Skip to main content
Log in

Wedged Insoles and Gait in Patients with Knee Osteoarthritis: A Biomechanical Review

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The study of gait biomechanics in individuals with knee osteoarthritis has become widespread, especially in regards to the knee adduction moment—a variable commonly believed to be associated with knee osteoarthritis progression. Unfortunately, this variable is often studied clinically without considering how it is derived, or what it means in a mechanical context. The use of footwear for knee osteoarthritis management has received much attention as well. However, in many cases, footwear is studied without regard for the mechanical effects they actually induce on the patient. Therefore, this review aims to summarize the current state of knowledge in regards to knee osteoarthritis gait and footwear biomechanics, by taking a step back to review the foundations of these two research areas. First, an overview of the calculation of the knee adduction moment is provided, along with mechanical considerations. Then, this is used to discuss current evidence for wedged insoles and highlight knowledge gaps. The intent was to place this mechanical information in a clinically-oriented framework for approachability by scientists, engineers and clinicians alike. Based on this discussion, areas for future investigation are proposed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2

Similar content being viewed by others

References

  1. Adouni, M., and A. Shirazi-Adl. Partitioning of knee joint internal forces in gait is dictated by the knee adduction angle and not by the knee adduction moment. J. Biomech. 47(7):1696–1703, 2014.

    Article  CAS  PubMed  Google Scholar 

  2. Altman, R., G. Alarcón, D. Appelrouth, et al. The American College of Rheumatology criteria for the classification and reporting of osteoarthritis of the hip. Arthritis Rheum. 34(5):505–514, 1991.

    Article  CAS  PubMed  Google Scholar 

  3. Andriacchi, T. P., A. Mündermann, R. L. Smith, E. J. Alexander, C. O. Dyrby, and S. Koo. A framework for the in vivo pathomechanics of osteoarthritis at the knee. Ann. Biomed. Eng. 32(3):447–457, 2004.

    Article  PubMed  Google Scholar 

  4. Arnold, J. B. Lateral wedge insoles for people with medial knee osteoarthritis: one size fits all, some or none? Osteoarthr. Cartil. 24(2):193–195, 2016.

    Article  CAS  PubMed  Google Scholar 

  5. Arroll, B., and F. Goodyear-Smith. Corticosteroid injections for osteoarthritis of the knee: meta-analysis. BMJ 328(7444):869, 2004.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Bellamy, N., J. Campbell, V. Robinson, T. Gee, R. Bourne, and G. Wells. Intraarticular corticosteroid for treatment of osteoarthritis of the knee. Cochrane Database Syst. Rev. 2:CD005328, 2006.

    Google Scholar 

  7. Bennell, K. L., K. A. Bowles, C. Payne, et al. Lateral wedge insoles for medial knee osteoarthritis: 12 month randomised controlled trial. BMJ 342:d2912, 2011.

    Article  PubMed  PubMed Central  Google Scholar 

  8. Bennell, K. L., K. A. Bowles, Y. Wang, F. Cicuttini, M. Davies-Tuck, and R. S. Hinman. Higher dynamic medial knee load predicts greater cartilage loss over 12 months in medial knee osteoarthritis. Ann. Rheum. Dis. 70(10):1770–1774, 2011.

    Article  PubMed  Google Scholar 

  9. Bennell, K. L., R. Buchbinder, and R. S. Hinman. Physical therapies in the management of osteoarthritis: current state of the evidence. Curr. Opin. Rheumatol. 27(3):304–311, 2015.

    Article  PubMed  Google Scholar 

  10. Bennell, K. L., D. J. Hunter, and R. S. Hinman. Management of osteoarthritis of the knee. BMJ 345:e4934, 2012.

    Article  PubMed  Google Scholar 

  11. Briem, K., M. J. Axe, and L. Snyder-Mackler. Medial knee joint loading increases in those who respond to hyaluronan injection for medial knee osteoarthritis. J. Orthop. Res. 27(11):1420–1425, 2009.

