Brain Organization Underlying Superior Mathematical Abilities in Children with Autism

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      Brain Organization Underlying Superior Mathematical
 5    Abilities in Children with Autism
      Teresa Iuculano, Miriam Rosenberg-Lee, Kaustubh Supekar, Charles J. Lynch, Amirah Khouzam,
 8    Jennifer Phillips, Lucina Q. Uddin, and Vinod Menon
10    Background: Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social and communication deﬁcits.
11    While such deﬁcits have been the focus of most research, recent evidence suggests that individuals with ASD may exhibit cognitive
12    strengths in domains such as mathematics.
14    Methods: Cognitive assessments and functional brain imaging were used to investigate mathematical abilities in 18 children with ASD
15    and 18 age-, gender-, and IQ-matched typically developing (TD) children. Multivariate classiﬁcation and regression analyses were used to
16    investigate whether brain activity patterns during numerical problem solving were signiﬁcantly different between the groups and
17    predictive of individual mathematical abilities.
19    Results: Children with ASD showed better numerical problem solving abilities and relied on sophisticated decomposition strategies for
24    TD children.
26    Conclusions: Our study suggests that superior mathematical information processing in children with ASD is characterized by a unique
28    Our ﬁndings of enhanced cognitive and neural resources for mathematics have critical implications for educational, professional, and
29    social outcomes for individuals with this lifelong disorder.
31                                                                                demonstrated a larger discrepancy between IQ and mathematical
32    Key Words: Autism, brain organization, cognitive strengths,                 abilities compared with other abilities such as reading (8).
      mathematical abilities, multivariate pattern analysis, support                  A seminal theoretical account proposes that systematic,           64
      vector machine                                                              logical, and analogical thinking are enhanced in individuals with     65
                                                                                  ASD (3), suggesting that “hyper-systemizing” may be an adaptive       66
                                                                                  mechanism to reduce environmental variance into a series of           67

              utism spectrum disorder (ASD), a neurodevelopmental dis-            regular sets with repeatable rules. Mathematics represents the        68
              order with an estimated prevalence rate greater than 1%             most concrete instantiation of such abilities, as it is built upon    69
              (1), is characterized by a complex phenotype that includes          systematic axiomatic procedures. Mathematical skills are essential    70
      social, communicative, and sensorimotor processing deﬁcits (2).             for educational and professional success and are also crucial         71
      Despite the clinical focus on cognitive deﬁcits, it has been noted          in everyday life (9). Thus, mathematics represents an ideal           72
      that the “altered developmental trajectory that deﬁnes ASD can              domain to experimentally measure potential cognitive strengths        73
      also lead to remarkable cognitive strengths” (3) and that children          in ASD.                                                               74
      with ASD might present “islets of ability” in various domains (4).              Here, we provide the ﬁrst simultaneous cognitive and neural       75
      One domain in which individuals with ASD often demonstrate                  characterization of mathematical abilities in children with ASD       76
      exceptional abilities is mathematics. Evidence for greater proﬁ-            compared with typically developing (TD) children. We predicted        77
      ciency in mathematics in ASD has been mostly anecdotal (5) and              that compared with TD children, children with ASD would show          78
      descriptive (6). It has been shown that scientists score higher than        better mathematical abilities, as measured by standardized            79
      nonscientists on self-administered questionnaires for “autism               neuropsychological assessments. We further hypothesized that          80
      associated traits” (6) and there is a “three- to seven-fold increase        compared with TD children, children with ASD would show               81
      for autism spectrum condition among mathematicians” (7).                    different patterns of brain responses during arithmetic problem       82
      Furthermore, a recent study in 14- to 16-year-olds with ASD                 solving, with greater reliance on posterior brain areas (10,11). We   83
                                                                                  further hypothesized that neural processes subserving mathe-          84
                                                                                  matical skills in children with ASD might rely on cortical areas      85
      From the Departments of Psychiatry and Behavioral Sciences (TI, MR-L, KS,                                                                         86
55       CJL, AK, JP, LQU, VM) and Neurology and Neurological Sciences (VM)
                                                                                  typically devoted to other cognitive abilities.
56       and Program in Neuroscience (VM), Stanford University, Stanford,                                                                               88
57       California; and Institute of Cognitive Neuroscience (TI), University     Methods and Materials                                                 89
58       College London, London, United Kingdom.                                                                                                        90
59    Address correspondence to Teresa Iuculano, Ph.D., Stanford University,      Participants
60       Department of Psychiatry, School of Medicine, Stanford Cognitive and        We studied eighteen 7- to 12-year-old children with ASD
61       Systems Neuroscience Lab, 401 Quarry Rd, Stanford, CA 94305; E-mail:     (14 male subjects; mean age = 9.60; SD = 1.64) and eighteen TD
62                                                   children (14 male subjects; mean age = 9.59, SD = 1.53). All
63    Received Oct 12, 2012; revised Jun 4, 2013; accepted Jun 16, 2013.          children in the ASD group were verbal and within an IQ range

      0006-3223/$36.00                                                                                           BIOL PSYCHIATRY 2013;]:]]]–]]]                                                      & 2013 Society of Biological Psychiatry
        2 BIOL PSYCHIATRY 2013;]:]]]–]]]                                                                                               T. Iuculano et al.

