Research Papers

Axons Pull on the Brain, But Tension Does Not Drive Cortical Folding

[+] Author and Article Information
Gang Xu

Department of Biomedical Engineering, Washington University, Saint Louis, MO 63130

Andrew K. Knutsen

Department of Mechanical, Aerospace, and Structural Engineering, Washington University, Saint Louis, MO 63130

Krikor Dikranian

Department of Anatomy and Neurobiology, Washington University, Saint Louis, MO 63130

Christopher D. Kroenke

Department of Behavioral Neuroscience, Oregon Health and Science University, Portland, OR 97239

Philip V. Bayly

Department of Biomedical Engineering, and Department of Mechanical, Aerospace, and Structural Engineering, Washington University, Saint Louis, MO 63130

Larry A. Taber1

Department of Biomedical Engineering, and Department of Mechanical, Aerospace, and Structural Engineering, Washington University, Saint Louis, MO 63130lat@wustl.edu


Corresponding author.

J Biomech Eng 132(7), 071013 (Jun 02, 2010) (8 pages) doi:10.1115/1.4001683 History: Received April 09, 2010; Revised April 12, 2010; Posted April 28, 2010; Published June 02, 2010; Online June 02, 2010

During human brain development, the cerebral cortex undergoes substantial folding, leading to its characteristic highly convoluted form. Folding is necessary to accommodate the expansion of the cerebral cortex; abnormal cortical folding is linked to various neurological disorders, including schizophrenia, epilepsy, autism, and mental retardation. Although this process requires mechanical forces, the specific force-generating mechanisms that drive folding remain unclear. The two most widely accepted hypotheses are as follows: (1) Folding is caused by differential growth of the cortex and (2) folding is caused by mechanical tension generated in axons. Direct evidence supporting either theory, however, is lacking. Here we show that axons are indeed under considerable tension in the developing ferret brain, but the patterns of tissue stress are not consistent with a causal role for axonal tension. In particular, microdissection assays reveal that significant tension exists along axons aligned circumferentially in subcortical white matter tracts, as well as those aligned radially inside developing gyri (outward folds). Contrary to previous speculation, however, axonal tension is not directed across developing gyri, suggesting that axon tension does not drive folding. On the other hand, using computational (finite element) models, we show that differential cortical growth accompanied by remodeling of the subplate leads to outward folds and stress fields that are consistent with our microdissection experiments, supporting a mechanism involving differential growth. Local perturbations, such as temporal differences in the initiation of cortical growth, can ensure consistent folding patterns. This study shows that a combination of experimental and computational mechanics can be used to evaluate competing hypotheses of morphogenesis, and illuminate the biomechanics of cortical folding.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 4

Structural anisotropy of developing ferret brain measured by DTI. The white dashed curves outline the boundaries between (I) cortex, (II) subplate, (III) subcortical white matter, and (IV) deep gray matter. Data were acquired ex vivo at postnatal days (P) 6, 21, and adult. Directions of yellow “whiskers” correspond to the direction of maximal diffusivity (the first eigenvector of the local diffusion tensor), which is indicative of fiber orientation in white matter, and radial glial orientation in immature gray matter. Whisker length and intensity are proportional to the local RA of the tissue.

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Figure 5

Histology of developing ferret brain. Coronal brain slices were obtained and selectively stained at postnatal days (P) 6, 17, and adult. Neuronal cell bodies were marked by Nissl staining (darker areas in a1, b1, and c1), while myelinated and unmyelinated axons (indicated by arrowheads) were stained by MBP and SMI312 (neurofilament marker) immunoreactivity, respectively. Indicated rectangles are relative regions where axon staining is shown. Regions of cortex, subplate, subcortical white matter (WM), and deep gray matter (dGM) are labeled.

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Figure 1

Schematics of postulated models for brain cortical folding. (a) Intracortical differential growth model (7). Brain cortex is roughly divided into two layers with the outer layer growing faster (indicated by “++”) than the inner layer (“+”). All other underlying tissue is treated as a softer elastic foundation without any growth (“0”). Differential growth results in cortical buckling. (b) Axon tension hypothesis (9). Tension (black arrows) in axons that strongly interconnect two cortical regions pulls them closer to each other to form an outward fold. An inward fold forms between two outward folds to separate weakly interconnected cortical regions (gray arrows). (a′) Phased differential growth model. Cortical growth in region 1 (t<tc) followed by cortical growth in region 2 (t>tc) produces two outward folds. The underlying subplate grows to provide stress relaxation in response to the cortical growth. (b′) Actual distributions of axon tension based on present dissection and histology data. Axons are under tension (black arrows), and the majority of them are located circumferentially in the subcortical white matter tract and radially in the subplate or the cores of outward folds (from around P18). No circumferential tension (gray arrows) or axons (gray dotted lines) was detected in the cores (subplate) of outward folds.

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Figure 2

Schematic and model geometry of the developing ferret brain. ((a) and (b)) Schematic of coronal section of ferret brain at postnatal days 6 (a) and 14 (b). Drawings were modified based on the tracings of ferret brain sections in Ref. 18). The ferret brain consists of four major layers: (I) cortex, (II) subplate, (III) subcortical white matter (WM), and (IV) deep gray matter (dGM). Tissue dissections (cuts) were made to reveal stress patterns in the developing brain. (c) Representative 2D finite element model for a brain section before folding. The geometry is partitioned into the four major layers I–IV, each composed of triangular mesh elements. To simulate phased differential growth, a quarter of the cortex and corresponding subplate regions are further divided into two regions (labeled 1 and 2).

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Figure 3

Microdissection assay of developing ferret brain. ((a1)–(c1)) Coronal brain sections at postnatal days (P) 6, 18, and adult. The dashed curves outline the boundaries between cortex, subplate, subcortical white matter (WM), and deep gray matter (dGM). Scale bars represent 1 mm. Rectangles indicate the regions shown in the close-ups to the right of each section. Cuts of various ranges (indicated by pairs of arrowheads) are made either radially (a2–a4, b2–b4, and c2–c4) or circumferentially (a5 and a6, b5 and b6, and c5 and c6) on developing gyri and sulci as marked. Significant openings are indicated by asterisks.

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Figure 6

Regional stiffness of developing ferret brain. Indentation stiffness is reported as mean±standard deviation. The total number of indentations for each case is shown in the corresponding column. Temporal differences: Between P6 and P18, significant changes in stiffness occurred only in the cortex (P<0.05). The stiffness of each region in adult brains was significantly larger than those at P6 and P18 (P<0.0001). Spatial differences: Despite some statistically significant differences between regions (shown in the figure), the stiffness at each developmental age is similar for the cortex, subplate, subcortical white matter (WM), and deep gray matter (dGM).

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Figure 7

Finite element model for cortical folding caused by phased differential growth. ((a)–(c)) Model geometry and stress distribution after each major simulation step (i–iii, see Sec. 3), leading to the formation of two gyri in designated regions. ((d)–(g)) A section of the model shown in (c) was used to simulate the effects of subsequent radial cuts within a gyrus ((d) and (e)) and a sulcus ((f) and (g)). The simulated cuts from the cortical surface through the subcortical white matter tract are indicated by pairs of arrowheads, and resulting openings are indicated by asterisks. (Panels (e) and (g) are close-ups of the dashed regions in (d) and (f), respectively.) Colors indicate circumferential stress (σθθ∗) normalized relative to the material shear modulus.



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