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Two-dimensional dynamic modeling of human knee joint
Abstracts
346 THE APPLlCATlON
OF ROENTGENSTEREOPHOTOCRAMMETRY
FOR EVALUATlONS OF KNEE-
JOINT KINEMATICS 1N VITRO
A. DE LANGE*, R. v. DuKt, R. HUISKES*,G. SELVIK: and TH. J. G. v. RENS*(‘Orthopaedic Biomechanics Lab., University of Nijmegen, The Netherlands; tDept. Orthopaedic Surgery, St. Lucas Hospital, Amsterdam, The Netherlands. , $Dept. Anatomy, University of Lund, Sweden) To obtain accurate data for the description of knee-joint motion, roentgenstereophotogrammetric measurement methods are used. The bones are provided with tantalum markers, of which the three-dimensional positional changes are determined with an accuracy of 0.02 mm. Applying rigid body kinematics, motion parameters are calculated. Results of five cadaveric knee joints are presented, including exo-rotation and ad-abduction angles, length patterns of posterior and anterior fibers of cruciate and collateral ligaments, and part of the posterior capsule, as a function of flexion-extension angle. Exoendorotation freedom of motion is studied as well, for various flexion-extension angles. Results show consistent behavior for the different specimens.
TWO-DIMENSIONAL
DYNAMIC MODELING
OF HUMAN KNEE JOINT
MANSSOURH. MOEINZADEH, ALI E. ENGIN (Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio 43210, U.S.A.) and NURI AKKAS(Department of Civil Engineering, Middle East Technical University, Ankara, Turkey) A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modeled as nonlinear elastic springs with realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are sotved numerically. Time derivatives are approximated by Newmark difference formulas and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.
VALIDATION
OF WElNBACH AND HANAVAN MODELS FOR EBTlMATlON OF FOREARM VOLUME AND POSITION OF CENTER OF MASS
DIANE RODRIGUEand MICHELINEGAGNON (Dlpartement d’bducation physique, Universit6 de Montrkl, 2100, boul. Edouard-Montpetit, Montreal, Qulbec H3C 357, Canada) The purpose of the present study was to validate Weinbach and Hanavan models for estimation of forearm volume and location of center of mass. The study was conducted using 20 forearms from embalmed cadavers of six men and four women. Mean error for volume determination was 5.05% and 7.43% for Weinbach and Hanavan models respectively, while mean error for location of center of mass was respectively 4.63% and 6.33%. Furthermore, locations of center of volume and center of mass may be considered to correspond to each other, when using the Weinbach model. Contrarily to the Hanavan model, the accuracy obtained with the Weinbach model is independent of the shape of the forearm.
BIOMECHANICAL
DIVISION OF EXTREMITIES FOR MEASUREMENT OF INERTlA PROPERTlES
WLODZIMIERZS. ERDMANN(Biomechanics
Laboratory, College of Physical Education, Wiejska 1.80-336 Gdalisk, Poland)
This paper concerns the problem of dismembering of human cadavers and the studies of the inertial properties of living bodies. In past investigations scientists separated the extremities from the trunk and divided the extremities through the axis of rotation. In the calculation of the inertial properties of e.g. the lower leg, femoral condyks were added to the lower leg, but they did not move when the lower leg moves. In future investigations of the human body, bony dismembering of extremities and the trunk and division of extremities has to be in the joint lines. The dismembering ofthe soft tissues should be along the line of bisection of the joint angles. The center of mass has at first to be assigned relative to the bony landmark. Then the previously accounted distance between the axis of a joint and the bony landmark must be added to or subtracted from the distance between the center of mass and the bony landmark.
