Fluorescent molecular tomography feasible region selection method
Through tetrahedral mesh division and combination of multiple algorithms, the pathological nature of the reverse problem in fluorescent molecular tomography is solved, and high-precision and high-quality fluorescent molecular tomography are achieved.
Patent Information
- Application Number
- CN202410204251.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-02-23
- Publication Date
- 2025-07-18
AI Technical Summary
In the prior art, the solution to the reverse problem of fluorescent molecular tomography is pathological, resulting in low imaging accuracy and quality. The existing feasible domain selection method cannot accurately determine the feasible imaging field.
The tetrahedral meshing method is used to establish linear equations, combine the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the fluorescence distribution information, and filter out the accurate feasible domain through iterative self-organized data analysis algorithm, and reconstruct it in the feasible domain of imaging, and adjust the regularization parameters to optimize the reconstruction quality.
The imaging accuracy and quality of fluorescent molecular tomography are improved, ensuring the accuracy and reliability of reconstruction results.
Smart Images
Figure CN120323918A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to biomedical molecular imaging, and particularly to a method for selecting a feasible region of fluorescence molecular tomography. Background Art
[0002] Currently, fluorescence molecular tomography (FMT) is a very important imaging technology in optical molecular imaging technology, which can non-invasively and dynamically locate targets in three-dimensional space at the cellular and molecular levels. Therefore, fluorescence molecular tomography technology has great significance in the early monitoring of diseases, drug development, and treatment evaluation.
[0003] The problems studied in fluorescence molecular tomography are divided into forward problems and inverse problems. The forward problem is to solve the light distribution process after light propagates in the organism, given the position and light intensity of the fluorescence target. The inverse problem is to invert the spatial distribution of the fluorescence target in the organism based on the light data on the surface of the organism, combined with the light transport model and a suitable reconstruction algorithm. The inverse problem has strong ill-posedness, and how to obtain a stable and efficient solution has always been the focus of inverse problem research.
[0004] The problems existing in the prior art are: the solution of the inverse problem has strong ill-posedness. In order to obtain a stable and efficient solution, when constructing the mathematical model of the reconstruction problem, a regularization method is used to constrain the solution, and at the same time, the feasible region strategy is also widely used to solve the inverse problem. The feasible region limits the range of the solution region, which greatly reduces the dimension of the linear equation established between the unknowns and the light data on the surface of the organism, and at the same time, the number of unknowns is also greatly reduced. Currently, the existing methods for selecting the feasible region cannot accurately determine the imaging feasible region, resulting in low imaging accuracy and poor imaging quality of fluorescence molecular tomography. Summary of the Invention
[0005] (1) Technical Problems to be Solved
[0006] In view of the above-mentioned disadvantages of the prior art, the present invention provides a method for selecting a feasible region of fluorescence molecular tomography, which can effectively overcome the defects of low imaging accuracy and poor imaging quality caused by the inability to accurately determine the imaging feasible region in the prior art.
[0007] (2) Technical Solutions
[0008] To achieve the above object, the present invention is realized through the following technical solutions:
[0009] A method for selecting a feasible region of fluorescence molecular tomography includes the following steps:
[0010] S1. Perform tetrahedral mesh division on the object to be imaged, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged;
[0011] S2. Solve the linear equation by using the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method respectively to obtain two sets of reconstruction results;
[0012] S3. Divide the positive domains of the two sets of reconstruction results and merge them to form the first target feasible domain;
[0013] S4. Reconstruct the fluorescence target in the entire domain to obtain the reconstruction result;
[0014] S5. Process the reconstruction result by using the iterative self-organizing data analysis algorithm, separate the reconstruction target and select the feasible domain by partition, and merge them to form the second target feasible domain;
[0015] S6. Determine the imaging feasible domain by combining the first target feasible domain and the second target feasible domain;
[0016] S7. Reconstruct the fluorescence target in the imaging feasible domain, analyze the reconstruction quality of the fluorescence target, and if the reconstruction quality does not meet the requirements, re-determine the imaging feasible domain according to the first target feasible domain and the second target feasible domain.
