# Clinical Application of Shock Wave in the Treatment of Avascular Necrosis of the Femoral Head in the Early and Middle Stages

Authors: Jingjing Bi; Wenjing Zhou; Huan Zhang; Yang Liu
Journal: Contrast Media & Molecular Imaging
 (2022)

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## Abstract

In order to observe the clinical efficacy of shock waves in the treatment of avascular necrosis of the femoral head in the early and middle stages, a clinical application method of a shock wave in the treatment of avascular necrosis of the femoral head in the early and middle stages was proposed. The method combines the CT image segmentation technology to further segment the hip joint image, thereby speeding up the treatment speed and achieving a better treatment effect. Experimental results show that CT image segmentation takes 10.9 hours with an average time of 8 seconds, which is faster than other methods. The shock wave is an effective treatment method for early avascular necrosis of the femoral head, and this method will become one of the main methods for the clinical treatment of this kind of disease.


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## Body

## 1. Introduction

The course of femoral head necrosis progresses rapidly, and subchondral fractures easily occur within 2 years without intervention. About 67% of asymptomatic patients and 85% of symptomatic patients will progress to femoral head collapse [1–3]. Although artificial hip replacement is feasible for patients with advanced ONFH, other effective treatments are urgently needed for patients who are young or cannot tolerate surgery. Studies in recent years have confirmed that extracorporeal shock wave therapy is effective in the treatment of early ONFH and can prevent the further development of the disease or even cure it, while there are few reports on the treatment of middle and late ONFH [4]. Radiative extracorporeal shock wave therapy has been an emerging physical therapy modality in recent years. Based on its good therapeutic effect and low risk for skeletal and musculoskeletal diseases, our department tried to apply rESWT in the treatment of intermediate and advanced ONFH and found that it had good effects in relieving hip pain and improving hip activity [5]. In 1988, Germany successfully applied ESWT in the treatment of nonunion. In addition, ESWT has the advantages of small adverse reactions, noninvasive, low cost, and reconstructions, so scholars at home and abroad began to widely apply ESWT in clinical practice and tried to treat ONFH and achieved good results.Medical image segmentation is the basis of medical image processing and analysis. The solution to this problem not only directly affects the successful application of computer graphics and image technology in medicine but also has important theoretical and practical significance [6, 7]. Medical image segmentation is a process of extracting regions of interest, and the segmentation results can provide a reference for subsequent disease diagnosis, treatment plan planning, and treatment effect evaluation. CT is widely used in the diagnosis of many systemic diseases because of its high resolution and its ability to display anatomical structures and pathological tissues more clearly.According to the above findings, CT images were used in the treatment of femoral head necrosis with shock waves in this article. The therapeutic effect of shock waves on femoral head necrosis was observed through CT images, and an automatic segmentation technology of three-dimensional hip CT images based on iterative adaptive threshold classification and Bayesian discriminant analysis was proposed to improve the cure rate of femoral head necrosis, as shown in Figure1.Figure 1
CT images in shock wave treatment of femoral head necrosis effect observation.


