Nonlinear back projection reconstruction method for open structure magnetic particle imaging

Abstract

The invention discloses a nonlinear back projection reconstruction method for open structure magnetic particle imaging, and belongs to the technical field of medical image processing and reconstruction, and the method specifically comprises the steps: S1, building a zero field line nonlinear change model; s2, deriving a nonlinear filtering back projection reconstruction formula; and S3, signal acquisition and image reconstruction. According to the method, the nonlinear bending rule of the zero field line in the open structure MPI system in the scanning process is constructed; meanwhile, the nonlinear model is embedded into a filtering back projection reconstruction framework, and a new nonlinear zero field line back projection reconstruction method is deduced; and rebuilt image edge distortion caused by zero field line bending is corrected through an algorithm, and high-precision imaging under an open-structure MPI large view field is realized.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing and reconstruction technology, specifically relating to an image reconstruction algorithm suitable for open-structure magnetic particle imaging systems, and in particular a nonlinear back-projection reconstruction method for open-structure magnetic particle imaging. Background Technology

[0002] Magnetic particle imaging (MPI) is a rapidly developing novel molecular imaging technique that has become a cutting-edge research hotspot internationally. Its imaging principle is based on the nonlinear magnetization response of superparamagnetic iron oxide nanoparticles (SPIOs) in a region without a magnetic field within a high-gradient magnetic field. By detecting this response, the three-dimensional concentration distribution of SPIOs in biological organisms can be quantitatively obtained. The voltage signal intensity acquired by MPI is proportional to the SPIO concentration; with appropriate modeling and analysis, the distribution of SPIOs in the biological organism can be reconstructed from the voltage signal. Because MPI specifically images only SPIOs, it is minimally affected by background tissue interference, thus exhibiting high sensitivity and high spatiotemporal resolution. Currently, this technology has been successfully applied in fields such as cell tracing, cardiovascular imaging, and neuroimaging.

[0003] In magnetic particle imaging, back-projection reconstruction algorithms based on the zero-field line are widely used due to their advantages of requiring no system matrix calibration and high reconstruction speed. Traditional algorithms are based on the assumption that the zero-field line remains an ideal straight line during scanning, as shown in the attached figure. Figure 1 As shown in the figure. The open-structure MPI system has its structure located on both sides of the object under test, with open sides, enabling the measurement of large objects with the same system power consumption. However, in the open-structure MPI system, due to its unique parallel coil pair structure, the zero-field line bends away from the center of the imaging field of view, exhibiting a non-linear change, as shown in the attached figure. Figure 2 and Figure 3 As shown, this nonlinear distortion results in severe positional distortion and structural artifacts at the edges of the field of view when the traditional linear back-projection algorithm is directly applied, leading to a decrease in imaging quality and a limited effective imaging field of view.

[0004] In existing technologies, reconstruction algorithms for closed MPI systems (x-space method) cannot be directly applied to the nonlinear zero-field line model of open structures. Therefore, there is an urgent need for a back-projection algorithm that can accurately model the nonlinear variation of the zero-field line and integrate it into the reconstruction process to solve the image distortion problem in large field-of-view imaging of open structure MPI systems. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a nonlinear back-projection reconstruction method for magnetic particle imaging of open structures.

[0006] This invention is achieved through the following method: a nonlinear back-projection reconstruction method for open-structure magnetic particle imaging, comprising the following steps: Step S1: Establish a nonlinear variation model of the zero field line.

[0007] The specific method is as follows: The spatial morphological changes of the zero-field line during the scanning process of the open structure MPI system were analyzed, and it was found that its bending trajectory conforms to the arc distribution. The scanning position parameters (the functional relationship between the central angle θ and the radius R of the arc) were established, where the translation distance of the zero-field line from the center of the field of view is d. The central angle θ is linearly related to the translation distance d: ; The radius R and the translation distance d have a power function relationship: ; in, These are constants related to the system coil structure, obtained through electromagnetic field simulation or actual measurement calibration.

[0008] Step S2: Derive the formula for nonlinear filtering back projection reconstruction.

