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NEUROIMAGE ARTICLE NO.
Visualizing Cortical Activation during Mental Calculation with Functional MRI LINDA RUECKERT,* NICHOLAS LANGE,† ARNAUD PARTIOT,* ILDEBRANDO APPOLLONIO,‡ IRENE LITVAN,§ DENIS LE BIHAN,¶ AND JORDAN GRAFMAN*,1 *Cognitive Neuroscience Section, MNB, NINDS, †Biometry Branch, NINDS, and §Neuroepidemiology Branch, NINDS; ¶Diagnostic Radiology Department, National Institutes of Health, Bethesda, Maryland 20892-1440; and ‡Ospedale San Gerardo, Monza, Italy Received September 5, 1995
Henschen (1920) localized acalculia to the left angular gyrus, as did Krapf (1937). However, Hecaen and his collaborators proposed that lesions in different cortical areas could result in different types of acalculia; left hemisphere lesions may lead to alexia and agraphia for numbers, and right hemisphere lesions may lead to spatial dyscalculia. Anarithmetia, an inability to carry out calculations correctly, was believed to follow bilateral lesions (Hecaen et al., 1961). On the other hand, Kahn and Whitaker (1991), after reviewing the literature, determined that lesions in numerous different brain regions could result in calculation disturbances and that calculation cannot be localized to a particular area. There are many possible explanations for these discrepant results, including different definitions of ‘‘calculation,’’ and individual differences in strategies used. The performance of arithmetic is obviously a complex task, involving several subcomponents (Ashcraft, 1992; McCloskey et al., 1985). These subcomponents may be controled by a distributed network, and damage to any component could result in some form of acalculia. To date, there have been only two reports of attempts to map the cortical areas involved in calculation in normal subjects. Roland and Friberg (1985) utilized intracarotid Xenon injection while normal subjects performed a subtraction task and found activation of the angular gyrus, with slightly greater activation on the left. They also found activity in the prefrontal cortex that did not seem to be specific to calculation (i.e., that region was also activated by recitation of a jingle and by a route-finding task). Recent advances in magnetic resonance imaging (MRI) technology allow high-resolution visualization of cortical activation by utilizing the magnetic properties of deoxyhemoglobin as an endogenous contrast medium (Ogawa et al., 1992; Thulborn et al., 1982; Turner et al., 1991). The noninvasive nature of this method allows hundreds of images to be obtained from an individual subject, making it especially useful for identifying individual differences in patterns of activation that are
Cortical activation during arithmetic calculation (silent subtraction by sevens) was compared to that observed during a control condition for which subjects were required to count forward by ones. Nine normal subjects underwent 1.5-T functional magnetic resonance imaging while performing these tasks. All subjects showed bilateral premotor, posterior parietal, and prefrontal cortex activation during serial calculation. There was a large degree of individual variation in activation outside of these areas. These results confirm the role of posterior parietal cortex in arithmetic calculation and implicate other regions, including prefrontal cortex. r 1996 Academic Press, Inc.
Localization of cortical areas involved in the performance of high-level cognitive tasks has been one of the most difficult challenges facing cognitive neuroscientists. Recent advances in neuroimaging have helped in mapping out the often elaborate distributed neural networks activated during the performance of complex tasks, particularly language (e.g., Frith et al., 1991; Petersen et al., 1989; Wise et al., 1991). However, the cortical basis of other higher level processes, such as arithmetic calculation, has remained largely unstudied. The investigation of impaired numerical calculation, or ‘‘acalculia,’’ in brain-damaged patients has a long history (for reviews, see Grafman, 1988; Grewel, 1969; Kahn and Whitaker, 1991; Spiers, 1987). While most authors now agree that acalculia does exist as a relatively ‘‘pure’’ syndrome, there is still much debate over the cortical regions involved. Many authors have stressed the predominance of left hemisphere lesions in calculation disturbance. Grafman et al. (1982) reported that the greatest deficits in calculation ability occurred after left posterior lesions. In one of the earliest studies,
