CN113057582B - MLEM-based quantitative cone beam X-ray luminescence computed tomography method for self-adaptive FISTA initial image - Google Patents

Abstract

The invention discloses a quantitative cone beam X-ray luminescence computed tomography method of an adaptive FISTA initial image based on MLEM, and cone beam X-ray luminescence computed tomography (CB-XLCT) is used as a novel dual-mode optical molecular imaging technology, and has great application prospect in tumor diagnosis and treatment. It needs to describe the quantitative relationship between PNPs concentration and reconstructed brightness, and in order to make quantitative evaluation feasible, the method has two main steps: firstly, the regularization parameters are automatically adjusted by the adaptive FISTA after iteration, and sparse solution is rapidly obtained. Secondly, the sparse solution is used as an initial iteration value of the MLEM, so that the reconstruction time is reduced, and the accuracy of the reconstruction value is improved. The results from digital simulations and phantom experiments show that ADMLEM can describe the quantitative relationship between PNPs concentration and reconstructed brightness.

Description

MLEM-based quantitative cone beam X-ray luminescence computed tomography method for self-adaptive FISTA initial image

Technical Field

The invention belongs to the technical field of medical optics, and particularly relates to a quantitative cone beam X-ray luminescence computed tomography method of an adaptive FISTA initial image based on MLEM.

Background

With the development of Phosphor Nanoparticles (PNPs), X-ray luminescence computed tomography (XLCT) is receiving increasing attention as a molecular imaging method combining X-ray and optical imaging. Theoretically, PNPs emit near-infrared (NIR) luminescent light signals at deep imaging tissues under X-ray excitation, which can be measured by Electron Multiplying Charge Coupled Device (EMCCD) cameras. And then the three-dimensional space distribution of the PNPs in the imaging tissue can be obtained by combining the projection data and the reconstruction model. Compared with bioluminescence tomography (BLT) and Fluorescence Molecular Tomography (FMT), XLCT can eliminate tissue autofluorescence, realize dual-mode imaging, has the advantages of large imaging depth by virtue of the characteristics of deep penetration and small attenuation of X-rays, and has wide attention in preclinical research such as early tumor detection, drug metabolism monitoring and the like.

Cone-beam XLCT (CB-XLCT) has important advantages in the aspect of researching biological structure information and function information as a novel dual-mode imaging mode. The method has the advantages of short scanning time and high X dose utilization rate, and provides feasibility for real-time in-vivo imaging in the future. This makes CB-XLCT with shorter scan times also have great potential for use in drug discovery. However, XLCT is difficult to solve the ill-conditioned problem of reconstructing PNPs due to incomplete data and lack of sufficient a priori information.

Disclosure of Invention

Aiming at the existing problems, the invention provides a quantitative cone beam X-ray luminescence computed tomography method of an adaptive FISTA initial image based on MLEM, which reconstructs the positioning and quantitative information of inversion PNPs and considers the sparsity and the statistical noise model of the reconstruction result, thereby realizing accurate reconstruction.

The technical solution for realizing the purpose of the invention is as follows:

the MLEM-based quantitative cone beam X-ray luminescence computed tomography method for the adaptive FISTA initial image is characterized by comprising the following steps of:

step 1: establishing an imaging model of CB-XLCT, which is divided into three parts:

1) The transmission process of the X-rays emitted by the cone-beam X-ray source through the biological tissue containing the nanoparticles is described as:

wherein, X ₀ The initial intensity of the X-ray source is X (r) respectively represents the X-ray intensity at a position r in the biological tissue, and mu (tau) represents the X-ray attenuation coefficient obtained by the CT technology;

2) The X-ray excites a nanoparticle target in a living body to generate visible light or near infrared light, and the expression is as follows:

S(r)＝εX(r)ρ(r) (2)，

wherein S (r) represents the light source emitted by the material, ρ (r) is the concentration of PNPs at position r, and ε is the luminescence yield;

3) The emitted light is modeled using the diffusion equation, which is:

wherein D (r) is an expansion coefficient, and the calculation formula is as follows:

μ _a (r) is the absorption coefficient, μ _s (r) is the reduced scattering coefficient, g is the anisotropy parameter, Φ (r) is the photon flux, Ω is the image domain;

and because the propagation of photons in a stable state in the tissue conforms to the Robin boundary, the following can be obtained:

where v (r) is the outward unit normal vector at the boundary and ρ is the mismatch factor at the boundary relative to the media on either side of the boundary;

according to the finite element method, the imaging model of the CB-XLCT can be expressed as follows:

Φ＝Ws (5)，

where Φ is the projection data for different angles, W is the irreversible system matrix, and s is the spatial distribution of the nanoparticles to be reconstructed.

