Abnormality of Early White Matter Development in Tuberous Sclerosis Complex and Autism Spectrum Disorder: Longitudinal Analysis of Diffusion Tensor Imaging Measures

Abstract

Background:

Abnormalities in white matter development may influence development of autism spectrum disorder in tuberous sclerosis complex (TSC). Our goals for this study were as follows: (1) use data from a longitudinal neuroimaging study of tuberous sclerosis complex (TACERN) to develop optimized linear mixed effects models for analyzing longitudinal, repeated diffusion tensor imaging metrics (fractional anisotropy, mean diffusivity) pertaining to select white matter tracts, in relation to positive Autism Diagnostic Observation Schedule–Second Edition classification at 36 months, and (2) perform an exploratory analysis using optimized models applied to all white matter tracts from these data.

Methods:

Eligible participants (3-12 months) underwent brain magnetic resonance imaging (MRI) at repeated time points from ages 3 to 36 months. Positive Autism Diagnostic Observation Schedule–Second Edition classification at 36 months was used. Linear mixed effects models were fine-tuned separately for fractional anisotropy values (using fractional anisotropy corpus callosum as test outcome) and mean diffusivity values (using mean diffusivity right posterior limb internal capsule as test outcome). Fixed effects included participant age, within-participant longitudinal age, and autism spectrum disorder diagnosis.

Results:

Analysis included data from n = 78. After selecting separate optimal models for fractional anisotropy and mean diffusivity values, we applied these models to fractional anisotropy and mean diffusivity of all 27 white matter tracts. Fractional anisotropy corpus callosum was related to positive Autism Diagnostic Observation Schedule–Second Edition classification (coefficient = 0.0093, P = .0612), and mean diffusivity right inferior cerebellar peduncle was related to positive Autism Diagnostic Observation Schedule–Second Edition classification (coefficient = −0.00002071, P = .0445), though these findings were not statistically significant after multiple comparisons correction.

Conclusion:

These optimized linear mixed effects models possibly implicate corpus callosum and cerebellar pathology in development of autism spectrum disorder in tuberous sclerosis complex, but future studies are needed to replicate these findings and explore contributors of heterogeneity in these models.

The expanding genetic landscape of autism spectrum disorder and intellectual disability¹ has resulted in increasing attention toward studying these neurodevelopmental conditions from the standpoint of specific single-gene disorders. Such an approach is rooted in the notion that autism spectrum disorder and intellectual disability may represent final common pathways in ostensibly distinct genetic disorders with a high prevalence of autism spectrum disorder and intellectual disability.² Improved understanding of the pathophysiological mechanisms that lead to autism spectrum disorder and intellectual disability in a specific genetic disorder may culminate in knowledge that is applicable to autism spectrum disorder and intellectual disability in general, paving the way to possible rational therapeutics.^3,4

Tuberous sclerosis complex (TSC), a multisystem genetic disorder caused by pathogenic variants in TSC1 or TSC2, is one such disorder linked to a high prevalence of autism spectrum disorder and intellectual disability. Systemic manifestations are broad and include abnormalities affecting the eyes, heart, lungs, kidneys, and skin.⁵ Central nervous system (CNS) findings include macrostructural abnormalities (such as cortical dysplasias, subependymal nodules, and subependymal giant cell astrocytomas⁶) and microstructural changes (such as hypomyelination and axonal loss^7–9). There is a broad spectrum of neurodevelopmental and neuropsychiatric issues associated with tuberous sclerosis complex that is termed tuberous sclerosis complex–associated neuropsychiatric disorders (TAND).¹⁰ Intellectual disability, affecting about 45% of individuals with tuberous sclerosis complex, ranges in severity from mild to profound.¹¹ Behavioral and psychiatric challenges associated with tuberous sclerosis complex include attention-deficit hyperactivity disorder (ADHD), anxiety, and depression.^10,12 Finally, the prevalence of autism spectrum disorder in tuberous sclerosis complex is about 25% to 50%.^13–15

In light of the high prevalence of autism spectrum disorder in tuberous sclerosis complex, prior work has attempted to elucidate biological factors associated with the development of autism spectrum disorder within the disorder, including focus on abnormalities in the white matter. Investigations using diffusion tensor imaging, which evaluates the diffusion of water molecules across structures in the brain, have shown evidence of altered microstructure in tubers,¹⁶ as well as grossly normal-appearing white matter¹⁷ in individuals with tuberous sclerosis complex. More specifically, in terms of the relationship between altered microstructure of specific white matter tracts and neurocognitive outcomes, lower fractional anisotropy (FA) and higher mean diffusivity (MD) values of the arcuate fasciculus, a key component of the language pathway, occur in individuals with tuberous sclerosis complex and autism spectrum disorder compared to individuals with tuberous sclerosis complex without autism spectrum disorder, based on one study involving children and adults.¹⁸ In another study, which involved affected individuals aged 1-27 years, fractional anisotropy values of the corpus callosum were lower in those with tuberous sclerosis complex compared to those with nonsyndromic autism spectrum disorder; the presence of intellectual disability, autism spectrum disorder, and epilepsy within the tuberous sclerosis complex group conferred even lower fractional anisotropy values.¹⁹ Of note, these studies, which involved both children and adults, did not necessarily focus on brain development in the first few years of life, when the symptoms of autism spectrum disorder emerge.

