Modeling and biomechanical characterization of femur and tibia bones using the Extended Mooney–Rivlin approach with mathematical validation

IF 1.5 Q3 ORTHOPEDICS

Journal of orthopaedics Pub Date : 2025-07-01 DOI:10.1016/j.jor.2025.06.035

Mohamed Hassan , A.S. Abdel-Rahman

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引用次数: 0

Abstract

Background

Understanding the non-linear mechanical behavior of human bone is critical for improving orthopedic modeling and developing personalized treatment strategies. The Mooney-Rivlin model, traditionally used in soft matters, has been extended to capture the complex stress–strain relationships of hard biological materials like bone.

Objective

To apply the Extended Mooney-Rivlin model to human bone specimens and quantify regional variations in mechanical parameters, with the goal of improving finite element simulations and biomechanical interpretations.

Participants and setting

The study analyzed bone specimens from the proximal femur as well as the midshaft, distal, and proximal sections of long bones in the lower limb, based on data obtained from the literature.

Methods

Experimental stress–strain data were collected from bone samples subjected to uniaxial loading. The Extended Mooney-Rivlin model was fitted to the data to extract four key parameters: B (overall stiffness), C₁ (shear resistance), C₂ (damping/energy dissipation), and H (non-linearity).

Results

The model demonstrated strong goodness-of-fit across all specimens (R² > 0.95). Stiffness (B) was significantly higher in midshaft regions compared to distal regions. Damping capacity (C₂) and linearity (H) were elevated in distal regions C₂, indicating enhanced shock-absorbing properties. Surprisingly, shear resistance (C₁) was also greater in trabecular-rich regions, reflecting greater adaptability to complex loading environments.

Conclusions

The Extended Mooney-Rivlin model effectively captures regional variations in bone mechanics, with clear distinctions between cortical and trabecular bone behavior. These findings support its application in advanced biomechanical modeling and suggest new directions for personalized orthopedic treatment. Future work should explore the influence of age, bone mineral density, and pathological changes on these mechanical parameters.

查看原文本刊更多论文

使用扩展Mooney-Rivlin方法进行股骨和胫骨的建模和生物力学表征，并进行数学验证

了解人类骨骼的非线性力学行为对于改进骨科建模和制定个性化治疗策略至关重要。Mooney-Rivlin模型，传统上用于软物质，已经扩展到捕获复杂的应力-应变关系的硬生物材料，如骨头。目的将扩展Mooney-Rivlin模型应用于人骨标本，量化力学参数的区域变化，以改进有限元模拟和生物力学解释。根据文献数据，该研究分析了股骨近端以及下肢长骨中轴、远端和近端部分的骨标本。方法采集单轴载荷下骨试样的应力应变实验数据。对数据拟合扩展Mooney-Rivlin模型，提取4个关键参数：B（整体刚度）、C1（抗剪阻力）、C2（阻尼/耗能）和H（非线性）。结果该模型在所有样本中均表现出较强的拟合优度(R2 >；0.95)。与远端区域相比，中轴区域的刚度(B)明显更高。阻尼能力（C2）和线性度(H)在远端C2区域得到提高，表明减震性能增强。令人惊讶的是，在小梁丰富的区域，剪切阻力（C1）也更大，反映出对复杂加载环境的更强适应性。结论扩展Mooney-Rivlin模型有效地捕捉了骨力学的区域差异，明确区分了骨皮质和骨小梁的行为。这些发现支持了其在高级生物力学建模中的应用，并为个性化矫形治疗提供了新的方向。未来的工作应探讨年龄、骨密度和病理变化对这些力学参数的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of orthopaedics ORTHOPEDICS-

CiteScore

3.50

自引率

6.70%

发文量

202

审稿时长

56 days

期刊介绍： Journal of Orthopaedics aims to be a leading journal in orthopaedics and contribute towards the improvement of quality of orthopedic health care. The journal publishes original research work and review articles related to different aspects of orthopaedics including Arthroplasty, Arthroscopy, Sports Medicine, Trauma, Spine and Spinal deformities, Pediatric orthopaedics, limb reconstruction procedures, hand surgery, and orthopaedic oncology. It also publishes articles on continuing education, health-related information, case reports and letters to the editor. It is requested to note that the journal has an international readership and all submissions should be aimed at specifying something about the setting in which the work was conducted. Authors must also provide any specific reasons for the research and also provide an elaborate description of the results.