CN107219483B - A kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging - Google Patents

A kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging Download PDF

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CN107219483B
CN107219483B CN201710268833.XA CN201710268833A CN107219483B CN 107219483 B CN107219483 B CN 107219483B CN 201710268833 A CN201710268833 A CN 201710268833A CN 107219483 B CN107219483 B CN 107219483B
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kurtosis
diffusion
radial
coefficient
tensor
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陈元园
赵欣
张�雄
刘亚男
何峰
周鹏
綦宏志
明东
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Tianjin University
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Abstract

A kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging, comprising: tensor is estimated by diffusion kurtosis imaging model according to initial data；Sagittal plane is defined according to diffusion tensor matrices D；Obtain the distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane；Calculate radial kurtosis KpAnisotropy.The present invention will acquire MRI signal and after pretreatment, be calculated using method of the present invention, it can be deduced that kurtosis distribution anisotropy index in the sagittal plane based on diffusion tensor and kurtosis tensor.The index can reflect construction geometry feature of the object in cross section, can reflect accurate structure feature more richer than diffusion information.Using the index, by a variety of analyses such as statistical analysis, sorting algorithm can accurately reflect neural white matter micro-structure is abnormal, anisotropic elasticity in the uneven characteristic of cross section, the development of tissue and pathologic structure are changed etc..

