Lecture Notes in Computer Science
Sensitivity and Uniformity in Detecting Motion Artifacts
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- 2 Measuring Motion Artifacts
- 2.1 Ratio Image Uniformity
- 2.2 Scaled Least-Squared Difference
- 2.3 Correlation Coefficient
- 2.7 Mean Distance to the Principal Component
- 3 Experimental Results
- Acknowledgments.
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Sensitivity and Uniformity in Detecting Motion Artifacts Wen-Chuang Chou 1 , Michelle Liou 1 , and Hong-Ren Su 1,2 1
128, Academia Rd. Sec.2, Taipei 115, Taiwan 2 Department of Computer Science, National Tsing Hwa University, 101, Sec.2, Kuang-Fu Rd., Hsinchu, 300 Taiwan {wcchou,mliou,stevensu}@stat.sinica.edu.tw Abstract. Removing artifacts due to head motion is a preprocessing proce- dure necessary for any fMRI analysis. In fMRI tool boxes, there have been standard algorithms for correcting motion artifacts. However, those tool boxes fail to indicate the extent to which the correction has been successfully done. Without knowing motion contamination especially after correction, the subsequent analysis using averaged fMRI data across subjects could be mis- leading. In this study, we proposed seven summary indices for measuring mo- tion artifacts. The indices can be applied after motion correction by the image registration algorithms. In the simulation studies, we analyzed a real fMRI data set using a statistical method and estimated the brain activation maps. The real image data were then randomly shifted or rotated to simulate differ- ent degrees of head motion. The data contaminated by random motion were then corrected using the SPM image coregistration algorithms. The indices of motion contamination were computed using the corrected images. The cor- rected images were then analyzed again using the same statistical method. The consistency between the brain activation maps based on real data and those based on simulated data was used as a standard to evaluate the useful- ness of the proposed seven indices. The results show that some indices are informative with regards to the degree of motion contamination in preproc- essed fMRI data. 1 Introduction Implementing image registration (or motion correction) in fMRI tool boxes has be- come a routine procedure before statistical analyses. A major purpose of image registration is to make a distinction between the change of signal intensity due to head motion and that due to brain activities. There are situations in which fMRI images are seriously contaminated by head motion and cannot be completely re- covered by image registration methods. It would be informative to have indices in- dicating motion contamination in the preprocessed data. Without knowing motion contamination, the subsequent analysis using averaged fMRI data across subjects could be misleading. Rather than focusing on motion correction algorithms [1], 210 W.-C. Chou, M. Liou, and H.-R. Su [2], [3], we propose seven indices for detecting motion contamination in preproc- essed fMRI data. The indices can be applied after motion correction by the image registration algorithms. In the simulation studies, we analyzed a real fMRI data set using a statistical method and estimated the brain activation maps. The image data were then randomly shifted or rotated to simulate different degrees of head motion. The data contaminated by random motion were corrected using the SPM image co- registration algorithms. The motion indices were computed using the corrected im- ages. The corrected images were then analyzed again using the same statistical method. The consistency between the activation maps of real data and those of simulated data was used as a standard to evaluate the usefulness of the proposed indices. In the next section, the seven indices are introduced in details. In Section 3, the performance of indices are evaluated by comparing their uniformity in and sensitivity to detecting motion artifacts in real fMRI data. We finally discuss the use of different indices. 2 Measuring Motion Artifacts The indices we propose here provide a summary measure for motion contamination especially in the preprocessed fMRI data without necessarily knowing real motion ar- tifacts. In real applications, it is nearly impossible to define the true errors caused by head movement or brain warping. In this study, we give a focus on finding adequate indices based on the notion that similarity between image volumes adjacent in the time domain would be a good indicator of any dislocation due to head movement in fMRI time series. The ensuing indices are therefore completely decided by the innate nature of image signals. In this section, we give seven indices and compare between them according to their sensitivity to small motion artifacts and uniformity in measur- ing different degrees of contamination.
