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1 Iproved Precision in the Measureent of Longitudinal Global and Regional Voluetric Changes via a Novel MRI Gradient Distortion Characterization and Correction Technique Vladiir S. Fonov 1, Andrew Janke 2, Zografos Caraanos 1, Douglas L. Arnold 1, Sridar Narayanan 1, G. Bruce Pike 1, and D. Louis Collins 1 1 McConnell Brain Iaging Center, Montreal Neurological Institute, McGill University Montreal Canada vladiir.fonov@gail.co, aki@rs.ni.cgill.ca, doug@rs.ni.cgill.ca, sridar@rs.ni.cgill.ca, bruce.pike@cgill.ca, louis.collins@cgill.ca 2 Departent of Geriatric Medicine, College of Medicine and Health Sciences, The Australian National University, Canberra Australia a.janke@gail.co Abstract. Reducing easureent variability in MRI-based orphoetric analysis of huan brain structures will increase statistical power to detect changes between groups and longitudinally over tie in individual subjects. One source of easureent error in anatoical MR is agnetic field gradientinduced geoetric distortion. This work proposes a ethod to characterize and copensate for these distortions using a novel iage processing technique relying on the iage acquisition of a phanto with known geoetrical diensions, without the need to acquire the agnetic field apping. The ethod is not specific to any particular shape of the phanto, as long as it provides enough coverage of the volue of interest and enough structure to densely saple the distortion field. The distortions are expressed in ters of spherical haronic functions, which are then used to define the distortion correction field for the volue of interest. Accuracy of the distortion easureent was evaluated using nuerical siulation and reproducibility was estiated using ultiple scans of the phanto in the sae scanner. Finally, scan-rescan experients with nine healthy subjects deonstrated that 90% of the distortion (in ters of local volue change) can be corrected with this technique. Keywords: Geoetric distortion, phanto, spherical haronics, MRI, orphoetric analysis. 1 Introduction Magnetic resonance iaging (MRI) is widely used in any longitudinal studies of noral brain developent and aging as well as the evaluation of neurological disease. H. Liao et al. (Eds.): MIAR 2010, LNCS 6326, pp , Springer-Verlag Berlin Heidelberg 2010

2 Iproved Precision in the Measureent of Longitudinal Global 325 Quantitative easureent of regional anatoical volues is often used in these studies. Magnetic field gradient nonlinearities result in geoetric distortion of the iages and this can have a significant ipact on the accuracy of volue easures and estiation of volue change between scans [1]. To correct for these distortions, two classes of ethods have been described: 1. indirect apping of the deforation field using a physical phanto with easily identifiable, known structures [2], [3]. MR iages of the phanto are used to estiate the deforation field and 2. direct easureent of each agnetic field gradient using specialized hardware. The easureents are then fit to a atheatical odel of the gradients, and the inverse proble is solved to estiate a distortion correction field [1], [4]. While the latter direct ethod is attractive on theoretical grounds, it requires spherical haronic inforation specific to each scanner and gradient set to which it will be applied, which in turn requires explicit apping of the agnetic field strength within the bore of the MRI agnet. Given that these easureents are coplex and require specialized equipent, this ethod generally is only feasible if the spherical haronics inforation can be obtained fro the scanner anufacturer. In practice, this inforation is difficult to obtain as it depends on sensitive easureents acquired by edical physicists or engineers. In the present study, we propose a procedure for easuring and correcting gradient-induced distortions fro the first class of indirect ethods that uses a siple geoetric phanto that is both inexpensive and easy to reproduce. It does not require changing the acquisition protocol; in fact the protocol used for subject data acquisition should be used to acquire the necessary data of the phanto for distortion correction. Furtherore, accurate positioning of the phanto at the agnetic center of the scanner is not needed the phanto siply has to cover the field of view where subject data will be acquired. The distortion correction field is expressed using a spherical haronic expansion and is based on a atheatical odel of the agnetic field gradient [5]. However, unlike the second class of ethods described in [4] and in [1], the proposed ethod does not require apping of the agnetic field. We have already reported the effect of the gradient-induced distortions on the longitudinal easureents of whole-brain atrophy [6]. In the current work we expand the proposed technique to copensate for the gradient-induced distortions and deonstrate its effect on the precision of the longitudinal voluetric analysis. 2 Methods 2.1 Distortion Model Our approach is based on the idea that the geoetric distortion field within the scanner ay be expressed using a spherical haronic expansion (SPH). However, in our ethod we do not try to easure the strength of the agnetic field explicitly to odel the distortion. Instead, we use apparent displaceents of corresponding points to calculate the coefficients of the coordinate apping functions (Eq. 1,2): [ ] P ( ) ( cosθ ) n ( r θ, φ ) r a cos( φ) b sin( φ) F = + (1) V, n,, V, n, V, n, n,

