GB2623864A - Method for bionic design of interbody fusion cage based on lumbar statistical shape model - Google Patents

Method for bionic design of interbody fusion cage based on lumbar statistical shape model Download PDF

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GB2623864A
GB2623864A GB2312651.9A GB202312651A GB2623864A GB 2623864 A GB2623864 A GB 2623864A GB 202312651 A GB202312651 A GB 202312651A GB 2623864 A GB2623864 A GB 2623864A
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lumbar
shape model
shape
model
statistical
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Qian Zhihui
Li Guanghui
Ren Lei
Jiang Zhende
Wang Kunyang
Song Guangsheng
Li Hongyun
Wu Jianan
Xie Jianxun
Xie Xia
Ren Luquan
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Jilin University
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Abstract

A method for bionic design of an interbody fusion cage based on a lumbar statistical shape model includes medical computer tomography (CT) data segmentation and preprocessing, automated construction of a lumbar statistical shape model database, classification analysis of the statistical shape model database to form shape model sub-databases in order to obtain an average shape model for each sub-databse, and bionic design of an interbody fusion cage. According to the method, the lumbar statistical shape model database can be automatically generated, and a large number of 3D lumbar shape models can be automatically and quickly generated. An interbody fusion cage that can meet the requirements of a larger group range and better conforms to a shape of an individual lumbar vertebra is obtained by extracting lumbar shape features and performing the classification analysis and the bionic design.

Description

METHOD FOR BIONIC DESIGN OF INTERBODY FUSION CAGE BASED ON
LUMBAR STATISTICAL SHAPE MODEL
TECHNICAL FIELD
[0001] The present disclosure relates to the field of bionic implant device design, and in particular, to a method for bionic design of an interbody fusion cage based on a lumbar statistical shape model.
BACKGROUND
[0002] Low back pain is a common lumbar disease, which is generally caused by lumbar degeneration and changes in lumbar anatomical structure and mechanical characteristics caused by specific occupational habits.
[0003] Interbody fusion is currently the most common and effective way to treat low back pain. An interbody fusion cage is used in the interbody fusion to perfomi vertebral fusion to maintain lumbar stability and relieve pain of patients with low back pain, and provides an important function in supporting bone growth and maintaining a normal physiological height of a lumbar vertebra [0004] Literature research shows that current development of the interbody fusion cage focuses on reducing the subsidence of the interbody fusion cage after implantation by adjusting a porosity and a material of the interbody fusion cage, so as to achieve a better fusion effect [0005] Clinically, an interbody fusion cage with a suitable dimension is usually selected from a limited number of commercially available interbody fusion cages by an experienced orthopedic surgeon according to a patient's medical images.
[0006] Due to great individual differences, interbody fusion cages clinically widely used at present cannot well match upper and lower vertebral endplates and vertebrae of patients in shape, which leads to uneven stress on the upper and lower endplates of the patients' lumbar vertebrae, thereby affecting the fusion effect and easily leading to problems such as subsidence after the fusion [0007] In recent years, some researchers have customized interbody fusion cages based on specific patients by combining a three-dimensional (3D) printing technology, so as to meet requirements that an interbody fusion cage fits with upper and lower vertebral endplates of a specific patient in shape. However, the steps of customizing an interbody fusion cage in this method are complicated and labor and time costs are high, so that it is difficult to apply the method in a large scale [0008] The statistical shape model is an effective method for describing shape changes of an object. The statistical shape model is established based on the principle that shape changes of an object satisfy Gaussian distribution when there are large samples of the object, and a changing law of the object shape may be described by combining an average shape model with a changing mode.
[0009] The statistical shape model enables a large number of object shape models to be effectively and quickly formed, and facilitates extraction of characteristics of object shape changes, thereby providing a new design idea for designing an interbody fusion cage that meets requirements of large-scale groups and conforms to the shape of an individual lumbar vertebra
SUMMARY
100101 Against the technical problem that it is difficult to use a current interbody cage design to meet requirements of a larger group and conform to a shape of an individual lumbar vertebra, the present disclosure provides a method for bionic design of an interbody fusion cage based on a lumbar statistical shape model.
