CN109615605B - Functional magnetic resonance imaging brain partitioning method and system based on quantum potential energy model - Google Patents
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Abstract
The invention discloses a functional magnetic resonance imaging brain partitioning method and system based on a quantum potential energy model. The functional magnetic resonance imaging brain partitioning method based on the quantum potential energy model comprises the steps of preprocessing an fMRI brain image; and partitioning the preprocessed fMRI brain image by using a quantum potential energy model. The invention utilizes the advantages of quantum algorithm in analyzing and processing big data and high-dimensional data to convert brain partitions into quantum potential energy models, and carries out clustering partitions on single tested or multiple tested fMRI data through quantum calculation.
Description
Technical Field
The invention belongs to the field of functional magnetic resonance imaging image processing, and particularly relates to a functional magnetic resonance imaging brain partitioning method and system based on a quantum potential energy model.
Background
Functional magnetic resonance imaging (fMRI) has been developed as a major tool in the neurocognitive field. Unlike positron emission tomography and electroencephalogram, fMRI uses blood oxygen level dependent signals to detect active regions in the brain, which has the advantages of being non-invasive, capable of detecting internal regions of the brain deeply, and the like, and thus has been widely used in various aspects of the field of brain science. However, the human brain contains about 860 billion neurons, and the complex brain structure causes fMRI research to generate massive data, which puts extremely high requirements on the performance of hardware and software and manpower. The existing scheme is to divide the brain into a plurality of brain areas, and through the analysis of the brain areas, excessive redundant data can be avoided to be processed, and the analysis efficiency is improved. The brain function partition technology is developed at the same time, and has attracted extensive attention in the fields of brain science and cognitive science.
The brain partitioning is a technology for dividing a brain space into a plurality of regions which are consistent and do not overlap with each other, and at present, three types of common brain partitioning technologies are available, namely, a brain partitioning technology based on analysis of an interested region, a brain atlas and data driving.
The region of interest based partitioning method places the points of interest for data analysis in a predefined area that can be selected based on a priori experimental results. At present, an analysis method based on an interested region is applied to analysis and research of fMRI data such as aging, pathology, brain network and the like. However, the analysis method based on the region of interest also has various disadvantages, which neglect signals outside the region of interest, so the quality of the partition result depends on the selection of the region of interest to some extent. Moreover, different populations have different brains to a certain extent, and the analysis based on the region of interest does not have universality for different populations.
Brain atlas, as the name implies, is the division of the brain into several anatomically or functionally interconnected regions according to prior knowledge. At present, the commonly used brain maps comprise an automatic anatomical labeling brain map, a Brodman zoning brain map and the like, but the brain maps are long-term and have not fine zoning on the human brain. And the existing brain maps have inconsistency. And because the brain atlas is made by collecting the data of a specific crowd, deviation may exist for a special crowd.
Different from a region-of-interest-based and brain atlas-based partitioning method, the data-driven brain partitioning method classifies data through a clustering algorithm, can fully extract intrinsic features of the data, and better reflects inherent attributes of the data. And the research on data-driven brain partitions at home and abroad is getting more and more popular in recent years, wherein the methods for the data-driven brain partitions comprise brain partitions based on k-means clustering, brain partitions based on hierarchical clustering, brain partitions based on spectral clustering and the like.
However, the above clustering methods have the defects of dependence on initial seed point selection, influence of subjective factors of people, incapability of performing rapid clustering analysis on images containing large data volume, and the like. Therefore, a method for accurately and rapidly classifying images containing a large amount of data is required.
Disclosure of Invention
In order to solve the defects of the prior art, a first object of the present invention is to provide a functional magnetic resonance imaging brain partitioning method based on a quantum potential energy model, which can quickly and accurately partition fMRI brain images containing large data volume.
The invention discloses a functional magnetic resonance imaging brain partitioning method based on a quantum potential energy model, which comprises the following steps:
preprocessing the fMRI brain image;
and partitioning the preprocessed fMRI brain image by using a quantum potential energy model.
