Ahmet Erdemir

09-01-1998, 06:01 PM

On Tue, 1 Sep 1998, Chung-huang YU wrote:

> Hi,

>

> I am wondering whether someone out there can help me.

>

> I have project which aims to model the 3D knee joint as realistic as

> possible: 3D artificulation surfaces, ligaments, muscles with wrapping

> points, patella, etc. I want to calculate the contact point and contact

> forces once the muscle activations are specified.

>

> I would think there are 6 d.o.f in the knee, and due to the constraints

> of muscle forces, ligaments, etc., the joint angle and contact points

> would be determined. My difficulty is how to device a surface contact

> algorithm for this task and how to do it, via a commerical package, or

> programming in C? Another difficulty is that the soft tissues wrap

> around the the bones, so the line of action is changeing during motion.

>

> Are there any packages avaiable or any reference papers for these

> probelms?

>

Hi,

I just finished my Master thesis related with the three-dimensional

modelling of the human knee joint. I don't know if you are trying to built

a dynamic model or a static model, and I am not sure if you model the

contact between the bones as rigid and deformable, but the references

below may help you to develop a model in either case.

Ahmet ERDEMIR

ODTU, ICHMT, Mak. Muh. Bol.

06531, Ankara, TURKEY

phone: +90 312 210 2541

fax: +90 312 210 1331

e-mail: erdemir@fiesta.me.metu.edu.tr

REFERENCES

Abdel-Rahman, E. (1995) Three-dimensional dynamic anatomically based model

of the human tibio-femoral joint. PhD dissertation. Dept. of Mech. Eng.,

Univ. of Toledo, Toledo, OH, USA.

Abdel-Rahman, E., Hefzy, M. S. (1993) A two-dimensional anatomical model

of the human knee joint. J. Biomech. Eng. 115, 357-365.

An, K. N., Himeno, S., Tsumura, H., Kawai, T., Chao, E. Y. S. (1990)

Pressure distribution on articular surfaces: application to joint

stability evaluation. J. Biomechanics 23, 1013-1020.

Andriacchi, T. P., Mikosz, R. P., Hampton, S. J., Galante, J. O. (1983)

Model studies of the stiffness characteristics of the human knee joint. J.

Biomechanics 16, 23-29.

Ateshian, G. A. (1993) A B-spline least-squares surface-fitting method for

articular surfaces of diarthrodial joints. J. Biomech. Eng. 115, 366-373.

Bendjaballah, M. Z., Shirazi-Adl, A., Zukor, D. J. (1995) Biomechanics of

the human knee in compression: Reconstruction, mesh generation and finite

element analysis. The Knee 2, 69-79.

Beynnon, B., Yu, J., Huston, D., Fleming, B., Johnson, R., Haugh, L.,

Pope, M. H. (1996) A sagittal plane model of the knee and cruciate

ligaments with application of a sensitivity analysis. J. Biomech. Eng.

118, 227-239.

Blankevoort, L. (1991) Passive motion characteristics of the human knee

joint: experiments and computer simulations. PhD dissertation, University

of Nijmegen, Nijmegen, The Netherlands.

Blankevoort, L., Huiskes, R. (1991) Ligament-bone interaction in a

three-dimensional model of the knee. J. Biomech. Eng. 113, 263-269.

Blankevoort, L., Huiskes, R., de Lange, A. (1988) The envelope of passive

knee-joint motion. J. Biomechanics 21, 705-720.

Blankevoort, L., Huiskes, R., de Lange, A. (1990) Helical axes of passive

knee-joint motions. J. Biomechanics 23, 1219-1229.

Blankevoort, L., Huiskes, R., Kuiper, J. H., Grootenboer, H. J. (1991a)

Articular contact in a three-dimensional model of the knee. J.

Biomechanics 24, 1019-1031.

Blankevoort, L., Huiskes, R., de Lange, A. (1991b) Recruitment of

knee-joint ligaments. J. Biomech. Eng. 113, 94-103.

Butler, D. L., Noyes, F. R., Grood, E. S. (1980) Ligamentous restraints to

anterior-posterior drawer in the human knee. J. Bone Jt. Surgery 62A,

259-270.