And 2, step: solving an ill-defined inversion problem in the CB-XLCT by adopting an MLEM method with a specific image based on the CB-XLCT model;

and 3, step 3: quantitative evaluation between PNPs concentration and reconstructed brightness was performed based on the obtained solution.

Further, the specific operation steps of step 2 include:

step 21: firstly, normalizing the system matrix W and the projection data phi, namely rewriting the formula (5) as follows:

Φ _new ＝W _new s (6)，

wherein phi _new And W _new Respectively normalized projection data and a system matrix;

and W _new ＝WW _nor ，

In the formula

Wherein W _i A weight value influenced by PNPs is set for each detection point;

step 22: based on the obtained normalized data, obtaining sparse reconstruction by using a self-adaptive FISTA method, and obtaining a reconstruction model by using an L1 regularizer, wherein the model expression is as follows:

wherein λ is a hyper-parameter that balances fidelity and regularization terms;

step 23: the solution s ^ obtained by the adaptive FISTA is used as an initial value of the MLEM, and the model is solved by using the traditional MLEM method of the Poisson noise model, namely:

wherein m is the number of projection data, and n is the number of reconstruction region points.

Further, the specific operation steps of the adaptive FISTA method in step 22 include:

step 221: let f(s) = | | W _new s-Φ _new || ² ,g(s)＝||s|| ₁ L = L (f), L being a function of

The lipschitz constant of maximum eigenvalue;

step 222: inputting a random initial value and setting an initial hyper-parameter: let y ₁ ＝s ₀ ,

t ₁ ＝1,λ ₁ K iterations of which the hyper-parameter λ is updated after each iteration =0 _k ：

s _k ＝p _L (y _k )，

λ _k+1 ＝λ _k +α|s _k |，

Wherein the content of the first and second substances,

step 223: obtaining sparse results s after k iterations _k 。

Compared with the prior art, the method has the following beneficial effects:

firstly, compared with the traditional method, the method provided by the invention has better reconstruction results and better linear relation between the concentration of the PNPs and the reconstruction brightness under different noise levels, and the method has better performance on the reconstruction quality and the positioning accuracy of the PNPs;

secondly, the method provided by the invention also uses self-adaptive FISTA, and compared with the method of directly putting the FISTA result into the MLEM, the method does not need to select proper hyper-parameters, so the method greatly reduces the running time, and on the other hand, the MLEM greatly reduces the number of reconstruction points and accelerates the reconstruction time by using the sparse prior of the FISTA sparse initial value;

in conclusion, the method provided by the invention proves the quantitative description of the relationship between the concentration of PNPs and the reconstructed brightness in numerical simulation and simulation experiments through the MLEM reconstruction of the self-adaptive FISTA initial image. The method makes full use of the sparse result obtained by the self-adaptive FISTA, and makes the rapid quantitative reconstruction and the improvement of the image quality possible.

Drawings

FIG. 1 is a schematic diagram of a CB-XLCT system for performing a simulation experiment according to the present invention;

FIG. 2 shows the reconstruction results of a single-target digital simulation performed by different methods at different noise levels of 1.5cm height, and FIG. 2 (a) shows the reconstruction results under noise-free conditions, and FIG. 2 (b) shows the reconstruction results when the signal-to-noise ratio is reduced to 5 dB;

FIG. 3 is a graph showing the change of CNR and Dice evaluation indexes with noise increase, which are reconstructed by different methods;

FIG. 4 is a graph showing the relationship between the reconstructed concentration and the actually set concentration under different noise and different reconstruction methods, and FIGS. 4 (a) - (e) are graphs showing the analysis of the reconstruction results of Adaptik, MAP, MLEM, FISTA, and ADMLEM, respectively;

