Journal of Computational Applied Mechanics

Sensitivity Analysis of the Finite Element Model of the Foot and Ankle Complex for Vibration Analysis

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

Biomechanical simulation and analysis of human organs are of paramount importance for improving the treatment and prevention of a variety of disorders and injuries. One of the organs that is very prone to injuries, especially among athletes and active individuals, is the foot. However, these injuries can be well-prevented by numerical modeling and analysis of the foot in different conditions. In the current study, after constructing a detailed parametric finite element (FE) model of the foot and ankle complex, a surrogate-based sensitivity analysis is performed to evaluate how the material and geometric properties of the bones, the ligaments, the soft tissue, and the skin affect the natural frequencies of the FE model. Based on the obtained results, Young’s modulus and the density of the cortical bone, the trabecular bone and the soft tissue have considerable effects on the natural frequencies. Also, Poisson’s ratio of the soft tissue and the thickness of the skin have significantly larger sensitivity indices compared to those of other similar parameters. The cross-sectional area of the fascia plantar also plays a more important role in the natural frequencies compared to those of other ligaments. These results are preliminary good indicators to rank the material and geometrical parameters based on their effects on the natural frequencies of the FE model.

Keywords

[1]        Y. Wang, D. W.-C. Wong, and M. Zhang, “Computational models of the foot and ankle for pathomechanics and clinical applications: a review,” Ann. Biomed. Eng., vol. 44, no. 1, pp. 213–221, 2016.
[2]        A. M. Takhakh, F. M. Kadhim, and J. S. Chiad, “Vibration Analysis and Measurement in Knee Ankle Foot Orthosis for Both Metal and Plastic KAFO Type,” in ASME International Mechanical Engineering Congress and Exposition, 2013, vol. 56222, p. V03BT03A050.
[3]        M. Zhang and Y. Fan, Computational biomechanics of the musculoskeletal system. CRC Press Boca Raton, FL, USA, 2015.
[4]        F. Rauch, “Vibration therapy,” Dev. Med. Child Neurol., vol. 51, pp. 166–168, 2009.
[5]        B. Önal, M. Sertel, and G. Karaca, “Effect of plantar vibration on static and dynamic balance in stroke patients: a randomised controlled study,” Physiotherapy, vol. 116, pp. 1–8, 2022.
[6]        M. Sabziparvar, S. Naghdi, N. N. Ansari, H. R. Fateh, and A. Nakhostin-Ansari, “Local plantar vibration for the treatment of diabetic neuropathy: a case report,” J. Diabetes Metab. Disord., vol. 20, no. 2, pp. 2115–2119, 2021.
[7]        L. Xie, S.-X. Yi, Q.-F. Peng, P. Liu, and H. Jiang, “Retrospective study of effect of whole-body vibration training on balance and walking function in stroke patients,” World J. Clin. cases, vol. 9, no. 22, p. 6268, 2021.
[8]        E. Morales-Orcajo, J. Bayod, and E. de Las Casas, “Computational foot modeling: scope and applications,” Arch. Comput. Methods Eng., vol. 23, no. 3, pp. 389–416, 2016.
[9]        S. M. A. Taleghani and L. Fatahi, “Application of Medical Imaging and Image Processing in Creating 3D Models of Human Organs,” in International Conference on Mechanics of Advanced Materials and Equipment, 2018, pp. 1–10.
[10]      X. Ge, L. Zhang, G. Xiang, Y. Hu, and D. Lun, “Cross-Sectional Area Measurement Techniques of Soft Tissue: A Literature Review,” Orthop. Surg., vol. 12, no. 6, pp. 1547–1566, 2020.
[11]      P. K. Phan et al., “In Silico Finite Element Analysis of the Foot Ankle Complex Biomechanics: A Literature Review,” J. Biomech. Eng., vol. 143, no. 9, 2021.
[12]      H. Ou, Z. Qaiser, L. Kang, and S. Johnson, “Effect of skin on finite element modeling of foot and ankle during balanced standing,” J. Shanghai Jiaotong Univ., vol. 23, no. 1, pp. 132–137, 2018.
[13]      C. Mkandawire, W. R. Ledoux, B. J. Sangeorzan, and R. P. Ching, “Foot and ankle ligament morphometry,” J. Rehabil. Res. Dev., vol. 42, no. 6, p. 809, 2005.
[14]      R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments. John Wiley & Sons, 2016.
[15]      V. R. Joseph, “Space-filling designs for computer experiments: A review,” Qual. Eng., vol. 28, no. 1, pp. 28–35, 2016.
[16]      M. E. Johnson, L. M. Moore, and D. Ylvisaker, “Minimax and maximin distance designs,” J. Stat. Plan. Inference, vol. 26, no. 2, pp. 131–148, 1990.
[17]      T. J. Santner, B. J. Williams, W. I. Notz, and B. J. Williams, The design and analysis of computer experiments, vol. 1. Springer, 2003.
Journal of Computational Applied Mechanics
Volume 54, Issue 1
March 2023
Pages 140-149
  • Receive Date: 13 December 2022
  • Accept Date: 31 December 2022