Gray matter imaging-based stratification coupled brain structure analysis method and system

Abstract

The application discloses a brain structure analysis method and system based on gray matter and white matter imageomics hierarchical coupling, and the method comprises the following steps: acquiring and preprocessing original three-dimensional T1 weighted structure magnetic resonance images, generating gray matter volume smoothing images and white matter volume smoothing images; extracting brain region level imageomics original features from the gray matter volume smoothing images and the white matter volume smoothing images respectively, obtaining a gray matter brain region level original feature set and a white matter brain region level original feature set; based on repeated scanning data, performing stability evaluation screening, same brain region cross-gray matter and white matter tissue candidate screening and redundancy removal processing on the gray matter brain region level original features and the white matter brain region level original features, and generating a brain region level reserved feature list; in each brain region, performing feature layering on the brain region level reserved feature list, and generating a first-order statistical feature layer and a texture feature layer; and constructing a gray matter and white matter coupling index based on the first-order statistical feature layer and the texture feature layer, so as to form a brain region level gray matter and white matter hierarchical coupling matrix.

Description

Technical Field

[0001] This invention relates to the field of medical image analysis and brain structural magnetic resonance image processing technology, and in particular to a brain structural analysis method and system based on gray and white matter radiomics hierarchical coupling. Background Technology

[0002] Structural magnetic resonance imaging (MRI) of the brain is an important tool for assessing the structural state of brain tissue and has been widely used in research on brain development, brain aging, neurodegenerative diseases, and mental disorders. Gray matter and white matter are two important tissue components in structural MRI images of the brain, and they differ in spatial distribution, tissue composition, and patterns of structural change. Analyzing brain structures based solely on a single tissue type, such as gray matter or white matter, is insufficient to comprehensively reflect the synergistic changes or structural imbalances among different tissue components within the same brain region.

[0003] Currently, brain structural magnetic resonance imaging analysis often employs methods such as voxel morphology analysis, brain region volume analysis, cortical thickness analysis, and regional average signal statistics to quantitatively characterize brain tissue structure. While these methods have significant application value in brain structure research, their characterization methods are mostly concentrated on low-dimensional indicators such as volume, thickness, and mean, making it difficult to fully reflect the more complex gray-level distribution, spatial heterogeneity, and fine-grained texture changes within brain tissue.

[0004] In recent years, radiomics methods have been introduced into the analysis of structural magnetic resonance imaging (MRI) images of the brain. These methods can extract first-order statistical features and multiple texture features from structural MRI images or their derived tissue images, thereby providing a more granular characterization of the gray-scale distribution and spatial arrangement patterns of brain tissue. Some existing brain structural radiomics methods typically focus on characterizing features of a single tissue type or a single brain region, or input gray matter and white matter features as parallel variables into the model; others construct similarity networks between brain regions based on brain region radiomics features. While these methods can describe brain structural features from different perspectives, they still lack direct, stable, and interpretable quantitative characterization of the pairing relationships and hierarchical differences between gray matter and white matter within the same brain region.

[0005] Furthermore, radiomics features are numerous, and there may be significant redundancy between different features. Some features also lack stability under repeated scanning conditions. If constraints are not placed on the stability of features under repeated scanning, their pairability across gray and white matter tissues, and their redundancy, the reliability of subsequent brain region-level indicators can be easily affected.

[0006] Therefore, it is necessary to propose a new brain structure analysis method that can characterize the structural features of gray matter and white matter separately at a unified brain region scale, and further perform stable quantitative analysis of the relationship between gray matter and white matter within the same brain region. Summary of the Invention

[0007] The purpose of this invention is to provide a brain structure analysis method and system based on gray and white matter imaging hierarchical coupling, in order to solve the problems in existing brain structure analysis where gray and white matter are often treated independently, making it difficult to quantitatively characterize the gray and white matter coupling relationship at a unified brain region scale, and lacking stability constraints.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] The first aspect is a brain structure analysis method based on the hierarchical coupling of gray and white matter radiomics, which includes the following steps:

[0010] S1. Acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image;

[0011] S2. Extract brain region-level radiomics raw features from the gray matter volume smoothing image and the white matter volume smoothing image respectively to obtain the gray matter brain region-level raw feature set and the white matter brain region-level raw feature set.

[0012] S3. Based on repeated scan data, perform stability evaluation and screening of gray matter brain region-level original features and white matter brain region-level original features, candidate screening across gray and white matter tissues in the same brain region, and redundancy removal to generate a list of brain region-level retained features.

[0013] S4. Within each brain region, the brain region-level retained feature list is hierarchically segmented to generate a first-order statistical feature layer and a texture feature layer; based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed to form a brain region-level gray-white matter hierarchical coupling matrix.

[0014] S5. Conduct cognitive assessment and effect verification of the brain region-level gray and white matter hierarchical coupling matrix.

[0015] Preferably, S1 includes:

[0016] S11. Obtain the original three-dimensional T1-weighted structural magnetic resonance images of each subject, and perform preprocessing based on the automated structural image processing workflow to obtain gray matter tissue images, white matter tissue images, nonlinear deformation fields from the subject to the standard space, and corresponding Jacobian determinant images; preprocessing includes brain tissue extraction, gray and white matter tissue segmentation, and nonlinear registration from the subject space to the standard space.

[0017] S12. Based on the Jacobian determinant image, volume modulation is performed on the gray matter and white matter images respectively to preserve the individual local volume change information of the subject's brain tissue; spatial smoothing is performed on the volume-modulated images to obtain gray matter volume smoothing images and white matter volume smoothing images aligned with the standard space.

[0018] Preferably, S2 includes:

[0019] S21. Read the standard brain region atlas and radiomics parameter configuration file, and instantiate the radiomics feature extractor based on the parameter configuration file;

[0020] S22. Using smoothed gray matter volume images and smoothed white matter volume images as input images, and standard brain region maps as label mask images; by specifying the current brain region label value, the brain region range corresponding to the current label is used as the feature calculation region, and the radiomics feature extractor is used to obtain the original gray matter radiomics features and the original white matter radiomics features of the subject in the current brain region respectively; brain region-level feature extraction is performed one by one according to the brain region label number, and after the feature extraction of all brain regions is completed, the original gray matter brain region-level feature set and the original white matter brain region-level feature set are obtained respectively.

