CN103393410A - Fluorescence molecular tomography reconstruction method based on alternative iterative operation - Google Patents

Abstract

The invention discloses a fluorescence molecular tomography reconstruction algorithm based on alternate iterative operations, which alternately uses weighted algebraic reconstruction technology and steepest descent method to solve the problem, and its realization steps are as follows: (1) acquire measurement data; (2) establish measurement The linear relationship between the data and the target distribution; (3) Construct a 2-norm minimization problem with constraints; (4) Alternately use the weighted algebraic reconstruction technique and the steepest descent method to solve the minimization problem and obtain the target distribution map . The present invention is based on light transmission theory and finite element method, utilizes prior information such as optical characteristic parameters and anatomical structure, adopts multi-point excitation and multi-point measurement, obtains measurement data as much as possible, and reduces the morbidity of the problem. Alternately using the weighted algebraic reconstruction technique and the steepest descent method to solve the problem effectively improves the reconstruction results of fluorescence molecular tomography, and has important application value in the fields of molecular imaging and reconstruction algorithms.

Description

A Fluorescence Molecular Tomography Reconstruction Method Based on Alternate Iterative Operation

technical field

The invention belongs to the field of molecular imaging, and further relates to a fluorescence molecular tomography reconstruction algorithm based on alternate iterative operations, which can be used for inverse reconstruction of in vivo fluorescence molecular tomography.

Background technique

Fluorescence molecular tomography (hereinafter referred to as FMT) is a new optical molecular imaging technology that has emerged in recent years. It uses certain molecules (generally mainly polycyclic aromatic hydrocarbons or heterocyclic compounds, etc.) Needles, fluorescent dyes, etc. mark reconstruction targets. Under the irradiation of an external excitation light source, the molecules will absorb the external excitation light, and then emit photons, and the intensity of the generated light is proportional to the number of marked targets. Outside the reconstruction target area, the photons transmitted out of the reconstruction target area can be directly detected by using high-sensitivity optical detection instruments, and the position and concentration of the fluorescent target inside the reconstruction target area can be obtained by using an effective fluorescence molecular tomography reconstruction algorithm .

Fluorescence molecular tomography is a reverse problem, which is seriously ill-conditioned. The essential reason is to reconstruct the strong scattering characteristics of light in the target area. The transmission of photons inside it no longer propagates along a straight line, but goes through a large number of irregular scattering processes. At the same time, the signal detected by the optical detection instrument at the boundary of the reconstruction target area is the value of the boundary point, and the number is limited, while the number of points inside the solution area is very large. Solving a large number of unknowns from a small amount of measurement data is an ill-posed problem with serious ill-conditioning. Its solution is not unique and is easily affected by measurement errors and noise. How to construct a fluorescent target that accurately reconstructs the target region is the core issue in the study of fluorescence molecular tomography.

Contents of the invention

In order to solve the morbidity and non-uniqueness of solutions in fluorescence molecular tomography, the present invention proposes a reconstruction method of fluorescence molecular tomography based on alternate iterative operations. In order to reduce the morbidity of the problem, the present invention adopts multi-point excitation and multi-angle measurement to obtain as much measurement data as possible. Combining the light transmission model and finite element theory, the optical characteristic parameters and anatomical structure information of the reconstructed target are used as prior information to establish a linear relationship between the measured data on the surface and the distribution of fluorescent targets inside the reconstructed target, and transform the linear relationship into a constrained condition The minimization problem of , is solved by alternately performing the weighted algebraic reconstruction technique and the steepest descent method, so as to obtain the three-dimensional distribution and concentration of the fluorescent target inside the reconstructed target.

To achieve the above object, the concrete steps of the present invention are as follows:

A fluorescence molecular tomography reconstruction method based on alternate iterative operations, characterized in that: based on the light transmission model and finite element theory, the optical characteristic parameters and anatomical structure information of the reconstruction target are used as prior information to establish surface measurement data and reconstruction The linear relationship of the fluorescent target distribution inside the target is transformed into a constrained minimization problem, and the weighted algebraic reconstruction technique and the steepest descent method are alternately performed to solve it, so as to obtain the three-dimensional distribution of the fluorescent target inside the reconstructed target and concentration.

As an improvement, the steps are as follows:

(1) Obtain measurement data

a. The excitation light source conducts multi-angle transmission tomography on the reconstruction target fixed on the electric control rotary table;

b. Obtain measurement data using an optical detection instrument to obtain the luminous flux density Φ _m .

(2) Obtain the anatomical structure information and optical characteristic parameters of the reconstructed target.

(3) Based on the light transmission model and finite element theory, the anatomical structure information and optical characteristic parameters of the reconstructed target are used as prior information, and the linear relationship between the measured data on the surface and the distribution of fluorescent targets inside the reconstructed target is established.

