Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 5, pp 1373–1388 | Cite as

Region-specific constitutive modeling of the plantar soft tissue

  • Haihua Ou
  • Peng Zhan
  • Liping Kang
  • Jialiang Su
  • Xiaodong Hu
  • Shane Johnson
Original Paper


Recent research has shown that hyperelastic properties of the plantar soft tissue consisting of adipose tissue and fibrous septa change from region to region. However, relatively little research has been conducted to develop analytical or computational models to describe the region-specific behavior of the plantar soft tissue. The objective of the research is to develop a region-specific constitutive model of the plantar soft tissue. Plantar soft tissue specimens were dissected from six regions [subcalcaneal (CA), sublateral (LA), subnavicular (Nav), 1st, 3rd, and 5th submetatarsal (M1, M3, M5)] from cadaveric foot samples, and a picrosirius red staining technique was used to visualize the collagen fibers in fibrous septa. The volume fractions of adipose tissue and fibrous septa and the volume fractions of the principal orientations of the fibrous septa were calculated with the intensity gradient method. Region-specific constitutive models were then developed in finite element analysis considering the microstructure of the plantar soft tissue. The hyperelastic region specific material properties of the plantar soft tissue were validated with experimental unconfined compression tests and indentation tests from the literature. The results show that the models give reasonable predictions of the stiffness of the soft tissue within a standard deviation of the tests. The region-specific constitutive models help to explain how changes in the constituents are related to mechanical behavior of the soft tissue on a region specific basis.


Foot and ankle Constitutive region specific Finite element analysis Plantar soft tissue Microstructure Collagen fibers 



This study was funded by National Nature Science Foundation of China under Grant Nos. 51505282 and 51550110233.

Compliance with ethical standards

Conflict of interest

The authors have no conflicts to report.


