CN104282021A - Parameter error estimation method and device of magnetic resonance diffusion tensor imaging - Google Patents

Abstract

The invention provides a parameter error estimation method and device of magnetic resonance diffusion tensor imaging. The method comprises the steps that through magnetic resonance scanning, a diffusion weighted graph is collected; the diffusion tensor of each pixel point in the diffusion weighted graph is estimated according to the diffusion weighted graph; anisotropy coefficients and average diffusion coefficients are calculated according to the diffusion tensors; an error graph of the diffusion weighted graph is calculated; the errors of the diffusion tensors are calculated according to the diffusion tensors and the error graph of the diffusion weighted graph; the errors of the diffusion tensors, the anisotropy coefficients and the average diffusion coefficients are substituted into a preset parameter error calculation model to calculate and obtain the average diffusion coefficient errors and the anisotropy coefficient errors. According to the method and device, the distribution condition of the errors in a magnetic resonance diffusion imaging parameter graph can be visually expressed, and therefore image quality estimation of diffusion tensor imaging is facilitated.

Description

Parameter error estimation method and device for magnetic resonance diffusion tensor imaging

Technical Field

The invention relates to the technical field of magnetic resonance imaging, in particular to a parameter error estimation method and device for magnetic resonance diffusion tensor imaging.

Background

Magnetic resonance Diffusion Tensor Imaging (DTI) is a special form of magnetic resonance imaging that exploits the principle of free thermal motion anisotropy of water molecules in tissue to probe the microstructure of the tissue. As a novel noninvasive detection technology, DTI can be used for imaging tissues and organs such as nervous system, muscle and the like, and provides important imaging data for early diagnosis of major diseases such as multiple sclerosis, diffuse brain injury, liver tumor, myocardial infarction and the like.

The diffusion tensor imaging process is as follows: a set of data is first acquired by magnetic resonance, including a T2-weighted image (commonly referred to as a b0 image) and a diffusion-weighted image (DWI) obtained by applying diffusion gradients in N different directions, both of which have magnitudes satisfying a single exponential model:wherein S is₀B0 image, S DWI, b diffusion weighting factor, g diffusion gradient direction, D diffusion tensor, 3X3 symmetric matrix containing 6 unknowns; then, fitting the dispersion tensor by a least square method, wherein the number N of the dispersion weighted images is at least 6 because the dispersion tensor has 6 unknowns; and finally, calculating dispersion related parameters such as anisotropy coefficient (FA), average dispersion coefficient (MD) and the like by using the dispersion tensor for research and diagnosis, wherein the calculation formula of FA and MD is as follows:

MD＝(λ₁+λ₂+λ₃)/3

<math> <mrow> <mi>FA</mi> <mo>=</mo> <msqrt> <mn>3</mn> <mo>[</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> <mo>/</mo> <mn>2</mn> <mrow> <mo>(</mo> <msubsup> <mi>&lambda;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </msqrt> </mrow> </math>

λ_i(i ═ 1,2,3) are the three eigenvalues of the diffusion tensor matrix D. Because the traditional magnetic resonance diffusion tensor imaging technology does not have a parameter error estimation method of magnetic resonance diffusion tensor imaging, the error distribution condition of a diffusion tensor imaging parameter map is difficult to estimate.

Disclosure of Invention

Based on this, it is necessary to provide a parameter error estimation method and apparatus for magnetic resonance diffusion tensor imaging that realizes estimation of an error distribution of a diffusion tensor imaging parameter map.

A method of parameter error estimation for magnetic resonance diffusion tensor imaging, the method comprising:

acquiring a diffusion weighted graph through magnetic resonance scanning;

respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph;

respectively calculating an anisotropic coefficient and an average diffusion coefficient according to the diffusion tensor;

calculating an error map of the dispersion-weighted map;

calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map;

and substituting the error of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate and obtain an average diffusion coefficient error and an anisotropic coefficient error.

In one embodiment, the step of respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph includes:

acquiring a diffusion weighting factor and a diffusion gradient direction in a diffusion weighting graph;

and respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph by using a least square method according to the diffusion weighting factor and the diffusion gradient direction.

In one embodiment, the step of calculating the error map of the diffusion-weighted graph includes:

acquiring a signal-to-noise ratio in the dispersion weighted graph;

simulating a plurality of noise graphs according to the signal-to-noise ratio, and taking the amplitude of the noise graphs as an error graph of the dispersion-weighted graph.

