Child Neuropsychology A Journal on Normal and Abnormal Development in Childhood and Adolescence
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Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks Bruno Gauthier, Véronique Parent & Philippe Lageix To cite this article: Bruno Gauthier, Véronique Parent & Philippe Lageix (2014): Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks, Child Neuropsychology, DOI: 10.1080/09297049.2014.988606 To link to this article: http://dx.doi.org/10.1080/09297049.2014.988606
Published online: 11 Dec 2014.
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Child Neuropsychology, 2014 http://dx.doi.org/10.1080/09297049.2014.988606
Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks
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Bruno Gauthier1,3, Véronique Parent2, and Philippe Lageix3 1
Département de psychologie, Université de Montréal, Laval, QC, Canada Département de psychologie, Université de Sherbrooke, Longueuil, QC, Canada 3 Hôpital Rivière-des-Prairies, Montréal, QC, Canada 2
The neuropsychology of attention deficit/hyperactivity disorder (ADHD) has been extensively studied, with a general focus on global performance measures of executive function. In this study, we compared how global (i.e., endpoint) versus process (i.e., dynamic) measures of performance may help characterize children with and without ADHD using a design fluency task as a case study. The secondary goal was to compare the sensitivity of standard versus connectionist statistical models to group differences in cognitive data. Thirty-four children diagnosed with ADHD and 37 children without ADHD aged 8–11 years old were tested on the Five-Point Test. The continuous process measure of performance, indexed as the number of produced designs at each consecutive 1 minute interval during 5 minutes, was analyzed against the discrete process measure, that is, the number of designs between first and last intervals and the standard global performance measure of total number of produced designs. Results show that the continuous process measure distinguished the two groups better than the two other measures. The detailed observation of production patterns revealed a decreasing linear trajectory in children without ADHD that contrasts with the flat, but fluctuating productivity pattern of children with ADHD. With regards to the second goal, results show that the connectionist and standard methods are equally sensitive to group differences for the three types of measures. This illustrates the utility of quantitative process measures together with the connectionist method in neuropsychological research and suggests great potential for a dynamical approach to cognition. Keywords: ADHD; Process measures; Design fluency; Executive function; Connectionism; Artificial neural networks; Self-organizing maps.
Research on the neuropsychology of attention deficit/hyperactivity disorder (ADHD) has produced vast amounts of insightful data in the past decades. Studies focusing on the cognitive profiles of ADHD generally make use of global, endpoint performance variables, that is, measurements that are collected at the end of a task. Common examples of global cognitive variables include total production or omission and commission errors, global speed, mean reaction time, and verbal and spatial span (c.f., Sergeant, Geurts, & Oosterlaan, 2002; Willcutt, Doyle, Nigg, Faraone, & Pennington, 2005; Willcutt, SonugaBarke, Nigg, & Sergeant, 2008). Global measures have proved very useful in Address correspondence to Bruno Gauthier, Département de psychologie, Université de Montréal, Laval, QC, H7N 0B6, Canada. E-mail: [email protected]
© 2014 Taylor & Francis
