High-resolution fluorescent molecular tomography method
Through tetrahedral mesh division and imitation model combined with hierarchical network model training, the problem of insufficient resolution of fluorescent molecular tomography technology during tissue imaging in organisms is solved, and high resolution and high accuracy imaging effects are achieved.
Patent Information
- Application Number
- CN202410204255.3
- 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
The existing fluorescent molecular tomography technology has insufficient spatial resolution during tissue imaging in organisms, which limits its application in biomedical science.
Tetrahedral mesh division and imitation model are used to construct the objective function in combination with least squares term and elastic network regularization term, and solve it using the relaxation alternating direction multiplier method, and high-resolution fluorescent molecular tomography is achieved through hierarchical network model training.
The imaging resolution and accuracy of tissues in biological organisms are improved, and high-resolution and high-accuracy fluorescent molecular tomography results are obtained.
Smart Images
Figure CN120339062A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to biomedical molecular imaging, and particularly to a high-resolution fluorescence molecular tomography method. Background Art
[0002] As a newly developed biomedical optical imaging modality in recent years, fluorescence molecular tomography (FMT) technology has been rapidly developed and has become an important branch in molecular imaging. By measuring the diffused light transmitted through the surface of the organism and based on the optical propagation model, FMT can not only describe the three-dimensional distribution of fluorescence probes at the centimeter scale from the organism surface, but also quantitatively reconstruct important parameters such as the concentration and lifetime of fluorescence probes, and is widely used in biomedical research.
[0003] However, affected by the inherent characteristic that light has strong scattering during the propagation in biological tissues, fluorescence molecular tomography has a low spatial resolution. To some extent, this limits the further application of FMT in biomedicine.
[0004] To break through the limitation of spatial resolution, in the field of optical microscopy imaging, researchers have proposed an ultra-high resolution fluorescence microscopy imaging technology based on the single-molecule localization strategy, such as stochastic optical reconstruction microscopy (STORM). By combining photo-switchable fluorescence probes and single-molecule localization, STORM technology has broken through the optical diffraction limit and improved the spatial resolution of traditional optical microscopy imaging technology by one order of magnitude, and can image intracellular organelles or macromolecular structures at the single-molecule level (nanoscale), but this technology is only applicable to single-molecule level imaging. Summary of the Invention
[0005] (1) Technical Problems to be Solved
[0006] In view of the above-mentioned drawbacks of the prior art, the present invention provides a high-resolution fluorescence molecular tomography method, which can effectively overcome the defect that the prior art cannot perform accurate high-resolution fluorescence molecular tomography on biological tissues.
[0007] (2) Technical Solutions
[0008] To achieve the above object, the present invention is realized through the following technical solutions:
[0009] A high-resolution fluorescence molecular tomography method, comprising the following steps:
[0010] S1. Perform tetrahedral mesh division on the object to be imaged, and map the fluorescence data of the object to be imaged into a discretized phantom model through coordinates;
[0011] S2. Perform forward model calculation based on the mapped phantom model to obtain 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;
[0012] S4. Based on the linear equation, construct an objective function by combining the least squares term and the elastic net regularization term;
[0013] S7. Solve the objective function using the relaxed alternating direction method of multipliers to obtain the first fluorescence molecular tomography result;
[0014] S5. Use the training data set and the training test set to train the hierarchical network model to obtain a trained fluorescence molecular tomography model;
[0015] S6. Input the fluorescence distribution information on the surface of the object to be imaged into the trained fluorescence molecular tomography model to obtain the second fluorescence molecular tomography result;
[0016] S7. Combine the first fluorescence molecular tomography result and the second fluorescence molecular tomography result to obtain a high-resolution fluorescence molecular tomography result.
[0017] Preferably, in S1, perform tetrahedral mesh division on the object to be imaged, and map the fluorescence data of the object to be imaged into the discretized phantom model through coordinates, including:
[0018] Use a high-performance CCD camera to collect fluorescence data of the object to be imaged at all angles;
[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] Map the fluorescence data of the object to be imaged at all angles into the discretized cylindrical phantom model through coordinates.