## 2. Literature Review

At present, the etiology and pathological mechanism of ONFH have not been completely clarified, but it is possible that the disease is due to the pathological process of necrosis and subsequent repair of bone cells and bone marrow components after interruption of blood supply and hypoxia or damage to the femoral head, which leads to structural changes in the femoral head, collapse of the femoral head, and joint dysfunction. The incidence of ONFH in China is increasing, and it occurs in young adults between 20 and 50 years (average 36 years), and the bilateral hip joint is involved in more than 70% of patients. The clinical manifestations of adult femoral head necrosis vary from person to person, most of which are pain, dysfunction, difficulty in walking, and a series of clinical symptoms, and even affect patients’ functional activities, resulting in a decline in quality of life. Hip pain is usually the first clinical symptom, sometimes hip and knee pain, and tenderness around the midpoint of the groin. For early ONFH, it may be accompanied by the abduction of the hip joint and mild limitation of internal and external rotation. An X-ray film is not helpful for early diagnosis but for lesions above stage II. Magnetic resonance scanning (MRI) has high specificity and sensitivity in the diagnosis of osteonecrosis. Isotope bone scanning (ECT) has high sensitivity but low specificity in the diagnosis of ONFH. A CT scan is helpful for the diagnosis of stage II and III lesions but not helpful for the diagnosis of stage I lesions [8–10].Medical image processing and analysis mainly include research directions of medical image segmentation, registration, 3D reconstruction, structure analysis, and motion analysis, among which medical image segmentation is the basis of other research directions because other studies are based on the accurate segmentation of processed data. Image segmentation results have many important uses, such as quantitative calculation of the volume of the target object, disease diagnosis, the location of the lesion area, the study of the anatomical structure, the design of treatment, and computer-aided surgery, so it is of great significance to study medical image segmentation. It can be said that the solution of this technology directly affects the successful application of computer-aided diagnosis technology in medicine. However, due to the existence of noise in the real environment and the defects of medical imaging equipment imaging technology, the obtained medical images are inevitably blurred, uneven, and local unclear edges of the target object, which inevitably increases the difficulty of accurate segmentation of medical images. Furthermore, the anatomical structure and shape of various organs in the human body are very complex, and the shape of the same organ may be very different among different individuals. Therefore, although many medical image segmentation algorithms have been proposed so far, the image segmentation task has not been well solved. So far, research on the medical image segmentation method is still a hot spot for scholars at home and abroad.CT pioneered digital imaging, but it is different from ordinary X-ray imaging. What CT shows is a sectional anatomical image, and its density resolution is much higher than that of the X-ray image so that the anatomical structures and pathological tissues that cannot be developed in X-ray imaging can be developed, thus significantly expanding the scope of human examination and improving the detection rate and diagnostic accuracy of lesions [11]. CT, as the first digital imaging device, has greatly promoted the development of medical imaging. At present, it has been widely used in clinical diagnosis of diseases of the following systems and organs: the central nervous system, head and neck, lungs, heart and great blood vessels, abdomen and pelvis, and skeletal muscle system.Because of the special diagnostic value of CT and its wide use in clinics and the importance of image segmentation relative to medical image processing and analysis, research on the CT image segmentation method has been widely concerned, especially for the study of CT images of bones, the chest, and the abdomen, because these parts are the multiple areas of human diseases, and CT examination has a higher detection rate of lesions in these parts.Based on the above study, this article applied CT image segmentation technology to the treatment of femoral head necrosis of the hip joint. Based on iterative adaptive threshold classification and Bayesian discriminant analysis, automatic segmentation technology for 3D HIP joint CT images was proposed. The segmentation using thresholding operation was performed on the femoral head image. The contrast between bone tissue and the surrounding soft tissue area was enhanced by the morphological dilation and corrosion combination technique. Then, the initial segmentation of the hip joint was achieved by using the optimal threshold method. Then, the complete segmentation of the hip joint was achieved by iterative adaptive classification based on Bayesian discriminant analysis.


## 3. Research Methods

### 3.1. CT Image-Related Theory

#### 3.1.1. CT Images and CT Values

CT images are composed of two parts: pixel intensity and pixel size. Pixel intensity reflects the degree of X-ray absorption of organs or tissues, and pixel size reflects the degree of image refinement, that is, the spatial resolution of the image. In the process of CT imaging, the measurement accuracy of the X-ray absorption coefficient of organs or tissues can reach 0.5%, so CT images have a higher density resolution than X-ray images. In reality, in order to express convenience, a CT value is usually used instead of an absorption coefficient to represent the absorption degree of X-ray by organs or tissues. The CT value corresponding to bone is the highest, the CT value corresponding to air is the lowest, and the CT value of other tissues of the human body is between the two [12].


#### 3.1.2. CT Slice

CT images are three-dimensional images of the human body, which are often observed and analyzed from different directions in practical applications [13]. In human anatomy, the section of the human body lengthwise cut into two parts along the left and right directions is called the coronal plane. The plane passing through the vertical and longitudinal axes of the human body and all the planes parallel to it are called the sagittal plane; the surface exposed by cutting the human body perpendicular to the axis of the human body is called a cross-section.


#### 3.1.3. Research Characteristics of CT Image Segmentation Methods

Compared with general images, CT images are characterized by the complexity of anatomical structure and shape, the inherent fuzziness of images, the heterogeneity of the gray level in tissues, and the mass of data. Therefore, the research on CT image segmentation methods presents the following characteristics:(1)
Due to the potential complexity and diversity of CT images and the difficulty of segmentation, no segmentation method has been applied to various tasks so far, but usually an appropriate segmentation algorithm is selected for a specific task. Furthermore, due to the limitations of various segmentation methods, people pay more attention to the combination of multiple segmentation methods while trying to explore new CT image segmentation methods.(2)
Although the CT images obtained exist in the form of 2D slices, with the improvement of computer performance, the research on 3D segmentation methods has attracted more and more attention. The reason is that the integrity of human organs guarantees the continuity of CT images of adjacent slices. Therefore, the 3D segmentation method can use more information between slices to guide the segmentation process and make the segmentation results more accurate.(3)
Medical images can be divided into anatomical images and functional images according to their functions. The former mainly describes the anatomical information of the human body, while the latter mainly describes the functional and metabolic information of the human body. CT images belong to anatomical images. In the process of CT image segmentation, other functional images are fused, such as positron emission tomography images, which gradually become a new trend to guide CT image segmentation [14].(4)
According to the degree of automation, image segmentation algorithms can be divided into automatic, interactive, and manual segmentations [15–17]. Due to the increasing precision of modern instruments, the amount of CT data is increasing, making manual segmentation almost impossible. The result of manual segmentation has a great relationship with the operator’s experience, and the result is not repeatable, so its application is greatly limited. Therefore, automatic segmentation is the goal of segmentation algorithm design. However, due to the complexity of CT images, the current automatic segmentation algorithm has achieved some success, but it is far from meeting the requirements of accuracy in clinical application. Therefore, the interactive CT image segmentation method with user participation and guidance has attracted more and more attention. The man-machine interactive segmentation method can not only use the subjective initiative of humans, so as to ensure the accuracy of the segmentation algorithm, but also make full use of the performance of the computer, so as to ensure the practicality of the segmentation algorithm.