[0021] Preferably, S3 includes:

[0022] S31. Based on repeated scan data of the same subject, stability evaluation indicators are calculated for each brain region, each tissue type and each radiomics feature to form a stability evaluation result across the whole brain. Based on the stability evaluation results, the original features at the gray matter brain region level and the original features at the white matter brain region level are screened to obtain the gray matter stable feature set and the white matter stable feature set, respectively.

[0023] S32. Perform same-name matching on the stable feature sets of gray matter and white matter, taking brain regions as units, retain common stable features that exist in both gray matter and white matter, and generate a set of candidate features that can be paired across gray and white matter tissues in the same brain region; generate a list of candidate features at the brain region level based on the candidate feature set.

[0024] S33. Redundancy is removed from the list of candidate features at the brain region level to generate a list of retained features at the brain region level.

[0025] Preferably, S31 includes:

[0026] Based on the subject information table, a repeated scan pairing relationship is constructed to generate a test-retest paired sample;

[0027] For the original feature sets at the gray matter and white matter brain regions, only radiomics features are retained to construct a feature set that is determined to participate in stability evaluation; radiomics features include shape features, first-order statistical features, and multiple texture features.

[0028] For the feature set involved in stability evaluation, repeated scans were performed to evaluate stability for each brain region, each tissue type, and each radiomics feature. The stability evaluation results were first cleaned for effectiveness, and shape features were removed. Then, feature removal was performed according to a preset stability threshold.

[0029] As a preferred method, the intragroup correlation coefficient (ICC) is used as the stability evaluation index.

[0030] Preferably, S32 includes:

[0031] Shape features are removed from the candidate feature set, and only first-order statistical features and texture features are retained. For each candidate feature, its stability evaluation index in gray matter and stability evaluation index in white matter are recorded respectively, and the average of the two is calculated as the comprehensive stability characterization value, thereby generating a list of brain region-level candidate features.

[0032] Preferably, S33 includes:

[0033] Using brain regions as units, the values ​​of all candidate features in each brain region are read in each subject to construct an eigenvalue matrix; Spearman correlation coefficients between candidate features are calculated based on the eigenvalue matrix; feature distances between candidate features are calculated based on the Spearman correlation coefficients to construct a feature distance matrix for the current brain region; hierarchical clustering analysis is performed on the feature distance matrix, and clusters are divided based on preset distance thresholds, and highly redundant feature clusters are identified by combining hierarchical clustering methods; for all candidate features divided into the same cluster, only the feature with the highest comprehensive stability characterization value is retained to obtain a brain region-level retained feature list.

[0034] Preferably, S4 includes:

[0035] S41. Taking brain regions as units, features whose feature names contain the firstorder identifier are assigned to the candidate feature set of the first-order statistical feature layer, and the remaining texture features are assigned to the candidate feature set of the texture feature layer.

[0036] Under the constraint of the brain region feature list, the hierarchical features of gray matter and white matter in the current brain region are extracted to form gray matter feature vectors and white matter feature vectors of the first-order statistical feature layer and gray matter feature vectors and white matter feature vectors of the texture feature layer.

[0037] S42. In each brain region and each feature layer, local standardization is performed on the gray matter feature vector and the white matter feature vector respectively. Then, the Euclidean distance between the gray matter feature vector and the white matter feature vector is calculated and defined as the gray-white matter coupling distance index under the current feature layer of the current brain region. The gray-white matter coupling distance index of the first-order statistical feature layer and the gray-white matter coupling distance index of the texture feature layer are obtained respectively.

[0038] Secondly, a brain structure analysis system based on the hierarchical coupling of gray and white matter radiomics includes:

[0039] The data acquisition and preprocessing module is used to acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image.

[0040] The radiomics feature extraction module is used to extract brain region-level radiomics raw features from gray matter volume smoothing images and white matter volume smoothing images, respectively, to obtain gray matter brain region-level raw feature sets and white matter brain region-level raw feature sets.

[0041] The feature selection module is used to perform stability evaluation and screening of gray matter and white matter brain region-level original features based on repeated scan data, candidate screening across gray and white matter tissues in the same brain region, and redundancy removal to generate a list of brain region-level retained features.

[0042] The feature layering coupling module is used to perform feature layering on the brain region-level reserved feature list within each brain region, generating a first-order statistical feature layer and a texture feature layer; based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed, thereby forming a brain region-level gray-white matter layering coupling matrix.

[0043] The assessment and validation module is used to perform cognitive assessment and effect validation of the brain region-level gray and white matter hierarchical coupling matrix.

[0044] The brain structure analysis system based on gray and white matter radiomics hierarchical coupling is used to implement the brain structure analysis method and steps based on gray and white matter radiomics hierarchical coupling as described in the first aspect.

[0045] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0046] 1. Unlike traditional techniques that only analyze a single tissue (gray or white matter) or simply concatenate gray and white matter features as ordinary high-dimensional variables into the model, this invention employs a combined approach: "gray and white matter brain region-level feature extraction under unified brain region constraints, repeated scan stability evaluation, same-name pairing screening across gray and white matter tissues within the same brain region, and redundancy removal within the brain region." This constructs a stable, pairable, and low-redundancy set of common gray and white matter radiomics features. Through this combined processing, features entering subsequent coupling calculations not only possess repeated scan stability in both gray and white matter but also share the same feature names within the same brain region and exhibit cross-gray and white matter tissue comparability, while reducing the repetitive expression of highly correlated features. This avoids the problem of information fragmentation between gray and white matter in traditional single-modal analysis and the redundancy and instability issues caused by simply concatenating high-dimensional features, resulting in higher reliability, repeatability, and cross-gray and white matter tissue interpretability of the subsequently constructed gray and white matter coupling index.

