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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1358652</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2024.1358652</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Intelligent diagnostic method for developmental hip dislocation</article-title>
<alt-title alt-title-type="left-running-head">Sun et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2024.1358652">10.3389/fphy.2024.1358652</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Sun</surname>
<given-names>Hang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2596070/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/funding-acquisition/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Li</surname>
<given-names>Hong</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1490311/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhao</surname>
<given-names>Yuhang</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
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<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Pan</surname>
<given-names>Shinong</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>School of Information Science and Engineering</institution>, <institution>Shenyang Ligong University</institution>, <addr-line>Shenyang</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>College of Medicine and Biological Information Engineering</institution>, <institution>Northeastern University</institution>, <addr-line>Shenyang</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Radiology</institution>, <institution>Shengjing Hospital of China Medical University</institution>, <addr-line>Shenyang</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/288927/overview">Udo Jochen Birk</ext-link>, University of Applied Sciences Graub&#xfc;nden, Switzerland</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1755851/overview">Giorgio De Nunzio</ext-link>, University of Salento, Italy</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/121618/overview">Georgia Damoraki</ext-link>, National and Kapodistrian University of Athens, Greece</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2151921/overview">Houping Chen</ext-link>, Guiyang children&#x2019;s Hospital, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Hang Sun, <email>sunhang84@126.com</email>; Hong Li, <email>lihong@bmie.neu.edu.cn</email>; Shinong Pan, <email>cjr.panshinong@vip.163.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>09</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>12</volume>
<elocation-id>1358652</elocation-id>
<history>
<date date-type="received">
<day>20</day>
<month>12</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>26</day>
<month>08</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Sun, Li, Zhao and Pan.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Sun, Li, Zhao and Pan</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<sec>
<title>Background</title>
<p>Developmental dislocation of the hip joint (DDH) is a condition that severely threatens children&#x2019;s healthy growth. Without timely and correct treatment, it will lead to osteoarthritis and hip dysfunction in the evolution of children.</p>
</sec>
<sec>
<title>Objective</title>
<p>It is essential to develop an intelligent model for diagnosing hip dislocation and performing accurate quantitative analysis.</p>
</sec>
<sec>
<title>Methods</title>
<p>In this paper, 46 cases of computed tomography (CT) images were retrospectively collected, including 19 cases of hip dislocation and 27 cases of healthy people. The experiment first uses ITK-SNAP to sketch the ilium and femoral head in the original image. Then, it uses 3D U-Net to send the label of the background, ilium, and femoral head into three channels, respectively, to realize the three-dimensional segmentation of the ilium and femoral head. Next, the extraction of the surface of the acetabulum and femoral head is performed. Subsequently, the erroneous points are eliminated, and the spherical surfaces of the acetabulum and femoral head are fitted using the least squares method. Ultimately, the spherical center distance is calculated quantitatively to predict whether the hip joint is dislocated.</p>
</sec>
<sec>
<title>Results</title>
<p>Under the independent test set, the segmentation average dice coefficients of the ilium and femoral head are 89% and 93%, respectively. The spherical center distance between the acetabulum and femoral head is calculated quantitatively. If the value exceeds 10&#xa0;mm, it is considered a hip dislocation. Compared with the doctor&#x2019;s diagnosis, the accuracy result is 94.4%.</p>
</sec>
<sec>
<title>Conclusion</title>
<p>This paper successfully implements a precise and automated intelligent diagnostic system for the identification of hip dislocation. Commencing with the development of a 3D segmentation algorithm for the ilium and femoral head, we further introduce a novel method that computes the spherical distance for the prediction of hip dislocation. This approach provides robust quantitative analysis, thereby facilitating more informed clinical decision-making.</p>
</sec>
</abstract>
<kwd-group>
<kwd>computed tomography image</kwd>
<kwd>hip dislocation</kwd>
<kwd>intelligent diagnostic</kwd>
<kwd>3D femoral head segmentation</kwd>
<kwd>3D iliac segmentation</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Medical Physics and Imaging</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The developmental dislocation of the hip joint (DDH) is the most common hip condition in pediatric orthopedics [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B2">2</xref>]. It refers to the position abnormality of the femoral head and acetabulum or the shape abnormality at birth or in the child&#x2019;s later growth [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B4">4</xref>]. It is generally divided into three manifestations of dislocation: internal, external, and central [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B6">6</xref>]. The diagnosis method mainly involves imaging examinations, including X-ray and 3D-computed tomography (CT) [<xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B8">8</xref>]. In clinical diagnosis, doctors mostly use subjective judgment and clinical experience to diagnose the lesion severity. Using multiple 2D sectional images in the CT image lacks an objective quantitative basis for a 3D geometric relationship, and the diagnostic accuracy is limited [<xref ref-type="bibr" rid="B9">9</xref>, <xref ref-type="bibr" rid="B10">10</xref>]. After the advent of 3D CT reconstruction technology, doctors can more intuitively observe the patient&#x2019;s hip joint and measure and analyze the data on different planes. Although 3D CT has provided many new ideas and methods for diagnosing and treating DDH, only some studies have focused on 3D quantitative analysis [<xref ref-type="bibr" rid="B11">11</xref>&#x2013;<xref ref-type="bibr" rid="B13">13</xref>]. Nonetheless, it is necessary to use quantitative values to reflect the severity of hip dislocation to assist doctors in diagnosis.</p>
