CN108523890B - Local field estimation method based on magnetic resonance dipole field spatial distribution - Google Patents
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Abstract
A local field estimation method based on magnetic resonance dipole field space distribution relates to nuclear magnetic resonance quantitative susceptibility imaging. Number of windings based on phase map; based on the standard deviation σ (r) of the gaussian convolution kernel modulated by the amplitude, gradient and number of wraps of the phase map; dividing the region of interest into a high susceptibility change region and a uniform susceptibility region based on the spatial information; the method can effectively remove the background fields of the strong magnetic field in different imaging directions and accurately estimate the local field, simultaneously reserves the integrity of brain tissues, and has an effect obviously superior to that of the existing method.
Description
Technical Field
The invention relates to nuclear magnetic resonance quantitative susceptibility imaging, in particular to a local field estimation method based on magnetic resonance dipole field spatial distribution.
Background
Magnetic susceptibility is an inherent property of a substance, can reflect the degree of magnetization of biological tissues under the action of an external Magnetic field, and is one of main signal sources of Magnetic Resonance Imaging (MRI). Because the magnetic susceptibility distribution of biological tissues is influenced by factors such as iron content, calcification and blood oxygen saturation of tissues, the magnetic susceptibility of different tissues of a human body and normal tissues and pathological tissues are different. The grey matter in human brain has iron deposition and shows paramagnetism, and the magnetic susceptibility value is positive; oxygenated hemoglobin in the blood vessel is diamagnetic and deoxygenated hemoglobin is paramagnetic; the main component of white matter of the brain is myelin, which exhibits diamagnetism, with negative magnetic susceptibility values.
Magnetic Susceptibility of tissue is commonly detected in MRI using Susceptibility Weighted Imaging (SWI) and R2 images, but these methods are less sensitive and specific, and SWI is only a qualitative measure of Susceptibility change, while R2 images are susceptible to intra-voxel spin phase dispersion at the edges of strong gradients. Quantitative Susceptibility imaging (QSM) utilizes phase information which is usually ignored in the past, obtains the change characteristic of a local magnetic field through the preprocessing of phase unwrapping and background field removal, and obtains a Quantitative Susceptibility diagram of a tissue through complex field-to-source inversion calculation[1,2]. QSM technology can effectively overcome the defects of SWI and R2, and has been widely applied to cerebral hemorrhage and multiple sclerosisIn the research of chemical symptoms and various degenerative nerve diseases, the clinical diagnosis of the diseases is of great significance[3-6]The magnetic resonance imaging system is complementary with the traditional MRI imaging technology, and shows high clinical value and application prospect.
QSM technology is a research hotspot in the field of medical imaging nowadays, and one of the main problems faced by QSM technology is how to remove the influence of a background field outside a Volume of Interest (VOI) on a field inside the VOI, so as to obtain an accurate local field estimation. The accuracy of the local field estimation directly affects the QSM accuracy. According to the physical principle of the background field, there are two important local field estimation models: one is dipole field Projection (PDF)[7]The method assumes that a local field and a background field are mutually orthogonal in the VOI, the inner product of the local field and the background field is zero, and the local field can be obtained by an equation optimization solution; second, it is a Phase data complex Harmonic Artifact suppression method (SHARP) for Phase data[8]Because of the use of the sphere mean convolution kernel, the voxel of the SHARP method in the edge region of the VOI is convolved with invalid signals outside the VOI, resulting in edge region ambiguities of equal diameter to the convolution kernel, and therefore these ambiguities are removed in the QSM reconstruction[9]V-SHARP method for changing convolution kernel radius[10]And corresponding improvement measures and the like all achieve certain effects.