In one embodiment, the method further comprises: the step of establishing a parameter error calculation model specifically comprises the following steps:

the method comprises the steps of converting diffusion parameters contained in a calculation formula of an average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula;

substituting the first calculation formula into an anisotropic coefficient calculation formula, and converting diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of a diffusion tensor matrix and a trace of a product of a diffusion tensor matrix transposition and the diffusion tensor matrix respectively to obtain a second calculation formula;

and deriving a parameter error calculation model represented by a diffusion tensor matrix according to an error transfer formula, a first calculation formula and a second calculation formula, wherein the parameter error calculation model comprises an average diffusion coefficient error calculation formula and an anisotropic coefficient error calculation formula.

In one embodiment, the average diffusion coefficient error is calculated by the following formula:

MD is mean dispersion coefficient error, D_kError that is diffusion tensor; the anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.

A parameter estimation apparatus for magnetic resonance diffusion tensor imaging, the apparatus comprising:

the image acquisition module is used for acquiring a dispersion weighted graph through magnetic resonance scanning;

the tensor estimation module is used for respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph;

the coefficient calculation module is used for respectively calculating an anisotropic coefficient and an average diffusion coefficient according to the diffusion tensor;

the error map calculation module is used for calculating an error map of the dispersion weighted map;

the first error calculation module is used for calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map;

and the second error calculation module is used for substituting the errors of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate and obtain an average diffusion coefficient error and an anisotropic coefficient error.

In one embodiment, the tensor estimation module comprises:

the parameter acquisition module is used for acquiring a diffusion weighting factor and a diffusion gradient direction in the diffusion weighting graph;

and the diffusion tensor estimation module is used for respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph by a least square method according to the diffusion weighting factor and the diffusion gradient direction.

In one embodiment, the error map calculation module includes:

the signal-to-noise ratio acquisition module is used for acquiring the signal-to-noise ratio in the dispersion weighted graph;

and the error map acquisition module is used for simulating a plurality of noise maps according to the signal-to-noise ratio and taking the amplitude of the noise maps as the error map of the dispersion weighted map.

In one embodiment, the apparatus further comprises: the calculation model establishing module is used for establishing a parameter error calculation model; the calculation model building module comprises:

the first calculation formula conversion module is used for converting the diffusion parameters contained in the calculation formula of the average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula;

the second calculation formula conversion module is used for substituting the first calculation formula into the anisotropic coefficient calculation formula, and converting the diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of a diffusion tensor matrix and a trace of a product of the transposition of the diffusion tensor matrix and the diffusion tensor matrix respectively to obtain a second calculation formula;

and the calculation model derivation module is used for deriving a parameter error calculation model represented by the diffusion tensor matrix according to the error transfer formula, the first calculation formula and the second calculation formula, wherein the parameter error calculation model comprises an average diffusion coefficient error calculation formula and an anisotropic coefficient error calculation formula.

In one embodiment, the average diffusion coefficient error is calculated by the following formula:

MD is mean dispersion coefficient error, D_kError that is diffusion tensor; the anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.

The parameter error estimation method and device for magnetic resonance diffusion tensor imaging can substitute the errors of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate the average diffusion coefficient error and the anisotropic coefficient error. Compared with the parameter estimation method without the magnetic resonance diffusion imaging in the traditional technology, the method and the device can intuitively express the error distribution condition in the magnetic resonance diffusion imaging parameter map, thereby facilitating the image quality evaluation of diffusion tensor imaging.

Drawings

FIG. 1 is a flow chart illustrating a method for estimating parameter errors in magnetic resonance diffusion tensor imaging according to an embodiment;

FIG. 2 is an error map of a diffusion weighted graph obtained from processing diffusion tensor imaging of a brain in one embodiment;

FIG. 3 is a diffusion tensor error map obtained by processing diffusion tensor imaging for the brain in one embodiment;

FIG. 4 is an average diffusion coefficient error plot obtained after processing diffusion tensor imaging for a brain in one embodiment;

FIG. 5 is an anisotropy coefficient error plot resulting from processing diffusion tensor imaging for a brain, under an embodiment;

FIG. 6 is a schematic diagram of a parameter estimation apparatus for magnetic resonance diffusion tensor imaging in one embodiment;

