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985AJNR:22,May 2001986NAGATA TABLE 1:Number of activated pixels in each region of interest (ROI)and laterality index values obtained by two methodsSubject No.No.in Left ROI No.inRight ROI No.in Both ROI LI-1(%)LI-2(%)Gap between LI-1and LI-2123456789101150385525204360201629282836512263111105378746026226991312634312838392822532292371812816827661282925377474014216214341446121st 2nd 3rd SD 672940345701061511003625416644311834126131st 2nd 3rd SD 271304119941446224551716491923204514644141st 2nd 3rd SD 64869516362980122124604153105338518732151st 2nd 3rd SD 212337402252339681009016616455573635161st 2nd 3rd SD 5181152550576131203424501338313044820171st 2nd 3rd SD3253221135743882949205218411831128221Note.—LI-1,indicates laterality index-1;LI-2,laterality index-2.The number of activated pixels and LI-1shown were obtained at the z score ϭ1.0.SD indicates standard deviation for the three measure-ments.this reason,it was difficult to evaluate lateralization quantitatively by the z score method previously re-ported in functional MR imaging studies (16,19,20).The drawback of this method was that LI was calculated from a simple above-threshold pixel count,whereas we found it of greater value to use more of the data.We describe our attempt to es-tablish a method for quantitatively evaluating lat-eralization of linguistic function on a continuous scale by functional MR imaging using the z score,and evaluate our new method according to the three criteria of optimality defined above.MethodsSubjectsSeventeen consecutive right-handed healthy adult subjects (16men and one woman;20–39years old)were recruited for this study;of these,six (subjects 12–17)were recruited for the investigation of reproducibility (see Table 1).Subjects gave written informed consent for functional MR imaging.Hand preference was assessed by the Edinburgh Handedness Inven-tory (EDI)(22),in which subjects were asked to indicate hand preference for each of the 12EDI items,and a handedness score was obtained for each subject.EDI scores varied from ϩ100to Ϫ100%,with ϩ100%meaning right-handedness and Ϫ100%meaning left-handedness.A subject was excluded if the EDI score was negative.Image AcquisitionThe subjects were informed of the purpose and meaning of the examination before imaging.Images were obtained on a 1.5-T MR unit with a gradient-echo echo-planar sequence with the following parameters:TR/TE (repetition time/echo time)ϭ2265/64,flip angle ϭ90Њ,field of view ϭ300mm,matrix ϭ84ϫ128,slice thickness ϭ10mm,scan time ϭ180ms.Three contiguous axial slices were obtained parallel to a ref-erence line through the superior edge of the anterior commis-sure and the inferior of the posterior commissure.These slices covered the pars opercularis (Brodmann’s areas 44and 45)(23).The subjects underwent seven alternating periods of a rest and a silent linguistic stimulation task.During each of the four rest periods and three task periods,10images were ob-tained for every slice.Thus,70images per slice were acquired.During the imaging examination,the room light was dimmed and the subject’s head was fixed tightly with foam pads bilat-erally to minimize motion artifacts.Subjects were instructed to close their eyes and to keep their head and eyes still.Task DesignThe word generation task was performed silently through internal speech.During the task periods,the subjects were asked to generate and ‘‘say’’silently as many words as pos-sible that were associated with the first word announced through an intercom at the beginning of the task period.The subjects were instructed to finish the task period when the word end was announced through an intercom.During the rest periods,the subjects were asked to rest and concentrate on their breathing.After the experiment,subjects were asked whether they believed they had performed the task success-fully.If their answer was negative,the examination was repeated.Data AnalysisBefore carrying out the data analysis,we discarded the first two images of each period,because activation/deactivation typ-ically lags several seconds behind stimulus onset/termination (24).Thus,56of the 70images per slice were used.Significant signal changes were identified by the z score (25–28),which was calculated using the following formula:ͦMt ϪMr ͦz score ϭ22͙␦t /Nt ϩ␦r /Nrwhere Mt is the mean signal during task periods,Mr is mean signal during rest periods,␦t is the standard deviation (SD)during task periods,␦r is the SD during rest periods,Nt is the image number during task periods,and Nr is the image number during rest periods.No correction was made for head motion,and no additional filtering or clustering algorithm was used.The pixels that were found to be significantly activated were superimposed on the T1-weighted structural images obtained with a spin-echo se-quence (500/12/2).The number of activated pixels was count-ed using Numaris software supplied by the manufacturer (Siemens).AJNR:22,May 2001LINGUISTIC FUNCTION LATERALIZATION987F IG 1.A and B,Scatter diagrams for subjects 5(A )and 10(B ).Circles indicate the values for the left ROI;squares,for the right ROI.Evaluation of LateralizationFor the evaluation of the lateralization of linguistic function,the LI was calculated by two methods:first by a method (LI-1)reported previously (16,19,20)and second by our new method (LI-2),which we describe here.The regions of interest (ROIs)were drawn on the superimposed images,focusing on the pars opercularis (Brodmann’s areas 44and 45)rather than on Wernicke’s area,because there is no consensus as to where Wernicke’s area is located (29–31).LI-1Method .—With this method,we kept the z score uni-form in all subjects,and the number of activated pixels was measured in each ROI (ie,the left pars opercularis and the right pars opercularis).LI-1was calculated using the following formula:LI-1ϭ[(Nl ϪNr)/(Nl ϩNr)]ϫ100(%)2)where Nl is the number of activated pixels in the left ROI,and Nr is the number of activated pixels in the right ROI.LI-2Method .—With this method,to first determine the cor-relation between the z scores and the number of activated pix-els in each ROI,we made a scatter diagram in which the x -axis represented the z scores and the y -axis represented the number of activated pixels (Fig 1).Robust and more detailed information could be obtained by fitting these ROI concave curves into a regression function.All functions fitting these ROI concave curves well could be used,but it was not possible to calculate a correlation coefficient between these ROI con-cave curves for all functions.A function having few parame-ters is ideal for calculating LI-2;in other words,a monomial expression is more suitable than a polynomial expression,be-cause it is difficult to select one parameter to represent a par-ticular value if the function has many parameters.We therefore chose (1/z score)n as the particular function.We transformed each of the z scores into (1/z score)n to calculate regression equations,and we investigated the correlation coefficient be-tween (1/z score)n and the number of activated pixels.The mean correlation coefficient differences were compared statis-tically using the Friedman test.We used the function that had the highest correlation coefficient.We then calculated the re-gression equations of the two curves from Figure 1.LI-2was calculated using the following formula:LI-2ϭ[{Fl(Z)ϪFr(Z)}/{Fl(Z)ϩFr(Z)}]ϫ100(%)3)where Fl(Z)is the regression equation that was calculated from the curve of the left ROI,and Fr(Z)is the regression equation that was calculated from the curve of the right ROI.LI-1and LI-2varied from ϩ100to Ϫ100%,in which ϩ100%indicates left hemisphere dominance and Ϫ100%indicates right hemi-sphere dominance.To compare the LI-1method with the LI-2method for re-producibility (degree of variation),we performed three func-tional MR imaging measurements at different times and on different days in six subjects (subjects 12–17),and the LI was obtained by both methods.A scatter plot of LI-1versus LI-2for all six subjects was made,and the SD between LI-1and LI-2for the three measurements was obtained for each subject (see Table).The SD between LI-1and LI-2was compared statistically using a Wilcoxon signed rank test.ResultsEDI scores were positive for all subjects.The mean EDI score was 90Ϯ5(%)(mean ϮSD);all subjects were considered strongly right-handed.All subjects performed the internal speech task suc-cessfully,and all showed evidence of a focal MR signal increase in the pars opercularis.The LI-1and LI-2scores were positive for all subjects,and we found that language lateralization was to the left in all subjects (see Table).LI-1The number of activated pixels in each ROI var-ied meaningfully with the z score (Fig 1);that is,the number depended on the z score.LI-1was ob-tained from the number of activated pixels in the right and left ROIs,assuming that the