Brain development of a school-aged boy with autism spectrum condition talented in arithmetic: a case report

Abstract Whereas autism spectrum condition is known for its social and communicative challenges, some autistic children demonstrate unusual islets of abilities including those related to mathematics, the neurobiological underpinnings of which are increasingly becoming the focus of research. Here we describe an 8-year-old autistic boy with intellectual and language challenges, yet exceptional arithmetic ability. He can perform verbal-based multiplication of three- and even four-digit numbers within 20 seconds. To gain insights into the neural basis of his talent, we investigated the gray matter in the child's brain in comparison to typical development, applying voxel-based morphometry to magnetic resonance imaging data. The case exhibited reduced gray matter volume in regions associated with arithmetic, which may suggest an accelerated development of brain regions with arithmetic compared to typically developing individuals: potentially a key factor contributing to his exceptional talent. Taken together, this case report describes an example of the neurodiversity of autism. Our research provides valuable insights into the potential neural basis of exceptional arithmetic abilities in individuals with the autism spectrum and its potential contribution to depicting the diversity and complexity of autism.


Introduction
Autism spectrum condition (ASC) encompasses a group of neur ode v elopmental conditions c har acterized by c hallenges in social interaction and communication, as well as the presence of repetitive behaviors or a narrow range of interests (American Psychiatric Association, 2013 ).Individuals with ASC typically demonstr ate div erse intellectual and langua ge de v elopment, leading to significant variations in cognitive profiles (Munson et al., 2008 ).Ho w e v er, they also possess a unique way of processing information.This unique processing style is not always indicative of disability and can e v en manifest as ar eas of exceptional talent (Baron-Cohen & Lombardo, 2022 ).Although robust epidemiological data are lacking, a few studies suggest that some individuals with ASC demonstrate exceptional abilities in specific domains, often in domains such as music, visuospatial skills, art, and arithmetic.These abilities can be notably superior to their other skills and may e v en be considered absolute strengths compared to their peers (Miller, 1999 ;Mottron et al., 2006 ;Baron-Cohen & Lombardo, 2022 ).
Numer ous theories hav e been pr oposed to explain the exceptional abilities observed in individuals with ASC, including Weak Centr al Coher ence, Enhanced P er ceptual Functioning, and hypersystematizing theories (Happé & Frith, 2006 ;Baron-Cohen et al., 2009 ;Mottron et al., 2009 ).These theories concentrate on the hyperattention to detail and hypersensitivity to sensory stimuli in ASC.Proponents of the hyper-systematizing theory have demonstrated the significance of the lateral frontoparietal regions and sensory and perceptual systems in the unique cognitiv e pr ocesses observed in ASC, suggesting a potential neural mechanism for the talent observed in ASC (Baron-Cohen & Lombardo, 2022 ).Brain imaging studies revealed that arithmetic engages a large network of interconnected brain regions including the dorsolateral prefr ontal cortex, v entr olater al pr efr ontal cortex, posterior parietal, occipito-temporal, anterior cingulate, and hippocampal areas (Peters & De Smedt, 2018 ).Voxel-based morphometry (VBM) is a neur oima ging tec hnique for anal yzing r egional differ ences in br ain tissue volume and density (Ashburner & Friston, 2000 ).VBM investigations hav e r e ported significant positi ve associations between gray matter in the left intraparietal sulcus and right hippocampus and arithmetic abilities in typically developing children (Li et al., 2013 ;Price et al., 2016 ).Conv ersel y, structur al ima ging inv estigations conducted on c hildr en with arithmetic difficulties have shown a reduction in gray matter within critical regions of the arithmetic network, including the inferior frontal gyrus, posterior parietal cortex, parahippocampal gyrus, and occipito-temporal cortex (Rotzer et al., 2008 ;Rykhlevskaia et al., 2009 ;Han et al., 2013 ;  Ranpura et al., 2013 ).These findings provide preliminary insights into the possible complex relationship between arithmetic ability and brain structure.
In this report, we presented a case of a sc hool-a ged boy with ASC who exhibited extraordinary arithmetic ability.We obtained structur al ma gnetic r esonance ima ging (MRI) scans of the case and conducted an extensive battery of behavioral assessments.We performed a gray matter analysis based on VBM to investigate the features of the arithmetic-related brain regions in the case and whether these featur es differ ed fr om those of typicall y de v eloping contr ols (TDCs).We hypothesized that the arithmeticr elated br ain r egions in the case ma y ha v e distinct structur al c haracteristics from those of TDCs, and that these structural differences may be the source of his extraordinary arithmetic ability.

