Workineh Zerihun G, Muñoz-Moya Estefano, Ruiz Wills Carlos, Lialios Dimitrios, Noailly Jérôme
BCN MedTech, Department of Engineering, Universitat Pompeu Fabra, Barcelona, Spain.
Department of Computer Applications in Science and Engineering (CASE), Barcelona Supercomputing Center, Barcelona, Spain.
Front Bioeng Biotechnol. 2025 Sep 5;13:1651786. doi: 10.3389/fbioe.2025.1651786. eCollection 2025.
Intervertebral disc (IVD) degeneration is a primary contributor to low back pain, with nutritional stress due to the IVD's avascularity recognized as a key factor. Solute transport within the disc relies predominantly on diffusion, which is governed by tissue morphology and mechanical deformation. However, the interplay between disc geometry, poro-mechanical strain, diffusion, and degeneration remains incompletely characterized. Previous specimen-specific models have captured inter-subject variability in metabolite transport, but the isolated effects of disc height and degeneration-dependent material composition have not been systematically assessed. Moreover, although strain-dependent diffusion coefficients are commonly modeled as porosity functions, the role of intra-element diffusivity gradients , arising under large deformation, has been largely overlooked.
The present study focuses on poro-mechanical finite element (FE) models of three patient-personalized L4-L5 lumbar IVD geometries, representing varying heights categorized as , , and IVDs. Three days of physiological mechanical load cycles, comprising 8 hours of rest and 16 hours of activity, were simulated, under both 'healthy' (Pfirrmann grade 1) and degenerated (Pfirrmann grade 3) tissue conditions.
Simulation outcomes demonstrated that a one-third reduction in disc height (relative to medium height) led to increases in oxygen and glucose concentrations and decreases in lactate levels, particularly in the nucleus and anterior regions. Conversely, a one-third height increase resulted in reductions in oxygen and glucose and a corresponding rise in lactate levels. These deviations were more pronounced in degenerated tissues, highlighting the synergistic role of morphology and matrix integrity in determining metabolic homeostasis. Importantly, the inclusion of in the diffusion-reaction model produced negligible changes in solute concentration profiles.
These findings underscore the predominant influence of disc geometry and matrix composition on IVD metabolic homeostasis, suggesting limited relevance of the term in practical simulations. Simplified diffusion models, without , may be sufficient for future IVD mechano-transport FE modeling.
椎间盘退变是腰痛的主要原因，椎间盘无血管导致的营养应激被认为是一个关键因素。椎间盘内的溶质转运主要依赖扩散，而扩散受组织形态和机械变形的控制。然而，椎间盘几何形状、孔隙-力学应变、扩散和退变之间的相互作用仍未得到充分表征。先前的特定标本模型已经捕捉到了代谢物转运中的个体间变异性，但椎间盘高度和退变相关材料组成的单独影响尚未得到系统评估。此外，尽管应变依赖的扩散系数通常被建模为孔隙率函数，但在大变形下产生的单元内扩散率梯度的作用在很大程度上被忽视了。
本研究聚焦于三个患者个性化的L4-L5腰椎间盘几何形状的孔隙-力学有限元（FE）模型，代表不同高度，分为低、中、高椎间盘。在“健康”（Pfirrmann 1级）和退变（Pfirrmann 3级）组织条件下，模拟了三天的生理机械负荷循环，包括8小时休息和16小时活动。
模拟结果表明，椎间盘高度降低三分之一（相对于中等高度）会导致氧气和葡萄糖浓度增加，乳酸水平降低，特别是在髓核和前部区域。相反，高度增加三分之一会导致氧气和葡萄糖减少，乳酸水平相应升高。这些偏差在退变组织中更为明显，突出了形态和基质完整性在确定代谢稳态中的协同作用。重要的是，在扩散-反应模型中纳入单元内扩散率梯度对溶质浓度分布的影响可忽略不计。
这些发现强调了椎间盘几何形状和基质组成对椎间盘代谢稳态的主要影响，表明在实际模拟中单元内扩散率梯度项的相关性有限。不含单元内扩散率梯度项的简化扩散模型可能足以用于未来的椎间盘力学-转运有限元建模。