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characterizing the heterogeneous nature of cognition in ADHD but also in highlighting recurrent deficits that have led to current mainstream dysexecutive and multipath theories of the disorder (e.g., Barkley, 1997; Sonuga-Barke, Bitsakou, & Thompson, 2010). However, global measures tend to depict cognition as a rather static construct. This may complicate linking cognition with its neural substrate, the latter being better described in dynamical terms (Port & Van Gelder, 1995). An alternative line of research suggests that process variables, that is, repetitive measurements of performance while the task is being executed, may help characterize the dynamics of cognition in children with ADHD (e.g., Metzger, 1995; Shallice et al., 2002). Process measures have been less studied than global ones but are required by some models of ADHD for supporting their claim. For example, the Cognitive-Energetic model (Sergeant, 2000) stipulates that a primary deficit in the brain’s level of arousal is responsible, at least in part, for the poor cognitive control, response organization, and executive function often observed in ADHD. To assess energetic mechanisms, researchers have used event rates or the speeds with which stimuli are presented during a task. This process measure has been shown useful in differentiating ADHD across a variety of tasks (Sergeant, Oosterlaan, & Van Der Meere, 1999; Sergeant & Scholten, 1985). Another relatively common process measure is the standard deviation of reaction time, large values of which seem to characterize the disorder (e.g., Epstein et al., 2003; Forbes, 1998; Sjöwall, Roth, Lindqvist, & Thorell, 2013; Sonuga-Barke et al., 2010). Despite the fact that response variability is characteristic but not specific to ADHD (Willcutt et al., 2008), process measures may be of great utility for characterizing variable response patterns and shedding light on the underlying neurocognitive mechanism taking place during neuropsychological testing. In this study, we further exploit process measures with a design fluency task for exploring the dynamics of cognition in children with and without ADHD. Design fluency is a nonverbal reasoning task that requires the coordination of multiple executive functions such as productivity, shifting set, self-monitoring, working memory, planning, use of strategies, and creative imagination (Delis, Kaplan, & Kramer, 2001; Lezak, 2004; Ruff, 1996). Different versions of the task exist. All involve a page divided in squares that contain arrays of dots and share the goal of producing as many different nonsymbolic designs as possible in a few minutes by connecting dots with straight lines in each square. Standard (global) measures of design fluency include a total or ratio number of produced designs and repetitive errors. In typically developing children, design fluency generally improves with age and is usually independent of gender and IQ (Albert, Opwis, & Regard, 2009; Klenberg, Korkman, & Lahti-Nuuttila, 2001; Korkman, Kemp, & Kirk, 2001; Levin et al., 1991; Regard, Strauss, & Knapp, 1982; Van Der Elst, Hurks, Wassenberg, Meijs, & Jolles, 2011), besides an effect of gender in Chinese children (Lee, Yuen, & Chan, 2002) and of IQ in the very superior zone (Arffa, 2007; Evans, Ruff, & Gualtieri, 1985). The few studies on design fluency in ADHD report no difference with typically developing children in global performance measures (Korkman et al., 2001; Loge, Staton, & Beatty, 1990) (although see Vélez-vanMeerbeke et al., 2013). No study so far has examined the time course of design fluency in children with and without ADHD. The first goal of this study was thus to compare design fluency process and global performance measures in their ability to characterize children with and without ADHD, expecting process measures to distinguish the two groups better. To test this hypothesis, we used standard group comparison methods followed by a connectionist analysis in the form of neural networks. Artificial neural networks are analytic techniques based on a
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simplification of how learning takes place in the brain. They have been used for differentiating the neuropsychological profiles of clinical syndromes (e.g., Quintana et al., 2012), as well as for revealing distinct behavioral/cognitive patterns in children with ADHD (e.g., Metzger, 1995). A secondary goal of this study was thus to explore the ability of artificial neural networks to detect significant group differences in cognitive performance in comparison with standard statistical analysis. The idea behind this goal goes further than merely proposing an alternative method for something that already works. We wished to put neural networks to use for their ability to find consistent patterns and to offer a variety of graphical methods for in-depth exploration of the data.