Referr al informa tion
The case was focused on a boy of 8 years and 11 months of age, diagnosed with ASC, who sho w ed remarkable arithmetic skills.He has been diagnosed with hearing impairment in his right ear, speech delay, attention deficit and hyperactivity disorder, and mental retardation (detailed information is provided in Table 1 ).According to his parents, he demonstrated remarkable arithmetic skills in first grade.He could perform calculations involving twodigit addition, subtr action, m ultiplication, and division within seconds, and he could complete multiplication calculations with three-and four-digit numbers in 20 seconds .Furthermore , he demonstrated a heightened sensitivity to time and distance; he could provide the current time based on the position of the Sun within a 2-minute margin of error, and he could estimate the distance tr av eled.

Assessment of symptoms of ASC
To assess a compr ehensiv e e v aluation of autism symptoms in the case, we used the following standardized measures: the Autism Dia gnostic Intervie w-Re vised (ADI-R), Autism Dia gnostic Observ ation Schedule, Second Edition (ADOS-2), Autism Behavior Checklist (ABC), Social Responsiveness Scale, and Repetitive Behavior Scale .T he ADI-R is a semi-structur ed dia gnostic intervie w that is typicall y administer ed to a car egiv er or par ent of an individual suspected of having autism (Rutter et al., 2003 ).The ADI-R results for the case exceeded the clinical cutoff for autism in all four diagnostic categories: social interaction issues (total score = 17, cutoff = 10), communication and language skills (total score = 13, cutoff = 8), re petiti ve and obsessi ve behaviors (total score = 5, cutoff = 3), and abnormality of de v elopment e vident at or befor e 36 months (total score = 4, cutoff = 1) ( Supplementary Table 1 ).The ADOS-2 is a semi-structured assessment administered by trained clinicians to e v aluate cor e symptoms of ASC (Lord et al., 2012 ;Kamp-Becker et al., 2018 ).The case achieved a score of 11 on the ADOS-2 (autism spectrum cutoff = 8, autism cutoff = 9), which corresponds to a diagnosis of autism ( Supplementary Table 2 ).The ABC is a standardized assessment that uses the observer's rating of a child's behavior to c har acteristics commonl y associated with ASC (Volkmar et al., 1988 ;Rellini et al., 2004 ).The total score on the five scales of the ABC is emplo y ed to assess the probability of autism.The case r eceiv ed a total score of 47 (autism threshold = 68, questionable autism score = 53) ( Supplementary Table 3 ).The Social Responsiveness Scale is utilized pr edominantl y to identify and quantify social impairments associated with ASC, with scores ranging from 0 to 195 (Constantino et al., 2003 ).The case r eceiv ed a total scor e of 105 ( Supplementary Table 3 ).The Re petiti ve Behavior Scale is a 44-item self-report questionnaire with six subscales that ca ptur es the scope of restricted and repetitive behavior in ASC (Bodfish et al., 1999 ).The case r eceiv ed a total score of 21 ( Supplementary Table 3 ).The Individualized Psychoeducational Assessment for Children with Autism Spectrum Disorders , T hird Edition, is an assessment tool used to e v aluate v arious skills, including rece pti ve and expressi ve language skills, communication abilities, and social interaction skills in children suspected of having ASC (Schopler et al., 2005 ).The results sho w ed that the case's de v elopmental a ge la gged behind the r eal a ge in all aspects ( Supplementary Table 4 ).In summary, the case exhibited significant autism symptoms across various standardized measures.

Assessment of intelligence quotient
The Wechsler Intelligence Scale for Children, Fourth Edition, is a widely used intelligence test for assessing the intellectual abilities of c hildr en.The case obtained a full intelligence quotient score of 54, indicating a mental deficiency ( Supplementary Table 5 ).Raven's Matrices is a nonv erbal gr oup test emplo y ed to e v aluate abstr act r easoning ability and non-v erbal pr oblem-solving skills (Ra ven, 2003 ).T he case received a score of 50, indicating a mental deficienc y.The P eabody Picture Vocabulary Test is a standar dized assessment that gauges an individual's r eceptiv e vocabulary skills through the recognition and comprehension of spoken w or ds, often used as an indicator of verbal intelligence quotient.The case obtained a standard score of 58.His percentile rank of 30 indicated that he scored ≥30% compared to examinees of his age.His test-a ge equiv alent was 4:4, and his performance in rece pti ve vocabulary comprehension fell within the extr emel y low range.In summary, the case exhibited mental retardation based on the intelligence quotient measures mentioned previously.

