The Neuroradiology Journal 20: 18-24, 2007
www. centauro. it
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements R. DAMBE*, S. HÄHNEL**, S. HEILAND* * Div. of Experimental Neuroradiology and ** Dept. of Neuroradiology, University of Heidelberg Medical Center; Heidelberg.Germany
Key words: magnetic resonance imaging, diffusion, diffusion tensor imaging, eddy current artefacts
SUMMARY – Diffusion tensor imaging (DTI) has been proposed for examination of cerebral white matter. However, this measurement needs sophisticated postprocessing and is susceptible to eddy current artefacts. The aim of this study was to examine whether diffusion measured in three anatomically well defined directions provides full and reliable information on diffusion anisotropy. Measurements were performed in water and gelatine phantoms and in 14 healthy volunteers. Diffusion was measured in six independent directions. For the full tensor DTI we diagonalised the diffusion tensor, for measurements with three directions we used only the diagonal elements. We then calculated the diffusion trace and the linear anisotropy index (AIl ). We measured a slight anisotropy in the phantoms, which was larger in the case of the full tensor DTI (AIl = 0.022) then for the three orthogonal diffusion directions (0.008-0.019). The linear anisotropy index measured in white matter regions within the right and left hemisphere ranged between 0.33 and 0.42. AIl values were moderately correlated between right and left hemisphere regions (correlation factor: 0.35-0.64). DTI using the full tensor information is more susceptible to systematic errors resulting from eddy current effects than the measurement of diffusion in three orthogonal directions. However, in the latter method the anisotropy index is systematically underestimated in anatomical structures that do not exhibit a principal diffusion parallel to one of the diffusion directions. Therefore it is recommended to use the full tensor method together with sophisticated methods for eddy current correction.
Introduction Diffusion-weighted magnetic resonance imaging (diffusion MRI) has become increasingly used method in clinical routine diagnostics in neuroradiology, particularly in the diagnosis of acute cerebral ischemia 1-3. Most clinical applications are based on diffusion trace imaging, where water diffusibility is measured independent of the diffusion direction. In this method, it is necessary to measure diffusion in three different, orthogonal directions (ADCx, ADCy, ADCz ) ; diffusion trace is then calculated as a mean of these three ADC values. Diffusion trace values are so widely used because the calculation method is robust and the diffusion changes are independent of the diffu18
sion direction in most clinical applications 4,5. However, when focusing on pathologies that mainly affect the white matter (WM) diffusion should be measured and examined in different directions separately. During the last decade, diffusion tensor imaging (DTI) was developed 6-7 . With this method it is possible to calculate maps of the fractional anisotropy as an invariant parameter, and of the principal diffusion direction. Furthermore, the data allows us to track the fiber bundles of white matter (fiber tracking) 8-9. DTI does not only need sophisticated postprocessing, but is also highly susceptible to any imperfections of the gradient system. Particularly in systems with poor eddy current correction, distortions and displacements lead to
R. Dambe
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements
a mismatch of the positions of a distinct voxel in the different direction-dependent diffusionweighted images. Therefore, the same pixel ADCi,j contains diffusion information of different voxels resulting in an over- or underestimation of the anisotropy and in gross miscalculation of the principal diffusion direction. The aim of this study was to examine the robustness of measurement of anisotropic diffusion in three and six directions. We were particularly interested in whether the diagonal diffusion directions yield additional information compared to diffusion measurement in three orthogonal directions the diffusion if gradient axes are defined strictly by anatomical landmarks and structures. Material and Methods Phantoms and Volunteers
Fourteen healthy volunteers (age: 22–31 y, mean: 26.1±2.7 y) were examined. Approval for this examination was obtained from the local ethics committee. To examine the effect of eddy current artefacts on the accuracy of the diffusion parameters, we also carried out MR examinations in three spherical phantoms (volume: 1 liter). One phantom contained purified water and the other two a gelatine solution with a concentration of 30 g/l and 120 g/l, respectively.