    Article  PubMed  Google Scholar 

  12. Butler, R. J., S. Marchesi, T. Royer, and I. S. Davis. The effect of a subject-specific amount of lateral wedge on knee mechanics in patients with medial knee osteoarthritis. J. Orthop. Res. 25(9):1121–1127, 2007.

    Article  PubMed  Google Scholar 

  13. Chapman, G. J., M. J. Parkes, L. Forsythe, D. T. Felson, and R. K. Jones. Ankle motion influences the external knee adduction moment and may predict who will respond to lateral wedge insoles?: an ancillary analysis from the SILK trial. Osteoarthr. Cartil. 23(8):1316–1322, 2015.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Clausen, B., T. P. Andriacchi, D. B. Nielsen, E. M. Roos, and A. Holsgaard-Larsen. Composition of the knee index, a three-dimensional biomechanical index for knee joint load, in subjects with mild to moderate knee osteoarthritis. Osteoarthr. Cartil. 22:S95–S96, 2014.

    Article  Google Scholar 

  15. Clauser, C. E., J. T. McConville, and J. W. Young. Weight, Volume, and Center of Mass of Segments of the Human Body. Ohio: Aerospace Medical Research Laboratory, Wright-Patterson Airforce Base, 1969.

    Google Scholar 

  16. Cole, G. K., B. M. Nigg, J. L. Ronsky, and M. R. Yeadon. Application of the joint coordinate system to three-dimensional joint attitude and movement representation: a standardization proposal. J. Biomech. Eng. 115(4A):344, 1993.

    Article  CAS  PubMed  Google Scholar 

  17. Crowninshield, R. D., and R. A. Brand. A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14(11):793–801, 1981.

    Article  CAS  PubMed  Google Scholar 

  18. Dempster, W. D. Space Requirements of the Seated Operator: Geometrical, Kinematic and Mechanical Aspects of the Body with Special Reference to the Limbs. Ohio: Aero Medical Laboratory, Wright-Patterson Airforce Base, 1955.

    Google Scholar 

  19. Duncan, R. C., E. M. Hay, J. Saklatvala, and P. R. Croft. Prevalence of radiographic osteoarthritis–it all depends on your point of view. Rheumatology 45(6):757–760, 2006.

    Article  CAS  PubMed  Google Scholar 

  20. Erhart, J. C., C. O. Dyrby, D. D. D’Lima, C. W. Colwell, and T. P. Andriacchi. Changes in in vivo knee loading with a variable-stiffness intervention shoe correlate with changes in the knee adduction moment. J. Orthop. Res. 28(12):1548–1553, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  21. Erhart, J. C., A. Mundermann, B. Elspas, N. J. Giori, and T. P. Andriacchi. Changes in knee adduction moment, pain, and functionality with a variable-stiffness walking shoe after 6 months. J. Orthop. Res. 28(7):873–879, 2010.

    PubMed  Google Scholar 

  22. Erhart, J. C., A. Mundermann, L. Mundermann, and T. P. Andriacchi. Predicting changes in knee adduction moment due to load-altering interventions from pressure distribution at the foot in healthy subjects. J. Biomech. 41(14):2989–2994, 2008.

    Article  PubMed  Google Scholar 

  23. Felson, D. T. Clinical practice. Osteoarthritis of the knee. N. Engl. J. Med. 354(8):841–848, 2006.

    Article  CAS  PubMed  Google Scholar 

  24. Foroughi, N., R. M. Smith, A. K. Lange, M. K. Baker, M. A. F. Singh, and B. Vanwanseele. Dynamic alignment and its association with knee adduction moment in medial knee osteoarthritis. Knee 17(3):210–216, 2010.

    Article  PubMed  Google Scholar 

  25. Foroughi, N., R. M. Smith, A. K. Lange, M. K. Baker, M. A. F. Singh, and B. Vanwanseele. Lower limb muscle strengthening does not change frontal plane moments in women with knee osteoarthritis: a randomized controlled trial. Clin. Biomech. 26(2):167–174, 2011.

