Experimental Measurement and Mathematical Quantification of Fixed-Charged Density in Rat and Pig Brain Tissue

Abstract

Cerebral edema is associated with poor prognosis because brain swelling within the rigid skull raises intracranial pressure, exacerbating secondary injuries following traumatic brain injury. Brain swelling can be characterized by triphasic biomechanics, which models brain tissue as a mixture of a deformable porous solid matrix with a negative fixed-charged density (FCD), water, and monovalent counterions. When brain cells die, the intracellular FCD is exposed, attracting cations into the cells. The increase in intracellular solute concentration generates osmotic pressure via the Gibbs-Donnan effect, driving water into cells and causing swelling. This study quantifies the FCD of rat and pig brain tissue by measuring the pressure generated by tissue within a confined volume as cells died. Rat brain tissue generated an averaged swelling pressure of 52.92 ± 20.40 mmHg (mean ± one standard deviation). Variations were observed between pig cortical white matter (7.14 ± 4.79 mmHg) and cortical gray matter (33.86 ± 11.89 mmHg). The corresponding FCD values were 42.54 ± 8.14 mEq/L for rat brain tissue, and 15.18 ± 5.38 mEq/L and 34.22 ± 6.31 mEq/L for pig cortical white and gray matter, respectively. Treating the rat brain tissue with DNAse, heparinase I, heparinase III, and chondroitinase ABC to degrade FCD significantly reduced swelling pressure. Good agreement between the experimental and numerically simulated responses supported the role of the FCD in cerebral edema formation. The reported FCD values can improve the biofidelity of computational models to predict post-traumatic cerebral edema, aiding the improvement of safety systems.

Keywords: Cerebral edema; Finite element modeling; Intracellular fixed-charged density; Traumatic brain injury; Triphasic swelling biomechanics.