parameters (slice thickness, FOV) were the same as in the T2-w sequence, the other sequence parameters were: TR: 4000 ms; TE: 108 ms; matrix: 64×94. We used b-values of 0 and 1000 s/mm2. Diffusion directions were (x,y,z) = (1,0,0), (0,1,0), (0,0,1), (0.71, 0.71, 0), (0, 0.71, 0.71), (0.71, 0, 0.71). Each measurement was repeated three times to measure the reliability of the method. Data Postprocessing
The DTI data were stored as DICOM images and were transferred to a PC. There they were postprocessed using a self-developed program written in DELPHI professional (version 5.62; Borland International, Inc. Scotts Valley, CA, USA). With this program, DTI data were imported, processed, and the interesting parameters (apparent diffusion coefficient, ADC; diffusion trace, Tr; linear anisotropy, AI l ) were calculated. The program further allowed visualisation and export of the ADC, Tr and AIl maps, respectively. In detail, the diffusion tensor D is calculated from the DTI measurements Dxy
Dxz
D = D yx
Dyy
Dyz
D zx
Dzy
Dzz ,
(
with
)
( )
Sii Dii = ADCii = – 1– ln b S0
MR Protocol
MR examinations were carried out using a 1.5 T MR scanner (Edge, MARCONI, Cleveland, OH, USA). The scanner was equipped with a gradient hardware (maximum gradient: 27 mT/m, slew rate: 72 mT/m/ms) capable of echo planar imaging (EPI). All measurements were performed with slice directions parallel to the connecting line between the anterior cingulum (AC) and posterior cingulum (PC). In each patient, we started the MR protocol with a T2-weighted turbo spin echo (TSE) sequence with the following sequence parameters: repetition time (TR): 2248 ms; echo time (TE): 90 ms (T2-w) / 20 ms (proton-density-w); field-of-view (FOV): 22 cm×19.25 cm; matrix: 192×256; number of signal averages (NSA): one; number of slices (NS): 19; slice thickness: 6 mm; interslice gap: 0.5 mm. In a second step we performed diffusionweighted imaging using a spin-echo (SE) EPI sequence. The slice positions and geometric
Dxx
and Dxy = 1– (A D C xy – A D C xx – A D C yy ), 2 Dxz = 1– (A D C xz – A D C xx – A D C zz ), 2 Dyz = 1– (A D C yz – A D C yy – A D C zz ). 2 An example for the Maps of the tensor elements Di,j is shown in figure 1. For exact calculation of the anisotropy, most authors proposed measurements in six or more different diffusion directions 10 because the anisotropy may be underestimated dramatically if only three different orthogonal directions are used. As we wanted to compare the full tensor (six directions) with the measurement of the orthogonal directions (three directions), we used the full tensor data set in two different ways. 19
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements
R. Dambe
Figure 1 Maps of the tensor elements Di,j (i,j = x,y,z) calculated in a healthy volunteer. The artefacts resulting from displacements and distortions due to the eddy currents are visible as a bright rim at the anterior rim of the brain.
A. Full tensor method
The diffusion tensor determined on a pixelby-pixel basis was diagonalised yielding the eigenvalues λ1, λ2, and λ3 and the respective eigenvectors. As scalar parameters we calculated the trace 20
Tr =
λ1+λ2+λ3 3
and the linear anisotropy index λ1–λ2 All = λ + λ +λ 1 2 3
www. centauro. it
As we wanted to compare the anisotropy measurements of datasets measured in three and six diffusion directions, we calculated the linear anisotropy index instead of the fractional anisotropy; for the latter the measurement of the full tensor is needed. Because the diffusion in white matter tracts can be considered as linear, i.e. λ1≫λ2≅λ3 , the lineal anisotropy index should correlate to the fractional anisotropy.
The Neuroradiology Journal 20: 18-24, 2007
spective anatomical regions within the right and left hemispheres and the correlation coefficient between the values measured at the first and the second data postprocessing. The statistical analysis was performed using Microsoft Excel (Microsoft Inc., Redmond, WA, USA). Furthermore we compared the image quality of the Tr and AIl parameter maps measured with three and six tensor elements.
