For each target curve s, Jk(s) represents the deformation marker at point k of the template curve. Statistical analyses were conducted using the following linear model

In this model γ(s) is a binary group variable: γ(s) equals to 1 when the target curve s belongs to the FES group and γ(s) equals to 0 when the target curve s belongs to the HC group. Xcov(s) denotes the covariate information and we covaried for age, gender, and total intracranial volume (TIV) in this study. εk(s) represents a Gaussian noise variable. For all points k on the template curve, we tested the null hypothesis that βk, 1 = 0. We used Fisher's method of randomization and permutation tests to quantify the statistical significance (p-value) of the difference between two groups under comparison (FES vs. HC within the entire group, the male group, as well as the female group) and the p-values were corrected for multiple comparisons by controlling the family-wise error rate (FWER) at a level of P ≤ 0.05. In the process of permutation tests, we generated 10,000 uniformly distributed random permutations by employing Monte Carlo simulations. We used −βk, 1 to denote the degree of a group difference, so that a positive value represents inward-deformation in the FES group relative to the HC group whereas a negative value represents expansion. We employed the same linear model and the same statistical analysis method to compare the CC area, gCC area, bCC area, and sCC area between HC and FES within the entire group, the male group, and the female group.

To investigate the interaction effect between gender and the FES status on CC's morphology (including both global area and localized shape), we first employed the above linear regression model considering also interaction effect. Specifically, the gender and group variables were included as two main factors and the age and TIV were included as two covariates. Interaction of the two main factors (gender and group) was also included in the model. Gender-specific post-hoc group comparison analyses would then be performed if that the interaction term was statistically significant. When analyzing each single-gender group, we only co-varied for age and TIV.

Cohen's d (54) was used to measure the effect size and to quantify the extent of a group difference in both global area analysis and localized shape analysis. There is a general explanation for the numerical value of Cohen's d: when d is around or smaller than 0.2, it suggests a small group difference; when d is around 0.5, it suggests a medium group difference; when d is larger than 0.8, it suggests a large group difference. The analysis flow of the entire pipeline is shown in Figure 1.

Analysis flow of the entire pipeline.

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