Further, the specific process of partitioning the preprocessed fMRI brain image by using the quantum potential energy model is as follows:
extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image;
converting the gray matter image into a two-dimensional matrix form M; the number of the rows is equal to the total prime number of the grey matter images, the number of the columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively;
the two-dimensional matrix M or the value of each column of the matrix formed after the principal component analysis of the two-dimensional matrix M is used as the input value of the quantum potential energy model to construct a quantum wave function, and further the voxel position coordinates and the gray value of the fMRI brain image are converted into the particle distribution of a quantum system;
inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of particle space potential energy of a quantum system, and further changing the process of searching for the center of a brain partition in a fMRI brain image into searching for a minimum value point of the potential energy in the quantum system;
calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
Further, the method further comprises: calling an OpenGL interface, and accurately presenting a brain partition result on a three-dimensional MNI standard brain model through three-dimensional rendering; and simultaneously displaying three views of an XZ plane, a YZ plane and an XY plane so as to obtain three views of a sagittal position, a coronal position and a transverse position of a brain partition result.
Further, the method further comprises: and outputting the partition result, wherein the partition result is output in an NIfTI format and is applied to fMRI functional connection and brain functional network analysis.
Further, the preprocessed fMRI brain image is subjected to dot multiplication with a gray matter template in a standard MNI space, and a gray matter part in the preprocessed fMRI brain image is extracted to obtain a gray matter image.
Further, the quantum wave function is:
wherein xi＝[β1,β2,…,βn]，β1,β2,…βnN principal component values respectively corresponding to the ith voxel, i.e. n elements of the ith row of the matrix M, x being an n-dimensional column vector space constructed from the input values, xiThe matrix is formed after principal component analysis is carried out on the two-dimensional matrix M; σ is the width parameter of the wave function, and the size of σ is related to the number of partitions.
Further, the method further comprises:
controlling the number of minimum value points by setting a threshold of the extreme value points, recording the number of the minimum value points after the threshold is set as l, and assigning the minimum value points to continuous label values 1,2 and … l from small to large according to x-axis, y-axis and z-axis position coordinates; wherein l is a positive integer greater than or equal to 1.
Further, the process of preprocessing the fMRI brain image includes:
correcting a temporal layer of the fMRI brain images;
correcting a spatial layer of the fMRI brain image;
registering individual fMRI brain images to an MNI spatial template;
performing spatial smoothing on the fMRI brain image registered to the MNI spatial template;
and filtering the fMRI brain image after the spatial smoothing processing.
The second purpose of the invention is to provide a functional magnetic resonance imaging brain partition method based on a quantum potential energy model, which is used for outputting partition results in an NIfTI format, and is applied to fMRI functional connection and brain functional network analysis, so that the accuracy of fMRI analysis is improved.
The invention also provides a functional magnetic resonance imaging brain partition system based on the quantum potential energy model.
The invention relates to a functional magnetic resonance imaging brain partition system based on a quantum potential energy model, which comprises a memory and a processor; the processor configured to perform the steps of:
preprocessing the fMRI brain image;
and partitioning the preprocessed fMRI brain image by using a quantum potential energy model.
Further, in the processor, the specific process of partitioning the preprocessed fMRI brain image by using the quantum potential energy model is as follows:
extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image;
converting the gray matter image into a two-dimensional matrix form M; the number of the rows is equal to the total prime number of the grey matter images, the number of the columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively;
the two-dimensional matrix M or the value of each column of the matrix formed after the principal component analysis of the two-dimensional matrix M is used as the input value of the quantum potential energy model to construct a quantum wave function, and further the voxel position coordinates and the gray value of the fMRI brain image are converted into the particle distribution of a quantum system;
inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of particle space potential energy of a quantum system, and further changing the process of searching for the center of a brain partition in a fMRI brain image into searching for a minimum value point of the potential energy in the quantum system;
calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
Further, the processor is configured to perform:
and outputting the partition result, wherein the partition result is output in an NIfTI format and is applied to the subsequent analysis of fMRI functional connection and brain functional network.
Further, in the processor, the preprocessing the fMRI brain image includes:
correcting a temporal layer of the fMRI brain images;
correcting a spatial layer of the fMRI brain image;
registering individual fMRI brain images to an MNI spatial template;
performing spatial smoothing on the fMRI brain image registered to the MNI spatial template;
and filtering the fMRI brain image after the spatial smoothing processing.