Addressing this limitation, our group previously evaluated the longitudinal trajectory of white matter connectivity preceding autism spectrum disorder diagnosis in tuberous sclerosis complex using data from a prospective, longitudinal study consortium, termed the TSC Autism Center of Excellence Research Network (TACERN). In 108 infants with tuberous sclerosis complex who underwent repeated brain magnetic resonance imaging (MRI; at time of recruitment, 12 months of age, and 24 months of age), the presence of Autism Diagnostic Observation Schedule Second Edition positive classification at 24 months of age contributed to a reduction in fractional anisotropy values in multiple white matter regions, based on linear mixed effects modeling of repeated measures.²⁰

In the interval period since this publication, the TACERN study has observed participants to 36 months of age. Our primary goals for the present study were 2-fold: (1) use data from TACERN to develop optimized linear mixed effects models for analyzing longitudinal, prospective diffusion tensor imaging metrics (fractional anisotropy, mean diffusivity) pertaining to select white matter tracts in infants and toddlers with tuberous sclerosis complex from age 3 months to 36 months, in relation to positive ADOS-2 classification at 36 months and (2) perform an exploratory analysis using optimized models applied to all white matter tracts from these data to see if changes in microstructural integrity over time of various white matter tracts is related to a positive ADOS-2 classification made at 36 months of age. This work expands our prior study, which performed a similar type of analysis²⁰ but with notable differences. Specifically, (1) we have incorporated positive Autism Diagnostic Observation Schedule–Second Edition classification made at 36 months instead of 24 months, (2) we have conducted tract-based rather than region of interest–based analysis, and (3) we have compared and fine-tuned different linear mixed effects regression models for this analysis. Regarding the third point, because of the strong parametric assumptions of linear mixed effects models,²¹ there are several nontrivial issues to evaluate, including assumption of linearity, assumption of normality of latent random effects and random errors, and selection of random and fixed effects.

Methods

Study Design

The TACERN study was a National Institutes of Health (NIH)–funded, multisite, prospective, longitudinal study to identify early biomarkers of autism spectrum disorder among infants with tuberous sclerosis complex (ClinicalTrials.gov NCT01780441). The objectives of the study were to characterize the developmental precursors of autism spectrum disorder in infants with tuberous sclerosis complex and to identify biomarkers using advanced diffusion tensor imaging and quantitative electroencephalography (EEG) to help predict development of autism spectrum disorder in tuberous sclerosis complex infants. Participants enrolled at 5 large children’s hospitals geographically distributed throughout the United States, each with a tuberous sclerosis complex specialty clinic recognized by the TSC Alliance. Infants 3-12 months old meeting molecular or clinical diagnostic criteria for tuberous sclerosis complex were eligible for participation. Full inclusion and exclusion criteria for the TACERN study are elaborated by Davis et al.²² Information about participant genotype, demographics, medical history, and family history were part of baseline data collection. Participants underwent physical examination, brain MRI, EEG, and developmental assessments at baseline and 12, 24, and 36 months of age; if feasible, they underwent additional EEG and developmental assessments at 6, 9, and 18 months of age.

Study Assessments

Autism spectrum disorder assessment.

We used positive Autism Diagnostic Observation Schedule–Second Edition classification status as a proxy for autism spectrum disorder at 36 months. The Autism Diagnostic Observation Schedule–Second Edition is a semi-structured, interactive assessment of social communication skills and restricted repetitive behaviors. The instrument consists of 5 modules, although the administrator uses only 1 module depending on the participant’s age and language abilities. The Toddler Module is for toddlers (12-30 months of age) without phrase speech; module 1 is for children at least 31 months of age without phrase speech; module 2 is for children with phrase speech who are not verbally fluent; module 3 is for children and younger adolescents who are verbally fluent; and module 4 is for older adolescents and adults who are verbally fluent. Each module yields a Social Affect total score and a Restricted and Repetitive Behavior total score. The Autism Diagnostic Observation Schedule–Second Edition uses an algorithm to generate module-specific cutoffs for Autism Diagnostic Observation Schedule–Second Edition classification of “autism,” “autism spectrum,” or “non-autism” in the case of modules 1 to 4 or range of concern (little to no concern, mild to moderate concern, moderate to severe concern) in the case of the Toddler Module. For modules 1 to 4, the algorithm also generates a comparison score to gauge symptom severity and facilitate comparison across time points and modules.²³ The TACERN study used only the Autism Diagnostic Observation Schedule–Second Edition Toddler Module (conducted at age 24 months), module 1 (conducted at age 24 and 36 months), and module 2 (conducted at age 24 and 36 months). We designated a “positive” Autism Diagnostic Observation Schedule–Second Edition classification at 36 months if modules 1 or 2 indicated “autism spectrum” or “autism.”

Brain MRI acquisition, processing.

Participants underwent MRI on 7 different 3-tesla (T) scanners using a TACERN-specific research imaging protocol. The protocol included T1-weighted, T2-weighted, and diffusion-weighted images, with detailed acquisition parameters and cross-scanner reliability published previously.²⁴ Participants used natural sleep or sedation to complete the scans. Prior to automated (and therefore objective and reproducible) analysis, we had carefully reviewed the images to detect the presence of any undesirable imaging artifacts that could, if present, lead to invalid data, and then to invalid data analysis.

Subsequent data-processing and analysis occurred using the Computational Radiology Kit (Computational Radiology Lab, Boston Children’s Hospital) via a fully automated processing pipeline. Processing steps included aligning and resampling images, segmenting the intracranial cavity, correcting magnetic susceptibility distortion, and computing fractional anisotropy and mean diffusivity. A nonlinear, dense registration procedure labeled white matter regions of interest using a fully automatic, multitemplate method. The basis for the template library was diffusion tensor imaging data from healthy children as well as regions of interest hand-drawn by an expert rater. Selection of white matter tracts was based on the automatically defined regions of interest. A stochastic tractography algorithm generated streamlines, with termination criteria based on gray matter contact, streamline curvature, and fractional anisotropy. The pipeline computed mean diffusivity and fractional anisotropy for each tract. The set of tracts are as follows:

• arcuate fasciculus, left dorsal

• arcuate fasciculus, left ventral

• arcuate fasciculus, right dorsal

• arcuate fasciculus, right ventral

• anterior limb internal capsule brainstem projections, left

• anterior limb internal capsule brainstem projections, right

• anterior thalamic radiation, left

• anterior thalamic radiation, right

• corpus callosum

• cingulum, left

• cingulum, right

• corticospinal tract, left

• corticospinal tract, right

• inferior cerebellar peduncle, left

• inferior cerebellar peduncle, right

• inferior longitudinal fasciculus, left

• inferior longitudinal fasciculus, right

• middle cerebellar peduncle, left

• middle cerebellar peduncle, right

• optic radiation, left

• optic radiation, right

• posterior limb internal capsule, left

• posterior limb internal capsule, right

• superior cerebellar peduncle, left

• superior cerebellar peduncle, right

• uncinate fasciculus, left

• uncinate fasciculus, right

Statistical Analysis

Developing and Comparing Models.

