Micromodel of traumatic brain injury
Citation for published version (APA):Cloots, R. J. H., Dommelen, van, J. A. W., Nyberg, T., & Geers, M. G. D. (2008). Micromodel of traumatic brain injury. Poster session presented at Mate Poster Award 2008 : 13th Annual Poster Contest.
Document status and date: Published: 01/01/2008 Document Version:
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Mechanics of Materials
Micromodel of Traumatic Brain Injury
R.J.H. Cloots∗, J.A.W. van Dommelen∗, T. Nyberg◦, and M.G.D. Geers∗
∗Eindhoven University of Technology, The Netherlands ◦Royal Institute of Technology, Stockholm, Sweden
/department of mechanical engineering
Introduction
The development of Traumatic Brain Injury (TBI) involves length scales ranging from the head level (i.e., dm) to the cellular level (i.e., µm), see Fig. 1. The aim of this study is to connect the cellular level to the tissue level.
mechanical load injury
cell body axon
neuron
Fig. 1 The length scales that are involved with TBI. Left: cross-section
of a human head. Right: schematic drawing of a neuron.
Methods
Microstructure
In the cortex (Fig. 2, A), the axons are oriented in a random fashion, whereas all the axons in the corpus callosum (Fig. 2, B) are aligned in one direction. Inside a single axon, the neuro-filaments are aligned with the axonal direction.
B A
axon
Fig. 2 Microstructures of the brain: orientations of the axons (A and B)
and theneurofilaments.
Cell injury
Pathological findings are:1
- Damage is observed at the locations in the axons where it has to deviate for an inclusion, e.g., a blood vessel, a cell body, or a glial cell (cf. Fig. 3).
- Damaged axons are found isolated between intact axons.
Numerical model
The geometry of the model in Fig. 3 represents a critical area for injury based on the pathological findings in literature.
or B A axon inclusion tissue
Fig. 3 Geometry and fiber orientations of the model. A and B refer to
the locations in Fig. 2.
The Cauchy stress tensor of the brain tissue and its constituents consists of an isotropic part and afiber contribution:2
σ= 2 J C10B˜ d + KJ 2 − 1 J2 I +σf σf= k1h ˜Efi κ ˜Bd+ ˜I4(1 − 3κ)(~n~n)d ˜ Ef = κ( ˜I1− 3) + (1 − 3κ)( ˜I4− 1)
where~n is the fiber vector with unit length and the preferred fiber direction andκ describes the dispersion of the fiber orientations around the preferred fiber direction. The Macaulay bracketsh·i take into account that the fibers contribute during tension only. The mechanical properties are derived from combining mechan-ical and structural properties at the tissue and cellular level ob-tained from literature.
Results
Figure 4 shows preliminary results of a simulation in which a shear strain is applied to three different configurations from lo-cation A (Fig. 2). Stress concentrations are observed in the curved part of the axon.
0 20 40 60 80 100 120 140 160 180 200 s[Pa]
Fig. 4 Equivalent stress fields of three different geometries.
Discussion and Conclusions
- TBI involves injury mechanisms at the cellular level. - First results agree with pathological findings.
References
[1] Povlishock (1992): Ann Emerg Med, 22, 980-986
