Electronic-Supplementary-Material_RSPA-2024-0789.zip from MRI elastography of human intervertebral disc based on an explicit inverse approach

Intervertebral disc (IVD) degeneration is a significant health issue that can lead to severe complications. Recent research has highlighted the close relationship between disc degeneration and the biomechanical properties of the IVD. This study introduces an innovative approach—magnetic resonance imaging (MRI) elastography of the human IVD—using an explicit inverse solver to identify the non-homogeneous shear modulus map of the IVD. The key advantage of this explicit solver is its streamlined optimization process, focusing only on the shear moduli of the nucleus pulposus (NP), annulus fibrosus (AF), and their interface. This approach reduces the optimization variables, making it more efficient than traditional pixel-based approaches. To validate this method, we conducted a plane strain numerical example, observing a consistent underestimation of the AF/NP shear modulus ratio by a scaling factor of approximately<i>in vitro</i> compression or bending, demonstrated its effectiveness, yielding an AF/NP shear modulus ratio within a reasonable range of 6–15. In summary, the proposed method offers a promising direction for MRI elastography of the human IVD.

椎间盘（Intervertebral disc, IVD）退变是一类重大健康问题，可引发严重并发症。近期研究证实，椎间盘退变与椎间盘的生物力学特性存在紧密关联。本研究提出一种创新方法——人类椎间盘磁共振成像（MRI）弹性成像技术，采用显式逆求解器来识别椎间盘的非均匀剪切模量分布图。该显式逆求解器的核心优势在于优化流程得到精简，仅聚焦于髓核（nucleus pulposus, NP）、纤维环（annulus fibrosus, AF）及其界面的剪切模量。此方法减少了优化变量，相较传统基于像素的方法具备更高的计算效率。为验证该方法的有效性，我们开展了平面应变数值算例，通过体外（in vitro）压缩或弯曲实验观察到，纤维环/髓核剪切模量比始终存在约缩放因子级别的低估，最终得到的纤维环/髓核剪切模量比处于6~15的合理区间内，证实了该方法的有效性。综上，本研究提出的方法为人类椎间盘的MRI弹性成像提供了颇具前景的研究方向。