Compared with the prior art, the invention has the beneficial effects that:
according to the functional magnetic resonance imaging brain partitioning method and system based on the quantum potential energy model, advantages of a quantum algorithm in analysis and processing of large data and high-dimensional data are utilized, the brain partitioning is converted into the quantum potential energy model, and clustering partitioning is performed on single tested data or multiple tested fMRI data through quantum calculation.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a functional magnetic resonance imaging brain partitioning method based on a quantum potential energy model according to the present invention;
FIG. 2 is a flow chart of partitioning a pre-processed fMRI brain image using a quantum potential energy model;
FIG. 3 is a schematic diagram of a process for obtaining gray matter images;
FIG. 4(a) is a partial view of a quantum potential energy model;
FIG. 4(b) is a potential energy threshold;
FIG. 4(c) is a cross-sectional view of layer 50;
FIG. 4(d) is an equipotential surface across a view of layer 50;
FIG. 5(a) is a three-dimensional brain partition result graph;
FIG. 5(b) is a view of a cross-sectional view result;
FIG. 5(c) is a sagittal view results plot;
FIG. 5(d) is a coronary view angle result chart.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
FIG. 1 is a flow chart of a functional magnetic resonance imaging brain partitioning method based on a quantum potential energy model.
As shown in fig. 1, a functional magnetic resonance imaging brain partition method based on a quantum potential energy model of the present invention includes:
step 1: the fMRI brain images are preprocessed.
The fMRI brain image input into the fMRI brain partition system based on the quantum potential energy model needs to be preprocessed. The fMRI brain image is a magnetic resonance brain image acquired by a fast imaging sequence such as a gradient echo planar imaging sequence and a spin echo sequence by using a blood oxygen level dependent technique.
Preprocessing employs Statistical Parametric Mapping (SPM) software commonly used for functional magnetic resonance image processing. In a particular embodiment, the process of pre-processing the fMRI brain image includes:
step 1.1: correcting a temporal layer of the fMRI brain images;
before correcting the time layer of the fMRI brain image, the method further comprises the following steps: and (3) converting the data format, namely converting the original DICOM format data into NIfTI format data commonly used by a computer.
Specifically, a Slice Timing module of the SPM is used to perform temporal layer correction on the data.
Step 1.2: the spatial layer of the fMRI brain image is corrected.
Specifically, the Realign module of the SPM is adopted to correct the spatial layer of the data.
Step 1.3: individual fMRI brain images are registered to the MNI spatial template.
Specifically, by using the normalation module of the SPM, the individual brain fMRI data can be registered to the Montreal Nerve Institute (MNI) standard brain space by three methods, namely, an EPI template, a structural image joint registration, or a differential homoembryo image fusion algorithm.
Step 1.4: and performing spatial smoothing on the fMRI brain image registered to the MNI spatial template.
Specifically, a smoothening module of the SPM is adopted, and a gaussian kernel of full width at half maximum can be selected to perform convolution processing on the image, and the full width at half maximum is generally 6-8 mm.
Step 1.5: and filtering the fMRI brain image after the spatial smoothing processing.
Specifically, the image data may be filtered using a band-selectable low-pass filter.
Step 2: and partitioning the preprocessed fMRI brain image by using a quantum potential energy model.
In a specific embodiment, as shown in fig. 2, a specific process of partitioning the preprocessed fMRI brain image by using the quantum potential energy model is as follows:
step 2.1: extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image;
specifically, the preprocessed fMRI brain image is dot-multiplied with a gray matter template in a standard MNI space, and a gray matter portion in the preprocessed fMRI brain image is extracted to obtain a gray matter image, as shown in fig. 3.
For example: and performing point multiplication on each preprocessed fMRI image to be tested and a binary gray matter template in a standard MNI space, extracting a gray matter part in the image, performing brain partition processing by adopting the gray matter image, and performing first-step gray matter extraction on the residual 67531 voxels in the image.
Step 2.2: converting the gray matter image into a two-dimensional matrix form M; the number of the rows is equal to the total prime number of the grey matter images, the number of the columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively.