Because the strong susceptibility value of the junction of the brain tissue and the paranasal sinus or the skull is very high, and the spatial distribution of the dipole field is related to the geometric structure and the imaging direction of the tissue, the strong dipole field generated in the region generates strong interference in different directions on the peripheral brain tissue along with the change of the imaging angle of the human brain, and has serious influence on the correct estimation of the local field[11]. By adopting the method, more serious phase residues are left on the local field patterns of the regions, and the phase residues are left in the subsequent QSM reconstructionSevere susceptibility artifacts, masking normal tissue structure details. To eliminate such effects, the above methods all require masking the brain tissue in the area to reduce phase residuals, thereby reducing QSM artifacts. However, the adoption of masks with different directions can cause serious loss of brain tissues, so that complete brain diagnostic information cannot be acquired, which is not favorable for the clinical application of QSM technology. Therefore, when the background field of the strong magnetic field in the multi-direction imaging is removed and the local field is accurately estimated, the above methods have the defects, or the brain tissue is seriously lost, or the phase residue is serious, and all the defects need to be further improved.
Reference documents:
[1]Shmueli,K.,de Zwart,J.A.,van Gelderen,P.,Li,T.Q.,Dodd,S.J.,Duyn,J.H.,2009.Magnetic susceptibility mapping of brain tissue in vivo using MRIphase data.Magn.Reson.Med.62,1510-1522.
[2]Haacke,E.M.,Liu,S.F.,Buch,S.,Zheng,W.L.,Wu,D.M.,Ye,Y.Q.,2015.Quantitative susceptibility mapping:current status and futuredirections.Magn.Reson.Imag.33,1-25.
[3]He,N.Ling,H.Ding,B.Huang,J.Zhang,Y.Zhang,Z.Liu,C.Chen,K.Yan,F,2015.Region-Specific Disturbed Iron Distribution in Early IdiopathicParkinson’s Disease Measured by Quantitative Susceptibility Mapping,HumanBrain Mapping,36,4407-4420.
[4]Wang,Y.,Liu,T.,2015.Quantitative susceptibility mapping(QSM):decoding MRI data for a tissue magnetic biomarker.Magn.Reson.Med.73,82-101.
[5]Bergen,J.,Hua,J.,Lim,I.A.L,Jones,C.K.,Margolis,R.L.,Ross,C.A.,P.C.M.van Zijl,Li,X,2016.Quantitative susceptibility mapping suggests alteredbrain iron in premanifest Huntington disease.Am.J.Neuroradiol.37,789-796.
[6]Lotfipour A K,Wharton S,Schwarz S T,et al,2012.High resolutionmagnetic susceptibility mapping of the substantia nigra in Parkinson'sdisease.[J].Journal of Magnetic Resonance Imaging Jmri,35,48–55.
[7]Liu,T.,Khalidov,I.,de Rochefort,L.,Spincemaille,P.,Liu,J.,Tsiouris,A.J.,2011.A novel background field removal method for MRI usingprojection onto diplole fields(PDF).NMR Biomed.24,1129-1136.
[8]Schweser,F.,Deistung,A.,Lehr,B.W.,Reichenbach,J.R.,2011.Quantitative imaging of intrinsic magnetic tissue properties using MRIsignal phase:an approach to in vivo brain iron metabolism？NeuroImage.54,2789-2807.
[9]Zhou,D.,Liu,T.,Spincemaille,P.,Wang,Y.,2014.Background fieldremoval by solving the Laplacian boundary value problem.NMR Biomed.27,312-319.
[10]Wu,B.,Li,W.,Guidon,A.,Liu,C.L.,2012.Whole brain susceptibilitymapping using compressed sensing.Magn.Reson.Med.67,137-147.
[11]Bao,L.Li,X.Cai,C.Chen,Z.,P.C.M.V.Zijl,2016.QuantitativeSusceptibility Mapping Using Structural Feature Based CollaborativeReconstruction(SFCR)in the Human Brain,IEEE Transactions on MedicalImaging.35,2040-2050.
disclosure of Invention
The invention aims to provide a local field estimation method based on magnetic resonance dipole field spatial distribution.
