阅读说明：本技术 基于磁滞效应的无磁场点磁纳米粒子成像方法 (Magnetic field point-free magnetic nanoparticle imaging method based on hysteresis effect ) 是由 田捷 李怡濛 惠辉 张鹏 杨鑫 于 2021-07-21 设计创作，主要内容包括：本发明公开了一种基于磁滞效应的无磁场点磁纳米粒子成像方法,包括以下步骤：获取超顺磁纳米粒子(Superparamagnetic Iron Oxide Nanoparticles,SPIO)的磁滞回线模型；基于正弦激励磁场和SPIO的磁滞回线模型,计算得到SPIO的点扩散函数(Point Spread Function,PSF)；基于无磁场点(Field Free Point,FFP)移动轨迹与电压信号,获取无磁场点磁纳米粒子成像(Field Free Point-Magnetic Particle Imaging,FFP-MPI)的原始重建图像；将原始图像对已考虑磁滞效应的PSF解卷积,获得最终重建图像。该方法减少了大粒径SPIO的磁滞效应对图像重建产生的伪影与相位误差,弥补了传统重建方法忽略磁滞效应进行重建的不足,极大提高重建速度与分辨率,拓宽了SPIO的应用范围。(The invention discloses a magnetic field point-free magnetic nanoparticle imaging method based on a hysteresis effect, which comprises the following steps of: obtaining a magnetic hysteresis loop model of Superparamagnetic Iron Oxide Nanoparticles (SPIO); calculating to obtain a Point Spread Function (PSF) of the SPIO based on the sinusoidal excitation magnetic field and a hysteresis loop model of the SPIO; acquiring an original reconstructed image of a Magnetic nanoparticle Imaging (FFP-MPI) of a Field-Free Point (FFP) based on a FFP moving track and a voltage signal; and deconvoluting the original image with the PSF with the hysteresis effect taken into account to obtain a final reconstructed image. The method reduces the artifacts and phase errors generated by the hysteresis effect of the large-particle-size SPIO on image reconstruction, overcomes the defect that the conventional reconstruction method is used for reconstructing by neglecting the hysteresis effect, greatly improves the reconstruction speed and resolution and widens the application range of the SPIO.)

1. A magnetic field point-free magnetic nanoparticle imaging method based on a hysteresis effect is characterized by comprising the following steps:

step S1: obtaining a hysteresis loop model of superparamagnetic nanoparticles (SPIO);

step S2: calculating to obtain a Point Spread Function (PSF) of the SPIO based on the magnetic hysteresis loop model of the sinusoidal excitation magnetic field and the SPIO;

step S3: acquiring an original reconstructed image of magnetic nanoparticle imaging (FFP-MPI) without a magnetic field point (FFP) based on a FFP moving track and a voltage signal;

step S4: and deconvolving the original reconstructed image with the PSF with the hysteresis effect taken into account to obtain a final reconstructed image.

2. The method of claim 1, wherein the method of obtaining the hysteresis loop of SPIO in step S1 is as follows:

measuring a plurality of groups of characteristic point data of the SPIO under the alternating current magnetic field, substituting the data into the M-H hysteresis curve model, and solving to obtain parameters: saturation magnetic vector M_sThe magnetic field coupling strength alpha, the magnetic domain density a, the average energy k and the magnetization reversibility c are obtained, and the parameters are substituted into the M-H hysteresis curve model to obtain the hysteresis loop of the SPIO.

3. The method of claim 2, wherein the M-H hysteresis curve model is:

where H is the applied excitation field, M is the magnetization vector of SPIO, μ₀Is the vacuum permeability; when the external excitation magnetic field is positively increased, delta is 1; when the applied excitation field decreases in the opposite direction, δ is-1.