 95                         Table 1. Demographic, IQ, and Diagnostic Measures                                                                               158
 96                                                                                                                                                         159
                            Measure                         ASD (n ¼18)                TD (n ¼18)             t Test        p Value
 97                                                                                                                                                         160
 98                         Male to Female Ratio                 14:4                       14:4                                                            161
 99                         Age (Years)                    9.60, SD ¼ 1.64            9.59, SD ¼ 1.53           .016          .988                          162
100                         IQ–WASI Scale                                                                                                                   163
101                           Full IQ                    113.27, SD ¼ 15.25        113.27, SD ¼ 15.5          À.022           .983                          164
102                           Verbal IQ                  112.00, SD ¼ 19.32        112.72, SD ¼ 16.64         À.139           .891                          165
103                           Performance IQ             112.05, SD ¼ 17.88        111.22, SD ¼ 16.65          .145           .886                          166
104                         ADI-R                                                                                                                           167
105                           Social                      19.00, SD ¼ 6.66                                                                                  168
106                           Communication               15.33, SD ¼ 6.03                                                                                  169
107                           Repetitive behavior          5.94, SD ¼ 2.80                                                                                  170
108                         ADOSa                                                                                                                           171
109                           Social                       8.24, SD ¼ 1.86                                                                                  172
110                           Communication                3.41, SD ¼ 1.46                                                                                  173
111                           Algorithm                   11.65, SD ¼ 3.10                                                                                  174
112                            Demographic and mean IQ scores are shown for the ASD and TD groups. Mean ADI-R and ADOS scores are                           175
113                         shown for the ASD group only. Note: df ¼ 1,34 for all analyses.                                                                 176
114                            ADI-R, Autism Diagnostic Interview-Revised; ADOS, Autism Diagnostic Observation Schedule; ASD, autism                        177
                            spectrum disorder; TD, typically developing; WASI, Wechsler Abbreviated Scale of Intelligence.
115                            a
                                 Missing score from one participant.
116                                                                                                                                                         179
117                                                                                                                                                         180
118     considered to be high-functioning. Children with ASD received a           strategy assessment due to time constraints. For each child, we           181
119     diagnosis based on scores from the Autism Diagnostic Interview-           computed the proportion of correctly answered problems solved             182
120     Revised (12,13) and/or the Autism Diagnostic Observation Sched-           by retrieval, counting, or decomposition strategies.                      183
121T1   ule (14) (Table 1). Children with ASD were screened through a                                                                                       184
122     parental phone interview and excluded if they had any history of          Functional Brain Imaging                                                  185
123     known genetic, psychiatric, or neurological disorders (e.g., fragile          Experimental Design. The fMRI experiment consisted of two             186
124     X syndrome or Tourette syndrome) or were currently being                  arithmetic conditions, complex addition and simple addition, and          187
125     prescribed antipsychotic medications. The TD cohort was selected          two nonarithmetic conditions, number identiﬁcation and passive            188
126     from a larger sample of children, based on matching of the                ﬁxation/rest. In the complex addition task, participants were             189
127     following parameters: age, full-scale IQ, and gender (Table 1).           presented with an equation involving two addends and asked                190
128         Parental consent and child assent forms were obtained for             to indicate, via a button box, whether the answer shown was               191
129     each child. All protocols were approved by the human partici-             correct or incorrect (e.g., 3     4 = 8). One operand ranged from         192
130     pants Institutional Review Board at the Stanford University School        2 to 9 and the other operand ranged from 2 to 5 (tie problems,            193
131     of Medicine. All participants were volunteers and were treated in         such as 5 5 = 10, were excluded), and answers were correct in             194
132     accordance with the American Psychological Association’s Ethical          50% of the trials. Incorrect answers deviated by 1 or 2 from              195
133     Principles of Psychologists and Code of Conduct.                          the correct sum. The simple addition task was identical except            196
134                                                                               that one of the addends was always 1 (e.g., 3         1 = 4). In the      197
135     Neuropsychological and Strategy Assessments                               number identiﬁcation task, arithmetic symbols were replaced by            198
136         Before the functional magnetic resonance imaging (fMRI) scan,         alternative keyboard symbols (e.g., 4 o 5 @ 7) and participants           199
137     each child participated in a neuropsychological assessment                were asked to assess if the number 5 was among the presented              200
138     session consisting of the Wechsler Abbreviated Scale of Intelli-          digits. Finally, in the passive ﬁxation task, the symbol * appeared       201
