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TECHNICAL PAPERS

Three-Dimensional Dynamic Simulation of Total Knee Replacement Motion During a Step-Up Task

[+] Author and Article Information
Stephen J. Piazza

Center for Locomotion Studies and Departments of Kinesiology and Mechanical & Nuclear Engineering, Pennsylvania State University, University Park, PA 16802

Scott L. Delp

Biomechanical Engineering Division, Mechanical Engineering Department, Stanford University, Stanford, CA 94305

J Biomech Eng 123(6), 599-606 (Jul 31, 2001) (8 pages) doi:10.1115/1.1406950 History: Received March 02, 1999; Revised July 31, 2001
Copyright © 2001 by ASME
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References

Hefzy,  M. S., and Cooke,  T. D. V., 1996, “Review of Knee Models: 1996 Update,” Appl. Mech. Rev., 49, pp. S187–S193.
Hefzy,  M. S., and Grood,  E. S., 1988, “Review of Knee Models,” Appl. Mech. Rev., 41, pp. 1–13.
Wismans,  J., Veldpaus,  F., Janssen,  J., Huson,  A., and Struben,  P., 1980, “A Three-Dimensional Mathematical Model of the Knee-Joint,” J. Biomech., 13, pp. 677–685.
Yamaguchi,  G. T., and Zajac,  F. E., 1989, “A Planar Model of the Knee Joint to Characterize the Knee Extensor Mechanism,” J. Biomech., 22, pp. 1–10.
Piazza,  S. J., and Delp,  S. L., 1996, “The Influence of Muscles on Knee Flexion During the Swing Phase of Gait,” J. Biomech., 29, pp. 723–733.
Moeinzadeh,  M. H., Engin,  A. E., and Akkas,  N., 1983, “Two-Dimensional Dynamic Modelling of Human Knee Joint,” J. Biomech., 16, pp. 253–264.
Engin,  A. E., and Tümer,  S. T., 1993, “Improved Dynamic Model of the Human Knee Joint and Its Response to Impact Loading on the Lower Leg,” ASME J. Biomech. Eng., 115, pp. 137–143.
Tümer,  S. T., and Engin,  A. E., 1993, “Three-Body Segment Dynamic Model of the Human Knee,” ASME J. Biomech. Eng., 115, pp. 350–356.
Wongchaisuwat,  C., Hemami,  H., and Buchner,  H. J., 1984, “Control of Sliding and Rolling at Natural Joints,” ASME J. Biomech. Eng., 106, pp. 368–375.
Abdel-Rahman,  E., and Hefzy,  M. S., 1993, “A Two-Dimensional Dynamic Anatomical Model of the Human Knee Joint,” ASME J. Biomech. Eng., 115, pp. 357–365.
Abdel-Rahman,  E. M., and Hefzy,  M. S., 1998, “Three-Dimensional Dynamic Behaviour of the Human Knee Joint Under Impact Loading,” Med. Eng. Phys., 20, pp. 276–290.
Kim,  S., and Pandy,  M. G., 1993, “A Two-Dimensional Dynamic Model of the Human Knee Joint,” Biomed. Sci. Instrum., 29, pp. 33–46.
Tümer,  S. T., Wang,  X., and Akkas,  N., 1995, “A Planar Dynamic Anatomical Model of the Human Lower Limb,” Biomed. Eng.—Applications, Basis & Communications, 7, pp. 365–378.
Mirtich, B., and Canny, J., 1995, “Impulse-Based Simulation of Rigid Bodies,” Proc. 1995 Symposium on Interactive 3D Graphics, pp. 181–188.
Banks,  S. A., Markovich,  G. D., and Hodge,  W. A., 1997, “In Vivo Kinematics of Cruciate-Retaining and -Substituting Knee Arthroplasties,” J. Arthroplasty, 12, pp. 297–304.
Yamaguchi, G. T., 1989, “Feasibility and Conceptual Design of Functional Neuromuscular Stimulation Systems for the Restoration of Natural Gait to Paraplegics Based on Dynamic Musculoskeletal Models,” Ph.D. Dissertation, Stanford University, Stanford, CA.
Rosenthal,  D. E., and Sherman,  M. A., 1986, “High Performance Multibody Simulations via Symbolic Equation Manipulation and Kane’s Method,” J. Astronaut. Sci., 34, pp. 223–239.
Zajac,  F. E., 1989, “Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control,” Crit. Rev. Biomed. Eng., 17, pp. 359–411.
Delp,  S. L., Loan,  J. P., Hoy,  M. G., Zajac,  F. E., Topp,  E. L., and Rosen,  J. M., 1990, “An Interactive Graphics-Based Model of the Lower Extremity to Study Orthopaedic Surgical Procedures,” IEEE Trans. Biomed. Eng., 37, pp. 757–767.
Schutte,  L. M., Rodgers,  M. M., Zajac,  F. E., and Glaser,  R. M., 1993, “Improving the Efficacy of Electrical Stimulation-Induced Leg Cycle Ergometry: An Analysis Based on a Dynamic Musculoskeletal Model,” IEEE Trans. Rehabil. Eng., 1, pp. 109–125.
Delp,  S. L., and Loan,  J. P., 1995, “A Graphics-Based Software System to Develop and Analyze Models of Musculoskeletal Structures,” Comput. Biol. Med., 25, pp. 21–34.