4. The method according to claim 1, wherein the method for calculating the PSF of SPIO in step S2 is as follows:

when the SPIO is excited by a sinusoidal excitation magnetic field, there are:

H(t)＝Acos(ωt)

where t is time, A is the magnetic field amplitude, ω is the angular frequency of the excitation magnetic field;

substituting the formula into a hysteresis loop model of the SIPO to obtain a function M (t) of the change of the magnetization vector of the SPIO along with time; deriving m (t) with respect to time to obtain the PSF of SPIO as follows:

5. the method of claim 1, wherein the step S3 of obtaining the original reconstructed image of the FFP-MPI based on the FFP movement trajectory and the voltage signal comprises:

moving the FFP according to a scanning track, wherein the moving speed is v, the position is r, and the whole visual field is scanned by adopting MPI to obtain a voltage signal u (t) of the induction coil;

the original reconstructed image is related to the voltage signal as follows:

IMG_raw＝u(t)/v＝c(r)***PSF

wherein, c (r) is the SPIO concentration variation distribution matrix with position, and is a three-dimensional convolution symbol;

and dividing the voltage signal by the scanning speed, and splicing the images according to the scanning track to obtain an original reconstructed image.

6. The method according to claim 1, wherein the step S4 deconvolves the original reconstructed image with the PSF with hysteresis effect taken into account, and the final reconstructed image is obtained by:

wherein the content of the first and second substances,is a three-dimensional deconvolution.

Technical Field

The invention belongs to the field of magnetic nanoparticle imaging, and particularly relates to a magnetic field point-free magnetic nanoparticle imaging method based on a hysteresis effect.

Background

Magnetic Particle Imaging (MPI) is a novel Imaging method, which constructs a Field Free Point (FFP) or a Field Free Line (FFL) so that Superparamagnetic Nanoparticles (SPIOs) in the Field Free Point or Field Free region respond to an excitation Magnetic Field, while SPIOs in other regions do not respond to the excitation Magnetic Field in a Magnetic saturation state, thereby achieving the purpose of spatially encoding and reconstructing Magnetic Particle distribution information and accurately positioning detection objects such as tumors. MPI has the characteristics of high time resolution, high spatial resolution and no harmful radiation, so that MPI has good application prospect in the medical field.

At present, the MPI image reconstruction theory method is based on the Langmuir function of magnetic particles, and the magnetic particles are considered to be aligned with an external excitation magnetic field adiabatically without hysteresis effect. However, in practical application, when the particle size of the SPIO particle is smaller than 14nm, the hysteresis effect of the particle is very small and can be ignored; however, when the particle size is larger than 14nm, the hysteresis effect of the particles is obvious, the basic assumption of the image reconstruction algorithm based on the Langmuir magnetization curve is not satisfied any more, and the reconstructed image has artifacts and deviation. At present, SPIO particles used for biomedical MPI imaging are mostly about 20nm, and the hysteresis effect is not negligible, so that an image reconstruction algorithm considering the hysteresis effect of the magnetic particles is needed.

Disclosure of Invention

In order to solve the problem of reconstructed image artifacts caused by the hysteresis effect of the SPIO in the prior art, the invention provides a magnetic field Point-free magnetic nanoparticle imaging method based on the hysteresis effect, which starts from the establishment of a hysteresis loop model of the SPIO, analyzes the change of the characteristic of a Point Spread Function (PSF) based on the hysteresis effect, reconstructs a voltage signal received by an induction coil according to a scanning track of an MPI system without a magnetic field Point to obtain an original reconstructed image, and finally performs deconvolution according to the hysteresis effect Point Spread Function to obtain a high-quality final reconstructed image, wherein the specific technical scheme is as follows:

a magnetic field point-free magnetic nanoparticle imaging method based on a hysteresis effect is characterized by comprising the following steps:

step S1: obtaining a hysteresis loop model of superparamagnetic nanoparticles (SPIO);

step S2: calculating to obtain a Point Spread Function (PSF) of the SPIO based on the magnetic hysteresis loop model of the sinusoidal excitation magnetic field and the SPIO;

step S3: acquiring an original reconstructed image of magnetic nanoparticle imaging (FFP-MPI) without a magnetic field point (FFP) based on a FFP moving track and a voltage signal;

step S4: and deconvolving the original reconstructed image with the PSF with the hysteresis effect taken into account to obtain a final reconstructed image.

