The demand for an accurate and accessible image segmentation to generate 3D models from CT scan data has been increasing as such models are required in many areas of orthopedics. In this paper, to find the optimal image segmentation to create a 3D model of the knee CT data, we compared and validated segmentation algorithms based on both objective comparisons and finite element (FE) analysis. For comparison purposes, we used 1 model reconstructed in accordance with the instructions of a clinical professional and 3 models reconstructed using image processing algorithms (Sobel operator, Laplacian of Gaussian operator, and Canny edge detection). Comparison was performed by inspecting intermodel morphological deviations with the iterative closest point (ICP) algorithm, and FE analysis was performed to examine the effects of the segmentation algorithm on the results of the knee joint movement analysis.
Recent developments and the greater availability of computer technology have enabled much actively conducted research combining digital imaging technologies such as CT and MRI with finite element (FE) analysis. This type of research has been increasing, particularly in the field of orthopedics, as the knee joint is relatively easy to model.
Also, a variety of studies have verified anatomical interpretations and performed sports rehabilitation simulations by examining stress distributions caused by movements of the knee.
Kim et al. [
Moreover, some studies have analyzed changes in ACL stress by focusing on the pretension of various steps and knee angles and then analyzing the stress distributions for ACL reconstruction by applying the same movements as that of the patients. Subsequently, they reconstructed knee bones from four angles by using a 3D FE model.
The model used in the research described above was a 3D bone model created from CT data and used for analysis under the assumption that ACL transplant grafts are cylindrical. To create a solid model of the body from CT imaging, an image processing method was used to segment a region of interest from a 2dimensional (2D) image of the bone. The 3D solid model was constructed by interpolating the slices made by stacking separate regions based on the image processing methods.
Therefore, clinicians must accurately segment edges. For segmentation of an exact region, the help of skilled expert was required, and it became problematic that the accuracy differed according to the expert’s proficiency. In order to solve this problem, a variety of image processing algorithms were applied.
The methods of applying a segmentation algorithm to a region of interest were investigated by applying the Sobel operator [
Antonelli et al. [
While theoretical comparative image processing algorithm research has been conducted, there has not been any research to date to determine the optimal algorithm to create a 3D model from human CT images.
This study aims to find the most suitable segmentation algorithm to reconstruct a 3D model from the knee (joint) CT images. To achieve this goal, we compare and validate segmentation algorithms based on both objective comparisons and FE analysis. Stress distributions are compared and analyzed for reconstructed 3D models by examining morphological errors and FE analysis using edge segmentation algorithms typically used in the field of image processing. First, we analyze the Sobel operator, LoG operator, and the Canny edge detection algorithm, which are commonly used to compare CT image segmentation performance. Additionally, we determine the reliability of each algorithm by comparing the model constructed using image processing algorithms to a model constructed manually by clinicians. Next, we compare the performance of each algorithm by using FE analysis of the segmented reconstructed ACL.
FE modeling for ACL analysis was created based on the CT data of the experimenter. CT data was provided in Digital Imaging and Communications in Medicine (DICOM), a format typically used in medical imaging and showed the internal biometric information as a single slice 1 to 2 mm in thickness. To reconstruct a 3D knee model, extracting the region from the acquired CT data is necessary, and this process is called segmentation. Stacked contours of segmented regions are used to create a 3D surface model through interpolation. This paper uses the Sobel operator, Laplacian of Gaussian operator, and Canny edge detection algorithms which are widely used in the medical image processing [
The simplest segmentation method is for clinicians to mark the region themselves. Knee joint CT data scanned in 2 mm intervals can result in more than 200 total slices (100 slices each of the femur and tibia), and the segmented area should be delineated manually to reconstruct a 3D knee model. This method depends on the knowledge, proficiency, and condition of the person who is delineating the region and has the disadvantage that the accuracy of the created model depends on individual proficiency.
The Sobel operator used for boundary detection is very sensitive for the boundary towards diagonal direction. The Sobel operator determines the magnitude of the gradient using
It is difficult to detect a detailed contour as the size of the kernel gets larger, whereas it becomes sensitive to noise as the one gets smaller.
This differential operator generally tends to be very sensitive to noise, resulting in malfunction by considering the noise pixel as an edge.