<p>There have been few research results in recent years related to hip dislocation. Most studies described hip joint segmentation [<xref ref-type="bibr" rid="B14">14</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. [<xref ref-type="bibr" rid="B15">15</xref>] employed a method that automatically segments the femoral head and acetabular cartilage by marking the region of interest. This method can better extract the desired information. The disadvantage is that the user needs more experience in labeling the region of interest. At the same time, there is no effective treatment method for cases where the hip joint has not yet fully developed. [<xref ref-type="bibr" rid="B18">18</xref>] developed an automated method for 3D quantitative evaluation and measurement of the &#x3b1;-angle of the head and neck joint of the femoral head using the bone model from the magnetic resonance image (MRI) of the hip joint.</p>
<p>Recently, radiomics and machine learning have made great progress in the diagnosis of DDH. [<xref ref-type="bibr" rid="B19">19</xref>] established a model that can automatically generate parameters of the hip joint based on the radiographic image using the encoder&#x2013;decoder convolutional neural network and obtained good results. [<xref ref-type="bibr" rid="B20">20</xref>] proposed an automatic segmentation algorithm based on edge detection and Hough transform. The results show that the segmentation accuracy of the acetabular angle is good. However, when calculating the central edge angle, segmentation accuracy is low, which may be due to the incomplete development of the femoral head of infants under 6&#xa0;months, which makes it possible for the automatic algorithm to miscalculate the angle. [<xref ref-type="bibr" rid="B21">21</xref>] incorporated clinical knowledge into the random walk formula in the form of intensity prior and proposed a semi-automatic method to segment the acetabular surface model from MRI. This method reduces the impact of signal loss at the boundary by using pixel information from adjacent slices. However, the proposed method does not consider the changes caused by signal nonuniformity and geometric distortion. Moreover, the segmentation technology is semi-automatic, requiring the user to select an initial seed point, which is relatively cumbersome.</p>
<p>This study proposes a 3D self-starting segmentation method of the ilium and femoral head based on CT images. At the same time, it produces a computer-aided diagnosis algorithm to distinguish hip dislocation and calculate the distance the hip joint needs to move for restoration.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>2 Materials and methods</title>
<sec id="s2-1">
<title>2.1 Patients and CT parameters</title>
<p>The research data are provided by the Shengjing Hospital of China Medical University. The CT images used in this experiment have a size of 512 &#xd7; 512, with a spatial resolution of 0.41&#x2013;0.74&#xa0;mm and a layer spacing of 1&#x2013;1.5&#xa0;mm, in DICOM format. In total, data on 46 cases, including 19 patients (17 girls and 2 boys) with dislocation of the hip joint (14 patients with unilateral dislocation and 5 patients with bilateral dislocation) were collected from 2013 to 2019. Because the incidence rate of this disease is low, about one thousandth, and most patients have no awareness of being ill, there are limited data for collection, so the period is extensive. Patients are between 13&#xa0;months and 7&#xa0;years old (DDH&#x2019;s regulated range is 0&#x2013;14&#xa0;years old), and about 68% of patients are between 15&#xa0;months and 23&#xa0;months old. The data on 27 healthy people were collected from 2019 to 2020, all of which were retrospective. Among them, there are 20 women and 7 men. The age range is from 13 to 62&#xa0;years old. The distribution of each age group is relatively uniform. Because CT radiation significantly impacts infants and young children, data collection on healthy people is not limited to 0&#x2013;14&#xa0;years old. Regardless of age, the structure of the hip joint is almost the same, and moreover, the difference in bone size does not affect the training of the deep learning network model. The images in this study are mainly cross-sectional images. <xref ref-type="fig" rid="F1">Figure 1</xref> shows the images of patients and healthy people. <xref ref-type="table" rid="T1">Table 1</xref> provides the clinical characteristics of the data.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Cross-sectional images: the first row displays the hip joints of some patients, and the second row displays normal persons&#x2019; hip joints.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g001.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Clinical characteristics of the data.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" align="center">Data</th>
<th align="center">Number</th>
<th align="center">Eligibility criteria</th>
<th align="center">Age/years (mean &#xb1; SD)</th>
<th align="center">Sex<break/>Female/male</th>
<th align="center">Onset of symptoms</th>
<th align="center">Outcomes/fitting ball center distance between the femoral head and acetabulum (mm)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">DDH</td>
<td align="center">Unilateral dislocation</td>
<td align="center">14</td>
<td rowspan="3" align="center">Undergone CT examination</td>
<td rowspan="2" align="center">1.08&#x2013;7 (2.78 &#xb1; 1.90)</td>
<td rowspan="2" align="center">17/2</td>
