The finite element analysis of the influence of the load change of the internal oblique muscle on the near end of the patellar tendon based on the three-dimensional image model of MRI

Abstract

Medical image segmentation is an important step of medical image processing, which divides medical image into thousands of regions and extracts the regions of tissues and organs of interest. The accuracy of segmentation is very important for the follow-up processing of medical image and doctors’ judgment of the real situation of diseases. Medical image segmentation is a classic problem in the field of image segmentation. 3D image reconstruction technology is to obtain 3D structure information from 2D images of objects, to provide users with realistic 3D graphics, and to restore the prototype of objects, so that users can observe and analyze from multiple perspectives, which greatly improves the accuracy of measurement and the scientific accuracy of medical diagnosis, and plays a very important role in assisting doctors in clinical diagnosis. Based on the three-dimensional image model of MRI, the load variation of the internal oblique muscle can be applied to the finite element analysis of the near end of the patellar tendon.

Keywords

Three-dimensional reconstruction technology medical image MRI

1 Introduction

In the current medical image analysis and diagnosis, mainly through the observation of a variety of two-dimensional fault sequence images to find the body, which often need to rely on the experience of doctors to determine [1]. It is very difficult to accurately determine the spatial position, size, geometrical shape and spatial relationship with the surrounding organs of the diseased body, only by observing the two-dimensional fault image [2]. Therefore, using computer image processing technology to analyze and deal with two-dimensional fault image, to realize the segmentation, three-dimensional reconstruction and display of human organs, soft tissue and diseased body, can assist doctors in qualitative and even quantitative analysis of lesions and other areas of interest, and greatly improve the accuracy and reliability of medical diagnosis [3]. In addition, medical image processing technology in medical teaching, surgery planning, surgery simulation and a variety of medical research can also play an important role in supporting [4]. In medical image processing technology, medical image segmentation has always been an interesting research field, medical images are usually composed of areas of interest and background, and the area of interest contains important diagnostic information, which can provide reliable basis for clinical diagnosis and treatment and pathology, although the area may be small in the whole picture. But the cost of the error description is very high, and the information of the background area is minor, so the segmentation of the area of interest is the focus of medical image processing [5]. In the medical field, image segmentation was often used in the study of region extraction, specific tissue measurement and image reconstruction, so it is very important to study medical image segmentation technology [6]. In the recent years, based on the three-dimensional image model of MRI, the load variation of the internal oblique muscle can be applied to the finite element analysis of the near end of the patellar tendon.

2 State of the art

Early medical image segmentation was purely artificial, that was, the expected contour boundary was directly drawn on the original medical image [7]. With the development of computer technology, some automatic segmentation techniques have emerged in the field of image segmentation in recent years, and these methods have applied a lot of new technologies, such as fuzzy technology and artificial intelligence technology [8]. The automatic segmentation method realizes the whole process of medical image segmentation by computer, and can completely disengage from human intervention [9]. However, due to the large number of automatic segmentation methods, most of the automatic segmentation methods are implemented on workstations [10]. Because medical images are generally characterized by low contrast, the variability of the tissue characteristics, the fuzziness of the boundary between soft tissue and the lesion, and the complexity of shape structure and microstructure such as blood vessel and nerve distribution, it is very difficult to develop automatic segmentation technology. Therefore, from the current application of image segmentation in clinic, the automatic segmentation method does not completely replace the artificial segmentation method and semi-automatic segmentation method. In practical application, in order to obtain the ideal segmentation effect, it was necessary to manually intervene the segmentation process. At present, most of the automatic segmentation methods still remain in the laboratory stage, the real can be applied to the clinical few. However, it is the goal to study the practical automatic segmentation method and finally to replace the tedious artificial segmentation method and the semi-automatic segmentation method with strong subjectivity, which is also the focus of the medical image segmentation method in recent years.

