CN116401889A - Cerebellum partitioning method based on functional connection optimization and spectral clustering - Google Patents

Abstract

The invention discloses a cerebellum partition method based on functional connection optimization and spectral clustering, which belongs to the technical field of biomedical image processing, and particularly relates to a functional connection optimization transformation mode and cerebellum partition construction of functional magnetic resonance images. The invention processes the magnetic resonance data by utilizing the functional connection metric optimization, the spectral clustering and the clustering integration algorithm, realizes the construction of the cerebellum multi-scale partition, and has higher repeatability, regional homogeneity and spatial continuity. The invention provides a new thought for cerebellum partition construction, and functional connection measurement optimization, spectral clustering and clustering integration algorithm are fused together for the first time to be applied to the cerebellum partition construction, can be used as a division reference of a subsequent cerebellum region, and can be applied to cerebellum analysis of various diseases.

Description

Cerebellum partitioning method based on functional connection optimization and spectral clustering

Technical Field

The invention belongs to the technical field of biomedical image processing, and particularly relates to an optimized transformation mode of functional connection and cerebellum partition construction of a functional magnetic resonance image.

Background

The cerebellum is a relatively independent area located at the rear lower part of the brain, and can be divided into a middle earthworm part and cerebellum hemispheres at two sides. Although the cerebellum volume is only 10% of the whole brain, 80% of neurons are contained. The research in the last twenty years shows that the cerebellum is far more than the function of motion control, plays an important role in space cognition and memory, language and emotion and other functions, and is also a key brain area for pathological changes of some neurodegenerative diseases such as parkinsonism. Recently, many researches find that functional signals of cerebellum have stronger individual specificity compared with brain, the difference between transverse distribution of anatomical structure and longitudinal distribution of functional signals is larger, signal heterogeneity in anatomical structure is stronger, and the functional signals are unsuitable for being used as functional partitions due to overlarge volume differences of various structural partitions. Although there are solutions to divide the cerebellum into functional partitions of different dimensions, these partitions suffer from drawbacks in terms of repeatability between individuals, continuity of cerebellum space, and signal homogeneity within the region, and fixed-scale partitions present application limitations. How to construct a cerebellum partition meeting the requirements of the above by using a relatively suitable model, and performing more accurate dimension reduction in space, so that the functional characteristics of the cerebellum can be better excavated, and the method is still a problem when applied to the study of cerebellum abnormality such as Parkinson and other diseases.

Disclosure of Invention

If the network model and the method are widely applied to the cerebellum functional magnetic resonance image, a proper cerebellum dividing method is needed, but the existing cerebellum partition has the problems of insufficient repeatability, weak signal homogeneity in the area, discontinuous space and the like, and is not beneficial to the model and the method in the data of the cerebellum functional magnetic resonance image. The invention provides a cerebellum partitioning method based on functional connection optimization and spectral clustering, which aims to solve the problems of improving the repeatability, the spatial continuity, the insufficient signal homogeneity and the like of cerebellum partitioning.

The specific implementation scheme of the technology is as follows: a cerebellum partitioning method based on functional connection optimization and spectral clustering, the method comprising:

step 1: acquiring functional magnetic resonance brain image data and preprocessing the brain image data, including: time layer correction, spatial normalization, covariate regression and filtering, but without performing spatial smoothing operation on the data, and finally extracting time sequence signals of the cerebellum region by using a cerebellum template;

step 2: constructing cerebellar partitions at the individual level:

step 2.1: for each individual data, a functional connection fc of all cerebellar voxels to the time sequence is calculated _i,j ：

Wherein the time sequence length is T, x _t Time series { x } representing voxel i _t Signal value at time t, y _t Time series { y } representing voxel j _t Signal value at time t,

time series { x } representing voxel i _t Mean }, ->

Time series { y } representing voxel j _t Mean; thereby obtaining a cerebellum function connection matrix formed by each cerebellum voxel pair;

step 2.2: calculating delta from spatial adjacency between voxels _ij Limiting the matrix value;

wherein dist (i, j) represents the spatial distance between voxel i and voxel j, and specifies the space between two adjacent voxels in the coordinate direction as unit distance 1;

step 2.3: applying a transformation function to the cerebellum functional connection matrix values using the following formula;

wherein k is a super parameter, so that a new similarity matrix is constructed;