METHOD Seventy-one children (44 boys) aged between 8 and 11 years participated in the study. Children with ADHD—combined presentation (n = 34; 26 boys) were recruited on the waiting list of the specialized ADHD clinic in Montreal Rivière-des-Prairies hospital. ADHD diagnosis was made according to the criteria in the Diagnostic and Statistical Manual of Mental Disorders, text revision (DSM-IV-TR; APA, 2000). Each child received a biopsychosocial standardized evaluation involving three steps: (a) a behavioral assessment with questionnaires completed by parents and teachers using the Child Behavior Checklist (CBCL/6-18) and Teacher’s Report Form from the Achenbach System of Empirically Based Assessment (Achenbach & Rescorla, 2001) and the ADHD Rating Scale—fourth edition (ARS-IV; DuPaul, Power, Anastopoulos, & Reid, 1998); (b) a cognitive evaluation including design fluency as well as other attention and executive function tests, and (c) a medical examination. The control group included 37 third to fifth graders (18 boys) from two regular schools in Quebec’s Eastern townships. The procedure for the control group included the standardized behavioral and cognitive assessments already described. Children with known intellectual delay or neurological disorder were excluded from the study. In a modified version of the design fluency 5-Point Test (Regard et al., 1982), children were instructed to produce as many different designs as possible within 5 minutes. They were next presented with two acceptable designs, asked for any questions and told to start. The number of produced designs was recorded at each 1 minute interval. The process measures included continuous and discrete representations of performance. The continuous performance pattern (production pattern) was taken as the sequence of number of designs produced at each five consecutive 1-minute intervals. The discrete performance pattern (production change) was indexed as the number of designs produced in the first minus last intervals. Global performance (global production) corresponded to the total number of produced designs. To compare process and global measures, we used analysis of covariance (ANCOVA), with Age and Gender as covariables, together with the Self-OrganizingMap (SOM; Kohonen, 1995). The SOM is a cluster analysis/feature extraction technique that uses unsupervised learning methods for discovering the structure of high dimensional data. Inspired by the topographic organization found in the nervous system, the SOM maps a continuous input space onto a discrete output map, grouping together similar input data points into neighboring prototype vectors (the map units—see Figure 1) (Kohonen, 1982). The visualization and topologically preserving properties of the SOM enable indepth analysis and exploration of complex data. The simplicity of its algorithm provides
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Figure 1 Illustration of the Self-Organizing Map: a two-dimensional continuous input space is mapped onto a square array of processing units by adaptive connection weights.
an attractive method for revealing invariant patterns in the data. The SOM can also act as an “expert diagnostic system” for classification purposes. In this study, we ran four simulations, three for examining the SOM’s sensitivity to group differences given the different process and global measures, and one for in-depth exploration of the main process measure under study, that is, the production pattern. In the first three simulations, the neural maps were two output units in order to force the data into two categories. In Simulation 1, the SOM had five input units (production pattern). The two other simulations had single input values as training materials (production change; global production). To further explore the structure of the data, Simulation 4 used the same input as in Simulation 1 with a 4 x 4 (16) output unit map. During training, the connection weights were gradually adapted towards input values with a random presentation of input tokens, with decreasing learning step size and neighborhood function (for the detailed algorithm of the model, see Gauthier, Shi, & Xu, 2007). Testing implied feeding the networks with all input tokens and watching their distribution on the maps according to the units they would land on.
RESULTS AND DISCUSSION We first compared the performance of both groups relative to the process and global measures of design fluency and will now discuss these results along with those obtained using the ANCOVA and SOM methods. Concerning the two process measures, the analysis of covariance showed a significant difference between groups on production pattern, F(4, 264) = 5.011, MSE = 32.405, p < .001, η2 = .071, as well as on production change, F(1, 66) = 10.730, MSE = 182.294, p < .002, η2 = .140. Congruently, the two-unit SOM trained with the production pattern in Simulation 1 classified a reasonable amount of participants from the clinical group in one “ADHD unit” (71%) and from the control group in the other “non-ADHD unit” (76%). Training the SOM with production change in Simulation 2 yielded better results for the clinical group (82%), but a poorer classification rate for the control group (62%). Concerning global production, the ANCOVA showed no significant difference between groups, F(1, 66) = 0.664, MSE = 70.264, p = .418. This corroborates Simulation 3, where the SOM trained with global production did not develop group-specific representations, that is, children with and without ADHD being equally distributed in both map units.
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These results show distinct production pattern and change, but similar global production between the two groups, indicating superiority of process over global measures in distinguishing children with and without ADHD, as expected. This also indicates that the clinical group produced on average as many designs as the control group, congruent with previous results (Korkman et al., 2001; Loge et al., 1990), suggesting that children with ADHD may differ from children without ADHD with regards to how they accomplish the task. Concerning the covariables of age and gender, the results showed that all three measures covaried significantly with age, production pattern: F(4, 264) = 3.490, MSE = 22.568, p < .008; production change: F(1, 66) = 10.317, MSE = 175.283, p < .002; global production: F(1, 66) = 26.947, MSE = 2849.929, p = .000, but not with gender, production pattern: F(4, 264) = 0.324, MSE = 2.094, p = .862; production change: F(2, 71) = 0.934, MSE = 15.869, p = .337; global production: F(1, 66) = 1.821, MSE = 192.545, p = .182. The age effect is not surprising, given that executive functions undergo a developmentally critical period between 8 and 12 years (Anderson, 2002). It is also congruent with previous findings, just as the absence of a gender effect is (Albert et al., 2009; Klenberg et al., 2001; Korkman et al., 2001; Levin et al., 1991; Regard et al., 1982; Van Der Elst et al., 2011). With respect to our second goal, the comparison of traditional and connectionist methods showed that both performed similarly in detecting significant differences in cognitive test performance. The SOM is thus at least as sensitive as standard group comparison methods, suggesting that it can be used in neuropsychological studies for basic analyses. Once this was settled, we could further investigate the SOM’s utility for deeper exploration of the data. Figure 2a illustrates the production patterns that the two(a) 10 Number of designs
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Figure 2 (a) Design fluency production patterns of children with ADHD (dotted line) and without ADHD (solid line); map distribution of (b) children with ADHD and (c) without ADHD; (d) U-Matrix.
