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The impact of Lego® Therapy on cognitive skills in Autism Spectrum Disorders: a brief discussion

  • Received: 19 March 2023 Revised: 14 June 2023 Accepted: 18 June 2023 Published: 30 June 2023
  • Over the years, several interventions have been implemented, including Lego® Therapy, with the aim of supporting and implementing social and communication skills impairments in Autism Spectrum Disorders (ASD). Although recent studies have shown that the ability to learn implicitly is preserved in ASDs, no study related to Lego® Therapy has analyzed whether and how this training can also affect aspects not directly treated. In this study, we report a first attempt of assessment of Lego® Therapy's effect on the specific area of cognitive skills in an ASD child. Over a period of 12 months, a child with ASD had weekly meetings with an expert operator of Lego® aiming to improve the child's ability to communicate, reduce impulsiveness and hyper verbalism, and encourage pro-social behavior. The intervention resulted in positive outcomes that were assessed after 12 months.

    Citation: Nicoletta Vegni, Caterina D'Ardia, Gloria Di Filippo, Francesco Maria Melchiori. The impact of Lego® Therapy on cognitive skills in Autism Spectrum Disorders: a brief discussion[J]. AIMS Neuroscience, 2023, 10(2): 190-199. doi: 10.3934/Neuroscience.2023016

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  • Over the years, several interventions have been implemented, including Lego® Therapy, with the aim of supporting and implementing social and communication skills impairments in Autism Spectrum Disorders (ASD). Although recent studies have shown that the ability to learn implicitly is preserved in ASDs, no study related to Lego® Therapy has analyzed whether and how this training can also affect aspects not directly treated. In this study, we report a first attempt of assessment of Lego® Therapy's effect on the specific area of cognitive skills in an ASD child. Over a period of 12 months, a child with ASD had weekly meetings with an expert operator of Lego® aiming to improve the child's ability to communicate, reduce impulsiveness and hyper verbalism, and encourage pro-social behavior. The intervention resulted in positive outcomes that were assessed after 12 months.



    Nonlinear equations arise always in electroanalytical chemistry with complex and esoteric nonlinear terms[1,2], though there are some advanced analytical methods to deal with nonlinear problems, for examples, the Gamma function method[3], Fourier spectral method[4], the reproducing kernel method[5], the perturbation method[6], the homotopy perturbation method[7,8], He's frequency formulation[9,10,11] and the dimensional method[12], chemists are always eager to have a simple one step method for nonlinear equations. This paper introduces an ancient Chinese algorithm called as the Ying Buzu algorithm[13] to solve nonlinear differential equations.

    We first introduce the Taylor series method[14]. Considering the nonlinear differential equation:

    d2udx2+F(u)=0. (0.1)

    The boundary conditions are

    dudx(a)=α, (0.2)
    u(b)=β. (0.3)

    If u(a) is known, we can use an infinite Taylor series to express the exact solution[14]. We assume that

    u(a)=c. (0.4)

    From (0.1), we have

    u(a)=F(u(a))=F(c),
    u(a)=F(c)uu(a)=αF(c)u.

    Other higher order derivatives can be obtained with ease, and its Taylor series solution is

    u(x)=u(a)+(xa)u(a)+12!(xa)2u(a)+13!(xa)3u(a)+...+1N!(xa)Nu(N)(a),

    the constant c can be determined by the boundary condition of (0.3).

    The Ying Buzu algorithm[15,16] was used to solve differential equations in 2006[13], it was further developed to He's frequency formulation for nonlinear oscillators[13,17,18,19,20,21,22,23] and Chun-Hui He's algorithm for numerical simulation[24].

    As c in (0.4) is unknown, according to the Ying Buzu algorithm[13,15,16], we can assume two initial guesses:

    u1(a)=c1,u2(a)=c2. (0.5)

    where c1 and c2 are given approximate values.

    Using the initial conditions given in (0.2) and (0.5), we can obtain the terminal values:

    u(b,c1)=β1,u(b,c2)=β2.

    According to the Ying Buzu algorithm[6,7,8,9,10,11,12], the initial guess can be updated as

    u(a)est=c3=c1(ββ2)c2(ββ1)(ββ2)(ββ1),

    and its terminal value can be calculated as

    u(b,c3)=β3.