<td rowspan="2" align="center">Hip pain, change in posture, or shortening deformity of the lower limbs</td>
<td rowspan="2" align="center">Less than 10</td>
</tr>
<tr>
<td align="center">Bilateral dislocation</td>
<td align="center">5</td>
</tr>
<tr>
<td colspan="2" align="center">Healthy people</td>
<td align="center">27</td>
<td align="center">13&#x2013;62 (43.20 &#xb1; 14.62)</td>
<td align="center">20/7</td>
<td align="center">None</td>
<td align="center">Greater than 10</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> shows that the hip joint appearance of patients is significantly different from that of healthy people. Comparing the shape of the femoral head, healthy individuals have a regular, round shape, while some patients undergo significant changes. The ilium and femoral head of healthy people are closely positioned, with the ilium wrapping around the femoral head. In contrast, in patients, the ilium and femoral head are farther apart.</p>
</sec>
<sec id="s2-2">
<title>2.2 Methods</title>
<p>The research content of this paper is mainly divided into two parts. The first part focuses on the realization of 3D automatic segmentation of the ilium and femoral head [<xref ref-type="bibr" rid="B22">22</xref>&#x2013;<xref ref-type="bibr" rid="B24">24</xref>], which lays the foundation for the subsequent quantitative analysis of hip dislocation. The second part involves extracting the boundary of the ilium and femoral head using the least squares method to fit the sphere, finding the spherical centers, calculating the distance between these two spherical centers, and quantifying the quantitative degree of hip dislocation. The overall process is shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Workflow chart of this paper.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g002.tif"/>
</fig>
<sec id="s2-2-1">
<title>2.2.1 3D segmentation method</title>
<sec id="s2-2-1-1">
<title>2.2.1.1 Label making</title>
<p>In this study, ITK-SNAP is used to produce labels for deep learning segmentation. The specific drawing process of the hip joint label is to mark the femoral head (green) and the ilium (red), as shown in <xref ref-type="fig" rid="F3">Figure 3</xref>. The 3D display of the labeled regions is shown in <xref ref-type="fig" rid="F4">Figure 4</xref>, in which we can more clearly observe whether the marked area is correct. The label production process was conducted under the guidance and confirmation of Professor S. Pan, who has been engaged in clinical work for over 30&#xa0;years.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The first row is the annotation of the patient&#x2019;s hip joint, and the second row is the annotation of the healthy person&#x2019;s hip joint.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>3D label display diagram.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g004.tif"/>
</fig>
</sec>
<sec id="s2-2-1-2">
<title>2.2.1.2 Dataset allocation</title>
<p>The image selections containing the regions of interest were used as the input of network training. Preliminarily, we converted the collected 46 groups of DICOM data into PNG format. The images containing the target area were chosen, and those without the target area were eliminated. A total of 282 images were collected. In the experiment, the data were randomly divided into training, verification, and test data sets according to the ratio of 6:2:2 to ensure that all images in each case were collected into the same group. Therefore, 222 images and the corresponding labels were randomly selected from 37 groups, including 177 images for training and 45 images for verification, and 60 images were taken from the remaining 9 groups for testing.</p>
<p>Due to the small amount of data, this experiment utilized a mirror image data augmentation method. Through this approach, 37 groups of training and validation images (177 images and 45 images) were increased to 74 groups of the learning set (354 images and 90 images). The segmentation model was obtained using the three-fold cross-validation method. The background pixels were marked as 0, the ilium pixels were marked as 1, and the femoral head pixels were marked as 2.</p>
</sec>
<sec id="s2-2-1-3">
<title>2.2.1.3 Segmentation model construction</title>
<p>This paper uses the 3D U-Net image segmentation network [<xref ref-type="bibr" rid="B25">25</xref>, <xref ref-type="bibr" rid="B26">26</xref>]. In this experiment, the Keras library with TensorFlow was used as the backend. All calculations were performed on a 64-bit Windows 10 computer with an Intel (R) Core (TM) i7-8700 K CPU (3.70&#xa0;GHz) processor and an NVIDIA GEFORCE GTX 1080Ti.</p>
<p>This experiment employs the classic 3D U-Net network architecture. The encoding part consists of a downsampling module, which includes two convolutional layers with 3 &#xd7; 3 &#xd7; 3 kernels and a stride of 1, followed by a max pooling layer with a 2 &#xd7; 2 &#xd7; 2 kernel and a stride of 2. The decoding part is composed of an upsampling convolutional layer (deconvolutional layer), a feature concatenation operation with a 2 &#xd7; 2 &#xd7; 2 kernel and a stride of 2, and two convolutional layers with 3 &#xd7; 3 &#xd7; 3 kernels and a stride of 1. The ReLU activation function is used throughout the process. In the final layer, a 1 &#xd7; 1 &#xd7; 1 convolutional layer reduces the number of output channels to the number of classes to be segmented in the labels.</p>
<p>The input data were changed to three-channel type data, with channel 1 as the background, channel 2 as the ilium, and channel 3 as the femoral head, so that different labeling information could be put into training at the same time. In this experiment, one-hot encoding was used for image three-channel processing [<xref ref-type="bibr" rid="B27">27</xref>]. <xref ref-type="fig" rid="F5">Figure 5</xref> shows the tag images of the background, ilium, and femoral head in the second to fourth columns sent into the three-channel network.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Labels: <bold>(A)</bold> original, <bold>(B)</bold> background, <bold>(C)</bold> iliac, and <bold>(D)</bold> femoral head.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g005.tif"/>
</fig>
</sec>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Quantitative analysis of hip dislocation</title>