Crowninshield, R., Pope, M. H., Johnson, R. J. (1976) An analytical model

of the knee. J. Biomechanics 9, 397-405.

Engin, A. E., Moeinzadeh, M. H. (1982) Modeling of human joint structures.

AFAMRL Report, AFAMRL-TR-81-117.

Engin, A. E., T|mer S. T. (1993) Improved dynamic model of the human knee

joint and its response to impact loading on the lower leg. J. Biomech.

Eng. 115, 137-143.

Essinger, J. R., Leyvraz, P. F., Heegard, J. H., Robertson, D. D. (1989) A

mathematical model for the evaluation of the behaviour during flexion of

condylar-type knee prostheses. J. Biomechanics 22, 1229-1241.

Garg, A., Walker, P. S. (1990) Prediction of total knee motion using a

three-dimensional computer-graphics model. J. Biomechanics 23, 45- 58.

Grood, E. S., Hefzy, M. S. (1982) An analytical technique for modeling

joint stiffness. Part I: Ligamentous forces. J. Biomech. Eng. 104,

330-337.

Grood, E. S., Suntay, W. J. (1983) A joint coordinate system for the

clinical description of three-dimensional motions: application of the

knee. J. Biomech. Eng. 105, 136-144.

Heegaard, J., Leyvraz, P. F., Curnier, A., Rakotomanana, L., Huiskes, R.

(1995) The biomechanics of the human patella during passive knee flexion.

J. Biomechanics 28, 1265-1279.

Hefzy, M. S., Cooke, T. D. V. (1996) Review of knee models: 1996 update.

Appl. Mech. Rev. 49, 187-193.

Hefzy, M. S., Grood, E. S. (1983) An analytical technique for modeling

joint stiffness. Part II: Ligamentous geometric nonlinearities. J.

Biomech. Eng. 105, 145-153.

Hefzy, M. S., Grood, E. S. (1988) Review of knee models. Appl. Mech. Rev.

41, 1-13.

Hirokawa, S. (1991) Three-dimensional mathematical model analysis of the

patellofemoral joint. J. Biomechanics 24, 659-671.

Hsieh, H. H., Walker, P. S. (1976) Stabilizing mechanisms of the loaded

and unloaded knee joint. J. Bone Jt. Surgery 58A, 87-93.

Kurasawa, H., Walker, P. S., Abe, S., Garg, A., Hunter, T. (1985) Geometry

and motion of the knee for implant and orthotic design. J. Biomechanics

18, 487-499.

Lafortune, M. A., Cavanagh, P. R., Sommer III, H. J., Kalenak, A. (1992)

Three-dimensional kinematics of the human knee during walking. J.

Biomechanics 25, 347-357.

Loch, D. A., Luo, Z., Lewis, J. L., Stewart, N. J. (1992) A theoretical

model of the knee and ACL: theory and experimental verification. J.

Biomechanics 25, 81-90.

Markolf, K. L., Bargar, W. L., Shoemaker, S. C., Amstutz, H. C. (1981) The

role of joint load in knee stability. J. Bone Jt. Surgery 63A, 570-585.

Markolf, K. L., Graff-Radford, A., Amstutz, H. C. (1978) In vivo knee

stability. A quantitative assessment using an instrumented clinical

testing apparatus. J. Bone Jt. Surgery 60A, 664-674.

Markolf, K. L., Gorek, J. F., Kabo, M., Shapiro, M. S. (1990) Direct

measurement of resultant forces in the anterior cruciate ligament. J. Bone

Jt. Surgery 72A, 557-567.

Markolf, K. L., Kochan, A., Amstutz, H. C. (1984) Measurement of knee

stiffness and laxity with documented absence of the anterior cruciate

ligament. J. Bone Jt. Surgery 66A, 242-252.

Markolf, K. L., Mensch, J. S., Amstutz, H. C. (1976) Stiffness and laxity

of the knee - the contribution of the supporting structures. A

quantitative in vitro study. J. Bone Jt. Surgery 58A, 583-594.

Martelli, S. (1997) Istituti Ortopedici Rizzoli, Laboratorio di

Biomeccanica, Bologna, Italy, private communication on internet.

