Biphasic analysis of rat brain slices under creep indentation shows nonlinear tension-compression behavior

Biphasic theory can provide a mechanistic description of deformation and transport phenomena in soft tissues, and has been used to model surgery and drug delivery in the brain for decades. Knowledge of corresponding mechanical properties of the brain is needed to accurately predict tissue deformation and flow transport in these applications. Previously in our group, creep indentation tests were conducted for multiple anatomical regions in acute rat brain tissue slices. In the current study, a biphasic finite element model of creep indentation was developed with which to compare these data. Considering the soft tissue structure of brain, the solid matrix was assumed to be composed of a neo-Hookean ground matrix reinforced by continuously distributed fibers that exhibits tension-compression nonlinearity during deformation. By fixing Poisson's ratio of the ground matrix, Young's modulus, fiber modulus and hydraulic permeability were estimated. Hydraulic permeability was found to be nearly independent of the properties of the solid matrix. Estimated modulus (40 Pa to 1.1 kPa for the ground matrix, 3.2-18.2 kPa for fibers) and hydraulic permeability (1.2-5.5×10^-13m⁴/N s) fell within an acceptable range compared with those in previous studies. Instantaneous indentation depth was dominated by tension provided by fibers, while the tissue response at equilibrium was sensitive to Poisson's ratio. Results of sensitivity analysis also point to the necessity of considering tension-compression nonlinearity in the solid phase when the biphasic material undergoes large creep deformation.