A Two-Dimensional Dynamic Anatomical Model of the Human Knee Joint

1993 ◽  
Vol 115 (4A) ◽  
pp. 357-365 ◽  
Author(s):  
Eihab Abdel-Rahman ◽  
Mohamed Samir Hefzy
Keyword(s):  
Knee Joint ◽  
Posterior Cruciate Ligament ◽  
Numerical Solutions ◽  
Cruciate Ligament ◽  
Posterior Part ◽  
Geometric Constraints ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Collateral Ligaments ◽  
Nonlinear Algebraic Equations

The objective of this study is to develop a two-dimensional dynamic model of the knee joint to simulate its response under sudden impact. The knee joint is modeled as two rigid bodies, representing a fixed femur and a moving tibia, connected by 10 nonlinear springs representing the different fibers of the anterior and posterior cruciate ligaments, the medial and lateral collateral ligaments, and the posterior part of the capsule. In the analysis, the joint profiles were represented by polynomials. Model equations include three nonlinear differential equations of motion and three nonlinear algebraic equations representing the geometric constraints. A single point contact was assumed to exist at all times. Numerical solutions were obtained by applying Newmark constant-average-acceleration scheme of differential approximation to transform the motion equations into a set of nonlinear simultaneous algebraic equations. The equations reduced thus to six nonlinear algebraic equations in six unknowns. The Newton-Raphson iteration technique was then used to obtain the solution. Knee response was determined under sudden rectangular pulsing posterior forces applied to the tibia and having different amplitudes and durations. The results indicate that increasing pulse amplitude and/or duration produced a decrease in the magnitude of the tibio-femoral contact force, indicating thus a reduction in the joint stiffness. It was found that the anterior fibers of the posterior cruciate and the medial collateral ligaments are the primary restraints for a posterior forcing pulse in the range of 20 to 90 degrees of knee flexion; this explains why most isolated posterior cruciate ligament injuries and combined injuries to the posterior cruciate ligament and the medial collateral results from a posterior impact on a flexed knee.

scholarly journals Recruitment of Knee Joint Ligaments

1991 ◽  
Vol 113 (1) ◽  
pp. 94-103 ◽  
Author(s):  
L. Blankevoort ◽  
R. Huiskes ◽  
A. de Lange
Keyword(s):  
Knee Joint ◽  
Posterior Cruciate Ligament ◽  
External Rotation ◽  
Cruciate Ligament ◽  
Fiber Bundles ◽  
Cruciate Ligaments ◽  
Collateral Ligaments ◽  
Lateral Collateral Ligaments ◽  
Length Changes ◽  
Anterior Cruciate

On the basis of earlier reported data on the in vitro kinematics of passive knee-joint motions of four knee specimens, the length changes of ligament fiber bundles were determined by using the points of insertion on the tibia and femur. The kinematic data and the insertions of the ligaments were obtained by using Roentgenstereophotogrammetry. Different fiber bundles of the anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments were identified. On the basis of an assumption for the maximal strain of each ligament fiber bundle during the experiments, the minimal recruitment length and the probability of recruitment were defined and determined. The motions covered the range from extension to 95 degrees flexion and the loading conditions included internal or external moments of 3 Nm and anterior or posterior forces of 30N. The ligament length and recruitment patterns were found to be consistent for some ligament bundles and less consistent for other ligament bundles. The most posterior bundle of each ligament was recruited in extension and the lower flexion angles, whereas the anterior bundle was recruited for the higher flexion angles. External rotation generally recruited the collateral ligaments, while internal rotation recruited the cruciate ligaments. However, the anterior bundle of the posterior cruciate ligament was recruited with external rotation at the higher flexion angles. At the lower flexion angles, the anterior cruciate and the lateral collateral ligaments were recruited with an anterior force. The recruitment of the posterior cruciate ligament with a posterior force showed that neither its most anterior nor its most posterior bundle was recruited at the lower flexion angles. Hence, the posterior restraint must have been provided by the intermediate fiber bundles, which were not considered in the experiment. At the higher flexion angles, the anterior bundles of the anterior cruciate ligament and the posterior cruciate ligament were found to be recruited with anterior and posterior forces, respectively. The minimal recruitment length and the recruitment probability of ligament fiber bundles are useful parameters for the evaluation of ligament length changes in those experiments where no other method can be used to determine the zero strain lengths, ligament strains and tensions.

scholarly journals The Effects of External Loads and Muscle Forces on the Knee Joint Ligaments during Walking: A Musculoskeletal Model Study