100111 According to the method, a lumbar statistical shape model database can be effectively and automatically constructed, and bionic design of an interbody fusion cage can be performed based on the lumbar statistical shape model database, so as to design a bionic interbody fusion cage that meets requirements of a larger group and better conforms to a shape of an individual lumbar vertebra.
100121 The specific technical solutions of the present disclosure are as follow: 10013] As shown in FIG. 1, a method for bionic design of an interbody fusion cage based on a lumbar statistical shape model includes the following steps: 100141 1) data preprocessing: segmenting N human lumbar vertebrae from medical computer tomography (CT) data, reconstructing a 3D lumbar shape model, outputting a standard template library (STL) file, and simplifying and optimizing a grid of the 3D lumbar shape model as a lumbar training set; [0015] 2) automatically building a lumbar statistical shape model database by applying a relevant algorithm and writing program, specifically including the following substeps: [0016] 2.01) randomly selecting one 3D lumbar shape model from the training set as a template model, and aligning the remaining 3D lumbar shape models with the template model by means of an iterative closest point algorithm; 100171 2.02) causing two point sets to coincide to a largest extent by rotation, translation and other transformation in the algorithm, so as to reduce shape errors caused by the rotation and the translation; f [0018] 2.03) assuming that a to-be-aligned point set s and a template point set is calculating whether a result of an objective function reaches a threshold as an index for determining whether to stop iteration, where M and X are point sets, and are points in the point sets, T is a translation matrix, R is a rotation matrix, and 1\ta1 is a number of points in the to-be-aligned point set; 100191 2.04) in order to unify 3D lumbar shape models with different numbers of points into 3D lumbar shape models with the same number of points and establish a corresponding relationship between points, registering the template model to the aligned 3D lumbar shape model by means of a non-rigid iterative closest point algorithm; [0020] 2.05) adding affine transformation to rigid transformation in the algorithm, so that the template model is deformed onto the to-be-registered 3D lumbar shape model to complete the registration process, establishing a corresponding relationship between the template model and points of the to-be-registered 3D lumbar shape model, and establishing a new lumbar training set; [0021] 2.06) analyzing a principal component of the registered lumbar training set; 100221 2.07) calculating an average shape model of the lumbar training set: , where n represents the number of 3D shape models in the lumbar training set, and X represents the 3D lumbar shape models; [0023], 2.08) calculating a covariance matrix of the lumbar training set: [0024] 2.09) obtaining an eigenvector and eigenvalue Sy, =1,(p, of the covariance matrix, where Ai represents the eigenvalue, (pi represents the eigenvector, the eigenvector represents a main pattern of a shape change, the eigenvalue represents a variance of the principal component, and a larger eigenvalue represents a greater amount of data retained in a direction corresponding to the eigenvector;
X
[0025] 2.10) expressing the lumbar statistical shape model database as where t represents sorting the eigenvalues in descending order, and for first t eigenyalues, a shape parameter b, is independent, obeys Gaussian distribution of (0, X.,), is used to control a change range of the shape, and is generally; and [0026] 2.11) executing a compiled automated program to automatically generate the lumbar statistical shape model database, 100271 3) performing classification analysis on the lumbar statistical shape model database to form lumbar statistical shape model sub-databases, and obtaining an average shape model for each of the sub-databases: 100281 3.01) obtaining a median sagittal plane of each shape model in the lumbar statistical shape model database by means of a mirror image method; [0029] 3.02) mirroring the 3D lumbar shape model in any sagittal plane in the mirror image method to obtain a new model, aligning the new model with the original model by means of the iterative closest point algorithm, and obtaining a symmetry plane with the aligned two models as a whole, that is, a median sagittal plane; [0030] 3.03) extracting required lumbar anatomical features, specifically, measuring an intervertebral disc height and a segmental lordosis angle on the sagittal plane of each 3D lumbar shape model in the lumbar statistical shape model database; [0031] 3.04) performing classification analysis on the lumbar statistical shape model database based on the intervertebral disc height and the segmental lordosis angle, and classifying 3D lumbar shape models with different intervertebral disc heights and different segmental lordosis angles; and [0032] 3.05) after the classification, forming a plurality of sub-databases, and obtaining an r----average shape model for each of the sub-databases, that is, , as a 3D lumbar shape model for bionic design, where j is a number of 3D lumbar shape models in each sub-database, and Xi represents the 3D lumbar shape models in the sub-databases; and [0033] 4) performing bionic design of an interbody fusion cage according to the average shape model for each of the sub-databases: 100341 4.01) extracting a design surface required for design, and extracting an upper endplate surface and a lower endplate surface of two adjacent vertebrae of the average shape model for each of the sub-databases; and [0035] 4.02) performing bionic design according to the extracted design surface to form a series of interbody fusion cages with bionic shapes.