139     gence (15), Wechsler Individual Achievement Test-Second Edition           at the center of the screen and participants were asked to focus          202
140     (WIAT-II) for mathematics (16), and the Working Memory Test               their attention to it. To aid children’s performance, speciﬁc task        203
141     Battery for Children (17). On the day of the fMRI session, children       instructions appeared below each problem. During the complex              204
142     performed a strategy assessment consisting of single-digit addi-          and simple addition tasks, the word “Solve” was presented below           205
143     tion problems (e.g., 5       6 ¼ ?) (18–21). The problems were            the problem. In the number identiﬁcation task, the word Find              206
144     presented one at a time on a computer screen. There were 18               appeared on the screen, and during the passive ﬁxation/rest trials,       207
145     problems that used random pairs of integers from 2 to 9 and               the word Look appeared on the screen.                                     208
146     sums ranging from 6 to 17. Children were given explicit examples             Stimuli were presented in a block fMRI design to optimize              209
147     of strategy use: just knew it (i.e., retrieval), counted on my ﬁngers,    signal detection. In each task, stimuli were displayed for 5 seconds      210
148     counted in my head (i.e., counting), and broke down the problem,          with an intertrial interval of 500 milliseconds. There were 18 trials     211
149     such as 9 5 = 9 (1           4) = (9       1)     4 = 10 4 = 14 (i.e.,    of each task condition, broken up into four blocks of 4 or 5 trials;      212
150     decomposition). Subsequently, children were instructed to say             thus, each block lasted either 22 or 27.5 seconds. The order of the       213
151     the answer out loud as soon as they had it in their head. The             blocks was randomized across participants with the following              214
152     experimenter then probed the child on which strategy was used             constraints: in every set of four blocks, all conditions were             215
153     during problem solving. Responses were categorized as retrieval,          presented and the complex and simple addition task blocks were            216
154     counting, and decomposition. Trials where the experimenter                always separated by either a Find or a passive ﬁxation/rest block.        217
155     noted overt signs of counting even when the child reported                All orders of arithmetic and nonarithmetic task conditions were           218
156     retrieval were classiﬁed as counting and not retrieval or decom-          equally likely. The total length of the experiment was 6 minutes          219
157     position. Six children (three in each group) did not complete the         and 36 seconds.                                                           220
       T. Iuculano et al.                                                                                BIOL PSYCHIATRY 2013;]:]]]–]]] 3

221       The present study focused on group differences in arithmetic        a height threshold of p         .001, with family-wise error (FWE)             284
222    complexity by contrasting behavioral and brain responses to the        correction for multiple spatial comparisons at p     .01, computed             285
223    complex and simple addition tasks. Behavioral research in adults       using Monte Carlo simulations (see Supplement 1 for details).                  286
224    suggests that the simple N        1 addition trials are solved by                                                                                     287
225    incremental counting (22) and performance on this task is              Multivariate Analyses                                                          288
226    characterized by higher accuracy and faster reaction times com-           Multivariate Pattern Analysis. The primary goal of this                     289
227    pared with complex addition problems (23,24). Moreover, because        analysis was to examine group differences in multivariate activa-              290
228    stimuli in the simple task have the same format as in the complex      tion patterns related to arithmetic problem complexity.                        291
229    task, it provides a high-level control for sensory and number                                                                                         292
230    processing, as well as decision making and response selection.                                                                                        293
231        fMRI Data Acquisition. Functional brain images were acquired                                                                                      294
  Q3   on a 3T GE Signa scanner. A total of 29 axial slices (4.0 mm                                                                                          295
233    thickness, .5 mm skip) parallel to the anterior commissure-                                                                                           296
234    posterior commissure and covering the whole brain were imaged                                                                                         297
235    using a T2* weighted gradient echo spiral-in/spiral-out pulse                                                                                         298
236    sequence with the following parameters: repetition time = 2 sec,                                                                                      299
237    echo time = 30 msec, ﬂip angle = 801, 1 interleave. The ﬁeld of                                                                                       300
238    view was 20 cm, and the matrix size was 64 Â 64, providing an in-                                                                                     301
239    plane spatial resolution of 3.125 mm. To reduce blurring and                                                                                          302
240    signal loss from ﬁeld inhomogeneity, an automated high-order                                                                                          303
241    shimming method based on a spiral acquisition was used before                                                                                         304
242    the acquisition of fMRI scans (25).                                                                                                                   305
243        fMRI Data Analysis. Data were analyzed using the general                                                                                          306
244    linear model implemented in SPM8 (http://www.ﬁ                                                                                        307
245    spm/). The ﬁrst ﬁve volumes were not analyzed to allow for signal                                                                                     308