### 3.2. Hip CT Image Segmentation Based on Adaptive Classification and Normal Direction Correction

#### 3.2.1. Initial Image Segmentation

After preprocessing the CT image of the hip joint, the initial segmentation of the image consists of two steps. The first step is the binarization of the image by using the global optimal threshold method [18]. Due to the higher density of the bone relative to the surrounding soft tissue, the bone has a higher intensity in CT images than the surrounding soft tissue. The threshold method is often used as the preferred method for bone rough segmentation due to its simple operation and high algorithm execution efficiency [19]. In the binary image, the general area of the bone is segmented, but due to the uneven bone density and the presence of bone lesions, the threshold method often causes holes in the bone and discontinuities in the bone boundary in the binary image. To solve the above problems, in the second step, the 3D mathematical morphology method is used to fill the holes and connect the boundary of the binary image.


#### 3.2.2. Thresholding Based on the Histogram

In this article, a multistep method is used to segment the hip joint. The basic steps of this method are initial segmentation of the CT image, then complete separation of bone and nonbone tissue by using the initial iterative adaptive segmentation algorithm based on the segmentation results, and finally accurate localization of the bone boundary by using a normal direction correction algorithm.There are many methods for the initial segmentation of bone, such as the threshold method, serpentine method, regional growth method, and watershed segmentation method. Compared with other segmentation methods, threshold segmentation is the most commonly used method for bone CT image segmentation. The reason is that in CT images, bone tissue generally has a higher density than surrounding soft tissues. The threshold method can be used to achieve simple and rapid segmentation of bone and then realize the rapid initialization of the iterative adaptive classification process, thus improving the execution efficiency of the whole algorithm. Due to a large amount of calculation, the efficiency of other methods is far lower than that of threshold segmentation [20].The advantages of threshold segmentation are that it is simple and fast. When the gray value of objects belonging to different classes or their eigenvalues are very different, it can effectively segment the objects. The thresholding segmentation method mainly consists of two steps.(1)
We determined the required segmentation threshold.(2)
The segmentation threshold was compared with the voxel gray value to classify voxels.In the above steps, determining the threshold value is the key to segmentation. When using the thresholding method to segment grayscale images, there are generally certain assumptions about images. In other words, it is based on a certain image model, such as assuming that the gray distribution of different categories in the image conforms to the Gaussian distribution. When specifically applied to CT images of the hip joint, the gray histogram of the hip joint can be regarded as a mixture of two single-peak histograms corresponding to bone and soft tissue, considering that bone has significantly higher strength than other soft tissues and the internal strength of soft tissue changes little.In this article, the Otsu algorithm is used to determine the initial segmentation threshold for the gray histogram, which is composed of two single-peak histograms. The basic idea of the Otsu algorithm is to find a threshold that maximizes the variance between classes and minimizes the variance within classes. According to discriminant analysis theory, such a threshold is the optimal segmentation threshold.The specific steps to determine the optimal threshold are as follows: first, we calculate the gray histogram of the hip joint area of interest (ROI). As the CT value of soft tissue is smaller than that of bone tissue and the voxel number of soft tissue accounts for a larger proportion in ROI, it can be judged from the histogram that the high mountain corresponds to the soft tissue and the low mountain corresponds to the bone tissue. In this chapter, it is assumed that soft tissue and bone tissue all obey Gaussian distribution. During the calculation of the optimal threshold, two Gaussian curves are used to fit the histogram curve, and the gray value corresponding to the intersection of the two Gaussian curves is the optimal segmentation threshold, as shown in Figure2.Figure 2
Threshold selection is based on the histogram.


#### 3.2.3. Morphological Operation of Binary Images

In the binary images obtained by the thresholding method, holes, discontinuities of bone edges, and misconnections between bones often appear in the bone tissue. These phenomena are caused by the uneven density of bone tissues, weak edge properties of bones, and a partial volume effect during CT imaging. In order to get the bone tissue region roughly for the subsequent accurate edge segmentation, this section uses the mathematical morphology method to fill the “holes” of the obtained binary image. In general, the selection of structural elements (size and shape) affects the results of morphological operations. Common structural elements are spherical, cubic, and diamond shapes. In order to reduce the incorrect connection between bones and bones caused by morphological methods as much as possible, 3 × 3 × 3 diamond structural elements are selected in this section.