[0017] Preferably, in S1, performing tetrahedral mesh division on the object to be imaged includes:
[0018] Collect fluorescence data of the object to be imaged at all angles by using a high-performance CCD camera;
[0019] Establish a cylindrical phantom model, discretize the cylindrical phantom model, and divide the imaging region Ω into m non-overlapping tetrahedral elements Ω1, Ω2,..., Ω m , and n grid nodes p1, p2,..., p n ;
[0020] Among them, the i-th grid node is denoted as p i , and the fluorescence yield value of the i-th grid node p i is denoted as F i .
[0021] Preferably, in S1, establishing a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged includes:
[0022] The linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged is expressed by the following formula:
[0023] Φ = AX;
[0024] Wherein, Φ is the light flux density on the surface of the object to be imaged, X is the three-dimensional distribution and concentration of the fluorescent target inside the object to be imaged, and A is the system matrix.
[0025] Preferably, in S2, the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method are respectively used to solve the linear equation, and two sets of reconstruction results are obtained, including:
[0026] Based on the same grid, the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method are respectively used to solve the linear equation, and two sets of fluorescence yield values of the grid nodes are obtained:
[0027] result1 = [F 11 , F 12 , …, F 1i , …, F 1n T ;
[0028] result2 = [F 21 , F 22 ,..., F 2i ,..., F 2n T 。
[0029] Preferably, in S3, the positive domains of the two sets of reconstruction results are divided and merged to form the first target feasible domain, including:
[0030] Set the initial threshold, and select the set of grid nodes belonging to the positive domain from the fluorescence yield values of the two sets of grid nodes according to the three-way decision theory;
[0031] Take the union of the set of grid nodes belonging to the positive domain in the fluorescence yield values of the two sets of grid nodes to obtain the first target feasible domain.
[0032] Preferably, in S4, the fluorescence target is reconstructed in the global domain, and the reconstruction result is obtained, including:
[0033] Using the finite element method and regularization, the reconstruction problem is transformed into a Laplacian regularization L2 norm minimization problem:
[0034]
[0035] Wherein, λ1 is the regularization parameter, and L is the Laplacian matrix of the finite element grid;
[0036] The Newton method and the conjugate gradient method are used for solving to obtain the reconstruction result of the three-dimensional distribution and concentration X of the fluorescent target inside the object to be imaged.
[0037] Preferably, in S7, the fluorescence target is reconstructed in the imaging feasible domain, including:
[0038] Establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the imaging feasible region;
[0039] Using the finite element method and regularization, transform the reconstruction problem into a minimization problem of the L1 norm of Laplacian regularization:
[0040]
[0041] where λ2 is the regularization parameter and A’ is the system matrix generated based on the imaging feasible region;
[0042] According to the actual situation, appropriately modify the regularization parameter λ2, and solve to obtain the three-dimensional distribution and concentration X’ of the fluorescence target inside the object to be imaged in the imaging feasible region.
[0043] Preferably, in S7, analyze the reconstruction quality of the fluorescence target. If the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region, including:
[0044] Generate a new system matrix based on the first target feasible region, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the first target feasible region. Again, use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation to obtain a new first target feasible region;
[0045] Reconstruct the fluorescence target in the second target feasible region to obtain a reconstruction result. Use the iterative self-organizing data analysis algorithm to process the reconstruction result, separate the reconstruction target, and then select the feasible region by partition and merge to form a new second target feasible region;
[0046] Re-determine the imaging feasible region by combining the new first target feasible region and the second target feasible region.