FIG. 5 is a graph showing the reconstruction results of different algorithms and the variation curve of the reconstruction concentration with the noise level under the same concentration dual target;

fig. 6 is a curve showing the reconstructed concentrations of different algorithms along with the change of noise under the same concentration dual targets, and fig. 6 (a) - (e) respectively show the relationship between the reconstructed concentrations of two targets along with the change of noise under the conditions of different noise intensities by Adaptik, MAP, MLEM, FISTA and admlim algorithms;

FIG. 7 shows the reconstruction and evaluation results of different algorithms under the dual target of 2:1 concentration ratio;

FIG. 8 is the concentration of fluorescent nanoprobes reconstructed by different methods under different noise for two different target concentrations, and FIGS. 8 (a) - (e) show the variation curves of Adaptik, FISTA, MAP, MLEM, and ADMLEM noise with concentration, respectively;

FIG. 9 shows the results of reconstruction and CT mixing of a phantom experiment under different concentration conditions for a single target and different methods;

FIG. 10 is a graph showing the variation between the reconstructed concentration and the actually set concentration of the fluorescent nanoprobe;

FIG. 11 is a reconstruction and CT mixed result of a dual-target same-concentration phantom experiment;

FIG. 12 is a dual target same concentration ratio reconstruction and CT blending result with EED set at 0mm for both targets.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the following description will be made with reference to the accompanying drawings and embodiments.

1. Theoretical method

(1) Imaging model

The transmission process of the X-rays emitted by the cone-beam X-ray source through the biological tissue containing the nanoparticles can be described as:

wherein, X ₀ The initial intensity of the X-ray source is X (r) respectively represents the X-ray intensity at a position r in the biological tissue, and mu (tau) represents the X-ray attenuation coefficient obtained by the CT technology;

x-rays excite nanoparticle targets in the organism, exciting them to produce visible or near infrared light (NIR), which can be expressed as:

S(r)＝εX(r)ρ(r) (2)，

where S (r) represents the light source emitted by the material, ρ (r) is the concentration of PNPs at location r, and ε is the luminescence yield.

The process of light transmission in tissue can be described by the Diffusion Equation (DE) according to the optical propagation properties of biological tissue, namely:

wherein D (r) is an expansion coefficient, and the calculation formula is as follows:

in the formula [ mu ] _a (r) is the absorption coefficient, μ _s (r) is the reduced scattering coefficient, g is the anisotropy parameter, Φ (r) is the photon flux, and Ω is the image domain.

In addition, the propagation of photons in steady state in tissue conforms to the Robin boundary, i.e.:

where v (r) is the outward unit normal vector at the boundary and ρ is the mismatch factor at the boundary relative to the media on either side of the boundary;

converting equation (4) from differential to integral, and combining the ideas of the finite element method, equation (4) is rewritten as:

Φ＝Ws (5)，

where Φ is the projection data for different angles, W is the irreversible system matrix, and s is the spatial distribution of the nanoparticles to be reconstructed. The formula (5) is the CB-XLCT imaging model.

(2) CB-XLCT imaging of MLEM reconstruction method based on specific initial image

Without considering the noise model, researchers have tried various approaches to solve the ill-defined inversion problem in CB-XLCT. While the regularization method may make the results sparse or smooth, it may lack detail, resulting in image distortion. In consideration of the advantages of an accurate noise model in the maximum likelihood expectation estimation MLEM algorithm and sparse priors in the regularization algorithm, the MLEM method (namely Adaptive-FISTA-MLEM) adopting a specific initial image is suitable for solving an ill-defined inversion problem and realizing quantitative evaluation between PNPs concentration and reconstructed brightness.

The method comprises the following three steps:

step 1: in this method, in order to slow down the depth sensitivity, overcome the selection of the iteration rate and speed up convergence in different data sets, the system matrix W is first normalized to 0-1, so equation (5) can be rewritten as:

Φ _new ＝W _new s (6)，

wherein phi _new And W _new Respectively normalized projection data and a system matrix;

in formula (6): w is a group of _new ＝WW _nor ，

And is

W in the formula _i A weight value influenced by PNPs is set for each detection point;

step 2: based on the normalized data obtained in step 1, in a second step, a self-adaptive FISTA is proposed for obtaining sparse reconstruction; for sparseness purposes, L1 regularization is used to suppress the reconstruction, and the optimization problem can be described as:

where λ is a hyper-parameter that balances fidelity and regularization terms, which is a difficult parameter to select;

under the inspiration of a machine learning method, one step of hyper-parameter iteration is added after each iteration, and an adaptive FISTA method can be used for solving the problem of uncertainty, so that a sparse result is obtained quickly.