#### 3.2.4. Calculation of the Iterative Reclassification Algorithm

(1) Calculate the Bone Boundary from the Current Segmentation. For a given voxel, if its directly connected neighbors can be divided into two distinct classes, the voxel is at the edge of either bone region B or nonbone region B. In order to calculate the voxel of the bone margin, a six-voxel neighborhood structure was first defined. In this chapter, the voxel set of the bone margin was E. Specifically, for every voxel x in B, if any of its six neighborhood voxels belongs to B¯, the voxel belongs to the set EB. For the convenience of subsequent explanation, this section specifically marks voxel x belonging to the set EB as x∗.


#### 3.2.5. Reclassification of Bone Boundary Regions Based on the Bayesian Decision Criteria

For each boundary voxelx, we first define a window Wx∗ centered on the x’s position. It is assumed that all voxels in Wx∗ are derived from two Gaussian distributions (bone region B and nonbone region B¯) with the mean and standard deviation μ1,σ1 and μ2,σ2, respectively. For convenience, we write φ1 = μ1,σ1,φ2 = μ2,σ2. The estimation methods for parameters φ1,φ2 will be discussed in detail later. According to Bayes’ theorem, for given voxel X, the proportion of bone components in the voxel can be calculated by following formula (1). Figures 3(a)–3(c) show the value of paxyx at different intensities.(1)paxyx=pyxaxpaxpyx.Figure 3
pax∣yx values at different intensities.
(a)(b)(c)


#### 3.2.6. Update the Current Segmentation Result

After each voxel was traversed, new bone region B and the nonbone region were obtained by the 3D mathematical morphology method. After the new bone and nonbone regions were obtained, the boundary voxel set was recalculated. If the voxel did not change during the two iterations, the iteration process was stopped. Otherwise, we return to the first step to recalculate bone boundary voxels and perform the entire iterative process until convergence.


### 3.3. Description of Shock Wave Therapy

Possible mechanisms of ESWT treatment of ONFH include the promotion of neovascularization, bone remodeling, and regeneration, which are associated with vascular endothelial growth factor, endothelial nitric oxide synthase, and bone morphogenetic protein-2. Animal experiments have shown that ESWT can promote new bone formation and cartilage regeneration. In vitro experiments have also confirmed that ESWT can promote osteoblast proliferation and promote bone healing by stimulating angiogenesis and bone formation, and vasodilation and neovascularization can alleviate bone marrow edema. ESWT can reduce pain information transmission and relieve pain by inhibiting the release of substance P. ESWT can also fight fibrosis and loosen adhesions by regulating fibre-related molecules.


## 3.1. CT Image-Related Theory

### 3.1.1. CT Images and CT Values

CT images are composed of two parts: pixel intensity and pixel size. Pixel intensity reflects the degree of X-ray absorption of organs or tissues, and pixel size reflects the degree of image refinement, that is, the spatial resolution of the image. In the process of CT imaging, the measurement accuracy of the X-ray absorption coefficient of organs or tissues can reach 0.5%, so CT images have a higher density resolution than X-ray images. In reality, in order to express convenience, a CT value is usually used instead of an absorption coefficient to represent the absorption degree of X-ray by organs or tissues. The CT value corresponding to bone is the highest, the CT value corresponding to air is the lowest, and the CT value of other tissues of the human body is between the two [12].


### 3.1.2. CT Slice

CT images are three-dimensional images of the human body, which are often observed and analyzed from different directions in practical applications [13]. In human anatomy, the section of the human body lengthwise cut into two parts along the left and right directions is called the coronal plane. The plane passing through the vertical and longitudinal axes of the human body and all the planes parallel to it are called the sagittal plane; the surface exposed by cutting the human body perpendicular to the axis of the human body is called a cross-section.


### 3.1.3. Research Characteristics of CT Image Segmentation Methods

Compared with general images, CT images are characterized by the complexity of anatomical structure and shape, the inherent fuzziness of images, the heterogeneity of the gray level in tissues, and the mass of data. Therefore, the research on CT image segmentation methods presents the following characteristics:(1)
Due to the potential complexity and diversity of CT images and the difficulty of segmentation, no segmentation method has been applied to various tasks so far, but usually an appropriate segmentation algorithm is selected for a specific task. Furthermore, due to the limitations of various segmentation methods, people pay more attention to the combination of multiple segmentation methods while trying to explore new CT image segmentation methods.(2)
Although the CT images obtained exist in the form of 2D slices, with the improvement of computer performance, the research on 3D segmentation methods has attracted more and more attention. The reason is that the integrity of human organs guarantees the continuity of CT images of adjacent slices. Therefore, the 3D segmentation method can use more information between slices to guide the segmentation process and make the segmentation results more accurate.(3)
Medical images can be divided into anatomical images and functional images according to their functions. The former mainly describes the anatomical information of the human body, while the latter mainly describes the functional and metabolic information of the human body. CT images belong to anatomical images. In the process of CT image segmentation, other functional images are fused, such as positron emission tomography images, which gradually become a new trend to guide CT image segmentation [14].(4)
According to the degree of automation, image segmentation algorithms can be divided into automatic, interactive, and manual segmentations [15–17]. Due to the increasing precision of modern instruments, the amount of CT data is increasing, making manual segmentation almost impossible. The result of manual segmentation has a great relationship with the operator’s experience, and the result is not repeatable, so its application is greatly limited. Therefore, automatic segmentation is the goal of segmentation algorithm design. However, due to the complexity of CT images, the current automatic segmentation algorithm has achieved some success, but it is far from meeting the requirements of accuracy in clinical application. Therefore, the interactive CT image segmentation method with user participation and guidance has attracted more and more attention. The man-machine interactive segmentation method can not only use the subjective initiative of humans, so as to ensure the accuracy of the segmentation algorithm, but also make full use of the performance of the computer, so as to ensure the practicality of the segmentation algorithm.