[0047] 2. Unlike traditional techniques that characterize brain structure based solely on single organizational features, regional average indicators, or unlayered comprehensive features, this invention employs a combined approach: a list of brain region-level gray and white matter tissue features, layering of first-order statistical and textural features, local standardization, and calculation of gray-white matter coupling distance. This results in a subject-level gray-white matter layered coupling matrix. Through this combined processing, this invention can quantify the structural differences between gray and white matter within the same brain region at both the grayscale distribution and spatial texture heterogeneity levels. The resulting indicators are no longer isolated representations of gray or white matter, but rather paired and coupled representations of gray and white matter with clear brain region and feature layer meanings. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0050] Figure 2 This is a flowchart of the original image preprocessing process in Embodiment 1 of the present invention;

[0051] Figure 3 This is a feature extraction diagram of the gray-white matter volume smoothing image of Embodiment 1 of the present invention;

[0052] Figure 4 This is a flowchart of the S3 process in Embodiment 1 of the present invention;

[0053] Figure 5 This is a flowchart illustrating the construction of the gray-white matter layered coupling matrix in Embodiment 1 of the present invention.

[0054] Figure 6 A heatmap comparing the prediction correlation coefficients (R) of different feature extraction strategies provided in Embodiment 1 of the present invention;

[0055] Figure 7 A heatmap comparing the prediction significance (P-value) of different feature extraction strategies provided in Embodiment 1 of the present invention;

[0056] Figure 8 A heatmap comparing the mean absolute error (MAE) of different feature extraction strategies provided in Embodiment 1 of the present invention;

[0057] Figure 9 A heatmap comparing the root mean square error (RMSE) of different feature extraction strategies provided in Embodiment 1 of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] This invention first performs tissue segmentation, standard spatial registration, modulation, and smoothing on the original three-dimensional T1-weighted structural magnetic resonance images to construct gray matter volume images and white matter volume images in a unified space. Then, under the constraint of standard brain region templates, brain region-level radiomics features are extracted from the gray matter volume images and white matter volume images, respectively. Furthermore, combined with repeated scan data, the extracted features are evaluated for repeated scan stability, screened for same-name pairing across gray and white matter tissues in the same brain region, and redundancy removal is performed within the brain region to obtain a list of brain region-level retained features. On this basis, gray and white matter hierarchical coupling indices are constructed in the first-order statistical feature layer and texture feature layer in the same brain region, respectively, to form a subject-level brain region hierarchical coupling matrix, which is used for cognitive ability assessment and performance verification.

[0060] Example 1:

[0061] like Figure 1 The brain structure analysis method based on gray and white matter radiomics hierarchical coupling shown includes the following steps:

[0062] S1. Acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image;

[0063] This step involves extracting brain tissue from the original 3D T1-weighted structural magnetic resonance images, segmenting gray and white matter, performing standard spatial nonlinear registration, Jacobian determinant volume modulation, and spatial smoothing. This results in the construction of smoothed gray and white matter volume images required for subsequent brain region-level gray and white matter volume radiomics feature extraction. The S1 workflow is as follows: Figure 2 As shown.

[0064] S11. Acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image;

[0065] In this embodiment, the original three-dimensional T1-weighted structural magnetic resonance images of each subject are first acquired, and the original images are preprocessed based on an automated structural image processing workflow. Preprocessing includes brain tissue extraction, gray and white matter segmentation, and nonlinear registration from the subject's spatial location to a standard spatial location. Through the above processing, gray matter images, white matter images, the nonlinear deformation field from the subject to the standard spatial location, and the corresponding Jacobian determinant images are obtained.

[0066] S12, Spatial smoothing, standard spatial alignment;

[0067] Building upon this, to improve the stability and consistency of subsequent regional-level radiomics feature extraction, spatial smoothing was performed on the gray matter volume image and the white matter volume image, generating smoothed gray matter volume images and smoothed white matter volume images, respectively. The smoothing was performed in standard space to reduce the impact of local noise fluctuations on radiomics feature calculation and enhance the continuity of structural information between adjacent voxels.

[0068] Through the above data construction and preprocessing process, smoothed gray matter and white matter volume images, aligned with the MNI152 2 mm standard space and preserving information on individual local volume changes, are finally obtained. These smoothed gray matter and white matter volume images serve as the input basis for subsequent extraction of original brain region-level radiomics features under unified brain region template constraints, and can be used to construct the original gray matter and white matter brain region-level feature sets, respectively.

[0069] S2. Extract brain region-level radiomics raw features from the gray matter volume smoothing image and the white matter volume smoothing image respectively to obtain the gray matter brain region-level raw feature set and the white matter brain region-level raw feature set.

[0070] This step is used to extract brain region-level radiomics raw features from the smoothed gray matter volume and smoothed white matter volume images of each subject under the constraint of a unified brain region template. This forms the set of raw gray matter brain region-level features and the set of raw white matter brain region-level features required for subsequent stability evaluation, cross-gray and white matter tissue pairing screening, redundancy removal, and gray and white matter hierarchical coupling construction.

[0071] In this embodiment, the Schaefer 200 brain region atlas is used as a unified brain region analysis template. The choice of brain region scale affects the stability of radiomics features and the ability to represent local structures: if the brain region scale is too large, it may mask local structural heterogeneity; if the brain region scale is too small, it may lead to unstable texture feature estimation due to insufficient effective voxels. Therefore, this embodiment uses 200 brain regions as a unified analysis scale to achieve a balance between local structure representation ability and feature stability. The feature extraction process is limited by a unified radiomics parameter configuration file to ensure the consistency and reproducibility of the feature extraction process among different subjects, different brain regions, and different tissue types. The original radiomics features include shape features, first-order statistical features, and multiple texture features. The original gray matter and white matter brain region features obtained therefrom serve as the basis for subsequent repeated scan stability evaluation, cross-tissue homonymous pairing screening within the same brain region, redundancy removal within the brain region, and construction of gray and white matter hierarchical coupling matrices. The S2 process is as follows: Figure 3 As shown, it specifically includes:

[0072] S21. Load configuration;

[0073] In this embodiment, a working directory and a feature output directory are first established. The standard brain region atlas and radiomics parameter configuration file are then read, and a radiomics feature extractor is instantiated based on the parameter configuration file. The standard brain region atlas uses the Schaefer2018_200Parcels_17Networks_order_FSLMNI152_2mm brain region atlas, which divides the whole brain into 200 brain regions with fixed label numbers. The radiomics parameter configuration file is used to uniformly define image types, feature categories, normalization methods, interpolation methods, resampling parameters, and grayscale discretization parameters to ensure the consistency and repeatability of the feature extraction process across different subjects, different brain regions, and different tissue types.

