Figure 1.
Mechanical Effects in Tissue Folding
(A) A simple mechanical model illustrates the deformation of tissue subjected to tangential force (F1) at an eccentricity (e) from the points of attachment, causing a moment, M. This mechanical deformation is represented by the general relation M = eF.
(B) The moment M causes the sheet to bend in a convex shape. The same principles apply to the second point of connection attachment, subjected to force F2, resulting in a convexity (gyrus) between connected regions, while a concavity (sulcus) forms between unconnected or weakly connected regions by default.
(C) Relative thickness (i.e., the ratio of the thickness of upper to lower cortical layers), changes when a 2-D section of cortical tissue, on the left, is bent into an annulus, on the right. Specifically, the relative thickness of the bent upper layers, d2, is smaller than that of the lower layers, d1. A mathematical derivation of these relations is given in Materials and Methods (“Bending a slab of layered neural tissue”).
Figure 2.
Three Types of Trajectories of Corticocortical Projections
The diagram shows straight (st; thick solid line), intermediate (im; intermediate dashed line), and curved (cu; thin dashed line) projections that link a tracer injection site (dark spot) with different areas, shown in a coronal section through the rhesus monkey prefrontal cortex. The curvature (c) of the trajectories is determined by the relation c = d/x, in which x is the minimum distance (in 3-D Euclidean space) between projection origin and termination, and d the maximum deviation of the actual projection from the minimum distance path. These measures are indicated for examples of curved and intermediate projections, resulting in curvatures of ccu = 0.71 and cim = 0.26. Since the trajectory of the straight projection follows the minimum distance path, its curvature is zero. The thickness of the projections depicts the posited link between connection density and axonal trajectory. Axes of section: medial is to the left; dorsal, top.
Figure 3.
Example of Three Types of Trajectories Linking Prefrontal Cortices
(A) Low-power darkfield photomicrograph of a coronal section through a middle level of the prefrontal cortex of a rhesus monkey brain showing an injection of HRP-WGA in area 9 (white area, “is”). Several projection sites can be seen (arrows). One projection with many labeled neurons is seen in the adjacent part of lateral area 9 (top, thick arrows); another projection is seen inferiorly in area 14 (medium arrows); a light projection is found in ventral area 46 below the principal sulcus (thin arrows), and another projection is seen in area 11. The dashed lines drawn in the white matter (appearing blue in darkfied) represent the shortest possible trajectory of axons in three of the projection sites. Axons linking lateral area 9 with the injection site (top) can take a fairly straight course. Labeled axons leaving the injection site are visible at this level (pink fibers in white matter), and some cross directly through layer VI (star). Axons linking area 14 with the injection site take a mildly deflected course through the white matter. Some labeled axons are seen exiting the injection site (pink fibers in white matter, below the depths of the cingulate [Cg] sulcus), and course inferiorly along the retrograde transport route to projection neurons. Axons linking ventral area 46 with the injection site travel below the principal sulcus (which is deep at this level) and must take a curved course.
(B) High magnification of a site from an adjacent section to the one depicted in (A), showing that some axons (gold) coursing below the injection site take a straight course through the deep layers of the cingulate cortex. The approximate limit of the white matter is denoted by the large arrow (bottom left). The tissue was photographed under dark field illumination to show labeled axons in the white matter (gold, to the left of the large arrow), as well as axons coursing among neurons (red, some indicated by arrows), photographed under bright field illumination. The two photographs were merged.
(C) Higher magnification of the mildly deflected projection in area 14 (from boxed area C in [A]) showing labeled neurons under brightfield illumination (blue pyramids). The labeled neurons at the top are in layer III, the ones at the bottom left corner are in layer V.
(D) Higher magnification of the curved projection from ventral area 46 (boxed area D from [A]), shows a few labeled neurons in layer III (blue) under brightfield illumination. The section was counterstained with neutral red.
Scale bars: (A) = 1 mm; (B–D), 100 μm. Orientation axes: medial, to the right; dorsal, on top.
Cg, cingulate; MO, medial orbital; P, principal; Ro, rostral.
Figure 4.