S _Root ＝(f _Root (δ _ij fc _ij ,k))；

step 2.4: based on the similarity matrix S _Root The NCUT spectral clustering method is applied to realize the partition of the cerebellum;

step 3: constructing cerebellum partitions at the group level;

step 3.1: taking the partition number K as an example, taking the partition result C= [ C ] of the individual ₁ ,c ₂ ,…c _i …,c _n ]Conversion to an adjacency representation matrix ar= (a) _ij ) Wherein any element a _ij The method meets the following conditions:

wherein c _i And c _j The partition labels of the ith and jth voxels are respectively represented, and the value range is an integer between 1 and K;

step 3.2: the contiguous representation matrix AR of N samples is averaged:

obtaining a group-level similarity matrix S _G ；

Step 3.3: according to the above group of horizontal similarity matrices S _G And (3) constructing the group level cerebellum partition by applying an NCUT spectral clustering method.

By applying the method and the flow, the repeatability of the partition can be effectively improved, and the continuity of the partition in space and the signal homogeneity can be ensured.

Drawings

FIG. 1 is a group level partition construction and evaluation flow of the present method;

FIG. 2 is a schematic diagram of the change of FC values by three transformation functions;

FIG. 3 is a schematic diagram of the change of the FC frequency distribution by three transformation functions;

fig. 4 is a schematic diagram of NMI similarity between group horizontal partitions and verification set individual partitions constructed based on different transformations;

FIG. 5 is a graph of the similarity of the Dice coefficients of the group horizontal partitions and the individual partitions of the validation set constructed based on different transformations;

FIG. 6 is a cerebellum partition plane visualization of 10, 15, 25, 45, 80, 120, 160, 200 partitions constructed based on Root transform functions;

FIG. 7 is a global signal consistency comparison of a partition constructed by the method with other disclosed partitions; representing the global consistency of the four new partitions when the number of the partitions is 10 to 200 and comparing the global consistency with the global consistency of the four public partitions;

FIG. 8 is a comparison of regional signal consistency of a partition constructed by the method with other disclosed partitions; a region uniformity bubble map representing eight partitions, bubble size representing region uniformity size, and bubble height representing log2 (region size) value.

Detailed Description

Specific embodiments of the invention will be described in further detail below with reference to the drawings and examples, which are given to illustrate the invention and are not intended to limit the scope of the invention.

The specific implementation steps are shown in FIG. 1

Step A: magnetic resonance data processing and cerebellum signal processing;

the data set used in this study was from the human brain connectivity group program (Human Connectome Project, HCP), 82 of which were selected for public fMRI data sets. The batch of images is obtained by adopting a gradient Echo Planar Imaging (EPI) sequence, the number of time points of the data is 1200, the time interval is 0.72s, and the voxel size is 2 multiplied by 2mm ³ The data space size was 91×109×91, flip angle (FOV) was 52 °, field angle (FOV) was 208×180mm (ro×)RE), each layer had a thickness of 2mm and the number of scan layers was 72. For the HCP dataset, B0 distortion correction, head motion correction, structural registration, normalization to a 4D average brain template, and nonlinear transformation to MNI spatial operation were achieved first using a minimum pre-processing pipeline. Then, the covariate regression processing is carried out on the heartbeat signal noise of the data, and the filtering of 0.01-0.1 Hz is extracted. It should be noted that although spatial smoothing of the whole brain signal in the data preprocessing can improve the signal-to-noise ratio of the data, this behavior can artificially improve the spatial correlation between local regions, which has a very significant influence on the subsequent computation, so that the spatial smoothing process is avoided in the present data preprocessing.

After the data preprocessing is completed, fMRI data signals of gray lobules and earthworm regions of the cerebellum region are extracted from the whole brain by using a SUIT cerebellum structure template, 18410 voxels are extracted in total, and finally the data dimension of each sample is 18410 ×1200 (the number of voxels×the time series length).

And (B) step (B): individual level cerebellum partition construction

(1) For each individual data, a functional connection fc of all cerebellar voxels to the time sequence is calculated _ij Thereby obtaining a cerebellum function connection matrix formed by each cerebellum voxel pair;

(2) for each individual functional connection matrix, limiting the functional connection matrix values according to the spatial adjacency relationship between voxels;

(3) for each individual function connection matrix, three transformation functions are used for carrying out order-preserving mapping on the function connection values, wherein the order-preserving mapping is respectively carried out on the function connection values;

thereby three kinds of similarity matrices are obtained

Wherein the super parameter k=1, α=2, a=1, and

S _Origin ＝(δ _ij fc _ij )

the similarity matrix is used as a reference for comparison.