(4) Transform the above linear relationship into a constrained minimization problem:

min||X|| ₂ , st|AX-Φ _m |≤ε, X≥0

ε is a non-negative error coefficient, which is a 2-norm minimization problem with constraints;

(5) For the constrained minimization problem in step (4), the weighted algebraic reconstruction technique is used to solve the constraints: |AX-Φ _m |≤ε, X≥0, while the 2-norm minimization problem is Solve using the method of steepest descent. The weighted algebraic reconstruction technique is of the form:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; x</span>}}{{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

in is the i-th row of matrix A, and β is a positive weight;

将测量的边界上光通量密度值Φ_m与计算值

之差

作为重建程序的停止准则。若

则结束重建程序，得到目标分布X；否则，执行步骤（7）；(6) Calculate the luminous flux density using the fluorescent target distribution results in step (5)

Compare the measured luminous flux density value Φ _m on the boundary with the calculated value

Difference

as a stopping criterion for rebuilding procedures. like

Then end the reconstruction procedure and obtain the target distribution X; otherwise, execute step (7);

(7) Use the solution of step (5) as the initial solution of the steepest descent method, iteratively solve the 2-norm minimization problem, and make the solution satisfy non-negativity:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; grad</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; dx</span>}<span\; class="notranslate">\; *</span>\frac{{<span\; class="notranslate">\; \&dtri;</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; \&dtri;</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; ;</span>$

是2-范数极小问题的梯度，是梯度的模值；where grad_dx is the iteration step size,

is the gradient of the 2-norm minima problem, is the modulus of the gradient;

将测量的边界上光通量密度值Φ_m与计算值

之差作为程序的停止准则。若

则结束重建程序，得到目标分布X；否则，执行步骤（9）；(8) Calculate the luminous flux density using the fluorescent target distribution results in step (7)

Compare the measured luminous flux density value Φ _m on the boundary with the calculated value

Difference as a stopping criterion for the program. like

Then end the reconstruction procedure and obtain the target distribution X; otherwise, execute step (9);

(9) Use the solution X obtained in step (7) in turn as the initial solution to perform the algebraic reconstruction technique, and go to step (5);

(10) Display the results, fuse the final reconstruction results with the anatomical structure of the imaging target, and display them with Tecplot software;

Owing to having adopted above-mentioned technical scheme, the advantage of the present invention is:

First, the present invention adopts multi-point excitation and multi-angle measurement, so that more measurement data can be obtained, which is beneficial to reduce the morbidity of the problem.

Second, the present invention uses optical characteristic parameters and anatomical structure information as prior knowledge to improve the accuracy of reconstruction results and the quality of reconstructed images.

Third, the present invention transforms the reconstruction problem into a constrained 2-norm minimization problem, and alternately uses the weighted algebraic reconstruction technique and the steepest descent method to solve it, so that the solution has good data continuity and satisfies the 2 Norm is the smallest.

Description of drawings

Fig. 1 is a flow chart of the reconstruction method of fluorescence tomography based on the present invention.

Figure 2 is the digital mouse model used in the simulation experiment.

Figure 3 is a surface light intensity distribution diagram obtained under a certain excitation light source.

Figure 4 is a map of fluorophore distribution obtained using the reconstruction algorithm of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings. It should be noted that the described embodiments are only intended to facilitate the understanding of the present invention, rather than limiting it in any way.

The steps of the present invention will be further described in conjunction with accompanying drawing 1.

(1) Obtain measurement data

a. The excitation light source performs multi-angle transmission tomographic imaging on the reconstruction target fixed on the electric control rotary table;

In transmission tomography, lasers and optical detection instruments are placed on both sides of the imaging target. The laser irradiates the reconstructed target to excite the fluorophore to emit fluorescence, and the fluorescence penetrates the imaging target to be detected by the optical detection instrument opposite the laser.

For multi-angle transmission tomography, the electronically controlled rotary table is controlled by a computer to rotate at equal intervals at a certain angle, generally not greater than 90° (in this case, 40° is selected), and the laser emits point-shaped laser light to irradiate the imaging target. Excitations are performed as many times as the angles are rotated, thereby realizing multi-angle transmission imaging.

b. Obtain measurement data using optical detection instruments to obtain luminous flux density Φ _m ;

In step a, the laser irradiates the imaging target once, and the optical detection instrument collects a set of fluorescent signals to obtain a set of measurement data, and multi-angle excitation corresponds to generate multiple sets of measurement data, which are described in the non-contact optical tomography method. The three-dimensional energy reconstruction technology of the biological surface obtains the three-dimensional fluorescence data distribution of the imaging target surface.

(2) Obtain the anatomical structure information and optical characteristic parameters of the reconstructed target

a. Reconstruct the anatomical structure information of the target, perform three-dimensional reconstruction on the computerized tomography projection data, and use 3DMED software to preprocess to obtain the three-dimensional volume data of the imaging target; use the human-computer interactive semi-automatic segmentation method in the 3DMED software to organize the volume data Segmentation to obtain the anatomical structure of the imaging target;

b. Acquiring optical characteristic parameters, using the anatomical structure information and applying the region-based diffusion optical tomography algorithm described in the method of optical three-dimensional reconstruction based on biological tissue specificity to obtain the optical characteristic parameters of each tissue in the imaging target.

