Residual stress in the adult mouse brain

Abstract

This work provides direct evidence that sustained tensile stress exists in white matter of the mature mouse brain. This finding has important implications for the mechanisms of brain development, as tension in neural axons has been hypothesized to drive cortical folding in the human brain. In addition, knowledge of residual stress is required to fully understand the mechanisms behind traumatic brain injury and changes in mechanical properties due to aging and disease. To estimate residual stress in the brain, we performed serial dissection experiments on 500-mum thick coronal slices from fresh adult mouse brains and developed finite element models for these experiments. Radial cuts were made either into cortical gray matter, or through the cortex and the underlying white matter tract composed of parallel neural axons. Cuts into cortical gray matter did not open, but cuts through both layers consistently opened at the point where the cut crossed the white matter. We infer that the cerebral white matter is under considerable tension in the circumferential direction in the coronal cerebral plane, parallel to most of the neural fibers, while the cerebral cortical gray matter is in compression. The models show that the observed deformation after cutting can be caused by more growth in the gray matter than in the white matter, with the estimated tensile stress in the white matter being on the order of 100-1,000 Pa.

Fig. 1

Schematic of experimental procedure for mouse brain dissection (not drawn to scale). a The whole brain was removed from 12–15-week-old adult mice. b The brain was then mounted on the platform of a sectioning vibratome and 500-μm thick coronal slices were cut. c Only the slices containing corpus callosum were collected. A typical brain slice contains three major regions: cortical gray matter (cGM), thalamus gray matter (tGM), and white matter tract consisting of corpus callosum (cc), cingulum (cg), and external capsule (ec). In the experiments, a razor blade was used to make the first radial cut only through the cortical gray matter, and the second radial cut was made deeper through either the white matter tract or the inner gray matter of thalamus. The cartoons shown in a and b were adapted from http://pages.slc.edu/~krader/animals/index.htm, and http://www.hms.harvard.edu/ research/brain/atlas.html, respectively

Fig. 2

Finite element model for the mouse brain in the coronal plane. a Schematic of model for intact brain slice. Due to symmetry, only half of the slice is analyzed. Symmetry conditions (represented by rollers) are specified along the straight vertical boundary (one point was fixed). Other boundaries are free. b Model geometry partitioned into triangular mesh elements. A narrow cut is simulated by removing a thin (10-μm wide) rectangular region. Note denser mesh for the white matter track and the cut region. c Close-up of mesh near the cut (dashed rectangle in b)

Fig. 3

Serial cuts made on a coronal slice of an adult mouse brain. a1, b1 Brain slice obtained by vibratome sectioning. a2, b2 The first radial cut (indicated by a pair of solid arrowheads) was made only through the cortical gray matter. The cut did not open. a3, b3 The second radial cut (indicated by a pair of open arrowheads) was made through the underlying white matter tract (a3) or deeper into inner thalamus gray matter (b3). The cut opened at the site of the white matter tract or inner gray matter. a4, b4 After about 15 min, the opening in the white matter tract became wider, but cuts through cortical gray matter stayed closed. The overall morphology of the slices in a1 and b1 is typical for the first and third corpus callosum-containing slices, respectively, obtained during coronal sectioning (from anterior to posterior part of the brain). c1–c4 Normalized circumferential stress ( ${\sigma }_{\theta }^{\ast }$) distribution in finite element models for the dissection experiments (μ^* = 0.5, ${\lambda }_{\mathrm{g}}^{\ast }=1.3$). Due to relatively more growth in gray matter, gray matter is in compression and white matter is in tension. Radial cuts were made into cortical gray matter (c2), white matter (c3), or inner gray matter (c4), respectively. The smaller outline shown in each plot is the same slice before growth

Fig. 4

White matter tract of mouse brain with and without the constraints of gray matter. a1 Brain slice obtained by vibratome sectioning. The overall morphology is typical for a slice just posterior to the one shown in Fig. 3a1. The angle (φ_intact = 150°) characterizing the white matter tract is shown. a2 Same slice with inner thalamus gray matter dissected away by scissors and cortical gray matter cut away with several straight cuts by a blade. In this specimen, the angle (φ_cut = 99°) of the white matter tract decreased by 33% (φ^* = 0.66) after these cuts. b1, b2 Normalized circumferential stress distributions in finite element models before and after dissections. The model for the intact slice (b1) is the same as that in Fig. 3c1. Similar to the experimental result, after removal of the majority of the gray matter, the white matter angle decreased dramatically (φ^* = 0.70), and straight cuts on the cortical gray matter became curved (b2)

Fig. 5

Dependence of the normalized white matter tract angle (φ^*) and residual circumferential stress ( ${\sigma }_{\theta }^{\ast }$) in the white matter on relative growth ( ${\lambda }_{\mathrm{g}}^{\ast }$) and stiffness (μ^*) from the finite element model. a Dependence of φ^* on ${\lambda }_{\mathrm{g}}^{\ast }$ and μ^*. The shadowed area is the relative growth range for gray matter when the normalized white matter angle matches the experimental data (φ^* = 0.67 ± 0.04). b Dependence of ${\sigma }_{\theta }^{\ast }$ on ${\lambda }_{\mathrm{g}}^{\ast }$ and μ^*. The white matter stress ${\sigma }_{\theta }^{\ast }$ represents the average value across the symmetry plane of the corpus callosum. The shadowed area corresponds to the same growth range for gray matter from a and covers the scope of expected residual stress level in the white matter