Specifically, the three-dimensional gray matter image is sequentially converted into a two-dimensional matrix form of 67531 rows and 4m columns according to the x-axis position coordinates, y-axis position coordinates and the gray value of each voxel, wherein m represents the number of fMRI images, and when only one tested fMRI image exists, m is 1. Each row corresponds to a voxel, each 4 columns correspond to the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel, and the 67531 row-4M-column two-dimensional matrix is marked as M.
Step 2.3: and (3) taking the value of each column of the two-dimensional matrix M or the matrix formed after the principal component analysis of the two-dimensional matrix M as an input value of the quantum potential energy model, constructing a quantum wave function, and further converting the voxel position coordinates and the gray value of the fMRI brain image into particle distribution of a quantum system.
When the input data is a plurality of pieces of fMRI data to be tested (m >1), principal component analysis may be employed, the main steps of which are:
(1) normalization: calculating the mean value of each column of the matrix M, subtracting the mean value corresponding to the column from each element of the column, and normalizing, wherein the normalized matrix is marked as M';
(2) calculating a covariance matrix C of the matrix M', calculating an eigenvalue lambda of the covariance matrix CiAnd orthogonalizing the eigenvector ai；
(3) The characteristic value lambda is measurediArranged from large to small such that λ1>λ2>…λiAnd the orthogonalized eigenvectors corresponding to the eigenvalues are also arranged according to the order of the eigenvalues, so that the ith principal component corresponding to the original matrix M is Fi＝ai'M'. N main components of the two-dimensional matrix M can be extracted as required for further analysis, the matrix output in the third step is F, and F has 67531 rows and n columns; when m is 1, the principal component analysis may not be performed, and this step may be skipped.
Specifically, the quantum wave function is:
wherein xi＝[β1,β2,…,βn]，β1,β2,…βnOf n principal components corresponding to ith voxelThe value, i.e. n elements of the ith row of the matrix M, x is an n-dimensional column vector space constructed from the input values, and if not specified, x is defaultediThe matrix is formed after principal component analysis is carried out on the two-dimensional matrix M; σ is the width parameter of the wave function, and the size of σ is related to the number of partitions.
Step 2.4: and inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of the particle space potential energy of the quantum system, and further changing the process of searching the center of the brain partition in the fMRI brain image into searching a minimum value point of the potential energy in the quantum system.
The form of Schrodinger equation is shown in formula (1)
Wherein H is a Hamiltonian, sigma is a width parameter of the wave function,
for Laplace operator, V (x) is space potential energy, psi is wave function describing quantum system, E is energy eigenvalue, E ═ d/2 is minimum possible eigenvalue, d is input data xiOf (c) is calculated. Constructing the quantum wave function in the fourth step
Inputting the formula (1), and solving the formula (1) to obtain the expression of V (x)
According to the principle of quantum mechanics, the lowest point of potential energy, i.e. the point where the quantum system is relatively stable, is often the point where the wave function takes the maximum value, and can be used as the center of the brain partition. Therefore, the process of searching the brain partition center in the fMRI image is changed into the process of searching the minimum value point of the potential energy in the quantum system.
Step 2.5: calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
specifically, the number of minimum points is controlled by setting a threshold of the minimum points, the number of minimum points after the threshold is set is recorded as l, and the minimum points are sequentially assigned to continuous label values 1,2 and … l from small to large according to x-axis, y-axis and z-axis position coordinates; wherein l is a positive integer greater than or equal to 1.
As shown in fig. 4(a) -4 (d), wherein fig. 4(a) is a partial diagram of a quantum potential energy model, and the quantum potential energy model in the partial diagram has a total of 1,2, 3, 4, and 5 potential energy minimum points, which can be used as the brain partition center; fig. 4(b) is a potential energy threshold, by setting the potential energy threshold, the minimum value points 2 and 4 do not reach the threshold, and only three minimum value points 1, 3, and 5 are left as the brain partition center after threshold screening. Fig. 4(c) shows the xy plane when z is 50, i.e., the 50 th layer transverse position view, the outer black boxes indicate fMRI scan fields, black is blank voxels, and white indicates effective fMRI voxels; fig. 4(d) is an equipotential surface of a cross-sectional view of layer 50, where the box is the potential minimum point, i.e., the center of the partition, passing a set threshold. The lines with the same gray level in the graph are planes formed by points with the same potential energy, namely equipotential surfaces, and the points in a certain potential energy range in the center of the partition can be associated to the center of the partition by setting the potential energy range, namely the equipotential surfaces, so that the partition of each voxel of the whole brain is completed.