[0009] Based on the circular arc zero-field line model established in step S1, the projection process is redescribed in a rotating coordinate system, assuming that the rotation angle is... At that time, the scanning position y The zero-field line is an arc in a coordinate system with the center of the imaging field of view as the origin, rotating with the FFL. x ', y In the circle, place the arc symmetrically within the circle. x On the axis.

[0010] S2.1: Define the geometric parameters and projection process of the circular arc

[0011] Let the zero field line of the circular arc be in the rotating coordinate system. x On the ' axis, the distance between its two endpoints is 2. a , a Given the field of view half-width, the central angle corresponding to the arc is 2α, the radius of curvature of the arc is R, and the center is located at point (0, -). y 0); According to geometric relations, we have R 2 = a 2 + y0 2 R = a / sinα, y0 = -a / tanα; The magnetic nanoparticle concentration distribution function to be reconstructed is c( x , y In a rotating coordinate system (x ', y In the diagram, integrating the concentration distribution along this circular path yields the nonlinear projection value at that scanning position. ρ ( y 0, ): (1) in It was Dirac δ The function is used to constrain the integration path to a circle with radius R and center in (0, -). y On the arc of 0).

[0012] S2.2: Simplification of Coordinate Transformation and Projection Equations

[0013] To handle nonlinear projections, a coordinate transformation function is introduced. ,in , representing the radial distance difference from the vertex of the arc to its center, thus mapping the arc projection geometry to polar coordinate space; global coordinates ( x , y Convert to polar coordinates And using the rotation coordinate relationship The projection equation can be rewritten as: (2) use δ Properties of functions And substitute it into the geometric relation R 2 = a 2 + y0 2 and The projection equation is rewritten as: (3).

[0014] S2.3: Constructing the standard filtered back projection form

[0015] make ,in ; make ,in , .

[0016] The projection equation then simplifies to: (4) right Regarding variables Perform a one-dimensional Fourier transform to obtain According to the Fourier slice theorem, It is a function The two-dimensional Fourier transform at angle A slice in a certain direction. (To) A two-dimensional inverse Fourier transform is performed, followed by a standard filtering and back-projection derivation process, which involves introducing a ramp filter. The reconstruction formula in the transformation space is obtained as follows: (5).

[0017] S2.4: Inverse transformation back to the original physical space

[0018] The solution of the transformation space Convert back to the original concentration distribution According to the relation get: (6) Will Substitute the expression and define the filter part as the filtered projection function. polar coordinates Convert back to Cartesian coordinates and noticed The formula for nonlinear filtering back projection reconstruction is obtained as follows: (7) in r 2 = x 2 + y 2 , s '( r )= a 2 ( a 2 + r 2 ) / ( a 2 - r 2 ) 2 , Represents the original projection data p ( y 0, After with The results of the relevant geometric calibration and ramp filtering.

[0019] Step S3: Signal acquisition and image reconstruction.

[0020] The system drives the zero-field line to rotate and translate along a preset trajectory; an alternating magnetic field is applied at each position to excite magnetic particles, and the induced voltage is collected as projection data. The arc geometry is determined according to the scanning parameters, the voltage is converted into a concentration value, and the nonlinear back projection formula is used to calculate the concentration image after distortion correction by superimposing the back projection results of all angles.

[0021] The specific method is as follows: S3.1: According to the preset scanning trajectory, the system control circuit drives the coil to complete the scanning of the zero-field line FFL in three-dimensional space. For each scanning position, the rotation angle is determined. Translation parameters y 0 is uniquely determined, and the system applies a frequency of 0. 0. Amplitude is H 0 alternating driving magnetic field At this point, the magnetic nanoparticles at the zero field line will generate a magnetization signal. Based on the principle of electromagnetic induction, the induced voltage signal of the magnetic nanoparticles is detected using a detection coil. u p ( t ); S3.2: Determine the data for each projection based on the system scanning coil current and scanning position parameters. ρ ( y 0, ), and the corresponding zero-field line arc parameters ( a , α , R ); S3.3: Project the data u p ( t Convert to particle concentration projection value p ( y 0, ); S3.4: Will p ( y 0, Substitute the scanning parameters and their corresponding scanning parameters into the nonlinear filtered back projection reconstruction formula derived in step S2 for calculation; S3.5) Summarize the backprojection results of all scanning angles to obtain the corrected final reconstructed image that eliminates the nonlinear distortion of the zero-field line. c ( x , y) .