3 Methodology

3.1 Basic model division method

Three-dimensional reconstruction refers to the establishment of three-dimensional objects suitable for computer representation and processing of the mathematical model, was in the computer environment for its processing, operation and analysis of its nature, but also in the computer to establish an objective world of virtual reality of the key technology. In computer vision, three-dimensional reconstruction refers to the process of reconstructing three-dimensional information based on a single view or a multi view image. Because of the incomplete information of single video, three-dimensional reconstruction requires the use of empirical knowledge. The three-dimensional reconstruction of multiple views (similar to human binocular positioning) was relatively easy, the method was to calibrate the camera first, that was, to calculate the camera’s image coordinate system and the world coordinate system. And then reconstruct the three-dimensional information with the information from multiple two-dimensional images. The contour curve of the Kass snake model C available parameters are defined as: v (s) = [x (s) , y (s)] , s ∈ [0, 1], the collection. Wherein: V(s) is the two-dimensional coordinate point on C, and S is normalized arc length. The energy of the contour curve C consists of internal energy eint and external energy eext, defined as: $E_{snake} = \int_{0}^{1} [E_{int} (v (s)) + E_{ext} (v (s))] ds = E_{int} + E_{ext}$ (1) $E_{int} (v) = [α (s) v^{'} (s)^{2} + β (s) v^{″} (s)^{2}] / 2$ (2)

The first order term in Eint is elastic energy, the second order term is rigid energy, which controls the continuity and smoothness of the curve C respectively, and is ermag by the image energy and constrained Energy Eext composition. An image energy E nage can be an edge, line, or other feature that induces the curve to approximate the contour line and was the basic external energy. Eext is an artificially added external control energy that can be used to control the deformation of the curve, depending on the form. Segmentation of the image to obtain the contour line, the final transformation to solve the snake curve of the energy function Esnake minimization, according to the variational principle, the energy functional esnake, minimized curve C to meet the following Euler (Euler) equation: $- α (s) \frac{\partial^{2} v}{\partial s^{2}} + β (s) \frac{\partial^{4} v}{\partial s^{4}} + \nabla E_{ext} (v (s)) = 0$ (3)

That was, the internal energy of the image is equal to the external energy to reach the equilibrium state. The evolution process of the snake curve is shown in the figure, where the dashed part represents the initial snake curve, and the solid line part represents the actual boundary of the object.

The evolution of the snake curve was the process of the initial contour curve moving closer to the actual boundary under the action of internal energy and external energy. The internal energy function was to maintain the curvature of the curve and other original characteristics, to prevent the curve was stretched and curved; the external energy drives the curve to deform and move to the correct object contour. When the two energies were in equilibrium, the contour curve of the object or region is obtained. The process of moving the deformation was accomplished by the movement of each control point on the initial contour line.

3.2 Improved snake algorithm

Because the snake model was sensitive to the initial contour line, it was required that the initial contour should be as close as possible to the real contour line, and the exact initialization of the snake model can greatly reduce the number of iterations and improve the running speed of the algorithm, otherwise the result of solution often does not reach the expected effect. There are two common ways to initialize contours: First, the contour line was initialized by sketching the image boundary manually, and the second was simply using the contour boundary of the previous image as the initial contour of the next image. These two methods have obvious shortages in practical application, the former was more complicated and difficult to realize automation, and the latter was less effective and undesirable in the case of two adjacent images with large deformation. In this paper, the initial contour prediction model of Snake is presented, and the initial contour of the undivided image was predicted by the segmented image contour, and the execution speed and precision of the snake model were improved. It was known from the foregoing that the energy function should be discretized in the process of Snake model realization. In the snake curve initial contour Prediction model, in order to facilitate the calculation and analysis, this paper snake curve V (s) along the arc length: Sampling into n points, each point was called a snaxel, expressed in SI, wherein i = 1, . . . , N such an energy function can be expressed as: $E_{snake} = \sum_{i = 1}^{N} [E_{int} (S_{i}) + E_{image} (S_{i}) + E_{con} (S_{i})]$ (4)