## 3.1.1. CT Images and CT Values

CT images are composed of two parts: pixel intensity and pixel size. Pixel intensity reflects the degree of X-ray absorption of organs or tissues, and pixel size reflects the degree of image refinement, that is, the spatial resolution of the image. In the process of CT imaging, the measurement accuracy of the X-ray absorption coefficient of organs or tissues can reach 0.5%, so CT images have a higher density resolution than X-ray images. In reality, in order to express convenience, a CT value is usually used instead of an absorption coefficient to represent the absorption degree of X-ray by organs or tissues. The CT value corresponding to bone is the highest, the CT value corresponding to air is the lowest, and the CT value of other tissues of the human body is between the two [12].


## 3.1.2. CT Slice

CT images are three-dimensional images of the human body, which are often observed and analyzed from different directions in practical applications [13]. In human anatomy, the section of the human body lengthwise cut into two parts along the left and right directions is called the coronal plane. The plane passing through the vertical and longitudinal axes of the human body and all the planes parallel to it are called the sagittal plane; the surface exposed by cutting the human body perpendicular to the axis of the human body is called a cross-section.


## 3.1.3. Research Characteristics of CT Image Segmentation Methods

Compared with general images, CT images are characterized by the complexity of anatomical structure and shape, the inherent fuzziness of images, the heterogeneity of the gray level in tissues, and the mass of data. Therefore, the research on CT image segmentation methods presents the following characteristics:(1)
Due to the potential complexity and diversity of CT images and the difficulty of segmentation, no segmentation method has been applied to various tasks so far, but usually an appropriate segmentation algorithm is selected for a specific task. Furthermore, due to the limitations of various segmentation methods, people pay more attention to the combination of multiple segmentation methods while trying to explore new CT image segmentation methods.(2)
Although the CT images obtained exist in the form of 2D slices, with the improvement of computer performance, the research on 3D segmentation methods has attracted more and more attention. The reason is that the integrity of human organs guarantees the continuity of CT images of adjacent slices. Therefore, the 3D segmentation method can use more information between slices to guide the segmentation process and make the segmentation results more accurate.(3)
Medical images can be divided into anatomical images and functional images according to their functions. The former mainly describes the anatomical information of the human body, while the latter mainly describes the functional and metabolic information of the human body. CT images belong to anatomical images. In the process of CT image segmentation, other functional images are fused, such as positron emission tomography images, which gradually become a new trend to guide CT image segmentation [14].(4)
According to the degree of automation, image segmentation algorithms can be divided into automatic, interactive, and manual segmentations [15–17]. Due to the increasing precision of modern instruments, the amount of CT data is increasing, making manual segmentation almost impossible. The result of manual segmentation has a great relationship with the operator’s experience, and the result is not repeatable, so its application is greatly limited. Therefore, automatic segmentation is the goal of segmentation algorithm design. However, due to the complexity of CT images, the current automatic segmentation algorithm has achieved some success, but it is far from meeting the requirements of accuracy in clinical application. Therefore, the interactive CT image segmentation method with user participation and guidance has attracted more and more attention. The man-machine interactive segmentation method can not only use the subjective initiative of humans, so as to ensure the accuracy of the segmentation algorithm, but also make full use of the performance of the computer, so as to ensure the practicality of the segmentation algorithm.


## 3.2. Hip CT Image Segmentation Based on Adaptive Classification and Normal Direction Correction

### 3.2.1. Initial Image Segmentation

After preprocessing the CT image of the hip joint, the initial segmentation of the image consists of two steps. The first step is the binarization of the image by using the global optimal threshold method [18]. Due to the higher density of the bone relative to the surrounding soft tissue, the bone has a higher intensity in CT images than the surrounding soft tissue. The threshold method is often used as the preferred method for bone rough segmentation due to its simple operation and high algorithm execution efficiency [19]. In the binary image, the general area of the bone is segmented, but due to the uneven bone density and the presence of bone lesions, the threshold method often causes holes in the bone and discontinuities in the bone boundary in the binary image. To solve the above problems, in the second step, the 3D mathematical morphology method is used to fill the holes and connect the boundary of the binary image.