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unit SOM extracted from the data during Simulation 1. The trajectories are a graphic display of the adapted connection weights revealing the internal representation of the network, usually referred to as the feature maps. The trajectory developed by the nonADHD unit is initially elevated and decreases almost linearly. One reasonable explanation for such a pattern is that children without ADHD generally approach the task rapidly because of the time constraint but reduce their production as the possibilities for new designs diminish. On the opposite side, children with ADHD on average seem to borrow a nonlinear (bumpier) road to achieve their goal, their production pattern changing direction two times instead of none. This singular pattern may be interpreted in light of the triple pathway model of ADHD (Sonuga-Barke et al., 2010), more specifically as reflecting a difficulty with time-keeping abilities. A lack of motivation seems unlikely given that on average, children with ADHD performed as well as the control group. Poor inhibition does not seem explanatory either, given that on average the clinical group is characterized by slower task initiation. It remains possible, however, that productivity is modulated at a more basic level of arousal, as proposed by the Cognitive-Energetic model (Sergeant et al., 1999; Sonuga-Barke & Castellanos, 2007). The lower initiation and flatter production pattern could reflect an inability to activate the task-specific brain areas for executing design fluency, in line with the default-mode interference hypothesis of ADHD (SonugaBarke & Castellanos, 2007). Future studies are needed to explore the neural correlates of design fluency production patterns. Finally, the present study is limited by the absence of fine motor control measures, which raises the possibility that the variable production pattern generally offered by the clinical group relates to a more primary deficit at the motor control level (c.f., Schoemaker, Ketelaars, Van Zonneveld, Minderaa, & Mulder, 2005). Figure 2b and c shows the distribution of children with and without ADHD on the 4 x 4 map trained with the production patterns in Simulation 4. Larger units contain more data. The two groups overlap, but globally occupy opposite corners (ADHD: lower left). This indicates some level of variability in the production patterns but supports our previously described results, suggesting that the dynamics of cognition differ in children with ADHD. To further dig into the nature of production patterns, we used the U-Matrix, a visualization technique that can be thought of as a landscape showing how far apart subgroups of subjects (the units) are one from another, larger distance being represented by darker values (for details, see Ultsch & Siemon, 1990). The U-matrix (Figure 2d) reveals an intricate structure of clusters and subclusters in the data, which mainly draws a separation line between children with and without ADHD, indicating substantial betweengroup dissimilarity. This suggests a natural boundary between the activation patterns of children with and without ADHD rather than this cognitive feature being continuously distributed between the two groups. This could have implications with regards to the use of dimensional versus categorical measures in studies on ADHD. Finally, although we only entered the production pattern into the 4 x 4 neural net, the SOM also offers the possibility of computing as many variables as collected and observing how important factors covary together. In conclusion, the present study brings additional evidence that quantitative process measures can be useful in studying the neuropsychology of ADHD and may contribute to characterize the disorder. This study also indicates that artificial neural networks can help our understanding of ADHD and eventually of other disorders. Further research is needed
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to elaborate and fully exploit these dynamic tools as a strategy for generating hypotheses on specific brain-behavior relationship and as a window on how cognition unfolds in time. Original manuscript received August 10, 2014 Revised manuscript accepted November 12, 2014 First published online December 11, 2014
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Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks Bruno Gauthier, Véronique Parent & Philippe Lageix To cite this article: Bruno Gauthier, Véronique Parent & Philippe Lageix (2014): Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks, Child Neuropsychology, DOI: 10.1080/09297049.2014.988606 To link to this article: http://dx.doi.org/10.1080/09297049.2014.988606
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Date: 13 November 2015, At: 13:11
Child Neuropsychology, 2014 http://dx.doi.org/10.1080/09297049.2014.988606
Exploring the dynamics of design fluency in children with and without ADHD using artificial neural networks
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Bruno Gauthier1,3, Véronique Parent2, and Philippe Lageix3 1
Département de psychologie, Université de Montréal, Laval, QC, Canada Département de psychologie, Université de Sherbrooke, Longueuil, QC, Canada 3 Hôpital Rivière-des-Prairies, Montréal, QC, Canada 2
The neuropsychology of attention deficit/hyperactivity disorder (ADHD) has been extensively studied, with a general focus on global performance measures of executive function. In this study, we compared how global (i.e., endpoint) versus process (i.e., dynamic) measures of performance may help characterize children with and without ADHD using a design fluency task as a case study. The secondary goal was to compare the sensitivity of standard versus connectionist statistical models to group differences in cognitive data. Thirty-four children diagnosed with ADHD and 37 children without ADHD aged 8–11 years old were tested on the Five-Point Test. The continuous process measure of performance, indexed as the number of produced designs at each consecutive 1 minute interval during 5 minutes, was analyzed against the discrete process measure, that is, the number of designs between first and last intervals and the standard global performance measure of total number of produced designs. Results show that the continuous process measure distinguished the two groups better than the two other measures. The detailed observation of production patterns revealed a decreasing linear trajectory in children without ADHD that contrasts with the flat, but fluctuating productivity pattern of children with ADHD. With regards to the second goal, results show that the connectionist and standard methods are equally sensitive to group differences for the three types of measures. This illustrates the utility of quantitative process measures together with the connectionist method in neuropsychological research and suggests great potential for a dynamical approach to cognition. Keywords: ADHD; Process measures; Design fluency; Executive function; Connectionism; Artificial neural networks; Self-organizing maps.