We compared linear mixed effects models as modeling tools for examining longitudinal changes in white matter development (assessed by diffusion tensor imaging tractography) over the first 36 months of life in infants/children with tuberous sclerosis complex. For these comparisons, we selected two different representative test outcome measures: fractional anisotropy of corpus callosum (designated hereafter as “FA_CC”) and mean diffusivity of right posterior limb internal capsule (designated hereafter as “MD_PLIC_R”).

We considered specific fixed effects as follows. We considered natural logarithm of age at MRI scan. To take into account effects of baseline participant age and within-participant longitudinal age,²¹ we considered (1) the natural logarithm of baseline age (natural logarithm of the age at the participant’s first MRI scan in the sample) and (2) the natural logarithm of longitudinal age (natural logarithm of age at MRI scan minus natural logarithm of baseline age). We considered autism spectrum disorder designation at 36 months based on the Autism Diagnostic Observation Schedule–Second Edition.

Separately for each of the 2 test outcome variables, we used maximum likelihood estimation (MLE) to test a set of models in order to determine a final linear mixed effects model for fractional anisotropy metrics and a final linear mixed effects model for mean diffusivity metrics for all tracts.

Step 1. We started with the following linear mixed effects models, assessing for both cross-sectional effects of age and longitudinal effects of time:

$$\begin{gathered} Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln (\text{Age}{B}_i) \\ +{\beta }_3[\ln ({\text{Age}}_{ij})-\ln (\text{Age}{B}_i)]+{\beta }_4{G}_i\ln (\text{Age}{B}_i) \\ +{\beta }_5{G}_i[\ln ({\text{Age}}_{ij})-\ln (\text{Age}{B}_i)]+b_{0i}+{ϵ}_{ij} \end{gathered}$$ (Model 1)

$$Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln ({\text{Age}}_{ij})+{\beta }_3{G}_i\ln ({\text{Age}}_{ij})+b_{0i}+{ϵ}_{ij},$$ (Model 2)

where $i$ indexes each participant, $j$ indexes the sequential scan number within each participant, $Y_{ij}$ denotes a diffusion tensor imaging measure (fractional anisotropy or mean diffusivity value) as the response variable, $\beta$ ’s are fixed effects coefficients, $b_{0i}$ is a random intercept, $G_i$ is the binary group variable (ie, positive Autism Diagnostic Observation Schedule–Second Edition classification at 36 months), $\text{Age}{B}_i$ represents the age of the participant $i$ at their first scan in the sample, and ${\text{Age}}_{ij}(j=1,2,3,\cdots ;{\text{Age}}_{ij}=\text{Age}{B}_i\text{when}j=1)$ represents the age at subsequent scans after the baseline scan. In each of these 2 models, we tested whether the coefficient of the interaction terms between group variable and age variables would be needed in the final models.

Step 2. If we determined the interaction terms between group variable and age variables were not needed in the final models, we fit the following 2 linear mixed effects models (model 3 and 4) without interaction terms between group variable and age variables. We compared these 2 models to each other to see if the simpler model (model 4) was comparable to the more complex model (model 3), allowing us to designate a favored model.

$$\begin{gathered} Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln (\text{Age}{B}_i) \\ +{\beta }_3[\ln ({\text{Age}}_{ij})-\ln (\text{Age}{B}_i)]+b_{0i}+{ϵ}_{ij} \end{gathered}$$ (Model 3)

$$Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln ({\text{Age}}_{ij})+b_{0i}+{ϵ}_{ij}$$ (Model 4)

Step 3. We used locally weighted scatterplot smoothing (LOWESS)²⁵ to assess the marginal linearity of natural logarithm of age at scan with respect to the outcome variables. If there was preservation of the linearity assumption between the test outcome measure and the natural logarithm of age, we moved on to step 3a. If there was violation of the linearity assumption between the test outcome measure and the natural logarithm of age, we moved on to step 3b.

Step 3a. If there was preservation of the linearity assumption between the test outcome measure and the natural logarithm of age, to the favored model chosen in step 2 (either model 3 or model 4), we added, one at a time, additional random slope for the natural logarithm of age and for the group (positive Autism Diagnostic Observation Schedule–Second Edition classification) variable. We determined whether these additional random slopes would improve the performance of the linear mixed effects model. We finalized our model at this point.

Step 3b. If there was violation of the linearity assumption between the test outcome measure and the natural logarithm of age, we evaluated one of the following 2, more complex, linear mixed effects models (model 5 if we determined that model 3 was the favored model in the previous step 2 or model 6 if we determined model 4 was the favored model in the previous step 2):

$$\begin{gathered} Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln ({\mathit{AgeB}}_i) \\ +{\beta }_3[\ln ({\mathit{Age}}_{ij})-\ln ({\mathit{AgeB}}_i)]+{\beta }_4{[\ln ({\mathit{AgeB}}_i)]}^2 \\ +{\beta }_5{[\ln ({\mathit{Age}}_{ij})-\ln ({\mathit{AgeB}}_i)]}^2+b_{0i}+{ϵ}_{ij} \end{gathered}$$ (Model 5)

$$Y_{ij}={\beta }_0+{\beta }_1{G}_i+{\beta }_2\ln ({\mathrm{Age}}_{ij})+{\beta }_3{[\ln ({\text{Age}}_{ij})]}^2+b_{0i}+{ϵ}_{ij}$$ (Model 6)

We compared either model 5 or 6 to the favored model in step 2 (either model 3 or model 4) to see if the simpler model 3 or 4 was comparable to the more complex model 5 or 6, potentially allowing us to update our favored model. To the updated favored model, we added, one at a time, additional random slope for the natural logarithm of age and for the group variable. We determined whether these additional random slopes would improve the performance of the linear mixed effects model. We finalized our model at this point.

Application of linear mixed effects models to all tracts.

After selecting the optimal model selected above for use with fractional anisotropy values, we applied this model to the fractional anisotropy values of all 27 white matter tracts. We did so similarly for the optimal model selected above for use with mean diffusivity values.

Statistics.