1 To whom correspondence and reprint requests should be addressed.
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1053-8119/96 $18.00 Copyright r 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
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likely to be found in complex tasks for which there is more than one possible way to solve a problem. Recent studies have examined patterns of cortical activation during performance of complex cognitive functions, such as language (Binder et al., 1993; Hinke et al., 1993; McCarthy et al., 1993; Rueckert et al., 1994), face recognition (Clark et al., 1995; Puce et al., 1995; Sabbah et al., 1995), and mental rotation (Cohen et al., 1995). In a preliminary study, Burbaud and his colleagues (1995) reported activation of the prefrontal cortex during performance of an arithmetic task. This activation was greater in the left than in the right hemisphere in rightbut not left-handers. However, the methods used in the Burbaud et al. study did not allow them to view cortical areas outside the frontal cortex. In the study reported here, fMRI was used to localize cortical regions involved in arithmetic calculation. To obtain a more complete picture of the cortical areas involved, images were obtained that covered most of the cerebral cortex. METHODS Subjects Nine males and three females, aged 22 to 36, participated as subjects and signed a consent form approved by the NINDS institutional review board. All subjects wrote with their right hands and completed a handedness questionnaire (Oldfield, 1971). The mean handedness quotient was 91 (SD 5 9.91) on a scale where 100 indicates complete right-handedness and -100 indicates complete left handedness. Apparatus Scanning was carried out using a 1.5-T Signa scanner (General Electric, Milwaukee, WI) fitted with a home-built z-gradient coil. A gradient-echo version of the echo-planar sequence was used that allows 64 3 64-pixel single-slice images to be produced in 40 ms (Stehling et al., 1991). The field of view was 20 cm, repetition time (TR) was 3 s, flip angle was 90°, and time to echo (TE) was 40 ms. A 5-in.-diameter surface coil, used to receive the NMR signal, was placed on the left or on the right side of each subject’s head so as to allow visualization of most of the cerebral cortex, with the exception of the occipital lobe. Four sagittal slices were collected in each 3-s interval, with collection of the four slices evenly distributed in time. Each slice was 7 mm thick, with a gap of 3 mm between slices. Left and right hemisphere slices were obtained in separate sets and were located the same distance from midline, usually centered at about 40 mm. The location of the slices was chosen to cover the angular gyrus as determined from T1-weighted coronal localizing images and with the help of a three-dimensional reference atlas (Duvernoy, 1991).
Procedure Each data set involved four alternating 30-s periods of control and calculation conditions, followed by a final 12-s period of the control condition. For the calculation condition, subjects were given a three-digit integer and asked to count backward by sevens. A different threedigit integer was given at the beginning of each 30-s period. For the control condition, subjects counted forward by ones, starting with one. Subjects were signaled to start counting or calculating by an auditory cue (the word ‘‘count’’ or a three-digit number). A comparison between the active and the control conditions should reflect cortical areas specifically involved in numerical calculation. To avoid head movement artifacts, subjects were asked to perform both tasks covertly, without actually speaking, and their heads were immobilized by foam cushions. They were asked to keep their eyes closed at all times. Each subject performed the entire procedure twice while in the magnet. The second replication followed directly after the first while the subject remained stationary. We used these replications in an attempt to locate brain regions that were activated consistently during the stimulus condition. To obtain a measure of how fast they were calculating, subjects were asked to report the final number reached in the last subtraction condition immediately after each set. In addition, each subject was asked to perform two sets of the calculation condition before going into the magnet and after coming out. This gave them a chance to practice subtracting and served as an index of each subjects’ arithmetic proficiency and practice effects. After coming out of the magnet, they were also asked to fill out a questionnaire on which they rated, on a scale from 1 to 5, the extent to which they employed a verbal or visual strategy while calculating. They were also encouraged to report any other strategy they might have used. Data exclusions and preprocessing. Initial data sets for each of the 12 subjects consisted of spatial time series of 44 images for four sagittal slices on both hemispheres. On-screen animation showed head motion artifacts in the data for 3 of the male subjects; these individuals were excluded from the analysis. There was no evidence of movement artifact, either within or between data sets, for the remaining 9 subjects. Images of the outermost slice in both hemispheres for all remaining subjects were discarded because preliminary analysis showed very little activity there. The size of these outer slices was very small, accounting for about one-eighth of the total data. In addition, the first three images of each remaining data set were discarded to protect against possible magnetic instabilities. To locate regions that were activated consistently during mental calculation, the first replication of the