The invention comprises the following steps:
1) the winding number based on the phase diagram is modeled as follows:
in the model, K (r) is the phase diagram winding number, gamma is the gyromagnetic ratio, TE is the echo time, BΔIs the total field value of the dipole field,
for the phase diagram after the unwrapping process,
for winding phase diagrams, W [. cndot.)]Is a phase winding operator;
2) based on the standard deviation σ (r) of the gaussian convolution kernel modulated by the amplitude, gradient and number of wraps of the phase map, the model is:
in the model, C is a positive tuning constant, BΔIn order to be the total field map,
a gradient of the total field map, being real numbers greater than zero, K (r) ∈ [0,1]For normalized phase-winding numbers, the convolution kernel thus established in relation to voxel-by-voxel spatial information is expressed as:
wherein (x, y, z) is the spatial coordinates of the Gaussian kernel points;
3) based on the spatial information, the region of interest is divided into a high magnetic susceptibility change region and a uniform magnetic susceptibility region, and the model is as follows:
in the model, the model is divided into a plurality of models,
is reciprocal of sigma (r), and is recorded as
For the region division threshold, defined as
Wherein,
and σmaxRespectively represent
The mean and maximum values of; as a unit impact function, BintIs a local field, and is,
in the case of a temporary variable,
representing a convolution operation; by passing
Dividing the region of interest into regions of high susceptibility variation D1And a region of uniform magnetic susceptibility D2And respectively carrying out convolution operation with the Gaussian convolution kernel and the spherical mean value convolution, and removing the background field to obtain a local field.
In step 1), the number of windings of the phase map may include the evolution results of different field map changes at different times, which may be used for local field estimation at any echo time.
In step 2), the spatial information composed of the amplitude, the gradient and the number of windings of the phase map can modulate the standard deviation of the gaussian convolution kernel voxel by voxel, and when the larger the spatial information value is, the stronger background field exists in the region, the smaller the gaussian standard deviation is obtained, that is, the weight of the corresponding gaussian kernel sphere center is high and the peripheral point value is rapidly attenuated, so that the background field can be better suppressed, and the accurate local field estimation can be obtained.
In the step 3), the region of interest is divided into a high magnetic susceptibility change region and a uniform magnetic susceptibility change region based on the spatial information, so that the operation speed of the algorithm can be increased, and the spatial information considers field map components in different imaging directions and can be used for multi-directional local field estimation.
The method utilizes the spatial information of the phase diagram, namely introduces the amplitude, the gradient and the winding number of the phase diagram to modulate the standard deviation of the Gaussian convolution kernel one by one voxel, and further the weights of the spherical center point and other points of the phase diagram.
Drawings
Fig. 1 is a data diagram of human brain in different imaging directions. (a) Unwrapped phase map, (b) spatial information value map, (c) local field map, (d) susceptibility map.
Fig. 2 is a simulation data experiment chart. (a) True susceptibility map, full field map and local field map for direction 1, (b) true susceptibility map, full field map and local field map for direction 2, (c) true susceptibility map, full field map and local field map for direction 3, (d) true susceptibility map, full field map and local field map for direction 4.
FIG. 3 shows the local field estimation result of simulation data. (a) The method comprises the following steps of (a) calculating a local field map by using three methods of PDF, R-SHARP and iRSHARP in the direction 1, (b) calculating a local field map by using three methods of PDF, R-SHARP and iRSHARP in the direction 2, (c) calculating a local field map by using three methods of PDF, R-SHARP and iRSHARP in the direction 3, and (d) calculating a local field map by using three methods of PDF, R-SHARP and iRSHARP in the direction 4.
Fig. 4 shows the estimation result of the local field of the human brain in different imaging directions. (a) Phase map after 4 directional unwrapping, (b) local field estimation by PDF method, (c) local field estimation by R-SHARP method, (d) local field estimation by iRSHARP method.
Fig. 5 shows the reconstruction result of the magnetic susceptibility of the human brain in different imaging directions. (a) A susceptibility result of local field reconstruction estimated from PDF, (b) a susceptibility result of local field reconstruction estimated from R-SHARP, (C) a susceptibility result of local field reconstruction estimated from iRSHARP.
Detailed Description
The following examples will further illustrate the present invention with reference to the accompanying drawings.
