A Quasi-Linear, Viscoelastic, Structural Model of the Plantar Soft Tissue With Frequency-Sensitive Damping Properties

[+] Author and Article Information
William R. Ledoux

Department of Veterans Affairs, RR&D Center for Excellence in Limb Loss Prevention and Prosthetic Engineering, VA Puget Sound Health Care System, Seattle WA, 98108Department of Mechanical Engineering and Department of Orthopaedics and Sports Medicine, University of Washington, Seattle, WA, 98195

David F. Meaney

Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104

Howard J. Hillstrom

Gait Study Center, Temple University School of Medicine, Philadelphia, PA 19107

J Biomech Eng 126(6), 831-837 (Feb 04, 2005) (7 pages) doi:10.1115/1.1824133 History: Received March 07, 2003; Revised July 02, 2004; Online February 04, 2005
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Sammarco, G. J., 1989, Biomechanics of the Foot, Lea & Febiger, Malvern, PA, pp. 163–181.
Sarrafian, S. K., 1993, Anatomy of the Foot and Ankle: Descriptive, Topographic, Functional, Lippincott, Philadelphia, PA.
Cavanagh, P. R., Valiant, G. A., et al. (1984). Biological Aspects of Modeling Shoe/Foot Interaction During Running, in Sports Shoes and Playing Surfaces: Biomechanical Properties, E. C. Fredericks, Champaign, Illinois, Human Kinetics Publishers, Inc: 24–46.
Kinoshita,  H., Ogawa,  T., Kuzuhara,  K., and Ikuta,  K., 1993, “In Vivo Examination of the Dynamic Properties of the Human Heel Pad.,” Int. J. Sports Med., 14(6), pp. 312–319.
Kinoshita,  H., Francis,  P. R., Murase,  T., Kawai,  S., and Ogawa,  T., 1996, “The Mechanical Properties of the Heel Pad in Elderly Adults,” European J. Appl. Physiol. Occup. Physiol.,73(5), pp. 404–409.
Bennett,  M. B., and Ker,  R. F., 1990, “The Mechanical Properties of the Human Subcalcaneal Fat Pad in Compression,” J. Anat., 171, pp. 131–138.
Aerts,  P., Ker,  R. F., De Clercq,  D., Ilsley,  D. W., and Alexander,  R. M., 1995, “The Mechanical Properties of the Human Heel Pad: A Paradox Resolved,” J. Biomech., 28(11), pp. 1299–1308.
Gooding,  G. A., Stess,  R. M., Graf,  P. M., Moss,  K. M., Louie,  K. S., and Grunfeld,  C., 1986, “Sonography of the Sole of the Foot. Evidence for Loss of Foot Pad Thickness in Diabetes and Its Relationship to Ulceration of the Foot,” Invest. Radiol., 21(1), pp. 45–48.
Jahss,  M. H., Michelson,  J. D., Desai,  P., Kaye,  R., Kummer,  F., Buschman,  W., Watkins,  F., and Reich,  S., 1992, “Investigations Into the Fat Pads of the Sole of the Foot: Anatomy and Histology,” Foot Ankle, 13(5), pp. 233–242.
Phinney,  S. D., Stern,  J. S., Burke,  K. E., Tang,  A. B., Miller,  G., and Holman,  R. T., 1994, “Human Subcutaneous Adipose Tissue Shows Site-Specific Differences in Fatty Acid Composition,” Am. J. Clin. Nutr., 60(5), pp. 725–729.
Buschmann,  W. R., Jahss,  M. H., Kummer,  F., Desai,  P., Gee,  R. O., and Ricci,  J. L., 1995, “Histology and Histomorphometric Analysis of the Normal and Atrophic Heel Fat Pad,” Foot Ankle Int., 16(5), pp. 254–258.
Hsu,  T. C., Wang,  C. L., Shau,  Y. W., Tang,  F. T., Li,  K. L., and Chen,  C. Y., 2000, “Altered Heel-Pad Mechanical Properties in Patients With Type 2 Diabetes Mellitus,” Diabetic Med., 17(12), pp. 854–859.
Miller-Young,  J. E., Duncan,  N. A., and Baroud,  G., 2002, “Material Properties of the Human Calcaneal Fat Pad in Compression: Experiment and Theory,” J. Biomech., 35(12), pp. 1523–1531.
Faure,  C., 1981, “The Skeleton of the Anterior Foot,” Anat. Clin., 3, pp. 49–65.
Ledoux,  W. R., and Hillstrom,  H. J., 2002, “The Distributed Plantar Vertical Force of Neutrally Aligned and Pes Planus Feet,” Gait Posture,15(1), pp. 1–9.