246    equilibration. Images were ﬁrst realigned to the ﬁrst scan to                                                                                         309
247    correct for motion and slice acquisition timing. Translational                                                                                        310
248    movement in millimeters (x, y, z) was calculated based on the                                                                                         311
249    SPM8 parameters for motion correction of the functional images                                                                                        312
250    in each subject. To correct for deviant volumes resulting from                                                                                        313
251    spikes in movement, we used despiking procedures similar to                                                                                           314
  Q4   those implemented in AFNI (26). Volumes with movement                                                                                                 315
253    exceeding .5 voxels (1.562 mm) or spikes in global signal                                                                                             316
254    exceeding 5% were interpolated using adjacent scans. In the                                                                                           317
255    ASD group, the majority of volumes repaired occurred in isolation.                                                                                    318
256    The same was true for the TD group. Moreover, the frequency                                                                                           319
257    distribution of adjacent repaired scans did not differ between                                                                                        320
258    groups (Fisher’s exact test p value ¼ .11). Finally, no participant                                                                                   321
259    had maximum scan-to-scan movement of 4.6 mm and no more                                                                                               322
260    than 8.5% of volumes were corrected. Crucially, movement                                                                                              323
261    parameters did not differ between the groups (Table S1 in                                                                                             324
262    Supplement 1). After the interpolation procedure, images were                                                                                         325
263    spatially normalized to standard Montreal Neurological Institute                                                                                      326
264    space, resampled to 2 mm isotropic voxels, and smoothed with a                                                                                        327
265    6-mm full-width at half maximum Gaussian kernel.                                                                                                      328
266                                                                                                                                                          329
267    Univariate Analyses                                                                                                                                   330
268        The primary goal of this analysis was to examine group                                                                                            331
269    differences in activation related to arithmetic problem complexity.                                                                                   332
270    Brain activation related to each task condition (complex addition,                                                                                    333
271    simple addition, number identiﬁcation) was ﬁrst modeled at the                                                                                        334
272    individual subject level using boxcar functions with a canonical                                                                                      335
273    hemodynamic response function and a temporal derivative to                                                                                            336
                                                                              Figure 1. Children with autism spectrum disorder (ASD) show signiﬁ-
274    account for voxel-wise latency differences in hemodynamic                                                                                             337
                                                                              cantly better mathematical abilities and sophisticated strategy use
275    response. Voxel-wise contrasts and t statistics images at the group    compared with their age-, gender-, and IQ-matched typically developing         338
276    level were then generated by contrasting complex versus simple         (TD) peers. (A) Standardized math achievement scores by group. Children        339
277    addition problems. Additional analyses were conducted using            with ASD performed better than TD children on the numerical operations         340
278    contrast images for the simple addition problems versus rest and       subtest of the Wechsler Individual Achievement Test. (B) Discrepancy           341
279    for the complex addition problems versus rest (Supplement 1).          scores between standardized math measure and full IQ scores by group.          342
                                                                              Children with ASD displayed a bigger discrepancy score than TD child-
280        Differences in brain activation between the ASD and TD groups                                                                                     343
                                                                              ren. (C) Different strategy use in ASD and TD. The groups differed
281    were compared using t tests on contrast images for complex             signiﬁcantly on the percentage of trials in which a decomposition strategy     344
282    versus simple addition problems. In both analyses, signiﬁcant          was used. Error bars indicate standard error of the mean. np      .05. n.s.,   345
283    clusters of activation were identiﬁed at the whole-brain level using   nonsigniﬁcant.                                                                 346


347     Multivariate pattern analysis (MVPA) was used to identify brain               calculated by subtracting full IQ scores from the standardized math          410
348     regions that discriminated spatial activation patterns to complex             measure of numerical operations, were higher for the ASD group               411
349     versus simple problems between children with ASD and TD                       compared with the TD group (t34 ¼ 2.293, p ¼ .028) (Figure 1B).              412