Figure 1 shows a data map of human brain for different imaging directions. The invention can effectively remove the background field, obtain the accurate local field and protect the integrity of the brain tissue. The method comprises the following specific implementation processes:
1) first, a numerical simulation experiment was performed. A 128 x 64 matrix was created in which a large ellipsoid was embedded to simulate the human brain, 5 smaller ellipsoids were regenerated to simulate sinus, blood vessels, substantia nigra, globus pallidus and caudate nucleus, respectively, with corresponding susceptibilities of 9.4ppm, 0.3ppm, 0.16ppm, 0.1ppm and 0.05ppm, the susceptibilities of the remaining parts of the brain region were set to 0ppm, and 1 additional ellipsoid with a susceptivity value of 9.4ppm was added outside the VOI to simulate other background field sources, and gaussian noise with SNR of 40 was added to the simulation data. The sinuses were rotated 10 deg. to the left, 20 deg. to the right, and 10 deg. backwards, respectively, to mimic different imaging orientations, as shown in fig. 2.
2) Next, L iu, the PDF (projection on to polar field) method proposed in t. 2011, and the R-SHARP (topological Artifact Reduction for phase Data Using regional Adaptive kernel) method proposed in 2017 are selected as a comparison to illustrate that the local field estimation algorithm based on the spatial distribution of the magnetic resonance Dipole field according to the present invention can effectively remove the background field of the strong magnetic susceptibility Region under multi-directional imaging, and can obtain an accurate local field, on the local field map (fig. 3), as shown by arrows, the local field estimation algorithm has strong phase residuals around the simulated nasal sinus, which will generate severe magnetic susceptibility, and the R-SHARP in the first direction can well remove the background field, but has small phase residuals in the other three directions, as shown in the enlarged diagram of fig. 3, the PDF Artifact method has no phase residual in four directions, and the running time is less than that of the R-SHARP in the first direction.
To verify the local field estimation of the method, the processing results of the three methods were quantitatively evaluated using Root Mean Square Error (RMSE). Wherein the root mean square error is defined as:
wherein, BintRepresenting the calculated local field map, B0Representing the real local field and n is the number of calculation points.
As can be seen from Table 1, the iRSHARP delocalized field estimate is better than the other two methods and the run time is shorter than R-SHARP.
Table 1: RMSE and run-time comparison of simulation plot experiments
| Method of producing a composite material | Direction 1 | |
Direction 3 | Direction 4 | Time(s) |
| 0.225 | 0.201 | 0.202 | 0.223 | 37.8 | |
| R-SHARP | 0.145 | 0.145 | 0.145 | 0.146 | 122.1 |
| iRSHARP | 0.144 | 0.144 | 0.144 | 0.144 | 58.9 |
3) The experimental data are acquired on a human body imager with Philips 7T and 32 channels, a three-dimensional gradient echo sequence is adopted, imaging parameters are TR/TE 1/delta TE which are 45ms, 2ms, 2ms and 8 echoes, an imaging visual field is 220mm × 220mm × 110mm, the layer thickness is 1mm, and a data matrix is 224 × 224 × 110. fig. 4 lists local field estimation results of three methods of PDF, R-SHARP and iRSHARP under different imaging directions, brain tissues above a nasal sinus of PDF leave obvious directional phase residues, and strong phase residues also exist in a brain tissue edge region, an R-SHARP method can well remove a background field in a direction 1, but weak phase residues exist in other three directions, an iRSHARP method can well remove artifacts in four directions, a local magnetization field obtained is subjected to magnetization inversion, a magnetization field obtained is shown in a brain tissue edge region 5, the magnetization field obtained by a magnetic field obtained by a background field reconstruction method can well remove the artifacts, and the residual magnetization of the brain tissues in other directions can be well reconstructed by a background magnetic field reconstruction method (RSHARP, RSRP is shown in a magnetic field) which can also be obtained by a visual residual field reconstruction method, and a residual magnetic field can be well removed by a visual field obtained by a visual residual field reconstruction method (RSRP) which is shown in a magnetic field obtained by a visual field obtained by a magnetic field obtained by a visual residual field obtained by a visual field reconstruction method) and a visual residual field reconstruction method, wherein the residual field is shown by a magnetic.