We used P values of coefficients of terms to determine whether to include these terms. We used the likelihood ratio test to compare linear mixed effects models to each other. We considered a P value <0.05 to be statistically significant. Where we denoted that we corrected for multiple comparisons, we used the Benjamini-Hochberg method.

Data sharing.

Study data are accessible through the National Institutes of Health Data Archive (NDA).

Results

Participants

We enrolled 169 subjects and performed MRI curation and quality control as previously described.²⁴ We excluded participants with missing Autism Diagnostic Observation Schedule–Second Edition data at 36 months, as well as participants with invalid Autism Diagnostic Observation Schedule–Second Edition at 36 months, such as those with a mental age below 18 months at the time of administration. After these quality control steps, this analysis included scans from a total of 78 participants. Figure 1 depicts the time points of MRI scans in the sample. Of note, there was 15 of 78 (19%) with only 1 scan available for use in the analysis. Descriptive data of the sample stratified by positive Autism Diagnostic Observation Schedule–Second Edition classification at 36 months are presented in Table 1. Of note, 5 subjects had MRI scans done prior to enrollment in the study, which we included in the analysis. Reasons for early MRI were as follows: 2 subjects with early seizure onset, 2 subjects with a positive family history of tuberous sclerosis complex and an echo showing cardiac rhabdomyomas, and 1 subject with an echocardiogram done on day of birth showing cardiac rhabdomyomas and positive genetic testing for tuberous sclerosis complex at 1 month of age.

Figure 1.

Depiction of longitudinal brain magnetic resonance imaging (MRI) scans from participants in the TACERN study included in our analysis. Each point represents an MRI scan. A horizontal line connecting multiple points represents repeated MRI scans for a single participant.

Table 1.

Demographic Characteristics of Participants in the TACERN Study Included in Our Analysis, Stratified by Positive ADOS-2 Classification at 36 Months.

Characteristic	Overall,a (N = 78)	Negative ADOS-2 classification,a (n = 51)	Positive ADOS-2 classification,a (n = 27)	P value b
Sex				.631
Female	33 / 78 (42)	23 / 51 (45)	10 / 27 (37)
Male	45 / 78 (58)	28 / 51 (55)	17 / 27 (63)
Age at baseline scan, y	1.04 ± 0.58	1.00 ± 0.60	1.11 ± 0.52	.257
Number of scans				.842
1	15 / 78 (19)	10 / 51 (20)	5 / 27 (19)
2	21/ 78 (27)	13 / 51 (25)	8 / 27 (30)
3	29 / 78 (37)	18 / 51 (35)	11 / 27 (41)
4	13 / 78 (17)	10 / 51 (20)	3 / 27 (11)

Abbreviation: ADOS-2, Autism Diagnostic Observation Schedule–Second Edition.

^aValues are expressed as n / N (%) or mean ± standard deviation.

^bFisher exact test; Wilcoxon rank sum test.

Development of Appropriate Linear Mixed Effects Models

Assessment of linearity.

The LOWESS estimates showed a nonlinear relationship between FA_CC and age in years (Figure 2A) as well as a linear relationship between FA_CC and natural logarithm of age (Figure 2B), suggesting that linearity assumption in linear mixed effects pertaining to FA_CC as the outcome measure was appropriate.

Figure 2.

Nonparametric locally weighted scatterplot smoothing (LOWESS) estimates for linearity assessment of corpus callosum FA (CC_FA) versus (A) age and (B) natural logarithm of age. FA, fractional anisotropy.

For MD_PLIC_R, the LOWESS estimates showed a nonlinear relationship between this metric and age in years (Figure 3A); however, the trend of nonlinearity was present even when comparing this outcome measure to natural logarithm of age (Figure 3B). As a result, we considered a quadratic term of natural logarithm of age in linear mixed effects pertaining to MD_PLIC_R.

Figure 3.

Nonparametric locally weighted scatterplot smoothing (LOWESS) estimates for linearity assessment of right posterior limb internal capsule MD (PLIC_R_MD) versus (A) age and (B) natural logarithm of age. MD, mean diffusivity.

Optimal linear mixed effects model for test outcome measure FA_CC.

For the outcome measure FA_CC, the linear mixed effects models 1 and 2 including separate terms for age and longitudinal age yielded nonsignificant P values for the terms corresponding to interactions between the group variable and age terms ($P=.090$ and $P=.599$ for ${\beta }_4$ and ${\beta }_5$, respectively, in model 1 and $P=.365$ for ${\beta }_3$ in model 2). This is a sign that the interaction did not exist between these variables.

After removing these interaction terms, we performed linear mixed effects modeling based on models 3 and 4. Comparing these models 3 and 4, likelihood ratio test yielded a P value of .925, indicating that the more complex model 3 was not better than the simpler model 4, making us favor the simpler model 4.

To model 4, we then added, one at a time, additional random slope for the natural logarithm of age and for the group variable (36-month positive Autism Diagnostic Observation Schedule–Second Edition classification). Likelihood ratio test yielded a P value of .442 and .876, respectively, indicating these additional random slopes would not improve the performance of the linear mixed effects modeling.

Our conclusion was that model 4 was the best model for the outcome variable FA_CC. We tested versions of model 4 using fractional anisotropy values of all tracts as the dependent variables. In these model versions, we included the additional terms of (a) the interaction between 36-month positive Autism Diagnostic Observation Schedule–Second Edition classification and natural logarithm of age, (b) the natural logarithm of age at baseline, and (c) the quadratic term of the natural logarithm of age. The P values of these estimated coefficients were not statistically significant after correction for multiple comparisons, suggesting that these additional coefficients would not be needed for modeling fractional anisotropy values of tracts other than the CC.

Optimal linear mixed effects model for test outcome measure MD_PLIC_R.

For the outcome variable MD_PLIC_R, the 2 linear mixed effects models 1 and 2 yielded nonsignificant P values for the 2 interaction terms involving the group variable and the age terms ($P=.679$ and $P=.147$ for ${\beta }_4$ and ${\beta }_5$, respectively, in model 1 and $P=.619$ for ${\beta }_3$ in model 2).