350     children (18). Additional analyses were conducted using simple                    Interestingly, compared with the TD group, the ASD group                 413
351     addition problems versus rest and complex addition problems                   showed greater use of decomposition (t28 ¼ 2.247, p ¼ .033), a               414
352     versus rest. Machine learning algorithms and cross-validation                 more sophisticated strategy for arithmetic problem solving that              415
353     procedures used in the MVPA are described in detail in                        involves transforming the original problem into two or more simpler          416
354     Supplement 1. The statistical map corresponding to group                      subproblems (24) (Figure 1C). No differences in the use of retrieval         417
355     differences in multivariate activation patterns was thresholded               or counting strategies were found between the groups (p ¼ .917               418
356     using the same height threshold in the univariate analyses (p                 and p ¼ .288, respectively). Furthermore, the two groups did not             419
357     .001), with FWE corrections at p     .01 for multiple comparisons             differ on any of the four working memory measures of the Working             420
358     computed using Monte Carlo simulations (Supplement 1).                        Memory Test Battery for Children (17) (Table S2 in Supplement 1).            421
359         Support Vector Regression Analysis. Support vector regres-                                                                                             422
360     sion (SVR) analysis (27,28) was used to assess whether brain                  Math Performance on Arithmetic Veriﬁcation Task                              423
361     activation could predict mathematical abilities in the two groups.               Behavioral performance during fMRI scanning was analyzed using            424
362     Regions of interest were deﬁned for each signiﬁcant cluster from              a two-way analysis of variance with within-subject factor problem type       425
363     the MVPA analysis. Within each region of interest, voxel values               (complex, simple) and between-subject factor group (ASD, TD). For            426
364     were used to predict the response variable of interest: perform-              accuracy, there was a main effect of problem type (F1,34 ¼ 6.41, p ¼         427
365     ance on the numerical operations subtest of the WIAT-II for each              .016), as complex addition problems were harder than simple addition         428
366     group. Details of the SVR analysis are provided in Supplement 1.              problems. There was no main effect of group (F1,34 ¼ .08, p ¼ .774)          429
367                                                                                   and no interaction (F1,34 ¼ 2.04, p ¼ .162). Reaction time also showed       430
368     Results                                                                       a main effect of problem type (F1,34 ¼ 48.15, p       .001); participants    431
369                                                                                   responded faster to simple than complex addition problems. There             432
370     Mathematical Ability and Problem Solving Strategies                           was no main effect of group (F1,34 ¼ .01, p ¼ .921) nor an interaction       433
371        Measures of math ability included two subtests of the WIAT-II              between group and problem type (F1,34 ¼ .38, p ¼ .847).                      434
372     (16) and an assessment of strategies used during arithmetic                                                                                                435
373     problem solving (18–21). Children in the ASD group scored higher              Functional Brain Imaging                                                     436
374     than TD children on the numerical operations subscale of the                     To identify the brain basis of superior mathematical abilities in         437
375     WIAT-II, which assesses basic numerical and arithmetic skills (t34 =          children with ASD, we compared fMRI activity between groups                  438
376F1   2.638, p = .012) (Figure 1A), while no group differences were found           during arithmetic problem solving. Functional magnetic reso-                 439
377     on the math reasoning subtest of the WIAT-II (t34 ¼ 1.52,                     nance imaging data were analyzed at the whole-brain level using              440
378     p ¼ .138) (Table S2 in Supplement 1). Discrepancy scores (8),                 both univariate and multivariate approaches.                                 441
379                                                                                                                                                                442
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403                                                                                                                                                                466
404                                                                                                                                                                467
405                                                                                                                                                                468
        Figure 2. Brain activity patterns during arithmetic problem solving distinguish children with autism spectrum disorder from their typically developing
406                                                                                                                                                                469
        peers. Multivariate pattern analysis revealed signiﬁcant differences in spatial activation patterns between autism spectrum disorder and typically
407     developing in the (A) ventral temporal-occipital cortex: bilateral inferior lateral occipital cortex (LOC) and fusiform gyrus; (B) parietal cortex: left   470
408     intraparietal sulcus (IPS), angular gyrus (AG), and left precuneus; and (C) medial temporal lobe: right entorhinal cortex and left hippocampus and         471
409     parahippocampal gyrus.                                                                                                                                     472

473   Table 2. Brain Areas that Showed Signiﬁcant Differences in Multivariate      cortex (VTOC), including bilateral inferior lateral occipital cortex and        536
474   Activation Patterns between ASD and TD Groups During Arithmetic              fusiform gyrus (Figure 2A; Table 2), as well as posterior parietal            537
                                                                                                                                                              F2 QT2
475   Problem Solving                                                              cortex, including the left intraparietal sulcus, angular gyrus, and the         538