We use the ratio image uniformity adopted in AIR 3.0 [4] as the first index I riu . The
ratio image is created by means of computing the ratio of intensity of two image vol- umes on a voxel-by-voxel basis, and then the uniformity of this ratio is represented by its standard deviation σ. Uniformity guarantees the similarity of volumes, and gives smaller standard deviations. In other words, we would expect small motion contami- nation in fMRI data if the ratio has a smaller standard deviation across image vol- umes. Here we denote the intensity value of the focal image as M, the intensity value of the reference image as N, and the voxel coordinate by r. The first index I
can be
simply expressed as ) ) ( ) ( ( r r N M I riu σ = . (1)
Sensitivity and Uniformity in Detecting Motion Artifacts 211
The second index I sls ,
referred to as scaled least-squared difference, is to describe the global intensity difference by using a modified least-squared approach [5]. In this in- dex, global intensity of one volume is rescaled to that of another volume. Given the total voxel number v, this normalized index can be shown as 2 )
2 ) ( 2 ) ( ) ( 1 r r r r r N M sls N N M M v I σ σ + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = ∑ , (2) with M and
N being the mean intensity of these two volumes, respectively. 2.3 Correlation Coefficient The information of how two images correlate with each other can refer to their correlation coefficient, here denoted as the third index I
[6]. The high correlation in- dicates that the image time-series are under a stable status. Let Cov(M,N) be the co- variance between M and N and the correlation coefficient is defined as ) (
( )) ( ), ( ( r r r r N M cc N M Cov I σ σ = . (3) 2.4 Joint Entropy The voxel similarity based on information theory has been broadly applied in image registration because of their accuracy and robustness [1], [7], [8]. The commonly- used joint entropy, as adopted here, measures the dispersion of a distribution com- puted from a joint intensity histogram. The joint distribution p
can be estimated by each entry in the joint histogram of two image volumes divided by the total number of voxels. The entropy is low when the images are so similar that two anatomical struc- tures overlap each other and their joint distribution shows certain concentrated clus- ters. The joint entropy of two images M and N can be calculated by the following equation: ∑ − = j i N M N M je j i p j i p I , , , ) , ( log
) , ( (4)
where i and j indicate the intensity value of M and N, respectively. 2.5 Relative Entropy The relative entropy, also called Kullback–Leibler divergence, measures the distance between two probability distributions. Given the probability of the focal image P
and that of the reference image P N ,
we can compute the relative entropy using the fol- lowing formula: 212 W.-C. Chou, M. Liou, and H.-R. Su ( ) ( )
1 ( )
( ) 2 ( ) ( ) N M re M N j j N M P j P j I P j P j P j P j ⎡ ⎤ = + ⎢ ⎥ ⎣ ⎦ ∑ ∑ . (5) where j denotes the jth intensity value. 2.6 Weighted Kappa The weighted kappa index I kw proposed by Cohen [13] is a measure of agreement be- tween two ratings of the same image. The calculation procedure follows the following steps:
Step 1: The observed weighted proportion of agreement is given by , ,
( , ) o M N i j P w i j p i j = ∑ , (6)
where the summation is over all possible intensity values, and the chance-expected proportion of agreement by , ( , )
( ) ( )
c M N i j P w i j p i p j = ∑ . (7)
In the equations above, the weights are computed by 1 1 ) , ( − − − = G j i j i w , (8) where G is the total number of distinct intensity values. Equation (8) assigns higher weights to intensity values closer to each other. Step 2: The weighted kappa value can be calculated by
− − = 1
(9) Cicchetti and Fleiss [14] gave the sample standard error of a kappa estimate, and the sample estimate in (9) can be tested for significance in applications.