Step 2.6: setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
step 2.7: outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
step 2.8: and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
In a specific implementation, the method further comprises:
step 2.9: and storing the result matrix as an NIfTI format file for output, and applying the NIfTI format file to subsequent analysis of fMRI functional connection and brain functional network.
In another embodiment, the method further comprises: calling an OpenGL interface, and accurately presenting a brain partition result on a three-dimensional MNI standard brain model through three-dimensional rendering; simultaneously displaying three views of an XZ plane, a YZ plane and an XY plane, and further obtaining three views of a sagittal position, a coronal position and a transverse position of a brain partition result, as shown in fig. 5(a) -5 (d), fig. 5(a) is a three-dimensional brain partition result graph; FIG. 5(b) is a cross-sectional view angle result chart; FIG. 5(c) is a sagittal view angle results plot; FIG. 5(d) is a coronary view angle result chart.
The functional magnetic resonance imaging brain partitioning method based on the quantum potential energy model utilizes the advantages of a quantum algorithm in analyzing and processing large data and high-dimensional data to convert brain partitioning into the quantum potential energy model, and clustering and partitioning are carried out on single tested fMRI data or a plurality of tested fMRI data through quantum calculation.
The invention also provides a functional magnetic resonance imaging brain partition system based on the quantum potential energy model.
The invention relates to a functional magnetic resonance imaging brain partition system based on a quantum potential energy model, which comprises a memory and a processor; the processor configured to perform the steps of:
(1) preprocessing the fMRI brain image;
specifically, the process of preprocessing the fMRI brain image includes:
the fMRI brain image input into the fMRI brain partition system based on the quantum potential energy model needs to be preprocessed. The fMRI brain image is a magnetic resonance brain image acquired by a fast imaging sequence such as a gradient echo planar imaging sequence and a spin echo sequence by using a blood oxygen level dependent technique.
Preprocessing employs Statistical Parametric Mapping (SPM) software commonly used for functional magnetic resonance image processing. In a particular embodiment, the process of pre-processing the fMRI brain image includes:
step 1.1: correcting a temporal layer of the fMRI brain images;
before correcting the time layer of the fMRI brain image, the method further comprises the following steps: and (3) converting the data format, namely converting the original DICOM format data into NIfTI format data commonly used by a computer.
Specifically, a Slice Timing module of the SPM is used to perform temporal layer correction on the data.
Step 1.2: the spatial layer of the fMRI brain image is corrected.
Specifically, the Realign module of the SPM is adopted to correct the spatial layer of the data.
Step 1.3: individual fMRI brain images are registered to the MNI spatial template.
Specifically, by using the normalation module of the SPM, the individual brain fMRI data can be registered to the Montreal Nerve Institute (MNI) standard brain space by three methods, namely, an EPI template, a structural image joint registration, or a differential homoembryo image fusion algorithm.
Step 1.4: and performing spatial smoothing on the fMRI brain image registered to the MNI spatial template.
Specifically, a smoothening module of the SPM is adopted, and a Gaussian kernel with the full width at half maximum can be selected to perform spatial processing on the image, wherein the full width at half maximum is 6-8 mm generally.
Step 1.5: and filtering the fMRI brain image after the spatial smoothing processing.
Specifically, the image data may be filtered using a band-selectable low-pass filter.
(2) And partitioning the preprocessed fMRI brain image by using a quantum potential energy model.
Specifically, as shown in fig. 2, the specific process of partitioning the preprocessed fMRI brain image by using the quantum potential energy model is as follows:
in a specific embodiment, as shown in fig. 2, a specific process of partitioning the preprocessed fMRI brain image by using the quantum potential energy model is as follows:
step 2.1: extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image;
specifically, the preprocessed fMRI brain image is dot-multiplied with a gray matter template in a standard MNI space, and a gray matter portion in the preprocessed fMRI brain image is extracted to obtain a gray matter image, as shown in fig. 3.
