CN110018432B - Diffusion tensor-based neural imaging method and device and magnetic resonance imaging equipment - Google Patents
Diffusion tensor-based neural imaging method and device and magnetic resonance imaging equipment Download PDFInfo
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Abstract
The invention relates to a medical imaging technology, in particular to a diffusion tensor imaging method and device for processing nerve fiber reconstruction in a nerve complex distribution area and magnetic resonance equipment. The method adopts a multivariate high-order tensor model to describe the diffuse motion in the voxel and solves the directions of all fibers in the voxel by combining a high-order tensor decomposition theory. The invention is particularly suitable for reconstructing nerve fibers in a nerve complex distribution area, and can effectively treat the conditions of crossing, branching and the like of nerve fiber bundles. The invention has important application value in neuroscience, medical imaging and other aspects.
Description
Technical Field
The invention relates to the fields of neuroscience, medical modeling, medical image processing and the like, in particular to a diffusion tensor imaging method for processing nerve fiber reconstruction in a nerve complex distribution area, a corresponding image processing device and magnetic resonance imaging equipment comprising the image processing device. The method and the device are suitable for research on brain structure and function based on diffusion tensor imaging, reconstruction of nerve fibers, diagnosis and treatment of diseases of parts such as brain and heart, preoperative planning of clinical neurosurgery and the like.
Background
Magnetic Resonance (MR) is the most common method of measuring diffusion movement in a fluid environment. The method applies radio frequency pulse with a certain specific frequency to a sample in a static magnetic field to excite hydrogen protons in the sample to generate a magnetic resonance phenomenon. After stopping the pulse, the protons produce an MR signal during relaxation. And then the MR signals are received, spatially encoded and image reconstructed. That is, under the action of an external magnetic field, the nuclei of the H atoms in water spin, and due to dispersion motion (brownian motion), the H atoms with different dispersion displacements have different nuclear spins arranged differently, thereby causing different magnetic field signal attenuations. The dispersion displacement is measured indirectly by measuring the degree of signal attenuation in different directions in the field. In scientific research, the degree of diffusion is often characterized by the diffusion coefficient (diffusion coefficient) D. In homogeneous liquids, such as water, the diffusivity is the same in all directions, i.e., isotropic. However, in many fluid environments containing biological tissue, such as inside the brain, the diffusion coefficient is different in all directions, i.e., anisotropic. Diffusion Tensor Magnetic Resonance Imaging (DTMRI), referred to as Diffusion Tensor Imaging (DTI) for short, is a non-invasive imaging method that measures diffusion coefficients in multiple directions and water molecule movement. Its measurement of anisotropic fluid environments has been widely used to reconstruct the spatial structure of various biological tissues (e.g., white matter of the brain) and fibers.
In a complex anisotropic liquid environment, it is crucial to obtain the diffusion coefficients in different directions. Through a number of existing MRI measurements of biological tissue, it was found that the diffusion distance of molecules (mainly water molecules) in the direction parallel to the nerve fiber bundles (equal to the oriented fibrous tissue) is significantly greater than the diffusion distance in the direction perpendicular to the nerve fiber bundles at a given time. On the basis, the original DTI technology provides a simplified model for the complex anisotropic diffusion: and (4) a dispersion ellipsoid. I.e. within any one measurement voxel (pixel element), there is at most a small segment of the nerve fiber bundle (or other directed fibrous tissue). Under this assumption, the spatial envelope surface formed by the liquid molecules released from the voxel center through dispersion motion within a specified time is an ellipsoid, and the long axis direction of the ellipsoid is the direction of the nerve fiber bundle in the voxel. Under a simplified model of "diffusion ellipsoid", anisotropic diffusion motion can be represented by a second-order symmetric tensor. It has only six independent components, i.e., six diffusion coefficients. Any second-order symmetric tensor corresponds to a geometrically three-dimensional ellipsoid. The three eigenvalues of the second-order symmetric tensor are the three half-axis lengths of the corresponding ellipsoid. This is called the "dispersion ellipsoid" or "dispersion coefficient ellipsoid". Generally, complete 'dispersion ellipsoids' in pixel elements can be obtained through calculation by measuring the attenuation of the magnetic field strength in six different directions (two non-collinear). However, in consideration of errors due to various factors such as noise, in actual measurement, more directions are generally taken. Assuming that the attenuation of the magnetic field strength in N directions is measured in each pixel element, N linear equations can be obtained through sorting, and the optimal solution of six independent components of the second-order symmetric tensor can be obtained by using the least square method.