Research on the neuropsychology of attention deficit/hyperactivity disorder (ADHD) has produced vast amounts of insightful data in the past decades. Studies focusing on the cognitive profiles of ADHD generally make use of global, endpoint performance variables, that is, measurements that are collected at the end of a task. Common examples of global cognitive variables include total production or omission and commission errors, global speed, mean reaction time, and verbal and spatial span (c.f., Sergeant, Geurts, & Oosterlaan, 2002; Willcutt, Doyle, Nigg, Faraone, & Pennington, 2005; Willcutt, SonugaBarke, Nigg, & Sergeant, 2008). Global measures have proved very useful in Address correspondence to Bruno Gauthier, Département de psychologie, Université de Montréal, Laval, QC, H7N 0B6, Canada. E-mail: [email protected]
© 2014 Taylor & Francis
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characterizing the heterogeneous nature of cognition in ADHD but also in highlighting recurrent deficits that have led to current mainstream dysexecutive and multipath theories of the disorder (e.g., Barkley, 1997; Sonuga-Barke, Bitsakou, & Thompson, 2010). However, global measures tend to depict cognition as a rather static construct. This may complicate linking cognition with its neural substrate, the latter being better described in dynamical terms (Port & Van Gelder, 1995). An alternative line of research suggests that process variables, that is, repetitive measurements of performance while the task is being executed, may help characterize the dynamics of cognition in children with ADHD (e.g., Metzger, 1995; Shallice et al., 2002). Process measures have been less studied than global ones but are required by some models of ADHD for supporting their claim. For example, the Cognitive-Energetic model (Sergeant, 2000) stipulates that a primary deficit in the brain’s level of arousal is responsible, at least in part, for the poor cognitive control, response organization, and executive function often observed in ADHD. To assess energetic mechanisms, researchers have used event rates or the speeds with which stimuli are presented during a task. This process measure has been shown useful in differentiating ADHD across a variety of tasks (Sergeant, Oosterlaan, & Van Der Meere, 1999; Sergeant & Scholten, 1985). Another relatively common process measure is the standard deviation of reaction time, large values of which seem to characterize the disorder (e.g., Epstein et al., 2003; Forbes, 1998; Sjöwall, Roth, Lindqvist, & Thorell, 2013; Sonuga-Barke et al., 2010). Despite the fact that response variability is characteristic but not specific to ADHD (Willcutt et al., 2008), process measures may be of great utility for characterizing variable response patterns and shedding light on the underlying neurocognitive mechanism taking place during neuropsychological testing. In this study, we further exploit process measures with a design fluency task for exploring the dynamics of cognition in children with and without ADHD. Design fluency is a nonverbal reasoning task that requires the coordination of multiple executive functions such as productivity, shifting set, self-monitoring, working memory, planning, use of strategies, and creative imagination (Delis, Kaplan, & Kramer, 2001; Lezak, 2004; Ruff, 1996). Different versions of the task exist. All involve a page divided in squares that contain arrays of dots and share the goal of producing as many different nonsymbolic designs as possible in a few minutes by connecting dots with straight lines in each square. Standard (global) measures of design fluency include a total or ratio number of produced designs and repetitive errors. In typically developing children, design fluency generally improves with age and is usually independent of gender and IQ (Albert, Opwis, & Regard, 2009; Klenberg, Korkman, & Lahti-Nuuttila, 2001; Korkman, Kemp, & Kirk, 2001; Levin et al., 1991; Regard, Strauss, & Knapp, 1982; Van Der Elst, Hurks, Wassenberg, Meijs, & Jolles, 2011), besides an effect of gender in Chinese children (Lee, Yuen, & Chan, 2002) and of IQ in the very superior zone (Arffa, 2007; Evans, Ruff, & Gualtieri, 1985). The few studies on design fluency in ADHD report no difference with typically developing children in global performance measures (Korkman et al., 2001; Loge, Staton, & Beatty, 1990) (although see Vélez-vanMeerbeke et al., 2013). No study so far has examined the time course of design fluency in children with and without ADHD. The first goal of this study was thus to compare design fluency process and global performance measures in their ability to characterize children with and without ADHD, expecting process measures to distinguish the two groups better. To test this hypothesis, we used standard group comparison methods followed by a connectionist analysis in the form of neural networks. Artificial neural networks are analytic techniques based on a
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simplification of how learning takes place in the brain. They have been used for differentiating the neuropsychological profiles of clinical syndromes (e.g., Quintana et al., 2012), as well as for revealing distinct behavioral/cognitive patterns in children with ADHD (e.g., Metzger, 1995). A secondary goal of this study was thus to explore the ability of artificial neural networks to detect significant group differences in cognitive performance in comparison with standard statistical analysis. The idea behind this goal goes further than merely proposing an alternative method for something that already works. We wished to put neural networks to use for their ability to find consistent patterns and to offer a variety of graphical methods for in-depth exploration of the data.