For example: and performing point multiplication on each preprocessed fMRI image to be tested and a binary gray matter template in a standard MNI space, extracting a gray matter part in the image, performing brain partition processing by adopting the gray matter image, and performing first-step gray matter extraction on the residual 67531 voxels in the image.
Step 2.2: converting the gray matter image into a two-dimensional matrix form M; the number of the rows is equal to the total prime number of the grey matter images, the number of the columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively.
Specifically, the three-dimensional gray matter image is sequentially converted into a two-dimensional matrix form of 67531 rows and 4m columns according to the x-axis position coordinates, y-axis position coordinates and the gray value of each voxel, wherein m represents the number of fMRI images, and when only one tested fMRI image exists, m is 1. Each row corresponds to a voxel, each 4 columns correspond to the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel, and the 67531 row-4M-column two-dimensional matrix is marked as M.
Step 2.3: and (3) taking the value of each column of the two-dimensional matrix M or the matrix formed after the principal component analysis of the two-dimensional matrix M as an input value of the quantum potential energy model, constructing a quantum wave function, and further converting the voxel position coordinates and the gray value of the fMRI brain image into particle distribution of a quantum system.
When the input data is a plurality of pieces of fMRI data to be tested (m >1), principal component analysis may be employed, the main steps of which are:
(1) normalization: calculating the mean value of each column of the matrix M, subtracting the mean value corresponding to the column from each element of the column, and normalizing, wherein the normalized matrix is marked as M';
(2) calculating a covariance matrix C of the matrix M', calculating an eigenvalue lambda of the covariance matrix CiAnd orthogonalizing the eigenvector ai；
(3) The characteristic value lambda is measurediArranged from large to small such that λ1>λ2>…λiAnd the orthogonalized eigenvectors corresponding to the eigenvalues are also arranged according to the order of the eigenvalues, so that the ith principal component corresponding to the original matrix M is Fi＝ai'M'. N main components of the two-dimensional matrix M can be extracted as required to be analyzed in the next step, the matrix output in the third step is recorded as F, and the F has 67531 rows and n columns; when m is 1, the principal component analysis may not be performed, and this step may be skipped.
Specifically, the quantum wave function is:
wherein xi＝[β1,β2,…,βn]，β1,β2,…βnN principal component values respectively corresponding to the ith voxel, i.e. n elements in the ith row of the matrix M, x is an n-dimensional column vector space constructed according to input values, and if no special description is given, x is defaultediA matrix F formed after principal component analysis is carried out on the two-dimensional matrix M; σ is the width parameter of the wave function, and the size of σ is related to the number of partitions.
Step 2.4: and inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of the particle space potential energy of the quantum system, and further changing the process of searching the center of the brain partition in the fMRI brain image into searching a minimum value point of the potential energy in the quantum system.
The form of Schrodinger equation is shown in formula (1)
Wherein H is a Hamiltonian, sigma is a width parameter of the wave function,
is Laplace operator, V (x) is space potential energy, psi is wave function describing quantum system, E is energy eigenvalueD/2 is the smallest possible eigenvalue, d is the input data xiOf (c) is calculated. Constructing the quantum wave function in the fourth step
Inputting the formula (1), and solving the formula (1) to obtain the expression of V (x)
According to the principle of quantum mechanics, the lowest point of potential energy, i.e. the point where the quantum system is relatively stable, is often the point where the wave function takes the maximum value, and can be used as the center of the brain partition. Therefore, the process of searching the brain partition center in the fMRI image is changed into the process of searching the minimum value point of the potential energy in the quantum system.
Step 2.5: calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
specifically, the number of minimum points is controlled by setting a threshold of the minimum points, the number of minimum points after the threshold is set is recorded as l, and the minimum points are sequentially assigned to continuous label values 1,2 and … l from small to large according to x-axis, y-axis and z-axis position coordinates; wherein l is a positive integer greater than or equal to 1.