    Article  Google Scholar 

  26. Friel, N. A., and C. R. Chu. The role of ACL injury in the development of posttraumatic knee osteoarthritis. Clin. Sports Med. 32(1):1–12, 2013.

    Article  PubMed  Google Scholar 

  27. Fukutani, N., H. Iijima, T. Fukumoto, et al. Association between varus thrust and “pain and stiffness” and “activities of daily living” in patients with medial knee osteoarthritis. Phys. Ther., 2015

  28. Grood, E. S., and W. J. Suntay. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J. Biomech. Eng. 105(2):136, 1983.

    Article  CAS  PubMed  Google Scholar 

  29. Hinman, R. S., K. A. Bowles, B. B. Metcalf, T. V. Wrigley, and K. L. Bennell. Lateral wedge insoles for medial knee osteoarthritis: effects on lower limb frontal plane biomechanics. Clin. Biomech. 27(1):27–33, 2012.

    Article  Google Scholar 

  30. Hinman, R. S., K. A. Bowles, C. Payne, and K. L. Bennell. Effect of length on laterally-wedged insoles in knee osteoarthritis. Arthritis Rheum. 59(1):144–147, 2008.

    Article  PubMed  Google Scholar 

  31. Hinman, R. S., M. A. Hunt, M. W. Creaby, T. V. Wrigley, F. J. McManus, and K. L. Bennell. Hip muscle weakness in individuals with medial knee osteoarthritis. Arthritis Care Res. 62(8):1190–1193, 2010.

    Article  Google Scholar 

  32. Hinman, R. S., C. Payne, B. R. Metcalf, T. V. Wrigley, and K. L. Bennell. Lateral wedges in knee osteoarthritis: what are their immediate clinical and biomechanical effects and can these predict a three-month clinical outcome? Arthritis Rheum. 59(3):408–415, 2008.

    Article  PubMed  Google Scholar 

  33. Hunter, D. J. Viscosupplementation for osteoarthritis of the knee. N. Engl. J. Med. 372(11):1040–1047, 2015.

    Article  CAS  PubMed  Google Scholar 

  34. Jones, R. K., G. J. Chapman, L. Forsythe, M. J. Parkes, and D. T. Felson. The relationship between reductions in knee loading and immediate pain response whilst wearing lateral wedged insoles in knee osteoarthritis. J. Orthop. Res. 32(9):1147–1154, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  35. Jones, R. K., C. J. Nester, J. D. Richards, et al. A comparison of the biomechanical effects of valgus knee braces and lateral wedged insoles in patients with knee osteoarthritis. Gait Posture 37(3):368–372, 2013.

    Article  PubMed  Google Scholar 

  36. Kadaba, M. P., H. K. Ramakrishnan, and M. E. Wootten. Measurement of lower extremity kinematics during level walking. J. Orthop. Res. 8(3):383–392, 1990.

    Article  CAS  PubMed  Google Scholar 

  37. Kakihana, W., M. Akai, K. Nakazawa, K. Naito, and S. Torii. Inconsistent knee varus moment reduction caused by a lateral wedge in knee osteoarthritis. Am. J. Phys. Med. Rehabil. 86(6):446–454, 2007.

    Article  PubMed  Google Scholar 

  38. Kakihana, W., M. Akai, K. Nakazawa, T. Takashima, K. Naito, and S. Torii. Effects of laterally wedged insoles on knee and subtalar joint moments. Arch. Phys. Med. Rehabil. 86(7):1465–1471, 2005.

    Article  PubMed  Google Scholar 

  39. Kean, C. O., K. L. Bennell, T. V. Wrigley, and R. S. Hinman. Relationship between hip abductor strength and external hip and knee adduction moments in medial knee osteoarthritis. Clin. Biomech. 30(3):226–230, 2015.

    Article  Google Scholar 

  40. Kerrigan, D. C., J. L. Lelas, J. Goggins, G. J. Merriman, R. J. Kaplan, and D. T. Felson. Effectiveness of a lateral-wedge insole on knee varus torque in patients with knee osteoarthritis. Arch. Phys. Med. Rehabil. 83(7):889–893, 2002.