METHOD Seventy-one children (44 boys) aged between 8 and 11 years participated in the study. Children with ADHD—combined presentation (n = 34; 26 boys) were recruited on the waiting list of the specialized ADHD clinic in Montreal Rivière-des-Prairies hospital. ADHD diagnosis was made according to the criteria in the Diagnostic and Statistical Manual of Mental Disorders, text revision (DSM-IV-TR; APA, 2000). Each child received a biopsychosocial standardized evaluation involving three steps: (a) a behavioral assessment with questionnaires completed by parents and teachers using the Child Behavior Checklist (CBCL/6-18) and Teacher’s Report Form from the Achenbach System of Empirically Based Assessment (Achenbach & Rescorla, 2001) and the ADHD Rating Scale—fourth edition (ARS-IV; DuPaul, Power, Anastopoulos, & Reid, 1998); (b) a cognitive evaluation including design fluency as well as other attention and executive function tests, and (c) a medical examination. The control group included 37 third to fifth graders (18 boys) from two regular schools in Quebec’s Eastern townships. The procedure for the control group included the standardized behavioral and cognitive assessments already described. Children with known intellectual delay or neurological disorder were excluded from the study. In a modified version of the design fluency 5-Point Test (Regard et al., 1982), children were instructed to produce as many different designs as possible within 5 minutes. They were next presented with two acceptable designs, asked for any questions and told to start. The number of produced designs was recorded at each 1 minute interval. The process measures included continuous and discrete representations of performance. The continuous performance pattern (production pattern) was taken as the sequence of number of designs produced at each five consecutive 1-minute intervals. The discrete performance pattern (production change) was indexed as the number of designs produced in the first minus last intervals. Global performance (global production) corresponded to the total number of produced designs. To compare process and global measures, we used analysis of covariance (ANCOVA), with Age and Gender as covariables, together with the Self-OrganizingMap (SOM; Kohonen, 1995). The SOM is a cluster analysis/feature extraction technique that uses unsupervised learning methods for discovering the structure of high dimensional data. Inspired by the topographic organization found in the nervous system, the SOM maps a continuous input space onto a discrete output map, grouping together similar input data points into neighboring prototype vectors (the map units—see Figure 1) (Kohonen, 1982). The visualization and topologically preserving properties of the SOM enable indepth analysis and exploration of complex data. The simplicity of its algorithm provides
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Figure 1 Illustration of the Self-Organizing Map: a two-dimensional continuous input space is mapped onto a square array of processing units by adaptive connection weights.
an attractive method for revealing invariant patterns in the data. The SOM can also act as an “expert diagnostic system” for classification purposes. In this study, we ran four simulations, three for examining the SOM’s sensitivity to group differences given the different process and global measures, and one for in-depth exploration of the main process measure under study, that is, the production pattern. In the first three simulations, the neural maps were two output units in order to force the data into two categories. In Simulation 1, the SOM had five input units (production pattern). The two other simulations had single input values as training materials (production change; global production). To further explore the structure of the data, Simulation 4 used the same input as in Simulation 1 with a 4 x 4 (16) output unit map. During training, the connection weights were gradually adapted towards input values with a random presentation of input tokens, with decreasing learning step size and neighborhood function (for the detailed algorithm of the model, see Gauthier, Shi, & Xu, 2007). Testing implied feeding the networks with all input tokens and watching their distribution on the maps according to the units they would land on.