The final index is defined as the average distance to the principal component. Here we use the principal components analysis [10] to find the principal axis in the joint histo- gram of two image volumes. The distance to the principal axis is defined as the or- thogonal projection of each voxel to the axis. The average of the distances can be used as an indicator of the degree of image contamination. Sensitivity and Uniformity in Detecting Motion Artifacts 213
In the empirical study, we used a real fMRI dataset collected in the Mechelli et al. study [11], which is a part of the general collection of the US fMRI Data Center. The data of the third subject in the Mechelli et al. study with 360 image volumes were se- lected for our empirical study. Based on the preprocessed images provided in the
Datasets 1 2 3 4 5 6 Degree of rotation - X axis 15 2 2 15 2 15 - Y axis
2 15 2 15 15 2 - Z axis 2 2 15 2 15 15 Motion Indices Ratio Image Uniformity mean 47.95 42.92 19.25 67.40 50.56 54.47 variance 2288.2 1374.8 128.64 2190.8 1350.0 1870.3 Least-squared mean
0.193 0.143 0.155 0.244 0.219 0.252 variance
0.0157 0.0085 0.0081 0.0112 0.0071 0.0126 Correlation Coefficient mean
0.903 0.927 0.922 0.877 0.889 0.873 variance
0.0040 0.0021 0.0020 0.0028 0.0018 0.0032 Joint Entropy mean 7.565 7.457 7.493 7.638 7.601 7.623 variance 0.109 0.113 0.098 0.066 0.045 0.064 Relative Entropy mean
0.0921 0.0756 0.0745 0.0805 0.0897 0.0731 variance
0.0154 0.0125 0.0120 0.0136 0.0205 0.0119 Weighted Kappa mean 0.773 0.802 0.789 0.741 0.747 0.706 variance 0.0066 0.0084 0.0045 0.0044 0.0033 0.0045 Mean Distance to the Principal Component mean
8.501 7.417 8.126 10.121 9.863 10.449 variance
11.586 8.333 8.571 8.113 5.710 8.518
214 W.-C. Chou, M. Liou, and H.-R. Su Reproducibility Maps (Original data) Reproducibility Maps (Dataset No. 1) Reproducibility Maps (Dataset No. 2) Reproducibility Maps (Dataset No. 3) Reproducibility Maps (Dataset No. 4) Reproducibility Maps (Dataset No. 5) Reproducibility Maps (Dataset No. 6)
reproducibility analysis for a few slices in the Mechelli et al. study. The increased and de- creased responses for Subject 3 are indicated by the red and green colors respectively. The superior frontal gyrus, and supramarginal gyrus are shown in the slices located in the upper yellow block, and the noise mainly appears in images located in the lower block. Sensitivity and Uniformity in Detecting Motion Artifacts 215 dataset, we conducted the reproducibility analysis to estimate the brain activation maps [12]. The activation maps are used as the standard to evaluate the performance of the proposed motion indices. In the simulation study, we rotated the preprocessed
Fig. 2. Plots of motion indices for the preprocessed images provided by the US fMRI Data Cen- ter and the corrected fMRI images in the datasets No. 2 and 6. The contaminated datasets were corrected for motion by maximizing mutual information based on the Powell algorithm. In the six plots, the gray line refers to the motion indices of the preprocessed images; the red line dot- ted with solid triangles and yellow line with empty reversed triangles respectively refer to the indices of corrected images in the datasets No. 2 and 6. The vertical and horizontal axes repre- sent the index values and image volumes along the time scale, respectively.
216 W.-C. Chou, M. Liou, and H.-R. Su data along the X-, Y-, and Z-directions randomly within the range shown in Table 1 to simulate different degrees of motion contamination. The contaminated images were then corrected using the maximization of normalized mutual information based on the Powell algorithm [7], [8]. The motion indices were also applied to the corrected im- ages. Finally, we conducted the reproducibility analysis again to estimate the brain ac- tivation maps based on the corrected images. Table 1 gives the means and standard deviations of motion indices for different simulated datasets. Datasets 1, 2 and 3 are less contaminated by motion as compared with datasets 4, 5 and 6. Therefore, a sensitive index should give larger values (or smaller correlations and kappa values) for datasets 4, 5 and 6. In general, the proposed motion indices more or less show the contrast between modest and serious motion contamination. The mean distance to the principal component tends to give greater contrast compared with other indices. Because the Mechelli et al. study was conducted for investigating the words and pseudo-words reading, the activation regions found by the reproducibility analysis correspond to the superior frontal gyrus and supramarginal gyrus. The activation maps based on corrected images are shown in Fig. 1. Among the three datasets with modest contamination, Dataset No. 2 after coregistration using the Powell al- gorithm gives almost the same activation maps as the original results. The mean distance to the principal component also outperforms other motion indices by giv- ing the smallest value to Dataset No. 2. In terms of uniformity, the