    For a given small threshold, ε, |ββ3|ε, we obtain u(a)=c3 as an approximate solution.

    Here, we take Michaelis Menten dynamics as an example to solve the equation. Michaelis Menten reaction diffusion equation is considered as follows[25,26]:

    d2udx2u1+u=0. (0.6)

    The boundary conditions of it are as follows:

    dudx(0)=0,u(1)=1. (0.7)

    We assume

    u(0)=c.

    From (0.6), we have

    u(0)=c1+c,
    u(0)=0, (0.8)
    u(4)=c(1+c)3.

    The 2nd order Taylor series solution is

    u(x)=u(0)+u(0)1!x+u(0)2!x2=c+c2(1+c)x2.

    In view of the boundary condition of (0.7), we have

    u(1)=c+c2(1+c)=1, (0.9)

    solving c from (0.9) results in

    c=0.7808.

    So we obtain the following approximate solution

    u(x)=0.7808+0.2192x2.

    Similarly the fourth order Taylor series solution is

    u(x)=c+c2!(1+c)x2+c4!(1+c)3x4.

    Incorporating the boundary condition, u(1)=1, we have

    c+c2!(1+c)+c4!(1+c)3=1. (0.10)

    We use the Ying Buzu algorithm to solve c, and write (0.10) in the form

    R(c)=c+c2(1+c)+c24(1+c)31.

    Assume the two initial solutions are

    c1=0.8,c2=0.5.

    We obtain the following residuals

    R1(0.8)=0.0279,R2(0.5)=0.3271.

    By the Ying Buzu algorithm, c can be calculated as

    c=R2c1R1c2R2R1=0.0279×0.5+0.3271×0.80.0279+0.3271=0.7764.

    The exact solution of (0.10) is

    c=0.7758.

    The 4th order Taylor series solution is

    u(x)=0.7758+0.2192x2+0.0057x4.

    Figure 1 shows the Taylor series solutions, which approximately meet the requirement of the boundary condition at x=1.

    Figure 1.  Taylor series solution.

    Now we use the Ying Buzu algorithm by choosing two initial guesses

    u1(0)=0.5,u2(0)=1,

    which lead to u1=0.6726 and u2=1.2550, respectively, see Figure 2 (a) and (b).

    Figure 2.  The shooting processes with different initial guesses.

    It is obvious that the terminal value at x=1 deviates from u(1)=1 for each guess, according to the Ying Buzu algorithm, the initial guess can be updated as

    u3(0)=0.5×(11.2550)1×(10.6726)(11.2550)(10.6726)=0.7810. (0.11)

    The shooting process using (0.11) results in

    u3(1)=1.0058,

    which deviates the exact value of u(1)=1 with a relative error of 0.5%, see Figure 3.

    Figure 3.  The shooting processes with an updated initial guess of u(0)=0.7810..

    We can continue the iteration process to obtain a higher accuracy by using two following two guesses u1(0)=0.5, u3(0)=0.7810:

    u4(0)=0.5×(11.0058)0.7810×(10.6726)(11.0058)(10.6726)=0.7761.

    Using this updated initial value, the shooting process leads to the result

    u(1)=1.0001,

    so the approximate u(0)=0.7761 has only a relative error of 0.01%.

    The above solution process couples the numerical method, and the ancient method can also be solved independently.

    We assume that solution is

    u(x)=c+(1c)x2. (0.12)

    Equation (0.12) meets all boundary conditions.

    The residual equation is

    R(x)=d2udx2u1+u.

    It is easy to find that

    R(0)=2(1c)c1+c.

    We choose two guesses:

    c1=0.5,c2=1.

    We obtain the following residuals

    R1(0)=2(10.5)0.51+0.5=23,
    R2(0)=2(11)11+1=12.

    The Ying Buzu algorithm leads to the updated result:

    c=c2R1(0)c1R2(0)R1(0)R2(0)=23×1+12×0.523+12=0.7857.

    The relative error is 1.2%, and the process can continue if a higher accuracy is still needed.

    The ancient Chinese algorithm provides a simple and straightforward tool to two-point boundary value problems arising in chemistry, and it can be used for fast insight into the solution property of a complex problem.

    The authors declare that they have no conflicts of interest to this work.



    Conflict of interest



    The authors declare no conflict of interest.