FIG. 7 is a diagram illustrating the structure of a tensor estimation module in one embodiment;

FIG. 8 is a block diagram of an error map calculation module in accordance with one embodiment.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The parameter error estimation for magnetic resonance diffusion tensor imaging needs to obtain a parameter error calculation model, and specifically, the parameter error calculation model establishment comprises the following steps:

the method comprises the steps of converting diffusion parameters contained in a calculation formula of an average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula; substituting the first calculation formula into an anisotropic coefficient calculation formula, and converting diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of a diffusion tensor matrix and a trace of a product of a diffusion tensor matrix transposition and the diffusion tensor matrix respectively to obtain a second calculation formula; and deriving a parameter error calculation model represented by a diffusion tensor matrix according to the error transfer formula, the first calculation formula and the second calculation formula, wherein the parameter error calculation model comprises an average diffusion coefficient error calculation formula and an anisotropic coefficient error calculation formula.

The average dispersion coefficient is calculated by the formula: MD ═ λ₁+λ₂+λ₃) (ii)/3, MD is the mean diffusion coefficient, wherein₁，λ₂，λ₃The eigenvalue is an eigenvalue of the diffusion tensor D, and the eigenvalue is a diffusion parameter.

In the conventional diffusion tensor model, the diffusion weighted graph s of the j-th_jThe image gray scale values of (a) can be expressed as:

$s_j=s_0{e}^{-b{g}_j^T{\mathrm{Dg}}_j}---\left(1\right)$

wherein S is₀B is the diffusion weighting factor, g_jIs the direction vector of the jth diffusion gradient, D is the diffusion tensor, D is a symmetric matrix of 3x3 (diffusion tensor matrix), $D=\left[\begin{array}{ccc}{D}_{\mathrm{xx}}& D_{\mathrm{xy}}& D_{\mathrm{xz}}\\ D_{\mathrm{yx}}& D_{\mathrm{yy}}& D_{\mathrm{yz}}\\ D_{\mathrm{zx}}& D_{\mathrm{zy}}& D_{\mathrm{zz}}\end{array}\right],$ wherein D is_mnSince (m, n ═ x, y, z) is called diffusion coefficient, the diffusion tensor of each pixel point of the diffusion weighted graph has six unknowns. The model in equation (1) is transformed into:

<math> <mrow> <msubsup> <mi>g</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msub> <mi>Dg</mi> <mi>j</mi> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>mj</mi> </msub> <msub> <mi>g</mi> <mi>nj</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>D</mi> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>j</mi> </msub> <mo>/</mo> <msub> <mi>s</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mi>b</mi> </mfrac> </mrow> </math>

applying diffusion gradients g in different directions_j(J ≧ 1.. gtoreq.J ≧ 6) obtaining a corresponding diffusion-weighted signal s_jA plurality of equations are combined and can be written asMatrix formWherein

<math> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <mn>2</mn> <msub> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <mn>2</mn> <msub> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mi>zj</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>t</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>g</mi> <mi>xJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>yJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>zJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>xJ</mi> </msub> <msub> <mi>g</mi> <mi>yJ</mi> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>xJ</mi> </msub> <msub> <mi>g</mi> <mi>zJ</mi> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>yJ</mi> </msub> <msub> <mi>g</mi> <mi>zJ</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

$B=-\frac{1}{b}{[\ln (s_1/s_0),\ln (s_2/s_0),...\ln (s_J/s_0)]}^T$

<math> <mrow> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>D</mi> <mi>xx</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>zz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yz</mi> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math>

Wherein,the value of D is estimated by the least square method,A⁺is defined as (A)^TA)^-1A^TThe corresponding diffusion tensor parameters can be obtained by D. The characteristic value of D is recorded as lambda_i(i ═ 1,2,3), according to the nature of the matrix tra (a) ═ Σ_iλ_iThe dispersion parameter can be expressed as the equation for D, i.e.