B. Measurement of three orthogonal directions
For this measurement we used the same data sets as in (A), but used only the diagonal elements (Dxx, Dyy, Dzz). As scalar parameters we calculated the trace Dxx+Dyy+Dzz Tr = 3 and the linear anisotropy index Max(Dxx,Dyy,Dzz)–Min(Dxx,Dyy,Dzz) AIl = Dxx+Dyy+Dzz C. Measurement of tensor scalars in ROIs and Statistical Postprocessing Measurements of Tr and AIl were performed in: • a user defined region of interest (ROI) in the center of each phantom; • six user defined ROIs in each volunteer: right and left pyramidal tract, right and left occipital white matter and right and left centrum semiovale. We used identical regions for the three- and six-directions DTI method. To assess the accuracy of the parameter calculation within the ROIs, we performed data postprocessing including the definitions of ROIs a second time three months after the first data postprocessing. As diffusion in the water and gelatine phantoms should be completely isotropic, the AIl is theoretically considered to be zero. If hardware imperfections, e.g. incomplete eddy current correction, nonlinear gradients or imperfect gradient calibration, influence the DTI method, however, we would expect AIl>0. We therefore calculated the mean AIl in water and gelatine as an indicator for the influence of eddy currents. To measure the influence of the off-diagonal elements of the diffusion tensor on the accuracy of the calculation of the linear anisotropy index, we calculated the correlation coefficient between the values of AIl measured in the re-
Results To examine the influence of the eddy currents on the calculated scalars, we firstly compared the diffusion trace and the linear anisotropy index in the water and gelatine phantoms. AIl was 0.022±0.002 (six directions) and 0.008±0.001 (three directions) in water, 0.022±0.001 (six directions) and 0.013±0.001 (three directions) in gelatine with normal concentration, and 0.022±0.001 (six directions) and 0.019±0.002 (three directions) in gelatine with fourfold concentration, respectively. There were no differences in diffusion trace between the three-directions and six-directions DTI: Tr was 1.11±0.02 × 10–3 mm2/s in water, 1.06±0.01 × 10–3 mm2/s in single dose gelatine, and 0.92±0.01 × 10–3 mm2/s in gelatine with fourfold concentration. Figures 2 and 3 show maps of the diffusion trace and the linear anisotropy index, respectively. It can be seen that the Tr maps do not differ significantly, whereas there are obvious differences between the AIl maps: The AIl map calculated with the full tensor (a) exhibits more noise compared to the AIl map calculated with diffusion measurements in three orthogonal diffusion directions (b). Furthermore AIl values are higher when calculated from the full tensor, particularly outside the large white matter bundles like the pyramidal tract and the corpus callosum. This, on the other hand, leads to a higher contrast between grey and white matter in the AIl map calculated from three orthogonal diffusion directions. Quantitative analysis of the data yielded a linear anisotropy index between 0.33 and 0.42 for all white matter regions considered (cf. table 1). There were no significant differences between either postprocessing method with regard to reliability and reproducibility (cf. tables 2 and 3). When comparing the AIl between the anatomical structures in the right and left hemispheres, we found a correlation with a high level of significance (p
www. centauro. it
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements R. DAMBE*, S. HÄHNEL**, S. HEILAND* * Div. of Experimental Neuroradiology and ** Dept. of Neuroradiology, University of Heidelberg Medical Center; Heidelberg.Germany
Key words: magnetic resonance imaging, diffusion, diffusion tensor imaging, eddy current artefacts
SUMMARY – Diffusion tensor imaging (DTI) has been proposed for examination of cerebral white matter. However, this measurement needs sophisticated postprocessing and is susceptible to eddy current artefacts. The aim of this study was to examine whether diffusion measured in three anatomically well defined directions provides full and reliable information on diffusion anisotropy. Measurements were performed in water and gelatine phantoms and in 14 healthy volunteers. Diffusion was measured in six independent directions. For the full tensor DTI we diagonalised the diffusion tensor, for measurements with three directions we used only the diagonal elements. We then calculated the diffusion trace and the linear anisotropy index (AIl ). We measured a slight anisotropy in the phantoms, which was larger in the case of the full tensor DTI (AIl = 0.022) then for the three orthogonal diffusion directions (0.008-0.019). The linear anisotropy index measured in white matter regions within the right and left hemisphere ranged between 0.33 and 0.42. AIl values were moderately correlated between right and left hemisphere regions (correlation factor: 0.35-0.64). DTI using the full tensor information is more susceptible to systematic errors resulting from eddy current effects than the measurement of diffusion in three orthogonal directions. However, in the latter method the anisotropy index is systematically underestimated in anatomical structures that do not exhibit a principal diffusion parallel to one of the diffusion directions. Therefore it is recommended to use the full tensor method together with sophisticated methods for eddy current correction.