In the three-dimensional image, the change of the contour boundary of the same object can be attributed to continuous translation and similar deformation, so the position and shape of the object in the current image can be predicted according to the position, shape and changing trend of the previous images. We define SK as the position of the first Snaxel in the K image, and the center of mass of the snake curve of the first breeder image, then there are: $W_{k} = \frac{1}{N} \sum_{i = 1}^{N} S_{k, i}$ (5)

The translation of the contour is represented by the movement of the centroid of the snake curve, as shown in Fig. 2, which was consistent for each snaxel. After eliminating the translation effect, the similarity deformation of the contour is represented by the movement of each snaxel along the outside or inside the contour of the normal direction of the point contour, as shown in Fig. 2.

Fig.1

The correspondence between points on the Snake model and the point on the real boundary.

Fig.2

Translation and similar deformation.

Fig.3

Control strategy principle of three converter stations.

In this paper, the velocity and acceleration were used to describe the movement and deformation of the contour, and the movement and deformation of the contour are regarded as the movement of each snaxel at a certain speed and acceleration. For translation, all snaxel have the same speed and acceleration, the K-image translation speed is defined as vkmove, and the acceleration was akmove, then there: $v_{move}^{k} = W_{k} - W_{k - 1}$ (6) $a_{move}^{k} = v_{move}^{k} - v_{move}^{k - 1}$ (7)

For deformation, each snaxel has its own velocity and acceleration, the definition of the first snaxel in the K image is $v_{move}^{k}$ , the acceleration is $a_{move}^{k}$ , then there are: $v_{deform}^{k, i} = (S_{k, i} - W_{k}) - (S_{k - 1, i} - W_{k - 1})$ (8) $a_{deform}^{k, i} = v_{deform}^{k, i} - a_{deform}^{k - 1, i}$ (9)

The main methods to minimize the dynamic contour model are: Variational method, dynamic programming based method and greedy algorithm. In the process of digital approximation of derivative numbers, the variational method may produce serious digital instability. The dynamic programming method is stable and can guarantee the global optimality of the solution. However, the dynamic programming method is computationally large, with time complexity O (MN) 3, where n is the number of snaxel in the contour curve, M is the size of the Snaxel search neighborhood in each iteration, and this algorithm requires a lot of storage space. Greedy algorithm, also known as greedy algorithm, to better than these two methods, the advantage of this algorithm was easy to add external binding, and the efficiency of the algorithm was high, time complexity O (MN). This paper uses greedy algorithm to realize energy minimization.

The basic idea of greedy algorithm was to approach the given target gradually from the initial solution of the problem, and to get the solution of the problem as soon as possible. The algorithm stops when one step in the algorithm can no longer move forward. The realization method was as follows, firstly, the initial contour line of the object was given by the prediction algorithm mentioned above S = (S₁, S₂, . . . , S_n); calculating the center of a dynamic contour $c = (\bar{X}, \bar{Y})$ . Each snaxel on the contour was used as the seed point to find the local minimum energy point in the neighborhood and as a new point of the current contour. For the DOT, set its neighborhood to M, which indicates the number of adjacent points in the outline where the snaxel may move. The energy value of each point in the neighborhood is computed Eik, then a sik of the least energy is found from the M energy value, and the total energy esnake of the snake model is computed by moving point Si to sik; Determine if the Esnak was equal to the last value, and if it ends, go to Step2 again. The final result was the optimal result, which was the real contour edge of the object $S = (S_{1}^{'}, S_{2}^{'}, . . ., S_{n}^{'})$ .