After removing these 2 interaction terms, we performed and compared models 3 and model 4. Likelihood ratio test between the 2 models yielded a P value of .182, indicating that the complex model 3 was not better than the simpler model 4, making us favor the simpler model 4.

We fit model 6 which included a quadratic term of natural logarithm of age and compared it to model 4. The comparison made by the likelihood ratio test generated a P value of .0002, suggesting that we should prefer the more complex model 6.

To model 6, we then added, one at a time, additional random slope for the natural logarithm of age and for the group variable. Likelihood ratio test yielded a P value of .531 and >.99, respectively, indicating these additional random slopes would not improve the performance of model 6.

Given these results, we concluded that model 6 was the one with the best performance in modeling the outcome variable MD_PLIC_R. We tested versions of model 4 using mean diffusivity values of all tracts as the dependent variables. In these model versions, we included the additional terms of (a) the interaction between 36-month positive Autism Diagnostic Observation Schedule–Second Edition classification and natural logarithm of age and (b) the natural logarithm of age at baseline. The P values of these estimated coefficients were not statistically significant after correction for multiple comparisons, suggesting that these additional coefficients would not be needed for modeling mean diffusivity values of tracts other than the PLIC_R.

Assessment of normality for chosen linear mixed effects models.

We plotted residuals of the selected best models for the outcome measures FA_CC (model 4) and MD_PLIC_R (model 6) (Figure 4) to assess the normality for both test outcome measures. Figure 4 shows that the residuals spread out evenly but slightly increased their absolute values along with the logarithm of age. This might have been a sign of within-group heteroscedasticity. Thus, we updated the selected models with heteroscedastic within-group errors by extending the multivariate normal within-group variance model to a variance model represented by a power of the absolute value of the fitted value $\mathit{Var}({ϵ}_{\mathit{ij}})={\sigma }^2{|v_{\mathit{ij}}|}^2$, in which ${\sigma }^2$ is a shared variance parameter and $v_{\mathit{ij}}$ represents the fitted value. It specifies a variance model in which within-group variances increase linearly with the fitted values, a common situation discovered in the outcomes related to growth.

Figure 4.

Residual plots of selected best models for the outcome measures (A) FA_CC (model 4) and (B) MD_PLIC_R (model 6). FA, fractional anisotropy; MD, mean diffusivity.

The likelihood ratio test comparing the selected models with the extended models with heteroscedastic within-group errors showed a P value of .504 pertaining to the outcome measure FA_CC and a P value of .380 for the outcome measure MD_PLIC_R. These results confirmed that the above selected models were preferable over the extended models.

Linear Mixed Effects Models Applied to All Tracts

We used the respective chosen linear mixed effects models to characterize the pattern of changes of fractional anisotropy and mean diffusivity values for all 27 tracts. We used model 4 as the basis for analyzing fractional anisotropies for all tracts and model 6 as the basis for analyzing mean diffusivities for all tracts. Table 2 and Table 3 display summaries of linear mixed effects models for fractional anisotropy and mean diffusivity values, respectively, including estimated coefficients, their 95% confidence intervals, and their P values.

Table 2.

Linear Mixed Effects Regression Modeling of the FA of Various White Matter Tracts, Showing Estimated Coefficients With 95% CIs and P Values.

Tract	Positive ADOS-2 classification		Natural logarithm of age
	Estimated coefficient (95% CI)	P	Estimated coefficient (95% CI)	P
Arcuate fasciculus, left dorsal	0.0101 (−0.0050, 0.0253)	.1909	0.0407 (0.0364, 0.0449)	<.0001
Arcuate fasciculus, left ventral	0.0076 (−0.0058, 0.0211)	.2658	0.0353 (0.0318, 0.0389)	<.0001
Arcuate fasciculus, right dorsal	0.0044 (−0.0076, 0.0164)	.472	0.0409 (0.0376, 0.0442)	<.0001
Arcuate fasciculus, right ventral	0.0019 (−0.0102, 0.0139)	.76	0.0316 (0.0283, 0.0348)	<.0001
Anterior limb internal capsule brainstem projections, left	0.0018 (−0.0082, 0.0119)	.7185	0.0380 (0.0343, 0.0417)	<.0001
Anterior limb internal capsule brainstem projections, right	−0.0012 (−0.0112, 0.0088)	.8099	0.0407 (0.0368, 0.0446)	<.0001
Anterior thalamic radiation, left	0.0049 (−0.0082, 0.0180)	.4635	0.0314 (0.0275, 0.0353)	<.0001
Anterior thalamic radiation, right	0.0023 (−0.0074, 0.0121)	.6375	0.0293 (0.0252, 0.0333)	<.0001
Corpus callosum	0.0093 (−0.0004, 0.0190)	.0612	0.0428 (0.0395, 0.0462)	<.0001
Cingulum, left	0.0042 (−0.0068, 0.0152)	.4489	0.0316 (0.0279, 0.0353)	<.0001
Cingulum, right	0.0032 (−0.0059, 0.0122)	.4918	0.0288 (0.0256, 0.0320)	<.0001
Corticospinal tract, left	0.0038 (−0.0149, 0.0224)	.6897	0.0347 (0.0304, 0.0391)	<.0001
Corticospinal tract, right	0.0065 (−0.0098, 0.0229)	.4341	0.0271 (0.0222, 0.0321)	<.0001
Inferior cerebellar peduncle, left	0.0036 (−0.0039, 0.0110)	.348	0.0391 (0.0357, 0.0426)	<.0001
Inferior cerebellar peduncle, right	0.0049 (−0.0024, 0.0122)	.1881	0.0385 (0.0349, 0.0420)	<.0001
Inferior longitudinal fasciculus, left	−0.0011 (−0.0116, 0.0095)	.8384	0.0349 (0.0314, 0.0383)	<.0001
Inferior longitudinal fasciculus, right	0.0024 (−0.0082, 0.0130)	.6529	0.0301 (0.0270, 0.0333)	<.0001
Middle cerebellar peduncle, left	0.0014 (−0.0095, 0.0123)	.8008	0.0492 (0.0447, 0.0537)	<.0001
Middle cerebellar peduncle, right	0.0073 (−0.0035, 0.0181)	.1884	0.0475 (0.0430, 0.0520)	<.0001
Optic-radiation, left	0.0063 (−0.0082, 0.0208)	.3955	0.0304 (0.0258, 0.0349)	<.0001
Optic-radiation, right	0.0049 (−0.0078, 0.0176)	.4435	0.0250 (0.0208, 0.0291)	<.0001
Posterior limb internal capsule, left	0.0024 (−0.0094, 0.0141)	.6925	0.0308 (0.0274, 0.0342)	<.0001
Posterior limb internal capsule, right	−0.0001 (−0.0093, 0.0092)	.9886	0.0271 (0.0239, 0.0303)	<.0001
Superior cerebellar peduncle, left	0.0027 (−0.0074, 0.0128)	.6003	0.0362 (0.0318, 0.0406)	<.0001
Superior cerebellar peduncle, right	0.0061 (−0.0047, 0.0170)	.2648	0.0361 (0.0320, 0.0403)	<.0001
Uncinate fasciculus, left	0.0029 (−0.0084, 0.0142)	.6098	0.0285 (0.0255, 0.0314)	<.0001
Uncinate fasciculus, right	0.0060 (−0.0027, 0.0147)	.1755	0.0256 (0.0226, 0.0287)	<.0001