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task was used to limit the regions analyzed in the second replication. Voxels were excluded from further consideration in the second replication if their temporal variability on the first replication fell below 10 on a scale of 0 to 150, for all subjects. This arbitrary yet objective exclusion criterion strengthens our analysis by focusing on time series for those voxels that show intensity changes both the first and the second time each subject performed the task. Image analysis. Linear effects were removed through simple detrending by ordinary least squares. Normalized cross-covariance maps were calculated (Friston et al., 1994; see Lange, 1996, for a detailed description). These maps used estimates of spatial and temporal smoothness derived from the time series themselves to protect against type I error. Temporal autocorrelation reduced the effective degrees of freedom to nearly one-half the nominal value (from 39 to between 19 and 21 in most cases). The normalized cross-covariance method also accounts for the temporal delay and dispersion of neuronal activation due to effects of the unobservable hemodynamic response. Hemodynamic response was modeled as a Poisson function with delay and dispersion parameters estimated from the data that ranged between 7 and 8 s, agreeing with the results of others (Bandettini et al., 1992; Friston et al., 1994; Friston et al., 1994). To ensure a global intrasubject type I error rate of less than 0.05, only voxels possessing time series with normalized cross-covariance above 4.8 were said to indicate cortical sites of significant activation (Adler, 1981; Friston et al., 1994; Hasofer, 1978; Poline and Mazoyer, 1993; Worsley et al., 1992). Maps of these active sites were superimposed on corresponding highresolution MRI scans obtained with a spoiled-GRASS sequence (TR 5 100 ms, TE 5 minimum, flip angle 5 70). This sequence was chosen to allow the visualization of larger blood vessels and would therefore let us determine whether the observed signal changes could be due to arteries or draining veins, rather than capillaries. Anatomical localization of activated regions was achieved with the aid of a threedimensional reference atlas (Duvernoy, 1991). RESULTS Normalized cross-covariance maps from two subjects are shown in Figs. 1 and 2. Figure 3 shows the percentage change in signal intensity over the course of the task for a region in the left angular gyrus of the brain depicted in Fig. 1. The percentage of signal change was 3%, on average. The numbers of subjects showing significant activation in various brain regions are given in Table 1. All showed activation in left prefrontal cortex, left posterior parietal cortex (angular and/or supramarginal
gyri), and bilateral motor/premotor cortex. Other areas showed individual variation, with some subjects showing activation in right prefrontal, bilateral posterior parietal cortex, left temporal lobe, bilateral primary somatosensory cortex, or the insula. All subjects also showed significant signal change along the Sylvian fissure of both hemispheres. However, inspection of the high-resolution images suggested that this latter signal change occurred only in the vicinity of large vessels, particularly the branches of the middle cerebral artery (see Fig. 2), indicating that it may not be indicative of the actual location of cortical areas involved in calculation. Although there was no significant difference between the left and the right hemispheres in the number of significant voxels (Wilcoxon signed-rank test, P . .4), three subjects showed a substantial asymmetry, with twice as many significant voxels in the left hemisphere. There was a significant correlation between asymmetry in the number of voxels activated ((left 2 right)/ (left 1 right)) and strength of handedness, indicating that strongly right-handed subjects showed relatively greater left hemisphere activation (Spearman’s r 5 .76, P , .02). All subjects reported using both verbal and visual strategies to some extent. The ‘‘verbalization’’ mean was 4.14 (SD 5 1.07), on a scale from 1 to 5 (1 5 no verbal strategy), and the ‘‘visualization’’ mean was 3.28 (SD 5 1.35). However, neither the overall number of voxels activated nor asymmetry correlated with their reported tendency to verbalize or visualize or with performance during the practice task. DISCUSSION Our results support those from lesion studies suggesting an important role for the posterior parietal area in arithmetic calculation (Grafman, 1988; Henschen, 1920). However, our data do not support a differential role for the angular gyrus, as had been suggested by Henschen (1920); the supramarginal gyrus was just as likely to show significant activation. Furthermore, neither the supramarginal nor the angular gyrus was activated in all nine subjects, although all nine did show activation in one or the other. Activation was not confined to the posterior parietal area in any subject, suggesting that calculation involves the coordinated effort of several different cortical areas. This is not surprising, given the complex nature of the calculation process. For example, McCloskey and his colleagues (1985) have proposed a model of arithmetic calculation that includes a numeral comprehension mechanism that serves to form an abstract internal representation of an arithmetic problem. The actual calculation involves separate mechanisms for the retrieval of arithmetic facts and the performance of calculation procedures. Evidence for the separation of
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FIG. 1. Cross-covariance maps, superimposed on high-resolution scans, for slices centered 35.5 mm left (left) and 35.5 mm right (right) of midline for subject PY. Red regions are those showing a significant cross-covariance with the paradigm. FIG. 2. Cross-covariance maps for slices centered 40.5 mm left and 40.5 mm right of midline for subject AP.