Fung, Y. C., 1993, Bioviscoelastic Solids, Springer, New York, pp. 242–320.
Woo,  S. L., Gomez,  M. A., and Akeson,  W. H., 1981, “The Time and History-Dependent Viscoelastic Properties of the Canine Medial Collateral Ligament,” J. Biomech. Eng., 103(4), pp. 293–298.
Myers,  B. S., McElhaney,  J. H., and Doherty,  B. J., 1991, “The Viscoelastic Responses of the Human Cervical Spine in Torsion: Experimental Limitations of Quasi-Linear Theory, and a Method for Reducing These Effects,” J. Biomech., 24(9), pp. 811–817.
Kwan,  M. K., Lin,  T. H., and Woo,  S. L., 1993, “On the Viscoelastic Properties of the Anteromedial Bundle of the Anterior Cruciate Ligament,” J. Biomech., 26(4–5), pp. 447–452.
Iatridis,  J. C., Setton,  L. A., Weidenbaum,  M., and Mow,  V. C., 1997, “The Viscoelastic Behavior of the Non-Degenerate Human Lumbar Nucleus Pulposus in Shear,” J. Biomech., 30(10), pp. 1005–1013.
Funk,  J. R., Hall,  G. W., Crandall,  J. R., and Pilkey,  W. D., 2000, “Linear and Quasi-Linear Viscoelastic Characterization of Ankle Ligaments,” J. Biomech. Eng., 122(1), pp. 15–22.
Cavanagh,  P. R., 1999, “Plantar Soft Tissue Thickness During Ground Contact in Walking,” J. Biomech., 32(6), pp. 623–628.
Gefen,  A., Megido-Ravid,  M., and Itzchak,  Y., 2001, “In Vivo Biomechanical Behavior of the Human Heel Pad During the Stance Phase of Gait,” J. Biomech., 34(12), pp. 1661–1665.
Sauren,  A. A., van Hout,  M. C., van Steenhoven,  A. A., Veldpaus,  F. E., and Janssen,  J. D., 1983, “The Mechanical Properties of Porcine Aortic Valve Tissues,” J. Biomech., 16(5), pp. 327–337.
Best,  T. M., McElhaney,  J., Garrett,  W. E., and Myers,  B. S., 1994, “Characterization of the Passive Responses of Live Skeletal Muscle Using the Quasi-Linear Theory of Viscoelasticity,” J. Biomech., 27(4), pp. 413–419.
Galbraith,  J. A., Thibault,  L. E., and Matteson,  D. R., 1993, “Mechanical and Electrical Responses of the Squid Giant Axon to Simple Elongation,” J. Biomech. Eng., 115(1), pp. 13–22.
Wang,  C. L., Hsu,  T. C., Shau,  Y. W., Shieh,  J. Y., and Hsu,  K. H., 1999, “Ultrasonographic Measurement of the Mechanical Properties of the Sole Under the Metatarsal Heads,” J. Orthop. Res., 17(5), pp. 709–713.
Zheng,  Y. P., Choi,  Y. K., Wong,  K., Chan,  S., and Mak,  A. F., 2000, “Biomechanical Assessment of Plantar Foot Tissue in Diabetic Patients Using an Ultrasound Indentation System,” Ultrasound Med. Biol., 26(3), pp. 451–456.
Abramowitz, M., and Stegun, A., 1964, A Handbook of Mathematical Functions, U.S. Government Printing Office, Washington, D.C.


Grahic Jump Location
A schematic of the testing apparatus and the mechanical input data input. In the schematic, the foot is viewed posteriorly. Note that the dorsal surface of the foot is placed into the PMMA. The graph is the input displacement for the experiment, including the haversines of increasing amplitude (0 to 5 s), the preconditioning (5 to 35 s), the delay period (35 to 195 s), and the ramp and hold (195 s to 375 s). Note that the x axis was not drawn proportionally.
Grahic Jump Location
The average stress relaxation (normalized force vs time) data (±1 S.D.) and the fit generated from the average QLV coefficients for the subcalcaneal, five submetarsal, and subhallucal areas
Grahic Jump Location
The average stress relaxation (unnormalized force vs time) data (±1 S.D.) and the fit generated from the average QLV coefficients for the subcalcaneal, five submetarsal, and subhallucal areas. BW=body weight.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In