno T, Hyodo K, Uesugi K and Yagi N 2003 Electron density measurement with dual-energy x-ray CT using synchrotron radiation Phys Med Biol. 48 673–85 Tsukihara M, Noto Y, Hayakawa T and Saito M 2013 Conversion of the energy-subtracted CT number to electron density based on a single linear relationship: an experimental verification using a clinical dual-source CT scanner Phys Med Biol. 58 N135–44 Yang M, Virshup G, Clayton J, Zhu XR, Mohan R and Dong L 2010 Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues Phys Med Biol. 55 1343–62
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