### 3.2.2. Thresholding Based on the Histogram

In this article, a multistep method is used to segment the hip joint. The basic steps of this method are initial segmentation of the CT image, then complete separation of bone and nonbone tissue by using the initial iterative adaptive segmentation algorithm based on the segmentation results, and finally accurate localization of the bone boundary by using a normal direction correction algorithm.There are many methods for the initial segmentation of bone, such as the threshold method, serpentine method, regional growth method, and watershed segmentation method. Compared with other segmentation methods, threshold segmentation is the most commonly used method for bone CT image segmentation. The reason is that in CT images, bone tissue generally has a higher density than surrounding soft tissues. The threshold method can be used to achieve simple and rapid segmentation of bone and then realize the rapid initialization of the iterative adaptive classification process, thus improving the execution efficiency of the whole algorithm. Due to a large amount of calculation, the efficiency of other methods is far lower than that of threshold segmentation [20].The advantages of threshold segmentation are that it is simple and fast. When the gray value of objects belonging to different classes or their eigenvalues are very different, it can effectively segment the objects. The thresholding segmentation method mainly consists of two steps.(1)
We determined the required segmentation threshold.(2)
The segmentation threshold was compared with the voxel gray value to classify voxels.In the above steps, determining the threshold value is the key to segmentation. When using the thresholding method to segment grayscale images, there are generally certain assumptions about images. In other words, it is based on a certain image model, such as assuming that the gray distribution of different categories in the image conforms to the Gaussian distribution. When specifically applied to CT images of the hip joint, the gray histogram of the hip joint can be regarded as a mixture of two single-peak histograms corresponding to bone and soft tissue, considering that bone has significantly higher strength than other soft tissues and the internal strength of soft tissue changes little.In this article, the Otsu algorithm is used to determine the initial segmentation threshold for the gray histogram, which is composed of two single-peak histograms. The basic idea of the Otsu algorithm is to find a threshold that maximizes the variance between classes and minimizes the variance within classes. According to discriminant analysis theory, such a threshold is the optimal segmentation threshold.The specific steps to determine the optimal threshold are as follows: first, we calculate the gray histogram of the hip joint area of interest (ROI). As the CT value of soft tissue is smaller than that of bone tissue and the voxel number of soft tissue accounts for a larger proportion in ROI, it can be judged from the histogram that the high mountain corresponds to the soft tissue and the low mountain corresponds to the bone tissue. In this chapter, it is assumed that soft tissue and bone tissue all obey Gaussian distribution. During the calculation of the optimal threshold, two Gaussian curves are used to fit the histogram curve, and the gray value corresponding to the intersection of the two Gaussian curves is the optimal segmentation threshold, as shown in Figure2.Figure 2
Threshold selection is based on the histogram.


### 3.2.3. Morphological Operation of Binary Images

In the binary images obtained by the thresholding method, holes, discontinuities of bone edges, and misconnections between bones often appear in the bone tissue. These phenomena are caused by the uneven density of bone tissues, weak edge properties of bones, and a partial volume effect during CT imaging. In order to get the bone tissue region roughly for the subsequent accurate edge segmentation, this section uses the mathematical morphology method to fill the “holes” of the obtained binary image. In general, the selection of structural elements (size and shape) affects the results of morphological operations. Common structural elements are spherical, cubic, and diamond shapes. In order to reduce the incorrect connection between bones and bones caused by morphological methods as much as possible, 3 × 3 × 3 diamond structural elements are selected in this section.


### 3.2.4. Calculation of the Iterative Reclassification Algorithm

(1) Calculate the Bone Boundary from the Current Segmentation. For a given voxel, if its directly connected neighbors can be divided into two distinct classes, the voxel is at the edge of either bone region B or nonbone region B. In order to calculate the voxel of the bone margin, a six-voxel neighborhood structure was first defined. In this chapter, the voxel set of the bone margin was E. Specifically, for every voxel x in B, if any of its six neighborhood voxels belongs to B¯, the voxel belongs to the set EB. For the convenience of subsequent explanation, this section specifically marks voxel x belonging to the set EB as x∗.