MD＝(λ₁+λ₂+λ₃) And/3 is tra (d)/3, tra (d) is a trace of the diffusion tensor matrix, which is the first calculation formula. Formula for substituting MD into formula for calculating anisotropy coefficientIn (1) obtaining

<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>FA</mi> <mo>=</mo> <msqrt> <mn>3</mn> <mo>[</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <mi>MD</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> <mo>/</mo> <mn>2</mn> <mrow> <mo>(</mo> <msubsup> <mi>&lambda;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <msqrt> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <msubsup> <mi>&lambda;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> </msqrt> </mtd> </mtr> </mtable> </mfenced> </math>

Wherein FA is the anisotropy coefficient, λ_i(i ═ 1,2,3) are the three eigenvalues of the diffusion tensor matrix D

Since D is a real symmetric matrix, matrix D is diagonalized with matrix C, i.e., C^TDC＝Λ，

Λ＝diag{λ₁,λ₂,λ₃"diag" refers to a diagonal matrix with the diagonal elements of λ₁,λ₂,λ₃T represents the transpose of the matrix, then <math> <mrow> <msup> <mi>&Lambda;</mi> <mi>T</mi> </msup> <mi>&Lambda;</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>C</mi> <mi>T</mi> </msup> <mi>DC</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msup> <mi>C</mi> <mi>T</mi> </msup> <mi>DC</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>C</mi> <mi>T</mi> </msup> <msup> <mi>D</mi> <mi>T</mi> </msup> <msup> <mi>CC</mi> <mi>T</mi> </msup> <mi>DC</mi> <mo>=</mo> <msup> <mi>C</mi> <mi>T</mi> </msup> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>DC</mi> <mo>=</mo> <mi>diag</mi> <mo>{</mo> <msubsup> <mi>&lambda;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>,</mo> <msubsup> <mi>&lambda;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>,</mo> <msubsup> <mi>&lambda;</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>}</mo> <mo>,</mo> </mrow> </math> Thus, it is possible to provideIs D^TA characteristic value of D, andthe expression is substituted into FA to obtain

Namely, the second calculation formula is obtainedWherein tra (D)^TD) The traces of the product of the diffusion tensor matrix are transposed for the diffusion tensor matrix.

The error transfer theory shows that: if q is { x₁,x₂...x_nThe equation of (1) and the error transfer formula of

x_iDenotes x_iThe error of (a) is detected,represents q vs. x_iQ represents the error of q.

And (3) deducing errors in the diffusion tensor D, FA and MD graphs according to the error transfer formula.

Let A⁺＝{a_kj},k＝1～6，c_j＝s_j/s₀，

<math> <mrow> <msub> <mi>&delta;c</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>s</mi> <mn>0</mn> </msub> </mfrac> <msqrt> <msup> <mrow> <mo>(</mo> <msub> <mi>&delta;s</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>s</mi> <mi>j</mi> </msub> <msub> <mi>s</mi> <mn>0</mn> </msub> </mfrac> <msub> <mi>&delta;s</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> Then <math> <mrow> <mi>&delta;B</mi> <mo>=</mo> <mo>{</mo> <msub> <mi>&delta;B</mi> <mi>j</mi> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <msup> <mrow> <mo>[</mo> <mfrac> <msub> <mi>&delta;c</mi> <mi>j</mi> </msub> <msub> <mi>c</mi> <mi>j</mi> </msub> </mfrac> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math>

Order to <math> <mrow> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>D</mi> <mi>xx</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>zz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yz</mi> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> </mrow> </math> The error in D can be expressed as:

<math> <mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>=</mo> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mi>J</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>kj</mi> </msub> <msub> <mi>&delta;B</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mi>J</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>a</mi> <mi>kj</mi> </msub> <msub> <mi>c</mi> <mi>j</mi> </msub> </mfrac> <msub> <mi>&delta;c</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </mrow> </math>

S₀the image signal-to-noise ratio is high, and the noise in the image signal-to-noise ratio is ignored, so that the error of D can be simplified as follows:

<math> <mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mi>J</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>a</mi> <mi>kj</mi> </msub> <msub> <mi>s</mi> <mi>j</mi> </msub> </mfrac> <msub> <mi>&delta;s</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </mrow> </math>

further, the error in MD can be expressed as:

i.e. the average dispersion coefficient error calculation formula, wherein MD is the average dispersion coefficient error, D_kError that is diffusion tensor;

the error of the FA can be expressed as:

<math> <mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>&delta;FA</mi> <mo>=</mo> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>FA</mi> </mrow> <msub> <mrow> <mo>&PartialD;</mo> <mi>D</mi> </mrow> <mi>k</mi> </msub> </mfrac> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> i.e. an anisotropic coefficient error calculation formula, wherein FA is the anisotropic coefficient error, FA is the anisotropic coefficient, tra (D) is the trace of the diffusion tensor matrix, and tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.