<p>The segmented images of the ilium and femoral head are used for quantitatively calculating hip dislocation. This method can provide accurate 3D spatial information to assist doctors in diagnosis.</p>
<sec id="s2-2-2-1">
<title>2.2.2.1 Spherical center calculation</title>
<p>First, the Sobel operator is used to extract the edge of the femoral head and acetabulum [<xref ref-type="bibr" rid="B28">28</xref>]. Then, the data containing the boundary information on the femoral head can be extracted to form a spatial coordinate sampling point set. However, the meniscus of the acetabulum is incomplete, and there are depressions or protrusions. Therefore, the equidistant grid sampling method [<xref ref-type="bibr" rid="B29">29</xref>, <xref ref-type="bibr" rid="B30">30</xref>] is selected to sample the spatial information on the acetabulum. The intersection of the equidistant grid lines and the target contour is the sampling point. Then, the least squares method is used to fit the sphere. In this process, the erroneous points need to be eliminated as follows:<list list-type="simple">
<list-item>
<p>Step 1: The previously extracted femoral head and hip joint data are processed, and the results obtained by fitting the data points with the once-received spherical surface are substituted into <xref ref-type="disp-formula" rid="e1">Formula 1</xref>. The femoral head and acetabular data are input separately, and the fitting residual <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of each collected data point is calculated:</p>
</list-item>
</list>
<disp-formula id="e1">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">v</mml:mi>
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<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">x</mml:mi>
<mml:mi mathvariant="bold">i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold">x</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
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</mml:mfenced>
</mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">y</mml:mi>
<mml:mi mathvariant="bold">i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold">y</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">z</mml:mi>
<mml:mi mathvariant="bold">i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold">z</mml:mi>
<mml:mn mathvariant="bold">0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi mathvariant="bold">R</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msup>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>Step 2: The Bessel formula is used to calculate the standard deviation valuation:</p>
</list-item>
</list>
<disp-formula id="e2">
<mml:math id="m3">
<mml:mrow>
<mml:mi mathvariant="bold">&#x3c3;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msqrt>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mi mathvariant="bold">n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold">v</mml:mi>
<mml:mi mathvariant="bold">i</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="bold">n</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:msqrt>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>Step 3: The Laiyite criterion is used to eliminate erroneous points: when <inline-formula id="inf2">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>v</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of a sampling point is greater than three times <inline-formula id="inf3">
<mml:math id="m5">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e2">Formula 2</xref>), the sampling point is considered a gross erroneous point, which belongs to abnormal data and can be eliminated. The reason for using triple <inline-formula id="inf4">
<mml:math id="m6">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is that, according to the normal distribution of random variables, the measured value falls within <inline-formula id="inf5">
<mml:math id="m7">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> of the average value in many tests, and the probability of occurrence is 99.73%. The likelihood of occurrence outside this range is only 0.27%, indicating that only one out of nearly 400 experiments would be expected to fall outside this range. This represents a small probability event, which is almost impossible.</p>
</list-item>
<list-item>
<p>Step 4: The sampling point set is updated, the previously calculated culling points are deleted, steps 1 to 3 are repeated, and the process is stopped when the new spatial sampling point set does not contain gross error points.</p>
</list-item>
</list>
</p>
</sec>
<sec id="s2-2-2-2">
<title>2.2.2.2 DDH measurement</title>
<p>The coordinates and radius of the left and right spherical centers of the femoral head and acetabulum can be calculated using the above spherical fitting method to calculate the distance between the left and right spherical centers. After statistical analysis of all distance values, the optimal threshold was selected as the critical value of hip dislocation and compared with the diagnosis of doctors to evaluate the effectiveness of this method.</p>
</sec>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 3D segmentation of the ilium and femoral head</title>
<p>This experiment introduces three-fold cross-validation in the training set, and the initial learning rate is [1 &#xd7; 10]&#x5e;(-3). During training, the learning rate will automatically decline. Affected by GPU memory, the batch size is 2, and the number of training epochs is 200. The loss function curve is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>. The abscissa in the figure represents the number of iterations, and the ordinate represents the value of the loss, IoU (intersection and combination ratio), loss_val, and IoU_val. Loss and IoU are calculated in the network&#x2019;s training process, indicating the network&#x2019;s fitting degree on the training set. Loss_val and IoU_val are the evaluation indicators of the verification set after each round of network training, which shows the degree of network fitting in the test set. In <xref ref-type="fig" rid="F6">Figures 6A&#x2013;C</xref>, the second fold is the best, so it is selected for training again. <xref ref-type="fig" rid="F6">Figure 6D</xref> shows the final index change chart of the training network model.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Network model training indicators:<bold>(A)</bold> first-fold,<bold>(B)</bold> second-fold, <bold>(C)</bold> third-fold, and <bold>(D)</bold> final network model.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g006.tif"/>