3 326 V.S. Fonov et al. where V= x,y,z are Cartesian coordinates; r, θ, φ are spherical coordinates in an ideal coordinate syste, and P (n,) are the associated Legendre polynoials, and X * V = F n, V, n, ( r,, φ) θ (2) where X V * are coordinates in the scanner specific coordinate syste. We use least squares approxiation to calculate the SPH coefficients based on the dense field of displaceents that is obtained by atching the ideal representation of the phanto to the acquired MRI scan using iterative nonlinear iage registration technique described below. Because we are using a relatively sall nuber of coefficients (105 for the 5 th order spherical coponents expansion), this ethod is quite robust to rando noise or partially issing inforation. Additionally, for soe acquisition protocols it is possible to assue cylindrical syetry around the Z axis, which decreases the nuber of coefficients for the 5 th order expansion fro 105 to 40 yielding an even ore robust solution. 2.2 Geoetric Phanto The proposed ethod does not require any particular phanto to be used in the iaging, as long as it covers the volue of interest (VOI), and contains enough structural features to densely saple the distortion field. It is possible, for exaple, to use the ADNI phanto [7] for this analysis, or any other phanto with known geoetrical inforation. For this study we have constructed a phanto consisting of 125 Lego DUPLO bricks ade of ABS plastic (Billund, Denark) assebled inside a polycarbonate Nalgene 8L container and filled with a water solution of 0.15M/L MnCL 2 and 2.8g/L NaCL, according to [8] (see Fig. 1). Lego DUPLO 2x4 bricks were chosen for the construction in order to have a phanto that can easily be reproduced across ultiple sites with inial cost and with high degree of accuracy, as anufacturing tolerances for LEGO bricks are 2μ [9]. 2.3 Data Processing As a preprocessing step, the ideal phanto volue is created nuerically using the knowledge of the location of the Lego DUPLO bricks and their geoetric properties. A siilar procedure is eployed for the ADNI phanto. As a first step of data processing, we invert the intensities of the MRI scan and reove the background using the orphological operators. A rigid body registration is then used to align the ideal phanto volue to the acquired scan data (see Fig. 2 A, B, C). Next, the hierarchical iterative process of estiating the coefficients for the geoetric distortion correction is run: 1. Start with coefficients describing the identity transforation. 2. For each pair of scanned and ideal phanto volues, calculate a nonlinear apping [10]. The algorith paraeters (level of blurring and node spacing) are reduced at each iteration in hierarchical fashion, starting with 8 steps between nodes and 4 full-width half-ax (FWHM) Gaussian blurring and ending with 2 steps and 1 FWHM Gaussian blurring.

Iproved Precision in the Measureent of Longitudinal Global 327 3.

Note that data fro ultiple acquisitions of the phanto can be cobined to iprove the accuracy or enlarge the coverage 4. Calculate a dense vector field for the next iteration using SPH expansion. 5.

LEGO DUPLO phanto, (A) photo of the exterior of the phanto, (B) sagittal slice of the T1w FLASH acquisition (Sieens Sonata 1.5T scanner) Fig. 2.

4 Iproved Precision in the Measureent of Longitudinal Global Fro the dense field of deforation vectors that defines the non-linear apping recovered in step 2, calculate the coefficients of the SPH using least squares approxiation. Note that data fro ultiple acquisitions of the phanto can be cobined to iprove the accuracy or enlarge the coverage 4. Calculate a dense vector field for the next iteration using SPH expansion. 5. Repeat the process, starting fro step 2 until the last step in the hierarchical schedule. A B Fig. 1. LEGO DUPLO phanto, (A) photo of the exterior of the phanto, (B) sagittal slice of the T1w FLASH acquisition (Sieens Sonata 1.5T scanner) Fig. 2. Overlay of the (A, B) intensity-inverted Lego phanto scan (red) and ADNI phanto scan (C) and the ideal reconstruction (green), before distortion correction and (D,E,F) after distortion correction. Note that where red and green lines are visible, the data fro the scanned and ideal phantos do not align. Yellow structures are well aligned (yellow = red + green). The transverse slice in B and E corresponds to the second row of bricks fro the top of the phanto, as seen in the sagittal iages in A and D.

