Knowledge about the knee cartilage deformation ratio as well as the knee cartilage stress distribution is of particular importance in clinical studies due to the fact that these represent some of the basic indicators of cartilage state and that they also provide information about joint cartilage wear so medical doctors can predict when it is necessary to perform surgery on a patient. In this research, we apply various kinds of sensors such as a system of infrared cameras and reflective markers, three-axis accelerometer, and force plate. The fluorescent marker and accelerometers are placed on the patient’s hip, knee, and ankle, respectively. During a normal walk we are recording the space position of markers, acceleration, and ground reaction force by force plate. Measured data are included in the biomechanical model of the knee joint. Geometry for this model is defined from CT images. This model includes the impact of ground reaction forces, contact force between femur and tibia, patient body weight, ligaments, and muscle forces. The boundary conditions are created for the finite element method in order to noninvasively determine the cartilage stress distribution.
Sports activities and daily routines such as standing, walking, running, jumping, and other recreational activities impose relatively large loads and movements on the human knee joint. These tasks could cause injuries and degenerations in the joint ligaments, menisci, cartilage, and bones. Thus, knowledge of in vivo joint motion and loading during functional activities is needed to improve our understanding of possible knee joint degeneration and restoration. Internal loadings of knee anatomical structures significantly depend on a lot of factors such as external loads, body weight, ligaments, strengths, and muscles forces.
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The purpose of this study was to estimate stress distribution in the knee cartilage. For that purpose the appropriate system of cameras and force plate platform were used. The deformation of cartilage was measured using marker position data and the 3D model of the lower leg segment. The models were established from computed tomography (CT) images. Simultaneously the deformation is assessed only matching single infrared camera images and CT image using software for image registration technique. In the experimental part the accelerometer sensor was used which potentially can provide more information about the gait. In the computer simulation the FEM analysis was applied with an adaptive change of mechanical parameters of tissue variation in order to match the measured force and deformation.
Knee joint motion represents a complex combination of rotations and translations. The major parts involved in the knee kinematical behavior include femur, tibia and patella. Forces that act at a knee joint are given in Figure
Forces on a knee joint.
The dominant forces that act at a knee joint are body weight and ground reaction force which are opposite to each other. Muscle forces as well as contact forces between femur and tibia are also included in the model. Equilibrium equations of the knee joint are given below [
A simplified spring-damper-mass model which was used in this study is shown in Figure
A simplified spring-damper-mass model used in the computer simulation. The components of the dynamics system presented are lower body rigid mass (
The total body mass was obtained from the participant. In the following system of equations (Equation (
Parameter for ground reaction model.
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Soft shoe | 106 | 1.56 | 2 × 104 | 0.73 | 1.0 |
Hard shoe | 106 | 1.38 | 2 × 104 | 0.75 | 1.0 |
Cartilage was considered as a porous deformable body filled with fluid occupying the whole pore volume. The physical quantities for this analysis were the displacement of solid
Here
In this study we used a commercial motion capture system OptiTrack. This system consists of six infrared cameras and four retroreflective markers. The markers are 1.5 cm in diameter and are attached at the precise anatomical locations of the participant’s leg for unilateral gain analysis. These locations were great trochanter region, femoral lateral epicondyle, tuberosity of the tibia, and the center of the anterior region of ankle joint (see Figure
Reflective markers position on the examinee leg.
The computerized camera system with accompanying software captures the exact motion of retroreflective markers and thus records their trajectory while the volunteer performs walking over the force plate. The cameras were connected to a computer that collects gait kinematical data. The result of motion tracking is a series of 3D coordinates for each numbered marker. To better understand kinematics and kinetics of gait we used a three-axial accelerometer.
We used Sun SPOT accelerometers (Sun Small Programmable Object Technology) to wirelessly detect the middle of the gait stance phase, that is, the moment when the ground reaction force reaches its maximum value. The Sun SPOT has a sensor board which consists of 2G/6G 3-axis accelerometer, temperature sensor, and light sensor. In the experimental part the Sun SPOT LIS3L02AQ accelerometer is used to measure the orientation or motion in three dimensions,
The volunteer performs walking along 2.5 meter distance path away with his own ordinary velocity and attached infrared marker and accelerometers sensor on the left leg. Results for marker coordinates and corresponding accelerations, measured by the three-axial accelerometer, are presented in Figure
Position of reflective marker during walking and corresponding three-axial acceleration.