Mommersteeg,  T. J., Blankevoort,  L., Huiskes,  R., Kooloos,  J. G., and Krauer,  J. M., 1996, “Characterization of the Mechanical Behavior of Human Knee Ligaments: A Numerical–Experimental Approach,” J. Biomech., 29, pp. 151–160.
Piazza,  S. J., Delp,  S. L., Stulberg,  S. D., and Stern,  S. H., 1998, “Anterior Placement of the Femoral Component in Total Knee Replacement Produces Collateral Ligament Laxity,” Trans. 44th Annu. Meet. — Orthop. Res. Soc., p. 1028.
Brantigan,  O. C., and Voshell,  A. F., 1941, “The Mechanics of the Ligaments and Menisci of the Knee Joint,” J. Bone Jt. Surg., Am. Vol., 23, pp. 44–66.
Trent,  P. S., Walker,  P. S., and Wolf,  B., 1976, “Ligament Length Patterns, Strength, and Rotational Axes of the Knee Joint,” Clin. Orthop. Relat. Res., 117, 263–70.
Haut,  R. C., and Powlison,  A. C., 1990, “The Effects of Test Environment and Cyclic Stretching on the Failure Properties of Human Patellar Tendons,” J. Orthop. Res., 8, pp. 532–540.
Harris,  N. L., Smith,  D. A., Lamoreaux,  L., and Purnell,  M., 1997, “Central Quadriceps Tendon for Anterior Cruciate Ligament Reconstruction. Part I: Morphometric and Biomechanical Evaluation,” Am. J. Sports Med., 25, pp. 23–28.
Bechtold,  J. E., Eastlund,  D. T., Butts,  M. K., Lagerborg,  D. F., and Kyle,  R. F., 1994, “The Effects of Freeze-Drying and Ethylene Oxide Sterilization on the Mechanical Properties of Human Patellar Tendon,” Am. J. Sports Med., 22, pp. 562–566.
Gottschalk, S., Lin, M. C., and Manocha, D., 1996, “OBBTree: A Hierarchical Structure for Rapid Interference Detection,” Proc. ACM SIGGRAPH Conference on Computer Graphics, pp. 171–180.
Lötstedt,  P., 1982, “Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 42, pp. 281–296.
Cottle, R. W., and Dantzig, G. B., 1968, “Complementary Pivot Theory of Mathematical Programming,” Linear Algebra and Its Applications, Vol. 1, pp. 103–125.
Baraff, D., 1994, “Fast Contact Force Computation for Nonpenetrating Rigid Bodies,” Proc. ACM SIGGRAPH Conference on Computer Graphics, pp. 23–34.
Beer, F. P., and Johnston, E. R., 1988, Vector Mechanics for Engineers: Statics and Dynamics, McGraw-Hill, New York.
Baraff, D., 1989, “Analytical Methods for Dynamic Simulation of Non-penetrating Rigid Bodies,” Trans. ACM Siggraph, pp. 223–232.
Piazza, S. J., 1998, “Simulation-Based Design of Total Knee Replacements,” Ph.D. Dissertation, Northwestern University, Evanston, IL.
Banks,  S. A., Backus,  S. I., Otis,  J. C., Haas,  S. B., and Laskin,  R. S., 2000, “Motions and Forces in Total Knee Replacements During Stair Rise,” Trans. 46th Annu. Meet. — Orthop. Res. Soc., p. 431.
Taylor,  S. J., Walker,  P. S., Perry,  J. S., Cannon,  S. R., and Woledge,  R., 1998, “The Forces in the Distal Femur and the Knee During Walking and Other Activities Measured by Telemetry,” J. Arthroplasty, 13, pp. 428–437.
Sathasivam,  S., and Walker,  P. S., 1997, “A Computer Model With Surface Friction for the Prediction of Total Knee Kinematics,” J. Biomech., 30, pp. 177–184.
Mochon,  S., and McMahon,  T. A., 1980, “Ballistic Walking: An Improved Model,” Math. Biosci., 52, pp. 241–260.
Yamaguchi,  G. T., and Zajac,  F. E., 1990, “Restoring Unassisted Natural Gait to Paraplegics via Functional Neuromuscular Stimulation: A Computer Simulation Study,” IEEE Trans. Biomed. Eng., 37, pp. 886–902.
Stauffer,  R. N., Chao,  E. Y., and Brewster,  R. C., 1977, “Force and Motion Analysis of the Normal, Diseased, and Prosthetic Ankle Joint,” Clin. Orthop. Relat. Res., 127, pp. 189–196.
Cottle,  R. W., 1968, “On a Problem in Linear Equalities,” J. London Math. Soc., 43, pp. 378–384.
Neptune,  R. R., and Hull,  M. L., 1998, “Evaluation of Performance Criteria for Simulation of Submaximal Steady-State Cycling Using a Forward Dynamic Model,” ASME J. Biomech. Eng., 120, pp. 334–341.
Winter, D. A., 1979, Biomechanics of Human Movement, Wiley, New York.
Huberti,  H. H., Hayes,  W. C., Stone,  J. L., and Shybut,  G. T., 1984, “Force Ratios in the Quadriceps Tendon and Ligamentum Patellae,” J. Orthop. Res., 2, pp. 49–54.
Miller,  R. K., Murray,  D. W., Gill,  H. S., O’Connor,  J. J., and Goodfellow,  J. W., 1997, “In Vitro Patellofemoral Joint Force Determined by a Non-Invasive Technique,” Clin. Biomech., 12, pp. 1–7.
Nisell,  R., 1985, “Mechanics of the Knee. A Study of Joint and Muscle Load With Clinical Applications,” Acta Orthop. Scand. Suppl., 216, pp. 1–42.

