Strain-enhanced rate dependence of apparent mechanical properties of brain tissue under large strain

The rate-dependent mechanical property of brain tissue is critical for understanding brain development, disease diagnosis (tumor growth, hydrocephalus, and traumatic brain injury), and treatment. However, the quantitative relationship for rate dependence under the large strain and low strain rates remains elusive. Brain tissue, composed of a deformable solid skeleton (cell, and extracellular matrix) and the interstitial fluid, exhibits the poroelastic behavior at low strain rates. In this study, unconfined compression tests were performed on porcine brain white matter at strain rates ranging from 10-4 to 2 s-1 and strains up to 50%. Results showed pronounced strain-enhanced rate dependence, with the influence of strain rate on the apparent Young’s modulus becoming more significant at the large strain. A power-law relation between the apparent Young’s modulus and strain rate was established in which the rate-dependent prefactor a and the rate-independent term c increase with strain, whereas the rate exponent b gradually decreases. Using the poroelastic framework, we derived a pore pressure formulation as a function of strain and strain rate. We then incorporated this into the effective stress expression, which yielded an apparent Young’s modulus consistent in form with the experimental results. This indicates that strain-enhanced rate dependence arises from the dual effects of solid skeleton stiffening and elevated pore pressure caused by reduced permeability and longer drained time at larger strains. These findings provide insights into the rate-dependent mechanical behavior of brain tissue and support the development of computational models for brain development, disease diagnosis, and treatment.