Reviewer #2 (Public Review):
In this manuscript, Wang and colleagues analyze the shapes of cerebral cortices from several primate species, including subgroups of young and old humans, to characterize commonalities in patterns of gyrification, cortical thickness, and cortical surface area. The work builds on the scaling law introduced previously by co-author Mota, and Herculano-Houzel. The authors state that the observed scaling law shares properties with fractals, where shape properties are similar across several spatial scales. One way the authors assess this is to perform a "cortical melting" operation that they have devised on surface models obtained from several primate species. The authors also explore differences in shape properties between the brains of young (~20 year old) and old (~80) humans. My main criticism of this manuscript is that the findings are presented in too abstract a manner for the scientific contribution to be recognized.
1. The series of operations to coarse-grain the cortex illustrated in Figure 1, constitute a novel procedure, but it is not strongly motivated, and it produces image segmentations that do not resemble real brains. The process to assign voxels in downsampled images to cortex and white matter is biased towards the former, as only 4 corners of a given voxel are needed to intersect the original pial surface, but all 8 corners are needed to be assigned a white matter voxel (section S2). This causes the cortical segmentation, such as the bottom row of Figure 1B, to increase in thickness with successive melting steps, to unrealistic values. For the rightmost figure panel, the cortex consists of several 4.9-sided voxels and thus a >2 cm thick cortex. A structure with these morphological properties is not consistent with the anatomical organization of a typical mammalian neocortex.
2. For the comparison between 20-year-old and 80-year-old brains, a well-documented difference is that the older age group possesses more cerebral spinal fluid due to tissue atrophy, and the distances between the walls of gyri becomes greater. This difference is born out in the left column of Figure 4c. It seems this additional spacing between gyri in 80-year-olds requires more extensive down-sampling (larger scale values in Figure 4a) to achieve a similar shape parameter K as for the 20-year-olds. A case could be made that the familiar way of describing brain tissue - cortical volume, white matter volume, thickness, etc. - is a more direct and intuitive way to describe differences between young and old adult brains than the obscure shape metric described in this manuscript. At a minimum, a demonstration of an advantage of the Figure 4a and 4b analyses over current methods for interpreting age-related differences would be valuable.
3. In Discussion lines 199-203, it is stated that self-similarity, operating on all length scales, should be used as a test for existing and future models of gyrification mechanisms. First, the authors do not show, (and it would be surprising if it were true) that self-similarity is observed for length scales smaller than the acquired MRI data for any of the datasets analyzed. The analysis is restricted to coarse (but not fine)-graining. Therefore, self-similarity on all length scales would seem to be too strong a constraint. Second, it is hard to imagine how this test could be used in practice. Specific examples of how gyrification mechanisms support or fail to support the generation of self-similarity across any length scale, would strengthen the authors' argument.
Some additional, specific comments are as follows:
4. The definition of the term A_e as the "exposed surface" was difficult to follow at first. It might be helpful to state that this parameter is operationally defined as the convex hull surface area. Also, for the pial surface, A_t, there are several who advocate instead for the analysis of a cortical mid-thickness surface area, as the pial surface area is subject to bias depending on the gyrification index and the shape of the gyri. It would be helpful to understand if the same results are obtained from mid-thickness surfaces.
5. In Figure 2c, the surfaces get smaller as the coarse-graining increases, making it impossible to visually assess the effects of coarse-graining on the shapes. Why aren't all cortical models shown at the same scale?
6. Text in Section 3.2 emphasizes that K is invariant with scale (horizontal lines in Figure 3), and asserts this is important for the formation of all cortices. However, I might be mistaken, but it appears that K varies with scale in Figure 4a, and the text indicates that differences in the S dependence are of importance for distinguishing young vs. old brains. Is this an inconsistency?