The Laplacian of Gaussian (LoG) operator is an algorithm, upgraded from Laplacian operator, that detects blob structures surrounded with the area separated by the level of the nearby pixels. The LoG operator is the second derivative edge detector and is less sensitive to noise. It can be expressed as the sum of the second derivative functions towards the horizontal and vertical orientation of gradient. The LoG operator performs Gaussian smoothing before applying the Laplacian filter. The Laplacian operator obtains the edge component on the first derivate inflection point where the second derivative is a zero and is sensitive to the noise on the point where the second derivative is obtained. LoG operator improves the robustness for the noise by applying Gaussian operator, as shown in (
The filter of the LoG operator is determined by the value of Gaussian standard deviation (
The Canny edge detection algorithm can be used as an optimal edge detector based on a set of criteria, which include finding the most edges by minimizing the error rate, marking edges as closely as possible to the actual edges to maximize localization, and marking edges only once when a single edge exists for a minimal response. Also, the result detected by Canny edge detection algorithm should reduce the loss of edge component and the error between the detected edge and the real gradient on original image. According to Canny, the optimal filter that meets all 3 criteria above can be efficiently approximated using the first derivative of a Gaussian function by (
The Gaussian filter is determined by the value of standard deviation (
Calculate the average magnitude. Consider
where
Calculate the density of the edge length. The density of the edge length is calculated from
where
The segmentation process using the three algorithms as described above is shown in Figures
Segmentation procedure for the knee joint by the Sobel operator algorithm.
Original DICOM image
Image after applying the image segmentation algorithm in MATLAB
Outer contours extracted to a separate binary from the regions of bone
Segmentation procedure for the knee joint by the Laplacian of Gaussian operator algorithm (where input parameters
Original DICOM image
Image after applying the image segmentation algorithm in MATLAB
Outer contours extracted to a separate binary from the regions of bone
Segmentation procedure for the knee joint by the Canny edge detection algorithm (where input parameters
Original DICOM image
Image after applying the image segmentation algorithm in MATLAB
Outer contours extracted to a separate binary from the regions of bone
In vivo measurements were made in a 27yearold man with no history of knee pathology or injury. The CT scan and data acquisition were performed on the right knee at the Hallym University Medical Center, Dongtan, Korea [
In this part, we compared each model shape by applying four types of algorithms to the 3D knee joint model created from CT image data and confirmed the effect of the segmentation algorithm result with FE analysis of ACL reconstruction surgery. We used three types of image processing algorithms (the Sobel operator, LoG operator, and Canny edge detector) for bone model segmentation. Additionally, we compared the models reconstructed using each algorithm to the model manually segmented by clinicians. The reconstructions performed using manual clinician segmentation, the Sobel operator, the LoG operator, and the Canny edge detection algorithms are described as Methods 1, 2, 3, and 4, respectively. Stacked contours (Figure
Knee model reconstruction using interpolation.
Segmented slices
Reconstructed bone models
Image processing algorithms were applied to CT images using MATLAB [
Experimental procedure.
The models reconstructed by each algorithm show different morphological errors according to the segmented area. Threedimensional morphological deviations between the models are obtained and analyzed by comparing the distances between the mesh of each model.
Morphological deviations were obtained to match points between Method 1 and Methods 2, 3, and 4. 3D surface matching was performed using the ICP algorithm [
In this section, we explain the process of generating a FE model, which was applied to the four segmentation algorithms to compare the effects of FE analysis. To generate a solid model with the same tunnel as is made in a real operation of the femur and tibia, 10 mm diameter tunnels were drilled in the center between the anteromedial (AM) bundle and the posterolateral (PL) bundle, as shown in Figure
Construction of the tunnel and ACL graft.
It is not easy to estimate the trajectories of knee joint movement because the human knee does not have a specific center of rotation. To overcome this difficulty, knee joint angle trajectories were mapped by imaging them in several positions while the experimental subject was executing knee movements. The simulations of the reconstructed models were then compared using the images obtained from four different angles (0°, 45°, 90°, and 135°) and the locations of the femur in each angle were superimposed based on the tibia. The superimposed femur was ensured by the Align function in Rapidform; the results are shown in Figure
Determining the superimposed position of the tibia.
The FE model consists of a mesh, and the femur and tibia were assumed to be rigid bodies considering computational burden and analysis time. The ACL was assumed to be a hyperelastic material. A hyperelastic material property is generally used in modeling rubber with very large deformations. The material characteristics of the bundles of the reconstructed ACL are expressed as (
Curve fitting using a hyperelastic material model of ACL.
From classical continuum mechanics, the right CauchyGreen deformation tensor is defined as
The Ogden model is a hyperelastic material model, which can describe the material behavior by means of the strain energy density function [
Because the high water content of ACL is assumed to be incompressible, that is, the Jacobian of the deformation gradient,
Mesh cannot be generated by only hexahedrons because bone is composed of curved surfaces. For this reason, the bones were generated as tetrahedrons, and the ACL model was generated as hexahedrons. The femur and tibia were modeled using a large number of linear tetrahedral elements (C3D4). The total number of nodes and elements for the femur was 16577 and 84018, respectively, and the total number of nodes and elements for the tibia was 16221 and 80274, respectively. The ACLs were modeled using a large number of linear hexahedral elements (C3D8R). The total number of nodes and elements for the ACL was 11832 and 10005, respectively. Boundary conditions, including load, contact, and tie, should be applied to perform the FE analysis of knee flexion. The loading condition was divided into two steps. In the first step, the translation and rotation of the tibia’s 6DOF (
Figure
Morphological comparison on two bones. (a) Shape comparisons for Methods 1 and 2, (b) Methods 1 and 3, (c) Methods 1 and 4, (d) the spectrum of colour map, and (e) morphological deviations distribution for ((a), (b), and (c)). (Dimensions larger than those of Method 1 model are indicated by the color red; smaller dimensions are represented by blue. When the models are similar and the morphological deviation approaches 0 mm, they are described as green.)