[0047] (III) Beneficial effects
[0048] Compared with the prior art, the fluorescence molecular tomography feasible region selection method provided by the present invention has the following beneficial effects:
[0049] 1) Perform tetrahedral mesh division on the object to be imaged, establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged, and use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation respectively to obtain two sets of reconstruction results. Divide the positive regions of the two sets of reconstruction results and merge them to form the first target feasible region. By using two linear equation solving methods to obtain two sets of reconstruction results, and screening out the set of grid nodes belonging to the positive region from the two sets of reconstruction results, the accurate first target feasible region can be obtained by taking the union;
[0050] 2) Reconstruct the fluorescence target in the global domain to obtain a reconstruction result. Use the iterative self-organizing data analysis algorithm to process the reconstruction result, separate the reconstructed target, then select the feasible region by partition, and merge them to form the second target feasible region. By reconstructing the fluorescence target in the global domain and using a suitable method to process the reconstruction result, an accurate second target feasible region can be obtained;
[0051] 3) Combining the first target feasible region and the second target feasible region can accurately determine the imaging feasible region. Then, reconstruct the fluorescence target in the imaging feasible region and analyze the reconstruction quality of the fluorescence target. If the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region, which can effectively ensure the imaging accuracy and imaging quality of fluorescence molecular tomography. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.
[0053] Figure 1 is a schematic flowchart of the present invention;
[0054] Figure 2 is a schematic flowchart of obtaining the first target feasible region in the present invention;
[0055] Figure 3 is a schematic flowchart of obtaining the second target feasible region in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.
[0057] A method for selecting the feasible region of fluorescence molecular tomography, as Figure 1 and Figure 2 shown, ① Perform tetrahedral mesh division on the object to be imaged, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged.
[0058] 1) Perform tetrahedral mesh division on the object to be imaged, including:
[0059] Collect fluorescence data of the object to be imaged at all angles using a high-performance CCD camera;
[0060] Establish a cylindrical phantom model, discretize the cylindrical phantom model, and divide the imaging region Ω into m non-overlapping tetrahedral elements Ω1, Ω2, …, Ω m , and n grid nodes p1, p2, …, p n ;
[0061] Among them, the i-th grid node is denoted as p i , and the fluorescence yield value of the i-th grid node p i is denoted as F i .
[0062] 2) Establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged, including:
[0063] The linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged is expressed by the following formula:
[0064] Φ = AX;
[0065] Among them, Φ is the light flux density on the surface of the object to be imaged, X is the three-dimensional distribution and concentration of the fluorescence target inside the object to be imaged, and A is the system matrix.
[0066] ② Respectively use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation to obtain two sets of reconstruction results, specifically including:
[0067] Based on the same grid, use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation respectively to obtain the fluorescence yield values of two sets of grid nodes:
[0068] result1 = [F 11 , F 12 ,..., F 1i ,..., F 1n T ;
[0069] result2 = [F 21 , F 22 ,..., F 2i ,..., F 2n T .
[0070] ③ Divide the positive domains of the two sets of reconstruction results and merge them to form the first target feasible domain, specifically including:
[0071] Set the initial threshold, and select the grid node set belonging to the positive domain from the fluorescence yield values of the two groups of grid nodes according to the three-way decision theory;
[0072] The first target feasible domain is obtained by taking the union of the grid node sets that belong to the positive domain in the fluorescence yield values of the two groups of grid nodes.
[0073] The above technical scheme divides the object to be imaged into tetrahedral grids, establishes a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescent target inside the object to be imaged, and solves the linear equation using the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method respectively to obtain two sets of reconstruction results, divide the positive domains of the two sets of reconstruction results, and merge them to form the feasible domain of the first target. Two sets of reconstruction results are obtained by using two linear equation solving methods, and the set of grid nodes belonging to the positive domain is screened out from the two sets of reconstruction results. After taking the union, the accurate feasible domain of the first target can be obtained.