[0074] S22, Brain region-by-brain feature extraction;

[0075] Subsequently, smoothed gray matter and white matter volume images of each subject were read, and brain region-level feature extraction was performed sequentially according to brain region label numbers from 1 to 200. Specifically, the current tissue image was used as the input image, and a standard brain region atlas was used as the label mask image. By specifying the current brain region label value label=roi, the brain region range corresponding to the current label was used as the feature calculation region, thereby obtaining the original gray matter radiomics features and original white matter radiomics features of the current subject in the current brain region. Thus, individualized gray matter brain region-level original features and individualized white matter brain region-level original features for each subject can be formed.

[0076] In this embodiment, the radiomics parameter configuration file only enables the Original image type as the basis for feature calculation, that is, it does not additionally enable LoG filtered images and wavelet transform images, so that the extracted features are directly derived from the gray matter volume smoothing image and the white matter volume smoothing image themselves. The original radiomics features include shape features, first-order statistical features, gray-level co-occurrence matrix features, gray-level run length matrix features, gray-level region size matrix features, and gray-level dependency matrix features.

[0077] After extracting features from all brain regions one by one, raw feature sets at the gray matter and white matter levels were obtained. These results served as the basic inputs for subsequent evaluation of repeated scan stability, screening of homonymous pairings across gray and white matter tissues, redundancy removal of candidate features, and construction of gray and white matter hierarchical coupling.

[0078] S3. Based on repeated scan data, perform stability evaluation and screening of gray matter brain region-level original features and white matter brain region-level original features, candidate screening across gray and white matter tissues in the same brain region, and redundancy removal to generate a list of brain region-level retained features.

[0079] This invention combines repeated scan stability evaluation, same-name pairing screening across gray and white matter tissues in the same brain region, and redundancy removal processing within the brain region in a specific order to solve the problems of unstable pairing of gray and white matter radiomic features and difficulty in comparison across gray and white matter tissues.

[0080] This step is used to evaluate the stability of the original gray matter and white matter brain region features obtained in S2 based on repeated scan data, screen candidates across gray and white matter tissues in the same brain region, and perform redundancy removal, thereby forming a list of brain region-level features to be retained for subsequent gray and white matter hierarchical coupling construction.

[0081] In the repetitive scan stability evaluation and paired feature screening stage, based on repetitive scan data from the same subject, the repetitive scan stability index (ICC) was calculated for each brain region, tissue type, and radiomics feature. The intragroup correlation coefficient of a fixed-effects single measurement was used as the stability evaluation index. Features reaching a preset threshold were retained, while features below the threshold, or those that were outliers or missing values, were removed. Subsequently, on a brain region basis, stable feature sets for gray matter and stable feature sets for white matter were extracted. Same-name matching was performed on the two types of features, retaining common stable features present in both gray and white matter, thus forming a set of pairable features across gray and white matter tissues within the same brain region. Further, shape features were removed, retaining only first-order statistical features and texture features for subsequent processing. The S3 workflow is as follows: Figure 4 As shown.

[0082] S31. Stability Evaluation and Screening

[0083] A. Screening the feature set for stability evaluation

[0084] In this embodiment, the subject information table is first read, and a repeated scan pairing relationship is constructed based on the subject identifier and scan time point information. Specifically, the subject identifier is used as the matching primary key to identify subjects with at least two scan records; for each subject that meets the conditions, the access number corresponding to their first two scans is extracted to form a set of test-retest paired samples. This establishes a one-to-one correspondence between the same subject under the two scan conditions, which is used for subsequent repeated measures consistency analysis of radiomic features.

[0085] Subsequently, the raw brain region-level radiomics feature files generated by S2 are read, and the feature set used for stability evaluation is determined. In this embodiment, any valid brain region feature file is used as a benchmark to read the feature field names, and diagnostic output fields and other non-radiomics fields are removed, retaining only the radiomics features that are actually used in subsequent analysis. Radiomics features include shape features, first-order statistical features, and multiple texture features.

[0086] B. Stability Evaluation

[0087] After determining the feature set, repeatability evaluation was performed for each brain region, tissue type, and radiomics feature. Specifically, all brain regions were processed sequentially by region number; within each brain region, gray matter and white matter were evaluated independently; and for each tissue type, all candidate features were iterated one by one. For any given brain region, tissue, and feature, the feature values ​​corresponding to two scans of the same subject were extracted, and a repeatability evaluation data table was constructed, where the subject was the evaluation object, the scan time point was the repeatability condition, and the feature value was the evaluation value.

[0088] In this embodiment, the stability evaluation index uses the intraclass correlation coefficient (ICC), and preferably uses ICC(3,1) under the fixed effects model as the specific evaluation type. When each subject has two scans, the number of repeated measurements is denoted as k=2, then ICC(3,1) can be expressed as:

[0089]

[0090] in, Indicates the mean square among subjects. The mean square of the error is represented. ICC calculation is performed only when the effective test-retest sample size for a specific brain region, tissue, and feature meets the calculation requirements, to avoid instability in the evaluation results due to insufficient sample size. Through the above processing, the ICC values ​​corresponding to each brain region, each tissue, and each radiomics feature can be obtained, forming a stability evaluation result table across the entire brain.

[0091] C. Stability screening

[0092] After obtaining the stability evaluation results for all features, a first round of stability screening is performed. Specifically, the stability evaluation results are cleaned to remove features with missing, infinite, or outlier stability values; shape features are also removed; and features are retained or removed based on preset thresholds. In this embodiment, features with a stability index greater than or equal to 0.6 are retained as stable features, while features with a stability index less than 0.6 are removed. Through this step, a set of stable features for gray matter and a set of stable features for white matter can be obtained respectively.