[0022] The beneficial effects of this invention are as follows: This invention establishes a circular arc model with nonlinear bending of the zero-field line for open-structure magnetic particle imaging systems, and derives a suitable nonlinear filtering back-projection reconstruction formula based on this model. This solves the serious positional distortion and structural artifacts generated at the edge of the field of view by traditional linear algorithms. This method requires no system matrix calibration, and while retaining the advantages of rapid reconstruction by back-projection algorithms, it significantly improves imaging accuracy and image quality under large field of view, effectively expanding the application range of open-structure MPI systems. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the back projection reconstruction method in the background technology.

[0024] Figure 2 This is a schematic diagram of an open-structure magnetic particle imaging system.

[0025] Figure 3 This describes the nonlinear variation during the zero-field line scanning process of an open-structure magnetic particle imaging system.

[0026] Figure 4 The diagram shows the geometric parameters of the zero-field line circular arc model, where (a) is the relationship between the rotated coordinate system and the original coordinate system, and (b) is the position of the FFL. x Rotational coordinate diagram of the axis.

[0027] Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0028] To better understand the present invention, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0029] A nonlinear back-projection reconstruction method for magnetic particle imaging of open structures, comprising the following steps: Step S1: Establish a nonlinear variation model of the zero field line.

[0030] The specific method is as follows: The spatial morphological changes of the zero-field line during the scanning process of the open structure MPI system were analyzed, and it was found that its bending trajectory conforms to the arc distribution. The scanning position parameters (the functional relationship between the central angle θ and the radius R of the arc) were established, where the translation distance of the zero-field line from the center of the field of view is d. The central angle θ is linearly related to the translation distance d: ; The radius R and the translation distance d have a power function relationship: ; in, These are constants related to the system coil structure, obtained through electromagnetic field simulation or actual measurement calibration.

[0031] Step S2: Derive the formula for nonlinear filtering back projection reconstruction.

[0032] Based on the circular arc zero-field line model established in step S1, the projection process is redescribed in a rotating coordinate system, assuming that the rotation angle is... At that time, the scanning position y The zero-field line is an arc in a coordinate system with the center of the imaging field of view as the origin, rotating with the FFL. x ', y In the circle, place the arc symmetrically within the circle. x On the axis.

[0033] S2.1: Define the geometric parameters and projection process of the circular arc

[0034] Let the zero field line of the circular arc be in the rotating coordinate system. x On the ' axis, the distance between its two endpoints is 2. a , a Given the field of view half-width, the central angle corresponding to the arc is 2α, the radius of curvature of the arc is R, and the center is located at point (0, -). y 0); According to geometric relations, we have R 2 = a 2 + y0 2 R = a / sinα, y0 = -a / tanα; The magnetic nanoparticle concentration distribution function to be reconstructed is c( x , y In a rotating coordinate system ( x ', y In the diagram, integrating the concentration distribution along this circular path yields the nonlinear projection value at that scanning position. ρ ( y 0, ): (1) in It was Dirac δ The function is used to constrain the integration path to a circle with radius R and center in (0, -). y On the arc of 0).

[0035] S2.2: Simplification of Coordinate Transformation and Projection Equations

[0036] To handle nonlinear projections, a coordinate transformation function is introduced. ,in , representing the radial distance difference from the vertex of the arc to its center, thus mapping the arc projection geometry to polar coordinate space; global coordinates ( x , y Convert to polar coordinates And using the rotation coordinate relationship The projection equation can be rewritten as: (2) use δ Properties of functions And substitute it into the geometric relation R 2 = a 2 + y0 2 and The projection equation is rewritten as: (3).