[0021] Preferably, in S2, perform forward model calculation based on the mapped phantom model to obtain 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:
[0022] Based on the mapped cylindrical phantom model, use the coupled diffusion approximation equation to describe the propagation process of fluorescence photons in the object to be imaged, and describe the refractive index deviation between the surface of the object to be imaged and the air through the Robin boundary condition;
[0023] Based on the propagation process of fluorescent photons in the object to be imaged and the refractive index deviation, a forward model is discretely solved by finite elements to obtain 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.
[0024] Preferably, 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:
[0025] Φ = AX;
[0026] 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 fluorescence target inside the object to be imaged, and A is the system matrix.
[0027] Preferably, in S3, based on the linear equation, an objective function is constructed by combining a least squares term and an elastic net regularization term, including:
[0028] The constructed objective function is expressed by the following formula:
[0029]
[0030] Wherein, is the L1 norm of ·, is the L2 norm of ·, λ1 and λ2 are elastic net regularization parameters, and λ2 ∈ [0, 1].
[0031] Preferably, in S4, the relaxed alternating direction method of multipliers is used to solve the objective function to obtain the first fluorescence molecular tomography result, including:
[0032] The relaxed alternating direction method of multipliers is used to equivalently transform the objective function into an objective function to be solved, and based on the variables in the objective function to be solved, an augmented Lagrangian function is constructed by combining a Lagrangian function and a quadratic penalty function term;
[0033] The augmented Lagrangian function is used to iteratively adjust the parameter constraints of the objective function to be solved, obtain the optimal solution of the objective function to be solved, and obtain the first fluorescence molecular tomography result.
[0034] Preferably, in S5, a hierarchical network model is trained by using a training data set and a training test set to obtain a trained fluorescence molecular tomography model, including:
[0035] Multiple groups of fluorescence distribution information on the surface of the object to be imaged and corresponding three-dimensional distribution and concentration data groups of the fluorescence target inside the object to be imaged are collected to form a training data set and a training test set;
[0036] A hierarchical network model is constructed, and the training data set and the training test set are input into the hierarchical network model for model training to obtain a trained fluorescence molecular tomography model.
[0037] Preferably, the construction of the hierarchical network model includes:
[0038] Determine the regularization objective function based on the diffusion approximation model of the radiative transfer equation, and calculate the gradient of the regularization objective function;
[0039] Use the gradient descent method for expansion to obtain the computational graph at each iteration;
[0040] Use the residual block structure of the multi-layer three-dimensional convolutional neural network to parameterize the gradient of the regularization term in the computational graph to obtain the parameterized computational graph at each iteration;
[0041] Take the parameterized computational graph at each iteration as a layer of network structure, and cascade all network structures to obtain the hierarchical network model.
[0042] Preferably, the determination of the regularization objective function based on the diffusion approximation model of the radiative transfer equation includes:
[0043] The regularization objective function is expressed by the following formula:
[0044]
[0045] where λ3 is the regularization parameter and M(X) is the regularization term.
[0046] Preferably, the use of the gradient descent method for expansion to obtain the computational graph at each iteration includes:
[0047] The computational graph is expressed by the following formula:
[0048]
[0049] where X k and X k-1 are respectively the three-dimensional distribution and concentration of the fluorescence target inside the object to be imaged output after the k-th and (k - 1)-th iterations, is the gradient of the k-th iteration, η k is the step size of the k-th iteration, and ReLU[·] is the rectified linear unit function.