The adaptive FISTA method may be described as the following steps:

s1: let f(s) = | | W _new s-Φ _new || ² ,g(s)＝||s|| ₁ L = L (f), L being a function of

The liphoz constant for the maximum eigenvalue.

S2: let y ₁ ＝s ₀ ,

t ₁ ＝1,λ ₁ =0, (i.e. input random initial value and set initial hyper-parameter) iterate k times, update hyper-parameter lambda after each iteration _k ；

s _k ＝p _L (y _k )，

λ _k+1 ＝λ _k +α|s _k |，

Wherein

S3: obtaining sparse results s after k iterations _k 。

L in S1 is a function of

The Lipschitz constant of the maximum feature vector, alpha is the gradient change step length (set to 0.01 in each data set), and the self-adaptive adjustment of the hyper-parameters is realized.

And step 3: the problem is solved using the conventional MLEM method based on poisson noise model and solved by the adaptive FISTA described above, the resulting solution s ^ is used as the initial value of MLEM, namely:

wherein m is the number of projection data, and n is the number of reconstruction region points.

Therefore, the problem of uncertain inversion can be solved accurately and quickly through the 3 steps to obtain the reconstructed brightness, and the quantitative evaluation between the PNPs concentration and the reconstructed brightness is realized through the linear relation of the functions.

2. Simulation experiment

Digital simulations and mock experiments were performed on the methods presented herein to assess the quantitative relationship between PNPs concentration and reconstructed brightness. And to illustrate the advantages of the method of the invention, it is compared to some conventional methods, such as ART, tikhonov, FISTA, MLEM, FISTA-MLEM, none of which are normalized or adaptively adjusted. The following experiments are described:

(1) CB-XLCT system

Digital simulations were performed according to the CB-XLCT system shown in FIG. 1. In the phantom experiments, the CB-XLCT system consists of a microfocus X-ray source (Oxford instruments, england) with a maximum power of 80W, an Electron Multiplying Charge Coupled Device (EMCCD) camera (IXonDU-897, andon, england) with a 50 mm f/1.8D lens (Nikon, meilville, N.y.) for collecting the luminescence signals and a CMOS X-ray detector (2. Sup. X-ray detector)

923, dexela, u.k) to collect X-ray signals.

(2) Numerical simulation

First, the method was tested using the CB-XLCT system. To simulate the environment of biological tissue, a cylindrical mold with a radius of 1.5cm and a height of 3.0cm was filled with a 1% solution of lactone. A probe having a radius of 0.2cm and a concentration of 1mg/mL,2mg/mL,3mg/mL,4mg/mL and 5mg/mL was placed at a height of 1.5 cm. The power of the X-ray source should be 40keV. 24 projection data are acquired uniformly every 15 ° over a 360 ° rotation range. Poisson and Gaussian noise are added into the projection data, and the signal-to-noise ratio is reduced to 5dB,10dB,15 dB,20dB and 25dB. To verify the accuracy of the simulation, the simulation probe was repeated at different locations. The concentration of PNPs is reconstructed using Tikhonov, FISTA, MLEM, ADMLEM without normalization or adaptive tuning.

In the second numerical simulation, two probes with radii of 2mm and 6mm edge-to-edge distance (EED) were placed at the same depth as the cylinder model in the first numerical simulation. The probe concentrations were set to 1mg/mL and 1mg/mL, respectively. Further, the concentration of the probe was set to 1mg/mL and 2mg/mL, and the method was evaluated at different concentration ratios. The acquisition of projection data, the increase of noise and the selection of the method are all the same as those of the single-target simulation.