[0037] S2.3: Constructing the standard filtered back projection form

[0038] make ,in ; make ,in , .

[0039] The projection equation then simplifies to: (4) right Regarding variables Perform a one-dimensional Fourier transform to obtain According to the Fourier slice theorem, It is a function The two-dimensional Fourier transform at angle A slice in a certain direction. (To) A two-dimensional inverse Fourier transform is performed, followed by a standard filtering and back-projection derivation process, which involves introducing a ramp filter. The reconstruction formula in the transformation space is obtained as follows: (5).

[0040] S2.4: Inverse transformation back to the original physical space

[0041] The solution of the transformation space Convert back to the original concentration distribution According to the relation get: (6) Will Substitute the expression and define the filter part as the filtered projection function. polar coordinates Convert back to Cartesian coordinates and noticed The formula for nonlinear filtering back projection reconstruction is obtained as follows: (7) in r 2 = x 2 + y 2 , s '( r )= a 2 ( a 2 + r 2 ) / ( a 2 - r 2 ) 2 , Represents the original projection data p ( y 0, After with The results of the relevant geometric calibration and ramp filtering.

[0042] Step S3: Signal acquisition and image reconstruction.

[0043] The system drives the zero-field line to rotate and translate along a preset trajectory; an alternating magnetic field is applied at each position to excite magnetic particles, and the induced voltage is collected as projection data. The arc geometry is determined according to the scanning parameters, the voltage is converted into a concentration value, and the nonlinear back projection formula is used to calculate the concentration image after distortion correction by superimposing the back projection results of all angles.

[0044] The specific method is as follows: S3.1: According to the preset scanning trajectory, the system control circuit drives the coil to complete the scanning of the zero-field line FFL in three-dimensional space. For each scanning position, the rotation angle is determined. Translation parameters y 0 is uniquely determined, and the system applies a frequency of 0. 0. Amplitude is H 0 alternating driving magnetic field At this point, the magnetic nanoparticles at the zero field line will generate a magnetization signal. Based on the principle of electromagnetic induction, the induced voltage signal of the magnetic nanoparticles is detected using a detection coil. u p ( t ); S3.2: Determine the data for each projection based on the system scanning coil current and scanning position parameters. ρ ( y 0, ), and the corresponding zero-field line arc parameters ( a , α , R); S3.3: Project the data u p ( t Convert to particle concentration projection value p ( y 0, ); S3.4: Will p ( y 0, Substitute the scanning parameters and their corresponding scanning parameters into the nonlinear filtered back projection reconstruction formula derived in step S2 for calculation; S3.5) Summarize the backprojection results of all scanning angles to obtain the corrected final reconstructed image that eliminates the nonlinear distortion of the zero-field line. c ( x , y) .

[0045] Example 1: The entire process of imaging an open-structure MPI system was simulated using computer simulation to verify the effectiveness and technical advantages of the method of the present invention.

[0046] (1) Simulation system modeling and data generation

[0047] 1) Open structure MPI electromagnetic field modeling: An electromagnetic model of the open-structure MPI system was established using finite element simulation software. The model includes two pairs of parallel-opposed Helmholtz coils (Coil-x and Coil-y) to generate linear zero-magnetic-field free lines. The coil geometry and relative positions were set according to the requirements of the open structure of the system.

[0048] 2) Zero-field line scanning and magnetic field calculation: a) Scan control: By controlling the current applied to Coil-x and Coil-y, the FFL can achieve scanning control. xy Rotation and translation within a plane. Setting the rotation angle. From 0° to 180°, in 5° increments (37 angles in total). At each fixed angle... The FFL is shifted along its normal direction by changing the driving current, with the current variation range from 0 A to 35 A and the step size being 5 A.

[0049] b) Obtaining the magnetic field distribution: For each scanning position ( , I The three-dimensional static magnetic field distribution of the entire detection area (80 mm × 80 mm) was obtained through simulation calculation. In particular, the spatial morphology of the zero magnetic field free line (i.e., the continuous region where the magnetic field strength is zero) was extracted and recorded.