(4) Based on the four similarity matrices S _Origin ,S _Root ,S _Square ,S _Gaussian The clustering number is selected from 10, and each individual is subjected to spectral clustering by taking 5 as a step length to 200, so that a series of partitions (the number of the partitions is from 10 to 200) of four similar matrixes are finally obtained.

Step C: constructing a group horizontal partition;

(1) all individual data were divided into an exploration set and a verification set, with 57 samples for the exploration set and 25 samples for the verification set.

(2) And converting the clustering result of the exploration set into an adjacent representation matrix AR, and respectively averaging the adjacent representation matrices of all the exploration sets according to different transformation functions and clustering numbers to obtain respective group level similarity matrices.

(3) And according to the group level similarity matrix under different conditions, constructing a group level cerebellum partition by using a spectral clustering algorithm.

Step D: evaluation of group horizontal partitions;

(1) according to the individual partition result of the verification set, NMI values and Dice coefficients of the group horizontal partition and the individual partition of the verification set are calculated one by one to evaluate the repeatability of the partition, and the repeatability of four transformation functions is shown in the graphs of fig. 4 and 5, wherein the Root transformation function has the strongest improvement on the repeatability of the partition.

(2) The cerebellar plane is visualized to assess spatially continuous properties. In fact, the spatial constraint similarity matrix construction method and the spectral clustering algorithm guarantee continuity of the partitions in principle. Visualization of the different partitions in fig. 6 also reveals that all partitions are spatially contiguous.

(3) Signals of all areas are respectively extracted by using a group horizontal partition and four public partition templates according to fMRI cerebellum image data of the verification set, and global signal consistency is calculated so as to evaluate the signal homogeneity of the partitions. Fig. 7 shows partition signal homogeneity. The graph shows that the signal homogeneity of the partitions constructed under the four transformation functions is consistent and is obviously better than that of the existing partitions.

(4) And respectively extracting signals of each region by using four Root partitions with the partition numbers of 10, 15, 25 and 45 and four public partition templates according to fMRI cerebellum image data of the verification set, and calculating the signal consistency of each region. The bubble in fig. 8 represents each of the eight partitions, the bubble height represents the size of the partition, and the bubble size represents the region signal uniformity intensity.

Claims (1)

1. A cerebellum partitioning method based on functional connection optimization and spectral clustering, the method comprising:

step 1: acquiring functional magnetic resonance brain image data and preprocessing the brain image data, including: time layer correction, spatial normalization, covariate regression and filtering, but without performing spatial smoothing operation on the data, and finally extracting time sequence signals of the cerebellum region by using a cerebellum template;

step 2: constructing cerebellar partitions at the individual level:

step 2.1: for each individual data, a functional connection fc of all cerebellar voxels to the time sequence is calculated _i,j ：

Wherein the time sequence length is T, x _t Time series { x } representing voxel i _t Signal value at time t, y _t Time series { y } representing voxel j _t Signal value at time t,

time series { x } representing voxel i _t Mean }, ->

Time series { y } representing voxel j _t Mean; thereby obtaining a cerebellum function connection matrix formed by each cerebellum voxel pair;

step 2.2: calculating delta from spatial adjacency between voxels _ij Limiting the matrix value;

wherein dist (i, j) represents the spatial distance between voxel i and voxel j, and specifies the space between two adjacent voxels in the coordinate direction as unit distance 1;

step 2.3: applying a transformation function to the cerebellum functional connection matrix values using the following formula;

wherein k is a super parameter, so that a new similarity matrix is constructed;

S _Root ＝(f _Root (δ _ij fc _ij ,k))；

step 2.4: based on the similarity matrix S _Root The NCUT spectral clustering method is applied to realize the partition of the cerebellum;

step 3: constructing cerebellum partitions at the group level;

step 3.1: taking the partition number K as an example, taking the partition result C= [ C ] of the individual ₁ ,c ₂ ,…c _i …,c _n ]Conversion to an adjacency representation matrix ar= (a) _ij ) Wherein any element a _ij The method meets the following conditions:

wherein c _i And c _j The partition labels of the ith and jth voxels are respectively represented, and the value range is an integer between 1 and K;

step 3.2: the contiguous representation matrix AR of N samples is averaged:

obtaining a group-level similarity matrix S _G ；

Step 3.3: according to the above group of horizontal similarity matrices S _G And (3) constructing the group level cerebellum partition by applying an NCUT spectral clustering method.

Images