As shown in fig. 4(a) -4 (d), wherein fig. 4(a) is a partial diagram of a quantum potential energy model, and the quantum potential energy model in the partial diagram has a total of 1,2, 3, 4, and 5 potential energy minimum points, which can be used as the brain partition center; fig. 4(b) is a potential energy threshold, by setting the potential energy threshold, the minimum value points 2 and 4 do not reach the threshold, and only three minimum value points 1, 3, and 5 are left as the brain partition center after threshold screening. Fig. 4(c) shows the xy plane when z is 50, i.e., the 50 th layer transverse position view, the outer black boxes indicate fMRI scan fields, black is blank voxels, and white indicates effective fMRI voxels; fig. 4(d) is an equipotential surface of a cross-sectional view of layer 50, where the box is the potential minimum point, i.e., the center of the partition, passing a set threshold. The lines with the same gray level in the graph are planes formed by points with the same potential energy, namely equipotential surfaces, and the points in a certain potential energy range in the center of the partition can be associated to the center of the partition by setting the potential energy range, namely the equipotential surfaces, so that the partition of each voxel of the whole brain is completed.
Step 2.6: setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
step 2.7: outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
step 2.8: and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
The processor is further configured to:
and storing the result matrix as an NIfTI format file for output, and applying the NIfTI format file to subsequent analysis of fMRI functional connection and brain functional network.
In a further embodiment of the method according to the invention,
the processor is further configured to:
calling an OpenGL interface, and accurately presenting a brain partition result on a three-dimensional MNI standard brain model through three-dimensional rendering; simultaneously displaying three views of an XZ plane, a YZ plane and an XY plane, and further obtaining three views of a sagittal position, a coronal position and a transverse position of a brain partition result, as shown in fig. 5(a) -5 (d), fig. 5(a) is a three-dimensional brain partition result graph; FIG. 5(b) is a cross-sectional view angle result chart; FIG. 5(c) is a sagittal view angle results plot; FIG. 5(d) is a coronary view angle result chart.
The functional magnetic resonance imaging brain partition system based on the quantum potential energy model utilizes the advantages of a quantum algorithm in analyzing and processing large data and high-dimensional data to convert the brain partition into the quantum potential energy model, and conducts clustering partition on single tested data or a plurality of tested fMRI data through quantum calculation.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (10)
1. A functional magnetic resonance imaging brain partitioning method based on a quantum potential energy model is characterized by comprising the following steps:
preprocessing the fMRI brain image;
partitioning the preprocessed fMRI brain image by using a quantum potential energy model, wherein the specific process comprises the following steps: extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image; converting the gray matter image into a two-dimensional matrix form M; the two-dimensional matrix M or the value of each column of the matrix formed after the principal component analysis of the two-dimensional matrix M is used as the input value of the quantum potential energy model to construct a quantum wave function, and further the voxel position coordinates and the gray value of the fMRI brain image are converted into the particle distribution of a quantum system;
inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of particle space potential energy of a quantum system, and further changing the process of searching for the center of a brain partition in a fMRI brain image into searching for a minimum value point of the potential energy in the quantum system;
calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
2. The functional magnetic resonance imaging brain partitioning method based on the quantum potential energy model is characterized in that the number of rows is equal to the total prime number of gray matter images, the number of columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively.
3. A method of functional mri brain segmentation based on quantum potential energy model as claimed in claim 2, characterized in that the method further comprises: calling an OpenGL interface, and accurately presenting a brain partition result on a three-dimensional MNI standard brain model through three-dimensional rendering; simultaneously displaying three views of an XZ plane, a YZ plane and an XY plane so as to obtain three views of a sagittal position, a coronal position and a transverse position of a brain partition result;
or the method further comprises: and outputting the partition result, wherein the partition result is output in an NIfTI format and is applied to fMRI functional connection and brain functional network analysis.
4. The functional magnetic resonance imaging brain partition method based on the quantum potential energy model as claimed in claim 2, wherein the gray matter part in the preprocessed fMRI brain image is extracted by dot multiplication of the preprocessed fMRI brain image and a gray matter template in a standard MNI space, so as to obtain a gray matter image.