Moeinzadeh, M. H., Engin, A. E., Akkas, N. (1983) Two-dimensional dynamic

modelling of human knee joint. J. Biomechanics 16, 253-264.

Mommersteeg, T. J. A., Blankevoort, L., Huiskes, R., Koolos, J. G. M.,

Kauer, J. M. G. (1996a) Characterization of the mechanical behavior of

human knee ligaments: a numerical-experimental approach. J. Biomechanics

29, 151-160.

Mommersteeg, T. J. A., Huiskes, R., Blankevoort, L., Koolos, J. G. M.,

Kauer, J. M. G., Maathuis, P. G. M. (1996b) A global verification study of

a quasi-static knee model with multi-bundle ligaments. J. Biomechanics 29,

1659-1664.

Morrison, J. B. (1970) The mechanics of the knee joint in relation to

normal walking. J. Biomechanics 3, 51-61.

Pandy, M. G., Shelburne, K. B. (1997) Dependence of cruciate-ligament

loading on muscle forces and external load. J. Biomechanics 30, 1015-1024.

Pennock, G. R., Clark, K. J. (1990) An anatomy based coordinate system for

the description of the kinematic displacements in the human knee. J.

Biomechanics 23, 1209-1218.

Piziali, R. L., Seering, W. P., Nagel, D. A., Schurman, D. J. (1980) The

function of the primary ligaments of the knee in anterior-posterior and

medial-lateral motions. J. Biomechanics 13, 777-784.

Press, W. H., Teukolsky, S. A., Vetterling, W. T. (1993) Numerical recipes

in C: The art of scientific computing. Cambridge University Press,

Cambridge.

Sathasivam, S., Walker, P. S. (1997) A computer model with surface

friction for the prediction of total knee kinematics. J. Biomechanics 30,

177-184.

Seirig, A., Arvikar, R. J. (1975) The prediction of muscular load sharing

and joint forces in the lower extremities during walking. J. Biomechanics

8, 89-102.

Shelburne, K. B., Pandy, M. G. (1997) A musculoskeletal model of the knee

for evaluating ligament forces during isometric contractions. J.

Biomechanics 30, 163-176.

Shirazi-Adl, A., Jilani, A., Bendjaballah, M. Z. (1998) Passive response

computation of tibiofemoral knee joint in internal/external torques.

Integrated Design and Process Technology IDPT-1, 13-18.

T|mer, S. T., Engin, A. E. (1993) Three-body segment dynamic model of the

human knee. J. Biomech. Eng. 115, 350-356.

Van Eijden, T. M. G. J., Kouwenhoven, E., Verburg, J., Weijs, W. A.

(1986), Mathematical model of the patello-femoral joint. J. Biomechanics

19, 219-229.

Walker, P. S., Rovick, J. S., Robertson, D. D. (1988) The effects of knee

brace hinge design and placement on joint mechanics. J. Biomechanics 21,

965-974.

Wang, C-J., Walker, P. S. (1973) The effects of flexion and rotation on

the length patterns of the ligaments of the knee. J. Biomechanics 6,

587-596.

Wang, C.-J., Walker, P. S. (1974) Rotatory laxity of the human knee joint.

J. Bone Jt. Surgery 56A, 161-170.

Wilson, D. R., O'Connor, J. J. (1997) A three-dimensional geometric model

of the knee for the study of joint forces in gait. Gait & Posture 5,

108-115.

Winter, D. A. (1990) Biomechanics and motor control of human movement,

Second Edition, New York, John Wiley & Sons.

Wismans, J. (1980) A three-dimensional mathematical model of the human

knee joint. PhD dissertation, Eindhoven University of Technology,

Eindhoven, The Netherlands.

Wismans, J., Veldpaus, F., Janssen, J., Huson, A., Struben, P. (1980) A

three-dimensional mathematical model of the knee-joint. J. Biomechanics

13, 677-685.

Wongchaisuwat, C., Hemami, H., Buchner, H. J. (1984) Control of sliding

and rolling at natural joints. J. Biomech. Eng. 106, 368-375.

Yamaguchi, G. T., Zajac, F. E. (1989) A planar model of the knee joint to

characterize the knee extensor mechanism. J. Biomechanics 22, 1-10.