Abbreviations: ADOS-2, Autism Diagnostic Observation Schedule–Second Edition; CI, confidence interval.

Table 3.

Linear Mixed Effects Regression Modeling of the MD of Various White Matter Tracts, Showing Estimated Coefficients With 95% Confidence Intervals and P values.

	Positive ADOS-2 classification		Natural logarithm of age (y)		Natural logarithm of age (y) ^ 2
Tract	Estimated coefficient (95% CI)	P	Estimated coefficient (95% CI)	P	Estimated coefficient (95% CI)	P
Arcuate fasciculus, left dorsal	−9.034E–6 (−3.497E–5, 1.690E–5)	.4944	−8.602E–5 (−9.253E–5, −7.952E–5)	<.0001	1.247E–5 (6.801E–6, 1.813E–5)	<.0001
Arcuate fasciculus, left ventral	−4.737E–6 (−3.282E–5, 2.334E–5)	.7404	−8.435E–5 (−9.087E–5, −7.783E–5)	<.0001	2.361E–5 (1.777E–5, 2.945E–5)	<.0001
Arcuate fasciculus, right dorsal	8.897E–6 (−1.113E–5, 2.892E–5)	.3838	−8.533E–5 (−9.101E–5, −7.966E–5)	<.0001	2.358E–5 (1.847E–5, 2.868E–5)	<.0001
Arcuate fasciculus, right ventral	4.436E–6 (−2.188E–5, 3.076E–5)	.7406	−8.072E–5 (−8.727E–5, −7.417E–5)	<.0001	2.247E–5 (1.660E–5, 2.834E–5)	<.0001
Anterior limb internal capsule brainstem projections, left	−7.050E–6 (−2.460E–5, 1.050E–5)	.4309	−6.440E–5 (−7.163E–5, −5.717E–5)	<.0001	5.516E–7 (−5.996E–6, 7.099E–6)	.8691
Anterior limb internal capsule brainstem projections, right	−6.003E–7 (−1.808E–5, 1.688E–5)	.9462	−5.817E–5 (−6.616E–5, −5.019E–5)	<.0001	4.180E–6 (−3.029E–6, 1.139E–5)	.2581
Anterior thalamic radiation, left	−3.357E–7 (−2.302E–5, 2.235E–5)	.9768	−7.257E–5 (−7.811E–5, −6.703E–5)	<.0001	5.492E–6 (5.310E–7, 1.045E–5)	.032
Anterior thalamic radiation, right	−2.950E–6 (−2.556E–5, 1.966E–5)	.7978	−6.694E–5 (−7.562E–5, −5.826E–5)	<.0001	8.268E–6 (4.223E–7, 1.611E–5)	.0411
Corpus callosum	−1.016E–5 (−3.604E–5, 1.573E–5)	.4416	−9.522E–5 (−1.018E–4, −8.863E–5)	<.0001	1.243E–5 (6.520E–6, 1.834E–5)	.0001
Cingulum, left	−6.830E–6 (−2.237E–5, 8.708E–6)	.3889	−7.890E–5 (−8.453E–5, −7.326E–5)	<.0001	1.819E–5 (1.310E–5, 2.327E–5)	<.0001
Cingulum, right	−6.559E–6 (−2.417E–5, 1.105E–5)	.465	−7.897E–5 (−8.472E–5, −7.321E–5)	<.0001	1.843E–5 (1.325E–5, 2.361E–5E–5)	<.0001
Corticospinaltract, left	8.839E–7 (−1.588E–5, 1.765E–5)	.9175	−5.294E–5 (−6.001E–5, −4.588E–5)	<.0001	5.971E–6 (−4.335E–7, 1.237E–5)	.0702
Corticospinaltract, right	−2.792E–6 (−1.914E–5, 1.356E–5)	.7374	−5.478E–5 (−6.171E–5, −4.785E–5)	<.0001	1.305E–5 (6.765E–6, 1.933E–5)	.0001
Inferior cerebellar peduncle, left	−1.363E–5 (−3.242E–5, 5.168E–6)	.1571	−4.451E–5 (−5.552E–5, −3.349E–5)	<.0001	1.224E–5 (2.153E–6, 2.232E–5)	.019
Inferior cerebellar peduncle, right	−2.071E–5 (−4.069E–5, −7.279E–7)	.0445	−5.430E–5 (−6.799E–5, −4.062E–5)	<.0001	2.248E–5 (9.893E–6, 3.507E–5)	.0007
Inferior longitudinal fasciculus, left	−1.281E–6 (−3.241E–5, 2.985E–5)	.9356	−7.995E–5 (−8.709E–5, −7.281E–5)	<.0001	2.648E–5 (2.008E–5, 3.287E–5)	<.0001
Inferior longitudinal fasciculus, right	7.113E–6 (−2.331E–5, 3.753E–5)	.6461	−7.822E–5 (−8.540E–5, −7.103E–5)	<.0001	2.375E–5 (1.731E–5, 3.018E–5)	<.0001
Middle cerebellar peduncle, left	−1.530E–5 (−4.324E–5, 1.265E–5)	.284	−7.106E–5 (−8.869E–5, −5.343E–5)	<.0001	1.531E–5 (−8.730E–7, 3.149E–5)	.0662
Middle cerebellar peduncle, right	−1.051E–5 (−3.729E–5, 1.626E–5)	.4413	−6.287E–5 (−8.081E–5, −4.494E–5)	<.0001	1.789E–5 (1.399E–6, 3.438E–5)	.0356
Optic-radiation, left	−3.547E–6 (−5.274E–5, 4.565E–5)	.8873	−6.777E–5 (−7.732E–5, −5.823E–5)	<.0001	1.671E–5 (8.185E–6, 2.524E–5)	.0002
Optic-radiation, right	3.631E–6 (−4.243E–5, 4.969E–5)	.8769	−5.944E–5 (−7.006E–5, −4.882E–5)	<.0001	8.442E–6 (–1.060E–6, 1.794E–5)	.0842
Posterior limb internal capsule, left	3.542E–7 (−1.567E–5, 1.638E–5)	.9654	−4.826E–5 (−5.523E–5, −4.129E–5)	<.0001	1.105E–5 (4.735E–6, 1.737E–5)	.0008
Posterior limb internal capsule, right	1.121E–5 (−4.421E–6, 2.684E–5)	.1616	−4.500E–5 (−5.163E–5, −3.837E–5)	<.0001	1.166E–5 (5.643E–6, 1.767E–5)	.0002
Superior cerebellar peduncle, left	−2.093E–5 (−5.183E–5, 9.976E–6)	.1859	−1.396E–5 (−2.902E–5, 1.113E–6)	.072	2.820E–5 (1.448E–5, 4.191E–5)	.0001
Superior cerebellar peduncle, right	−1.967E–5 (−4.872E–5, 9.386E–6)	.1861	−2.835E–5 (−4.179E–5, −1.492E–5)	.0001	2.098E–5 (8.771E–6, 3.319E–5)	.001
Uncinate fasciculus, left	−1.378E–5 (−3.164E–5, 4.089E–6)	.1326	−6.924E–5 (−7.447E–5, −6.401E–5)	<.0001	1.135E–5 (6.650E–6, 1.605E–5)	<.0001
Uncinate fasciculus, right	−9.156E–6 (−2.625E–5, 7.942E–6)	.2945	−6.729E–5 (−7.300E–5, −6.159E–5)	<.0001	1.290E–5 (7.761E–6, 1.804E–5)	<.0001