[0050] 3) Projection data simulation generation: a) Imaging target model: Design a magnetic nanoparticle concentration distribution model as the simulation target, including single-target models and multi-target models of different sizes and positions.

[0051] b) Signal simulation: At each scan position, it is assumed that a sinusoidal alternating driving magnetic field along the z-axis is applied to the FFL. ,in H 0 = 10kHz. Based on the Langevin magnetization model, calculate the total induced voltage signal generated by the target model at this scanning position. Process and integrate this signal; the resulting signal amplitude is used as the projection data for this scanning position. p ( y 0, ).in y 0 represents the translation distance of the FFL.

[0052] (2) Implementation process of reconstruction method

[0053] Step S1: Model the nonlinear characteristics of the zero-field line.

[0054] Based on the magnetic field data obtained from simulation calculations at all scanning positions, the nonlinear variation law of FFL is quantitatively analyzed. The specific operation is as follows: (1) For each scanning position, extract the magnetic induction intensity at each point on the FFL. z Quantity B z The distribution of .

[0055] right B z Perform a circular fit along the distribution along the FFL direction. Record the radius R of the fitted arc and the central angle subtended by the arc at each position. θ .

[0056] Establish FFL translation distance d (Right now y 0) The quantitative relationship between the central angle and the fitted parameters. The central angle is obtained through data fitting. θ and translation distance d There is a linear relationship (correlation coefficient 0.9589). Radius R and translation distance... d The relationship exhibits a power function (correlation coefficient 0.9964). This rule holds true for all rotation angles.

[0057] Steps S2 and S3: Model building and reconstruction formula application.

[0058] Based on the pattern established in step S1, the FFL at any position during the scan is modeled as an arc. For example... Figure 3 As shown, the arc is located in a rotating coordinate system ( x ', y ')ofx On the axis, its geometric features are determined by parameters a (arc and) x 'Half width of the intersection of axes', radius And 2α description.

[0059] Substituting the above circular arc projection model into the theoretical framework of filtered back projection, we obtain the nonlinear filtered back projection reconstruction formula:

[0060] in, r 2 = x 2 + y 2 , a The field of view half-width is 40 mm in this example. s '( r )= a 2 ( a 2 + r 2 ) / ( a 2 - r 2 ) 2 For geometric weighting functions, This is the filtered projection data.

[0061] Step S4: Projection data preprocessing.

[0062] All projection data generated by simulation p ( y 0, Normalize the result and perform one-dimensional filtering using a ramp filter to obtain the desired result. .

[0063] Step S5: Nonlinear back projection reconstruction.

[0064] Filtered projection data Substituting the formula into the nonlinear filtering backprojection reconstruction formula, backprojection integration is performed on an 80 mm × 80 mm discrete grid to finally obtain the reconstructed image matrix. .