[0036] The method according to the present disclosure mainly includes four processes: medical CT data segmentation and preprocessing, automated construction of a lumbar statistical shape model database, classification analysis of the statistical shape model database, and bionic design of an interbody fusion cage.
[0037] According to the present disclosure, collected medical CT images are first preprocessed, and the lumbar statistical shape model database is automatically established by means of alignment, registration, principal component analysis and other processes [0038] Classification analysis is performed on the established lumbar statistical shape model database to form a plurality of sub-databases, and an average shape model is obtained for each of the sub-databases.
100391 The bionic design of an interbody fusion cage is performed according to the obtained lumbar average shape model for each of the sub-databases.
[0040] The present disclosure has following beneficial effects: [0041] 1. The lumbar statistical shape model database is automatically established, and a large number of 3D lumbar shape models can be automatically and quickly generated, which facilitates extraction of lumbar shape features, and effectively reduces time and labor costs. 100421 2. Based on the lumbar statistical shape model, by classification analysis and bionic design, an interbody fusion cage that can meet requirements of a larger group range and better conforms to a shape of an individual lumbar vertebra is designed, which significantly improves fit between the fusion cage and a patient's vertebra, and further helps to reduce the risk of loosening and subsidence.
BRIEF DESCRIPTION OF THE DRAWINGS
[0043] FIG. t is a flowchart of the present disclosure; [0044] FIG. 2 is an effect diagram after alignment of two L4-L5 lumbar vertebrae by means of an iterative closest point algorithm and registration thereof by means of a non-rigid iterative closest point algorithm; [0045] FIG. 3 is an effect diagram of changes under a first principal component of L4-L5 lumbar vertebrae; [0046] FIG. 4 is a schematic diagram of measuring an intervertebral disc height and a segmental lordosis angle on a median sagittal plane of an L4-L5 3D lumbar shape model, and [0047] FIG. 5 is a schematic diagram of designing an anterior interbody fusion cage with a bionic shape based on a sub-database.
DETAILED DESCRIPTION OF THE EMBODIMENTS
[0048] The following further describes specific implementations of the present disclosure in detail with reference to accompanying drawings [0049] In a specific implementation, taking L4-L5 vertebrae as an example, a statistical shape model thereof is established, and an anterior interbody fusion cage is designed based on the statistical shape model [0050] Medical CT images of 30 volunteers' lumbar vertebrae were segmented, an L4-L5 3D lumbar shape model was reconstructed, and an STL format file was outputted.
[0051] The L4-L5 3D lumbar shape model was further processed, and grids were simplified and optimized to keep a number of vertices between 4000 and 5000, so as to improve efficiency of a subsequent algorithm.
100521 Through preprocessing, a training set containing 30 3D shape model samples of L4-L5 lumbar vertebrae was obtained.
[0053] The 3D shape model samples of L4-L5 lumbar vertebrae in the training set might be expressed as follows: [0054] X = (xii, vii, zii, xin, yin, zit), where xin, yin and zin represent coordinates of points of the samples.
100551 The L4-L5 lumbar training set might be expressed as follows: X = (Xi, X2, ..., X:40). 100561 One L4-L5 3D lumbar shape model Xi was randomly selected from the L4-L5 3D lumbar shape model training set as a template model, and the remaining L4-L5 3D lumbar shape models were aligned with the template model by means of an iterative closest point algorithm. [0057] This process was to minimize position errors caused by different people and different photographing environments.
[0058] The training set of the aligned L4-L5 3D lumbar shape models was updated to: X = [0059] After the alignment, the template model Xi was registered to the training set of the aligned L4-L5 3D lumbar shape models by means of a non-rigid iterative closest point algorithm. [0060] In this process, by registration by means of the non-rigid iterative closest point algorithm, the training set of the L4-L5 3D lumbar shape models with the same number of points and corresponding points was obtained.
