Supplementary Material

Table S1. Detailed information about the administered tests.

Executive Functions Domains

Neuropsychological Tests Description Raw Score

ASDMean (SD)

[Range]

TPMean (SD)

[Range]

Attention

Digit Forward (Wechsler Scales)

The subject must repeat sequences of numbers in the same order as presented aloud by the examiner. Maximum number

of recalled items

5.14(0.85)[4-7]

6.00(1.30)[4-9]

Continuous Performance Test II

A letter at once is sequentially presented on the computer screen. The subject must respond to targets (all letters excepting ‘X’) by pressing the space bar and refrain from responding to non-targets (letter ‘X’).

Number of correct responses

296.76(25.27)[218-323]

308.48(23.02)[231-328]

Mean hit reaction time

0.64sec(0.28)[0.32-1.41]

0.48sec(0.18)[0.26-1.13]

Working Memory

Digit Backward (Wechsler Scales)

The subject must repeat sequences of numbers in the reverse order as presented aloud by the examiner.

Maximum number of recalled items

4.0(0.95)[2-6]

4.52(1.33)[2-7]

Number-Letter Sequencing

(Wechsler Scales)

A randomly ordered sequence of number and letters are presented aloud by the examiner. The subject is asked to respond by stating the number first in ascending order and the letter second in alphabetical order.

Maximum number of recalled items

4.62(0.92)[2-6]

5.0(1.0)[4-7]

Mental Flexibility

Mental Trail Making Test

This test has two parts. On part A the participant must draw a line linking a set of numbers in ascending order (1-25). On the part B the participant must draw a line linking alternating numbers and letters in ascending order (1, A, 2, B- 13). In all trials the participant must do it as quickly but as accurately as possible.

(Time to complete TMT(B)-Time to

complete TMT(A))/Time to complete TMT(A)

1.32min(0.67)[0.13-2.62]

1.43min(0.81)[0.09-2.98]

Wisconsin Card Sorting Test

A number of stimulus cards are presented to the participant. The figures on the cards vary according to three perceptual dimensions (color, form, number). The subject must find the correct classification principle by trial and error and examiner feedback (‘Yes’=correct match; ‘No’=incorrect match), as a way of learning for future decision. The cards need to be matched first by colour, then by form and finally by number. After 10 consecutive correct answers, the rule changes without warning, demanding a

Number of perseverative

errors

24.43(15.55)[3-77]

14.81(11.36)[3-45]

Number of errors 48.52(22.0)[12-96]

31.81(21.52)[7-85]

flexible shift in the set.Executive Functions

DomainsNeuropsychological

Tests Description Raw ScoreASD

Mean (SD)[Range]

TPMean (SD)

[Range]

Number of perseverative

responses

29.71(20.73)[3-101]

17.19(13.11)[3-52]

Response Inhibition

Continuous Performance Test II

A letter at once is sequentially presented on the computer screen. The subject must respond to targets (all letters excepting ‘X’) by pressing the space bar and refrain from responding to non-targets (letter ‘X’).

Number of Commissions

24.43(6.74)[12-34]

17.95(7.9)[3-35]

Colour Word Stroop Test (STROOP)

Three different pages are presented to the subject: (1) a word page with color words printed in black ink, (2) a color page with ‘Xs’ printed in color, and a color-word page with words from the first page printed in colors from the second page (the color and the word do not match). The must read the words in (1) or naming the ink colors in (2) and (3) as quickly as possible within a time limit (45 seconds).

Interference score

-0.03(4.02)[-7.0-6.61]

4.02(10.2)[-27.0-18.72]

Problem Solving Wisconsin Card Sorting Test

A number of stimulus cards are presented to the participant. The figures on the cards vary according to three perceptual dimensions (color, form, number). The subject must find the correct classification principle by trial and error and examiner feedback (‘Yes’=correct match; ‘No’=incorrect match), as a way of learning for future decision. The cards need to be matched first by colour, then by form and finally by number. After 10 consecutive correct answers, the rule changes without warning, demanding a flexible shift in the set.

Number of categories completed

56.29(17.39)[3-84]

62.71(17.74)[13-89]

Conceptual level responses

4.05(1.72)[0-6]

5.43(1.08)[2-6]

Number of correct responses

69.14(12.93)[32-86]

72.19(11.78)(43-97)

ASD = Male participants with autism spectrum disorders; TP = Typically developing male participants; SD = Standard Deviation.