</fig>
<p>The loss value of the training and verification sets gradually flattens after a rapid decline shown in <xref ref-type="fig" rid="F6">Figure 6D</xref> and finally converges to 0.0263. The change in the intersection ratio of the training set joins at 0.9626, which is opposite to the loss function. The results are shown in <xref ref-type="fig" rid="F7">Figure 7</xref>.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Segmentation results: <bold>(A)</bold> original, <bold>(B)</bold> label, <bold>(C)</bold> femoral head, and <bold>(D)</bold> iliac.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g007.tif"/>
</fig>
<p>In the experiment, the accuracy (ACC), dice coefficient, IoU, precision (PRE), and specificity (SPE) of nine independent test sets were calculated as evaluation parameters. <xref ref-type="table" rid="T2">Table 2</xref> provides the evaluation of the segmentation results of the ilium, and <xref ref-type="table" rid="T3">Table 3</xref> provides the evaluation of the segmentation results of the femoral head.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Evaluation of ilium segmentation results.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Number</th>
<th align="center">ACC</th>
<th align="center">Dice</th>
<th align="center">REC</th>
<th align="center">PRE</th>
<th align="center">IoU</th>
<th align="center">SPE</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">0.9977</td>
<td align="center">0.9209</td>
<td align="center">0.8856</td>
<td align="center">0.9592</td>
<td align="center">0.8534</td>
<td align="center">0.9994</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">0.9939</td>
<td align="center">0.7972</td>
<td align="center">0.8331</td>
<td align="center">0.7643</td>
<td align="center">0.6628</td>
<td align="center">0.9962</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">0.9972</td>
<td align="center">0.8941</td>
<td align="center">0.8629</td>
<td align="center">0.9276</td>
<td align="center">0.8084</td>
<td align="center">0.9991</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">0.9963</td>
<td align="center">0.8670</td>
<td align="center">0.9228</td>
<td align="center">0.8177</td>
<td align="center">0.7653</td>
<td align="center">0.9973</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">0.9950</td>
<td align="center">0.9120</td>
<td align="center">0.9084</td>
<td align="center">0.9156</td>
<td align="center">0.8382</td>
<td align="center">0.9975</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">0.9960</td>
<td align="center">0.9074</td>
<td align="center">0.9284</td>
<td align="center">0.8873</td>
<td align="center">0.8305</td>
<td align="center">0.9975</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">0.9967</td>
<td align="center">0.8908</td>
<td align="center">0.8760</td>
<td align="center">0.9061</td>
<td align="center">0.8031</td>
<td align="center">0.9986</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">0.9966</td>
<td align="center">0.9083</td>
<td align="center">0.9176</td>
<td align="center">0.8992</td>
<td align="center">0.8320</td>
<td align="center">0.9981</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">0.9959</td>
<td align="center">0.9114</td>
<td align="center">0.8933</td>
<td align="center">0.8724</td>
<td align="center">0.8438</td>
<td align="center">0.9974</td>
</tr>
<tr>
<td align="center">Average</td>
<td align="center">0.9962</td>
<td align="center">0.8899</td>
<td align="center">0.8920</td>
<td align="center">0.8833</td>
<td align="center">0.8042</td>
<td align="center">0.9979</td>
</tr>
<tr>
<td align="center">Standard deviation</td>
<td align="center">0.0011</td>
<td align="center">0.0360</td>
<td align="center">0.0295</td>
<td align="center">0.0559</td>
<td align="center">0.0559</td>
<td align="center">0.0009</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Evaluation of femoral head segmentation results.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Number</th>
<th align="center">ACC</th>
<th align="center">Dice</th>
<th align="center">REC</th>
<th align="center">PRE</th>
<th align="center">IoU</th>
<th align="center">SPE</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">0.9992</td>
<td align="center">0.9659</td>
<td align="center">0.9628</td>
<td align="center">0.9691</td>
<td align="center">0.9341</td>
<td align="center">0.9996</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">0.9965</td>
<td align="center">0.8189</td>
<td align="center">0.9259</td>
<td align="center">0.7341</td>
<td align="center">0.6933</td>
<td align="center">0.9971</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">0.9993</td>
<td align="center">0.9638</td>
<td align="center">0.9526</td>
<td align="center">0.9753</td>
<td align="center">0.9302</td>
<td align="center">0.9998</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">0.9989</td>
<td align="center">0.8993</td>
<td align="center">0.8701</td>
<td align="center">0.9305</td>
<td align="center">0.8170</td>
<td align="center">0.9996</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">0.9974</td>
<td align="center">0.9389</td>
<td align="center">0.9003</td>
<td align="center">0.9810</td>
<td align="center">0.8848</td>
<td align="center">0.9996</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">0.9983</td>
<td align="center">0.9437</td>
<td align="center">0.9268</td>
<td align="center">0.9612</td>
<td align="center">0.8933</td>
<td align="center">0.9994</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">0.9990</td>
<td align="center">0.9573</td>
<td align="center">0.9749</td>
<td align="center">0.9403</td>
<td align="center">0.9181</td>
<td align="center">0.9993</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">0.9986</td>
<td align="center">0.9435</td>
<td align="center">0.9547</td>
<td align="center">0.9325</td>
<td align="center">0.8930</td>
<td align="center">0.9991</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">0.9987</td>
<td align="center">0.9276</td>
<td align="center">0.9473</td>
<td align="center">0.9519</td>
<td align="center">0.9043</td>
<td align="center">0.9995</td>
</tr>
<tr>
<td align="center">Average value</td>
<td align="center">0.9984</td>
<td align="center">0.9288</td>