[0050] (III) Beneficial Effects
[0051] Compared with the prior art, the high-resolution fluorescence molecular tomography method provided by the present invention has the following beneficial effects:
[0052] 1) Perform tetrahedral meshing on the object to be imaged, map the fluorescence data of the object to be imaged into the discretized phantom model through coordinates, perform forward model calculation based on the mapped phantom model to obtain 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, construct an objective function based on the linear equation in combination with the least square term and the elastic net regularization term, and use the relaxed alternating direction method of multipliers to solve the objective function to obtain the first fluorescence molecular tomography result. By establishing a phantom model and discretizing it, the fluorescence data of the object to be imaged can be accurately mapped into the discretized phantom model, ensuring that the fluorescence distribution information on the surface of the object to be imaged can accurately reflect the three-dimensional distribution of the fluorescence target inside the object to be imaged. By constructing and solving the objective function, a high-resolution first fluorescence molecular tomography result is obtained;
[0053] 2) Use the training data set and the training test set to train the hierarchical network model to obtain a trained fluorescence molecular tomography model. Input the fluorescence distribution information on the surface of the object to be imaged into the trained fluorescence molecular tomography model to obtain the second fluorescence molecular tomography result. Based on the hierarchical network model, construct a fluorescence molecular tomography model and perform model training. Using the fluorescence molecular tomography model, a second fluorescence molecular tomography result with high accuracy can be obtained;
[0054] 3) Combine the first fluorescence molecular tomography result and the second fluorescence molecular tomography result, so that the finally obtained fluorescence molecular tomography result has the characteristics of high resolution and high accuracy, effectively improving the imaging reduction degree of tissues in the organism. Description of the Drawings
[0055] 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 following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0056] Figure 1 It is a schematic flowchart of the present invention;
[0057] Figure 2 It is a schematic flowchart of obtaining the first fluorescence molecular tomography result in the present invention;
[0058] Figure 3 It is a schematic flowchart of obtaining the second fluorescence molecular tomography result in the present invention. Detailed Embodiments
[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying 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 based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0060] A high-resolution fluorescence molecular tomography method, as Figure 1 and Figure 2 shown, ① perform tetrahedral mesh division on the object to be imaged, and map the fluorescence data of the object to be imaged into a discretized phantom model through coordinates, specifically including:
[0061] Use a high-performance CCD camera to collect fluorescence data of the object to be imaged at all angles;
[0062] 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 ;
[0063] Map the fluorescence data of the object to be imaged at all angles into the discretized cylindrical phantom model through coordinates.
[0064] ② Based on the mapped phantom model, perform forward model calculation to obtain 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, specifically including:
[0065] Based on the mapped cylindrical phantom model, use the coupled diffusion approximation equation to describe the propagation process of fluorescence photons in the object to be imaged, and describe the refractive index deviation between the surface of the object to be imaged and the air through the Robin boundary condition;
[0066] Based on the propagation process of fluorescence photons in the object to be imaged and the refractive index deviation, solve the forward model through finite element discretization to obtain 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.
[0067] Specifically, 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:
[0068] Φ = AX;
[0069] 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.
[0070] ③Based on the linear equation, a target function is constructed by combining the least squares term and the elastic net regularization term, specifically including:
[0071] The constructed target function is expressed by the following formula:
[0072]
[0073] where is the L1 norm of ·, is the L2 norm of ·, and λ1, λ2 are elastic net regularization parameters, with λ2 ∈ [0, 1].
[0074] ④The relaxed alternating direction method of multipliers is used to solve the target function, obtaining the first fluorescence molecular tomography result, specifically including:
[0075] The relaxed alternating direction method of multipliers is used to equivalently transform the target function into an equivalent target function to be solved, and based on the variables in the equivalent target function to be solved, an augmented Lagrangian function is constructed by combining the Lagrangian function and the quadratic penalty function term;
[0076] The parameter constraints of the equivalent target function to be solved are adjusted iteratively using the augmented Lagrangian function to obtain the optimal solution of the equivalent target function to be solved, and the first fluorescence molecular tomography result is obtained.
[0077] In the above technical solution, the object to be imaged is divided into tetrahedral meshes, the fluorescence data of the object to be imaged is mapped to the discretized phantom model through coordinates, forward model calculations are performed based on the mapped phantom model to obtain 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. Based on the linear equation, a target function is constructed by combining the least squares term and the elastic net regularization term, and the relaxed alternating direction method of multipliers is used to solve the target function to obtain the first fluorescence molecular tomography result. By establishing a phantom model and discretizing the phantom model, the fluorescence data of the object to be imaged can be accurately mapped to the discretized phantom model, ensuring that the fluorescence distribution information on the surface of the object to be imaged can accurately reflect the three-dimensional distribution of the fluorescence target inside the object to be imaged. By constructing and solving the target function, a first fluorescence molecular tomography result with high resolution is obtained.