Further, the method for acquiring the hysteresis loop of SPIO in step S1 includes:

measuring a plurality of groups of characteristic point data of the SPIO under the alternating current magnetic field, substituting the data into the M-H hysteresis curve model, and solving to obtain parameters: saturation magnetic vector M_sThe magnetic field coupling strength alpha, the magnetic domain density a, the average energy k and the magnetization reversibility c are obtained, and the parameters are substituted into the M-H hysteresis curve model to obtain the hysteresis loop of the SPIO.

Further, the M-H hysteresis curve model is as follows:

where H is the applied excitation field, M is the magnetization vector of SPIO, μ₀Is the vacuum permeability; when the external excitation magnetic field is positively increased, delta is 1; when the applied excitation field decreases in the opposite direction, δ is-1.

Further, the method for calculating the PSF of the SPIO in step S2 includes:

when the SPIO is excited by a sinusoidal excitation magnetic field, there are:

H(t)＝Acos(ωt)

where t is time, A is the magnetic field amplitude, ω is the angular frequency of the excitation magnetic field;

substituting the formula into a hysteresis loop model of the SIPO to obtain a function M (t) of the change of the magnetization vector of the SPIO along with time; deriving m (t) with respect to time to obtain the PSF of SPIO as follows:

further, in step S3, the method for obtaining the original reconstructed image of the FFP-MPI based on the FFP movement trajectory and the voltage signal includes:

moving the FFP according to a scanning track, wherein the moving speed is v, the position is r, and the whole visual field is scanned by adopting MPI to obtain a voltage signal u (t) of the induction coil;

the original reconstructed image is related to the voltage signal as follows:

IMG_raw＝u(t)/v＝c(r)***PSF

wherein c (r) is a concentration-as-position variation distribution matrix, which is a three-dimensional convolution symbol;

and dividing the voltage signal by the scanning speed, and splicing the images according to the scanning track to obtain an original reconstructed image.

Further, in step S4, the method for deconvolving the original reconstructed image with the PSF considering the hysteresis effect to obtain the final reconstructed image includes:

wherein the content of the first and second substances,is a three-dimensional deconvolution.

The invention has the beneficial effects that:

(1) the method starts from a hysteresis loop of the SPIO, calculates the PSF considering the hysteresis effect, obtains an original reconstruction image, deconvolves the original reconstruction image to obtain a final reconstruction result, adds the hysteresis effect influence of the SPIO into an image reconstruction algorithm, reduces artifacts and phase errors generated by the hysteresis effect of the SPIO particles with large particle size on image reconstruction, makes up the defect that the traditional reconstruction method reconstructs the image by neglecting the hysteresis effect, greatly improves the reconstruction speed and resolution and enhances the image reconstruction effect.

(2) The method has universality for FFP-MPI equipment with different structure types and different tracers. When the magnetic nanoparticles are changed, only the magnetic particle spectrometer is needed to measure parameters in a hysteresis loop theoretical model, and a hysteresis loop function in theoretical calculation is changed, so that a new PSF can be quickly obtained, and high-quality image reconstruction is realized.

(3) The method widens the application of the SPIO, and allows the SPIO with larger particle size to be used for MPI, thereby increasing the induction voltage and improving the detection sensitivity.

Drawings

FIG. 1 is a flow chart of a magnetic field point-free magnetic nanoparticle imaging method based on hysteresis effect.

Fig. 2 is an M-H hysteresis loop taking hysteresis effects into account and a magnetization curve in which hysteresis effects are ideally ignored.

Fig. 3 is a graph of the variation of the magnetization vector with time, taking into account the hysteresis effect and ideally ignoring the hysteresis effect.

Fig. 4 is a graph of the PSF versus time that considers the hysteresis effect and ideally ignores the hysteresis effect.

FIG. 5 is an original reconstructed image of FFP-MPI.

FIG. 6 is the final reconstructed image of FFP-MPI.

Detailed Description

The invention will be described in further detail below with reference to the drawings and examples.