z score was a fixed value (eg,z score ϭ1.0).The number of activated pixels at threshold z ϭ1.0in each ROI varied among subjects,showing a marked variation in activation grade among subjects (see Table).Within the same subject,LI-1varied with the z score.At higher thresholds,LI-1reached 100%,be-cause the number of activated pixels in the right ROI became too small (Fig 2).Therefore,we con-firmed that LI-1varied markedly and was depen-dent on the z score.A threshold in the relatively flat part of LI-1versus the threshold (a cross-cor-relation method)has been reported (16);however,such a threshold in the z score could not be deter-mined from our results.AJNR:22,May 2001988NAGATA F IG 2.A–D,Brain activity images (viewed from below)of subject 5at thresholds 1.0(A )and 1.5(B )and of subject 10at thresh-olds 1.0(C )and 1.5(D ).Black boxes in-dicate ROIs.LI-2The scatter diagrams (in which the x -axis rep-resents the z scores and the y -axis the number of activated pixels)showed similar concave curves in all subjects,regardless of the difference in the grade of activation.We chose (1/z score)n as the particular function.When the value of n ranged from 1to 10,the correlation coefficient between (1/z score)n and the number of activated pixels was very high.A Friedman test revealed that the mean correlation coefficient differences for both sides,for the left side,and for the right side were statis-tically significant (P Ͻ.0001).The mean correla-tion coefficients for both sides,for the left side,and for the right side showed a maximum at n ϭ4.The mean values at n ϭ4for both sides,for the left side,and for the right side were .989Ϯ.006(mean ϮSD),.988Ϯ.12,and .989Ϯ.009,re-spectively (Fig 3).We therefore used (1/z score)4as the function.Because the value of the correlation coefficient was very high,regression functions of the concave curves could be calculated with the following formulas (Fig 4).Number of activated pixels in the left 4)4ROI ϭA ϫ(1/z score)Number of activated pixels in the right 5)4ROI ϭB/(1/z score)where A and B are the fixed values calculated from the scatter diagrams.In nearly all 17subjects,a difference in the num-ber of plots of concave curves (ie,in the df between the two ROI curves)was observed.For example,in subject 5,the df of the left ROI curve was 27and that of the right ROI curve was 10.However,there was a negligible difference in the correlation coefficient between the two ROI curves,which was very high.We therefore surmised that there was no significant difference in the reliability between the fixed values A and B used in the above formulas.LI-2was calculated using the following formula:LI-2ϭ[{Fl(Z)ϪFr(Z)}/{Fl(Z)ϩFr(Z)}]6)ϫ100(%)44ϭ{A ϫ(1/z score)ϪB ϫ(1/z score)}44Ϭ{A ϫ(1/z score)ϩB ϫ(1/z score)}ϫ100(%)ϭ{(A ϪB)/(A ϩB)}ϫ100(%)Thus,LI-2was a fixed value and independent ofAJNR:22,May2001LINGUISTIC FUNCTION LATERALIZATION989F IG 3.A–C,The mean correlation coefficient between(1/z score),(1/z score)2...(1/z score)10,and the number of activated pixels for all subjects on both sides(A),on the left side(B),and on the right side(C).the z score,and we were able to evaluate laterali-zation independent of the z score.The values of A and B did not change significantly when the num-ber of the plots of the concave curves was changed.A relationship between LI-1and LI-2was ob-served.The gap between the two indexes tended to be larger when the number of activated pixels in both ROIs was small(Table and Fig5).When comparing the two LI methods for repro-ducibility,the scatter plots of LI-1versus LI-2 scores for six subjects indicated a slight slant(Fig 6),and the SD of the LI-2scores was statistically smaller than that of the LI-1scores(Wilcoxon signed rank test,PϽ.05).DiscussionIn this study,we evaluated lateralization of lin-guistic function on a continuous scale with both the well-known LI-1method and our new LI-2meth-od.A suitable and useful medical examination should meet the following three criteria:1)the re-sults from the examination should represent robust information about the subject,2)the results should be easily compared across subjects,and3)the ex-amination should have good reproducibility(21). The LI-1scores of our subjects were found to vary with the z score.In this regard,the LI-1method did not meet thefirst criterion.Because the number of activated pixels at a cer-tain threshold varied among subjects,it may be that the reliability of the LI-1scores differed,even when