5 328 V.S. Fonov et al. Once the process is finished, a distortion correction field is produced that can be applied directly to unwarp scans to copensate for gradient-induced distortions, See Fig. 2-D & E for the result of applying the distortion correction field to the Lego phanto itself and Fig. 2-F for the results of application of the ethod to the ADNI phanto scans. 3 Experients Three sets of experients were conducted to validate the algorith. All were perfored with the Lego phanto. The first used nuerical siulations to test the algorith in a fully controlled environent. The second used two sets of MRI experients with ultiple scans of the phanto to evaluate the precision of the algorith using ultiple acquisitions in the sae scanner. Finally, the third set of experients evaluated how the distortion correction procedure affects voluetric easureents using MRI of huan subjects. 3.1 Nuerical Siulations The perforance of the algorith was first characterized with nuerical siulations to recover a realistic known geoetric distortion (which were recovered fro the real experient). One thousand two hundred nuerical siulations were perfored. For each siulation, the sae receive coil inhoogeneity was applied to the ideal reconstruction of the phanto together with sall rando rotations ( -5-5 around x, y and z axis), shifts ( in x, y and z directions) and known distortion field. Also, independent instantiations of Rician noise at a SNR of 20 (300 siulations) and 40 (300 siulations) were applied. For each level of SNR, both cylindrically-syetric and non-syetric odels were applied using a 5 th order approxiation yielding a total of 1200 siulations. RMS differences between siulated and estiated distortions were coputed within a 200 diaeter sphere centered at the isocenter of the gradients. 3.2 Precision of Distortion Measureents Precision of the distortion-correction field was estiated by scanning the phanto with a T1-weighted FLASH sequence on a Sieens Sonata 1.5T scanner at different positions (at the isocenter of the agnet, ±10- displaceent along the X- and Y- axes, and ±50- displaceent along the Z-axis). Two data processing scenarios were used, both using a 5 th -order syetric odel. In the first scenario, each scan was processed independently and RMS differences between distortion fields recovered fro these seven scans were easured within a 200 diaeter sphere centered at the agnet s isocenter. In the second scenario, a leave-one-out approach was used. RMS differences between recovered distortion fields (estiated on the reaining 6 scans) were easured within a 200 diaeter sphere centered at the agnet s isocenter.

6 Iproved Precision in the Measureent of Longitudinal Global Huan Experients Nine healthy subjects were scanned three ties on the sae day on a Sieens Sonata 1.5T scanner using the sae sequence (sagittal T1w 3D FLASH, TE=10 s, TR=22 s, Flip angle=30, voxel size 1x1x1.5, atrix size 256x256x144). The study was approved by the Research Ethics Board of the Montreal Neurological Institute, and infored consent was obtained fro all participants. Each subject was first scanned at the isocenter of the gradients (tered baseline scan, S). Then, the scanner bed was shifted forward 50- and the scan repeated (Z-shifted scan, Z). The subject was then taken out of the scanner, repositioned at the isocenter and scanned again (reposition scan, R). The distortion correction field was estiated using three phanto scans acquired with the sae sequence and paraeters: one at the agnet isocenter, one shifted by +50 in the bore (Z) direction and the third, -50 in the bore direction. Each of the subject iages were corrected for intensity non-unifority using the N3 algorith [11]. The iage pairs (S-R and S-Z) were co-registered in native space using a rigid-body transforation using a cross-correlation objective function; both pairs of scans were resapled in a half-way space. Non-linear registration [10] was used to estiate the residual anatoical isalignent due to the geoetric distortion inside the brain. Local volue differences due to geoetric distortion were estiated by coputing the Jacobian-deterinant of the non-linear deforation field. Finally, the Jacobian deterinant field was resapled into stereotactic space using linear registration of the scan into MNI152 space [12]. The procedure described above was applied to the subject data with and without distortion correction to evaluate the iproveent due to the distortion-correction ethod. This was evaluated by perforing statistical analysis on soothed (Gaussian kernel with FWHM of 10-) Jacobian-deterinant fields in a siilar anner to that described in [13]. Absolute Jacobian-deterinants were averaged between subjects in a voxel-wise anner and two-sided t-tests were perfored to identify voxels where absolute distortion was significantly saller (or greater) after distortion correction. 4 Results 4.1 Nuerical Siulations The nuerical siulations deonstrated that, without the assuption of cylindrical syetry, the RMS difference between known and recovered distortion correction fields was ~0.6 for SNRs of 20 and 40; with the assuption of cylindrical syetry, this difference decreased to ~0.3 (see Fig. 3). The difference between cylindrical and non-cylindrical odels is statistically significant with p<0.001.

330 V.S. Fonov et al. Syetric SNR 20 40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Non syetric SNR 20 40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 RMS error () Fig. 3.