Table S2. Image Quality Ratings of the T1-weighted images.

Participant IQR Participant IQR1 81.13 22 80.142 80.99 23 80.933 75.64 24 80.864 79.49 25 82.175 83.12 26 81.306 75.06 27 81.277 80.36 28 79.488 76.99 29 79.969 80.80 30 75.06

10 80.60 31 80.6911 79.40 32 79.4512 81.73 33 81.7413 79.55 34 80.8214 71.36 35 81.6715 80.76 36 82.1716 82.57 37 81.4017 78.48 38 78.5318 81.31 39 78.8119 78.18 40 82.0420 80.56 41 76.1821 82.03 42 82.87

IQR, Image Quality Rating.

Tests of different neuroimaging projects such as ADNI, IXI, INDI, OASIS, PPMI etc. demonstrated that published structural MRI data overall got good IQRs (http://dbm.neuro.uni-jena.de/cat/index.html#QA). Please note that excellent IQRs (> 90%) are defined for extraordinary good images that were acquired by

repeated long-time scans with ultra-high resolution on high field systems and that typical scientific data is expected to get good to satisfactory ratings (90%-70%, see also http://dbm.neuro.uni-jena.de/cat/index.html#QA).Table S3. Between-group differences on four measures of DTI data quality.

ASD = Male participants with autism spectrum disorders; TP = Typically developing male participants; SD = Standard Deviation

ASD TP pAverage translation mean (SD) 0.936 (0.154) 1.1040(0.505) 0.16

Average rotation mean (SD) 0.005(0.003) 0.007 (0.008) 0.44

Percentage bad slices mean (SD) 0 (0) 0 (0)

Average Dropout score mean (SD) 1 (0) 1 (0)

Table S4. F and p values for the effect of Diagnosis, Age and Diagnosis-by-Age interaction on the executive function domains. q-values obtained after FDR correction are also provided.

ANCOVA Models (Effects) ATT WM MF RI PS

Diagnosis F-value 8.366 3.116 4.578 13.093 4.235p-value 0.006 0.086 0.039 0.001 0.046q-value 0.039 0.241 0.144 0.009 0.161

Age F-value 1.261 9.349 7.785 2.204 4.131p-value 0.268 0.004 0.008 0.146 0.049q-value 0.500 0.026 0.048 0.347 0.164

Diagnosis by Age F-value 0.081 1.938 0.133 0.014 0.004p-value 0.777 0.172 0.718 0.907 0.949q-value 0.852 0.389 0.821 0.946 0.969

FDR corrected (alpha = 0.05). ATT= Attention; WM = Working Memory; MF = Mental Flexibility; RI = Response Inhibition; PS = Problem Solving.

Table S5. Pearson’s r and p values for the within-groups correlations between the executive function domains and age. q-values obtained after FDR correction are also provided.

Correlations ATT WM MF RI PS

Age

ASD r-value 0.194 0.242 0.295 0.208 0.263p-value 0.399 0.291 0.194 0.366 0.250q-value 0.623 0.518 0.410 0.583 0.488

TP r-value 0.169 0.552 0.546 0.255 0.391p-value 0.464 0.009 0.009 0.265 0.080q-value 0.672 0.050 0.050 0.497 0.228

FDR corrected (alpha = 0.05). ATT= Attention; WM = Working Memory; MF = Mental Flexibility; RI = Response Inhibition; PS = Problem Solving. ASD = Male participants with autism spectrum disorders; TP = Typically developing male participants.

Table S6. F and p values for the effect of Diagnosis, Age and Diagnosis-by-Age interaction on the white matter measurements per tract. q-values obtained after FDR correction are also provided.

