Biomechanical Systems

Techniques and Applications, Volume III: Musculoskeletal Models and Techniques

Cornelius T. Leondes

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9780429525438
• Topic: Medicine
• Subtopic: Biotechnology in Medicine

Because of developments in powerful computer technology, computational techniques, advances in a wide spectrum of diverse technologies, and other advances coupled with cross disciplinary pursuits between technology and its greatly significant applied implications in human body processes, the field of biomechanics is evolving as a broadly significant area. This Third Volume presents the advances in widely diverse areas with significant implications for human betterment that occur continuously at a high rate. These include dynamics of musculo-skeletal systems; mechanics of hard and soft tissues; mechanics of muscle; mechanics of bone remodeling; mechanics of implant-tissue interfaces; cardiovascular and respiratory biomechanics; mechanics of blood flow, air flow, flow-prosthesis interfaces; mechanics of impact; dynamics of man machine interaction; and numerous other areas. The great breadth and depth of the field of biomechanics on the international scene requires at least four volumes for adequate treatment. These four volumes constitute a well integrated set that can be utilized as individual volumes. They provide a substantively significant and rather comprehensive, in-depth treatment of biomechanic systems and techniques that is most surely unique on the international scene.

1

Three-Dimensional Dynamic Anatomical Modeling of the Human Knee Joint

Mohamed Samir Hefzy

University of Toledo

Eihab Muhammed Abdel-Rahman

Virginia Polytechnic Institute

1.1 Background

Biomechanical Systems • Physical Knee Models • Phenomenological Mathematical Knee Models • Anatomically Based Mathematical Knee Models

1.2 Three-Dimensional Dynamic Modeling of the Tibio-Femoral Joint: Model Formulation

Kinematic Analysis • Contact and Geometric Compatibility Conditions • Ligamentous Forces • Contact Forces • Equations of Motion

1.3 Solution Algorithm

DAE Solvers • Load Vector and Stiffness Matrix

1.4 Model Calculations

1.5 Discussion

Varus-Valgus Rotation • Tibial Rotation • Femoral and Tibial Contact Pathways • Velocity of the Tibia • Magnitude of the Tibio-Femoral Contact Forces • Ligamentous Forces

1.6 Conclusions

1.7 Future Work

Three-dimensional dynamic anatomical modeling of the human musculo-skeletal joints is a versatile tool for the study of the internal forces in these joints and their behavior under different loading conditions following ligamentous injuries and different reconstruction procedures. This chapter describes the threedimensional dynamic response of the tibio-femoral joint when subjected to sudden external pulsing loads utilizing an anatomical dynamic knee model. The model consists of two body segments in contact (the femur and the tibia) executing a general three-dimensional dynamic motion within the constraints of the ligamentous structures. Each of the articular surfaces at the tibio-femoral joint is represented by a separate mathematical function. The joint ligaments are modeled as nonlinear elastic springs. The six degrees-of-freedom joint motions are characterized using six kinematic parameters and ligamentous forces are expressed in terms of these six parameters. In this formulation, all the coordinates of the ligamentous attachment points are dependent variables which allow one to easily introduce more ligaments and/or split each ligament into several fiber bundles. Model equations consist of nonlinear second order ordinary differential equations coupled with nonlinear algebraic constraints. An algorithm was developed to solve this differential-algebraic equation (DAE) system by employing a DAE solver, namely, the Differential Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory.

Model calculations show that as the knee was flexed from 15 to 90°, it underwent internal tibial rotation. However, in the first 15° of knee flexion, this trend was reversed: the tibia rotated internally as the knee was extended from 15° to full extension. This indicates that the screw-home mechanism that calls for external rotation in the final stages of knee extension was not predicted by this model. This finding is important since it is in agreement with the emerging thinking about the need to re-evaluate this mechanism.

It was also found that increasing the pulse amplitude and duration of the applied load caused a decrease in the magnitude of the tibio-femoral contact force at a given flexion angle. These results suggest that increasing load level caused a decrease in joint stiffness. On the other hand, increasing pulse amplitude did not change the load sharing relations between the different ligamentous structures. This was expected since the forces in a ligament depend on its length which is a function of the relative position of the tibia with respect to the femur.

Reciprocal load patterns were found in the anterior and posterior fibers of both anterior and posterior ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• 1 Three-Dimensional Dynamic Anatomical Modeling of the Human Knee Joint
• 2 Techniques and Applications of Adaptive Bone Remodeling Concepts
• 3 Techniques in the Dynamic Modeling of Human Joints with a Special Application to the Human Knee
• 4 Techniques and Applications of Scanning Acoustic Microscopy in Bone Remodeling Studies
• 5 Techniques and Applications for Strain Measurements of Skeletal Muscle
• 6 A Review of the Technologies and Methodologies Used to Quantify Muscle-Tendon Structure and Function
• 7 A Technique for the Measurement of Tension in Small Ligaments
• Index