<td align="center">0.9350</td>
<td align="center">0.9307</td>
<td align="center">0.8742</td>
<td align="center">0.9992</td>
</tr>
<tr>
<td align="center">Standard deviation</td>
<td align="center">0.0009</td>
<td align="center">0.0433</td>
<td align="center">0.0312</td>
<td align="center">0.0716</td>
<td align="center">0.0718</td>
<td align="center">0.0008</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The result of multi-class hip joint segmentation using the 3D U-Net is good, and the average dice coefficient of the ilium reaches 88.99%. Although the ilium contour is over-segmented, it is due to the low definition of the edge. The average dice coefficient of the femoral head segmentation result reaches 92.88%, which indicates that this method is quite good.</p>
</sec>
<sec id="s3-2">
<title>3.2 DDH intelligent diagnosis</title>
<p>The edge extraction and data point extraction results are shown in <xref ref-type="fig" rid="F8">Figures 8</xref>&#x2013;<xref ref-type="fig" rid="F10">10</xref>. <xref ref-type="fig" rid="F8">Figure 8</xref> shows the edge extraction results of the femoral head and ilium, <xref ref-type="fig" rid="F9">Figure 9</xref> shows the femoral head point extraction results, and <xref ref-type="fig" rid="F10">Figure 10</xref> shows the acetabular point extraction results.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>The first line shows the extraction results of the femoral head edge, and the second line shows the extraction results of the iliac edge.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g008.tif"/>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Extraction results of femoral head data points.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Extraction results of acetabular data points.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g010.tif"/>
</fig>
<p>The results of spherical fitting are shown in <xref ref-type="fig" rid="F11">Figures 11</xref>, <xref ref-type="fig" rid="F12">12</xref>. They are the fitting results of the femoral head and acetabulum, respectively, (a) left side and (b) right side. The calculated spherical center results are shown in the table. <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref> are the spherical center and radius calculation results of the femoral head and acetabulum, respectively.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Fitting results of the spherical surface of the femoral head: <bold>(A)</bold> left and <bold>(B)</bold> right.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g011.tif"/>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Fitting results of the acetabular spherical surface: <bold>(A)</bold> left and <bold>(B)</bold> right.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g012.tif"/>
</fig>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Ball center and radius of the femoral head.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Number</th>
<th colspan="4" align="center">Coordinate-left</th>
<th colspan="4" align="center">Coordinate-right</th>
</tr>
<tr>
<th align="center">x</th>
<th align="center">y</th>
<th align="center">z</th>
<th align="center">Radius</th>
<th align="center">x</th>
<th align="center">y</th>
<th align="center">z</th>
<th align="center">Radius</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">108.152</td>
<td align="center">72.424</td>
<td align="center">36.769</td>
<td align="center">15.319</td>
<td align="center">106.462</td>
<td align="center">55.954</td>
<td align="center">34.602</td>
<td align="center">14.857</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">96.358</td>
<td align="center">63.031</td>
<td align="center">42.101</td>
<td align="center">15.116</td>
<td align="center">99.296</td>
<td align="center">71.342</td>
<td align="center">25.495</td>
<td align="center">15.779</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">120.487</td>
<td align="center">69.809</td>
<td align="center">27.101</td>
<td align="center">11.573</td>
<td align="center">100.355</td>
<td align="center">73.972</td>
<td align="center">36.452</td>
<td align="center">17.352</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">59.241</td>
<td align="center">74.834</td>
<td align="center">34.176</td>
<td align="center">13.386</td>
<td align="center">56.459</td>
<td align="center">71.121</td>
<td align="center">32.297</td>
<td align="center">12.561</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">118.000</td>
<td align="center">65.165</td>
<td align="center">35.227</td>
<td align="center">18.981</td>
<td align="center">127.188</td>
<td align="center">70.137</td>
<td align="center">35.010</td>
<td align="center">18.412</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">110.395</td>
<td align="center">67.832</td>
<td align="center">31.644</td>
<td align="center">15.834</td>
<td align="center">117.232</td>
<td align="center">63.201</td>
<td align="center">35.365</td>
<td align="center">17.111</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">88.691</td>
<td align="center">71.953</td>
<td align="center">35.228</td>
<td align="center">14.812</td>
<td align="center">92.999</td>
<td align="center">52.270</td>
<td align="center">35.016</td>
<td align="center">14.377</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">113.129</td>
<td align="center">69.039</td>
<td align="center">32.719</td>
<td align="center">14.869</td>
<td align="center">114.277</td>
<td align="center">62.960</td>
<td align="center">35.944</td>
<td align="center">15.607</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">101.807</td>
<td align="center">69.261</td>
<td align="center">34.371</td>
<td align="center">14.986</td>
<td align="center">101.783</td>
<td align="center">65.120</td>
<td align="center">33.772</td>
<td align="center">15.757</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Acetabular center and radius.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Number</th>
<th colspan="4" align="center">Coordinate-left</th>
<th colspan="4" align="center">Coordinate-right</th>
</tr>
<tr>
<th align="center">x</th>
<th align="center">y</th>
<th align="center">z</th>
<th align="center">Radius</th>
<th align="center">x</th>
<th align="center">y</th>
<th align="center">z</th>
<th align="center">Radius</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">107.800</td>
<td align="center">70.950</td>