(3) Simulation experiment

The relation between the concentration of PNPs and the reconstructed brightness is researched by adopting a single-target biomimetic experiment. First, a glass column A (diameter 3.0 cm) was filled with a 1% solution of lactone, having an absorption coefficient of:

μ _a (r)＝0.02cm ^-1 decrease the scattering coefficient mu _s (r)＝10cm ^-1 ；

Then, a glass column B (diameter: 0.4 cm) was filled with Gd ₂ O ₃ :E ³⁺ And placed in glass column a. To test the reconstructed brightness at different concentrations, the concentrations in B were set to 10mg/mL,20mg/mL,40mg/mL,60mg/mL and 80mg/mL, respectively.

In order to evaluate the impact of the number of targets, a dual-target mock-up experiment was also designed. First, in a CB-XLCT system, two glass columns (0.4 cm diameter) containing 50mg/mL and 50mg/mL PNPs were placed in a glass column as in a single target mock experiment. In order to test the influence of different EEDs on the column body, the EEDs of the column body are respectively set to be 1.7mm, 2.3mm and 5mm; next, to evaluate the method at different concentration ratios, two glass columns containing 50mg/mL and 50mg/mL, 50mg/mL and 100mg/mL, 50mg/mL and 150mg/mL PNPs, respectively, were placed in three binocular mock experiments.

In the full-mode experiment, the power of the X-ray source was set to 40keV,0.5mA, and the phantom was placed at the same position of the CB-XLCT system, rotating both of them by 360 deg.. During the rotation, the EMCCD camera acquires 24 projection images every 15 °. The exposure time, EM gain, and binarization of the EMC CD are set to 1s, 260, and 1 × 1, respectively.

(4) Evaluation index

In order to evaluate the image contrast of a region of interest (ROI) and to determine the image quality, an evaluation is carried out using the contrast-to-noise ratio (CNR), which is calculated as follows:

wherein, mu _ROI And σ ² _ROI Respectively representing the mean and variance of a region of interest (ROI); mu.s _Back And σ ² _Back Respectively representing the mean and variance of the background area;

furthermore, dice is also used to compare the similarity between the actual region obtained by CT and the reconstructed target region obtained by various methods, and is calculated as:

where x represents the reconstruction region and x ^ represents the region of interest.

The larger CNR and Dice mean the better reconstruction effect, and in order to quantitatively evaluate the relationship between the concentration of PNPs and the reconstructed brightness, it is necessary to obtain an evaluation index to describe the reconstructed brightness. The reconstructed luminance is described as follows: the reconstruction results reconstruct the mean of the luminance within the ROI region.

3. Results of the experiment

(1) Numerical simulation results

FIG. 2 shows the tomographic imaging results of a single target under different noise conditions at different concentrations and different reconstruction algorithms at a height of 1.5cm, wherein FIG. 2 (a) shows the reconstruction results under the noise-free condition, and FIG. 2 (b) shows the reconstruction results under the condition of a signal-to-noise ratio of 5dB. In each figure, the different reconstruction methods are indicated from top to bottom as Adaptik, MAP, MLEM, FISTA, and ADMLEM, respectively, and from left to right as fluorescent nanoprobes at concentrations of 1mg/mL,2mg/mL,3mg/mL,4mg/mL, and 5mg/mL, respectively. Wherein the red large circle represents the cylinder, and the yellow small circle represents the real position of the fluorescent nanoprobe. And reconstruction accuracy evaluation indices such as CNR and Dice are given in FIG. 3, in which FIGS. 3 (a 1), (a 2), (a 3), (a 4) and (a 5) show CNR result curves at concentrations of 1mg/mL,2mg/mL,3mg/mL,4mg/mL and 5mg/mL, respectively. FIGS. 3 (b 1), (b 2), (b 3), (b 4) and (b 5) show Dice result curves at concentrations of 1mg/mL,2mg/mL,3mg/mL,4mg/mL and 5mg/mL, respectively.

In addition, fig. 4 shows the relationship between reconstructed concentrations and the actually set concentrations under different noises and different reconstruction methods, wherein fig. 4 (a), (b), (c), (d) and (e) respectively show the analysis of the reconstruction results of Adaptik, MAP, MLEM, FISTA and admlemm, and each image is compared by six different noises.

Experimental results show that although all methods have a good linear relationship between PNPs concentration and reconstructed brightness under a noise-free condition, many methods cannot accurately reconstruct and describe the relationship between the PNPs concentration and the reconstructed brightness, and other conventional methods are very sensitive to noise except that the method of the present invention can accurately reconstruct and correctly describe the relationship between the PNPs concentration and the reconstructed brightness as the signal-to-noise ratio decreases. In addition, the approach herein greatly reduces run time through adaptive parameter tuning and sparse matrices.