Examples of the Relationship of Projection Density to Axonal Trajectory
(A) Low-power brightfield photomicrograph of a coronal section through the posterior prefrontal cortex of a rhesus monkey brain, showing the halo of an injection of HRP-WGA in ventral area 46, below the principal sulcus (dark area). Green arrows point to a projection site in area 46 in the depths of the lower bank of the principal sulcus (dark blotch). Another projection is found in the upper bank of the lower limb of the arcuate (“A”) sulcus (dark blotch, red arrow); axons from these projection sites can take a mildly deflected or straight course to the injection site.
(B) Top: higher magnification under darkfield illumination of the depths and lower bank of the principal sulcus in the same section shows that the projection in ventral area 46 has many labeled neurons (gold, green arrows), and labeled axons (pink, white arrowhead) as they leave the halo of the injection site. Note that the dense projection abruptly terminates as the sulcus curves towards the upper bank of the principal sulcus, towards dorsal area 46. The magnified site at the lower right inset (blue arrow, brightfield illumination) shows only a few scattered labeled neurons in dorsal area 46 (white arrowheads), taken from the region with the corresponding blue arrows in (A, brightfield) and (B, darkfield). In contrast, the “straight” projection in the arcuate sulcus has many labeled neurons (lower left inset in [B], red arrow; darkfield illumination). The section was counterstained with neutral red.
(C) Low-power darkfield photomicrograph of a coronal section through the caudal prefrontal cortex of a rhesus monkey brain showing the halo of the injection site in area OPAll/OPro (white area, bottom, center), and a resultant robust projection site of labeled neurons (white) arranged in a columnar pattern in area 25 (white arrows). The labeled fibers (white) around the putamen (Put) and in the internal capsule (interposed between the caudate and putamen, white) link the injection site with subcortical structures.
(D) The columns of labeled neurons are shown at higher magnification. The inferiorly situated broad column of neurons (thick arrow) has a fairly straight course from the injection site, while the one above is deflected. Axons leaving the halo of the injection site are visible at this level (white fibers in white matter, which appears blue under darkfield illumination).
Scale bars: (A), (C), 1 mm; (B), (D), 0.5 mm. Orientation axes: Medial, is to the left; dorsal, at the top.
Figure 5.
Relationship of Axonal Trajectories to Connections
(A) Relative densities of individual projections in the different trajectory classes, straight (st), intermediate (im), and curved (cu). Horizontal lines denote median values. (Spearman's rank correlation of individual projections with trajectory class: ρ = −0.27, p < 0. 00001).
(B) Relative distribution of projection trajectories. Relative density of projections (on the x-axis) was calculated as the number of corticocortical projection neurons in each area, divided by the total number of labeled neurons found for all areas in the prefrontal cortex for one injection case. The y-axis indicates the relative frequency of all projections in the given density interval (normalized by all projections in a trajectory class). The diagram demonstrates that weak projections (<10% of relative density) tended to form mostly curved, then intermediate and straight trajectories, whereas greater densities (>10%) resulted predominantly in straight trajectories.
(C) Average cumulative density of straight, intermediate, and curved projections originating from individual prefrontal areas. The individual density values also followed the trend displayed here (rank correlation, ρ = −0.50, p < 0.0001).
Figure 6.
Effect of Cortical Folding on Absolute and Relative Thickness of Cortical Layers
Coronal section through medial prefrontal cortex of a rhesus monkey brain in the anterior cingulate. Note the expanded deep layers (below dotted line demarcating the upper boundary of cortical layer V) in the gyral regions (large arrows), contrasted by reduced thickness of the deep layers at the bottom of the cingulate sulcus (arrowhead) and the expanded layer I (small arrow) in comparison with layer I in gyral cortex. The brain section was immunoreacted for NeuN, a neuronal marker (brown), and then stained for Nissl (blue).
Table 1.
Cross-Correlations of Relative Laminar Cortical Thickness
Figure 7.
Effect of Cortical Folding on Neuron Number
Number of neurons found below a unit of 1 mm2 surface area and extending to the variable width of the upper (II+III+IV) and deep (V+VI) layers of gyral, intermediate, and sulcal cortices. Layer I was excluded from the analyses because of its separate developmental path and paucity of neurons [31]. There were significantly fewer neurons in layers V+VI of intermediate areas than in gyral areas and in the deep layers of sulcal than intermediate areas (pairwise t tests, Bonferroni-adjusted, p < 0.05). Conversely, there were more neurons in the upper layers of sulcal areas than in intermediate or gyral areas.
Table 2.
Classification of Prefrontal Areas Based on their Curvature