    Author contributions



    Conceptualization, N, V. and C.D.; data curation, G.D.F. and F.M.M.; formal analysis, G.D.F. and F.M.M.; writing—original draft, N.V.; writing—review & editing, N.V. and F.M.M. All authors have read and agreed to the published version of the manuscript.

    [1] (2013) American Psychiatric AssociationDiagnostic and Statistical Manual of Mental Disorders (Fifth Edition). American Psychiatric Association. https://doi.org/10.1176/appi.books.9780890425596
    [2] Pollard NL (1998) Development of Social Interaction Skills in Preschool Children with Autism: A Review of the Literature. Child Fam Behav Ther 20: 1-16. https://doi.org/10.1300/J019v20n02_01
    [3] Scheeren AM, Koot HM, Begeer S (2012) Social Interaction Style of Children and Adolescents with High-Functioning Autism Spectrum Disorder. J Autism Dev Disord 42: 2046-2055. https://doi.org/10.1007/s10803-012-1451-x
    [4] Dean M, Kasari C, Shih W, et al. (2014) The peer relationships of girls with ASD at school: Comparison to boys and girls with and without ASD. J Child Psychol Psyc 55: 1218-1225. https://doi.org/10.1111/jcpp.12242
    [5] Clark BG, Magill-Evans JE, Koning CJ (2015) Youth With Autism Spectrum Disorders: Self- and Proxy-Reported Quality of Life and Adaptive Functioning. Focus Autism Dev Dis 30: 57-64. https://doi.org/10.1177/1088357614522289
    [6] Peterson CC, Garnett M, Kelly A, et al. (2009) Everyday social and conversation applications of theory-of-mind understanding by children with autism-spectrum disorders or typical development. Eur Child Adoles Psy 18: 105-115. https://doi.org/10.1007/s00787-008-0711-y
    [7] Shaw DS, Owens EB, Vondra JI, et al. (1996) Early risk factors and pathways in the development of early disruptive behavior problems. Dev Psychopathol 8: 679-699. https://doi.org/10.1017/S0954579400007367
    [8] McConnell SR (2002) Interventions to Facilitate Social Interaction for Young Children with Autism: Review of Available Research and Recommendations for Educational Intervention and Future Research. J Autism Dev Disord 32: 351-372. https://doi.org/10.1023/A:1020537805154
    [9] Peterson C (2014) Theory of mind understanding and empathic behavior in children with autism spectrum disorders. Int J Dev Neurosci 39: 16-21. https://doi.org/10.1016/j.ijdevneu.2014.05.002
    [10] Kimhi Y (2014) Theory of Mind Abilities and Deficits in Autism Spectrum Disorders. Top Lang Disord 34: 329-343. https://doi.org/10.1097/TLD.0000000000000033
    [11] Andreou M, Skrimpa V (2020) Theory of Mind Deficits and Neurophysiological Operations in Autism Spectrum Disorders: A Review. Brain Sci 10: 393. https://doi.org/10.3390/brainsci10060393
    [12] Vegni N, D'Ardia C, Torregiani G (2021) Empathy, Mentalization, and Theory of Mind in Borderline Personality Disorder: Possible Overlap With Autism Spectrum Disorders. Front Psychol 12: 626353. https://doi.org/10.3389/fpsyg.2021.626353
    [13] Vanegas SB, Davidson D (2015) Investigating distinct and related contributions of Weak Central Coherence, Executive Dysfunction, and Systemizing theories to the cognitive profiles of children with Autism Spectrum Disorders and typically developing children. Res Autism Spect Dis 11: 77-92. https://doi.org/10.1016/j.rasd.2014.12.005
    [14] Pellicano E, Maybery M, Durkin K, et al. (2006) Multiple cognitive capabilities/deficits in children with an autism spectrum disorder: “Weak” central coherence and its relationship to theory of mind and executive control. Dev Psychopathol 18. https://doi.org/10.1017/S0954579406060056
    [15] Demetriou EA, Lampit A, Quintana DS, et al. (2018) Autism spectrum disorders: A meta-analysis of executive function. Mol Psychiatr 23: 1198-1204. https://doi.org/10.1038/mp.2017.75