Table 1

MRI scan parameters of knee joint

	TR (ms)	TE (MS)	(mm/mm)	FOV	Matrix	NEX	Time	Turn angle
T1WI	558	13	3/3	159	256*320	2	4^′49^″	90
T2WI+PDWI	3098	32/79	3/3	159	512*512	1	4^′36^″	150
STIR	4097	26	3/3	159	512*512	1	4^′54^″	150

4 Result analysis and discussion

In order to verify the feasibility and effectiveness of the algorithm, the improved snake algorithm was used to segment the brain MRI sequence images. From August 2018 to October 2019, we collected 37 images of 33 cases of patellofemoral arthritis in our hospital, which were examined in the laboratory and diagnosed as simple patellofemoral arthritis. The MRI features were analyzed retrospectively in order to improve the accuracy of the diagnosis of the disease and provide relevant reliable basis for clinical diagnosis and treatment. 1–2 is a female, 34 years old, with simple bone marrow edema in the lateral subchondral bone of patella. The subchondral bone shows a small signal with unclear boundary. 3–5 is a female, 42 years old. There is a simple cystic lesion in the subchondral bone of the lateral patella. On the sagittal plane, there is a clear contour of the subchondral bone under the patella. 6–7 were male, 45 years old. The third grade injury of trochlear cartilage was accompanied by bone marrow edema like lesions of subchondral bone. The sagittal and axial images showed that the cartilage in the central groove of trochlear was thinned, the edge was interrupted, the abnormal signal penetrated into the cartilage area, and the subchondral bone showed a large abnormal signal with unclear boundary. 8–9 is a female, 51 years old, with grade IV injury of lateral patellar cartilage, subchondral osteosclerosis, cystic change and myeloedema like lesions (arrow): T1 weighted image in sagittal plane (Fig. 8), T2 weighted image in sagittal plane (Fig. 9), showing obvious thinning of patellar cartilage, nearly disappearance of subchondral bone, multiple irregular abnormal signals (in Fig. 4)

By observing the sequence images (Fig. 4), we analyzed 37 cases of patellofemoral arthritis. Lesions involved: 13 (13/37) lesions in the lateral patella, 3 (3/37) lesions in the internal patella, 3 (3/37) lesions in the longitudinal ridge of patella, 2 (2/37) lesions in the medial trochlear surface, 3 (3/37) lesions in the lateral trochlear surface, 2 (2/37) lesions in the central groove of femur, 11 (11/37) mixed multiple lesions. There were 9 cases (9/37) with simple subchondral bone marrow edema. There were 3 cases of simple subchondral cystic lesions (3/37). At the same time, 25 cases (25/37) of subchondral bone abnormalities were found in cartilage injury, 2 cases in grade I, 3 cases in grade II, 9 cases in grade III, 11 cases in grade IV, bone marrow edema like lesions in different degrees in grade I, and osteosclerosis, cystoid and bone marrow in different degrees in grade II–IV In the same case of knee joint with multiple cartilage injuries of different degrees, the highest level is the diagnostic standard. In this group, there were 37 knee joints, 9 with a small amount of hydrops in the suprapatellar capsule, 13 with osteophyte formation in the upper and lower edge of the patella, all cases had symmetrical patellofemoral joint space, no obvious stenosis, and no abnormal changes in the shape and signal of the infrapatellar fat pad.

Fig.4

MRI imaging of patellofemoral.

5 Conclusion

With the continuous improvement of medical imaging equipment and the increasing requirement of clinical assistant diagnosis, image segmentation and three-dimensional reconstruction have become an eternal research topic in Medical image processing field, although the existing methods still have some limitations, but I believe that with the joint efforts of the researchers, With the continuous progress of image processing technology and computer technology as the support, the research of medical image segmentation and three-dimensional reconstruction will definitely have a greater breakthrough, and it will play a greater value in clinical application. The three-dimensional reconstruction of medical images provides a real and intuitive reflection for the human body structure, which was convenient for medical personnel to observe the lesion and to carry out the operation. But the image three-dimensional reconstruction programming was difficult to be mastered by the non-computer professionals. On the basis of image segmentation, this paper uses the image processing Toolbox in software to realize three-dimensional surface rendering and volume rendering of medical fault sequence images, which is simple in principle and convenient in programming. In the experiment of three-dimensional surface reconstruction and body reconstruction of brain image, the reconstruction speed is fast and the display effect was good, which is convenient for all kinds of non-computer professionals to popularize.

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