ANCOVA Models (Effects)

FA MD RD

Diagnosis Age Diagnosis by Age Diagnosis Age Diagnosis

by Age Diagnosis Age Diagnosis by Age

Forceps MajorF-value 0.570 8.188 0.017 0.313 11.832 6.492 1.967 18.628 0.029p-value 0.455 0.007 0.897 0.579 0.001 0.015 0.169 <0.0005 0.866q-value 0.666 0.042 0.947 0.741 0.013 0.073 0.386 0.002 0.924

Forceps MinorF-value 0.494 10.402 3.77 2.886 27.014 1.846 1.837 11.618 11.656p-value 0.486 0.003 0.060 0.098 <0.0005 0.182 0.183 0.002 0.002q-value 0.691 0.018 0.187 0.266 0.001 0.401 0.402 0.013 0.013

Left ATRF-value 0.778 19.649 5.223 1.191 4.247 10.631 0.537 31.309 13.769p-value 0.383 <0.0005 0.028 0.282 0.046 0.002 0.468 <0.0005 0.001q-value 0.606 0.002 0.114 0.509 0.162 0.017 0.673 <0.0005 0.007

Left CABF-value 0.357 3.41 0.773 1.072 20.119 11.22 0.308 7.416 3.369p-value 0.554 0.073 0.385 0.307 <0.0005 0.002 0.582 0.0100 0.074q-value 0.74 0.216 0.606 0.526 0.002 0.014 0.742 0.053 0.218

Left CCGF-value 0.018 19.081 4.933 1.820 5.104 3.830 0.34 25.992 6.372p-value 0.893 <0.0005 0.032 0.185 0.030 0.058 0.564 <0.0005 0.016q-value 0.945 0.002 0.126 0.399 0.117 0.185 0.737 0.001 0.075

Left CSTF-value 0.956 6.464 2.262 0.357 15.554 4.430 0.376 19.573 4.285p-value 0.334 0.015 0.141 0.554 <0.0005 0.042 0.543 <0.0005 0.045q-value 0.553 0.073 0.339 0.738 0.004 0.153 0.736 0.002 0.160

Left ILFF-value 2.238 5.403 <0.0005 0.188 20.113 3.783 4.036 14.12 0.757p-value 0.143 0.026 0.986 0.667 <0.0005 0.059 0.052 0.001 0.390q-value 0.342 0.106 0.990 0.799 0.002 0.188 0.171 0.006 0.610

ANCOVA Models (Effects)

FA MD RD

Diagnosis Age Diagnosis by Age Diagnosis Age Diagnosis

by Age Diagnosis Age Diagnosis by Age

Left SLF-PF-value 0.540 6.268 0.455 1.89 12.667 2.77 0.455 11.561 1.255p-value 0.467 0.017 0.504 0.177 0.001 0.104 0.504 0.002 0.270q-value 0.673 0.078 0.706 0.396 0.010 0.279 0.708 0.013 0.501

Left SLF-TF-value 0.038 7.637 1.028 0.527 8.904 1.722 0.933 14.443 2.530p-value 0.846 0.009 0.317 0.472 0.005 0.197 0.34 0.001 0.120q-value 0.911 0.050 0.531 0.675 0.032 0.410 0.559 0.006 0.310

Left UNCF-value 2.399 1.203 1.253 2.092 16.675 3.893 2.705 2.419 0.015p-value 0.130 0.280 0.270 0.156 <0.0005 0.056 0.108 0.128 0.902q-value 0.318 0.509 0.500 0.367 0.003 0.181 0.285 0.319 0.944

Right ATRF-value 0.222 10.879 1.222 2.085 4.706 1.134 0.655 26.463 5.206p-value 0.640 0.002 0.276 0.157 0.036 0.294 0.423 <0.0005 0.028q-value 0.782 0.016 0.508 0.367 0.137 0.513 0.632 0.001 0.114

Right CABF-value 0.144 7.001 1.357 0.195 16.575 3.776 0.502 10.168 2.942p-value 0.706 0.012 0.251 0.661 <0.0005 0.059 0.483 0.003 0.094q-value 0.817 0.060 0.488 0.795 0.003 0.188 0.688 0.020 0.259

Right CCGF-value 0.924 37.561 5.485 0.185 4.342 1.344 0.17 35.673 3.469p-value 0.343 <0.0005 0.025 0.670 0.044 0.254 0.682 <0.0005 0.070q-value 0.556 <0.0005 0.104 0.799 0.157 0.490 0.803 <0.0005 0.211

Right CSTF-value 0.792 8.761 1.327 0.105 11.67 0.929 0.314 21.42 1.463p-value 0.379 0.005 0.257 0.748 0.002 0.341 0.578 <0.0005 0.234q-value 0.601 0.033 0.49 0.842 0.013 0.557 0.742 0.001 0.461

ANCOVA Models (Effects)

