TY - JOUR
T1 - A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints
AU - Kwak, S. D.
AU - Blankevoort, L.
AU - Ateshian, G. A.
PY - 2000
Y1 - 2000
N2 - This study describes a general set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean +/- stand. dev. error in translation: 0.63 +/- 1.19 mm, 0.10 +/- 0.71 mm, -0.29 +/- 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 +/- 1.71 degrees, 0.27 +/- 2.38 degrees, -1.13 +/- 1.83 degrees in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room
AB - This study describes a general set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean +/- stand. dev. error in translation: 0.63 +/- 1.19 mm, 0.10 +/- 0.71 mm, -0.29 +/- 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 +/- 1.71 degrees, 0.27 +/- 2.38 degrees, -1.13 +/- 1.83 degrees in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room
U2 - https://doi.org/10.1080/10255840008915253
DO - https://doi.org/10.1080/10255840008915253
M3 - Article
C2 - 11264838
SN - 1025-5842
VL - 3
SP - 41
EP - 64
JO - Computer Methods in Biomechanics and Biomedical Engineering
JF - Computer Methods in Biomechanics and Biomedical Engineering
IS - 1
ER -