7 330 V.S. Fonov et al. Syetric SNR Non syetric SNR RMS error () Fig. 3. Nuerical siulation, RMS difference between known and recovered distortion for SNR of 20 and 40. Cylindrically syetric (top) and non syetric (botto) odel of distortion field. 4.2 Reproducibility of Distortion Measureents The repeated acquisitions of the Lego phanto deonstrated that the distortion field could be reproduced between phanto acquisitions with an RMS difference of 0.4 across the seven trials in the case where a single acquisition was used to estiate the distortion. When 6 of 7 acquisitions were used to estiate the distortion field, the RMS difference between the 7 estiates was Huan Data Fig. 4 shows intensity difference aps between baseline and Z-shifted scan of one subject. Qualitatively it is visible that uncorrected data shows uch greater variability in the cortex. Over all subjects, voxel-wise analysis shows that voluetric distortions within ore than 86% of the brain volue were reduced in a statistically significant fashion. Fig. 5 shows the average Jacobian-deterinant ap of the distortions before correction and Fig. 6 - after correction (i.e the residual error), where a value of 0.1 A B Fig. 4. Intensity difference iages (scans S - Z) before (A) and after (B) distortion correction. Note the reduced intensity difference after correction, especially near the edges of sulci.

Iproved Precision in the Measureent of Longitudinal Global 331 Fig. 5. Average Jacobian-deterinant ap, uncorrected iages, coparing scans S & Z.

Average Jacobian deterinant ap coparing S & Z iages, after applying the distortion correction (residual error). Note alost perfect correction throughout the field of view. Fig.7.

t>10. corresponds to a 10% change in local volue. Fig.

8 Iproved Precision in the Measureent of Longitudinal Global 331 Fig. 5. Average Jacobian-deterinant ap, uncorrected iages, coparing scans S & Z. Shifting the subject by 50 along the bore of the agnet results in an apparent increase in volue of 7-8% at the vertex and a decrease of approxiately 10% in the region of the cerebellu. Fig. 6. Average Jacobian deterinant ap coparing S & Z iages, after applying the distortion correction (residual error). Note alost perfect correction throughout the field of view. Fig.7. Statistical t-ap of the iproveent (positive t eans that absolute local-voluevariation is saller after distortion correction). Note that the large white region corresponds significant iproveent, ie. t>10. corresponds to a 10% change in local volue. Fig. 7 shows the t-ap of the statistical significance of the reduction of average absolute Jacobian-deterinants after distortion-correction: with the t-threshold set at 3.0 (for a false-discovery rate of 0.01), (i) 86% of the brain volue showed significantly decreased distortions (i.e., was associated with a t-value > 3.0); but (ii) only 0.1% of the brain volue showed increased distortions (i.e., was associated with a t-value < -3.0). On average, the ean (between-subjects) absolute Jacobian-deterinant within the brain was reduced by 90%.

9 332 V.S. Fonov et al. 5 Discussion and Conclusions Gradient-induced geoetric distortion can be an iportant coponent of the variance of estiated structure volues. Indeed, the results shown in Fig. 5 deonstrate that a 5c shift in along the bore of the agnet can result in large apparent changes in volue: regions near the top of the brain increase in volue by 7-8% while structures near the cerebellu shrink by approxiately 10%. While a 5c shift ight appear extraordinarily large, a previous study of clinical trial data [6] has shown that the repositioning error in the z direction can be quite large and soeties larger that 10c. Even though ost data is acquired within 35, the subjects brains will be subitted to different parts of the geoetric distortion field and this will result in unwanted variability in volue estiation. Given that any studies ai to detect (very) sall changes, for exaple 1%/year change in hippocapal volue in patients with ild cognitive ipairent, any geoetric distortion will result in added easureent variance and in a reduced power to detect change. This paper has deonstrated a phanto-based technique for distortion correction that is both siple and inexpensive to use. In our scanner, this procedure reduces the distortions significantly for 86% of the volue covered by the brain, reducing the agnitude of the distortions by 90% (in ters of local volue change). In the reaining 14% of the brain, geoetric distortion was negligible before correction. The practical consequence of application of such a procedure will be reduced easureent variability and iproved power to detect change. The distortion correction ethod presented here is shown to be reproducible to within 0.4 in ters of the distortion recovery in the case of one phanto acquisition, and as good as 0.04 when ultiple phanto acquisitions are cobined. This is partly due to the fact that, by cobining ultiple acquisitions we are siply increasing nuber of averages, thus increasing SNR. In addition, by cobining scans collected at different locations within the scanner we are increasing the volue within which our ethod works as interpolation rather then extrapolation, thus reducing uncertainty in defining the paraeters of the distortion field. Restricting the odel of the distortion field to be cylindrically syetric also iproves the reproducibility by reducing the nuber of unknowns, but special care should be taken in ensuring that this assuption is applicable to the particular acquisition protocol: for exaple if a read out direction other than the z-direction is used this assuption becoes invalid and the full 3D odel should be used to odel the deforation field. Finally, it is iportant to note that the actual agnitude of the distortions estiated here are specific to the scanner used in this study (Sieens Sonata 1.5 T). Nevertheless, whereas the degree and pattern of distortion will vary between scanner anufacturer and odel, the procedure is applicable to all scanners. While a few of the latest-generation scanners have anufacturer-supplied 3D distortion-correction capabilities, the ajority of scanners currently in use do not, or have liited 2D distortion correction capabilities. It also is worth noting that this ethod ay be applied retrospectively to the studies in which a geoetrical phanto (for exaple, the ADNI phanto) was acquired, provided that the geoetrical description of the phanto used is available or ay be easured.

