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Research Papers

Opening Angles and Material Properties of the Early Embryonic Chick Brain

[+] Author and Article Information
Gang Xu, Philip S. Kemp, Joyce A. Hwu, Adam M. Beagley

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

Philip V. Bayly

Department of Mechanical, Aerospace, and Structural Engineering and Department of Biomedical 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

1

Corresponding author.

J Biomech Eng 132(1), 011005 (Dec 09, 2009) (7 pages) doi:10.1115/1.4000169 History: Received May 18, 2009; Revised July 24, 2009; Posted September 04, 2009; Published December 09, 2009; Online December 09, 2009

Mechanical forces play an important role during brain development. In the early embryo, the anterior end of the neural tube enlarges and differentiates into the major brain subdivisions, including three expanding vesicles (forebrain, midbrain, and hindbrain) separated by two constrictions. Once the anterior neuropore and the spinal neurocoel occlude, the brain tube undergoes further regional growth and expansion in response to increasing cerebrospinal fluid pressure. Although this is known to be a response to mechanical loads, the mechanical properties of the developing brain remain largely unknown. In this work, we measured regional opening angles (due to residual stress) and stiffness of the embryonic chick brain during Hamburger–Hamilton stages 11–13 (approximately 42–51 h incubation). Opening angles resulting from a radial cut on transverse brain slices were about 40–110 deg (depending on region and stage) and served as an indicator of circumferential residual stress. In addition, using a custom-made microindentation device and finite-element models, we determined regional indentation stiffness and material properties. The results indicate that the modulus is relatively independent of position and stage of development with the average shear modulus being about 220 Pa for stages 11–13 chick brains. Information on the regional material properties of the early embryonic brain will help illuminate the process of early brain morphogenesis.

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Figures

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Figure 1

Early embryonic chick brain. (a)–(c) Dorsal view of the chick embryo at stages 11, 12, and 13, respectively. Embryos in (a)–(c) have the same scale bar, which is 1 mm. (d)–(f) Close-ups of the brain region from the embryo in (a)–(c) (dashed rectangle), respectively. Major subdivisions of the brain include three vesicles: forebrain (F), midbrain (M), and hindbrain (H) with two constrictions, which are FM valley and MH valley. The optic vesicles (ov) are also shown. The brain is surrounded by head mesenchyme (hm) (scale bar is 100 μm).

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Figure 6

Finite-element models for studying effects of local geometry on indentation. (a)–(c) Models showing 20 μm indentation on a longitudinally convex, straight, and concave cylinder, respectively. Scale bar in (a) represents 100 μm for (a)–(c). (d) Force-indentation curves from these models. Solid line is from the model for the stage-12 midbrain shown in Fig. 5. (e) Stiffnesses given by the models where the stiffness values are the slopes of force-indentation curves from linear regressions and are normalized by that from the model for the stage-12 midbrain. See text for details.

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Figure 7

Opening angles and material properties of chick brains at stages 11–13. (a) Regional opening angles where asterisks ( ∗) represent statistically significant difference between two regions at each stage, (b) regional indentation stiffness from experiments (columns with error bars) and models (filled symbols), and (c) shear moduli computed from models in Fig. 5. Error bars represent standard deviations.

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Figure 5

Finite-element models for estimating material properties. (a)–(c) 3D models for indenting the midbrain region at stages 11, 12, and 13, respectively. Undeformed model geometries resemble the overall morphology of the chick brain at each stage. The forebrain region is simplified without optic vesicles. Scale bar in (a) represents 100 μm for (a)–(d). (d) Deformed model geometry showing the stage-12 midbrain being indented about 20 μm. (e) Close-up near the indenter tip in (d) (scale bar is 10 μm).

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Figure 4

Finite-element modeling of the effect of residual stress on indentation stiffness. (a) Distribution of circumferential residual stress (σθ∗=σθ/μ) in unloaded cylinder model after specified growth. The geometry after growth is close to the average stage-12 midbrain (scale bar is 100 μm for (a)–(c)). (b) Approximate zero-stress state of the cylinder after a simulated cut. The opening angle (116 deg) is close to the average experimental value (108 deg) for the stage-12 midbrain (see Fig. 7). (c) Model of indenting a residual stress-containing sphere (rendered in wire frames). The geometry and residual stress distributions are approximately the same as those of the cylinder model in (a). (d) Close-up of the region near the indenter tip (dashed rectangle in (c)). Arrows indicate the specified boundary displacement to simulate indentation (scale bar is 10 μm). (e) Force-indentation curves for sphere models of the same geometry with and without residual stress (RS). Residual stress has a relatively small effect on indentation stiffness.

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Figure 3

Microindentation tests on a chick brain. (a)–(b) Video micrographs showing the indenter tip (with an ink mark) approaching (a) and indenting (b) the midbrain region of a stage-12 chick brain. The brain is held by a micropipette on the opposite side of the indenter (scale bar is 100 μm). (c) Beam deflection and indentation depth are determined from the indenter tip displacements between control (no contact) and actual indentations. The product of beam deflection with beam stiffness yields indentation force. (d) All experimental force-indentation curves (symbols, n=8) for the stage-12 midbrain. The slopes of linear regressions (dashed lines) to these curves yield stiffness values for each tested midbrain, the average of which is represented by the solid gray line.

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Figure 2

Microdissection of the early embryonic chick brain. (a) A thin midbrain slice (M) from a stage-12 chick embryo surrounded by head mesenchyme (hm), (b) the brain slice after most surrounding tissue was removed, and (c) a radial cut on the dorsal side of the brain slice (indicated by dashed line in (b)). The resulting approximate zero-stress state of the brain slice is characterized by the opening angle (θ). (d)–(f) Demonstration of how surrounding tissue affects the opening angle of a stage-12 midbrain slice. Dashed lines in (d) and (e) are radial cuts on the slice that resulted in the shapes shown in (e) and (f), respectively (see text for details). All images are at the same scale with scale bars representing 100 μm.

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