Introduction

Although the cerebral cortex varies greatly in size, folding degree and patterns across species in adult mammalian brains, an intrinsic relationship between surface area, cortical thickness and folding was found. Specifically, given A_t as the total surface area, T as the average cortical thickness, A_e as the exposed surface area, the mathematic description of A_tT^1/2=kA_e^1.305 was discovered ¹, where k is a constant. This was further confirmed in recent MRI studies of older human children and adults ², and was thought to closely relate to a mechanism of cortical folding that minimizes an effective free energy term ^1,2 and predicts the relation of A_tT^1/2=kA_e^5/4. However, it remains unclear whether this relationship presents in human neonates, and how it evolves during the dynamic brain development in the first two years, with dramatic increase of surface area, cortical thickness and folding ^3,4. To fill this knowledge gap, we jointly analyze surface area, cortical thickness, and folding at birth, 1, and 2 years of age, using 219 longitudinal MRI scans.

Methods

The complete sets of 219 longitudinal MRI scans at 0, 1, and 2 years of age were acquired from 73 normal infants (42 males and 31 females) ^3,4. All infants were scanned unsedated and no significant age difference between males and females was found at each scanning age. Images were acquired on a Siemens head-only 3T scanner. T1-weighted images (160 sagittal slices) were obtained by using the 3D magnetization-prepared rapid gradient echo sequence (TR, 1900 ms; TE, 4.38 ms; inversion time, 1100 ms; flip angle, 7°; resolution, 1 × 1 × 1 mm3). T2-weighted images (70 transverse slices) were acquired with turbo spin-echo sequences (TR, 7380 ms; TE, 119 ms; flip angle, 150°; resolution, 1.25 × 1.25 × 1.95 mm3). Each MR image was processed using an infant-specific computational pipeline ^3,4. Briefly, it included the following major steps: 1) skull stripping and cerebellum removal; 2) correction of intensity inhomogeneity; 3) tissue segmentation using a longitudinally-guided level-set method; 4) separation of left/right hemispheres; 5) topology correction; 6) reconstruction of inner and outer cortical surfaces using a deformable surface method; 7) reconstruction of the cerebral hull surface (the interface running along the margins of gyri without dipping into sulci). The cortical thickness for each vertex was computed as the average value of the minimum distance between inner and outer surfaces. By excluding non-cortical regions, the average cortical thickness T and the total surface area A_t were computed based on the remaining vertices on the outer surface. By excluding non-cortical regions (mapped from the outer surface) on cerebral hull surface, the exposure surface area A_e was computed based on the remaining vertices on the cerebral hull surface.

Results

Fig. 1 displays the distributions of log₁₀(A_e) and log₁₀(A_t*T^1/2) with the age for the 73 subjects. As we can see, both variables increase dynamically in the first year and then continue to increase in the second year. Meanwhile, both values are generally larger in males than in females at each age, consistent with the adult study ². Fig. 2 shows the relationship between x=log₁₀(A_e) and y=log₁₀(A_t*T^1/2) and their fitting models at 0, 1 and 2 years of age for all 73 subjects. At each age, although there is large inter-subject variability in x and y, there clearly exists a linear fitting model, with p < 0.00001. We carried out a multiple linear regression analysis with gender as a categorical variable, and found no significant gender effect at each age, agreeing with the adult MRI study ². During the first year, the fitting model changes significantly in both slope and offset, from y = 1.477x - 1.4966 (R² = 0.9452) at year 0 to y = 1.2868x - 0.64 (R² = 0.9037) at year 1, which then changes only subtly to y = 1.2632x - 0.5219 (R² = 0.9358) at year 2. Of note, the slopes for year 1 and year 2 are close to the theoretically predicted slope ¹ of 1.25.

Discussion and Conclusion

We systematically investigated the relationship between surface area, cortical thickness, and folding in infants. We unprecedentedly revealed that this relationship is gender-independent, but age-specific, with a significant change in the first year, likely related to the differential biological mechanisms and developmental trajectories of surface area, cortical thickness and folding ^3,4. In future, we will further investigate the age-specific relationship using more densely sampled data points during the first year and also study how neurodevelopmental disorders change this relationship.

Acknowledgements

This work was supported in part by NIH grants (MH100217, MH108914 and MH107815).