[0074] like Figure 1 and Figure 3 As shown, ④ reconstruct the fluorescent target in the whole domain to obtain the reconstruction result, which specifically includes:
[0075] Using finite elements and regularization, the reconstruction problem is transformed into a Laplace regularized L2 norm minimization problem:
[0076]
[0077] Where λ1 is the regularization parameter, L is the Laplace matrix of the finite element mesh;
[0078] Newton's method and conjugate gradient method are used to solve the problem, and the reconstruction results of the three-dimensional distribution and concentration X of the fluorescent target inside the object to be imaged are obtained.
[0079] ⑤ Use the iterative self-organizing data analysis algorithm to process the reconstruction results, separate the reconstruction target, select the feasible domain by partition, and merge them to form the feasible domain of the second target.
[0080] The above technical scheme reconstructs the fluorescent target in the entire domain to obtain a reconstruction result, processes the reconstruction result using an iterative self-organizing data analysis algorithm, separates the reconstructed target and then selects the feasible domain by partition, which is merged to form a second target feasible domain. By reconstructing the fluorescent target in the entire domain and processing the reconstruction result using a suitable method, an accurate second target feasible domain can be obtained.
[0081] like Figure 1 As shown, ⑥ the imaging feasible domain is determined by combining the first target feasible domain and the second target feasible domain.
[0082] ⑦Reconstruct the fluorescence target in the imaging feasible region, analyze the reconstruction quality of the fluorescence target, and if the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region.
[0083] 1) Reconstruct the fluorescence target in the imaging feasible region, including:
[0084] Establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the imaging feasible region;
[0085] Using the finite element method and regularization, transform the reconstruction problem into a minimization problem of the L1 norm of Laplacian regularization:
[0086]
[0087] where λ2 is the regularization parameter and A’ is the system matrix generated based on the imaging feasible region;
[0088] Modify the regularization parameter λ2 appropriately according to the actual situation, and solve to obtain the three-dimensional distribution and concentration X’ of the fluorescence target inside the object to be imaged in the imaging feasible region.
[0089] 2) Analyze the reconstruction quality of the fluorescence target. If the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region, including:
[0090] Generate a new system matrix based on the first target feasible region, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the first target feasible region. Again, use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation to obtain a new first target feasible region;
[0091] Reconstruct the fluorescence target in the second target feasible region to obtain a reconstruction result. Use the iterative self-organizing data analysis algorithm to process the reconstruction result, separate the reconstruction target, then select the feasible region by partition, and merge to form a new second target feasible region;
[0092] Combine the new first target feasible region and the second target feasible region to re-determine the imaging feasible region.
[0093] The above technical solution can accurately determine the imaging feasible region by combining the first target feasible region and the second target feasible region, and reconstruct the fluorescence target in the imaging feasible region, analyze the reconstruction quality of the fluorescence target. If the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region, which can effectively ensure the imaging accuracy and imaging quality of fluorescence molecular tomography.
[0094] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for selecting the feasible region of fluorescence molecular tomography, characterized in that: It includes the following steps: S1. Perform tetrahedral mesh division on the object to be imaged, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged; S2. Solve the linear equation by using the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method respectively to obtain two sets of reconstruction results; S3. Divide the positive domains of the two sets of reconstruction results and merge them to form the first target feasible domain; S4. Reconstruct the fluorescence target in the entire domain to obtain the reconstruction result; S5. Process the reconstruction result by using the iterative self-organizing data analysis algorithm, separate the reconstructed target and select the feasible domain by partition, and merge them to form the second target feasible domain; S6. Determine the imaging feasible domain by combining the first target feasible domain and the second target feasible domain; S7. Reconstruct the fluorescence target in the imaging feasible domain, analyze the reconstruction quality of the fluorescence target, and if the reconstruction quality does not meet the requirements, re-determine the imaging feasible domain according to the first target feasible domain and the second target feasible domain.