476                                                                                left precuneus (Figure 2B; Table 2). Medial temporal lobe areas,                539
                                           Cluster Max        MNI Coordinates
477                                                                                including the posterior hippocampus and parahippocampal gyrus,                  540
478   Region                                Size   CA (%)      X      Y      Z     as well the entorhinal cortex in the anterior aspects of the medial             541
479                                                                                temporal lobe also showed signiﬁcant between-group differences                  542
      Ventral Temporal-Occipital Cortex
480                                                                                in multivariate activity patterns (Figure 2C; Table 2). High classi-            543
        L lateral occipital cortex           378      89      À50   À58     À4
481     R fusiform gyrus                     131      89       24   À74    À14
                                                                                   ﬁcation accuracies were also found in the left dorsolateral                     544
482     L fusiform gyrus                      59      83      À46   À72    À18     prefrontal cortex (DLPFC), the left orbital frontal cortex, the left            545
483     R lateral occipital cortex            74      86       38   À66      2     anterior cingulate cortex, and the right frontal pole, as well as the           546
484     L occipital pole                      64      86      À32   À94     À6     basal ganglia (Table 2). Additional analyses were conducted to                  547
485     R lingual gyrus                       52      86        8   À66    À10     examine whether these differences arose from brain responses to                 548
486     R occipital pole                      80      83        8   À96     À4     simple addition problems. To address this question, group differ-               549
487     R lateral occipital cortex           130      83       58   À58      4     ences in multivariate activation patterns were examined for simple              550
488   Parietal Cortex                                                              addition problems contrasted with the rest baseline. No overlap                 551
489     R superior parietal lobule            56      89       32   À38      52    was observed with ﬁndings from the arithmetic complexity-related                552
490     L precuneus                          152      86       À6   À58      32    group differences (Figure S1A in Supplement 1).                                 553
491     R supramarginal gyrus                183      86       60   À20      20        Support Vector Regression Analyses. To further investigate                  554
492     L intraparietal sulcus                57      83      À38   À60      44    neural organization for mathematical problems in children with                  555
493     L angular gyrus                       87      83      À54   À56      24    ASD, we focused on brain areas that distinguished the ASD and TD                556
494     R angular gyrus                      188      83       42   À52      20    groups and examined whether multivariate activation patterns in                 557
495     R retrosplenial cortex                59      83       10   À44      20    these areas were related to individual differences in math abilities.           558
496     R posterior cingulate cortex          45      81        2   À26      32    Speciﬁcally, we used SVR (27,29) to examine whether multivariate                559
497     R supramarginal gyrus                 48      81       66   À42      14    activity patterns in these areas could predict math abilities assessed          560
      Medial and Lateral Temporal Lobe
498                                                                                using the numerical operations subtest of the WIAT-II (16). Our                 561
        L hippocampus                        378      86      À28   À34     À2
499                                                                                analysis focused on the numerical operations subtest because                    562
        R perirhinal cortex                   66      86       24    À8    À42
500                                                                                children with ASD showed signiﬁcantly better performance on this                563
        R superior temporal gyrus             54      86       62   À18     À2
501                                                                                standardized measure of math abilities (Figure 1A), even after                  564
        L middle temporal gyrus              137      83      À64   À24    À18
502     R parahippocampal gyrus               90      83       30   À48     À4     controlling for IQ, age, gender, and working memory abilities                   565
503   Frontal Cortex                                                               (Table 1; Table S2 in Supplement 1). Our SVR analysis revealed that             566
504     L dorsomedial prefrontal cortex      278      86       À2    36     44     numerical abilities in the ASD group were predicted by the pattern              567
505     L orbitofrontal cortex                47      86      À26    34     À8     of neural activity in an area of the left VTOC encompassing the left            568
506     L dorsolateral prefrontal cortex      66      86       À4    20     60     fusiform gyrus and lateral occipital cortex (R2 ¼ .69, q ¼ .04,                 569
507     R ventromedial prefrontal cortex      82      83       10    62     À2     Cohen’s f 2 effect size ¼ 2.28, signiﬁcance of R2 was tested                    570
508     R dorsomedial prefrontal cortex       69      83       26    26     58     nonparametrically with permutation tests, as described in                       571
509     L anterior cingulate cortex           70      81       À4   À10     30     Supplement 1). These voxels show prominent overlap with VTOC                    572
510   Subcortical Areas                                                            face-processing regions identiﬁed using Bayesian meta-analysis of               573
511     L cerebellum                          59      89      À42   À72    À26     406 studies ( (30) (Figure 3A) and with                 F3   574
512     R cerebellum                          68      86       28   À60    À36     cytoarchitectonically deﬁned maps of the posterior fusiform gyrus               575
513     L brain stem                          77      83       À2   À26    À26     (31) (Figure 3B, C). In the TD group, numerical abilities were                  576
514     L putamen                             60      83      À28   À16     10     predicted by neural activity patterns in the left DLPFC (R2 ¼ .64,              577
515     L cerebellum                          45      83      À52   À52    À30     q ¼ .02, Cohen’s f 2 effect size ¼ 1.79, signiﬁcance of R2 was tested           578