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> Hi,

>

> I am wondering whether someone out there can help me.

>

> I have project which aims to model the 3D knee joint as realistic as

> possible: 3D artificulation surfaces, ligaments, muscles with wrapping

> points, patella, etc. I want to calculate the contact point and contact

> forces once the muscle activations are specified.

>

> I would think there are 6 d.o.f in the knee, and due to the constraints

> of muscle forces, ligaments, etc., the joint angle and contact points

> would be determined. My difficulty is how to device a surface contact

> algorithm for this task and how to do it, via a commerical package, or

> programming in C? Another difficulty is that the soft tissues wrap

> around the the bones, so the line of action is changeing during motion.

>

> Are there any packages avaiable or any reference papers for these

> probelms?

>

Hi,

I just finished my Master thesis related with the three-dimensional

modelling of the human knee joint. I don't know if you are trying to built

a dynamic model or a static model, and I am not sure if you model the

contact between the bones as rigid and deformable, but the references

below may help you to develop a model in either case.

Ahmet ERDEMIR

ODTU, ICHMT, Mak. Muh. Bol.

06531, Ankara, TURKEY

phone: +90 312 210 2541

fax: +90 312 210 1331

e-mail: erdemir@fiesta.me.metu.edu.tr

REFERENCES

Abdel-Rahman, E. (1995) Three-dimensional dynamic anatomically based model

of the human tibio-femoral joint. PhD dissertation. Dept. of Mech. Eng.,

Univ. of Toledo, Toledo, OH, USA.

Abdel-Rahman, E., Hefzy, M. S. (1993) A two-dimensional anatomical model

of the human knee joint. J. Biomech. Eng. 115, 357-365.

An, K. N., Himeno, S., Tsumura, H., Kawai, T., Chao, E. Y. S. (1990)

Pressure distribution on articular surfaces: application to joint

stability evaluation. J. Biomechanics 23, 1013-1020.

Andriacchi, T. P., Mikosz, R. P., Hampton, S. J., Galante, J. O. (1983)

Model studies of the stiffness characteristics of the human knee joint. J.

Biomechanics 16, 23-29.

Ateshian, G. A. (1993) A B-spline least-squares surface-fitting method for

articular surfaces of diarthrodial joints. J. Biomech. Eng. 115, 366-373.

Bendjaballah, M. Z., Shirazi-Adl, A., Zukor, D. J. (1995) Biomechanics of

the human knee in compression: Reconstruction, mesh generation and finite

element analysis. The Knee 2, 69-79.

Beynnon, B., Yu, J., Huston, D., Fleming, B., Johnson, R., Haugh, L.,

Pope, M. H. (1996) A sagittal plane model of the knee and cruciate

ligaments with application of a sensitivity analysis. J. Biomech. Eng.

118, 227-239.

Blankevoort, L. (1991) Passive motion characteristics of the human knee

joint: experiments and computer simulations. PhD dissertation, University

of Nijmegen, Nijmegen, The Netherlands.

Blankevoort, L., Huiskes, R. (1991) Ligament-bone interaction in a

three-dimensional model of the knee. J. Biomech. Eng. 113, 263-269.

Blankevoort, L., Huiskes, R., de Lange, A. (1988) The envelope of passive

knee-joint motion. J. Biomechanics 21, 705-720.

Blankevoort, L., Huiskes, R., de Lange, A. (1990) Helical axes of passive

knee-joint motions. J. Biomechanics 23, 1219-1229.

Blankevoort, L., Huiskes, R., Kuiper, J. H., Grootenboer, H. J. (1991a)

Articular contact in a three-dimensional model of the knee. J.

Biomechanics 24, 1019-1031.

Blankevoort, L., Huiskes, R., de Lange, A. (1991b) Recruitment of

knee-joint ligaments. J. Biomech. Eng. 113, 94-103.

Butler, D. L., Noyes, F. R., Grood, E. S. (1980) Ligamentous restraints to

anterior-posterior drawer in the human knee. J. Bone Jt. Surgery 62A,

259-270.