scaled least- squared, correlation coefficient, joint entropy, weight kappa, and mean distance to the principal component indices yield reasonable results. The five indices are also sensitive to motion contamination. Freire et al. reported similar unfavorable results for the ratio image uniformity index [1]. The change in marginal intensity probabili- ties between adjacent image volumes are not sensitive to serious head motion. Therefore the relative entropy index fails to detect motion contamination for the simulated datasets. In Fig. 2, we plot the motion indices (except for the relative entropy index) across image volumes based on the original preprocessed images, and the corrected images for the simulated datasets No. 2 and No. 6. The sharp peaks in the plots for the original fMRI data suggests the dislocations (head motion) between two adja- cent image volumes. The plots suggest that the scaled least-squared, correlation co- efficient, and mean distance to the principal component indices serve as good crite- ria by comparing between the ensuring reproducibility maps of original data and those of simulated data. However, the plots for joint entropy and weighted kappa suggest that the two indices do not differentiate the degree of contamination in datasets No. 2 and No. 6. The algorithm used for correcting motion contamination was based on maximizing the normalized mutual information defined as (H M (i)+H N (i))/H M,N (i,j). If the maximized normalized mutual information and indi- vidual marginal entropy of corrected images in datasets No. 2 and No. 6 are similar, we can always obtain similar joint entropy. Sensitivity and Uniformity in Detecting Motion Artifacts 217
In this study, we have proposed the use of seven indices for detecting motion con- tamination in fMRI data. Based on the empirical results, the scaled least-squared, cor- relation coefficient, joint entropy, weighted kappa and mean distance to the principal component perform uniformly in measuring dislocations between two image volumes. In applications, the plotting of motion indices across image volumes before and after image registration would be informative for detecting possible effects due to motion contamination on the subsequent statistical analyses. Among the five indices, the mean distance to the principal component is the best choice for informing the useful- ness of preprocessed fMRI data. Although we have some conclusions in this study, much quantitative work has to be done to further verify the performance of these indices.
001-MY3 from the National Science Council (Taiwan). References 1. Freire, L., Mangin, J.F.: Motion correction algorithms create spurious brain activations in the absence of subject motion. Neuroimage 14, 709–722 (2001) 2. Hellier, P., Barillot, C., Corouge, I., Gibaud, B., Le Goualher, G., Collins, D.L., Evans, A., Malandaln, G., Ayache, N., Christensen, G.E., Johnson, H.J.: Retrospective evaluation of intersubject brain registration. IEEE Transactions on Medical Imaging 22, 1120–1130 (2003) 3. Oakes, T.R., Johnstone, T., Walsh, K.S.O., Greischar, L.L., Alexander, A.L., Fox, A.S., Davidson, R.J.: Comparison of fMRI motion correction software tools. Neuroimage 28, 529–543 (2005) 4. Woods, R.P., Grafton, S.T., Holmes, C.J., Cherry, S.R., Mazziotta, J.C.: Automated image registration: I. General methods and intrasubject, intramodality validation. Journal of Computer Assisted Tomography 22, 139–152 (1998) 5. Alpert, N.M., Berdichevsky, D., Levin, Z., Morris, E.D., Fischman, A.J.: Improved meth- ods for image registration. Neuroimage 3, 10–18 (1996) 6. Ghahramani, S.: Fundamentals of Probability, 2nd edn (2000) 7. Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multimodality im- age registration by maximization of mutual information. IEEE Transactions on Medical Imaging 16, 187–198 (1997) 8. Studholme, C., Hill, D.L.G., Hawkes, D.J.: An overlap invariant entropy measure of 3D medical image alignment. Pattern Recognition 32, 71–86 (1999) 9. Cohen, J.: Weighted Kappa: nominal scale agreement with provision for scaled disagree- ment or partial credit. Psychological Bulletin 70, 213–220 (1968) 10. Cicchetti, D.V., Fleiss, J.L.: Comparison of the null distributions of weighted kappa and the C ordinal statistic. Applied Psychological Measurement 1, 195–201 (1977)
218 W.-C. Chou, M. Liou, and H.-R. Su 11. Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002) 12. Mechelli, A., Friston, K.J., Price, C.J.: The effects of presentation rate during word and pseudoword reading: A comparison of PET and fMRI. Journal of Cognitive Neurosci- ence 12, 145–156 (2000) 13. Liou, M., Su, H.R., Lee, J.D., Aston, J.A.D., Tsai, A.C., Cheng, P.E.: A method for gener- ating reproducible evidence in fMRI studies. Neuroimage 29, 383–395 (2006) M. Ishikawa et al. (Eds.): ICONIP 2007, Part I, LNCS 4984, pp. 219–227, 2008. © Springer-Verlag Berlin Heidelberg 2008 Download 12.42 Mb. Do'stlaringiz bilan baham: 
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