2021 ◽  
Vol 11 (5) ◽  
pp. 2356
Author(s):  
Carlo Albino Frigo ◽  
Lucia Donno
Keyword(s):  
Knee Joint ◽  
Cruciate Ligament ◽  
Musculoskeletal Model ◽  
Optimization Approach ◽  
Muscle Forces ◽  
Collateral Ligaments ◽  
Flexion Extension ◽  
Lateral Collateral Ligaments ◽  
Gastrocnemius Muscles ◽  
External Loads

A musculoskeletal model was developed to analyze the tensions of the knee joint ligaments during walking and to understand how they change with changes in the muscle forces. The model included the femur, tibia, patella and all components of cruciate and collateral ligaments, quadriceps, hamstrings and gastrocnemius muscles. Inputs to the model were the muscle forces, estimated by a static optimization approach, the external loads (ground reaction forces and moments) and the knee flexion/extension movement corresponding to natural walking. The remaining rotational and translational movements were obtained as a result of the dynamic equilibrium of forces. The validation of the model was done by comparing our results with literature data. Several simulations were carried out by sequentially removing the forces of the different muscle groups. Deactivation of the quadriceps produced a decrease of tension in the anterior cruciate ligament (ACL) and an increase in the posterior cruciate ligament (PCL). By removing the hamstrings, the tension of ACL increased at the late swing phase, while the PCL force dropped to zero. Specific effects were observed also at the medial and lateral collateral ligaments. The removal of gastrocnemius muscles produced an increase of tension only on PCL and lateral collateral ligaments. These results demonstrate how musculoskeletal models can contribute to knowledge about complex biomechanical systems as the knee joint.

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

scholarly journals On the properties of numerical solutions of dynamical systems obtained using the midpoint method

2019 ◽  
Vol 27 (3) ◽  
pp. 242-262 ◽  
Author(s):  
Vladimir P. Gerdt ◽  
Mikhail D. Malykh ◽  
Leonid A. Sevastianov ◽  
Yu Ying
Keyword(s):  
Difference Scheme ◽  
Coupled Oscillators ◽  
Numerical Solutions ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Integrals Of Motion ◽  
Midpoint Method ◽  
Nonlinear Algebraic Equations ◽  
The Difference

The article considers the midpoint scheme as a finite-difference scheme for a dynamical system of the form ̇ = (). This scheme is remarkable because according to Cooper’s theorem, it preserves all quadratic integrals of motion, moreover, it is the simplest scheme among symplectic Runge-Kutta schemes possessing this property. The properties of approximate solutions were studied in the framework of numerical experiments with linear and nonlinear oscillators, as well as with a system of several coupled oscillators. It is shown that in addition to the conservation of all integrals of motion, approximate solutions inherit the periodicity of motion. At the same time, attention is paid to the discussion of introducing the concept of periodicity of an approximate solution found by the difference scheme. In the case of a nonlinear oscillator, each step requires solving a system of nonlinear algebraic equations. The issues of organizing computations using such schemes are discussed. Comparison with other schemes, including those symmetric with respect to permutation of and .̂

scholarly journals Evaluation of Knee Joint after Open Reduction and Internal Fixation Surgery of Posterior Cruciate Ligament in Patients with Avulsion Fracture

2019 ◽  
Vol 7 (6) ◽  
pp. 982-986
Author(s):  
Navid Salehi ◽  
Faeze Azarifar ◽  
Arman Jahanshahi ◽  
Hamidreza Mohammadi
Keyword(s):  
Knee Joint ◽  
Internal Fixation ◽  
Posterior Cruciate Ligament ◽  
Open Reduction ◽  
Avulsion Fracture ◽  
Cruciate Ligament ◽  
Common Mechanism ◽  
Knee Score ◽  
Normal Knee ◽  
Lysholm Knee Score

BACKGROUND: The posterior cruciate ligament is one of the important tissues and structures sustaining the knee joint, and its rupture or detachment may lead to joint instability or destruction. AIM: The present study aimed at investigating the Open Reduction and Internal Fixation surgery of posterior cruciate ligament and comparing it to the normal knee of the same side. METHODS: In this study, 25 patients with avulsion fracture at the PCL joint were treated with open surgery and screw fixation. The patients were followed up by Lysholm knee score for at least 12 months after surgery. RESULTS: All patients were male with an average age of 25 years over the years 2010-2018. The common mechanism of injury in these patients was motorcycle-car accident. In the study with Lysholm knee score, 21 patients (80%) obtained the good score of 60-90 while 20% of patients were placed in the fair group (30-59). The average score was 86. CONCLUSION: The obtained score of knee function questionnaire in this study had no significant difference from other similar studies, and most patients achieved a good and acceptable score after the surgery. There was no knee instability and functional impairment in the patients compared to the normal knee. Considering the clinical results after the fixation of the PCL avulsion fracture causing a significant improvement in patients, the surgery could be considered as an acceptable and effective method for treating such impairment and fracture.

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