Advisor: Dr. Pelegri

Lab Members involved: Mohit Agarwal

Abstract:

Shear and torsional load on soft solids such as brain white matter purportedly exhibits the Poynting
Effect. It is a typical nonlinear phenomenon associated with soft materials whereby they tend to
elongate (positive Poynting effect) or contract (negative Poynting effect) in a direction perpendicular to
the shearing or twisting plane. As part of this research, novel 3D micromechanical Finite Element Models
(FEMs) have been formulated to describe the Poynting effect in bi-phasic modeled brain white matter
(BWM) representative volume element (RVE) with axons tracts embedded in surrounding extracellular
matrix (ECM) for simulating brain matter's response to pure and simple shear.

In the developed BWM 3D FEMs, nonlinear Ogden hyper-elastic material model is deployed to interpret
axons and ECM material phases. The modeled bi-phasic RVEs have axons tied to the surrounding ECM. In
this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear case were
analyzed. Root mean square deviation (RMSD) was calculated for stress and deformation response plots
to understand the effect of axon-ECM orientations and loading conditions on the degree of Poynting
behavior. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane underscored
the significance of axonal fiber-matrix interactions.

From the simulated ensemble of cases, a transitional dominance trend is noticed, as simple sheared
axons showed pronounced Poynting behavior, but shear deformation build-up in the purely sheared
brain model exhibited the highest Poynting behavior at higher strain % limits. At lower strain limits,
simple shear imparted across and perpendicular to axonal tract directions emerged as the dominant
Poynting effect configurations. At high strains, the stress-strain% plots manifested mild strain stiffening
effects and bending stresses in purely sheared axons, substantiated the strong non-linearity in brain
tissues' response.

These studies provide critical insights into the nonlinear biomechanics of brain tissues under shear and
torsion loads. By elucidating the Poynting effect in brain white matter, this research paves the way for
advancements in medical imaging and monitoring technologies. The ability to predict tissue response
under various mechanical conditions can significantly enhance the diagnosis and treatment of brain
trauma and diffuse axonal injuries. Furthermore, the findings highlight the importance of axonal fiber-
matrix interactions in determining brain tissue behavior, which could inform the design of more
effective therapeutic strategies. This research not only deepens our understanding of brain
microarchitecture but also holds the potential to improve clinical outcomes for patients suffering from
neurological injuries.