Description

A kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging
Technical field
The present invention relates to a kind of radial kurtosis anisotropic quantitative approach.It is fixed more particularly to a kind of imaging of diffusion magnetic resonance Measure the radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging of parameter index.
Background technique
Detection and the acquisition of information of multiple modalities can be presented in magnetic resonance scanner to object or biological tissue, hydrone Diffusion property is the microcosmos structure characteristic that very universal phenomenon in biological tissue also can sufficiently reflect substance.Magnetic resonance diffusion Weighted imaging (MR-DWI, diffusion weighted imaging) is the technology of water diffusion behavior in detection object, Diffusion kurtosis imaging (DKI, diffusion kurtosis imaging) technology is exactly by the MRI letter in acquisition multiple directions Number, the diffusion profile situation of hydrone in object is obtained, and then study the intracorporal microcosmos structure characteristic of object.
It introduces high order tensor and high-order model carries out the reconstruction of micro-structure and measurement has been current information detection technology Development trend, but the introducing of high-order amount face be high-order amount parsing.Spread diffusion tensor obtained in kurtosis imaging It is second-order tensor, and kurtosis tensor is a tetradic, feature analysis is not resolved always.Pass through low order diffusion tensor With the combination of high-order kurtosis tensor, it perhaps can avoid and solve the problems, such as this.Meanwhile diffusion tensor detection technique is always all from complete Office sets out in space, rebuilds microstructure model.And in fact, the micro-structure of diffusion detection technique faced mostly is anisotropy , there are axially and radially two cardinal points.The parsing advantage of tensor is played in axial or radial part, perhaps can Obtain the stronger more sensitive more accurate micro structure testing index of specificity.
Summary of the invention
The technical problem to be solved by the invention is to provide a kind of structure that can reflect tranquillization more richer than diffusion information is special The radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging of sign.
The technical scheme adopted by the invention is that: a kind of radial kurtosis anisotropic quantitative square based on diffusion kurtosis imaging Method includes the following steps:
1) tensor is estimated by diffusion kurtosis imaging model according to initial data；
2) sagittal plane is defined according to diffusion tensor matrices D；
3) distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane is obtained；
4) radial kurtosis K is calculatedpAnisotropy, radial kurtosis anisotropy calculates as follows:
Wherein,It is average radial kurtosis value；P represents the number of unit vector, KpRepresent pth Radial kurtosis on a unit vector, RKA represent radial kurtosis anisotropic.
Initial data described in step 1) includes: b=0 without Diffusion-Weighted MR Imaging signal, under several non-zero b values Diffusion-Weighted MR Imaging signal, and the imaging signal comes from the same object.
Step 1) includes:
(1) respectively obtaining the apparent diffusion on N number of direction by diffusion kurtosis imaging model estimation according to initial data is Number DappWith apparent coefficient of kurtosis Kapp；
(2) apparent diffusion coefficient D is respectively obtainedappExpression formula and apparent coefficient of kurtosis KappExpression formula is as follows:
Wherein,
Due to symmetry, diffusion tensor matrices D only has 6 unknown quantitys, and kurtosis tensor matrix W only has 15 unknown quantitys,
In formula, x1、x2、x3The respectively coordinate of three dimensions of three-dimensional vector, i, j, k, l represent the number of dimension, value 1 Or 2 or 3, DijRepresent the i-th row jth column element of diffusion tensor matrices D, WijklRepresent i-th/j/k/l dimension of kurtosis tensor matrix W Spend element；
(3) to apparent diffusion coefficient DappExpression formula and apparent coefficient of kurtosis KappExpression formula is obtained by Least Square Method To all elements of diffusion tensor matrices D and kurtosis tensor matrix W.
Step 2) includes:
Diagonalization is carried out to diffusion tensor matrices D, obtains feature vector v1v2v3And eigenvalue λ1λ2λ3, and λ1≥λ2≥λ3 It is as follows:
Wherein maximum eigenvalue λ1Corresponding feature vector v1Direction definition is axial direction, is with axially vertical plane definition Sagittal plane.
5. a kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging according to claim 1, It is characterized in that, step 3) includes:
Unit circle is obtained by the unit center of circle of sagittal plane central point, chooses P unit being uniformly distributed on unit circle Vector xp, P >=3, p=1,2,3 ... P calculates the kurtosis value K on each unit vector directionp,
Wherein,It is unit vector xpThe diffusion coefficient in direction；It is diameter To average diffusion coefficient,Calculate the distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane.
A kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging of the invention, will acquire MRI signal And after pretreatment, calculated using method of the present invention, it can be deduced that be based on diffusion tensor and kurtosis tensor Sagittal plane in kurtosis distribution anisotropy's index.The index can reflect construction geometry feature of the object in cross section, can be anti- Reflect accurate structure feature (such as Fig. 1) more richer than diffusion information.It is more by statistical analysis, sorting algorithm etc. using the index Kind of analysis can accurately reflect neural white matter micro-structure is abnormal, anisotropic elasticity in the uneven characteristic of cross section, to tissue Development and pathologic structure change etc..
Detailed description of the invention
Fig. 1 is the schematic diagram that sagittal plane is defined according to the feature vector of amount of expansion matrix D diagonalization；
Fig. 2 is that the present invention is based on the flow charts of the radial kurtosis anisotropic quantitative approach of diffusion kurtosis imaging.
Specific embodiment
Below with reference to embodiment and attached drawing to a kind of radial kurtosis anisotropic based on diffusion kurtosis imaging of the invention Quantitative approach is described in detail.
As shown in Fig. 2, a kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging of the invention, including Following steps:
1) tensor is estimated by diffusion kurtosis imaging model according to initial data；
The initial data includes: b=0 without Diffusion-Weighted MR Imaging signal, the diffusion under several non-zero b values adds Imaging signal is weighed, and the imaging signal comes from the same object.Diffusion-Weighted MR Imaging signal acquisition tool it is directive according to Lai Xing.More accurate structural informations in order to obtain, actual acquisition will be on multiple directions that space uniform is distributed (N >=15) The Diffusion-Weighted MR Imaging signal acquisition of several (M >=2) non-zero b values is carried out, N is acquisition direction number here, and M is non-zero weighting b It is worth number.
Described estimates tensor by diffusion kurtosis imaging model according to initial data, comprising:
(1) respectively obtaining the apparent diffusion on N number of direction by diffusion kurtosis imaging model estimation according to initial data is Number DappWith apparent coefficient of kurtosis Kapp；
(2) apparent diffusion coefficient D is respectively obtainedappExpression formula and apparent coefficient of kurtosis KappExpression formula is as follows:
Wherein,
Due to symmetry, diffusion tensor matrices D only has 6 unknown quantitys, and kurtosis tensor matrix W only has 15 unknown quantitys,
In formula, x1、x2、x3The respectively coordinate of three dimensions of three-dimensional vector, i, j, k, l represent the number of dimension, value 1 Or 2 or 3, DijRepresent the i-th row jth column element of diffusion tensor matrices D, WijklRepresent i-th/j/k/l dimension of kurtosis tensor matrix W Spend element；
(3) to apparent diffusion coefficient DappExpression formula and apparent coefficient of kurtosis KappExpression formula is obtained by Least Square Method To all elements of diffusion tensor matrices D and kurtosis tensor matrix W.
2) sagittal plane is defined according to diffusion tensor matrices D；Include:
Diagonalization is carried out to diffusion tensor matrices D, obtains feature vector v1v2v3And eigenvalue λ1λ2λ3, and λ1≥λ2≥λ3 It is as follows:
Wherein maximum eigenvalue λ1Corresponding feature vector v1Direction definition is axial direction, is with axially vertical plane definition Sagittal plane, as shown in Figure 1.
3) distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane is obtained；Include:
Unit circle is obtained by the unit center of circle of sagittal plane central point, chooses P unit being uniformly distributed on unit circle Vector xp, P >=3, p=1,2,3 ... P calculates the kurtosis value K on each unit vector directionp,
Wherein,It is unit vector xpThe diffusion coefficient in direction；It is diameter To average diffusion coefficient,The distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane is calculated, such as Shown in Fig. 1.
4) radial kurtosis K is calculatedpAnisotropy,
Radial kurtosis anisotropy (Radial Kurtosis Anisotropic, RKA) calculates as follows:
Wherein,It is average radial kurtosis value；P represents the number of unit vector, KpRepresent pth Radial kurtosis on a unit vector, RKA represent radial kurtosis anisotropic.