  1. Anderson K, Elsheikh A, Newson T (2003) Modelling the biomechanical effect of increasing intraocullar pressure on the porcine cornea. Paper presented at the 16th ASCE engineering mechanics conference. University of Washington, SeattleGoogle Scholar
  2. Antunes P, Dias G, Coelho A, Rebelo F, Pereira T (2008) Non-linear finite element modelling of anatomically detailed 3D foot model Report paper, 1–11Google Scholar
  3. Blechschmidt E (1982) The structure of the calcaneal padding. Foot Ankle 2:260–283CrossRefGoogle Scholar
  4. Buschmann WR, Jahss MH, Kummer F, Desai P, Gee RO, Ricci JL (1995) Histology and histomorphometric analysis of the normal and atrophic heel fat pad. Foot Ankle Int 16:254–258CrossRefGoogle Scholar
  5. Chen WP, Tang FT, Ju CW (2001) Stress distribution of the foot during mid-stance to push-off in barefoot gait: a 3-D finite element analysis. Clin Biomech 16:614–620. CrossRefGoogle Scholar
  6. Cheung JT-M, Zhang M (2006) Finite element modeling of the human foot and footwear. Paper presented at the ABAQUS users’ conferenceGoogle Scholar
  7. Cheung JT-M, Zhang M, An K-N (2006) Effect of Achilles tendon loading on plantar fascia tension in the standing foot. Clin Biomech 21:194–203CrossRefGoogle Scholar
  8. Cheung JTM, Zhang M, Leung AKL, Fan YB (2005) Three-dimensional finite element analysis of the foot during standing: a material sensitivity study. J Biomech 38:1045–1054. CrossRefGoogle Scholar
  9. Cichowitz A, Pan WR, Ashton M (2009) The heel anatomy, blood supply, and the pathophysiology of pressure ulcers. Ann Plast Surg 62:423–429. CrossRefGoogle Scholar
  10. Comley K, Fleck NA (2010) A micromechanical model for the Young’s modulus of adipose tissue. Int J Solids Struct 47:2982–2990. CrossRefzbMATHGoogle Scholar
  11. Erdemir A, Viveiros ML, Ulbrecht JS, Cavanagh PR (2006) An inverse finite-element model of heel-pad indentation. J Biomech 39:1279–1286. CrossRefGoogle Scholar
  12. Gefen A (2002) Stress analysis of the standing foot following surgical plantar fascia release. J Biomech 35:629–637. CrossRefGoogle Scholar
  13. Grytz R, Meschke G (2009) Constitutive modeling of crimped collagen fibrils in soft tissues. J Mech Behav Biomed Mater 2:522–533. CrossRefGoogle Scholar
  14. Guler HC, Berme N, Simon SR (1998) A viscoelastic sphere model for the representation of plantar soft tissue during simulations. J Biomech 31:847–853CrossRefGoogle Scholar
  15. Hills AP, Hennig EM, McDonald M, Bar-Or O (2001) Plantar pressure differences between obese and non-obese adults: a biomechanical analysis. Int J Obes 25:1674–1679. CrossRefGoogle Scholar
  16. Hsu C-C, Tsai W-C, Wang C-L, Pao S-H, Shau Y-W, Chuan Y-S (2007) Microchambers and macrochambers in heel pads: are they functionally different? J Appl Physiol 102:2227–2231. CrossRefGoogle Scholar
  17. Hsu CC, Tsai WC, Chen CPC, Shau YW, Wang CL, Chen MJL, Chang KJ (2005) Effects of aging on the plantar soft tissue properties under the metatarsal heads at different impact velocities. Ultrasound Med Biol 31:1423–1429. CrossRefGoogle Scholar
  18. Isvilanonda V, Dengler E, Iaquinto JM, Sangeorzan BJ, Ledoux WR (2012) Finite element analysis of the foot: model validation and comparison between two common treatments of the clawed hallux deformity. Clin Biomech 27:837–844. CrossRefGoogle Scholar
  19. Jacob S, Patil MK (1999) Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen’s disease with muscle paralysis. J Rehabil Res Dev 36:252–263Google Scholar
  20. Jahss MH et al (1992) Investigations into the fat pads of the sole of the foot: anatomy and histology. Foot Ankle 13:233–242CrossRefGoogle Scholar
  21. Johnson S, Kang L, Akil HM (2016) Mechanical behavior of jute hybrid bio-composites. Compos B Eng 91:83–93. CrossRefGoogle Scholar
  22. Johnson S, Kang L, Zhan P (2016) Multi-scale constitutive region specific modelling of the plantar soft tissue. Paper presented at the Foot International 2016 Congress, Berlin, Germany, June 23–25Google Scholar
  23. Junqueira LC, Bignolas G, Brentani RR (1979) Picrosirius staining plus polarization microscopy, a specific method for collagen detection in tissue sections. Histochem J 11:447–455. CrossRefGoogle Scholar
  24. Karlon WJ, Covell JW, McCulloch AD, Hunter JJ, Omens JH (1998) Automated measurement of myofiber disarray in transgenic mice with ventricular expression of ras. Anat Rec 252:612–625.<612::aid-ar12>;2-1 CrossRefGoogle Scholar
  25. Klaesner JW, Hastings MK, Zou DQ, Lewis C, Mueller MJ (2002) Plantar tissue stiffness in patients with diabetes mellitus and peripheral neuropathy. Arch Phys Med Rehabil 83:1796–1801. CrossRefGoogle Scholar
  26. Ledoux WR, Blevins JJ (2007) The compressive material properties of the plantar soft tissue. J Biomech 40:2975–2981. CrossRefGoogle Scholar
  27. Lemmon D, Shiang TY, Hashmi A, Ulbrecht JS, Cavanagh PR (1997) The effect of insoles in therapeutic footwear: a finite element approach. J Biomech 30:615–620. CrossRefGoogle Scholar
  28. López Jiménez F (2016) On the isotropy of randomly generated representative volume elements for fiber-reinforced elastomers. Compos B Eng 87:33–39. CrossRefGoogle Scholar
  29. Miller-Young JE, Duncan NA, Baroud G (2002) Material properties of the human calcaneal fat pad in compression: experiment and theory. J Biomech 35:1523–1531. CrossRefGoogle Scholar
  30. Pai S, Ledoux WR (2010) The compressive mechanical properties of diabetic and non-diabetic plantar soft tissue. J Biomech 43:1754–1760. CrossRefGoogle Scholar
  31. Scott SH, Winter DA (1993) Biomechanical model of the human foot: kinematics and kinetics during the stance phase of walking. J Biomech 26:1091–1104. CrossRefGoogle Scholar
  32. Spears IR, Miller-Young JE, Waters M, Rome K (2005) The effect of loading conditions on stress in the barefooted heel pad. Med Sci Sports Exerc 37:1030–1036. CrossRefGoogle Scholar
  33. Tao K, Wang D, Wang C, Wang X, Liu A, Nester CJ, Howard D (2009) An in vivo experimental validation of a computational model of human foot. J Bionic Eng 6:387–397. CrossRefGoogle Scholar
  34. Thomas VJ, Patil KM, Radhakrishnan S (2004) Three-dimensional, stress analysis for the mechanics of plantar ulcers in diabetic neuropathy. Med Biol Eng Comput 42:230–235. CrossRefGoogle Scholar
  35. Tran P, Ngo TD, Ghazlan A, Hui D (2017) Bimaterial 3D printing and numerical analysis of bio-inspired composite structures under in-plane and transverse loadings. Compos B Eng 108:210–223. CrossRefGoogle Scholar
  36. Wafai L, Zayegh A, Woulfe J, Aziz SM, Begg R (2015) Identification of foot pathologies based on plantar pressure. Asymmetry Sens 15:20392–20408. CrossRefGoogle Scholar
  37. Wang Y-N, Lee K, Ledoux WR (2011) Histomorphological evaluation of diabetic and non-diabetic plantar soft tissue. Foot Ankle Int 32:802–810. CrossRefGoogle Scholar
  38. Wang Y-N, Lee K, Shofer JB, Ledoux WR (2017) Histomorphological and biochemical properties of plantar soft tissue in diabetes. Foot 33:1–6. CrossRefGoogle Scholar
  39. Yang LT (2008) Mechanical properties of collagen fibrils and elastic fibers explored by AFM. University of TwenteGoogle Scholar
  40. Zhan P, Ou H, Johnson S (2016) Development of a constitutive multi-scale region specific nested finite element model for the plantar soft tissue. Paper presented at the 12th World Congress on Computational Mechanics (WCCM XII), Seoul, South Korea, July 24–29Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Haihua Ou
    • 1
  • Peng Zhan
    • 1
  • Liping Kang
    • 1
  • Jialiang Su
    • 1
  • Xiaodong Hu
    • 3
  • Shane Johnson
    • 1
    • 2
  1. 1.University of Michigan and Shanghai Jiao Tong University Joint InstituteShanghai Jiao Tong UniversityShanghaiChina
  2. 2.State Key Laboratory of Mechanical Systems and VibrationShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Department of Human Anatomy, Histology and EmbryologyShanghai Jiao Tong UniversityShanghaiChina

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