346 THE APPLlCATlON
OF ROENTGENSTEREOPHOTOCRAMMETRY
FOR EVALUATlONS OF KNEE-
JOINT KINEMATICS 1N VITRO
A. DE LANGE*, R. v. DuKt, R. HUISKES*,G. SELVIK: and TH. J. G. v. RENS*(‘Orthopaedic Biomechanics Lab., University of Nijmegen, The Netherlands; tDept. Orthopaedic Surgery, St. Lucas Hospital, Amsterdam, The Netherlands. , $Dept. Anatomy, University of Lund, Sweden) To obtain accurate data for the description of knee-joint motion, roentgenstereophotogrammetric measurement methods are used. The bones are provided with tantalum markers, of which the three-dimensional positional changes are determined with an accuracy of 0.02 mm. Applying rigid body kinematics, motion parameters are calculated. Results of five cadaveric knee joints are presented, including exo-rotation and ad-abduction angles, length patterns of posterior and anterior fibers of cruciate and collateral ligaments, and part of the posterior capsule, as a function of flexion-extension angle. Exoendorotation freedom of motion is studied as well, for various flexion-extension angles. Results show consistent behavior for the different specimens.
TWO-DIMENSIONAL
DYNAMIC MODELING
OF HUMAN KNEE JOINT
MANSSOURH. MOEINZADEH, ALI E. ENGIN (Department of Engineering Mechanics, The Ohio State University, Columbus, Ohio 43210, U.S.A.) and NURI AKKAS(Department of Civil Engineering, Middle East Technical University, Ankara, Turkey) A mathematical dynamic model of the two-dimensional representation of the knee joint is presented. The profiles of the joint surfaces are determined from X-ray films and they are represented by polynomials. The joint ligaments are modeled as nonlinear elastic springs with realistic stiffness properties. Nonlinear equations of motion coupled with nonlinear constraint conditions are sotved numerically. Time derivatives are approximated by Newmark difference formulas and the resulting nonlinear algebraic equations are solved employing the Newton-Raphson iteration scheme. Several dynamic loads are applied to the center of mass of the tibia and the ensuing motion is investigated. Numerical results on ligament forces, contact point locations between femur and tibia, and the orientation of tibia relative to femur are presented. The results are shown to be consistent with the anatomy of the knee joint.
VALIDATION
OF WElNBACH AND HANAVAN MODELS FOR EBTlMATlON OF FOREARM VOLUME AND POSITION OF CENTER OF MASS
DIANE RODRIGUEand MICHELINEGAGNON (Dlpartement d’bducation physique, Universit6 de Montrkl, 2100, boul. Edouard-Montpetit, Montreal, Qulbec H3C 357, Canada) The purpose of the present study was to validate Weinbach and Hanavan models for estimation of forearm volume and location of center of mass. The study was conducted using 20 forearms from embalmed cadavers of six men and four women. Mean error for volume determination was 5.05% and 7.43% for Weinbach and Hanavan models respectively, while mean error for location of center of mass was respectively 4.63% and 6.33%. Furthermore, locations of center of volume and center of mass may be considered to correspond to each other, when using the Weinbach model. Contrarily to the Hanavan model, the accuracy obtained with the Weinbach model is independent of the shape of the forearm.
BIOMECHANICAL
DIVISION OF EXTREMITIES FOR MEASUREMENT OF INERTlA PROPERTlES
WLODZIMIERZS. ERDMANN(Biomechanics
Laboratory, College of Physical Education, Wiejska 1.80-336 Gdalisk, Poland)
This paper concerns the problem of dismembering of human cadavers and the studies of the inertial properties of living bodies. In past investigations scientists separated the extremities from the trunk and divided the extremities through the axis of rotation. In the calculation of the inertial properties of e.g. the lower leg, femoral condyks were added to the lower leg, but they did not move when the lower leg moves. In future investigations of the human body, bony dismembering of extremities and the trunk and division of extremities has to be in the joint lines. The dismembering ofthe soft tissues should be along the line of bisection of the joint angles. The center of mass has at first to be assigned relative to the bony landmark. Then the previously accounted distance between the axis of a joint and the bony landmark must be added to or subtracted from the distance between the center of mass and the bony landmark.