The reconstructed results of the two-object digital simulation of the same concentration and different concentration ratios of different methods at different noise levels at a height of 1.5cm, and the variation curves of CNR and Dice at different noise levels are shown in fig. 5 and 7, respectively. Wherein, fig. 5 (a) shows the reconstruction results of Adaptik, MAP, MLEM, FISTA, and admlim from top to bottom, which correspond to the reconstruction results without noise, with snr of 25db,20db,15db,10db, and 5dB, respectively, from left to right. FIGS. 5 (b) and (c) are graphs showing the variation of the quantitative evaluation indices CNR and Dice with noise under five different reconstruction methods, respectively; FIG. 7 (a) shows the reconstruction results of Adaptik, FISTA, MAP, MLEM, and ADMLEM from top to bottom, corresponding to the reconstruction results of noise-free, signal-to-noise ratios of 25dB,20dB,15dB,10dB, and 5dB, respectively, from left to right. Fig. 7 (b) and (c) show curves of the quantitative evaluation indices CNR and rice as a function of noise under five different reconstruction methods, respectively. As can be seen from the results of fig. 5 and 7, ADMLEM not only has a better evaluation of CNR or Dice, but also in fig. 6 and 8, it is shown that the ADMLEM method has a better linear relationship between the two targets than other methods, i.e. the reconstruction results can well describe the relative relationship when the probe concentrations are the same or different.

(2) Simulation experiment

The simulation experiment is an indispensable part for verifying the effectiveness of the method. FIG. 7 shows the reconstruction results in a single target mock experiment by ADMLEM and conventional methods. Wherein the actual positions of the two target PNPs obtained by CT are marked with small red circles. The reconstruction results and quality evaluations are shown in fig. 9, fig. 10 and tables 1, 2 and 3. Wherein, the first column to the fifth column of FIG. 9 represent the reconstruction results of different reconstruction algorithms at concentrations of 10mg/mL,20mg/mL,40mg/mL,60mg/mL, and 80mg/mL, respectively, and the first row to the fifth row represent Adaptik, FISTA, MAP, MLEM, ADMLEM algorithms, respectively; from the point of view of reconstruction results and quality evaluation, the ADMLEM algorithm obtains the highest score on two indexes, and shows that the ADMLEM has better effects on the shape recovery and contrast of imaging.

TABLE 1 CNR index of reconstruction results of fluorescent nanoprobes of different concentrations under single target

TABLE 2 Dice index of single target different concentration fluorescent nano probe reconstruction result

TABLE 3 Linear correlation coefficient and Linear analysis of the reconstruction results at different concentrations

In addition, the reconstruction and CT mixed results of the dual-target same-concentration phantom experiment are shown in FIG. 11. FIG. 11 shows the results of reconstitution of the same concentration of PNPs in different EEDs (5.0 mm,2.3mm and 1.7 mm) by the methods Adaptik, MAP, MLEM, FISTA, ADMLEM in that order. Tables 4 and 5 are evaluations of the ratio of localization accuracy to reconstructed concentration. The traditional ART, tikhonov and other methods are difficult to reconstruct the actual position. Although considering sparseness of the reconstruction result, the FISTA cannot obtain a high quality reconstruction result due to measurement noise. From tables 4 and 5 it can be seen that the method ADM proposed herein has good reconstruction results in different EEDs.

TABLE 4 reconstruction results CNR and Dice index for two targets with EEDs set at 5.0mm,2.3mm,1.7mm

TABLE 5 concentration ratio of two targets with the same concentration at different edge distances

FIG. 12 shows the reconstruction results of PNPs at different concentrations, the reconstruction methods are Adaptik, FISTA, MAP, MLEM, and ADMLEM in sequence. The first two concentration ratios are 50mg/mL to 50mg/mL, and the second two concentration ratios are 50mg/mL to 100mg/mL. As can be seen from the figure, it is difficult to reconstruct the image well when the concentration of the two objects is large or the EED of the two objects is small. Whereas the ADMLEM method proposed herein reflects better results in terms of the location and concentration of PNPs compared to other methods, table 6 below is the reconstituted concentration ratio of the same concentration to different concentrations.