these two modules comes from reports of braindamaged patients who show deficits in either fact retrieval or the performance of calculation procedures, but not both (McCloskey et al., 1991; Warrington, 1987). Finally, numeral production mechanisms are responsible for translating the abstract representation of the result of the numerical calculation into a written or spoken output. Although not specifically stated, it is likely that these different mechanisms are performed by different parts of the brain. The mental subtraction task used in the present study probably loaded heavily on the retrieval of arithmetic facts and on calculation performance. These two procedures may be localized to the posterior parietal area, although we have no way of differentiating between cortical regions that may be specific to one or the other. The premotor and motor cortex activation found in all subjects suggests that this task may also call upon output mechanisms to some degree, despite the fact that subjects were specifically asked not to move their
mouths while calculating. This is consistent with other fMRI studies reporting activation of motor areas when subjects are thinking about tasks that would involve motor cortex if performed overtly (Hinke et al., 1993; Rueckert et al., 1994). However, this result must be interpreted with caution, since no electromyographic recordings were obtained to rule out possible subtle movement. Under an alternative model, proposed by Campbell and Clark (1988), calculation takes place through the interaction of numerous different types of numerical ‘‘codes’’ (i.e., a verbal code, a visuospatial code, etc.), rather than in one modular abstract representation. They believe that different people may utilize these various codes to different extents. Our data also fit with this model, in that we found a great deal of individual variation in some of the activated regions and in the asymmetry of activation (see below). All subjects showed some degree of prefrontal activation. Although the frontal lobes have not typically been
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FIG. 3. Solid line: percentage change in signal intensity for a pixel located in the left angular gyrus of the subject depicted in Fig. 1 (see arrow in Fig. 1). Broken line: data used for the normalized cross-covariance, corrected for temporal delay and dispersion.
implicated in acalculia, brain imaging studies in normal subjects have reported prefrontal activation (Burbaud et al., 1995; Roland and Friberg, 1985). Prefrontal cortex has been shown to be involved in working memory (Cohen et al., 1994; Goldman-Rakic, 1988). The prefrontal activation during this task may be due to the involvement of working memory required to maintain the continuing sequence of subtraction events. This is supported by Roland and Friberg’s report that similar prefrontal activation occurred during performance of cognitive tasks other than arithmetic. Because fMRI allows the detection of individual differences, we were also able to detect activation in the TABLE 1 Number of Subjects Showing Significant Activation in Specific Cortical Regions Region
Left hemisphere
Right hemisphere
Prefrontal cortex Motor/premotor cortex Postcentral gyrus (somatosensory) Supramarginal gyrus Angular gyrus Parallel sulcus Insula Superior temporal gyrus Middle temporal gyrus Inferior temporal gyrus
9 9 6 7 6 3 5 2 3 2
7 9 7 7 6 0 5 2 0 0
Note. N 5 9.
temporal lobe and insula of some subjects. These individual differences in normal subjects may help to explain the widely varying results in the localization of calculation reported in the lesion literature (Grafman, 1988; Grewel, 1969; Henschen, 1920; Kahn and Whitaker, 1991; Spiers, 1987). Although we did not find a statistically significant asymmetry, there was a tendency toward greater left hemisphere activation. This asymmetry was especially pronounced for three of the nine subjects, suggesting that there is a great deal of individual variation in asymmetry for arithmetic. A key to the mechanism behind this individual variation may lie in the significant correlation between cortical asymmetry and strength of handedness, with relatively more activated left hemisphere voxels in strongly right-handed subjects. This result is concordant with the results of a preliminary report of greater lateralization of frontal activation in right than left-handers for arithmetic calculation (Burbaud et al., 1995). One potential problem with the interpretation of fMRI data is the possible contribution of signal changes from large vessels (either feeding arteries or draining veins) that could reflect neuronal activity that is actually occurring several millimeters away (Weiskoff et al., 1994; for a review of this problem see Appollonio et al., in press). In fact, when the activation maps were overlaid on high-resolution images showing the larger vessels, some activation, particularly that along the Sylvian fissure, was located on top of these vessels. However, the activation detected in the prefrontal and posterior parietal cortex did not occur in the location of any large vessels. Furthermore, the location of this activation is consistent with the previously cited studies that have implicated these regions in calculation, using methods that are not subject to this problem. Nevertheless, any interpretation of the precise localization of activated regions must be made with caution. These results show that fMRI is a viable technique for detecting cortical activation during performance of complex computational tasks, such as calculation. The high spatial resolution of fMRI and its ability to detect subtle individual differences in activated regions may lead to a better understanding of the distributed neuronal networks involved in these high-level cognitive tasks. The potential benefits of neuroimaging technology for understanding calculation are only beginning to be tapped. Future studies should be aimed at mapping patterns of cortical activation onto cognitive models of arithmetic calculation. ACKNOWLEDGMENTS Dr. Appollonio was supported by a grant from the Italian National Research Council and by the generous sponsorship of the Lions Club
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‘‘Milan Al Cenacolo Vinciano’’—Italy. We thank two anonymous reviewers for their helpful comments on an earlier version of the manuscript.
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