5. The method as claimed in claim 2, wherein the quantum potential energy model-based functional magnetic resonance imaging brain partition method is characterized in that the quantum wave function is:
wherein xi＝[β1,β2,…,βn]，β1,β2,…βnN principal component values respectively corresponding to the ith voxel, i.e. n elements of the ith row of the matrix M, x being an n-dimensional column vector space constructed from the input values, xiThe matrix is formed after principal component analysis is carried out on the two-dimensional matrix M; σ is the width parameter of the wave function, and the size of σ is related to the number of partitions.
6. A method of functional mri brain segmentation based on quantum potential energy model as claimed in claim 2, characterized in that the method further comprises:
controlling the number of minimum value points by setting a threshold of the extreme value points, recording the number of the minimum value points after the threshold is set as I, and assigning the minimum value points to continuous label values 1,2 and … l from small to large according to x-axis, y-axis and z-axis position coordinates; wherein l is a positive integer greater than or equal to 1.
7. The functional magnetic resonance imaging brain partition method based on the quantum potential energy model, as recited in claim 1, wherein the process of preprocessing the fMRI brain image comprises:
correcting a temporal layer of the fMRI brain images;
correcting a spatial layer of the fMRI brain image;
registering individual fMRI brain images to an MNI spatial template;
performing spatial smoothing on the fMRI brain image registered to the MNI spatial template;
and filtering the fMRI brain image after the spatial smoothing processing.
8. A functional magnetic resonance imaging brain partition system based on a quantum potential energy model is characterized by comprising a memory and a processor; the processor configured to perform the steps of:
preprocessing the fMRI brain image;
partitioning the preprocessed fMRI brain image by using a quantum potential energy model, wherein the specific process comprises the following steps: extracting a gray matter part in the preprocessed fMRI brain image to obtain a gray matter image; converting the gray matter image into a two-dimensional matrix form M; the two-dimensional matrix M or the value of each column of the matrix formed after the principal component analysis of the two-dimensional matrix M is used as the input value of the quantum potential energy model to construct a quantum wave function, and further the voxel position coordinates and the gray value of the fMRI brain image are converted into the particle distribution of a quantum system;
inputting the constructed quantum wave function into a Schrodinger equation to obtain an expression of particle space potential energy of a quantum system, and further changing the process of searching for the center of a brain partition in a fMRI brain image into searching for a minimum value point of the potential energy in the quantum system;
calculating all minimum value points of the particle space potential energy of the quantum system as the center of the brain subarea;
setting a potential energy range, associating the voxels within the potential energy range from the center of the brain partition to the corresponding partition, and modifying the gray value of the voxels to be the label value corresponding to the center of the partition;
outputting a result matrix; the number of columns of the result matrix is integral multiple of 4, the multiple is equal to the number of fMRI brain images to be partitioned, and each 4 columns are respectively the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of a voxel and a corresponding label value; the number of rows is equal to the number of voxels, and each row corresponds to one voxel;
and projecting the corresponding voxels to a three-dimensional curved surface standard MNI brain model according to the x-axis, y-axis and z-axis position coordinates of the voxels in the result matrix, and displaying different colors by using different label values to obtain a brain partition result.
9. The functional magnetic resonance imaging brain partition system based on the quantum potential energy model, according to claim 8, wherein in the processor, the number of rows is equal to the total number of pixels of the gray matter image, the number of columns is an integral multiple of 4, and the multiple is equal to the number of fMRI brain images to be partitioned; each row represents a voxel, and each 4 columns represent the x-axis position coordinate, the y-axis position coordinate and the z-axis position coordinate of the voxel and the gray value of the voxel respectively.
10. The functional mri brain-partitioning system according to claim 8, wherein the process of partitioning the pre-processed fMRI brain image using the quantum potential energy model in the processor further comprises:
outputting a partition result, outputting the partition result in an NIfTI format, and applying the partition result to subsequent fMRI functional connection and brain functional network analysis;
or in the processor, the process of preprocessing the fMRI brain image comprises:
correcting a temporal layer of the fMRI brain images;
correcting a spatial layer of the fMRI brain image;
registering individual fMRI brain images to an MNI spatial template;
performing spatial smoothing on the fMRI brain image registered to the MNI spatial template;
and filtering the fMRI brain image after the spatial smoothing processing.
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