[0093] S32, Paired Screening Across Gray and White Matter Tissue

[0094] Based on the stability screening described above, further screening of candidate features across gray and white matter tissues within the same brain region is performed. Specifically, on a brain region basis, stable feature sets for gray matter and stable feature sets for white matter are extracted separately, and feature matching with the same name is performed within the same brain region. For common features that exist in both the stable feature sets for gray matter and white matter, they are determined to be candidate features that can be used for subsequent gray-white matter coupling analysis within that brain region; features that exist only in a single tissue are not included in subsequent processing. Furthermore, in this embodiment, shape features are removed, and only first-order statistical features and texture features are retained as candidate coupling features. This is because although gray matter and white matter are constrained by a unified brain region template, they have natural differences in the way they occupy regional boundaries and the morphology of tissue distribution. If shape features are directly introduced, it is easy to bring tissue boundary differences into subsequent coupling indices, thereby weakening the ability to characterize the coupling relationship between gray-scale distribution and microstructure texture.

[0095] For each candidate feature, its stability index in the gray matter is recorded. and stability indicators in white matter And calculate the average of the two as the comprehensive stability characterization value:

[0096]

[0097] This results in a list of candidate features at the brain region level. This step ensures that each candidate feature entering subsequent processing simultaneously meets the following conditions: first, it has sufficient repetitive scanning stability in gray matter; second, it has sufficient repetitive scanning stability in white matter; and third, it has consistent feature names and cross-gray-white matter tissue comparability between gray and white matter within the same brain region.

[0098] S33, Feature Redundancy Removal

[0099] In the redundancy removal stage, a candidate feature value matrix is ​​constructed for each brain region, based on the aforementioned set of pairable features. It's important to note that this stage does not perform global redundancy removal on all original radiomics features directly. Instead, it performs intra-regional redundancy removal within the set of candidate features that already meet the stability requirements for repeated scans and can form gray-white matter pairings within the same brain region. Specifically, the correlation between candidate features within the same brain region is calculated, and a feature distance matrix is ​​constructed. The Spearman correlation coefficient is used to measure the correlation between features, and hierarchical clustering is combined to identify highly redundant feature clusters. For candidate features within the same cluster, their stability in gray and white matter is considered, and the representative feature with the highest average stability index is retained, while other redundant features are removed, thus obtaining a stable, pairable, and low-redundancy brain region-level retained feature list.

[0100] After obtaining the aforementioned list of candidate brain region-level features, this embodiment further reduces redundancy among high-dimensional features by performing redundancy removal processing on the candidate features. Specifically, taking a brain region as a unit, the values ​​of all candidate features in each subject are read to construct a feature value matrix. In this embodiment, the candidate feature value matrix of the brain region corresponding to the gray matter channel is preferably used as a redundant structure reference to calculate the cross-subject correlation between candidate features within the same brain region. Features with high stability but high correlation often reflect similar structural information. If all of them are retained, it is easy to cause information duplication and feature dimension expansion in subsequent coupling calculations. Therefore, it is necessary to further compress them.

[0101] In terms of correlation measurement, this embodiment uses the Spearman correlation coefficient to measure the monotonic correlation between different candidate features within the same brain region. Let the Spearman correlation coefficient between candidate feature i and candidate feature j be denoted as . The feature distance between the two is defined as:

[0102]

[0103] This constructs a distance matrix between features of the current brain region. Subsequently, hierarchical clustering analysis is performed on the distance matrix, and a clustering tree is constructed using complete linkage. In this embodiment, candidate features are further clustered according to a preset distance threshold t=0.2. This threshold corresponds to candidate features with an absolute correlation coefficient greater than or equal to 0.8 being considered highly redundant. For candidate features grouped into the same cluster, they are considered a group of features with high redundancy; only the feature with the highest comprehensive stability characterization value is retained in the final retention list, and the remaining features are discarded.

[0104] Through the aforementioned continuous processing flow of "repeated scan pairing—ICC stability evaluation—threshold screening—screening of candidate features with the same name across gray and white matter tissues in the same brain region—correlation clustering for redundancy removal," a list of retained features after redundancy removal is finally formed. The list of retained features includes brain region numbers, feature names, and their corresponding stability information, which can serve as the feature basis for subsequently extracting common features of the first-order statistical layer and texture layer in each brain region and constructing a gray and white matter hierarchical coupling distance index.

[0105] S4. Within each brain region, the brain region-level retained feature list is hierarchically segmented to generate a first-order statistical feature layer and a texture feature layer; based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed to form a brain region-level gray-white matter hierarchical coupling matrix.

[0106] This step is used to construct gray-white matter coupling indices for a first-order statistical feature layer and a texture feature layer in each brain region based on the redundancy-retaining feature list output by S3, thereby forming a brain region-level gray-white matter hierarchical coupling matrix and quantitatively characterizing the degree of coupling imbalance between gray matter and white matter at different feature levels within the same brain region.

[0107] In the gray-white matter hierarchical coupling construction stage, the list of retained features after redundancy removal is read according to brain regions, and the retained features are divided into a first-order statistical feature layer and a texture feature layer. It should be noted that this stage does not directly standardize and calculate the distance between arbitrary gray and white matter features, but is performed under the constraints of stability evaluation, cross-gray-white matter tissue same-name pairing screening within the same brain region, and the retained feature list obtained after redundancy removal within the brain region. Under the constraints of the retained feature list of the current brain region, the hierarchical features coexisting in gray and white matter are extracted, and gray matter feature vectors and white matter feature vectors are constructed respectively. The coupling calculation of the feature layer of the current brain region is only performed when the number of effective features coexisting in gray and white matter within the current feature layer of the current brain region meets the preset lower limit. Subsequently, local standardization is performed on the gray matter feature vector and the white matter feature vector respectively, and the Euclidean distance between them is calculated as the gray-white matter coupling index under the current feature layer of the current brain region. The resulting coupling index is used to characterize the structural differences between gray and white matter in the same brain region at corresponding feature layers. The first-order statistical feature layer primarily reflects the differences between gray and white matter at the grayscale distribution level, while the texture feature layer primarily reflects the differences between gray and white matter at the spatial texture heterogeneity level. The S4 process is as follows: Figure 5 As shown.

