Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy

Abstract

Multiple length scales are involved in the development of traumatic brain injury, where the global mechanics of the head level are responsible for local physiological impairment of brain cells. In this study, a relation between the mechanical state at the tissue level and the cellular level is established. A model has been developed that is based on pathological observations of local axonal injury. The model contains axons surrounding an obstacle (e.g., a blood vessel or a brain soma). The axons, which are described by an anisotropic fiber-reinforced material model, have several physically different orientations. The results of the simulations reveal axonal strains being higher than the applied maximum principal tissue strain. For anisotropic brain tissue with a relatively stiff inclusion, the relative logarithmic strain increase is above 60%. Furthermore, it is concluded that individual axons oriented away from the main axonal direction at a specific site can be subjected to even higher axonal strains in a stress-driven process, e.g., invoked by inertial forces in the brain. These axons can have a logarithmic strain of about 2.5 times the maximum logarithmic strain of the axons in the main axonal direction over the complete range of loading directions. The results indicate that cellular level heterogeneities have an important influence on the axonal strain, leading to an orientation and location-dependent sensitivity of the tissue to mechanical loads. Therefore, these effects should be

Multi-scale mechanics of traumatic brain injury: predicting axonal strains from head loads

“…In a previous study (Cloots et al 2011), it was shown that anisotropy at the tissue level causes the strains to become smaller in the main axonal direction, but larger in other directions for the same stress levels. For a homogeneous axonal alignment (e.g., without the presence of an inclusion), this would also lead to reduced axonal strains, even for the higher strain levels in other directions than the main axonal direction, since then the loading direction is not aligned with the axons anymore.…”

“…By means of the Macaulay brackets · , the fibers contribute only in tension and not in compression, as Ẽ becomes 0 ifẼ is negative. The fiber contribution to the stiffness is assumed linear (i.e., k 2 → 0) (Cloots et al 2011). Viscoelasticity is added by using:…”

“…The first type of injury occurs for example in the brainstem and the corpus callosum and is described by Povlishock (1993), who observed that axonal injury was present at locations where the axons have to deviate from a straight path because of an obstruction (e.g., a blood vessel or a cell body). In a previous study (Cloots et al 2011), mechanical heterogeneities at the axonal level, leading to axons being subjected to locally higher strains than the tissue-level strains, were investigated as a possible source for this pathological observation. Based on a micro-level critical volume element (CVE), it was concluded in Cloots et al (2011) that the geometrical configuration of deviating axons near an inclusion leads to increased axonal loading and that, therefore, if present, these regions may be critical for axonal injury.…”

“…In a previous study (Cloots et al 2011), mechanical heterogeneities at the axonal level, leading to axons being subjected to locally higher strains than the tissue-level strains, were investigated as a possible source for this pathological observation. Based on a micro-level critical volume element (CVE), it was concluded in Cloots et al (2011) that the geometrical configuration of deviating axons near an inclusion leads to increased axonal loading and that, therefore, if present, these regions may be critical for axonal injury.…”

Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue

“…A value of 1214 Pa is assigned to the shear modulus G while 11 590 Pa is assigned to the mechanical parameter k 1 in respect of the ratio of 0.105 experimentally identified by Ning et al [20]. A value of 0 is chosen for k 2 as the fibre contribution to the stiffness is assumed to be linear [30]. The bulk modulus K, even though experimental observations show that its magnitude is around 2.1 GPa, is instead assigned a value of 50 MPa to prevent volumetric locking of the elements during the FE simulation.…”