### 3.2.5. Reclassification of Bone Boundary Regions Based on the Bayesian Decision Criteria

For each boundary voxelx, we first define a window Wx∗ centered on the x’s position. It is assumed that all voxels in Wx∗ are derived from two Gaussian distributions (bone region B and nonbone region B¯) with the mean and standard deviation μ1,σ1 and μ2,σ2, respectively. For convenience, we write φ1 = μ1,σ1,φ2 = μ2,σ2. The estimation methods for parameters φ1,φ2 will be discussed in detail later. According to Bayes’ theorem, for given voxel X, the proportion of bone components in the voxel can be calculated by following formula (1). Figures 3(a)–3(c) show the value of paxyx at different intensities.(1)paxyx=pyxaxpaxpyx.Figure 3
pax∣yx values at different intensities.
(a)(b)(c)


### 3.2.6. Update the Current Segmentation Result

After each voxel was traversed, new bone region B and the nonbone region were obtained by the 3D mathematical morphology method. After the new bone and nonbone regions were obtained, the boundary voxel set was recalculated. If the voxel did not change during the two iterations, the iteration process was stopped. Otherwise, we return to the first step to recalculate bone boundary voxels and perform the entire iterative process until convergence.


## 3.2.1. Initial Image Segmentation

After preprocessing the CT image of the hip joint, the initial segmentation of the image consists of two steps. The first step is the binarization of the image by using the global optimal threshold method [18]. Due to the higher density of the bone relative to the surrounding soft tissue, the bone has a higher intensity in CT images than the surrounding soft tissue. The threshold method is often used as the preferred method for bone rough segmentation due to its simple operation and high algorithm execution efficiency [19]. In the binary image, the general area of the bone is segmented, but due to the uneven bone density and the presence of bone lesions, the threshold method often causes holes in the bone and discontinuities in the bone boundary in the binary image. To solve the above problems, in the second step, the 3D mathematical morphology method is used to fill the holes and connect the boundary of the binary image.


## 3.2.2. Thresholding Based on the Histogram

In this article, a multistep method is used to segment the hip joint. The basic steps of this method are initial segmentation of the CT image, then complete separation of bone and nonbone tissue by using the initial iterative adaptive segmentation algorithm based on the segmentation results, and finally accurate localization of the bone boundary by using a normal direction correction algorithm.There are many methods for the initial segmentation of bone, such as the threshold method, serpentine method, regional growth method, and watershed segmentation method. Compared with other segmentation methods, threshold segmentation is the most commonly used method for bone CT image segmentation. The reason is that in CT images, bone tissue generally has a higher density than surrounding soft tissues. The threshold method can be used to achieve simple and rapid segmentation of bone and then realize the rapid initialization of the iterative adaptive classification process, thus improving the execution efficiency of the whole algorithm. Due to a large amount of calculation, the efficiency of other methods is far lower than that of threshold segmentation [20].The advantages of threshold segmentation are that it is simple and fast. When the gray value of objects belonging to different classes or their eigenvalues are very different, it can effectively segment the objects. The thresholding segmentation method mainly consists of two steps.(1)
We determined the required segmentation threshold.(2)
The segmentation threshold was compared with the voxel gray value to classify voxels.In the above steps, determining the threshold value is the key to segmentation. When using the thresholding method to segment grayscale images, there are generally certain assumptions about images. In other words, it is based on a certain image model, such as assuming that the gray distribution of different categories in the image conforms to the Gaussian distribution. When specifically applied to CT images of the hip joint, the gray histogram of the hip joint can be regarded as a mixture of two single-peak histograms corresponding to bone and soft tissue, considering that bone has significantly higher strength than other soft tissues and the internal strength of soft tissue changes little.In this article, the Otsu algorithm is used to determine the initial segmentation threshold for the gray histogram, which is composed of two single-peak histograms. The basic idea of the Otsu algorithm is to find a threshold that maximizes the variance between classes and minimizes the variance within classes. According to discriminant analysis theory, such a threshold is the optimal segmentation threshold.The specific steps to determine the optimal threshold are as follows: first, we calculate the gray histogram of the hip joint area of interest (ROI). As the CT value of soft tissue is smaller than that of bone tissue and the voxel number of soft tissue accounts for a larger proportion in ROI, it can be judged from the histogram that the high mountain corresponds to the soft tissue and the low mountain corresponds to the bone tissue. In this chapter, it is assumed that soft tissue and bone tissue all obey Gaussian distribution. During the calculation of the optimal threshold, two Gaussian curves are used to fit the histogram curve, and the gray value corresponding to the intersection of the two Gaussian curves is the optimal segmentation threshold, as shown in Figure2.Figure 2
Threshold selection is based on the histogram.


## 3.2.3. Morphological Operation of Binary Images

In the binary images obtained by the thresholding method, holes, discontinuities of bone edges, and misconnections between bones often appear in the bone tissue. These phenomena are caused by the uneven density of bone tissues, weak edge properties of bones, and a partial volume effect during CT imaging. In order to get the bone tissue region roughly for the subsequent accurate edge segmentation, this section uses the mathematical morphology method to fill the “holes” of the obtained binary image. In general, the selection of structural elements (size and shape) affects the results of morphological operations. Common structural elements are spherical, cubic, and diamond shapes. In order to reduce the incorrect connection between bones and bones caused by morphological methods as much as possible, 3 × 3 × 3 diamond structural elements are selected in this section.