    Article  PubMed  Google Scholar 

  41. Kito, N., K. Shinkoda, T. Yamasaki, et al. Contribution of knee adduction moment impulse to pain and disability in Japanese women with medial knee osteoarthritis. Clin. Biomech. 25(9):914–919, 2010.

    Article  Google Scholar 

  42. Lewinson, R. T., K. H. Collins, I. A. Vallerand, et al. Reduced knee joint loading with lateral and medial wedge insoles for management of knee osteoarthritis: a protocol for a randomized controlled trial. BMC Musculoskelet. Disord. 15:405, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Lewinson, R. T., C. A. Fukuchi, J. T. Worobets, and D. J. Stefanyshyn. The effects of wedged footwear on lower limb frontal plane biomechanics during running. Clin. J. Sport Med. 23(3):208–215, 2013.

    Article  PubMed  Google Scholar 

  44. Lewinson, R. T., and D. J. Stefanyshyn. Prediction of knee joint moment changes during walking in response to wedged insole interventions. Proc. Inst. Mech. Eng. H 230(4):335–342, 2016.

    Article  PubMed  Google Scholar 

  45. Lewinson, R. T., J. T. Worobets, and D. J. Stefanyshyn. The relationship between maximal hip abductor strength and resultant loading at the knee during walking. Proc. Inst. Mech. Eng. H 228(12):1258–1263, 2014.

    Article  PubMed  Google Scholar 

  46. Lewinson, R. T., J. T. Worobets, and D. J. Stefanyshyn. Calculation of external knee adduction moments: A comparison of an inverse dynamics approach and a simplified lever-arm approach. Knee 22(4):292–297, 2015.

    Article  PubMed  Google Scholar 

  47. Lewinson, R. T., J. T. Worobets, and D. J. Stefanyshyn. Control conditions for footwear insole and orthotic research. Gait Posture 48:99–105, 2016.

    Article  PubMed  Google Scholar 

  48. Liu, X., and M. Zhang. Redistribution of knee stress using laterally wedged insole intervention: finite element analysis of knee-ankle-foot complex. Clin. Biomech. 28(1):61–67, 2013.

    Article  Google Scholar 

  49. Loughlin, J. Genetic contribution to osteoarthritis development: current state of evidence. Curr. Opin. Rheumatol. 27(3):284–288, 2015.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Lynn, S. K., T. Kajaks, and P. A. Costigan. The effect of internal and external foot rotation on the adduction moment and lateral-medial shear force at the knee during gait. J. Sci. Med. Sport 11(5):444–451, 2008.

    Article  PubMed  Google Scholar 

  51. Maly, M. R. Abnormal and cumulative loading in knee osteoarthritis. Curr. Opin. Rheumatol. 20(5):547–552, 2008.

    Article  PubMed  Google Scholar 

  52. McCormick, C. J., D. R. Bonanno, and K. B. Landorf. The effect of customised and sham foot orthoses on plantar pressures. J Foot Ankle Res. 6:19, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  53. Messier, S. P., S. L. Mihalko, C. Legault, et al. Effects of intensive diet and exercise on knee joint loads, inflammation, and clinical outcomes among overweight and obese adults with knee osteoarthritis: the IDEA randomized clinical trial. JAMA 310(12):1263–1273, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Miyazaki, T. Dynamic load at baseline can predict radiographic disease progression in medial compartment knee osteoarthritis. Ann. Rheum. Dis. 61(7):617–622, 2002.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Moyer, R. F., T. B. Birmingham, D. M. Bryant, J. R. Giffin, K. A. Marriott, and K. M. Leitch. Biomechanical effects of valgus knee bracing: a systematic review and meta-analysis. Osteoarthr. Cartil. 23(2):178–188, 2015.

    Article  CAS  PubMed  Google Scholar 

  56. Nigg, B. M., and W. Herzog. Biomechanics of the Musculo-Skeletal System (3rd ed.). Hoboken, NJ: Wiley, 2007.

    Google Scholar 

  57. Nigg, B. M., P. Stergiou, G. Cole, D. Stefanyshyn, A. Mundermann, and N. Humble. Effect of shoe inserts on kinematics, center of pressure, and leg joint moments during running. Med. Sci. Sports Exerc. 35(2):314–319, 2003.

