Resulting graph of the topological data analysis using the NYU dataset.

<p>(<b>A</b>) The ADHD-like subjects are ordered by the magnitude of deviation from the HSM. Each node is colored by the mean of the filter map on the points. Blue nodes contain normal-like subjects whose total deviations of the functional network from HSM are small (normal and normal-like subjects). Red nodes contain ADHD-like subjects whose deviations of the functional connectivity vector from HSM are large. The image of filter function was subdivided into 10 intervals with 85% overlap. (<b>B</b>) The number of subjects for each group versus node index. (<b>C</b>) The occupation ratio of group members in each node as function of node index.</p

Distribution of the magnitude of the disease component (or the values of the filter function) for each group: the TDC group (gray bars) and the ADHD group (white bars).

<p>Distribution of the magnitude of the disease component (or the values of the filter function) for each group: the TDC group (gray bars) and the ADHD group (white bars).</p

A New Approach to Investigate the Association between Brain Functional Connectivity and Disease Characteristics of Attention-Deficit/Hyperactivity Disorder: Topological Neuroimaging Data Analysis

<div><p>Background</p><p>Attention-deficit/hyperactivity disorder (ADHD) is currently diagnosed by a diagnostic interview, mainly based on subjective reports from parents or teachers. It is necessary to develop methods that rely on objectively measureable neurobiological data to assess brain-behavior relationship in patients with ADHD. We investigated the application of a topological data analysis tool, <i>Mapper</i>, to analyze the brain functional connectivity data from ADHD patients.</p><p>Methods</p><p>To quantify the disease severity using the neuroimaging data, the decomposition of individual functional networks into normal and disease components by the healthy state model (HSM) was performed, and the magnitude of the disease component (MDC) was computed. Topological data analysis using <i>Mapper</i> was performed to distinguish children with ADHD (<i>n</i> = 196) from typically developing controls (TDC) (<i>n</i> = 214).</p><p>Results</p><p>In the topological data analysis, the partial clustering results of patients with ADHD and normal subjects were shown in a chain-like graph. In the correlation analysis, the MDC showed a significant increase with lower intelligence scores in TDC. We also found that the rates of comorbidity in ADHD significantly increased when the deviation of the functional connectivity from HSM was large. In addition, a significant correlation between ADHD symptom severity and MDC was found in part of the dataset.</p><p>Conclusions</p><p>The application of HSM and topological data analysis methods in assessing the brain functional connectivity seem to be promising tools to quantify ADHD symptom severity and to reveal the hidden relationship between clinical phenotypic variables and brain connectivity.</p></div

Scatter plots for the value of the filter function versus clinical phenotype variables.

<p>In the ADHD group, correlation coefficients with the ADHD index were evaluated for (<b>A</b>) the NYU dataset and (<b>B</b>) the PU dataset. In the TDC group, correlation coefficients with full-scale IQ were evaluated for (<b>C</b>) the NYU dataset and (<b>D</b>) PU dataset.</p

Correlations between values of the filter function and clinical phenotypes (symptom severity and intelligence).

<p>Values are Pearson’s correlation coefficients (plus corresponding <i>p</i>-values).</p><p>The statistically significant thresholds are labeled as *<i>P</i> < 0.05</p><p>**<i>P</i> < 0.005.</p><p>Correlations between values of the filter function and clinical phenotypes (symptom severity and intelligence).</p

Group means and standard deviations of the filter function value for TDC and three ADHD subtype groups.

<p>ADHD, attention-deficit/hyperactivity disorder; C, combined type; H, hyperactivity/impulsivity type; I, inattentive type; F, female; M, male; NYU, New York University Child Study Center; PU, Peking University; TDC, typically developing children</p><p>Group differences were evaluated using one-way analysis of variance</p><p>Group means and standard deviations of the filter function value for TDC and three ADHD subtype groups.</p

Subgroup comparisons in demographics and clinical variables.

<p>IQ, Intelligence quotient; SD, standard deviation; TDC1, 10 TDC subjects with the lowest values of the filter function; TDC2, 10 TDC subjects with the highest value of the filter function; VFF, value of the filter function.</p><p>†chi2 test were performed.</p><p>Subgroup comparisons in demographics and clinical variables.</p

Demographic variables and ADHD diagnoses.

<p>ADHD, attention-deficit/hyperactivity disorder; F, female; M, male; NYU, New York University Child Study Center; PU, Peking University; SD, standard deviation; TDC, typically developing children</p><p>Demographic variables and ADHD diagnoses.</p

Visualization of the clinical phenotype data as a function of the node index in the NYU data.

<p>(<b>A</b>) Average symptom severity in each bin of graph. (<b>B</b>) Average intelligence scores in each bin of graph.</p

Schematic procedures of the functional network construction.

<p>(<b>A</b>) Functional network matrix, <b>[<i>R</i></b>_{<b><i>ij</i></b>}<b>]</b>, for a subject. (<b>B</b>) Upper triangular matrix of <b>[<i>R</i></b>_{<b><i>ij</i></b>}<b>]</b>. (<b>C</b>) Vectorization of the upper triangular matrix. (<b>D</b>) Stacking <b><i>T</i></b>_{<b><i>i</i></b>} for all subjects to construct <b><i>D</i></b>, where the vector <b><i>T</i></b>_{<b><i>i</i></b>} is the <i>i</i>-th row vector of <b><i>D</i> = [<i>D</i></b>_{<b><i>ij</i></b>}<b>]</b>.</p