<td align="center">35.709</td>
<td align="center">15.460</td>
<td align="center">105.692</td>
<td align="center">57.081</td>
<td align="center">32.603</td>
<td align="center">14.990</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">96.263</td>
<td align="center">66.743</td>
<td align="center">39.528</td>
<td align="center">17.677</td>
<td align="center">92.370</td>
<td align="center">69.838</td>
<td align="center">35.094</td>
<td align="center">19.683</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">113.127</td>
<td align="center">71.730</td>
<td align="center">35.319</td>
<td align="center">17.817</td>
<td align="center">110.168</td>
<td align="center">58.480</td>
<td align="center">30.964</td>
<td align="center">25.629</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">59.639</td>
<td align="center">55.956</td>
<td align="center">29.140</td>
<td align="center">24.366</td>
<td align="center">64.860</td>
<td align="center">58.831</td>
<td align="center">33.927</td>
<td align="center">23.465</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">118.239</td>
<td align="center">63.198</td>
<td align="center">34.495</td>
<td align="center">20.897</td>
<td align="center">126.756</td>
<td align="center">70.872</td>
<td align="center">33.831</td>
<td align="center">18.479</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">111.916</td>
<td align="center">67.122</td>
<td align="center">34.545</td>
<td align="center">17.032</td>
<td align="center">116.684</td>
<td align="center">64.836</td>
<td align="center">34.875</td>
<td align="center">18.255</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">87.774</td>
<td align="center">69.246</td>
<td align="center">35.424</td>
<td align="center">16.424</td>
<td align="center">92.995</td>
<td align="center">55.838</td>
<td align="center">35.339</td>
<td align="center">15.966</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">112.917</td>
<td align="center">70.158</td>
<td align="center">36.382</td>
<td align="center">15.961</td>
<td align="center">113.690</td>
<td align="center">64.766</td>
<td align="center">35.009</td>
<td align="center">15.718</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">100.959</td>
<td align="center">66.888</td>
<td align="center">35.068</td>
<td align="center">18.204</td>
<td align="center">102.902</td>
<td align="center">62.568</td>
<td align="center">33.955</td>
<td align="center">19.023</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F13">Figure 13</xref> shows the spherical center distance between the femoral head and the acetabulum&#x2019;s meniscus. The abscissa is the serial number of the hip joint. A case is sorted by dividing it into two hip joints. The ordinate is the distance between the spherical centers in millimeters. Blue represents the normal hip joint, and orange represents the hip dislocation. A hip joint less than 10&#xa0;mm is considered normal, while a hip joint greater than 10&#xa0;mm is considered hip dislocation. Compared to the doctor&#x2019;s diagnosis, only the No.8 hip joint differed from the doctor&#x2019;s assessment. Because the patient is younger, the shape of the femoral head is not fully grown, and there is a difference in the shape of the sphere. The accuracy rate is 94.4%.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Fitting ball center distance between the femoral head and acetabulum.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g013.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussion</title>
<p>We compared the 2D and 3D U-Net segmentation results. The 2D segmentation results are shown in <xref ref-type="fig" rid="F14">Figure 14</xref>. The average value of the dice coefficient reaches 87.9%. There is an over-segmentation phenomenon because of the low definition. In addition, 2D data do not have layer position information, and the structure is different, significantly impacting the training. The edge information on the femoral head and ilium cannot be well-extracted, which cannot meet the needs of subsequent experiments.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>2D U-Net segmentation results: <bold>(A)</bold> original, <bold>(B)</bold> label, and <bold>(C)</bold> hip joint.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g014.tif"/>
</fig>
<p>Unlike 2D U-Net, 3D U-Net has better results in segmentation and can better learn and train 3D information to obtain a better model. <xref ref-type="fig" rid="F15">Figure 15</xref> shows the result of the 3D segmentation of the hip joint. There is almost no difference compared to the marked image, and the accuracy is high. However, some images are not segmented accurately at the narrow gap between the ilium and femoral head, resulting in over-segmentation.</p>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>3D U-Net segmentation results: <bold>(A)</bold> original, <bold>(B)</bold> label, and <bold>(C)</bold> hip joint.</p>
</caption>
<graphic xlink:href="fphy-12-1358652-g015.tif"/>
</fig>
<p>Comparing the evaluation parameters of 2D and 3D segmentation in <xref ref-type="table" rid="T6">Table 6</xref>, the average dice coefficient of 3D U-Net reached 87.9%. However, the narrow gap between the femoral head and the ilium caused over-segmentation. Marking labels separately in the experiment solved the problem. <xref ref-type="table" rid="T2">Tables 2</xref> and <xref ref-type="table" rid="T3">3</xref> provide the evaluation results.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Evaluation results of 2D and 3D U-Net segmentation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th colspan="2" align="center">ACC</th>
<th colspan="2" align="center">Dice</th>
<th colspan="2" align="center">REC</th>
<th colspan="2" align="center">PRE</th>
<th colspan="2" align="center">IoU</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left"/>
<td align="center">2D</td>
<td align="center">3D</td>
<td align="center">2D</td>
<td align="center">3D</td>
<td align="center">2D</td>
<td align="center">3D</td>
<td align="center">2D</td>
<td align="center">3D</td>
<td align="center">2D</td>
<td align="center">3D</td>
</tr>
<tr>
<td align="center">Average value</td>
<td align="center">0.992</td>
<td align="center">0.995</td>
<td align="center">0.870</td>
<td align="center">0.879</td>
<td align="center">0.889</td>
<td align="center">0.8852</td>
