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TECHNICAL PAPERS

Modeling of Microstructural Kinematics During Simple Elongation of Central Nervous System Tissue

[+] Author and Article Information
Allison C. Bain, David I. Shreiber, David F. Meaney

Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104-6392

J Biomech Eng 125(6), 798-804 (Jan 09, 2004) (7 pages) doi:10.1115/1.1632627 History: Received January 14, 2002; Revised June 24, 2003; Online January 09, 2004
Copyright © 2003 by ASME
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Figures

Grahic Jump Location
Analysis of the axonal microstructure in the guinea pig optic nerve (a) Digital image of an longitudinal optic nerve section stained for non-phosphorylated neurofilament (SMI31 antibody), showing the undulated appearance of individual axons in the nerve. (b) Axonal microstructure was described using an undulation parameter (U), based on the end-to-end distance length of an axon (LU), and the true path length (LT) of the axon. Undulation parameters closest to 1.0 indicated axons that appeared nearly straight; increasing levels of undulation above 1.0 described axons that were undulated, or ‘wavy’ in appearance.
Grahic Jump Location
Schematic depicting the model assuming a tight coupling between the axonal population and the glial cell network. (a) The axon path is represented by a periodic wave with amplitude, Ao, and period, To. (b) When elongated to a stretch ratio of 1, the amplitude of the path decreases to Ao−1/2, while the path period increases to λTo. Therefore, both the computed path length and the end-to-end distance of the axon will change for the applied stretch condition, yielding a new undulation value (Ut) that is approximated by the equation shown.
Grahic Jump Location
Schematic depicting the model of axonal microstructure with no coupling to the glial cell network. At stretch ratios less than the axon’s undulation value, the applied displacement is transferred directly to increase the axon’s end-to-end distance (LU), with no change in the true path length of the axon (LT). Therefore, the transformed undulation of the axon after stretch (Ut) is transformed according equation shown. At stretch ratios greater than the original undulation, the axon is completely straight and has an undulation of 1.0.
Grahic Jump Location
Measured changes in the axonal microstructure under simple extension. In the resting in situ state (a; λ=1.0), axons are compressed and show undulation characteristics across a broad range. At increasing levels of applied tensile stretch (bd), the axonal microstructure changes to a more oriented geometry, with most of the axons appearing nearly straight at the highest level of stretch (d, λ=1.25).
Grahic Jump Location
Predicted (lines) and measured (symbols) changes in the axonal microstructure. Models assuming either a complete coupling to glial matrix (a) or an absence of coupling of the glial matrix (b) during simple extension do not follow either the average undulation values or the distribution of undulation values measured in stretched optic nerves (symbols). Additionally, the distribution of undulation values measured in stretched optic nerves, described with the 25th and 75th percentile values (bars), were not predicted well with either of these two models (dashed lines). (c) A more accurate prediction of the average undulation, as well as the spread in the distribution of the undulation values, was found using a model that assumed a gradual recruitment of the glial cell matrix at lower undulation values (c).

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