As the shape of the model applied to each algorithm affects the interpretation result, we analyzed the changes in ACL tension from bending movements of the knee. We measured the von Mises stress, reaction force, and contact stress at 0°, 45°, 90°, and 135° in order to compare the interpretation results from the reference model (Method 1) with those of the models (Methods 2, 3, and 4) from the application of each algorithm. Moreover, the same ACL model and tension were applied in identical environments to match the conditions. We compared the error rate of Method 1 to that of Methods 2, 3, and 4.
As von Mises stress is the sum of all stresses damaging the ACL bundle from flexing the knee, we measured the stress occurring at each angle by selecting the node where stress distribution occurs most significantly in the ACL bundle. The simulation results from each model under equivalent stress are shown in Figure
von Mises stress of the simulation results for the models using (a) Method 1, (b) Method 2, (c) Method 3, and (d) Method 4.
According to the analysis results, stress was represented in the middle of the ACL by movement of the femur. A quantitative comparison of stress distribution results based on the node of strongest stress is shown in Figure
Changes in the von Mises stress of models at different angles.
Reaction force simulation result for the tied sections of the models: (a) Method 1, (b) Method 2, (c) Method 3, and (d) Method 4.
Reaction force changes in the tied sections of the models.
Measurements between the ACL bundle and the bone tunnel (both femur and tibia) with flexed knee are shown in Figure
Contact regions and analysis results between bone and ACL: (a) Method 1, (b) Method 2, (c) Method 3, and (d) Method 4.
Contact stress changes in the models between bone and ACL.
Table
Error rates between Method 1 and Methods 2, 3, and 4.
Interpretation type  0°  45°  90°  135° 


von Mises stress (MPa)  
Method 1  7.447  6.356  5.67  6.371  — 
Method 2  8.06  6.694  5.858  6.082  1.428 
Method 3  7.520  6.460  5.335  5.444  1.439 
Method 4  7.468  6.544  5.479  5.619  1.152 
Reaction force (N)  
Method 1  9.878  6.43  6.324  6.354  — 
Method 2  9.153  8.996  9.256  8.885  8.754 
Method 3  8.317  6.333  6.1732  6.06  2.103 
Method 4  7.695  6.808  6.510  6.459  2.852 
Contact stress (MPa)  
Method 1  
Femur  11.391  7.278  5.235  3.914  — 
Tibia  0.66  0.907  0.432  2.651  — 
Method 2  
Femur  13.89  7.335  6.302  6.778  6.487 
Tibia  0  0.7  1.669  2.774  2.227 
Method 3  
Femur  20.319  8.87  5.185  3.728  10.756 
Tibia  0  0.765  0.606  2.435  1.192 
Method 4  
Femur  11.853  9.128  5.587  3.612  2.966 
Tibia  0  0  0.77  2.147  2.409 
(
We applied the root mean squares (RMS) error as shown in (
Method 4 had an error rate comparable to that of Method 1 (
With high demand for image segmentation to generate 3D model from CT data, interest in objective assessment on the 3D models obtained using various segmentation methods has been increasing. Objective comparison and FE analysis were introduced to find the most suitable segmentation to create a 3D model of the knee joint CT images in this paper. We analyzed the stress distributions and morphological errors in 3D reconstruction by using edge segmentation algorithms. 3D solid models were reconstructed by three types of algorithms typically used in the field of image processing.
What this study found can be summarized as the following.
From the morphological deviations and FE analysis results (von Mises stress, reaction force, and contact stress) of the ACL graft compared, it was proven that it is possible to obtain reliable data from image processing algorithms without the aid of a clinician.
The morphological comparison results from the experiment showed that 83.23% of all nodes showed a deviation of less than 0.227 mm.
In measurements of the von Mises stress, reaction force, and contact stress by FE analysis, Method 4 and Method 3 showed lower error rates for von Mises stress and reaction force, respectively.
For contact stress, Method 4 and Method 3 showed lower contact error rates for femurACL stress and tibiaACL stress, respectively.
In conclusion, the Canny edge detection algorithm (Method 4) showed good performance in the results of 3 out of 5 experiments, demonstrating that it is optimal for the reconstruction of a 3D solid model (Method 4, Method 3, and Method 2 in order).
The authors declare that there is no conflict of interests regarding the publication of this paper.