Figures

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(A) The three-dimensional body model used to simulate step-up. The swing foot passes through the step because knee and ankle motion in the swing leg were not modeled. The stance knee was fitted with a total knee replacement and the stance foot was fixed to the step throughout the simulation. (B) Illustration of the six body segments modeled. (C) Orientation of each of the six segment-fixed coordinate systems.
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Flow chart describing the organization of the simulation. Implant motions were determined by using the SD/FAST software package to create differential equations of motion. These equations were numerically integrated to calculate motions while forces were computed and applied that represented the actions of muscles and ligaments and the effects of prescribed motion. SD/FAST input files and routines that computed muscle and ligament forces during the simulation were created using Dynamics Pipeline, a second software package.
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EMG data that has been rectified, filtered, averaged, and smoothed. These seven curves were used to prescribe the activation input of 11 of the 13 musculotendon actuators. The two remaining actuators, representing tensor fascia lata and sartorius, received no activation input.
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Knee flexion versus time during step-ups performed by a normal subject (dashed line and shaded area represent the mean and one standard deviation above and below the mean), and simulated knee flexion (solid line)
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Simulated and measured forces at the prosthetic knee plotted against knee flexion angle. Net intersegmental forces at the knee in the present simulation (solid curves) were defined as the difference between resultant muscle force and the articular contact force 44. Corresponding net intersegmental forces, averaged over five patients with posterior cruciate-substituting knee implants, were reported by Banks et al. 36 (dashed curves with shading representing ± one standard deviation). All forces have been normalized by body weight (BW). The components of the tibiofemoral articular contact forces (dash-dot curves) are also presented. (A) Superior–inferior forces. Positive net force indicates a net upward force applied to the tibia and positive articular contact force indicates a force applied to the tibia downward along its long axis. (B) Anterior–posterior forces. Positive net force is in the anterior direction and positive articular contact force indicates a posteriorly directed force applied to the tibia. (C) Medial–lateral forces. Positive net force is in the lateral direction and positive articular contact force indicates a medially directed force applied to the tibia.
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Anteroposterior positions of the lowest points on the lateral (top) and medial (middle) femoral condyles relative to the tibial component, and the minimum distance separating the femoral cam and tibial spine (bottom). Anteroposterior condyle positions are specified relative to the anteroposterior midline of the tibial component (anterior positive). Dashed lines with shading are the mean lowest-point positions (±one standard deviation) and spine-cam separations measured by Banks et al. 15 in patients who had received the same implant as that modeled in the present study.
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Ratios of patellar ligament force (Fpl) to quadriceps force (Fq) computed during the present simulation and measured in cadavers 454647.

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