516     R caudate/nucleus accumbens           45      83       12    10     À8     nonparametrically with permutation tests, as described in                       579
517     ASD, autism spectrum disorder; CA, classiﬁcation accuracy; L, left; MNI,   Supplement 1).                                                                  580
518   Montreal Neurological Institute; R, right; TD, typically developing.                                                                                         581
519                                                                                Discussion                                                                      582
520                                                                                                                                                                583
521   Univariate Analyses                                                              Building on prior descriptive (6) and anecdotal evidence (5) in             584
522       Between-group t tests showed no signiﬁcant differences in                adults, our study provides new evidence for numerical problem                   585
523   activation levels between the ASD and TD groups for complex                  solving as a domain of cognitive strength in children with ASD (8).             586
524   versus simple problems—height threshold p            .001, with FWE          Compared with a group of well-matched TD peers, children with                   587
525   correction for multiple spatial comparisons at p .01. No signiﬁcant          ASD showed signiﬁcantly better abilities on standardized measures               588
526   group differences were found on the other two contrasts: simple              of numerical problem solving. Notably, the speciﬁc group difference             589
527   addition problems versus rest and complex addition problems                  seen on the numerical operations, but not on the mathematical                   590
528   versus rest (height threshold: p    .001, extent threshold: p   .01).        reasoning, subtest points to an enhanced ability of children with               591
529                                                                                ASD to perform arithmetical computations, while their ability to                592
530   Multivariate Analyses                                                        solve word and language based problems is within the normal                     593
531       Multivariate Pattern Analysis. Multivariate pattern analysis             range. Critically, there were no differences in IQ and working                  594
532   highlighted several cortical regions where arithmetic complexity-            memory abilities between the groups, pointing to domain-speciﬁc                 595
533   related activity patterns differed signiﬁcantly between children with        strengths independent of general cognitive abilities. Furthermore,              596
534   ASD and their TD peers. Notably, high cross-validation classiﬁcation         compared with their TD peers, children with ASD showed greater                  597
535   accuracies (80% to 90%) were found in ventral temporal-occipital             reliance on sophisticated analytic strategies when solving single-digit         598


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      Figure 3. Brain regions predicting numerical problem-solving abilities in children with autism spectrum disorder (ASD) overlap with face-processing
630   regions and cytoarchitectonically deﬁned regional maps. Voxels in the left ventral temporal-occipital cortex, encompassing inferior lateral occipital cortex   693
631   (LOC) and fusiform gyrus (shown in cyan), predicted better numerical abilities (R2 ¼ .69, q ¼ .04, Cohen’s f 2 effect size ¼ 2.28) in children with ASD.       694
632   (A) Voxels predicting better numerical abilities in ASD (cyan) show prominent overlap with ventral temporal-occipital cortex face-processing regions           695
633   identiﬁed using Bayesian meta-analysis of 406 studies (blue) ( (30). (B) Voxels predicting better numerical abilities in ASD (cyan) show    696
634   prominent overlap with cytoarchitectonically deﬁned maps of the posterior fusiform gyrus, FG1 (green) and FG2 (violet) (31). (C) Maximum probability           697
      map (MPM) of the visual cortex. Other cytoarchitectonically delineated areas are abbreviated using the following nomenclature: hOc (human Occipital
635                                                                                                                                                                  698
      cortex). Ordinal numbers 1 through 4 refer to the cytoarchitectonically deﬁned visual areas moving laterally from the primary visual cortex (Brodmann area
636   17/primary visual cortex) (45). [Reproduced with permission from Caspers et al. (31)].                                                                         699
637                                                                                                                                                                  700
638                                                                                                                                                                  701
639   addition problems. The decomposition strategy involves solving                      Although no previous studies have investigated the brain basis             702
640   problems by breaking them into easier problems. Greater use of this             of math abilities in children or adults with ASD, greater engage-              703
641   analytic strategy in children with ASD might reﬂect a better ability to         ment of posterior brain areas has been posited as a general                    704
642   partition arithmetic problems into simpler ones by focusing on the              mechanism underlying the analytical brain in ASD (3,10,11).                    705
643   intrinsic details of the equation’s properties, rather than relying on          Accordingly, we hypothesized that posterior brain areas including              706
644   effortful and less efﬁcient strategies. Notably, decomposition strat-           primary sensory cortex might show heightened activation in                     707
645   egies are highly successful, even in typical development, as children           children with ASD. However, we found no evidence for differ-                   708
646   adopting these strategies tend to be at a more advanced stage of                ences in activation levels in either extra-striate cortex, visual              709
647   math skill development than their peers who rely on less sophisti-              association, or parietal cortex. Rather, we found that children with           710
648   cated strategies such as ﬁnger counting (24).                                   ASD engaged these brain areas to the same extent as TD children.               711