    Article  PubMed  Google Scholar 

  58. Pagani, C. H. F., M. Hinrichs, and G. P. Bruggemann. Kinetic and kinematic changes with the use of valgus knee brace and lateral wedge insoles in patients with medial knee osteoarthritis. J. Orthop. Res. 30(7):1125–1132, 2012.

    Article  Google Scholar 

  59. Park, S. K., and D. J. Stefanyshyn. Greater Q angle may not be a risk factor of patellofemoral pain syndrome. Clin. Biomech. 26(4):392–396, 2011.

    Article  Google Scholar 

  60. Parkes, M. J., N. Maricar, M. Lunt, et al. Lateral wedge insoles as a conservative treatment for pain in patients with medial knee osteoarthritis: a meta-analysis. JAMA 310(7):722–730, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Pham, T., J. F. Maillefert, C. Hudry, et al. Laterally elevated wedged insoles in the treatment of medial knee osteoarthritis. A two-year prospective randomized controlled study. Osteoarthr. Cartil. 12(1):46–55, 2004.

    Article  CAS  PubMed  Google Scholar 

  62. Public Health Agency of Canada. Arthritis in Canada: An Ongoing Challenge. Ottawa: Health Canada, 2003.

  63. Reeves, N. D., and F. L. Bowling. Conservative biomechanical strategies for knee osteoarthritis. Nat. Rev. Rheumatol. 7(2):113–122, 2011.

    Article  PubMed  Google Scholar 

  64. Robertson, D. G. E., G. E. Caldwell, J. Hamill, G. Kamen, and S. N. Whittlesey. Research Methods in Biomechanics (1st ed.). Champaign, IL: Human Kinetics, 2004.

    Google Scholar 

  65. Ruhdorfer, A. S., T. Dannhauer, W. Wirth, et al. Thigh muscle cross-sectional areas and strength in knees with early vs knees without radiographic knee osteoarthritis: a between-knee, within-person comparison. Osteoarthr. Cartil. 22(10):1634–1638, 2014.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Rutjes, A. W., P. Juni, B. R. da Costa, S. Trelle, E. Nuesch, and S. Reichenbach. Viscosupplementation for osteoarthritis of the knee: a systematic review and meta-analysis. Ann. Intern. Med. 157(3):180–191, 2012.

    Article  PubMed  Google Scholar 

  67. Schache, A. G., B. J. Fregly, K. M. Crossley, R. S. Hinman, and M. G. Pandy. The effect of gait modification on the external knee adduction moment is reference frame dependent. Clin. Biomech. (Bristol, Avon) 23(5):601–608, 2008.

    Article  Google Scholar 

  68. Schmalz, T., S. Blumentritt, H. Drewitz, and M. Freslier. The influence of sole wedges on frontal plane knee kinetics, in isolation and in combination with representative rigid and semi-rigid ankle-foot-orthoses. Clin. Biomech. 21(6):631–639, 2006.

    Article  Google Scholar 

  69. Sharma, L., D. E. Hurwitz, E. J. M. A. Thonar, et al. Knee adduction moment, serum hyaluronan level, and disease severity in medial tibiofemoral osteoarthritis. Arthritis Rheum. 41(7):1233–1240, 1998.

    Article  CAS  PubMed  Google Scholar 

  70. Sharma, L., J. Song, D. T. Felson, S. Cahue, E. Shamiyeh, and D. D. Dunop. The role of knee alignment in disease progression and functional decline in knee osteoarthritis. JAMA 286(2):188–195, 2001.

    Article  CAS  PubMed  Google Scholar 

  71. Stefanyshyn, D. J., P. Stergiou, V. M. Lun, W. H. Meeuwisse, and J. T. Worobets. Knee angular impulse as a predictor of patellofemoral pain in runners. Am. J. Sports Med. 34(11):1844–1851, 2006.