A magnetic field point-free magnetic nanoparticle imaging method based on a hysteresis effect comprises the following steps:

step S1: measuring parameters through a magnetic particle spectrometer, and then combining an M-H curve model of a hysteresis effect to obtain a hysteresis loop of the SPIO;

the SPIO is excited by a high-frequency (20-45 kHz) sinusoidal excitation magnetic field in the MPI equipment, and the magnetization process of the SPIO follows an M-H hysteresis curve model:

where H is the applied excitation field, M is the magnetization vector of SPIO, μ₀Is the vacuum permeability. In the model of formula (1.1), when the applied magnetic field increases in the positive direction, δ becomes 1; when the applied field decreases in the opposite direction, δ is-1. Three sets of data of SPIO under an ac Magnetic field can be measured by a Magnetic Particle Spectrometer (MPS): residual hysteresis M when H is 0_rCoercive field strength H when M is 0_cMaximum magnetic field strength H_maxTime maximum magnetization vector M_maxThese three sets of data were substituted into equation (1.1) to solve the following parameters: m_sSaturation magnetic vector, alpha magnetic field coupling strength, a magnetic domain density, k average energy and c magnetization reversibility. And substituting the parameters into an M-H hysteresis curve model to obtain a hysteresis loop of the SPIO. For example, when the diameter of SPIO is 30nm, a hysteresis loop in which hysteresis effect is considered is shown as a hysteresis loop having hysteresis effect in fig. 2, and ideally a magnetization curve in which hysteresis effect is not considered is shown as a hysteresis curve having no hysteresis effect in fig. 2.

Step S2: based on a sinusoidal excitation magnetic field, combining a magnetic hysteresis loop of the SPIO to obtain a response magnetization vector of the SPIO, and deriving the response magnetization vector with time to obtain a point spread function PSF of the SPIO;

when the SPIO is excited by a sinusoidal excitation magnetic field:

H(t)＝Acos(ωt) (1.2)

where t is time, A is the magnetic field amplitude, and ω is the angular frequency of the excitation magnetic field. The function m (t) of the change of the magnetization vector of SPIO with time is obtained by substituting formula (1.2) into formula (1.1), as shown in fig. 3, the change curve of the magnetization vector with time considering the hysteresis effect is shown by a hysteresis effect curve, and the change of the magnetization vector neglecting the hysteresis effect in an ideal case is shown by a hysteresis-free effect curve.

PSF is the derivative of the magnetization vector with respect to time, so:

the PSF time-varying curve is shown in fig. 4, the hysteresis effect curve represents a PSF in which the hysteresis effect is considered, and the phase is shifted by Δ x more than a PSF without the hysteresis effect curve in which the hysteresis effect is ignored, and the shapes of both are the same.

Step S3: acquiring an original reconstructed image of the FFP-MPI based on the FFP movement track and the voltage signal;

the scanning trajectory of FFP is generally: cartesian scanning trajectories, lissajous scanning trajectories. And moving the FFP according to a certain scanning track, wherein the moving speed v and the position are changed into r (t) along time, and scanning the visual field of the MPI once to obtain a voltage signal u (t) of the induction coil. The original reconstructed image is related to the voltage signal as follows:

IMG_raw＝u(t)/v＝c(r)***PSF (1.4)

wherein c (r) is a concentration-as-position variation distribution matrix, and is a three-dimensional convolution symbol. And dividing the voltage signal by the scanning speed, and splicing the images according to the scanning track to obtain an original reconstructed image. The image result used in the MPI field is an original reconstructed image which can reflect the approximate condition of the SPIO concentration distribution, but is not an accurate concentration distribution result, the resolution is poor, the phase shift of the PSF caused by the hysteresis effect is ignored, and further image optimization is needed. For example, MPI scans two parallel strip samples and the original reconstructed image is shown in fig. 5.

Step S4: deconvoluting the original reconstructed image by considering the PSF of the hysteresis effect to obtain a final reconstructed image;

the original reconstructed image ignores the phase backward shift effect of the hysteresis effect of the SPIO, and a position error is generated in the process of corresponding to each FFP from a time domain voltage signal. Deconvolving the original reconstructed image with a PSF function, correcting phase shift errors caused by hysteresis effect by using the PSF, wherein the result after deconvolution is the final reconstruction result:

wherein the content of the first and second substances,is a three-dimensional deconvolution. For example, MPI scans two parallel strip samples and the final reconstructed image after deconvolution is shown in fig. 6.

The above description is only exemplary of the present invention and should not be taken as limiting the scope of the present invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention should be included in the scope of the present invention.