Abbreviations: ADOS-2, Autism Diagnostic Observation Schedule–Second Edition; CI, confidence interval; MD, mean diffusivity.

For all tracts, fractional anisotropy values significantly increased with the natural logarithm of age (all P values < .0001, and these P values remained statistically significant after correction for multiple comparisons). For all tracts except for superior cerebellar peduncle left, mean diffusivities significantly decreased with the natural logarithm of age (all P values ≤.0001, and these P values remained statistically significant after correction for multiple comparisons). The main statistically significant or trend to statistically significant effect of positive Autism Diagnostic Observation Schedule–Second Edition classification was with respect to the outcome measure of fractional anisotropy corpus callosum (estimated coefficient of positive Autism Diagnostic Observation Schedule–Second Edition classification term: 0.0093, P value =.0612) and mean diffusivity right inferior cerebellar peduncle (estimated coefficient of positive Autism Diagnostic Observation Schedule–Second Edition classification term: −0.00002071, P value=.0445). However, neither of these coefficients were statistically significant after correction for multiple comparisons. No statistical significance was confirmed for the main effect of positive Autism Diagnostic Observation Schedule–Second Edition classification on the fractional anisotropies and mean diffusivity values for the rest of the tracts.

Discussion

In this work, we have carefully evaluated different linear mixed effects models and chosen ones optimally suited for detecting changes in diffusion tensor imaging metrics of white matter tracts in infants and toddlers with tuberous sclerosis complex with and without autism risk behaviors as noted by the Autism Diagnostic Observation Schedule–Second Edition. For modeling longitudinal changes in fractional anisotropy and mean diffusivity values of these tracts, we have designated model 4 and model 6, respectively, as the optimal models, with the outcome measure being the diffusion tensor imaging metric and the main independent variables being the natural logarithm of age and 36-month positive Autism Diagnostic Observation Schedule–Second Edition classification. Compared with model 4, model 6 has an additional quadratic term of the natural logarithm of age. We have applied these selected models to fractional anisotropy and mean diffusivity values of white matter tracts using data from the TACERN, showing a possible impact of positive Autism Diagnostic Observation Schedule–Second Edition classification on the trajectory of fractional anisotropy of the corpus callosum (increased fractional anisotropy values in those with a positive Autism Diagnostic Observation Schedule–Second Edition classification) and mean diffusivity of the right inferior cerebellar peduncle (decreased mean diffusivity values in those with a positive Autism Diagnostic Observation Schedule–Second Edition classification), though these results were not statistically significant after correction for multiple comparisons.

We considered multiple aspects during our process of linear mixed effects model selection. We conducted our analysis under a reasonable assumption that the data were missing completely at random.²⁶ In the linear mixed effects models, we did not find any graphically unusual patterns or within-group heteroscedasticity; we determined that the cross-sectional effect of natural logarithm of age was a “nuisance” factor and that there was no interaction between the natural logarithm of age and 36-month positive Autism Diagnostic Observation Schedule–Second Edition classification. In essence, we determined that with careful linear mixed effects model selection and adjustment, this type of parametric modeling for repeated measures can properly characterize the pattern and change of fractional anisotropy and mean diffusivity values of white matter tracts, allowing hypothesis testing regarding the binary group variable of 36-month positive Autism Diagnostic Observation Schedule–Second Edition classification.

The approach of using repeated measures analysis for diffusion tensor imaging tractography of white matter tracts in tuberous sclerosis complex offers advantages compared with a cross-sectional approach involving single time points. The latter has the downside of inadequately reflecting the shape and position of neuroanatomic structures in each individual. In contrast, our model incorporates tractography for each MRI scan of an individual.