2. The method for selecting the feasible region of fluorescence molecular tomography according to claim 1, wherein: The tetrahedral mesh division of the object to be imaged in S1 includes: Use a high-performance CCD camera to collect fluorescence data of the object to be imaged at all angles; Establish a cylindrical phantom model, and discretize the cylindrical phantom model. Divide the imaging region Ω into m non-overlapping tetrahedral elements Ω1, Ω2, …, Ω m , and n grid nodes p1, p2, …, p n ; Among them, the i-th grid node is denoted as p i , and the fluorescence yield value of the i-th grid node p i is denoted as F i .
3. The method for selecting the feasible region of fluorescence molecular tomography according to claim 2, wherein: The establishment of the linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in S1 includes: The linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged is expressed by the following formula: Φ = AX; Where, Φ is the light flux density on the surface of the object to be imaged, X is the three-dimensional distribution and concentration of the fluorescence target inside the object to be imaged, and A is the system matrix.
4. The method for selecting the feasible region of fluorescence molecular tomography according to claim 3, wherein: The solving of the linear equation by using the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method respectively in S2 to obtain two sets of reconstruction results includes: Based on the same grid, solve the linear equation by using the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method respectively to obtain the fluorescence yield values of two sets of grid nodes; result1 = [F 11 , F 12 ,..., F 1i ,..., F 1n T ; result2 = [F 21 , F 22 ,..., F 2i ,..., F 2n T 。 5. The method for selecting the feasible region of fluorescence molecular tomography according to claim 4, wherein: The division of the positive domains of the two sets of reconstruction results and the merging to form the first target feasible domain in S3 includes: Set the initial threshold, and select the set of grid nodes belonging to the positive domain from the fluorescence yield values of the two sets of grid nodes according to the three-way decision theory; Take the union of the set of grid nodes belonging to the positive domain in the fluorescence yield values of the two sets of grid nodes to obtain the first target feasible domain.
6. The method for selecting the feasible region of fluorescence molecular tomography according to claim 5, wherein: The reconstruction of the fluorescence target in the entire domain in S4 to obtain the reconstruction result includes: Use finite element and regularization to transform the reconstruction problem into a minimization problem of the L2 norm of Laplacian regularization: Where, λ1 is the regularization parameter, and L is the Laplacian matrix of the finite element grid; Use the Newton method and the conjugate gradient method to solve to obtain the reconstruction result of the three-dimensional distribution and concentration X of the fluorescence target inside the object to be imaged.
7. The method for selecting the feasible region of fluorescence molecular tomography according to claim 6, wherein: The reconstruction of the fluorescence target in the imaging feasible domain in S7 includes: Establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the imaging feasible domain; Use finite element and regularization to transform the reconstruction problem into a minimization problem of the L1 norm of Laplacian regularization: Where, λ2 is the regularization parameter, and A' is the system matrix generated based on the imaging feasible domain; Appropriately modify the regularization parameter λ2 according to the actual situation, and solve to obtain the three-dimensional distribution and concentration X' of the fluorescence target inside the object to be imaged in the imaging feasible region.
8. The method for selecting the feasible region of fluorescence molecular tomography according to claim 7, characterized in that: Analyze the reconstruction quality of the fluorescence target in S7. If the reconstruction quality does not meet the requirements, re-determine the imaging feasible region according to the first target feasible region and the second target feasible region, including: Generate a new system matrix based on the first target feasible region, and establish a linear equation between the fluorescence distribution information on the surface of the object to be imaged and the fluorescence target inside the object to be imaged in the first target feasible region. Then, use the incomplete variable truncated conjugate gradient method and the conjugate gradient least squares method to solve the linear equation again to obtain a new first target feasible region; Reconstruct the fluorescence target in the second target feasible region to obtain a reconstruction result. Use the iterative self-organizing data analysis algorithm to process the reconstruction result, separate the reconstruction target, select the feasible region by partition, and merge to form a new second target feasible region; Re-determine the imaging feasible region by combining the new first target feasible region and the second target feasible region.