Introduction Diffusion-weighted magnetic resonance imaging (diffusion MRI) has become increasingly used method in clinical routine diagnostics in neuroradiology, particularly in the diagnosis of acute cerebral ischemia 1-3. Most clinical applications are based on diffusion trace imaging, where water diffusibility is measured independent of the diffusion direction. In this method, it is necessary to measure diffusion in three different, orthogonal directions (ADCx, ADCy, ADCz ) ; diffusion trace is then calculated as a mean of these three ADC values. Diffusion trace values are so widely used because the calculation method is robust and the diffusion changes are independent of the diffu18
sion direction in most clinical applications 4,5. However, when focusing on pathologies that mainly affect the white matter (WM) diffusion should be measured and examined in different directions separately. During the last decade, diffusion tensor imaging (DTI) was developed 6-7 . With this method it is possible to calculate maps of the fractional anisotropy as an invariant parameter, and of the principal diffusion direction. Furthermore, the data allows us to track the fiber bundles of white matter (fiber tracking) 8-9. DTI does not only need sophisticated postprocessing, but is also highly susceptible to any imperfections of the gradient system. Particularly in systems with poor eddy current correction, distortions and displacements lead to
R. Dambe
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements
a mismatch of the positions of a distinct voxel in the different direction-dependent diffusionweighted images. Therefore, the same pixel ADCi,j contains diffusion information of different voxels resulting in an over- or underestimation of the anisotropy and in gross miscalculation of the principal diffusion direction. The aim of this study was to examine the robustness of measurement of anisotropic diffusion in three and six directions. We were particularly interested in whether the diagonal diffusion directions yield additional information compared to diffusion measurement in three orthogonal directions the diffusion if gradient axes are defined strictly by anatomical landmarks and structures. Material and Methods Phantoms and Volunteers
Fourteen healthy volunteers (age: 22–31 y, mean: 26.1±2.7 y) were examined. Approval for this examination was obtained from the local ethics committee. To examine the effect of eddy current artefacts on the accuracy of the diffusion parameters, we also carried out MR examinations in three spherical phantoms (volume: 1 liter). One phantom contained purified water and the other two a gelatine solution with a concentration of 30 g/l and 120 g/l, respectively.
parameters (slice thickness, FOV) were the same as in the T2-w sequence, the other sequence parameters were: TR: 4000 ms; TE: 108 ms; matrix: 64×94. We used b-values of 0 and 1000 s/mm2. Diffusion directions were (x,y,z) = (1,0,0), (0,1,0), (0,0,1), (0.71, 0.71, 0), (0, 0.71, 0.71), (0.71, 0, 0.71). Each measurement was repeated three times to measure the reliability of the method. Data Postprocessing
The DTI data were stored as DICOM images and were transferred to a PC. There they were postprocessed using a self-developed program written in DELPHI professional (version 5.62; Borland International, Inc. Scotts Valley, CA, USA). With this program, DTI data were imported, processed, and the interesting parameters (apparent diffusion coefficient, ADC; diffusion trace, Tr; linear anisotropy, AI l ) were calculated. The program further allowed visualisation and export of the ADC, Tr and AIl maps, respectively. In detail, the diffusion tensor D is calculated from the DTI measurements Dxy
Dxz
D = D yx
Dyy
Dyz
D zx
Dzy
Dzz ,
(
with
)
( )
Sii Dii = ADCii = – 1– ln b S0
MR Protocol
MR examinations were carried out using a 1.5 T MR scanner (Edge, MARCONI, Cleveland, OH, USA). The scanner was equipped with a gradient hardware (maximum gradient: 27 mT/m, slew rate: 72 mT/m/ms) capable of echo planar imaging (EPI). All measurements were performed with slice directions parallel to the connecting line between the anterior cingulum (AC) and posterior cingulum (PC). In each patient, we started the MR protocol with a T2-weighted turbo spin echo (TSE) sequence with the following sequence parameters: repetition time (TR): 2248 ms; echo time (TE): 90 ms (T2-w) / 20 ms (proton-density-w); field-of-view (FOV): 22 cm×19.25 cm; matrix: 192×256; number of signal averages (NSA): one; number of slices (NS): 19; slice thickness: 6 mm; interslice gap: 0.5 mm. In a second step we performed diffusionweighted imaging using a spin-echo (SE) EPI sequence. The slice positions and geometric
Dxx
and Dxy = 1– (A D C xy – A D C xx – A D C yy ), 2 Dxz = 1– (A D C xz – A D C xx – A D C zz ), 2 Dyz = 1– (A D C yz – A D C yy – A D C zz ). 2 An example for the Maps of the tensor elements Di,j is shown in figure 1. For exact calculation of the anisotropy, most authors proposed measurements in six or more different diffusion directions 10 because the anisotropy may be underestimated dramatically if only three different orthogonal directions are used. As we wanted to compare the full tensor (six directions) with the measurement of the orthogonal directions (three directions), we used the full tensor data set in two different ways. 19
Measuring Anisotropic Brain Diffusion in Three and Six Directions: Influence of the Off-Diagonal Tensor Elements
R. Dambe
Figure 1 Maps of the tensor elements Di,j (i,j = x,y,z) calculated in a healthy volunteer. The artefacts resulting from displacements and distortions due to the eddy currents are visible as a bright rim at the anterior rim of the brain.