Claims

1. A nonlinear back-projection reconstruction method for magnetic particle imaging of open structures, characterized in that, The steps are as follows: Step S1: Establish a nonlinear variation model of the zero field line Step S2: Derive the formula for nonlinear filtering back projection reconstruction Based on the circular arc zero-field line model established in step S1, the projection process is redescribed in a rotating coordinate system, assuming that the rotation angle is... At that time, the scanning position y The zero-field line is an arc in a coordinate system with the center of the imaging field of view as the origin, rotating with the FFL. x ', y In the circle, place the arc symmetrically within the circle. x On the axis; S2.1: Define the geometric parameters and projection process of the circular arc Let the zero field line of the circular arc be in the rotating coordinate system. x On the ' axis, the distance between its two endpoints is 2. a , a Given the field of view half-width, the central angle corresponding to the arc is 2α, the radius of curvature of the arc is R, and the center is located at point (0, -). y 0); According to geometric relations, we have R 2 = a 2 + y0 2 R = a / sinα, y0 = -a / tanα; The magnetic nanoparticle concentration distribution function to be reconstructed is c( x , y In a rotating coordinate system ( x ', y In the diagram, integrating the concentration distribution along this circular path yields the nonlinear projection value at that scanning position. ρ ( y 0, ): （1） in It was Dirac δ The function is used to constrain the integration path to a circle with radius R and center in (0, -). y On the arc of 0); S2.2: Simplification of Coordinate Transformation and Projection Equations To handle nonlinear projections, a coordinate transformation function is introduced. ,in , representing the radial distance difference from the vertex of the arc to its center, thus mapping the arc projection geometry to polar coordinate space; global coordinates ( x , y Convert to polar coordinates And using the rotation coordinate relationship The projection equation can be rewritten as: （2） use δ Properties of functions And substitute it into the geometric relation R 2 = a 2 + y0 2 and The projection equation is rewritten as: （3） S2.3: Constructing the standard filtered back projection form make ,in ; make ,in , . The projection equation then simplifies to: （4） right Regarding variables Perform a one-dimensional Fourier transform to obtain ; According to the Fourier slice theorem It is a function The two-dimensional Fourier transform at angle A slice in a certain direction. (To) A two-dimensional inverse Fourier transform is performed, followed by a standard filtering and back-projection derivation process, which involves introducing a ramp filter. The reconstruction formula in the transformation space is obtained as follows: （5） S2.4: Inverse transformation back to the original physical space The solution of the transformation space Convert back to the original concentration distribution According to the relation get: （6） Will Substitute the expression and define the filter part as the filtered projection function. polar coordinates Convert back to Cartesian coordinates and noticed The formula for nonlinear filtering back projection reconstruction is obtained as follows: （7） in r 2 = x 2 + y 2 , s '( r )= a 2 ( a 2 + r 2 ) / ( a 2 - r 2 ) 2 , Represents the original projection data p ( y 0, After with The results of the relevant geometric calibration and ramp filtering; Step S3: Signal Acquisition and Image Reconstruction The system drives the zero-field line to rotate and translate along a preset trajectory; an alternating magnetic field is applied at each position to excite magnetic particles, and the induced voltage is collected as projection data. The arc geometry is determined according to the scanning parameters, the voltage is converted into a concentration value, and the nonlinear back projection formula is used to calculate the concentration image after distortion correction by superimposing the back projection results of all angles.

2. The nonlinear back-projection reconstruction method for open-structure magnetic particle imaging according to claim 1, characterized in that, In step S1, the specific method is as follows: The spatial morphological changes of the zero-field line during the scanning process of the open structure MPI system were analyzed, and it was found that its bending trajectory conforms to the arc distribution. The scanning position parameters (the functional relationship between the central angle θ and the radius R of the arc) were established, where the translation distance of the zero-field line from the center of the field of view is d. The central angle θ is linearly related to the translation distance d: ; The radius R and the translation distance d have a power function relationship: ; in, These are constants related to the system coil structure, obtained through electromagnetic field simulation or actual measurement calibration.

3. The nonlinear back-projection reconstruction method for open-structure magnetic particle imaging according to claim 1, characterized in that, In step S3, the specific method is as follows: S3.1: According to the preset scanning trajectory, the system control circuit drives the coil to complete the scanning of the zero-field line FFL in three-dimensional space. For each scanning position, the rotation angle is determined. Translation parameters y 0 is uniquely determined, and the system applies a frequency of 0.

0. Amplitude is H 0 alternating driving magnetic field At this point, the magnetic nanoparticles at the zero field line will generate a magnetization signal. Based on the principle of electromagnetic induction, the induced voltage signal of the magnetic nanoparticles is detected using a detection coil. u p ( t ); S3.2: Determine the data for each projection based on the system scanning coil current and scanning position parameters. ρ ( y 0, ), and the corresponding zero-field line arc parameters ( a , α , R ); S3.3: Project the data u p ( t Convert to particle concentration projection value p ( y 0, ); S3.4: Will p ( y 0, Substitute the scanning parameters and their corresponding scanning parameters into the nonlinear filtered back projection reconstruction formula derived in step S2 for calculation; S3.5) Summarize the backprojection results of all scanning angles to obtain the corrected final reconstructed image that eliminates the nonlinear distortion of the zero-field line. c ( x , y) .

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