As shown in fig. 1, in one embodiment, a method for estimating parameter errors in magnetic resonance diffusion tensor imaging is provided, which includes the following steps:

step 101, acquiring a diffusion weighted graph through magnetic resonance scanning.

Specifically, a T2 weighted image S0 and a diffusion weighted graph Sj obtained by applying diffusion gradients in J different directions are obtained by scanning with a magnetic resonance scanner.

And step 102, respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph.

In this embodiment, the diffusion weighting factor and the diffusion in the diffusion weighted graph are obtainedA gradient direction; and respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph by using a least square method according to the diffusion weighting factor and the diffusion gradient direction. Specifically, the diffusion tensor estimated by the least square method is obtained according to the following formula

<math> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <mn>2</mn> <msub> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <mn>2</mn> <msub> <mi>g</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>z</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>y</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>g</mi> <mi>zj</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>x</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>x</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>g</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mrow> <mi>y</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>t</mi> <mrow> <mi>z</mi> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> <mtd> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>g</mi> <mi>xJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>yJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msubsup> <mi>g</mi> <mi>zJ</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>xJ</mi> </msub> <msub> <mi>g</mi> <mi>yJ</mi> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>xJ</mi> </msub> <msub> <mi>g</mi> <mi>zJ</mi> </msub> <mo>,</mo> </mtd> <mtd> <msub> <mrow> <mn>2</mn> <mi>g</mi> </mrow> <mi>yJ</mi> </msub> <msub> <mi>g</mi> <mi>zJ</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

$B=-\frac{1}{b}{[\ln (s_1/s_0),\ln (s_2/s_0),...\ln (s_J/s_0)]}^T$

<math> <mrow> <mover> <mi>D</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msub> <mi>D</mi> <mi>xx</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>zz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xy</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>xz</mi> </msub> <mo>,</mo> <msub> <mi>D</mi> <mi>yz</mi> </msub> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math>

Wherein b is a diffusion weighting factor, g is a diffusion gradient in different directions, and D is a diffusion tensor.

And 103, respectively calculating an anisotropic coefficient and an average diffusion coefficient according to the diffusion tensor.

Specifically, the average diffusion coefficient is calculated according to the formula MD ═ tra (d)/3, where MD is the average diffusion coefficient, and tra (d) represents the traces of the diffusion tensor matrix.

According to the formulaAnd calculating an anisotropy coefficient, wherein FA is the anisotropy coefficient, and λ 1, λ 2 and λ 3 are eigenvalues of the diffusion tensor D.

And step 104, calculating an error map of the diffusion weighted map.

In the embodiment, the signal-to-noise ratio in the dispersion weighted graph is obtained; and simulating a plurality of noise graphs according to the signal-to-noise ratio, and taking the amplitude of the noise graphs as an error graph of the dispersion-weighted graph. The signal-to-noise ratio (SNR) is the signal mean/noise variance, and therefore, the noise variance is the signal mean/SNR, a J-number of complex gaussian white noise maps having the same size as the dispersion weighted map are simulated according to the noise variance, and the modulus of the complex gaussian white noise maps is used as an error map of the dispersion weighted map, as shown in fig. 2, the error map of the dispersion weighted map obtained after the brain is processed by dispersion tensor imaging.

And 105, calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map. In this embodiment, according to the formulaError of diffusion tensor is calculated, D_kIs the error of the diffusion tensor. Fig. 3 shows a diffusion tensor error map obtained by processing diffusion tensor imaging of the brain.

And 106, substituting the dispersion tensor error, the anisotropic coefficient and the average dispersion coefficient into a pre-established parameter error calculation model to calculate and obtain an average dispersion coefficient error and an anisotropic coefficient error.

In this embodiment, the parameter error calculation model includes an average dispersion coefficient error calculation formula and an anisotropic coefficient error calculation formula, where the average dispersion coefficient error calculation formula is:MD is mean dispersion coefficient error, D_kThe mean diffusion tensor error map is an error map of the diffusion tensor obtained by processing the diffusion tensor imaging of the brain as shown in fig. 4.

The anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix, obtained by processing the diffusion tensor imaging of the brain as shown in fig. 5Anisotropy coefficient error map. The distribution of the error can be visually observed from the error map, for example, it can be clearly observed from fig. 4 that the error of the cerebrospinal fluid part is larger, and the error of other brain tissues is smaller.