In the last two decades, DTI technology has played a crucial role in the field of medical imaging, but its mathematical model limitations are evident. The basic assumption of the DTI principle is that within any one voxel, there is at most a small segment of the nerve fiber bundle (or other directed fibrous tissue). However, in practical applications, the size of each voxel cannot be made too small in view of the efficiency of the calculation process and the spatial resolution. The spatial resolution of a typical MRI apparatus is 1-2 mm, but the size of the brain nerve fibers is in the order of 10-100 microns, that is, in each pixel element, the distribution of nerve fiber bundles may have a complex situation of crossing, branching and even multiple branches. At this point, the assumption of "diffuse ellipsoid" obviously no longer applies. For example, assume that there are two identical nerve fiber bundles A and B within a pixel element that intersect within the pixel element. If the DTI technology is used for measuring the dispersion motion of water molecules in the voxel, the long axis direction of the obtained 'dispersion ellipsoid' points to neither the A direction nor the B direction. This example illustrates that conventional DTIs, built on the "diffuse ellipsoid" assumption, yield erroneous results when dealing with the presence of nerve fiber bundle crossings within voxels. Similarly, if a fiber bundle is split or a plurality of fiber bundles are crossed in a voxel, the result obtained by the conventional DTI is not reliable. The case of diffuse motion in voxels is described by a second-order symmetric tensor, i.e. six independent diffusion coefficients to describe anisotropic diffusion which can be very complex, and the model is mathematically simplistic. On the other hand, if the diffusion in each direction in a voxel is described directly by a second-order symmetric tensor, it has been assumed in practice that the diffusions in different directions are not all independent, i.e., the diffusion motion there has some spatial symmetry, not complete anisotropy. Therefore, a high-order tensor model which selects the number of independent variables is adopted to describe the diffuse motion in the voxel, and the directions of all fibers in the voxel are solved by combining a high-order tensor decomposition theory. The method is particularly suitable for reconstructing nerve fibers of a nerve complex distribution area, the order of the high-order tensor is not limited in advance, and the reserved order can be freely selected according to the precision requirement.
Disclosure of Invention
Based on the above purpose and thought, the invention provides a diffusion tensor imaging method and an image processing device for processing nerve fiber reconstruction in a nerve complex distribution region, wherein the diffusion tensor imaging method can be called enhanced diffusion tensor imaging and is abbreviated as EDTI. Specifically, the present invention is realized as such.
A method of diffusion tensor-based neuroimaging, comprising:
step 2, calculating diffusion coefficients D in all sampling directions in the voxel according to the attenuation intensity of the signals;
step 3, calculating the dispersion displacement x in unit time in each sampling direction in the voxel according to the dispersion coefficient D;
step 4. selecting a basis function
And the expansion order n is combined with the dispersion displacement x in each sampling direction to restore the dispersion motion envelope surface in the voxel
θ，
Is a spatial parameter;
and 6, reconstructing the fiber distribution of the nerve according to the direction of the nerve fiber bundle.
According to an aspect of the present invention, there is provided an image processing apparatus based on a diffusion tensor, including:
the sampling unit is used for selecting a sampling scheme and measuring the attenuation intensity of the signal in each sampling direction in each voxel;
the calculating unit is used for calculating a dispersion coefficient D in each sampling direction in the voxel according to the attenuation intensity of the signal and calculating a dispersion displacement x in unit time in each sampling direction in the voxel according to the dispersion coefficient D;
a restoration unit for selecting the basis function
And the expansion order n is combined with the dispersion displacement x in each sampling direction to restore the dispersion motion envelope surface in the voxel
θ，
Is a spatial parameter;
a searching unit, which is used for determining the direction of the nerve fiber bundle in the voxel according to the restored diffusion motion enveloping surface;
a reconstruction unit for reconstructing a fiber distribution of a nerve according to a direction of the nerve fiber bundle.