According to [
The force plate is positioned in the first half of the walking path. During the experiment, the participants were asked to walk along so the force plate records the value of the ground reaction force (Figure
Ground reaction forces during standing on the force plate.
The force value is zero in the beginning of the walk and when the participant stands on the force plate, starting with the heel, the force gradually increases and reaches the maximum and then drops to zero again when the foot is detached by the force plate.
One of the main tasks for preparing data for FEM simulation is matching the infrared reflective marker position obtained by infrared camera and landmark position on the CT images when cartilage is unreformed. This procedure is known as image registration and ANTs (Free software for image registration) is used [
Main goal of the registration process is obtained from the transformation parameter that maps the marker position in deformed and undeformed knee cartilage. In general this process is finding the optimal transformation that maps every pixel of image with the presence of deformation and another static image when cartilage is undeformed. As similarity measure of image the mutual information is used. The standard algorithm in registration process is elastic deformation procedure. The idea is to model the contours on one of the matching images as elastic object which deformed under the influence of some external forces [
Registration infrared image and CT image. (a) Infrared camera image; (b) CT image; (c) registered image.
Simultaneously, we create a 3D model using CT slices. The CT slices are segmented using a threshold value and compared with gray value of the image pixel. The segmented images are submitted by the edge detection operator for boundary extraction. The merging of adjacent boundary is done in each slice and final 3D model is created (Figure
The anatomical point (tuberosity of tibia and femoral lateral epicondyle) can be easily detected in the model and initial position of the marker can be obtained. Using the measured position of infrared marker (Figure
3D model of knee. (a) Raw CT slices; (b) segmented CT images; (c) 3D model with marker position.
Using the same procedure for image segmentation, a full model of knee joint is created. The model consists of femur, tibia, and cartilage.
We used measured values for the displacement and ground reaction force in order to calculate corresponding matrix elements in the relation (
FEM analysis model. (a) Model filled with the tetrahedral mesh element; (b) knee von Misses stress distribution in [Pa].
For modeling the cartilage and meniscus we implemented a finite element formulation where the nodal variables are displacements of solid,
The tetrahedral mesh model had 20537 elements and 4693 nodes (Figure
The initial mechanical characteristic, Young’s modulus, and Poisson’s ratio, for the femur and tibia, were amounted to
These values were adaptively changed for the purpose of correspondence between the measured deformation and ground reaction force.
The final value of the Young’s modulus of the cartilage is 5.62 MPa with error of estimation of 0.01 MPa. The Young’s modulus for the femur and tibia is adapted to the 18 GPa while the Poison’s ratio is 0.45.
Resultant stress distribution of the FEM analysis for the elements of the knee joint is given in Figure
The von Mises stress on the cartilage is presented in Figure
Knee cartilage von Misses stress distribution [Pa].
The procedure described in this study can offer very useful information for physicians in order to better understand injury formation and improve the process of rehabilitation and, in some perspective, as a support in clinical decision making.
The main goal of this study was to introduce a new approach towards a noninvasive effective stress calculation for a specific participant. Input data were provided from the experimental measurements during the participant’s walking test whereupon finite element analysis was performed giving the distribution of the effective stress in the major anatomical elements of the knee joint: femur, tibia, and cartilage. This approach demonstrates a great possibility for preoperative and postoperative surgical planning and treatment of the knee injuries for specific patients.
This study contains some limitations. We neglected the skin movement artifact during the experiment and the influence of ligament presence. However, the current model allows us to investigate the effect of different biomechanical factors and loads on the stress distribution at the knee joint. In this study we used data obtained from infrared cameras and force plate sensors. Besides, in our future work we will try to replace a relatively expensive system of infrared cameras with a much cost effective system of accelerometers so that we will be able to calculate positional data of anatomical points of the lower extremities solely by using their accelerations. The very promising are techniques of the image registration that can be used for assessment of gait parameter using a cheaper mobile cell camera. This will be a consideration of the future work.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Projects numbers III41007 and ON 174028).