A. Full tensor method
The diffusion tensor determined on a pixelby-pixel basis was diagonalised yielding the eigenvalues λ1, λ2, and λ3 and the respective eigenvectors. As scalar parameters we calculated the trace 20
Tr =
λ1+λ2+λ3 3
and the linear anisotropy index λ1–λ2 All = λ + λ +λ 1 2 3
www. centauro. it
As we wanted to compare the anisotropy measurements of datasets measured in three and six diffusion directions, we calculated the linear anisotropy index instead of the fractional anisotropy; for the latter the measurement of the full tensor is needed. Because the diffusion in white matter tracts can be considered as linear, i.e. λ1≫λ2≅λ3 , the lineal anisotropy index should correlate to the fractional anisotropy.
The Neuroradiology Journal 20: 18-24, 2007
spective anatomical regions within the right and left hemispheres and the correlation coefficient between the values measured at the first and the second data postprocessing. The statistical analysis was performed using Microsoft Excel (Microsoft Inc., Redmond, WA, USA). Furthermore we compared the image quality of the Tr and AIl parameter maps measured with three and six tensor elements.
B. Measurement of three orthogonal directions
For this measurement we used the same data sets as in (A), but used only the diagonal elements (Dxx, Dyy, Dzz). As scalar parameters we calculated the trace Dxx+Dyy+Dzz Tr = 3 and the linear anisotropy index Max(Dxx,Dyy,Dzz)–Min(Dxx,Dyy,Dzz) AIl = Dxx+Dyy+Dzz C. Measurement of tensor scalars in ROIs and Statistical Postprocessing Measurements of Tr and AIl were performed in: • a user defined region of interest (ROI) in the center of each phantom; • six user defined ROIs in each volunteer: right and left pyramidal tract, right and left occipital white matter and right and left centrum semiovale. We used identical regions for the three- and six-directions DTI method. To assess the accuracy of the parameter calculation within the ROIs, we performed data postprocessing including the definitions of ROIs a second time three months after the first data postprocessing. As diffusion in the water and gelatine phantoms should be completely isotropic, the AIl is theoretically considered to be zero. If hardware imperfections, e.g. incomplete eddy current correction, nonlinear gradients or imperfect gradient calibration, influence the DTI method, however, we would expect AIl>0. We therefore calculated the mean AIl in water and gelatine as an indicator for the influence of eddy currents. To measure the influence of the off-diagonal elements of the diffusion tensor on the accuracy of the calculation of the linear anisotropy index, we calculated the correlation coefficient between the values of AIl measured in the re-
Results To examine the influence of the eddy currents on the calculated scalars, we firstly compared the diffusion trace and the linear anisotropy index in the water and gelatine phantoms. AIl was 0.022±0.002 (six directions) and 0.008±0.001 (three directions) in water, 0.022±0.001 (six directions) and 0.013±0.001 (three directions) in gelatine with normal concentration, and 0.022±0.001 (six directions) and 0.019±0.002 (three directions) in gelatine with fourfold concentration, respectively. There were no differences in diffusion trace between the three-directions and six-directions DTI: Tr was 1.11±0.02 × 10–3 mm2/s in water, 1.06±0.01 × 10–3 mm2/s in single dose gelatine, and 0.92±0.01 × 10–3 mm2/s in gelatine with fourfold concentration. Figures 2 and 3 show maps of the diffusion trace and the linear anisotropy index, respectively. It can be seen that the Tr maps do not differ significantly, whereas there are obvious differences between the AIl maps: The AIl map calculated with the full tensor (a) exhibits more noise compared to the AIl map calculated with diffusion measurements in three orthogonal diffusion directions (b). Furthermore AIl values are higher when calculated from the full tensor, particularly outside the large white matter bundles like the pyramidal tract and the corpus callosum. This, on the other hand, leads to a higher contrast between grey and white matter in the AIl map calculated from three orthogonal diffusion directions. Quantitative analysis of the data yielded a linear anisotropy index between 0.33 and 0.42 for all white matter regions considered (cf. table 1). There were no significant differences between either postprocessing method with regard to reliability and reproducibility (cf. tables 2 and 3). When comparing the AIl between the anatomical structures in the right and left hemispheres, we found a correlation with a high level of significance (p