649       Our neuroimaging ﬁndings provide novel evidence that                        However, they showed signiﬁcantly different activation patterns                712
650   children with ASD exhibit unique patterns of brain organization                 in these (Figure 2A,B; Table 2), as well as multiple other brain               713
651   for mathematical information processing. Children with ASD                      regions (Figure 2C; Table 2).                                                  714
652   engaged similar brain areas as their TD peers, and overall levels                   Of particular interest is our ﬁnding of differential multivariate          715
653   of activation did not differ between the two groups. However,                   activation patterns between the two groups in the left VTOC. This              716
654   they showed different multivariate activation patterns in regions               region showed one of the highest classiﬁcation rates in distin-                717
655   of the prefrontal, posterior parietal, and ventral temporal-occipital           guishing between the two groups, and it was also the only brain                718
656   cortices (Figure 2; Table 2) that have been consistently implicated             area in which multivariate activation patterns predicted numerical             719
657   in numerical problem solving (20,32,33). Furthermore, our ﬁnd-                  problem solving skills in children with ASD. In contrast, multi-               720
658   ings relating standardized measures of numerical abilities with                 variate activation patterns predicted numerical problem solving                721
659   distinct multivariate activation patterns in the two groups provide             skills in TD children in the left DLPFC but not in the VTOC or any             722
660   further evidence for unique patterns of brain organization for                  other brain region. These results provide further evidence that                723
661   numerical information processing in children with ASD.                          children with ASD engage posterior brain areas differently than                724

725   their TD peers. Anatomically, VTOC encompasses multiple divi-              by grants from the Singer Foundation, the Stanford Institute for                  788
726   sions of the visual association cortex and has been linked with            Neuroscience, and the National Institutes of Health (MH084164,                    789
727   processing of various types of category-speciﬁc information such           HD047520, DC011095) to VM.                                                        790
728   as words and numbers (32,34), objects (35), and faces (36,37). The            We thank Dr. Antonio Hardan for his help in accessing the                      791
729   diversity of functional specialization in this region suggests that it     Stanford Autism Registry, Dr. Tianwen Chen for assistance with data               792
730   might be subject to high competition for cortical space (34,38),           analysis, and three anonymous reviewers for their valuable                        793
731   especially during the earlier stages of development (39). Interest-        suggestions.                                                                      794
732   ingly, voxels that predicted better numerical problem-solving                 The authors report no biomedical ﬁnancial interests or potential               795
733   ability in children with ASD showed prominent overlap with VTOC            conﬂicts of interest.                                                             796
734   face-processing regions identiﬁed using a meta-analysis of 406                                                                                               797
735   brain imaging studies (30) (Figure 3A). Furthermore, these voxels             Supplementary material cited in this article is available online at            798
736   were localized to the cytoarchitectonically deﬁned subdivisions                                   799
737   FG1 and FG2 of the fusiform gyrus (31) (Figure 3B, C). These                                                                                                 800
738   posterior VTOC regions show a high level of expertise-related               1. Autism and Developmental Disabilities Monitoring Network Surveil-             801
739   plasticity (34,40), suggesting that differences in activation pat-             lance Year 2008 Principal Investigators; Centers for Disease Control          802
740   terns could be the consequence of experience with speciﬁc types                and Prevention (2012): Prevalence of autism spectrum disorders–               803
741   of stimuli (41). Ventral temporal-occipital cortex regions, partic-            Autism and Developmental Disabilities Monitoring Network, 14 sites,           804
                                                                                     United States, 2008. MMWR Surveill Summ 61:1–19.
742   ularly the fusiform gyrus, respond preferentially to classes of                                                                                              805
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743   objects for which an individual has perceptual expertise                       pervasive developmental disorders. J Child Psychol Psychiatry 45:             806
744   (34,38,40). Intriguingly, recent studies suggest that brain activity           135–170.                                                                      807
745   in these regions can be enhanced through extensive perceptual               3. Baron-Cohen S, Belmonte MK (2005): Autism: A window onto the                  808
746   training (35). Consequently, inadequate attention to faces, a                  development of the social and the analytic brain. Annu Rev Neurosci           809
747   behavioral characteristic of ASD (42), within critical periods of              28:109–126.                                                                   810
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748   neural plasticity could promote better representations for certain                                                                                           811
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750   Critically, multivariate activation patterns in the left VTOC pre-             Yarmouth, MA: J. Curley & Associates.                                         813
751   dicted abilities on standardized tests involving basic numerical            6. Baron-Cohen S, Wheelwright S, Skinner R, Martin J, Clubley E (2001):          814
752   operations in the ASD group but not in TD children. These                      The autism-spectrum quotient (AQ): Evidence from Asperger syn-                815
753   observations suggest that enhanced attention to numbers and                    drome/high-functioning autism, males and females, scientists and              816
                                                                                     mathematicians. J Autism Dev Disord 31:5–17.
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