Continuum modeling of a neuronal cell under blast loading

Abstract

Traumatic brain injuries have recently been put under the spotlight as one of the most important causes of accidental brain dysfunctions. Significant experimental and modeling efforts are thus underway to study the associated biological, mechanical and physical mechanisms. In the field of cell mechanics, progress is also being made at the experimental and modeling levels to better characterize many of the cell functions, including differentiation, growth, migration and death. The work presented here aims to bridge both efforts by proposing a continuum model of a neuronal cell submitted to blast loading. In this approach, the cytoplasm, nucleus and membrane (plus cortex) are differentiated in a representative cell geometry, and different suitable material constitutive models are chosen for each one. The material parameters are calibrated against published experimental work on cell nanoindentation at multiple rates. The final cell model is ultimately subjected to blast loading within a complete computational framework of fluid-structure interaction. The results are compared to the nanoindentation simulation, and the specific effects of the blast wave on the pressure and shear levels at the interfaces are identified. As a conclusion, the presented model successfully captures some of the intrinsic intracellular phenomena occurring during the cellular deformation under blast loading that potentially lead to cell damage. It suggests, more particularly, that the localization of damage at the nucleus membrane is similar to what has already been observed at the overall cell membrane. This degree of damage is additionally predicted to be worsened by a longer blast positive phase duration. In conclusion, the proposed model ultimately provides a new three-dimensional computational tool to evaluate intracellular damage during blast loading.

Figure 1

First order generalized Maxwell model

Figure 2

2D axisymmetric mesh of the neuron used for nanoindentation (distances in μm)

Figure 3

Finite element setup of the blast simulation

Figure 4

Indentation force v.s. displacement for the fast cycle (10μm.s⁻¹)

Figure 5

Indentation force v.s. displacement for the medium cycle (1μm.s⁻¹)

Figure 6

Indentation force v.s. displacement for the slow cycle (0.1μm.s⁻¹)

Figure 7

Pressure field (kPa) for the nanoidentation and blast simulations at 26.88 s and 65.5 ns respectively for the three regions; a quarter of the mesh for the blast simulation was taken out for visualization purposes

Figure 8

Von Mises stress field (kPa) for the nanoidentation and blast simulations at 26.88 s and 65.5 ns respectively for the three regions; a quarter of the mesh for the blast simulation was taken out for visualization purposes

Figure 9

Temperature increase field (K) for the blast simulation at 65.5 ns for the whole cell; a quarter of the mesh was taken out for visualization purposes

Figure 10

Pressure, von Mises stress, longitudinal strain and strain-rate evolution at the nucleus-cytoplasm interface, and ~75 % of the nucleus height, for three initial positive phase durations: 5, 10 and 15 ns