FA MD RD

Diagnosis Age Diagnosis by Age Diagnosis Age Diagnosis

by Age Diagnosis Age Diagnosis by Age

Right ILFF-value 0.629 18.945 0.075 1.196 10.504 0.271 0.01 18.347 2.512p-value 0.433 <0.0005 0.786 0.281 0.002 0.605 0.919 <0.0005 0.121q-value 0.64 0.002 0.858 0.509 0.018 0.76 0.952 0.002 0.310

Right SLF-PF-value 0.011 12.072 0.059 0.355 5.228 4.204 0.014 17.872 0.718p-value 0.917 0.001 0.81 0.555 0.028 0.047 0.908 <0.0005 0.402q-value 0.954 0.012 0.875 0.738 0.115 0.162 0.946 0.002 0.623

Right SLF-TF-value 2.513 16.775 1.071 0.107 14.205 0.908 0.08 24.837 1.940p-value 0.121 <0.0005 0.307 0.746 0.001 0.347 0.779 <0.0005 0.172q-value 0.311 0.003 0.524 0.843 0.006 0.56 0.852 0.001 0.390

Right UNCF-value 0.245 5.573 0.082 0.005 16.886 1.318 0.64 9.784 1.867p-value 0.624 0.023 0.776 0.944 <0.0005 0.258 0.429 0.003 0.180q-value 0.769 0.103 0.852 0.97 0.003 0.489 0.636 0.023 0.398

FDR corrected (alpha = 0.05). ATR = Anterior Thalamic Radiation, CAB = Cingulum Angular Bundle, CCG = Cingulum Cingulate Gyrus, CST = Corticospinal Tract, ILF = Inferior Longitudinal Fasciculus, SLF-P = Superior Longitudinal Fasciculus – Parietal, SLF-T = Superior Longitudinal Fasciculus – Temporal, UNC = Uncinate Fasciculus, FA=Fractional Anisotropy, MD=Mean Diffusivity, RD=Radial Diffusivity.

Table S7. F and p values for the effect of each executive function domain and Diagnosis-by-EF domain performance on the white matter microstructure measurements for the Forceps Minor, Left Anterior Thalamic Radiation, and Left Cingulum Angular Bundle. q-values obtained after FDR correction are also provided.

FDR corrected (alpha = 0.05). Significant results (uncorrected; alpha = 0.05)

ANCOVA Models (Effects)

Forceps Minor Left Anterior Thalamic Radiation Left Cingulum Angular Bundle

FA MD RD FA MD RD FA MD RD

AttentionF-value 1.068 1.587 0.377 0.097 0.072 0.164 1.011 0.363 0.678

p-value 0.308 0.216 0.543 0.757 0.791 0.688 0.321 0.551 0.416q-value 0.524 0.432 0.735 0.84 0.86 0.807 0.537 0.735 0.631

AttentionBy

Diagnosis

F-value 0.000 3.65 0.175 1.452 0.351 2.496 0.395 2.355 2.114p-value 0.995 0.064 0.678 0.236 0.557 0.123 0.534 0.133 0.154q-value 0.995 0.198 0.8 0.461 0.735 0.310 0.732 0.324 0.365

Working Memory

F-value 0.032 0.707 0.49 1.831 1.899 6.039 1.618 6.879 7.681p-value 0.86 0.406 0.488 0.184 0.177 0.019 0.211 0.013 0.009q-value 0.919 0.625 0.69 0.398 0.396 0.087 0.43 0.063 0.050

Working MemoryBy

Diagnosis

F-value 0.082 0.67 0.178 1.757 0.659 4.361 0.011 4.491 1.818p-value 0.776 0.418 0.676 0.193 0.422 0.044 0.918 0.041 0.186q-value 0.852 0.631 0.800 0.408 0.632 0.157 0.949 0.150 0.398

Mental Flexibility

F-value 0.353 0.262 0.644 4.827 0.696 0.889 0.566 0.216 0.325p-value 0.556 0.611 0.427 0.034 0.409 0.352 0.457 0.645 0.572q-value 0.735 0.761 0.636 0.131 0.627 0.565 0.666 0.785 0.741

Mental FlexibilityBy

Diagnosis

F-value 1.144 0.491 2.097 7.352 1.509 2.653 0.295 0.906 0.253

p-value 0.292 0.488 0.156 0.010 0.227 0.112 0.59 0.347 0.618q-value 0.513 0.69 0.365 0.054 0.450 0.292 0.748 0.559 0.767