TABLE 6 concentration ratio of two targets with the same edge distance reconstructed at different actual concentrations

Ratio of true concentration	Reconstituted concentration ratio
		50mg/mL:50mg/mL	1:1.14
50mg/mL:100mg/mL	1:1.73

Those not described in detail in this specification are within the skill of the art. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and modifications of the invention can be made, and equivalents of some features of the invention can be substituted, and any changes, equivalents, improvements and the like, which fall within the spirit and principle of the invention, are intended to be included within the scope of the invention.

Claims (1)

1. The MLEM-based quantitative cone beam X-ray luminescence computed tomography method of the self-adaptive FISTA initial image is characterized by comprising the following steps of:

step 1: establishing an imaging model of CB-XLCT, which is divided into three parts:

1) The transmission process of the X-rays emitted by the cone-beam X-ray source through the biological tissue containing the nanoparticles is described as:

wherein X ₀ X (r) is the intensity of X-rays at a position r in the biological tissue, and μ (τ) is the intensity obtained by CT techniqueAn X-ray attenuation coefficient;

2) The X-ray excites a nanoparticle target in a living body to generate visible light or near infrared light, and the expression is as follows:

S(r)＝εX(r)ρ(r) (2)，

wherein S (r) represents the light source emitted by the material, ρ (r) is the concentration of PNPs at position r, and ε is the luminescence yield;

3) The emitted light is modeled using the diffusion equation, which is:

wherein the content of the first and second substances,

and D (r) is the coefficient of expansion, μ _a (r) is the absorption coefficient, μ _s (r) is the reduced scattering coefficient, g is the anisotropy parameter, Φ (r) is the photon flux, Ω is the image domain;

and because the propagation of photons in a stable state in the tissue conforms to the Robin boundary, the following can be obtained:

where v (r) is the outward unit normal vector at the boundary and ρ is the mismatch factor at the boundary relative to the media on either side of the boundary; d (r) is an expansion coefficient; Φ (r) is the photon flux;

according to the finite element method, the imaging model of the CB-XLCT can be expressed as follows:

Φ＝Ws (5)，

wherein Φ is projection data at different angles, W is an irreversible system matrix, and s is the spatial distribution of the nanoparticles to be reconstructed;

and 2, step: solving an ill-defined inversion problem in the CB-XLCT by adopting an MLEM method with a specific image based on the CB-XLCT model;

and 3, step 3: carrying out quantitative evaluation between the concentration of PNPs and the reconstructed brightness according to the obtained solution;

the specific operation steps of the step 2 comprise:

step 21: firstly, normalizing the system matrix W and the projection data phi, namely rewriting the formula (5) as follows:

Φ _new ＝W _new s (6)，

wherein phi is _new And W _new Respectively normalized projection data and a system matrix; and:

W _new ＝WW _nor ；

wherein W _i A weighted value of each detection point influenced by PNPs is set;

step 22: based on the obtained normalized data, obtaining sparse reconstruction by using a self-adaptive FISTA method, and obtaining a reconstruction model by using an L1 regularizer, wherein the model expression is as follows:

wherein λ is a hyper-parameter that balances fidelity and regularization terms;

step 23: solution obtained from adaptive FISTA

The method is used as an initial value of the MLEM, and then a traditional MLEM method of a Poisson noise model is utilized to solve the model, namely:

wherein m is the number of projection data, and n is the number of reconstruction region points;

the specific operation steps of the adaptive FISTA method described in step 22 include:

step 221: let f(s) = | | W _new s-Φ _new || ² ,g(s)＝||s|| ₁ L = L (f), L being a function of

The liphoz constant for the maximum eigenvalue;

step 222: inputting a random initial value and setting an initial hyper-parameter: let y ₁ ＝s ₀ ,

t ₁ ＝1,λ ₁ K iterations of which the hyper-parameter λ is updated after each iteration =0 _k ：

s _k ＝p _L (y _k )，

λ _k+1 ＝λ _k +α|s _k |，

Wherein the content of the first and second substances,

step 223: obtaining sparse results s after k iterations _k 。

Images