RESULTS AND DISCUSSION We first compared the performance of both groups relative to the process and global measures of design fluency and will now discuss these results along with those obtained using the ANCOVA and SOM methods. Concerning the two process measures, the analysis of covariance showed a significant difference between groups on production pattern, F(4, 264) = 5.011, MSE = 32.405, p < .001, η2 = .071, as well as on production change, F(1, 66) = 10.730, MSE = 182.294, p < .002, η2 = .140. Congruently, the two-unit SOM trained with the production pattern in Simulation 1 classified a reasonable amount of participants from the clinical group in one “ADHD unit” (71%) and from the control group in the other “non-ADHD unit” (76%). Training the SOM with production change in Simulation 2 yielded better results for the clinical group (82%), but a poorer classification rate for the control group (62%). Concerning global production, the ANCOVA showed no significant difference between groups, F(1, 66) = 0.664, MSE = 70.264, p = .418. This corroborates Simulation 3, where the SOM trained with global production did not develop group-specific representations, that is, children with and without ADHD being equally distributed in both map units.
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These results show distinct production pattern and change, but similar global production between the two groups, indicating superiority of process over global measures in distinguishing children with and without ADHD, as expected. This also indicates that the clinical group produced on average as many designs as the control group, congruent with previous results (Korkman et al., 2001; Loge et al., 1990), suggesting that children with ADHD may differ from children without ADHD with regards to how they accomplish the task. Concerning the covariables of age and gender, the results showed that all three measures covaried significantly with age, production pattern: F(4, 264) = 3.490, MSE = 22.568, p < .008; production change: F(1, 66) = 10.317, MSE = 175.283, p < .002; global production: F(1, 66) = 26.947, MSE = 2849.929, p = .000, but not with gender, production pattern: F(4, 264) = 0.324, MSE = 2.094, p = .862; production change: F(2, 71) = 0.934, MSE = 15.869, p = .337; global production: F(1, 66) = 1.821, MSE = 192.545, p = .182. The age effect is not surprising, given that executive functions undergo a developmentally critical period between 8 and 12 years (Anderson, 2002). It is also congruent with previous findings, just as the absence of a gender effect is (Albert et al., 2009; Klenberg et al., 2001; Korkman et al., 2001; Levin et al., 1991; Regard et al., 1982; Van Der Elst et al., 2011). With respect to our second goal, the comparison of traditional and connectionist methods showed that both performed similarly in detecting significant differences in cognitive test performance. The SOM is thus at least as sensitive as standard group comparison methods, suggesting that it can be used in neuropsychological studies for basic analyses. Once this was settled, we could further investigate the SOM’s utility for deeper exploration of the data. Figure 2a illustrates the production patterns that the two(a) 10 Number of designs
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Figure 2 (a) Design fluency production patterns of children with ADHD (dotted line) and without ADHD (solid line); map distribution of (b) children with ADHD and (c) without ADHD; (d) U-Matrix.