those scores were the same.For example,in one subject,the number of activated pixels in the left ROI was40and the number in the right ROI was20;the subject’s LI-1score was therefore33%. In another subject,the number in the left ROI was 4and the number in the right ROI was2;this sub-ject’s LI-1score was therefore also33%.The LI-1 scores were the same,but the reliability of LI-1 differed(ie,it was higher in thefirst subject). Therefore,it was not possible to compare the two LI-1scores,and therefore,the LI-1method did not meet the second criterion described above.For the calculation of LI-2,we made scatter di-agrams.Interestingly,the scatter diagrams showed similar concave curves in all subjects.We thought that the concave curves were unique to functional MR imaging using the z score,and that each con-cave curve represented robust and more detailed information.The two regression coefficients of the regression lines were calculated from the scatter di-agram.The regression coefficient of the regression line represented the rate of decrease of the activated pixels.LI-2yielded the difference between the rate of decrease in the left hemisphere and that in the right hemisphere.LI-2was afixedfigure,indepen-dent of the z score and thus,LI-2was believed to represent a quantitative lateralization across the two hemispheres.The LI-2method was thought to meet thefirst criterion,concerning robust information. The reliability of LI-2did not differ even if the regression coefficient of the regression line differed significantly among subjects,because each regres-sion coefficient was based on a sufficient amount of information.The LI-2method was thus thought to meet the second criterion regarding intersubject comparisons.As for reproducibility,the LI-2meth-od was found to be more suitable than the LI-1 method,even though the three LI-2scores of sev-eral subjects differed somewhat.The intrasubject variability in LI might be attributed to the inherent variability in the subjects’responses,but we were not able to identify the cause of intrasubject vari-ability in this study.The LI-2method differed from the LI-1method in its ability to evaluate weak activated pixels.TheAJNR:22,May 2001990NAGATA F IG 4.A and B,The regression line of subjects 5(A )and 10(B ).Circles indicate the left ROI;squares,the right ROI.The underlined fixed values indicate the regression coefficient of the regression line for each ROI (regression analysis,R ;correlation coefficient).F IG 5.Scatter plot shows gap between LI-1and LI-2(regression analysis,r 2ϭ.244,P Ͻ.01,n ϭ28).F IG 6.Scatter plot for LI-1versus LI-2for subjects 12through 17.LI-1method could not evaluate the weak activated pixels.The functional MR imaging technique has been used to localize the centers of primary func-tions,such as motor,sensory,and visual functions.For localizing such a functional center,it is nec-essary to set the threshold (z score)at a high value to exclude secondarily activated areas.It is,how-ever,not appropriate to set too high a threshold,because many true and weak activated pixels might be missed.We suspected that weak activated pixels played an important role in language function.LI-2was calculated on the basis of both weak and strong activated pixels (ie,on the concave curves).To our knowledge,the LI-2method thus met all three criteria for a useful medical examination.ConclusionIn evaluating the lateralization of linguistic func-tion,we found that a comparison of the number ofactivated pixels at only one threshold was not a correct method,since the correlation between the two hemispheres regarding the number of activated pixels at one threshold did not always represent the correlation at another threshold.Therefore,we es-tablished a more suitable method by fitting the con-cave curve from the scatter diagrams into a func-tion to allow more robust and detailed information.In this study,(1/z score)4was found to be the op-timal function with the highest correlation coeffi-cient.We did not create a theoretical foundation for selecting (1/z score)4as the function;therefore,it might be possible that another function exists that would fit the concave curve better than (1/z score)4.At the least,we strongly believe that a comparisonAJNR:22,May2001LINGUISTIC FUNCTION LATERALIZATION991of the concave curves between the two hemispheres is a more accurate,sound,and reliable method than a comparison of the 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