Assessment of arithmetic ability
The Arithmetic Test for Primary 1, was r e vised fr om the Woodcock-Johnson IV Tests of Achievement to assess the arithmetic ability of the case (Wendling, 2014 ).This test consists of: (i) 22 two-digit addition and subtraction problems, eight multiplication problems with single-digit numbers, and four division problems with two-digit numbers divided by one-digit numbers; and (ii) math concept questions: 16 two-digit applied addition and subtr action pr oblems, four form ula pr oblems that c hange the addition formula into the multiplication formula, and four computation problems that change the multiplication formula into the addition formula (all with single-digit numbers).The case completed the test in 8 minutes and 12 seconds (time limit of 30 minutes).His percentile rank in the top 5% indicated that he scored ≥95% of examinees of his age, attaining the talented le v el.The r esults are based on a normative sample of 1569 individuals.Notably, his abilities extended beyond the simple computational problems on the test, as he pr oficientl y solv ed e v en thr ee-digit m ultiplication pr oblems.Consequentl y, we r andoml y gener ated (i) 10 m ultiplication problems with two digits by two digits and (ii) 10 multiplication problems with three digits by three digits to evaluate his computational proficiency with more challenging problems.He completed the exam in 5 minutes with 100% accuracy on the first section and 80% on the second.These results indicated that his arithmetic abilities far surpass those of his peers.

Gr ay ma tter volume anal ysis
We conducted structural MRI scans using a 3 Tesla GE MRI scanner.The control group consisted of 110 typically developing individuals, including 17 males of the same age as the case (as shown in Table 2 ).The r esearc h pr otocol for the discovery cohort was granted ethical approval by the University of Electronic Science and Technology of China's Research Ethics Committee .T he T1-weighted images were performed using the Computation Anatomy Toolbox (CAT 12, https://neuro-jena.github.io/ cat12-help/ ) and Statistical P ar ameter Ma pping v.12 toolbox (SPM12, https:// www.fil.ion.ucl.ac.uk/ spm/ software/ spm12/ ) for VBM analysis.VBM is a neuroimaging analysis technique that entails segmentation, normalization, and smoothing stages to obtain the gray matter volume (GMV) of the brain (Ashburner & Friston, 2000 ).Gaussian process regression (GPR) is a probabilistic machine learning technique that models the relationship betw een tw o v ariables as a r ange of possible functions, allowing it to make predictions with uncertainty estimates (Deringer et al., 2021 ).We emplo y ed GPR to model the de v elopmental tr ajectory of GMV across the age range of 3 to 12 years, using data from 110 TDCs.Age and sex were treated as independent variables, while GMV served as the dependent variable.We optimized the GPR model by adjusting the parameters to minimize the negative log marginal likelihood.Subsequently, the trained model was used to predict GMV for ages ranging from 3 to 12 years, and the de v elopmental tr ajectories of arithmetic-r elated br ain r egions were visualized through plotting.The brain regions involved include the dorsolater al pr efr ontal cortex, v entr olater al pr efr ontal cortex, inferior frontal gyrus, anterior cingulate gyrus, hippocampus , parahippocampal gyrus , temporo-parietal cortex, and v entr al occipito-tempor al cortex.Additionall y, based on the Automated Anatomical Labeling Atlas, we computed deviation scores for each br ain r egion for the case in comparison to TDCs (Tzourio-Mazo y er et al., 2002 ).These scores were derived from the relative deviation of the case's GMV from the developmental trajectories of gray matter in typically developing children.A negative deviation score r epr esents the case has a lo w er GMV in that br ain r egion than TDCs.As shown in Fig. 1 , the case exhibited reduced GMV in the bilater al dorsolater al pr efr ontal cortex, left v entr olater al pr efr ontal cortex, left inferior frontal gyrus, bilateral temporo-parietal cortex, and bilateral ventral occipito-temporal cortex.Taking into account the effect of the de v elopment of brain and whole-brain GMV, we calculated the GMV percentage in the aforementioned br ain r egions.Figur e 1 depicts the GMV percenta ges of br ain r egions in the case and a ge-matc hed contr ol individuals .T he GMV percentages of the case were lower than those of controls in the left inferior frontal gyrus, bilateral temporo-parietal cortex, and left v entr al occipito-tempor al cortex.On the contr ary, the GMV percentage in the left parahippocampal gyrus of the case was higher.