The parameter error estimation method and device for magnetic resonance diffusion tensor imaging can substitute the errors of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate the average diffusion coefficient error and the anisotropic coefficient error. Compared with the parameter estimation method without the magnetic resonance diffusion imaging in the traditional technology, the method and the device can intuitively express the error distribution condition in the magnetic resonance diffusion imaging parameter map, thereby facilitating the image quality evaluation of diffusion tensor imaging.

As shown in fig. 6, in one embodiment, there is provided a parameter estimation apparatus for magnetic resonance diffusion tensor imaging, the apparatus comprising:

and an image acquisition module 60 for acquiring a diffusion weighted graph by magnetic resonance scanning.

And the tensor estimation module 61 is used for respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph.

And a coefficient calculating module 62, configured to calculate an anisotropic coefficient and an average diffusion coefficient respectively according to the diffusion tensor.

And an error map calculation module 63, configured to calculate an error map of the dispersion-weighted map.

And a first error calculation module 64 for calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map.

And a second error calculation module 65, configured to substitute the error of the diffusion tensor, the anisotropic coefficient, and the average diffusion coefficient into a pre-established parameter error calculation model to calculate an average diffusion coefficient error and an anisotropic coefficient error.

As shown in fig. 7, in one embodiment, tensor estimation module 61 includes:

and the parameter obtaining module 610 is configured to obtain a diffusion weighting factor and a diffusion gradient direction in the diffusion-weighted graph.

And the diffusion tensor estimation module 612 is configured to estimate the diffusion tensor of each pixel point in the diffusion weighted graph by using a least square method according to the diffusion weighting factor and the diffusion gradient direction.

As shown in fig. 8, in one embodiment, the error map calculation module 63 includes:

and a signal-to-noise ratio obtaining module 631, configured to obtain a signal-to-noise ratio in the dispersion-weighted graph.

And an error map obtaining module 632, configured to simulate a plurality of noise maps according to the signal-to-noise ratio, and use the amplitude of the noise maps as an error map of the dispersion weighted map.

The parameter estimation device for magnetic resonance diffusion tensor imaging further comprises: and the calculation model establishing module is used for establishing a parameter error calculation model. The calculation model building module comprises:

and the first calculation formula conversion module is used for converting the diffusion parameters contained in the calculation formula of the average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula.

And the second calculation formula conversion module is used for substituting the first calculation formula into the anisotropic coefficient calculation formula, and converting the diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of the diffusion tensor matrix and a trace of the product of the transposition of the diffusion tensor matrix and the diffusion tensor matrix respectively to obtain a second calculation formula.

And the calculation model derivation module is used for deriving a parameter error calculation model represented by the diffusion tensor matrix according to the error transfer formula, the first calculation formula and the second calculation formula.

The parameter error calculation model comprises an average dispersion coefficient error calculation formula and an anisotropic coefficient error calculation formula. AverageThe dispersion coefficient error calculation formula is as follows:MD is mean dispersion coefficient error, D_kError that is diffusion tensor; the anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) For transferring the diffusion tensor matrixTrace of the product of the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.

The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method of parameter error estimation for magnetic resonance diffusion tensor imaging, the method comprising:

acquiring a diffusion weighted graph through magnetic resonance scanning;

respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph;

respectively calculating an anisotropic coefficient and an average diffusion coefficient according to the diffusion tensor;

calculating an error map of the dispersion-weighted map;

calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map;

and substituting the error of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate and obtain an average diffusion coefficient error and an anisotropic coefficient error.

2. The method according to claim 1, wherein the step of separately estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph comprises:

acquiring a diffusion weighting factor and a diffusion gradient direction in a diffusion weighting graph;

and respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph by using a least square method according to the diffusion weighting factor and the diffusion gradient direction.

3. The method of claim 1, wherein the step of computing an error map of the dispersion-weighted map comprises:

acquiring a signal-to-noise ratio in the dispersion weighted graph;

simulating a plurality of noise graphs according to the signal-to-noise ratio, and taking the amplitude of the noise graphs as an error graph of the dispersion-weighted graph.