10 Iproved Precision in the Measureent of Longitudinal Global 333 Instructions for the Lego phanto creation and the analysis software are available at Application of this ethod iproves voluetric scan-to-scan reproducibility, and could be adapted to the requireents of a specific study and available geoetrical phanto, and thus will have a positive effect on the power of longitudinal and cross sectional studies References 1. Jovicich, J., Czanner, S., Greve, D., Haley, E., van der Kouwe, A., Gollub, R., Kennedy, D., Schitt, F., Brown, G., Macfall, J., Fischl, B., Dale, A.: Reliability in ulti-site structural MRI studies: effects of gradient non-linearity correction on phanto and huan data. Neuroiage 30, (2006) 2. Wang, D., Doddrell, D.M., Cowin, G.: A novel phanto and ethod for coprehensive 3- diensional easureent and correction of geoetric distortion in agnetic resonance iaging. Magnetic Resonance Iaging 22, (2004) 3. Baldwin, L., Wachowicz, K., Thoas, S., Rivest, R., Fallone, G.: Characterization, prediction, and correction of geoetric distortion in 3 T MR iages. Medical Physics 34, (2007) 4. Janke, A., Zhao, H., Cowin, G.J., Galloway, G.J., Doddrell, D.M.: Use of spherical haronic deconvolution ethods to copensate for nonlinear gradient effects on MRI iages. Magnetic Resonance in Medicine 52, (2004) 5. Krieg, R.S.O.: Method for three-diensionally correcting distortions and agnetic resonance apparatus for ipleenting the ethod, Patent 6,501,273 (2002) 6. Caraanos, Z., Fonov, V.S., Francis, S.J., Narayanan, S., Pike, G.B., Collins, D.L., Arnold, D.L.: Gradient distortions in MRI: Characterizing and correcting for their effects on SIENA-generated easures of brain volue change. NeuroIage 49, (2010) 7. Magphan Quantitative Iaging Phanto (ADNI) (2010) 8. Price, R.R., Axel, L., Morgan, T., Newan, R., Peran, W., Schneiders, N., Selikson, M., Wood, M., Thoas, S.R.: Quality assurance ethods and phantos for agnetic resonance iaging: Report of AAPM nuclear agnetic resonance Task Group No. 1. Medical Physics 17, (1990) 9. LEGO Copany Profile (2007) 10. Collins, D.L., Evans, A.C.: Anial: Validation and Applications of Nonlinear Registration-Based Segentation. International Journal of Pattern Recognition and Artificial Intelligence (IJPRAI) 11, (1997) 11. Sled, J.G., Zijdenbos, A.P., Evans, A.C.: A nonparaetric ethod for autoatic correction of intensity nonunifority in MRI data. IEEE Trans. Med. Iaging 17, (1998) 12. Collins, D.L., Neelin, P., Peters, T.M., Evans, A.C.: Autoatic 3D intersubject registration of MR voluetric data in standardized Talairach space. Journal of Coputer Assisted Toography 18, (1994) 13. Leow, A.D., Klunder, A.D., Jack, J.C.R., Toga, A.W., Dale, A.M., Bernstein, M.A., Britson, P.J., Gunter, J.L., Ward, C.P., Whitwell, J.L., Borowski, B.J., Fleisher, A.S., Fox, N.C., Harvey, D., Kornak, J., Schuff, N., Studhole, C., Alexander, G.E., Weiner, M.W., Thopson, P.M.: Longitudinal stability of MRI for apping brain change using tensorbased orphoetry. NeuroIage 31, (2006)

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