Viscoelastic response of gray matter and white matter brain tissues under creep and relaxation

Accurate measurement of the mechanical properties of brain tissue is of paramount importance for understanding its mechanics-biology relationship. Most published studies on brain viscoelasticity have been conducted using a single relaxation test, without validating the validity of linear viscoelasticity, which is insufficient to establish an accurate constitutive equation for brain tissue. We obtained the creep and relaxation profiles of fresh adult porcine white matter (N = 120) and gray matter (N = 56) under finite step-and-hold uniaxial compression, using a mechanical testing machine, with 16.67 mm/s loading rate and 80 s hold time. These curves were employed to determine viscoelastic properties and demonstrated an excellent fit with a concise power-law function. The average initial modulus for gray matter (GM) was 6.619 kPa, higher than that for white matter under transverse loading (WM-2D) at 5.579 kPa (p < 0.01), yet lower than that for white matter under axial loading (WM-1D) at 6.759 kPa (p = 0.0121). Notably, WM-2D exhibited the highest degree of fluidity (β = 0.216). Our findings reveal that gray matter behaves as a linear viscoelastic material with power-law creep compliance and relaxation modulus. Conversely, the creep and relaxation behavior of white matter deviates from the verification relationship derived from linear viscoelastic theory, indicating its nonlinearity. This fact underscores the inaccuracy of assuming a linear constitutive relationship to characterize the viscoelastic properties of white matter. By combining the power-law function with the experimentally obtained creep compliance and relaxation modulus, we offer a unique approach to determining the viscoelastic characteristics of brain tissue.