[0078] As Figure 1 and Figure 3 shown, ⑤The hierarchical network model is trained using the training data set and the training test set to obtain a trained fluorescence molecular tomography model, specifically including:
[0079] Multiple groups of fluorescence distribution information on the surface of the object to be imaged and the corresponding three-dimensional distribution and concentration data sets of the fluorescence target inside the object to be imaged are collected to form the training data set and the training test set;
[0080] Construct a hierarchical network model, input the training data set and the training test set into the hierarchical network model for model training, and obtain a trained fluorescence molecular tomography model.
[0081] Specifically, constructing a hierarchical network model includes:
[0082] Determine the regularization objective function based on the diffusion approximation model of the radiative transfer equation, and calculate the gradient of the regularization objective function;
[0083] Use the gradient descent method for expansion to obtain the computational graph at each iteration;
[0084] Use the residual block structure of the multi-layer three-dimensional convolutional neural network to parameterize the gradient of the regularization term in the computational graph, and obtain the parameterized computational graph at each iteration;
[0085] Take the parameterized computational graphs at each iteration as a layer of network structure respectively, and cascade all the network structures to obtain a hierarchical network model.
[0086] 1) Determine the regularization objective function based on the diffusion approximation model of the radiative transfer equation, including:
[0087] The regularization objective function is expressed by the following formula:
[0088]
[0089] Among them, λ3 is the regularization parameter, and M(X) is the regularization term.
[0090] 2) Use the gradient descent method for expansion to obtain the computational graph at each iteration, including:
[0091] The computational graph is expressed by the following formula:
[0092]
[0093] Among them, X k 、X k-1 are respectively the three-dimensional distribution and concentration of the fluorescence target inside the object to be imaged output after the k-th and the (k - 1)-th iteration, is the gradient of the k-th iteration, η k is the step size of the k-th iteration, and ReLU[·] is the rectified linear unit function.
[0094] ⑥ Input the fluorescence distribution information on the surface of the object to be imaged into the trained fluorescence molecular tomography model to obtain the second fluorescence molecular tomography result.
[0095] ⑦ Combine the first fluorescence molecular tomography result and the second fluorescence molecular tomography result to obtain a high-resolution fluorescence molecular tomography result.
[0096] In the above technical solution, a hierarchical network model is trained using a training data set and a training test set to obtain a trained fluorescence molecular tomography model. The fluorescence distribution information on the surface of the object to be imaged is input into the trained fluorescence molecular tomography model to obtain a second fluorescence molecular tomography result. A fluorescence molecular tomography model is constructed based on the hierarchical network model and trained. Using the fluorescence molecular tomography model, a second fluorescence molecular tomography result with high accuracy can be obtained.
[0097] Meanwhile, by combining the first fluorescence molecular tomography result and the second fluorescence molecular tomography result, the finally obtained fluorescence molecular tomography result has the characteristics of high resolution and high accuracy, effectively improving the imaging reduction degree of tissues in vivo.
[0098] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. 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 described in the foregoing embodiments, or perform equivalent replacements on some of the technical features. These modifications or replacements do 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 high-resolution fluorescence molecular tomography method, characterized in that: It includes the following steps: S1. Conduct tetrahedral mesh division on the object to be imaged, and map the fluorescence data of the object to be imaged into the discretized phantom model through coordinates; S2. Based on the mapped phantom model, perform forward model calculation to obtain 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; S3. Based on the linear equation, construct an objective function by combining the least squares term and the elastic net regularization term; S4. Use the relaxed alternating direction method of multipliers to solve the objective function to obtain the first fluorescence molecular tomography result; S5. Use the training data set and the training test set to train the hierarchical network model to obtain a trained fluorescence molecular tomography model; S6. Input the fluorescence distribution information on the surface of the object to be imaged into the trained fluorescence molecular tomography model to obtain the second fluorescence molecular tomography result; S7. Combine the first fluorescence molecular tomography result and the second fluorescence molecular tomography result to obtain a high-resolution fluorescence molecular tomography result.