In our application of the 2 selected linear mixed effects models to fractional anisotropy and mean diffusivity values of all white matter tracts in the TACERN data, the finding of increased fractional anisotropy values and decreased mean diffusivity values across the majority of white matter tracts with increasing scan age was not surprising. Brain development in the first 2-3 years of life is a dynamic process, which is supported by changes in diffusion properties of both white matter and gray matter structures. For example, in one cross-sectional study of 30 healthy children (ages 1 month-17 years), average diffusion constant values decreased in gray matter and white matter structures, particularly during the first 2 years of life.²⁷ In another study, which involved retrospective analysis of diffusion tensor imaging data in 202 healthy children (age 0-18 years), there was a rapid increase in fractional anisotropy values and decrease in mean diffusivity values of white matter tracts in the first 2-3 years of life.²⁸

More surprising is the finding that a positive Autism Diagnostic Observation Schedule–Second Edition classification was not related to increases (or decreases) in fractional anisotropy values of any of the white matter tracts, except for possibly the corpus callosum. A previous cross-sectional study comparing diffusion tensor imaging metrics of the corpus callosum across 4 groups (tuberous sclerosis complex, tuberous sclerosis complex and autism spectrum disorder, autism spectrum disorder, and healthy controls) (age 1-27 years) noted that the comorbid diagnosis of autism spectrum disorder in an individual with tuberous sclerosis complex may have an additive effect on corpus callosum fractional anisotropy values, although conclusions about the subgroup represented by those aged <3 years were not reachable because of the small number of participants within the subgroup.¹⁹ Moreover, in the region of interest–based longitudinal analysis our group had previously conducted using the TACERN data from 3 to 24 months of age, albeit using a different linear mixed effects model, the presence of a positive Autism Diagnostic Observation Schedule–Second Edition classification led to decreases in fractional anisotropy values of several of the white matter tracts, including the arcuate fasciculus, cingulum, corpus callosum, anterior limbs of the internal capsule, and the sagittal stratum.²⁰

In the context of these findings from our prior work,²⁰ there are a few possible explanations for the unexpected finding that a positive Autism Diagnostic Observation Schedule–Second Edition classification was not related to fractional anisotropy values for any of the tracts in the present study. First, the trajectory of white matter development in the first 2 years of life in tuberous sclerosis complex may be different from that in the first 3 years of life. Second, whereas our previous study performed region of interest–based analysis, this study involved tract-based analysis. Third, the numbers of participants in the current cohort is a subset of the 108 participants included in our previous study.

In the current study, decreased mean diffusivity of right inferior cerebellar peduncle was related to a positive Autism Diagnostic Observation Schedule–Second Edition classification (though this finding was not statistically significant after correction for multiple comparisons). It is worthwhile to note that in general, studies involving diffusion tensor imaging analysis of cortico-cerebellar connectivity in relation to autism spectrum disorder have led to mixed results.²⁹ One study of a population of children with autism spectrum disorder (n=24 males and n=3 females, mean age 5.0 years, range=2.6-9 years) vs typically developing controls used a region of interest approach and identified increased mean diffusivity of bilateral superior cerebellar peduncles in the autism spectrum disorder group compared to the controls.³⁰ However, generalizability of these findings to the current cohort is limited, especially given the older, largely male cohort. In a volumetric neuroimaging study of 1-year-olds with tuberous sclerosis complex, cerebellar volume was related to neurodevelopmental severity (as measured by the Mullen Scales of Early Learning) in those with pathogenic TSC2 variants, suggesting that the cerebellum may play a role in brain functioning in tuberous sclerosis complex.³¹ Further study is needed to evaluate longitudinal, microstructural white matter changes involved in cerebellar pathways in infants and young children with tuberous sclerosis complex.

Our study had some limitations. Nineteen percent of participants had only 1 MRI scan. However, the observations from these patients were also included in the data analysis, as the unbalanced longitudinal data can still be fit to the linear mixed effects models with maximum log-likelihood or restricted log-likelihood. We used autism spectrum disorder classification using Autism Diagnostic Observation Schedule–Second Edition, which is not applicable to every individual with tuberous sclerosis complex, particularly those with a mental age < 18 months, for whom the Autism Diagnostic Observation Schedule–Second Edition is not validated. Importantly, more than half of individuals with tuberous sclerosis complex have intellectual disability,³² many of whom may be below a mental age of 18 months at a chronologic age of 3 years. In addition, there are other approaches for arriving at an autism spectrum disorder classification, including best estimate clinical diagnosis through multidisciplinary assessment.³³ Future directions could involve applications of linear mixed effects models developed here with different approaches for autism spectrum disorder ascertainment.

In summary, we have developed linear mixed effects models for assessing changes in fractional anisotropy and mean diffusivity of white matter tracts in infants and toddlers with tuberous sclerosis complex. Applying these models to the TACERN data, we have highlighted that positive Autism Diagnostic Observation Schedule–Second Edition classification at 36 months may be potentially related to changes in the fractional anisotropy corpus callosum and mean diffusivity right inferior cerebellar peduncle. If our findings are replicated in larger cohorts, they could potentially highlight the role of early diffusion tensor imaging in children with tuberous sclerosis complex to identify those at high risk for having an autism spectrum disorder diagnosis at 36 months of age. However, future studies are needed to explore other contributors of heterogeneity in models of longitudinal trajectory of fractional anisotropy and mean diffusivity values of various white matter tracts in tuberous sclerosis complex.

TACERN Study Group

Simon K. Warfield, PhD, Jurriaan M. Peters, MD, PhD, Monisha Goyal, MD, Deborah A. Pearson, PhD, Marian E. Williams, PhD, Ellen Hanson, PhD, Nicole Bing, PsyD, Bridget Kent, MA, CCC-SLP, Sarah O’Kelley, PhD, Rajna Filip-Dhima, MS, Kira Dies, ScM, CGC, Stephanie Bruns, Benoit Scherrer, PhD, Gary Cutter, PhD, Donna S. Murray, PhD, Steven L. Roberds, PhD, Jamie Capal, MD, Peter E. Davis, MD (see Supplementary Material).