According to another aspect of the present invention, there is provided a magnetic resonance imaging apparatus including an image processing device according to an embodiment of the present invention.
By the EDTI method and the EDTI device, a more detailed nerve fiber structure can be drawn, and richer information about fibers can be analyzed.
Drawings
FIG. 1 is a flow chart of a method of neuroimaging according to the invention;
fig. 2 is a block diagram of an example of the configuration of a medical image processing apparatus according to the present invention;
fig. 3 is a block diagram of a configuration example of a magnetic resonance imaging apparatus according to an embodiment of the present invention;
FIG. 4 is an alternative sampling scheme in the neuroimaging method of the present invention, namely: 12, 42, 162 and 642
And the sampling directions are uniformly distributed on the unit spherical surface. The sampling scheme in the specific implementation process is not limited to the above 4 sampling schemes.
FIG. 5 is a schematic geometric diagram of the 1-5 order basis functions of a three-dimensional spherical harmonic selected by an embodiment of the present invention;
fig. 6 is an image obtained by restoring a closed three-dimensional image by linear interpolation and discrete integration. The sampling scheme chosen was 162 sampling directions as shown in fig. 4;
FIGS. 7-9 are graphs comparing the imaging results of EDTI and DTI for a set of MR data sets (data sources: ISMRM-2015-Traco-challenge-data) for brain nerves (giving three views of nerve fiber imaging results, top down: top view, front view, left view, respectively);
fig. 10 is a comparison of local fiber reconstruction using the EDTI method with the other two imaging methods, QBI, QGI. From the same seed point, the EDTI recovers more fiber bundles in the red frame than QBI, QGI.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, is a flow chart of the neuroimaging method of the present invention, which includes the following steps:
step S110: the sampling scheme is determined by selecting a plurality of directions (e.g. 12, 42, 162, 642, etc. in fig. 4) uniformly distributed on the unit sphere, and measuring the attenuation of the signal intensity in these directions in each voxel by using the prior art. Such as Magnetic Resonance Imaging (MRI).
Step S120: calculating dispersion coefficients D in all directions according to the signal attenuation intensity obtained in the step (1),
Step S130: calculating the dispersion displacement x in unit time (1s) in each direction according to the dispersion coefficient D,
step S140: the envelope of the diffusion motion within the voxel is reconstructed from the diffusion displacements in a finite number of directions. For a three-dimensional envelope surface, taking one point inside the envelope surface to establish a coordinate system, the graph can be expressed as a radial length r and a direction unit vector
Functional relationship between
I.e. given direction
Can be composed of
The radial length r in that direction is determined. And function of
Can be unfolded into the following forms:
wherein D is1，D2...DrRespectively, a vector (first order tensor), a second order tensor … r order tensor. The form of the decomposition is similar to Taylor expansion (x is replaced by x
The higher derivative is replaced with a higher tensor). According to the irreducible decomposition in the theory of higher-order tensor decomposition, any higher-order tensor can be decomposed into a combination of a series of irreducible tensors,
can ultimately be expressed as a series of irreducible tensors and unit vectors
Sum of shrinkage of (c).
In the invention, the dispersion motion enveloping surface is set as
θ，
For spatial parameters, the following decomposition can be performed according to the above theory:
wherein the content of the first and second substances,
a complete set of orthogonal unfolded bases in three-dimensional space. In two dimensions, the substrate may be taken as a Fourier function (sinm θ, cosm θ), and the above equation is a Fourier expansion. a ismFor coefficient of expansion, from envelope surface
And a given substrate
The integral can be obtained. For the problems to be solved by the present invention, the unfolded substrate may also be taken as a three-dimensional spherical harmonic whose mathematical expression is as follows:
wherein
The method for reconstructing the dispersion motion envelope surface through dispersion displacement in the limited directions comprises the following specific steps:
(a) and dividing a grid on the unit spherical surface, wherein the node of the grid is the measuring direction. Basis function
(taking three-dimensional spherical harmonic expansion as an example) and the dispersion displacement in the node direction (obtained by calculation in step 130) are known, and the expansion coefficient a is calculated by an interpolation method and discrete integrationm,r,bm,r: in each grid, obtaining the dispersion displacement at the center of the grid by linear interpolation according to the dispersion displacement in the node direction; replacing the whole grid with the dispersion displacement, trigonometric function value and basis function value at the center of the grid
sinr θ, cosr θ and
approximate calculation of a by multiplying function value by grid aream,r,bm,rThe value of the integral in the expression on the grid; traversing all grids, and summing the integral values on the grids to obtain the expansion coefficient am,r,bm,r。
In addition, the grid can be further subdivided, the original large grid is divided into a plurality of small grids, and the dispersion displacement at the center of each small grid is obtained through dispersion displacement interpolation in the node direction of the large grid. Further, the expansion coefficient is calculated by multiplying the function value by the area of the small grid; besides linear interpolation, other interpolation methods such as quadratic interpolation, polynomial interpolation and the like can be adopted; besides the central point, the function value at other positions of the grid can be selected as the integral value (i.e. the function value on the whole grid is replaced by the integral value), for example, for a triangular grid, the Gaussian point in the triangular grid can be selected.
