Toward understanding the brain tissue behavior due to preconditioning: an experimental study and RVE approach

Abstract

Brain tissue under preconditioning, as a complex issue, refers to repeated loading-unloading cycles applied in mechanical testing protocols. In previous studies, only the mechanical behavior of the tissue under preconditioning was investigated; However, the link between macrostructural mechanical behavior and microstructural changes in brain tissue remains underexplored. This study aims to bridge this gap by investigating bovine brain tissue responses both before and after preconditioning. We employed a dual approach: experimental mechanical testing and computational modeling. Experimental tests were conducted to observe microstructural changes in mechanical behavior due to preconditioning, with a focus on axonal damage. Concurrently, we developed multiscale models using statistically representative volume elements (RVE) to simulate the tissue's microstructural response. These RVEs, featuring randomly distributed axonal fibers within the extracellular matrix, provide a realistic depiction of the white matter microstructure. Our findings show that preconditioning induces significant changes in the mechanical properties of brain tissue and affects axonal integrity. The RVE models successfully captured localized stresses and facilitated the microscopic analysis of axonal injury mechanisms. These results underscore the importance of considering both macro and micro scales in understanding brain tissue behavior under mechanical loading. This comprehensive approach offers valuable insights into mechanotransduction processes and improves the analysis of microstructural phenomena in brain tissue.

Keywords: FEA; brain tissue microstructure; embedded element technique; histological investigation; multiscale simulation; preconditioning.

FIGURE 1

Application of periodic boundary conditions (PBC) on the boundaries of the representative volume element (RVE) in the microsampling domain.

FIGURE 2

The present study includes samples taken from a specific region of the white matter of the bovine brain: the corona radiata (CR), highlighted in a coronal section. The Red lines indicate the orientations of axonal fibers. Samples were extracted aligned to the direction of axon fibers. The scale bar provides a sense of size: the white scale bar represents 10 mm.

FIGURE 3

Experimental mechanical test setup; (A) An example of cylindrical bovine brain tissue sample obtained from corona radiata(CR) region from the white matter, (B) The uniaxial testing device used for the experiment and positioning of the sample within the testing machine.

FIGURE 4

The microstructure of the samples of the control and preconditioned groups from the CR region of the cow brain, cut in two directions: perpendicularly and along the length of the axon fibers, using the Luxol fast blue staining method. The magnification increases from right to left: 20x, 100x, and 200x. The cross-sectional images show the diameter and position of the axons, and the longitudinal section images show the orientation of the axons.

FIGURE 5

Process of construction the statistical volume element; (A, B) The cumulative distribution functions of axonal diameters and orientations presented for a representative structure of white matter, specifically the CR for the Control group. (C) The spherical components of the orientation vector $\vec{p}$ assigned to the axons within the RVE model. (D, E) The cumulative distribution functions of axonal diameters and orientations presented for a representative CR structure for the Preconditioned group. These distributions are based on experimental histological data analysis from the present study. (F) Schematic of a histology-informed RVE featuring random positions, diameters, and orientations of axons.

FIGURE 6

Representation of RVE applying Embedded Element Technique with independent mesh grids for the host and guest domains.

FIGURE 7

3D host meshes employed to model the matrix substance. The same element size was used for all RVEs.

FIGURE 8

Sensitivity analysis of the overall and local responses of the RVE models for two groups: before preconditioning and after preconditioning. (A, B) the effect of the grid size; (C, D) the effect of the RVE edge length.

FIGURE 9

Histological image of the transverse section of the white matter’s CR region shows regular and irregular axons of the preconditioned sample.

FIGURE 10

The mechanical response of the two before and after preconditioning groups of RVEs using optimized material properties were compared with the experimental data obtained from the current study under quasi-static tensile load. Error bars represent standard deviations of experimental tests.

FIGURE 11

Deformed configurations and normal stress (S11) contour plots show RVE models in two before and after preconditioning groups under 20% quasi-static longitudinal tension, respectively. Configurations are shown separately for host and guest domains. Stress values are expressed in mega pascals (MPa). RVE size increases from left to right.