Crowninshield, R., Pope, M. H., Johnson, R. J. (1976) An analytical model

of the knee. J. Biomechanics 9, 397-405.

Engin, A. E., Moeinzadeh, M. H. (1982) Modeling of human joint structures.

AFAMRL Report, AFAMRL-TR-81-117.

Engin, A. E., T|mer S. T. (1993) Improved dynamic model of the human knee

joint and its response to impact loading on the lower leg. J. Biomech.

Eng. 115, 137-143.

Essinger, J. R., Leyvraz, P. F., Heegard, J. H., Robertson, D. D. (1989) A

mathematical model for the evaluation of the behaviour during flexion of

condylar-type knee prostheses. J. Biomechanics 22, 1229-1241.

Garg, A., Walker, P. S. (1990) Prediction of total knee motion using a

three-dimensional computer-graphics model. J. Biomechanics 23, 45- 58.

Grood, E. S., Hefzy, M. S. (1982) An analytical technique for modeling

joint stiffness. Part I: Ligamentous forces. J. Biomech. Eng. 104,

330-337.

Grood, E. S., Suntay, W. J. (1983) A joint coordinate system for the

clinical description of three-dimensional motions: application of the

knee. J. Biomech. Eng. 105, 136-144.

Heegaard, J., Leyvraz, P. F., Curnier, A., Rakotomanana, L., Huiskes, R.

(1995) The biomechanics of the human patella during passive knee flexion.

J. Biomechanics 28, 1265-1279.

Hefzy, M. S., Cooke, T. D. V. (1996) Review of knee models: 1996 update.

Appl. Mech. Rev. 49, 187-193.

Hefzy, M. S., Grood, E. S. (1983) An analytical technique for modeling

joint stiffness. Part II: Ligamentous geometric nonlinearities. J.

Biomech. Eng. 105, 145-153.

Hefzy, M. S., Grood, E. S. (1988) Review of knee models. Appl. Mech. Rev.

41, 1-13.

Hirokawa, S. (1991) Three-dimensional mathematical model analysis of the

patellofemoral joint. J. Biomechanics 24, 659-671.

Hsieh, H. H., Walker, P. S. (1976) Stabilizing mechanisms of the loaded

and unloaded knee joint. J. Bone Jt. Surgery 58A, 87-93.

Kurasawa, H., Walker, P. S., Abe, S., Garg, A., Hunter, T. (1985) Geometry

and motion of the knee for implant and orthotic design. J. Biomechanics

18, 487-499.

Lafortune, M. A., Cavanagh, P. R., Sommer III, H. J., Kalenak, A. (1992)

Three-dimensional kinematics of the human knee during walking. J.

Biomechanics 25, 347-357.

Loch, D. A., Luo, Z., Lewis, J. L., Stewart, N. J. (1992) A theoretical

model of the knee and ACL: theory and experimental verification. J.

Biomechanics 25, 81-90.

Markolf, K. L., Bargar, W. L., Shoemaker, S. C., Amstutz, H. C. (1981) The

role of joint load in knee stability. J. Bone Jt. Surgery 63A, 570-585.

Markolf, K. L., Graff-Radford, A., Amstutz, H. C. (1978) In vivo knee

stability. A quantitative assessment using an instrumented clinical

testing apparatus. J. Bone Jt. Surgery 60A, 664-674.

Markolf, K. L., Gorek, J. F., Kabo, M., Shapiro, M. S. (1990) Direct

measurement of resultant forces in the anterior cruciate ligament. J. Bone

Jt. Surgery 72A, 557-567.

Markolf, K. L., Kochan, A., Amstutz, H. C. (1984) Measurement of knee

stiffness and laxity with documented absence of the anterior cruciate

ligament. J. Bone Jt. Surgery 66A, 242-252.

Markolf, K. L., Mensch, J. S., Amstutz, H. C. (1976) Stiffness and laxity

of the knee - the contribution of the supporting structures. A

quantitative in vitro study. J. Bone Jt. Surgery 58A, 583-594.

Martelli, S. (1997) Istituti Ortopedici Rizzoli, Laboratorio di

Biomeccanica, Bologna, Italy, private communication on internet.