    Article  PubMed  Google Scholar 

  72. Teoh, J. C., J. H. Low, Y. B. Lim, et al. Investigation of the biomechanical effect of variable stiffness shoe on external knee adduction moment in various dynamic exercises. J. Foot Ankle Res. 6(1):39, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  73. The Arthritis Society of Canada. Arthritis Facts & Figures, pp. 1–8, 2015.

  74. The Centers for Disease Control and Prevention. Osteoarthritis, 16 May 2014. http://www.cdc.gov/arthritis/basics/osteoarthritis.htm2015.

  75. Toda, Y., N. Tsukimura, and N. Segal. An optimal duration of daily wear for an insole with subtalar strapping in patients with varus deformity osteoarthritis of the knee. Osteoarthr. Cartil. 13(4):353–360, 2005.

    Article  CAS  PubMed  Google Scholar 

  76. Waller, K. A., L. X. Zhang, K. A. Elsaid, B. C. Fleming, M. L. Warman, and G. D. Jay. Role of lubricin and boundary lubrication in the prevention of chondrocyte apoptosis. Proc. Natl. Acad. Sci. USA 110(15):5852–5857, 2013.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Walter, J. P., D. D. D’Lima, C. W. Colwell, Jr, and B. J. Fregly. Decreased knee adduction moment does not guarantee decreased medial contact force during gait. J. Orthop. Res. 28(10):1348–1354, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  78. Wang, S. Y., B. Olson-Kellogg, T. A. Shamliyan, J. Y. Choi, R. Ramakrishnan, and R. L. Kane. Physical therapy interventions for knee pain secondary to osteoarthritis: a systematic review. Ann. Intern. Med. 157(9):632–644, 2012.

    Article  PubMed  Google Scholar 

  79. Winter, D. A. Biomechanics and Motor Control of Human Movement (4th ed.). Hoboken, NJ: WIley, 2009.

    Book  Google Scholar 

  80. Wise, B. L., J. Niu, M. Yang, et al. Patterns of compartment involvement in tibiofemoral osteoarthritis in men and women and in whites and African Americans. Arthritis Care Res. 64(6):847–852, 2012.

    Article  Google Scholar 

  81. Wong, B. L., S. H. Kim, J. M. Antonacci, C. W. McIlwraith, and R. L. Sah. Cartilage shear dynamics during tibio-femoral articulation: effect of acute joint injury and tribosupplementation on synovial fluid lubrication. Osteoarthr. Cartil. 18(3):464–471, 2010.

    Article  CAS  PubMed  Google Scholar 

  82. Youssef, A. R., D. Longino, R. Seerattan, T. Leonard, and W. Herzog. Muscle weakness causes joint degeneration in rabbits. Osteoarthr. Cartil. 17(9):1228–1235, 2009.

    Article  Google Scholar 

  83. Zhang, W., R. W. Moskowitz, G. Nuki, et al. OARSI recommendations for the management of hip and knee osteoarthritis, Part II: OARSI evidence-based, expert consensus guidelines. Osteoarthr. Cartil. 16(2):137–162, 2008.

    Article  CAS  PubMed  Google Scholar 

  84. Zhuo, Q., W. Yang, J. Chen, and Y. Wang. Metabolic syndrome meets osteoarthritis. Nat. Rev. Rheumatol. 8(12):729–737, 2012.

    Article  CAS  PubMed  Google Scholar 

Download references

Funding

RTL is funded by an Alberta Innovates-Health Solutions MD-PhD Studentship. Funding agencies played no role in the development of this article.

Conflict of interest

RTL and DJS have filed a US Provisional Patent 62/183,055.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ryan T. Lewinson.

Additional information

Associate Editor Michael R. Torry oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lewinson, R.T., Stefanyshyn, D.J. Wedged Insoles and Gait in Patients with Knee Osteoarthritis: A Biomechanical Review. Ann Biomed Eng 44, 3173–3185 (2016). https://doi.org/10.1007/s10439-016-1696-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-016-1696-1

Keywords

Navigation