4. The method of claim 1, further comprising: the step of establishing a parameter error calculation model specifically comprises the following steps:

the method comprises the steps of converting diffusion parameters contained in a calculation formula of an average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula;

substituting the first calculation formula into an anisotropic coefficient calculation formula, and converting diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of a diffusion tensor matrix and a trace of a product of a diffusion tensor matrix transposition and the diffusion tensor matrix respectively to obtain a second calculation formula;

and deriving a parameter error calculation model represented by a diffusion tensor matrix according to an error transfer formula, a first calculation formula and a second calculation formula, wherein the parameter error calculation model comprises an average diffusion coefficient error calculation formula and an anisotropic coefficient error calculation formula.

5. The method of claim 4, wherein the mean diffusion coefficient error is calculated by:MD is mean dispersion coefficient error, D_kError that is diffusion tensor; the anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.

6. A parameter estimation apparatus for magnetic resonance diffusion tensor imaging, the apparatus comprising:

the image acquisition module is used for acquiring a dispersion weighted graph through magnetic resonance scanning;

the tensor estimation module is used for respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph according to the diffusion weighted graph;

the coefficient calculation module is used for respectively calculating an anisotropic coefficient and an average diffusion coefficient according to the diffusion tensor;

the error map calculation module is used for calculating an error map of the dispersion weighted map;

the first error calculation module is used for calculating the error of the diffusion tensor according to the diffusion tensor and the error map of the diffusion weighted map;

and the second error calculation module is used for substituting the errors of the diffusion tensor, the anisotropic coefficient and the average diffusion coefficient into a pre-established parameter error calculation model to calculate and obtain an average diffusion coefficient error and an anisotropic coefficient error.

7. The apparatus of claim 6, wherein the tensor estimation module comprises:

the parameter acquisition module is used for acquiring a diffusion weighting factor and a diffusion gradient direction in the diffusion weighting graph;

and the diffusion tensor estimation module is used for respectively estimating the diffusion tensor of each pixel point in the diffusion weighted graph by a least square method according to the diffusion weighting factor and the diffusion gradient direction.

8. The apparatus of claim 6, wherein the error map calculation module comprises:

the signal-to-noise ratio acquisition module is used for acquiring the signal-to-noise ratio in the dispersion weighted graph;

and the error map acquisition module is used for simulating a plurality of noise maps according to the signal-to-noise ratio and taking the amplitude of the noise maps as the error map of the dispersion weighted map.

9. The apparatus of claim 6, further comprising: the calculation model establishing module is used for establishing a parameter error calculation model; the calculation model building module comprises:

the first calculation formula conversion module is used for converting the diffusion parameters contained in the calculation formula of the average diffusion coefficient into traces of a diffusion tensor matrix to obtain a first calculation formula;

the second calculation formula conversion module is used for substituting the first calculation formula into the anisotropic coefficient calculation formula, and converting the diffusion parameters contained in the anisotropic coefficient calculation formula into a trace of a diffusion tensor matrix and a trace of a product of the transposition of the diffusion tensor matrix and the diffusion tensor matrix respectively to obtain a second calculation formula;

and the calculation model derivation module is used for deriving a parameter error calculation model represented by the diffusion tensor matrix according to the error transfer formula, the first calculation formula and the second calculation formula, wherein the parameter error calculation model comprises an average diffusion coefficient error calculation formula and an anisotropic coefficient error calculation formula.

10. The apparatus of claim 9, wherein the mean diffusion coefficient error is calculated by:MD is mean dispersion coefficient error, D_kError that is diffusion tensor; the anisotropy coefficient error is calculated by the formula:

<math> <mrow> <mi>&delta;FA</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>FA</mi> </mrow> </mfrac> <msqrt> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </munder> <msup> <mrow> <mo>(</mo> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <mo>-</mo> <mfrac> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>4</mn> <mo>~</mo> <mn>6</mn> </mrow> </munder> <mn>2</mn> <msup> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <mi>tra</mi> <mrow> <mo>(</mo> <msup> <mi>D</mi> <mi>T</mi> </msup> <mi>D</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <msub> <mi>D</mi> <mi>k</mi> </msub> <msub> <mi>&delta;D</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </msqrt> <mo>,</mo> </mrow> </math> FA is the anisotropy coefficient error, FA is the anisotropy coefficient, tra (D) is the trace of the diffusion tensor matrix, tra (D)^TD) Traces for transposing the diffusion tensor matrix and multiplying the diffusion tensor matrix, D_kError of diffusion tensor, D_kIs a diffusion tensor matrix.