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unit SOM extracted from the data during Simulation 1. The trajectories are a graphic display of the adapted connection weights revealing the internal representation of the network, usually referred to as the feature maps. The trajectory developed by the nonADHD unit is initially elevated and decreases almost linearly. One reasonable explanation for such a pattern is that children without ADHD generally approach the task rapidly because of the time constraint but reduce their production as the possibilities for new designs diminish. On the opposite side, children with ADHD on average seem to borrow a nonlinear (bumpier) road to achieve their goal, their production pattern changing direction two times instead of none. This singular pattern may be interpreted in light of the triple pathway model of ADHD (Sonuga-Barke et al., 2010), more specifically as reflecting a difficulty with time-keeping abilities. A lack of motivation seems unlikely given that on average, children with ADHD performed as well as the control group. Poor inhibition does not seem explanatory either, given that on average the clinical group is characterized by slower task initiation. It remains possible, however, that productivity is modulated at a more basic level of arousal, as proposed by the Cognitive-Energetic model (Sergeant et al., 1999; Sonuga-Barke & Castellanos, 2007). The lower initiation and flatter production pattern could reflect an inability to activate the task-specific brain areas for executing design fluency, in line with the default-mode interference hypothesis of ADHD (SonugaBarke & Castellanos, 2007). Future studies are needed to explore the neural correlates of design fluency production patterns. Finally, the present study is limited by the absence of fine motor control measures, which raises the possibility that the variable production pattern generally offered by the clinical group relates to a more primary deficit at the motor control level (c.f., Schoemaker, Ketelaars, Van Zonneveld, Minderaa, & Mulder, 2005). Figure 2b and c shows the distribution of children with and without ADHD on the 4 x 4 map trained with the production patterns in Simulation 4. Larger units contain more data. The two groups overlap, but globally occupy opposite corners (ADHD: lower left). This indicates some level of variability in the production patterns but supports our previously described results, suggesting that the dynamics of cognition differ in children with ADHD. To further dig into the nature of production patterns, we used the U-Matrix, a visualization technique that can be thought of as a landscape showing how far apart subgroups of subjects (the units) are one from another, larger distance being represented by darker values (for details, see Ultsch & Siemon, 1990). The U-matrix (Figure 2d) reveals an intricate structure of clusters and subclusters in the data, which mainly draws a separation line between children with and without ADHD, indicating substantial betweengroup dissimilarity. This suggests a natural boundary between the activation patterns of children with and without ADHD rather than this cognitive feature being continuously distributed between the two groups. This could have implications with regards to the use of dimensional versus categorical measures in studies on ADHD. Finally, although we only entered the production pattern into the 4 x 4 neural net, the SOM also offers the possibility of computing as many variables as collected and observing how important factors covary together. In conclusion, the present study brings additional evidence that quantitative process measures can be useful in studying the neuropsychology of ADHD and may contribute to characterize the disorder. This study also indicates that artificial neural networks can help our understanding of ADHD and eventually of other disorders. Further research is needed
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to elaborate and fully exploit these dynamic tools as a strategy for generating hypotheses on specific brain-behavior relationship and as a window on how cognition unfolds in time. Original manuscript received August 10, 2014 Revised manuscript accepted November 12, 2014 First published online December 11, 2014
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