2. The high-resolution fluorescence molecular tomography method according to claim 1, characterized in that: In S1, when conducting tetrahedral mesh division on the object to be imaged and mapping the fluorescence data of the object to be imaged into the discretized phantom model through coordinates, it includes: Use a high-performance CCD camera to collect the fluorescence data of the object to be imaged at all angles; Build 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 ; Map the fluorescence data of the object to be imaged at all angles into the discretized cylindrical phantom model through coordinates.
3. The high-resolution fluorescence molecular tomography method according to claim 2, wherein: In S2, when performing forward model calculation based on the mapped phantom model to obtain 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, it includes: Based on the mapped cylindrical phantom model, use the coupled diffusion approximation equation to describe the propagation process of fluorescence photons in the object to be imaged, and describe the refractive index deviation between the surface of the object to be imaged and the air through the Robin boundary condition; Based on the propagation process of fluorescence photons in the object to be imaged and the refractive index deviation, solve the forward model by finite element discretization to obtain 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.
4. The high-resolution fluorescence molecular tomography method according to claim 3, wherein: 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.
5. The high-resolution fluorescence molecular tomography method according to claim 4, wherein: In S3, when constructing an objective function based on the linear equation by combining the least squares term and the elastic net regularization term, it includes: The constructed objective function is expressed by the following formula: where, is the L1 norm of ·, is the L2 norm of ·, and λ1, λ2 are elastic net regularization parameters, where λ2 ∈ [0, 1].
6. The high-resolution fluorescence molecular tomography method according to claim 5, characterized in that: In S4, when using the relaxed alternating direction method of multipliers to solve the objective function to obtain the first fluorescence molecular tomography result, it includes: Use the relaxed alternating direction method of multipliers to equivalently transform the objective function into an equivalent objective function to be solved, and based on the variables in the equivalent objective function to be solved, construct an augmented Lagrangian function by combining the Lagrangian function and the quadratic penalty function term; Use the augmented Lagrangian function to iteratively adjust the parameter constraints of the equivalent objective function to be solved, obtain the optimal solution of the equivalent objective function to be solved, and obtain the first fluorescence molecular tomography result.
7. The high-resolution fluorescence molecular tomography method according to claim 1, characterized in that: In S5, the hierarchical network model is trained using the training dataset and the training test set to obtain a trained fluorescence molecular tomography model, including: Collecting multiple groups of fluorescence distribution information on the surface of the object to be imaged and the three-dimensional distribution and concentration data groups of the fluorescence targets inside the object to be imaged, and constituting the training dataset and the training test set; Constructing a hierarchical network model, inputting the training dataset and the training test set into the hierarchical network model for model training, and obtaining a trained fluorescence molecular tomography model.
8. The high-resolution fluorescence molecular tomography method according to claim 7, characterized in that: The constructing of the hierarchical network model includes: Determining the regularization objective function based on the diffusion approximation model of the radiative transfer equation and calculating the gradient of the regularization objective function; Using the gradient descent method for expansion to obtain the computational graph at each iteration; Using the residual block structure of the multi-layer three-dimensional convolutional neural network to parameterize the regularization term gradient in the computational graph to obtain the parameterized computational graph at each iteration; Taking the parameterized computational graphs at each iteration as a layer of network structure respectively, and cascading all the network structures to obtain the hierarchical network model.
9. The high-resolution fluorescence molecular tomography method according to claim 8, wherein: The determining of the regularization objective function based on the diffusion approximation model of the radiative transfer equation includes: The regularization objective function is expressed by the following formula: where λ3 is the regularization parameter and M(X) is the regularization term.
10. The high-resolution fluorescence molecular tomography method according to claim 9, wherein: The using of the gradient descent method for expansion to obtain the computational graph at each iteration includes: The computational graph is expressed by the following formula: Among them, X k and X k-1 are respectively the three-dimensional distribution and concentration of the fluorescence target inside the object to be imaged output after the k-th and (k - 1)-th iterations, is the gradient of the k-th iteration, η k is the step size of the k-th iteration, and ReLU[·] is the rectified linear unit function.