[0108] S41. Feature Layering and Extraction

[0109] In this embodiment, the redundancy-retaining feature list output by S3 is first read. The retaining feature list contains brain region numbers, feature names, and their corresponding stability information. Then, features belonging to the current brain region are extracted on a region-by-region basis and categorized hierarchically according to feature names. Specifically, features in the current brain region whose names contain the "firstorder" identifier are assigned to the first-order statistical feature layer candidate feature set, while the remaining retained texture features are assigned to the texture feature layer candidate feature set. Texture features include related features derived from gray-level co-occurrence matrix features, gray-level run-length matrix features, gray-level region size matrix features, and gray-level dependency matrix features.

[0110] Subsequently, the raw gray matter and raw white matter feature files for each subject and each brain region were read from the target dataset. For each subject and each brain region, under the constraint of retaining the feature list for the current brain region, the hierarchical features coexisting with gray and white matter were extracted. For the first-order statistical feature layer, the gray matter feature vector and white matter feature vector of the current brain region were formed; for the texture feature layer, the gray matter feature vector and white matter feature vector of the current brain region were formed.

[0111] In this embodiment, coupling calculation for a brain region and its layer is performed only if the number of effective features where gray and white matter coexist in the current feature layer of the current brain region meets a preset lower limit; if the number of effective features is insufficient, the coupling index for that brain region and its layer is not constructed. In the current implementation, the lower limit for the number of effective features is set to 4.

[0112] S42. Local standardization and calculation of coupling distance, construction of brain region-level hierarchical coupling index matrix.

[0113] To eliminate the influence of differences in feature dimensions and numerical ranges on the coupling distance, local standardization is performed on the gray matter feature vector and white matter feature vector within each brain region and each feature layer. Let the gray matter feature vector of the current brain region and current feature layer be:

[0114]

[0115] White matter feature vector is

[0116]

[0117] Where n is the number of valid features that coexist with gray matter and white matter in the current feature layer of the current brain region, and n≥4.

[0118] Let the mean of the gray matter eigenvectors be denoted separately. Sum of standard deviation The mean and standard deviation of the white matter eigenvectors are: and Then, the locally standardized gray matter feature vector and white matter feature vector are respectively:

[0119]

[0120]

[0121] After local standardization, the Euclidean distance between the standardized gray matter feature vector and the standardized white matter feature vector is calculated and defined as the gray-white matter coupling distance index under the current feature layer of the current brain region. The Euclidean distance is defined as:

[0122]

[0123] in, This represents the i-th eigenvalue in the standardized gray matter eigenvector. This represents the i-th eigenvalue in the standardized white matter eigenvector. The smaller the Euclidean distance, the closer the structural phenotypes of gray matter and white matter in the corresponding feature layer of the brain region are, and the more coordinated their coupling is; the larger the Euclidean distance, the more obvious the differences between gray matter and white matter in the corresponding feature layer of the brain region, and the higher the degree of coupling imbalance.

[0124] Using the above method, for each brain region, gray-white matter coupling distance indices for the first-order statistical feature layer and the texture feature layer can be obtained respectively. Preferably, the brain region number and feature layer type are jointly encoded to form a brain region-level hierarchical coupling index matrix. In the current embodiment, if the whole brain contains 200 brain regions, theoretically a hierarchical coupling matrix containing 200 first-order statistical feature layer coupling indices and 200 texture feature layer coupling indices can be formed, with a total dimension of 400. In specific implementation, if the number of effective common features of some brain regions in a certain feature layer does not reach the preset lower limit, the corresponding index for that layer will not be constructed. Therefore, the final actual effective dimension can be less than the theoretical 400 dimensions.

[0125] Through the aforementioned process of constructing gray-white matter hierarchical coupling based on locally normalized Euclidean distance, the redundancy-preserving features output by S3 can be further transformed into brain region-level coupling indices with clear hierarchical interpretations. Specifically, the first-order statistical feature layer coupling index characterizes the coupling relationship between gray and white matter at the gray-level distribution, while the texture feature layer coupling index characterizes the coupling relationship between gray and white matter at the microstructural texture level. The resulting brain region-level gray-white matter hierarchical coupling matrix can serve as the foundation for subsequent analyses.

[0126] S5. Conduct cognitive assessment and effect verification of the brain region-level gray and white matter hierarchical coupling matrix.

[0127] This step is used to verify the application effect of the gray-white matter hierarchical coupling matrix constructed in S4 on the cognitive assessment task. It should be noted that the prediction model construction and evaluation index calculation in this step are not the main inventive points of this invention, but rather as a means of effect verification to evaluate the technical effect of the gray-white matter hierarchical coupling matrix.

[0128] In the subsequent application validation phase, the gray-white matter hierarchical coupling matrix, gray matter feature matrix, white matter feature matrix, and cognitive scoring table were read and aligned and merged based on the subject identifiers. For the gray-white matter hierarchical coupling matrix, invalid feature dimensions that were null in all subjects were first removed, followed by missing value processing and standardization. Subsequently, gray-white matter hierarchical coupling strategies, gray matter single-channel strategies, and white matter single-channel strategies were constructed respectively, and the cognitive indicators were compared and validated. By comparing the correlation between the actual cognitive values ​​and predicted values ​​under different strategies, the effectiveness and application value of the gray-white matter hierarchical coupling index constructed in this invention can be verified.

[0129] In this embodiment, gray-white matter hierarchical coupling matrix, gray matter single-modal feature matrix, and white matter single-modal feature matrix are used as input features to construct gray-white matter hierarchical coupling strategy, gray matter single-modal strategy, and white matter single-modal strategy, respectively. Each strategy adopts the same data alignment method, missing value handling method, feature standardization process, prediction model, and parameter search rules to eliminate the influence of differences in model process on the comparison results.