ANCOVA Models (Effects)

Forceps Minor Left Anterior Thalamic Radiation Left Cingulum Angular Bundle

FA MD RD FA MD RD FA MD RD

Response Inhibition F-value 1.808 0.270 1.002 6.545 0.192 2.304 0.582 0.476 0.670p-value 0.187 0.606 0.323 0.015 0.664 0.138 0.451 0.495 0.418q-value 0.399 0.759 0.538 0.072 0.797 0.332 0.661 0.697 0.631

Response InhibitionBy

Diagnosis

F-value 1.884 0.002 0.108 5.767 0.563 1.033 0.353 0.017 0.023p-value 0.178 0.965 0.744 0.021 0.458 0.316 0.556 0.898 0.880q-value 0.396 0.976 0.839 0.095 0.666 0.531 0.735 0.943 0.933

Problem Solving

F-value 3.059 0.686 5.428 0.148 3.500 0.176 0.340 0.282 0.001p-value 0.089 0.413 0.025 0.703 0.069 0.678 0.563 0.599 0.977q-value 0.245 0.628 0.106 0.815 0.210 0.800 0.737 0.753 0.983

Problem SolvingBy

Diagnosis

F-value 4.238 1.832 7.071 2.582 4.205 1.337 0.701 0.93 0.002

p-value 0.047 0.184 0.012 0.117 0.047 0.255 0.408 0.341 0.966q-value 0.161 0.398 0.059 0.303 0.161 0.489 0.626 0.555 0.976

Table S8. Validation of findings declared as significant in Step 3 (Diagnostic differences in the relationship between executive function domain performance and white matter microstructure measurements) using bootstrap sampling technique and random permutation of data. Blue shaded cells correspond to results from 5000 samples generated using bootstrap sampling technique. Orange shaded cells correspond to results from 5000 random datasets built randomly permuting the data.

Figure S1. The eighteen major white matter tracts reconstructed using the Tracts Constrained by UnderLying Anatomy (TRACULA) software.

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Figure 3 a.FA Left Anterior Thalamic Radiation - Response Inhibition

ANCOVA ModelF (RI) 6.545 8.075 7.912 8.237 1.130 1.084 1.176 0.018F (RI-by-Diagnosis) 5.767 7.283 7.115 7.45 0.710 0.681 0.738 0.004

Within-Groups Correlations

r (TP) 0.504 0.504 0.498 0.509 0.002 -0.004 0.008 0.014r (ASD) -0.133 -0.111 -0.118 -0.104 -0.002 -0.008 0.004 0.706

Figure 3 b.RD Forceps Minor - Problem Solving

ANCOVA ModelF (PS) 5.428 7.268 7.068 7.468 0.978 0.938 1.017 0.020F (PS-by-Diagnosis) 7.071 9.173 8.93 9.417 0.831 0.798 0.865 0.012

Within-Groups Correlations

r (TP) -0.448 -0.419 -0.426 -0.413 -0.004 -0.010 0.003 0.969r (ASD) 0.149 0.161 0.155 0.167 0.000 -0.006 0.007 0.265

Figure 3 c.RD Left Cingulum Angular Bundle - Working Memory

ANCOVA ModelF (WM) 7.681 9.207 9.026 9.387 1.262 1.210 1.315 0.014F (WM-by-Diagnosis) 7.681 3.102 3.015 3.189 0.598 0.573 0.623 0.001

Within-Groups Correlations

r (TP) -0.420 -0.408 -0.413 -0.404 0.003 -0.003 0.01 0.970

r (ASD) -0.148 -0.116 -0.122 -0.109 0.003 -0.004 0.009 0.744

Figure S2. Scatter plots depicting the EF domain performance–WMS measurements relationship (r, p), controlling for the effect of age, for tracts where a significant effect of EF domain and/or diagnosis-by-EF domain performance were found (uncorrected). ASD = Male participants with autism spectrum disorders, TP = Typically developing male participants, FA = Fractional Anisotropy, MD = Mean Diffusion, RD = Radial Diffusion, FMinor = Forceps Minor, ATR = Anterior Thalamic Radiation, CAB = Cingulum Angular Bundle.