(b) From a substrate
And a calculated in (a)m,r,bm,rRestoring a diffusion envelope
For a general basis function, the above equation can be written as:
n is an expansion order, factors such as a basis function, precision requirements and calculation cost need to be considered comprehensively, and the factors are selected carefully, so that the error is large due to too low order, and the subsequent imaging quality is influenced; too high an order increases the amount of computation and slows down the entire imaging process. Conventional diffusion tensor imaging and its improved methods are also based on tensor models. For example, common high-angular resolution diffusion imaging and generalized diffusion tensor imaging, the former describes diffuse motion by using a set of second-order symmetric tensors, and the latter is based on a fourth-order or sixth-order tensor model. Although these methods also involve higher-order tensors, unlike the present invention, it is necessary to select the order of the tensor model in advance, and after the order is determined, only the tensor of that order is used to describe the diffuse motion without separating the lower-order information. For example, in generalized diffusion tensor imaging, if a sixth-order tensor model is selected, only one sixth-order tensor is used to describe the diffuse motion in a voxel, and low-order information is also contained in the sixth-order tensor; whereas, with the present invention, if the expansion order is 6, the information of the first six orders is stored in the expansion coefficient a, respectively1～a6In, combined basis functions
The calculation result is equivalent to one of a first-order tensor, a second-order tensor, a third-order tensor, a fourth-order tensor, a fifth-order tensor and a sixth-order tensor. Obviously, for describing diffuse motion in a voxel, it is more effective and more accurate to store information of each order in the tensor of the corresponding order than in the same higher-order tensor. This is also an advantage of the present invention over previous improvements.
Step S150: the direction of the nerve fiber bundles within the voxel is determined by the diffusion motion envelope. Due to basis function
Is continuous on a unit sphere, so that the restored dispersion motion envelope surface
As well as being continuous.
The parameters of the number of the lines theta are set,
the value range (theta: 0-2 pi,
0-pi) is equally divided into a plurality of parts to obtain a series of uniformly distributed points on the unit spherical surface. Traverse the envelope surface by
Calculating dispersion displacement of each point in the corresponding direction, and comparing the dispersion displacement of adjacent points in the corresponding direction; if the dispersion displacement in the direction corresponding to a certain point is larger than all adjacent points (dispersion displacement in the corresponding direction), the direction is the direction in which the dispersion displacement on the envelope surface takes the maximum value. Furthermore, the heat exchange can also be realized by directly passing
For the number of theta,
and (5) carrying out derivative calculation and determining the direction of the maximum value. This direction is the direction of the nerve fiber bundle within the voxel. There may be multiple such directions, all saved.
Step S160: the fiber distribution in space is plotted. Reconstruction of the nerve fibers can be accomplished using a fiber-tracing imaging method. Starting from a certain voxel, the operation is continued by proceeding a specified length along the direction of the nerve fiber bundle in the voxel to the next voxel. Until the boundary of the measurement space is reached; or the "diffusion envelope" within a voxel degenerates substantially to a spherical surface (i.e., the fluid environment within the voxel is isotropic, without nerve fiber bundles); or the angle between the nerve fiber bundles in the two connected voxels is greater than a predetermined threshold (typically 60 degrees). The directions of the nerve fiber bundles in the series of voxels are connected in space, so that the overall direction of the nerve fiber bundles in the space is obtained. If there are multiple directions stored in the voxel, the above operation is performed along each direction. All the voxels and all the directions in the voxels are traversed, and all the nerve fiber bundles in the space can be obtained.