    [16] Demetriou EA, DeMayo MM, Guastella AJ (2019) Executive Function in Autism Spectrum Disorder: History, Theoretical Models, Empirical Findings, and Potential as an Endophenotype. Front Psychiatry 10: 753. https://doi.org/10.3389/fpsyt.2019.00753
    [17] Happé F, Vital P (2009) What aspects of autism predispose to talent?. Philos T R Soc B 364: 1369-1375. https://doi.org/10.1098/rstb.2008.0332
    [18] Happé F, Frith U (2010) Autism and talent. Oxford University Press.
    [19] Baron-Cohen S, Ashwin E, Ashwin C, et al. (2009) Talent in autism: Hyper-systemizing, hyper-attention to detail and sensory hypersensitivity. Philos T R Soc B 364: 1377-1383. https://doi.org/10.1098/rstb.2008.0337
    [20] Grandin T (2009) How does visual thinking work in the mind of a person with autism? A personal account. Philos T R Soc B 364: 1437-1442. https://doi.org/10.1098/rstb.2008.0297
    [21] Legoff DB, Gomez De La Cuesta G, Krauss GW, et al. (2014). LEGO-Based Therapy: How to build social competence through Lego-Based Clubs for children with autism and related conditions. Jessica Kingsley Publishers
    [22] Lindsay S, Hounsell KG, Cassiani C (2017) A scoping review of the role of LEGO ® therapy for improving inclusion and social skills among children and youth with autism. Disabil Health J 10: 173-182. https://doi.org/10.1016/j.dhjo.2016.10.010
    [23] Attwood T (2008) The complete guide to Asperger's syndrome. Jessica Kingsley Publishers.
    [24] McGee GG, Feldman RS, Morrier MJ (1997) Benchmarks of Social Treatment for Children with Autism. J Autism Dev Disord 27: 353-364. https://doi.org/10.1023/A:1025849220209
    [25] Ozonoff S, Cathcart K (1998) Effectiveness of a Home Program Intervention for Young Children with Autism. J Autism Dev Disord 28: 25-32. https://doi.org/10.1023/A:1026006818310
    [26] Legoff DB (2004) Use of LEGO© as a Therapeutic Medium for Improving Social Competence. J Autism Dev Disord 34: 557-571. https://doi.org/10.1007/s10803-004-2550-0
    [27] Legoff DB, Sherman M (2006) Long-term outcome of social skills intervention based on interactive LEGO© play. Autism 10: 317-329. https://doi.org/10.1177/1362361306064403
    [28] Owen-DeSchryver JS, Carr EG, Cale SI, et al. (2008) Promoting Social Interactions Between Students With Autism Spectrum Disorders and Their Peers in Inclusive School Settings. Focus Autism Dev Dis 23: 15-28. https://doi.org/10.1177/1088357608314370
    [29] Seger CA (1994) Implicit learning. Psychol Bull 115: 163-196. https://doi.org/10.1037/0033-2909.115.2.163
    [30] Narzisi A, Sesso G, Berloffa S, et al. (2021) Could You Give Me the Blue Brick? LEGO®-Based Therapy as a Social Development Program for Children with Autism Spectrum Disorder: A Systematic Review. Brain Sci 11: 702. https://doi.org/10.3390/brainsci11060702
    [31] McGeorge P, Crawford JR, Kelly SW (1997) The relationships between psychometric intelligence and learning in an explicit and an implicit task. J Exp Psychol Learn 23: 239-245. https://doi.org/10.1037/0278-7393.23.1.239
    [32] Foti F, De Crescenzo F, Vivanti G, et al. (2015) Implicit learning in individuals with autism spectrum disorders: A meta-analysis. Psychol Med 45: 897-910. https://doi.org/10.1017/S0033291714001950
    [33] Orsini A, Picone L (2006) WISC-3.: Contributo alla taratura italiana. Firenze Press.
    [34] Fancello GS, Vio C, Cianchetti C TOL. Torre di Londra. Test di valutazione delle funzioni esecutive (pianificazione e problem solving). Con CD-ROM. Edizioni Erickson (2006).
    [35] Ferri R, Orsini A, Rea M Adaptive Behavior Assessment System-: contributo alla taratura italiana (1-18 anni). In Adaptive Behavior Assessment System-Second Edition: Contributo alla taratura italiana (1-18 anni) (pp. 1-153). Giunti OS (2014).
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