[0061] After the registration, the training set of the L4-L5 3D lumbar shape models was updated to: X = (Xi, X2, ..., X30).
[0062] FIG. 2 is an effect diagram showing alignment and registration of one L4-L5 3D lumbar shape model and a template model.
[0063] A principal component of the training set of the L4-L5 3D lumbar shape models is analyzed: [0064] An average shape model of the training set of the L4-L5 3D lumbar shape models is calculated as follows.
100651 A covariance matrix of the training set of the L4-L5 3D lumbar shape models is calculated as follows: [0066] [0067] An eigenvalue and an eigenvector of the covariance matrix are calculated as follows: Scpi = ki(pi, where X represents the eigenvalue of the covariance matrix, eigenvalues are sequentially arranged from large to small, and (pi represents the eigenvector.
[00681 [0069] where m is a number of change patterns, k represents first k change patterns, and P represents a probability of the first k change patterns in the total change patterns, with a value of P 95%.
100701 In this example, when k = 8, the probability was 96.7%, which was greater than 95%, so it was set that k = 8.
100711 An L4-L5 lumbar statistical shape model database might be expressed as follows: = [0072] A program for automatically establishing a lumbar statistical shape database is run to automatically generate an L4-L5 lumbar statistical shape model database.
[0073] FIG. 3 is an effect diagram of changes under a first principal component of L4-L5 lumbar vertebrae.
[0074] Classification analysis is performed on the obtained L4-L5 lumbar statistical shape model database.
[0075] This process involves measurement of an intervertebral disc height and a segmental lordosis angle on a median sagittal plane of each L4-L5 3D lumbar shape model.
[0076] A median sagittal plane of the L4-L5 3D lumbar shape model is obtained by means of a mirror image method.
100771 The L4-L5 3D lumbar shape model needs to be mirrored in any sagittal plane in the mirror image method to obtain a new model, the new model is aligned with the original model by means of the iterative closest point algorithm, and a symmetry plane with the aligned two models as a whole, that is, a median sagittal plane is obtained.
100781 Required L4-L5 lumbar anatomical features are extracted, specifically, an intervertebral disc height and a segmental lordosis angle are measured on the median sagittal plane of each L4-L5 3D lumbar shape model, and classification analysis is performed on the measured L4-L5 lumbar statistical shape model database based on the intervertebral disc height and the segmental lordosis angle, to obtain different sub-databases.
[0079] The different sub-databases differ in different intervertebral disc heights and segmental lordosis angles, and an average shape model is obtained for each sub-database.
[0080] FIG. 4 is a schematic diagram of measuring an intervertebral disc height and a segmental lordosis angle on a median sagittal plane of an L4-L5 3D lumbar shape model [0081] The bionic design of an interbody fusion cage is performed according to the obtained average shape model for the sub-database, and a lower endplate surface of an L4 vertebra and an upper endplate surface of an LS vertebra are extracted as design surfaces of the interbody fusion cage 100821 Based on the design surfaces, the bionic design of the interbody fusion cage is performed, and an anterior interbody fusion cage that can meet requirements of a larger group range and better conforms to a shape of an individual lumbar vertebra is designed.
[0083] FIG. 5 shows an anterior interbody fusion cage with a bionic shape designed based on an average shape model of a sub-database.
[0084] In conclusion, according to the present disclosure, the lumbar statistical shape model can be automatically established, the bionic design of the interbody fusion cage is performed based on the lumbar statistical shape model through classification analysis, and specific examples illustrate the principle and effects of the present disclosure.