As shown in fig. 2, it is a schematic structural diagram of the image processing apparatus of the present invention. The image processing apparatus 200 of the embodiment of the present invention includes a sampling unit 210, a calculating unit 220, a restoring unit 230, a searching unit 240, and a reconstructing unit 250. In the above description of the neuroimaging method, specific implementation procedures of some steps have been disclosed, and hereinafter, an overview of the units of the image processing apparatus is given without repeating some details that have already been discussed. Specifically, the method comprises the following steps: the image processing apparatus 200 includes:
a sampling unit 210, configured to select a sampling scheme, select multiple directions (e.g., 12, 42, 162, 642, etc. in fig. 4) uniformly distributed on a unit sphere, and measure the attenuation intensity of a signal in each sampling direction in each voxel;
a calculating unit 220 for calculating a diffusion coefficient D in each sampling direction within the voxel according to the attenuation intensity of the signal,
b is the instrument parameter, S0Is the raw signal intensity, S is the measured intensity; and calculating the dispersion displacement x in unit time in each sampling direction in the voxel according to the dispersion coefficient D,
a restoration unit 230 for selecting the basis function
And the expansion order n is combined with the dispersion displacement x in each sampling direction to recover the dispersion in the voxelEnvelope surface of motion
θ，
Is a spatial parameter; diffusion motion envelope surface in the recovery unit
The recovery is carried out by the following steps:
setting the envelope surface of the dispersion movement as
θ，
For spatial parameters, the following decomposition is done:
selecting expansion order n as basis function, calculating expansion coefficient a by means of linear interpolation, quadratic interpolation or polynomial interpolation and discrete integralmIn combination with basis functions
Restoring a diffusion motion envelope in said voxel
The basis function
Is a general family of perfect orthogonal functions, such as: fourier function, spherical harmonicFunction, ridge function, wavelet function. In calculating the discrete integration, the grid integration point is a point inside the grid, such as a grid center point or a gaussian point. In addition, when calculating the discrete integration, the discrete integration can be directly calculated on the original grid, or the original grid can be further subdivided.
A searching unit 240 for determining the direction of the nerve fiber bundle in the voxel according to the restored diffusion motion envelope; the direction of the nerve fiber bundle within the voxel is determined in the search unit 240 by: searching a maximum value on the diffusion motion enveloping surface, and determining the direction of the maximum value, wherein the direction of the maximum value is the direction of the nerve fiber bundle in the voxel. Or by directly aligning the reconstructed diffusion envelope
Derivative is taken to determine the direction of the maxima.
A reconstruction unit 250 for reconstructing a fiber distribution of a nerve according to a direction of the nerve fiber bundle. Reconstruction of the nerve fibers can be accomplished using a fiber-tracing imaging method. Starting from a certain voxel, the operation is continued by proceeding a specified length along the direction of the nerve fiber bundle in the voxel to the next voxel. Until the boundary of the measurement space is reached; or the "diffusion envelope" within a voxel degenerates substantially to a spherical surface (i.e., the fluid environment within the voxel is isotropic, without nerve fiber bundles); or the angle between the nerve fiber bundles in the two connected voxels is greater than a predetermined threshold (typically 60 degrees). The directions of the nerve fiber bundles in the series of voxels are connected in space, so that the overall direction of the nerve fiber bundles in the space is obtained. If there are multiple directions stored in the voxel, the above operation is performed along each direction. All the voxels and all the directions in the voxels are traversed, and all the nerve fiber bundles in the space can be obtained.
In addition, embodiments of the present disclosure also include a magnetic resonance imaging apparatus. As shown in fig. 3, the magnetic resonance imaging apparatus 300 includes a medical image processing device 200. The medical image processing apparatus 200 may be the configuration referring to the embodiment of fig. 2.