## 3.2.4. Calculation of the Iterative Reclassification Algorithm

(1) Calculate the Bone Boundary from the Current Segmentation. For a given voxel, if its directly connected neighbors can be divided into two distinct classes, the voxel is at the edge of either bone region B or nonbone region B. In order to calculate the voxel of the bone margin, a six-voxel neighborhood structure was first defined. In this chapter, the voxel set of the bone margin was E. Specifically, for every voxel x in B, if any of its six neighborhood voxels belongs to B¯, the voxel belongs to the set EB. For the convenience of subsequent explanation, this section specifically marks voxel x belonging to the set EB as x∗.


## 3.2.5. Reclassification of Bone Boundary Regions Based on the Bayesian Decision Criteria

For each boundary voxelx, we first define a window Wx∗ centered on the x’s position. It is assumed that all voxels in Wx∗ are derived from two Gaussian distributions (bone region B and nonbone region B¯) with the mean and standard deviation μ1,σ1 and μ2,σ2, respectively. For convenience, we write φ1 = μ1,σ1,φ2 = μ2,σ2. The estimation methods for parameters φ1,φ2 will be discussed in detail later. According to Bayes’ theorem, for given voxel X, the proportion of bone components in the voxel can be calculated by following formula (1). Figures 3(a)–3(c) show the value of paxyx at different intensities.(1)paxyx=pyxaxpaxpyx.Figure 3
pax∣yx values at different intensities.
(a)(b)(c)


## 3.2.6. Update the Current Segmentation Result

After each voxel was traversed, new bone region B and the nonbone region were obtained by the 3D mathematical morphology method. After the new bone and nonbone regions were obtained, the boundary voxel set was recalculated. If the voxel did not change during the two iterations, the iteration process was stopped. Otherwise, we return to the first step to recalculate bone boundary voxels and perform the entire iterative process until convergence.


## 3.3. Description of Shock Wave Therapy

Possible mechanisms of ESWT treatment of ONFH include the promotion of neovascularization, bone remodeling, and regeneration, which are associated with vascular endothelial growth factor, endothelial nitric oxide synthase, and bone morphogenetic protein-2. Animal experiments have shown that ESWT can promote new bone formation and cartilage regeneration. In vitro experiments have also confirmed that ESWT can promote osteoblast proliferation and promote bone healing by stimulating angiogenesis and bone formation, and vasodilation and neovascularization can alleviate bone marrow edema. ESWT can reduce pain information transmission and relieve pain by inhibiting the release of substance P. ESWT can also fight fibrosis and loosen adhesions by regulating fibre-related molecules.


## 4. Results and Discussion

The experimental results were retrospectively analyzed in this article. 55 sets of CT data images were collected in this study, including 110 hip joints. Experimental data were obtained by using the GE Pro Speed CT machine. The plane resolution of slices was 512 × 512, the intraplane pixel spacing was 0.68 mm, the distance between slices was 1.5 mm, and the number of slices ranged from 85 to 95. The experimental environment is Lab6.5, 2.33 GHz processor, and 2 GB memory. 110 hip images contained data ranging from normal to severe lesions. The results of manual segmentation of all data were given by radiologists.In order to verify the applicability of the proposed method, the 110 hip images obtained were divided into four groups according to the anatomical and imaging characteristics (e.g. proximity of the femoral head to the acetabulum, deformity degree of the femoral head, and uneven degree of bone density). The number of the four groups was 16, 31, 51, and 12 respectively. Figure4 shows the correction diagram of an image triangulation surface.Figure 4
Normal method correction process.Further research shows that this method is a model-based segmentation method, and the shape information of the object to be segmented is added as prior constraint knowledge in the segmentation process. Therefore, this segmentation method is more robust for the hip joint with serious lesions.Table1 shows the comparison result of segmentation time between this method and other two methods.Table 1
Comparison results of 110 hip joint data segmentation time with the three methods.
Zoroofi’s methodYokota’s methodOur methodTotal (h)12.918.510.9Average time (s)9.513.68It can be seen that the method used in this article takes a total of 10.9 hours, with an average time of 8 seconds, much shorter than time taken by the other two methods, indicating that the method in this article has great advantages in the field of image segmentation.


## 5. Conclusion

In this article, a CT image-based shock wave treatment method for femoral head necrosis is proposed, which is further supplemented by combining CT image segmentation technology for shock wave treatment of femoral head necrosis. Based on iterative adaptive threshold classification and Bayesian discriminant analysis, automatic segmentation technology for 3D HIP joint CT images was proposed. The segmentation using thresholding operation was performed on the femoral head image. The experimental results show that the method used in this article takes a total of 10.9 hours and an average of 8 seconds, which is much shorter than time taken by the other two methods. It indicates that the shock wave therapy for femoral head necrosis based on CT images proposed in this article can effectively improve the treatment effect and speed up the treatment.



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