In the magnetic resonance quantitative magnetic susceptibility imaging, the dipole field distribution of brain tissues is related to the geometrical structure of the tissues and the included angle between the tissues and a main magnetic field, so that strong background field interferences in different directions are generated on peripheral brain tissues by strong magnetic susceptibility regions such as nasal sinuses, the junction of the tissues and skull bones and the like along with the change of the imaging included angle between the head and the main magnetic field, and the accurate estimation of a local field is influenced. A local field estimation algorithm based on magnetic resonance dipole field spatial distribution utilizes spatial information composed of gradient values, phase amplitude values and normalized phase winding numbers of a phase diagram to detect and obtain a strong magnetic susceptibility region in brain tissues. The spatial information contains the evolution results of dipole fields at different time and different directions, so that the central weight of the Gaussian convolution kernel is modulated by the spatial information, the background fields of the high magnetic susceptibility region at different directions can be effectively eliminated, the local field information generated by the tissue is accurately reserved, and the magnetic susceptibility artifact is effectively inhibited. Therefore, in a multidirectional human brain data experiment, the method does not need to remove strong magnetic tissue around the paranasal sinuses and can ensure the integrity of human brain tissue, the effect is obviously superior to other existing methods, and the method has potential clinical application value.
Claims (4)
1. A local field estimation algorithm based on magnetic resonance dipole field spatial distribution is characterized by comprising the following steps:
1) based on the number of wraps in the phase map, the model is,
in the model, K (r) is the phase diagram winding number, gamma is the gyromagnetic ratio, TE is the echo time, BΔIs the overall field pattern of the dipole field,
for the phase diagram after the unwrapping process,
for winding phase diagrams, W [. cndot.)]Is a phase winding operator, and r is the space coordinate of a voxel in a dipole field total field image;
2) based on the standard deviation σ (r) of the gaussian convolution kernel modulated by the amplitude, gradient and number of wraps of the phase map, the model is:
in the model, C is a positive tuning constant, BΔIs the overall field pattern of the dipole field,
is a dipoleThe gradient of the total field map is a real number greater than zero, KN(r)∈[0,1]The number of wraps for the normalized phase map; the convolution kernel thus established in relation to the voxel-wise spatial information is represented as:
wherein σ (r) is a standard deviation of a Gaussian convolution kernel;
3) based on the spatial information, the region of interest is divided into a high magnetic susceptibility change region and a uniform magnetic susceptibility region, and the model is as follows:
in the model, the model is divided into a plurality of models,
is reciprocal of sigma (r), and is recorded as
For the region division threshold, defined as
Wherein
And σmaxRepresenting all voxels in the total field map of the dipole field separately
The mean and maximum values of; as a unit impact function, BintIs a local field, and is,
in the case of a temporary variable,
representing a convolution operation; by passing
Dividing the region of interest into regions of high susceptibility variation D1And a region of uniform magnetic susceptibility D2And respectively carrying out convolution operation with the Gaussian convolution kernel and the spherical mean value convolution, and removing the background field to obtain a local field.
2. The local field estimation algorithm based on the spatial distribution of the magnetic resonance dipole field as claimed in claim 1, wherein in step 1), the winding number of the phase map comprises the evolution results of different field map variations at different times for local field estimation at any echo time.
3. The local field estimation algorithm based on spatial distribution of magnetic resonance dipole field according to claim 1, wherein in step 2), the spatial information composed of the amplitude, gradient and number of windings of the phase map is the standard deviation of the gaussian convolution kernel modulated voxel by voxel, when the larger the value of the spatial information indicates that there is a strong background field in the region, the smaller the gaussian standard deviation is obtained, i.e. the weight of the corresponding gaussian kernel center is high and the peripheral point value is rapidly attenuated, so as to better suppress the background field and obtain an accurate local field estimation.
4. The local field estimation algorithm based on the spatial distribution of the magnetic resonance dipole field according to claim 1, wherein in step 3), the step of dividing the region of interest into the high magnetic susceptibility change region and the uniform magnetic susceptibility change region based on the spatial information is to increase the operation speed of the algorithm, and the spatial information considers the field pattern components in different imaging directions and is used for multi-directional local field estimation.
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