Moeinzadeh, M. H., Engin, A. E., Akkas, N. (1983) Two-dimensional dynamic

modelling of human knee joint. J. Biomechanics 16, 253-264.

Mommersteeg, T. J. A., Blankevoort, L., Huiskes, R., Koolos, J. G. M.,

Kauer, J. M. G. (1996a) Characterization of the mechanical behavior of

human knee ligaments: a numerical-experimental approach. J. Biomechanics

29, 151-160.

Mommersteeg, T. J. A., Huiskes, R., Blankevoort, L., Koolos, J. G. M.,

Kauer, J. M. G., Maathuis, P. G. M. (1996b) A global verification study of

a quasi-static knee model with multi-bundle ligaments. J. Biomechanics 29,

1659-1664.

Morrison, J. B. (1970) The mechanics of the knee joint in relation to

normal walking. J. Biomechanics 3, 51-61.

Pandy, M. G., Shelburne, K. B. (1997) Dependence of cruciate-ligament

loading on muscle forces and external load. J. Biomechanics 30, 1015-1024.

Pennock, G. R., Clark, K. J. (1990) An anatomy based coordinate system for

the description of the kinematic displacements in the human knee. J.

Biomechanics 23, 1209-1218.

Piziali, R. L., Seering, W. P., Nagel, D. A., Schurman, D. J. (1980) The

function of the primary ligaments of the knee in anterior-posterior and

medial-lateral motions. J. Biomechanics 13, 777-784.

Press, W. H., Teukolsky, S. A., Vetterling, W. T. (1993) Numerical recipes

in C: The art of scientific computing. Cambridge University Press,

Cambridge.

Sathasivam, S., Walker, P. S. (1997) A computer model with surface

friction for the prediction of total knee kinematics. J. Biomechanics 30,

177-184.

Seirig, A., Arvikar, R. J. (1975) The prediction of muscular load sharing

and joint forces in the lower extremities during walking. J. Biomechanics

8, 89-102.

Shelburne, K. B., Pandy, M. G. (1997) A musculoskeletal model of the knee

for evaluating ligament forces during isometric contractions. J.

Biomechanics 30, 163-176.

Shirazi-Adl, A., Jilani, A., Bendjaballah, M. Z. (1998) Passive response

computation of tibiofemoral knee joint in internal/external torques.

Integrated Design and Process Technology IDPT-1, 13-18.

T|mer, S. T., Engin, A. E. (1993) Three-body segment dynamic model of the

human knee. J. Biomech. Eng. 115, 350-356.

Van Eijden, T. M. G. J., Kouwenhoven, E., Verburg, J., Weijs, W. A.

(1986), Mathematical model of the patello-femoral joint. J. Biomechanics

19, 219-229.

Walker, P. S., Rovick, J. S., Robertson, D. D. (1988) The effects of knee

brace hinge design and placement on joint mechanics. J. Biomechanics 21,

965-974.

Wang, C-J., Walker, P. S. (1973) The effects of flexion and rotation on

the length patterns of the ligaments of the knee. J. Biomechanics 6,

587-596.

Wang, C.-J., Walker, P. S. (1974) Rotatory laxity of the human knee joint.

J. Bone Jt. Surgery 56A, 161-170.

Wilson, D. R., O'Connor, J. J. (1997) A three-dimensional geometric model

of the knee for the study of joint forces in gait. Gait & Posture 5,

108-115.

Winter, D. A. (1990) Biomechanics and motor control of human movement,

Second Edition, New York, John Wiley & Sons.

Wismans, J. (1980) A three-dimensional mathematical model of the human

knee joint. PhD dissertation, Eindhoven University of Technology,

Eindhoven, The Netherlands.

Wismans, J., Veldpaus, F., Janssen, J., Huson, A., Struben, P. (1980) A

three-dimensional mathematical model of the knee-joint. J. Biomechanics

13, 677-685.

Wongchaisuwat, C., Hemami, H., Buchner, H. J. (1984) Control of sliding

and rolling at natural joints. J. Biomech. Eng. 106, 368-375.

Yamaguchi, G. T., Zajac, F. E. (1989) A planar model of the knee joint to

characterize the knee extensor mechanism. J. Biomechanics 22, 1-10.

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