[0130] During the performance evaluation phase, cross-validation was used to calculate the correlation coefficient, significance level, mean absolute error, and root mean square error between predicted and actual cognitive values. The gray-white matter hierarchical coupling strategy was also compared with the gray matter monomodal strategy and the white matter monomodal strategy. Through these validations, the application value of the gray-white matter hierarchical coupling matrix constructed in this invention in representing brain structure-cognitive relationships can be evaluated.

[0131] Specifically, such as Figures 6 to 9 As shown, among the 13 cognitive assessment indicators in this embodiment, the gray-white matter hierarchical coupling strategy outperforms the gray-matter monomodal strategy and the white-matter monomodal strategy in terms of predictive correlation coefficients. Figure 6 As shown, the gray-white matter hierarchical coupling strategy achieved the highest predictive correlation coefficients in 12 out of 13 cognitive assessment indicators, only slightly lower than the gray matter monomodal strategy in the Hopkins delayed recognition accuracy indicator. For indicators such as the symbol substitution test, delayed conditional task, and Raven's inference correctness, the predictive correlation coefficients of the gray-white matter hierarchical coupling strategy reached 0.602, 0.571, and 0.566, respectively, all higher than or close to the corresponding results of gray matter original features and white matter original features, indicating that the hierarchical coupling matrix can effectively characterize the relationship between brain structure and cognitive performance.

[0132] like Figure 7As shown, in terms of statistical significance, the gray-white matter hierarchical coupling strategy achieved statistical significance in all 13 cognitive assessment indicators. The p-values ​​for the first 12 cognitive indicators were all less than 0.001, and it achieved the smallest p-value among the three feature strategies for most indicators. This indicates that the gray-white matter hierarchical coupling strategy has a relatively stable statistical predictive effect.

[0133] like Figure 8 and Figure 9 As shown, the gray-white matter hierarchical coupling strategy also exhibits good error control capabilities in terms of prediction error. In the mean absolute error index, the gray-white matter hierarchical coupling strategy achieved the lowest error in 11 out of 13 cognitive evaluation indicators; in the root mean square error index, the gray-white matter hierarchical coupling strategy achieved the lowest error in all 13 cognitive evaluation indicators. These results demonstrate that the gray-white matter hierarchical coupling matrix constructed in this invention not only improves prediction relevance and statistical stability but also reduces prediction error.

[0134] comprehensive Figures 6 to 9 The results show that, compared with directly using raw gray matter or white matter radiomics features, the gray-white matter hierarchical coupling matrix constructed in this invention achieves better or more stable cognitive prediction results at a lower feature dimension. This result indicates that the gray-white matter hierarchical coupling matrix is ​​not a simple concatenation of gray and white matter features, but rather an effective brain structure representation formed through the combined effects of cross-gray-white matter tissue pairing, stability constraints, redundancy removal, and hierarchical coupling computation, which can improve the stability and interpretability of brain structure-cognitive relationship analysis.

[0135] Example 2:

[0136] A brain structure analysis system based on hierarchical coupling of gray and white matter radiomics includes:

[0137] The data acquisition and preprocessing module is used to acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image.

[0138] The radiomics feature extraction module is used to extract brain region-level radiomics raw features from gray matter volume smoothing images and white matter volume smoothing images, respectively, to obtain gray matter brain region-level raw feature sets and white matter brain region-level raw feature sets.

[0139] The feature selection module is used to perform stability evaluation and screening of gray matter and white matter brain region-level original features based on repeated scan data, candidate screening across gray and white matter tissues in the same brain region, and redundancy removal to generate a list of brain region-level retained features.

[0140] The feature layering coupling module is used to perform feature layering on the brain region-level reserved feature list within each brain region, generating a first-order statistical feature layer and a texture feature layer; based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed, thereby forming a brain region-level gray-white matter layering coupling matrix.

[0141] The assessment and validation module is used to perform cognitive assessment and effect validation of the brain region-level gray and white matter hierarchical coupling matrix.

Claims

1. A brain structure analysis method based on hierarchical coupling of gray and white matter radiomics, characterized in that, Includes the following steps: S1. Acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image; S2. Extract brain region-level radiomics raw features from the gray matter volume smoothing image and the white matter volume smoothing image respectively to obtain the gray matter brain region-level raw feature set and the white matter brain region-level raw feature set. S3. Based on repeated scan data, perform stability evaluation and screening of original features at the gray matter and white matter levels, candidate features across gray and white matter tissues within the same brain region, and redundancy removal to generate a list of retained brain region features; S3 includes: S31. Based on repeated scan data of the same subject, stability evaluation indicators are calculated for each brain region, each tissue type and each radiomics feature to form a stability evaluation result across the whole brain. Based on the stability evaluation results, the original features at the gray matter brain region level and the original features at the white matter brain region level are screened to obtain the gray matter stable feature set and the white matter stable feature set, respectively. S32. Perform same-name matching on the stable feature sets of gray matter and white matter, taking brain regions as units, retain common stable features that exist in both gray matter and white matter, and generate a set of candidate features that can be paired across gray and white matter tissues in the same brain region; generate a list of candidate features at the brain region level based on the candidate feature set. S33. Redundancy is removed from the list of candidate features at the brain region level to generate a list of retained features at the brain region level. S4. Within each brain region, the brain region-level retained feature list is hierarchically structured to generate a first-order statistical feature layer and a texture feature layer; based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed to form a brain region-level gray-white matter hierarchical coupling matrix; S4 includes: S41. Taking brain regions as units, features whose feature names contain the firstorder identifier are assigned to the candidate feature set of the first-order statistical feature layer, and the remaining texture features are assigned to the candidate feature set of the texture feature layer. Under the constraint of the brain region feature list, the hierarchical features of gray matter and white matter in the current brain region are extracted to form gray matter feature vectors and white matter feature vectors of the first-order statistical feature layer and gray matter feature vectors and white matter feature vectors of the texture feature layer. S42. In each brain region and each feature layer, the gray matter feature vector and the white matter feature vector are locally standardized. Then, the Euclidean distance between the gray matter feature vector and the white matter feature vector is calculated and defined as the gray-white matter coupling distance index under the current feature layer of the current brain region. The gray-white matter coupling distance index of the first-order statistical feature layer and the gray-white matter coupling distance index of the texture feature layer are obtained respectively. S5. Conduct cognitive assessment and effect verification of the brain region-level gray and white matter hierarchical coupling matrix.

2. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 1, characterized in that, S1 includes: S11. Obtain the original three-dimensional T1-weighted structural magnetic resonance images of each subject, and perform preprocessing based on the automated structural image processing workflow to obtain gray matter tissue images, white matter tissue images, nonlinear deformation fields of the subject to standard space, and corresponding Jacobian determinant images. Preprocessing includes brain tissue extraction, gray and white matter segmentation, and nonlinear registration from the subject space to the standard space; S12. Based on the Jacobian determinant image, volume modulation is performed on the gray matter and white matter images respectively to preserve the individual local volume change information of the subject's brain tissue; spatial smoothing is performed on the volume-modulated images to obtain gray matter volume smoothing images and white matter volume smoothing images aligned with the standard space.

3. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 1, characterized in that, S2 include: S21. Read the standard brain region atlas and radiomics parameter configuration file, and instantiate the radiomics feature extractor based on the parameter configuration file; S22. Using smoothed gray matter volume images and smoothed white matter volume images as input images, and standard brain region maps as label mask images; by specifying the current brain region label value, the brain region range corresponding to the current label is used as the feature calculation region, and the radiomics feature extractor is used to obtain the original gray matter radiomics features and the original white matter radiomics features of the subject in the current brain region respectively; brain region-level feature extraction is performed one by one according to the brain region label number, and after the feature extraction of all brain regions is completed, the original gray matter brain region-level feature set and the original white matter brain region-level feature set are obtained respectively.

4. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 1, characterized in that, S31 includes: Based on the subject information table, a repeated scan pairing relationship is constructed to generate a test-retest paired sample; For the original feature sets at the gray matter and white matter brain regions, only radiomics features are retained to construct a feature set that is determined to participate in stability evaluation; radiomics features include shape features, first-order statistical features, and multiple texture features. For the feature set involved in stability evaluation, repeated scans were performed to evaluate stability for each brain region, each tissue type, and each radiomics feature. The stability evaluation results were first cleaned for effectiveness, and shape features were removed. Then, feature removal was performed according to a preset stability threshold.

5. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 1, characterized in that, The stability evaluation index used was the intragroup correlation coefficient (ICC).

6. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 4, characterized in that, S32 includes: Shape features are removed from the candidate feature set, and only first-order statistical features and texture features are retained. For each candidate feature, its stability evaluation index in gray matter and stability evaluation index in white matter are recorded respectively, and the average of the two is calculated as the comprehensive stability characterization value, thereby generating a list of brain region-level candidate features.

7. The brain structure analysis method based on gray and white matter radiomics hierarchical coupling according to claim 6, characterized in that, S33 includes: Using brain regions as units, the values ​​of all candidate features in each brain region are read in each subject to construct an eigenvalue matrix; Spearman correlation coefficients between candidate features are calculated based on the eigenvalue matrix; feature distances between candidate features are calculated based on the Spearman correlation coefficients to construct a feature distance matrix for the current brain region; hierarchical clustering analysis is performed on the feature distance matrix, and clusters are divided based on preset distance thresholds, and highly redundant feature clusters are identified by combining hierarchical clustering methods; for all candidate features divided into the same cluster, only the feature with the highest comprehensive stability characterization value is retained to obtain a brain region-level retained feature list.

8. A brain structure analysis system based on hierarchical coupling of gray and white matter radiomics, characterized in that, include: The data acquisition and preprocessing module is used to acquire and preprocess the original three-dimensional T1-weighted structured magnetic resonance image to generate gray matter volume smoothing image and white matter volume smoothing image. The radiomics feature extraction module is used to extract brain region-level radiomics raw features from gray matter volume smoothing images and white matter volume smoothing images, respectively, to obtain gray matter brain region-level raw feature sets and white matter brain region-level raw feature sets. The feature selection module is used to perform stability evaluation and selection of original features at the gray matter and white matter levels based on repeated scan data, candidate feature selection across gray and white matter tissues within the same brain region, and redundancy removal to generate a brain region-level list of retained features. This includes: calculating stability evaluation indices for each brain region, tissue type, and radiomics feature based on repeated scan data from the same subject, forming a whole-brain stability evaluation result; selecting original features at the gray matter and white matter levels based on the stability evaluation results, obtaining stable feature sets for gray matter and white matter respectively; performing same-name matching on the stable feature sets for gray matter and white matter at the brain region level, retaining common stable features present in both gray and white matter, generating a set of candidate features that can be paired across gray and white matter tissues within the same brain region; generating a brain region-level list of candidate features based on the candidate feature sets; and removing redundancy from the brain region-level list of candidate features to generate a brain region-level list of retained features. The feature layering coupling module is used to perform feature layering on the brain region-level retained feature list within each brain region, generating a first-order statistical feature layer and a texture feature layer. Based on the first-order statistical feature layer and the texture feature layer, a gray-white matter coupling index is constructed, thus forming a brain region-level gray-white matter layering coupling matrix. This includes: assigning features with the firstorder identifier in their feature names to the candidate feature set of the first-order statistical feature layer, and assigning the remaining retained texture features to the candidate feature set of the texture feature layer; under the constraint of the brain region retained feature list, extracting the layered features coexisting in gray and white matter within the current brain region, forming gray and white matter feature vectors for the first-order statistical feature layer and the texture feature layer; performing local standardization on the gray and white matter feature vectors within each brain region and each feature layer, then calculating the Euclidean distance between the gray and white matter feature vectors, and defining it as the gray-white matter coupling distance index for the current brain region and current feature layer, thus obtaining the gray-white matter coupling distance index for the first-order statistical feature layer and the gray-white matter coupling distance index for the texture feature layer. The assessment and validation module is used to perform cognitive assessment and effect validation of the brain region-level gray and white matter hierarchical coupling matrix. The brain structure analysis system based on gray and white matter radiomics hierarchical coupling is used to implement the brain structure analysis method and steps based on gray and white matter radiomics hierarchical coupling as described in claim 1.

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