Focus on diffuse axonal injury

Focus on diffuse axonal injury

Citation for published version (APA):

Cloots, R. J. H., Dommelen, van, J. A. W., Nyberg, T., & Geers, M. G. D. (2009). Focus on diffuse axonal injury. Poster session presented at Mate Poster Award 2009 : 14th Annual Poster Contest.

Document status and date: Published: 01/01/2009 Document Version:

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Introduction

In Diffuse Axonal Injury (DAI), injury is widespread over the brain. Despite this name, focal injury is occurring at the cellular level [1]. The aim of this study is to focus on the mechanical aspects of DAI at the cellular level.

Tissue level Cellular level

~1 cm ~10 μm Head level

~1 dm

Figure 1: Length scales involved in DAI from a human head via tissue level structures to the brain cells.

Method

Geometry

The geometry (50x50μm) of the plane strain model con-tains one inclusion (e.g., a cell body) that is surrounded by axons (Fig. 2b). The neurofilaments, which give the axons its mechanical strength, are modeled as fibers. Three configurations are made, in which the diversion angleϕ of the fiber orientations are 30◦, 45◦and 60◦.

ϕ θ a b c e1 m2 e2 m1

Figure 2: a) Mesh and b) fiber orientations, whereϕ represents the variation in fiber orientations. c) Deformation with loading angleθ.

Boundary conditions

An isochoric deformation with a principal stretch direc-tion m₁that varies with angleθ (Fig. 2c) is imposed on the model via periodic boundary conditions [2].

Material model

The material behavior is described by a fiber reinforced constitutive model [3]. The Cauchy stress tensor is

σ = σh₊ 1

J



G˜Bd+ 2k ˜I4− 1 ˜I4(nn)d



where˜I₄andn are the fiber stretch and the fiber di-rection, respectively.

Results

The logarithmic axonal strain with respect to the applied logarithmic tissue strain depends on the loading angle and is highest atθ = 0◦(Fig. 3). An increase of either the fiber diversion angleϕ or the inclusion shear modu-lus results in a higher relative strain, which can be over 1.6. The equivalent stress is concentrated equatorial to the inclusion with respect to the loading direction .

q [degrees]

elog,axon/elog,tissue elog,axon/elog,tissue

s [Pa] [-] [-] φ = 30° φ = 45° φ = 60° 15 30 45 60 75 90 -0.5 0 0.5 1 1.5 Ginclusion/Gtissue[-] 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1.2 1.0 1.4 1.6 8 6 4 2 0

Figure 3: Relative axonal strain versus loading angle θ (for Ginclusion/Gtissue = 3) and relative shear modulus (for θ = 0◦). Inset: equivalent stress field.

Discussion and conclusions

A relative high shear modulus inclusion in brain tissue combined with a loading direction in the main axonal di-rection can increase the logarithmic strain of the axons locally by more than 60%, which might lead to axonal in-jury. Therefore, the heterogeneities at the cellular level have to be accounted for in the understanding of DAI.

References

1. Povlishock (1993) Ann. Emerg. Med. 22, 980–986 2. Kouznetsova et al. (2001) Comp. Mech. 27, 37–48 3. Gasser et al. (2006) J. R. Soc. Interface 3, 15–35

Focus on Diffuse Axonal Injury

∗_{Eindhoven University of Technology}