Discussion
This report describes an autistic child who demonstrated exceptional talent in arithmetic.The case was diagnosed with ASC accompanied by intellectual and language disorders .Gra y matter analysis indicated a reduction in GMV in distinct regions within the pr e viousl y mentioned arithmetic network of the case, deviating from the typical gray matter developmental trajectories observed in TDCs .T he GMV percentages in the left inferior frontal gyrus, bilater al tempor o-parietal cortex, and left v entr olater al pr efr ontal cortex wer e lo w er in the case compared to TDCs of the same a ge, wher eas the GMV percenta ge of his left parahippocampal gyrus was higher.These findings indicate distinctions in arithmetic network structure between the case and typically de v eloping individuals, whic h may be associated with the case's exceptional arithmetic abilities.
A volumetric study in c hildr en with dyscalculia r e v ealed a r eduction in GMV in the parahippocampal gyrus, whereas the case demonstrated the opposite (Ranpura et al., 2013 ).Studies of typical de v elopment hav e shown that the cortical GMV under goes c hange swiftly during the initial years of life, r eac hing its peaks during earl y c hildhood, and then decr eases with unique r egional tr ajectories (Narvacan et al., 2017 ).Specifically, an extensive array of regions spanning the entir e br ain hav e commonl y demonstr ated inv erted U-sha ped de v elopmental tr ajectories or a decline in GMV in the fr ontal, tempor al, and parietal cortices during late childhood and adolescence (Mills et al., 2014 ).Ov er all, the r eduction in GMV indicates the completion of a de v elopmental pr ocess.It seems possible that the reduction in GMV in the subject was because these brain regions were developing more rapidly than in typicall y de v eloping individuals.We hypothesized that the reduced GMV in the case may be the result of a unique pattern of brain de v elopment in which his brain underwent a form of hyperde v elopment, which does not exactly imply functional impairment but might instead be related to his exceptional arithmetic abilities.Lo w er v olumes do not necessarily equate to poorer functioning, and regions with lo w er v olumes may reflect enhanced efficienc y in functioning or adaptations and r esilience, whic h could be particularl y a ppar ent in arithmetic skills (Mills et al., 2014 ).Ho w e v er, additional r esearc h is needed to confirm these hypotheses.
Ov er all, we conducted a multifaceted and detailed behavioral assessment of the case and performed an MRI-based analysis of his br ain de v elopment, contributing pr eliminary hypotheses that provide a detailed example within the study of such extraordinary c hildr en.Ho w e v er, additional r esearc h is r equir ed to substantiate our hypothesis.We intend to conduct further investigations to support our findings, and we plan to longitudinally track this case over an extended period to gain a more comprehensive understanding.Future studies could employ larger sample sizes and mor e m ultifaceted neur oima ging methods to delv e deeper into the complexities of brain development in individuals with ASC and how the unique c har acteristics of br ain de v elopment in these individuals influence their cognitive abilities and talents.

Conclusion
In summary, this case report highlights the unique situation of a child with ASC who possesses exceptional arithmetic abilities.While displaying typical ASC symptoms, the child's arithmetic pro w ess has sparked interest in the brain's structural aspects.His GMV in the arithmetic network deviates from typically developing individuals.While there may be a link between this neural deviation and his talent, further research is necessary.In conclusion, the case emphasizes the diversity and complexity of ASC.While individuals with ASC may experience challenges in social and communication domains, differences in neurodevelop-ment may lead to a different way of processing information and learning, which may not necessarily result in impairment but may be an example of "neur odiv ersity" and lead to talent.Ne vertheless, br ain de v elopment should follow established patterns, and a better understanding of br ain de v elopment in ASC would also have important implications for educational and behavioral pr ogr ams.

Figure 1 :
Figure 1: GMV comparision between the case and TDCs.( A )-( H ). The gray matter de v elopmental tr ajectories of arithmetic-r elated br ain r egions (top) and comparison of GMV percentages (below).The gray matter de v elopmental tr ajectories wer e ma pped fr om GMV of 110 TDCs using the GPR.GMV per centages w ere calculated using data from 17 males of comparable age, with error bars indicating a standard deviation of ±1. ( I ) Deviation scores br ain ma p.The de viation scor es wer e calculated based on the r elativ e de viation of the GMV of the case fr om the gr ay matter de v elopmental trajectories .T he regions framed by the black lines correspond to brain regions associated with arithmetic.The color bar indicates the deviation scores.

Table 1 :
Clinical: symptoms and de v elopment by age.

Table 2 :
Demogr a phic: information of contr ol gr oup.