Claims (3)

1. a kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging, which comprises the steps of:
1) tensor is estimated by diffusion kurtosis imaging model according to initial data；
2) sagittal plane is defined according to diffusion tensor matrices D, comprising:
Diagonalization is carried out to diffusion tensor matrices D, obtains feature vector v1v2v3And eigenvalue λ1λ2λ3, and λ1≥λ2≥λ3It is as follows:
Wherein maximum eigenvalue λ1Corresponding feature vector v1Direction definition is axial, is radial with axially vertical plane definition Plane；
3) distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane is obtained, comprising:
Unit circle is obtained by the unit center of circle of sagittal plane central point, chooses P unit vector being uniformly distributed on unit circle xp, P >=3, p=1,2,3...P calculate the kurtosis value K on each unit vector directionp,
Wherein,It is unit vector xpThe diffusion coefficient in direction；It is radial flat Equal diffusion coefficient,Calculate the distribution of the diffusion coefficient and coefficient of kurtosis in sagittal plane；
4) radial kurtosis K is calculatedpAnisotropy, radial kurtosis anisotropy calculates as follows:
Wherein,It is average radial kurtosis value；P represents the number of unit vector, KpRepresent p-th of unit Radial kurtosis on vector, RKA represent radial kurtosis anisotropic.
2. a kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging according to claim 1, special Sign is that initial data described in step 1) includes: b=0 without Diffusion-Weighted MR Imaging signal, under several non-zero b values Diffusion-Weighted MR Imaging signal, and the imaging signal comes from the same object.
3. a kind of radial kurtosis anisotropic quantitative approach based on diffusion kurtosis imaging according to claim 1, special Sign is that step 1) includes:
(1) the apparent diffusion coefficient D on N number of direction is respectively obtained by diffusion kurtosis imaging model estimation according to initial dataapp With apparent coefficient of kurtosis Kapp；
(2) apparent diffusion coefficient D is respectively obtainedappExpression formula and apparent coefficient of kurtosis KappExpression formula is as follows:
Wherein,
Due to symmetry, diffusion tensor matrices D only has 6 unknown quantitys, and kurtosis tensor matrix W only has 15 unknown quantitys,
In formula, x1、x2、x3The respectively coordinate of three dimensions of three-dimensional vector, i, j, k, l represent the number of dimension, value 1 or 2 or 3, DijRepresent the i-th row jth column element of diffusion tensor matrices D, WijklRepresent i-th/j/k/l dimension member of kurtosis tensor matrix W Element；
(3) to apparent diffusion coefficient DappExpression formula and apparent coefficient of kurtosis KappExpression formula is expanded by Least Square Method Dissipate all elements of tensor matrix D and kurtosis tensor matrix W.
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