Claims (4)

  1. WHAT IS CLAIMED IS: I. A method for bionic design of an interbody fusion cage based on a lumbar statistical shape model, comprising the following steps: 1) data preprocessing: segmenting N human lumbar vertebrae from medical computer tomography (CT) data, reconstructing a three-dimensional (3D) lumbar shape model, outputting a standard template library (STL) file, and simplifying and optimizing a grid of the 3D lumbar shape model as a lumbar training set; 2) automatically building a lumbar statistical shape model database by applying a relevant algorithm and writing program; 3) performing classification analysis on the lumbar statistical shape model database to form lumbar statistical shape model sub-databases, and obtaining an average shape model for each of the sub-databases; and 4) performing bionic design of an interbody fusion cage according to the average shape model for each of the sub-databases.2. The method for bionic design of an interbody fusion cage based on a lumbar statistical shape model according to claim 1, wherein the automatically building a lumbar statistical shape model database in step 2) comprises the following substeps: 2.01) randomly selecting one 3D lumbar shape model from the training set as a template model, and aligning the remaining 3D lumbar shape models with the template model by means of an iterative closest point algorithm; 2.02) causing two point sets to coincide to a largest extent by rotation, translation and other transformation in the algorithm, so as to reduce shape errors caused by the rotation and the translation; 2.04 assuming that a to-be-aligned point set is and a template point set is calculating whether a result of an objective function reaches a threshold as an index for determining whether to stop iteration, wherein M and X are point sets, and xj are points in the point sets, T is a translation matrix, R is a rotation matrix, and N. is a number of points in the template point set; 2.04) in order to unify 3D lumbar shape models with different numbers of points into 3D lumbar shape models with the same number of points and establish a corresponding relationship between points, registering the template model to the aligned 3D lumbar shape model by means of a non-rigid iterative closest point algorithm, 2 05) adding affine transformation to rigid transformation in the algorithm, so that the template model is deformed onto the to-be-registered 3D lumbar shape model to complete the registration process, establishing a corresponding relationship between the template model and points of the to-be-registered 3D lumbar shape model, and establishing a new lumbar training set; 2.06) analyzing a principal component of the registered lumbar training set; 2.07) calculating an average shape model of the lumbar training set: , wherein n represents the number of 3D shape models in the lumbar training set, and X represents the 3D lumbar shape models; 2.08) calculating a covariance matrix of the lumbar training set.
  2. 2.09) obtaining an eigenvector and eigenvalue ST; = kipi of the covariance matrix, wherein Xi represents the eigenvalue, (pi represents the eigenvector, the eigenvector represents a main pattern of a shape change, the eigenvalue represents a variance of the principal component, and a larger eigenvalue represents a greater amount of data retained in a direction corresponding to the eigenvector; 2.10) expressing the lumbar statistical shape model database as wherein t represents sorting the eigenvalues in descending order, and for first t eigenvalues, a shape parameter bi is independent, obeys Gaussian distribution of (0, Ai), is used to control a change range of the shape, and is generally and 2.11) executing a compiled automated program to automatically generate the lumbar statistical shape model database.
  3. 3. The method for bionic design of an interbody fusion cage based on a lumbar statistical shape model according to claim 1, wherein the performing classification analysis on the lumbar statistical shape model database to form lumbar statistical shape model sub-databases, and obtaining an average shape model for each of the sub-databases in step 3) comprises the following sub step s: 3.01) obtaining a median sagittal plane of each shape model in the lumbar statistical shape model database by means of a mirror image method; 3.02) mirroring the 3D lumbar shape model in any sagittal plane in the mirror image method to obtain a new model, aligning the new model with the original model by means of the iterative closest point algorithm, and obtaining a symmetry plane with the aligned two models as a whole, that is, a median sagittal plane; 3.03) extracting required lumbar anatomical features, specifically, measuring an 10 intervertebral disc height and a segmental lordosis angle on the sagittal plane of each 3D lumbar shape model in the lumbar statistical shape model database; 3.04) performing classification analysis on the lumbar statistical shape model database based on the intervertebral disc height and the segmental lordosis angle, and classifying 3D lumbar shape models with different intervertebral disc heights and different segmental lordosis angles; and 3.05) after the classification analysis, forming a plurality of sub-databases, and obtaining an average shape model for each of the sub-databases, that is, , as a 3D lumbar shape model for bionic design, wherein j is a number of 3D lumbar shape models in each sub-database, and X, represents the 3D lumbar shape models in the sub-databases
  4. 4. The method for bionic design of an interbody fusion cage based on a lumbar statistical shape model according to claim 1, wherein the performing bionic design of an interbody fusion cage according to the average shape model for each of the sub-databases in step 4) comprises the following steps: 4.01) extracting a design surface required for design, and extracting an upper endplate surface and a lower endplate surface of two adjacent vertebrae of the average shape model for each of the sub-databases; and 4.02) performing bionic design according to the extracted design surface to form a series of interbody fusion cages with bionic shapes.
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