<td align="center">0.876</td>
<td align="center">0.876</td>
<td align="center">0.783</td>
<td align="center">0.785</td>
</tr>
<tr>
<td align="center">Standard deviation</td>
<td align="center">0.006</td>
<td align="center">0.002</td>
<td align="center">0.109</td>
<td align="center">0.022</td>
<td align="center">0.175</td>
<td align="center">0.0525</td>
<td align="center">0.046</td>
<td align="center">0.036</td>
<td align="center">0.146</td>
<td align="center">0.036</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Regarding time efficiency, the 2D segmentation method took 2&#xa0;h to complete the network training process, and it took less than 20&#xa0;s to segment approximately 60<sup>&#x2212;&#x394;&#x394;CT</sup> slices. The 3D segmentation method took 10&#xa0;h to complete the training process of the network. It took less than 30&#xa0;s to segment approximately 300<sup>&#x2212;&#x394;&#x394;CT</sup> slices.</p>
<p>Due to the low incidence of hip dislocation in children, our study was based on only 46 cases. Despite the limited data, the research outcomes are promising. In subsequent studies, we aim to continue collecting more data to improve the robustness of our method.</p>
<p>
<xref ref-type="table" rid="T7">Table 7</xref> presents a comparison of our paper&#x2019;s results with those from other studies. When compared to the results of Xia et al., who utilized an active shape model-based algorithm for automated 3D bone reconstructions of the proximal femur, the femoral head segmentation in our paper is slightly inferior. However, our method performs better when only healthy individuals are considered. In contrast to Hareendranathan et al., who integrated clinical knowledge through intensity priors into a random Walker formulation, our method outperforms theirs in ilium segmentation. In comparison to the methods of Chu et al., which combine fast random forest regression-based landmark detection, multi-atlas-based segmentation, and articulated statistical shape model-based fitting, our study extends the scope to include both normal and dislocated hip joints. For normal individuals, our paper achieves a segmentation accuracy of 95%. Additionally, our method&#x2019;s execution time is significantly longer than theirs.</p>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Comparison with other methods.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Method</th>
<th align="center">Femoral head</th>
<th align="center">Ilium</th>
<th align="center">Time</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">[<xref ref-type="bibr" rid="B18">18</xref>]</td>
<td align="center">Bilateral, 0.95</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">[<xref ref-type="bibr" rid="B21">21</xref>]</td>
<td align="left"/>
<td align="center">Left, 0.84; right, 0.86</td>
<td align="center">4&#xa0;s/slice</td>
</tr>
<tr>
<td align="center">[<xref ref-type="bibr" rid="B22">22</xref>]</td>
<td align="center">Left, 0.973; right, 0.974</td>
<td align="center">Bilateral, 0.957</td>
<td align="center">7.9&#xa0;min/case</td>
</tr>
<tr>
<td align="center">Proposed</td>
<td align="center">Bilateral, 0.9288</td>
<td align="center">Bilateral, 0.89</td>
<td align="center">10&#xa0;s/case</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>This paper presents the quantitative and intelligent diagnosis of hip dislocation based on CT images. First, a 3D automatic segmentation method of the ilium and femoral head is proposed. Then, the boundary information is extracted from the segmentation results, and spherical fitting is performed. Finally, the distance between the two spherical centers is calculated and a quantitative intelligent diagnosis model is obtained.</p>
<p>In terms of treatment, for most infants under 6&#xa0;months with DDH, after diagnosis, good treatment outcomes can be achieved through external hip abduction devices such as Pavlik harnesses and Von Rosen splints. For children who fail to respond to Pavlik treatment, treatment options include closed reduction or open reduction. The experimental results show that the method proposed in this study has good performance on independent testing sets, which can provide quantitative analysis support for clinical decision-making.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The datasets presented in this article are not readily available because data usage must be restricted to researchers in the relevant field, and communication with the corresponding authors via email is required. Requests to access the datasets should be directed to Shinong Pan, <email>cjr.panshinong@vip.163.com</email>; Hang Sun, <email>sunhang84@126.com</email>.</p>
</sec>
<sec id="s7">
<title>Ethics statement</title>
<p>The studies involving humans were approved by the Ethics Committee of Shengjing Hospital of China Medical University. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.</p>
</sec>
<sec id="s8">
<title>Author contributions</title>
<p>HS: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, supervision, and writing&#x2013;review and editing. HL: conceptualization, investigation, supervision, validation, and writing&#x2013;original draft. YZ: data curation, investigation, methodology, software, validation, visualization, and writing&#x2013;original draft. SP: conceptualization, data curation, supervision, validation, and writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s9">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This study was supported in part by the Natural Science Foundation of Liaoning Provincial Department of Science, Technology&#x2014;Doctoral Initiation Fund (No. 2022-BS-074) and Shenyang Ligong University High-Level Talent Scientific Research Support Fund Initiative (No. 1010147001251), the Special Fund for Basic Scientific Research Operations of Undergraduate Colleges and Universities in Liaoning Province (No. 1030055000854) and the Basic Scientific Research Project, Department of Education of Liaoning province (No. LJKMZ20221163).</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s12">
<title>Abbreviations</title>
<p>DDH, developmental dislocation of the hip joint; CT, computed tomography; MRI, magnetic resonance image; ACC, accuracy; IoU, intersection and combination ratio; PRE, precision; SPE, specificity.</p>
</sec>
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