Spatial scale of indentation explains shift in ratio between spinal cord gray and white matter stiffness

The structural integrity of spinal cord tissue and the transmission of mechanical stimuli across the different levels of tissue microarchitecture and varying spatial scales of mechanical loading challenge experimental and computational efforts to accurately model, simulate and interpret tissue mechanics, leading to conflicting findings in existing literature. Here, we demonstrate that the bead size used in spherical indentation tests significantly affects the stiffness ratio of spinal cord gray to white matter, a dependence which we only observe on the transverse plane and not the coronal plane of the tissue. Our study reveals a shift in stiffness ratio such that for smaller spherical indenters gray matter is stiffer than white matter, while for larger indenters, white matter is stiffer than gray matter. The mean relative change from the 100 {micro}m bead to the 500 {micro}m bead differed between anatomical planes, with transverse sections showing a decrease in gray matter (-13.3%) and an increase in white matter stiffness (+26.9%), accompanied by a reduction in the gray-to-white matter stiffness ratio from 1.07 to 0.76, whereas coronal sections exhibited increases in both gray (+21.0%) and white matter (+33.8%), along with a change in the ratio from 0.99 to 1.14. These findings contribute to explaining previously contradictory results in the literature and underscore the relevance of spatial scales in mechanical characterization studies.