As an example, each step of the above-described neuroimaging method and each constituent module and/or unit of the above-described image processing apparatus may be implemented as software, firmware, hardware, or a combination thereof. In the case of implementation by software or firmware, a program constituting software for implementing the above method may be installed from a storage medium or a network to a computer having a dedicated hardware configuration, and the computer may execute various functions and the like when various programs are installed.
The invention also provides a program product with machine readable instruction codes stored. The instruction codes can be read and executed by a machine to execute the nerve imaging method according to the embodiment of the invention.
Accordingly, a storage medium carrying the above-described program product having machine-readable instruction code stored thereon is also included in the present disclosure. Including, but not limited to, floppy disks, optical disks, magneto-optical disks, memory cards, memory sticks, and the like.
In the foregoing description of specific embodiments of the invention, features described and/or illustrated with respect to one embodiment may be used in the same or similar way in one or more other embodiments, in combination with or instead of the features of the other embodiments.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, elements, steps or components, but does not preclude the presence or addition of one or more other features, elements, steps or components.
In the above embodiments and examples, numerical reference numerals have been used to indicate various steps and/or elements. It will be appreciated by those of ordinary skill in the art that these reference numerals are merely for convenience of description and drawing and do not denote any order or any other limitation.
While the present invention has been disclosed above by the description of specific embodiments thereof, it should be understood that all of the embodiments and examples described above are illustrative and not restrictive. Various modifications, improvements and equivalents of the invention may be devised by those skilled in the art within the spirit and scope of the appended claims. Such modifications, improvements and equivalents are also intended to be included within the scope of the present invention.
Claims (8)
1. A diffusion tensor-based neural imaging method is characterized in that: the method comprises the following steps:
step 1, selecting a sampling scheme, and measuring the attenuation intensity of signals in each sampling direction in each voxel;
step 2, calculating diffusion coefficients D in all sampling directions in the voxel according to the attenuation intensity of the signals; wherein the content of the first and second substances,
b is the instrument parameter, S0Is the raw signal intensity, S is the measured intensity;
step 3, calculating the dispersion displacement x in unit time in each sampling direction in the voxel according to the dispersion coefficient D; wherein the content of the first and second substances,
step 4. selecting a basis function
And the expansion order n is combined with the dispersion displacement x in each sampling direction to restore the dispersion motion envelope surface in the voxel
θ、
Is a spatial parameter; the basis function
Is a general complete orthogonal function family;
step 5, determining the direction of the nerve fiber bundle in the voxel according to the diffusion motion enveloping surface;
and 6, reconstructing the fiber distribution of the nerve according to the direction of the nerve fiber bundle.
2. The neuroimaging method of claim 1, wherein: the basis function
A fourier function, a spherical harmonic function, a ridge function or a wavelet function.
3. The neuroimaging method of claim 1, wherein: the nerve fiber distribution is reconstructed by a fiber tracer imaging method.
4. The neuroimaging method of claim 1, wherein: the expansion order n is 5-10.
5. An image processing apparatus based on a diffusion tensor is characterized in that: comprises the following units:
the sampling unit is used for selecting a sampling scheme and measuring the attenuation intensity of the signal in each sampling direction in each voxel;
the calculating unit is used for calculating a dispersion coefficient D in each sampling direction in the voxel according to the attenuation intensity of the signal and calculating a dispersion displacement x in unit time in each sampling direction in the voxel according to the dispersion coefficient D; wherein the content of the first and second substances,
b is the instrument parameter, S0Is the raw signal intensity, S is the measured intensity;
a restoration unit for selecting the basis function
And the expansion order n is combined with the dispersion displacement x in each sampling direction to restore the dispersion motion envelope surface in the voxel
θ、
Is a spatial parameter; the basis function
Is a general complete orthogonal function family;
a searching unit, which is used for determining the direction of the nerve fiber bundle in the voxel according to the restored diffusion motion enveloping surface;
a reconstruction unit for reconstructing a fiber distribution of a nerve according to a direction of the nerve fiber bundle.
6. The image processing apparatus according to claim 5, characterized in that: the basis function
A fourier function, a spherical harmonic function, a ridge function or a wavelet function.
7. The image processing apparatus according to claim 5, characterized in that: the expansion order n is 5-10.
8. A magnetic resonance imaging apparatus comprising an image processing device as claimed in any one of claims 5-7.
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