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<p>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&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\upmu\)</EquationSource> </InlineEquation>m bead to the 500&#xa0;<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\upmu\)</EquationSource> </InlineEquation>m bead differed between anatomical planes, with transverse sections showing a decrease in gray matter (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(-13.3\%\)</EquationSource> </InlineEquation>) and an increase in white matter stiffness (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(+26.9\%\)</EquationSource> </InlineEquation>), 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 (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(+21.0\%\)</EquationSource> </InlineEquation>) and white matter (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(+33.8\%\)</EquationSource> </InlineEquation>), 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.</p>

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

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  • 出版模式：

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  • 发表日期：

    2026年6月2日

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  • Oskar Neumann,
  • Harsh Vardhan Surana,
  • Maik Hintze,
  • Stefanie Kuerten,
  • Thomas Franz,
  • Rahul Gopalan Ramachandran,
  • Paul Steinmann,
  • Silvia Budday

摘要

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  \(\upmu\) m bead to the 500  \(\upmu\) 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.