(3) Based on the light transmission model and finite element theory, the anatomical structure information and optical characteristic parameters of the reconstructed target are used as prior information, and the linear relationship between the measured data on the surface and the distribution of fluorescent targets inside the reconstructed target is established.

a. The light transmission model, using the diffusion approximation equation to describe the transmission process of light in the imaging target;

b. Use Amira software to discretize the grid of the imaging target, and obtain the discrete grid data of the imaging target;

c. According to the finite element theory, and fusing the anatomical structure information and optical characteristic parameters of the reconstructed target obtained in step (2), the diffusion approximation equation is discretized, and the linear relationship between the measurement data of the surface and the distribution of fluorescent targets inside the reconstructed target is constructed:

Φ _m =AX

Among them, A is the system matrix, and X is the three-dimensional distribution and concentration of the fluorescent target to be solved, which is non-negative.

(4) Transform the above linear relationship into a constrained minimization problem:

min||X|| ₂ , st|AX-Φ _m |≤ε, X≥0

ε is a non-negative error coefficient, which is a 2-norm minimization problem with constraints.

(5) For the constrained minimization problem in step (4), the weighted algebraic reconstruction technique is used to solve the constraints: |AX-Φ _m |≤ε, X≥0, while the 2-norm minimization problem is Solve using the method of steepest descent. The weighted algebraic reconstruction technique is of the form:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; x</span>}}{{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

是矩阵A的第i行，β是正的权值。in

is the i-th row of matrix A, and β is a positive weight.

之差

作为重建程序的停止准则。若

则结束重建程序，得到目标分布X；否则，执行步骤（7）。(6) Calculate the luminous flux density using the fluorescent target distribution results in step (5) Compare the measured luminous flux density value Φ _m on the boundary with the calculated value

Difference

as a stopping criterion for rebuilding procedures. like

Then end the reconstruction procedure and get the target distribution X; otherwise, go to step (7).

(7) Use the solution of step (5) as the initial solution of the steepest descent method, iteratively solve the 2-norm minimization problem, and make the solution satisfy non-negativity:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; grad</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; *</span>}\frac{{<span\; class="notranslate">\; \&dtri;</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; \&dtri;</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; ;</span>$

where grad_dx is the iteration step size, is the gradient of the 2-norm minima problem, is the modulus of the gradient.

将测量的边界上光通量密度值Φ_m与计算值之差

作为程序的停止准则。若

则结束重建程序，得到目标分布X；否则，执行步骤（9）。(8) Calculate the luminous flux density using the fluorescent target distribution results in step (7)

Compare the measured luminous flux density value Φ _m on the boundary with the calculated value Difference

as a stopping criterion for the program. like

Then end the reconstruction procedure and get the target distribution X; otherwise, go to step (9).

(9) Use the solution X obtained in step (7) in turn as the initial solution to perform the algebraic reconstruction technique, and go to step (5).

(10) To display the results, perform image fusion of the final reconstruction results and the anatomical structure of the imaging target, and display them with Tecplot software.

A specific embodiment is also given below, and the reconstruction results of the present invention will be further described in conjunction with accompanying drawings 2 , 3 , and 4 .

Accompanying drawing 2 is used for the digital mouse model of simulation experiment. Figure (a) shows a heterogeneous digital mouse model with light source, including several main organs, such as heart (big red part), lung (blue part), liver (yellow part), stomach (rose red part) part), kidney (green part), muscle tissue (lavender part). Panel (b) shows the torso part of the digital mouse and the fluorescent target (large red sphere) to be reconstructed.

Accompanying drawing 3 is the location diagram of the excitation light source on the cross section and the light intensity distribution diagram on the surface of the digital mouse. Figure (a) is the location map of the 9 excitation light source points on the cross section. Figure (b) is a surface light intensity distribution diagram of emitted light under a certain excitation light source.

Accompanying drawing 4 is the reconstruction result based on the present invention. It is shown as a plot of fluorescent target distribution versus concentration for a z=16.4 mm section. The real center position of the reconstructed target is (21.910.4, 16.4) mm, and the target center position obtained by the algorithm is (22.0, 10.7, 16.9) mm. The position error is $\mathrm{LE}=\sqrt{{(x-x_0)}^2+{(\mathrm{the\; y}-{\mathrm{the\; y}}_0)}^2+{(z-z_0)}^2}\&ap;0.42\mathrm{mm}.$ The maximum concentration of the reconstructed target is 5183.6nM/L, and its relative error is RE=|C _c -C _real |/C _real ≈13.3%. The reconstruction based on the invention has small position error and small concentration relative error, and is an effective reconstruction algorithm for fluorescent molecular tomography.

Claims (2)

1. one kind based on the fluorescent molecule tomography rebuilding method of interative computation alternately, it is characterized in that: based on light mode and finite element theory, with the optical property parameter of reconstructed object and anatomical information as prior information, set up the measurement data on surface and the linear relationship that the inner fluorescent target of reconstructed object distributes, this linear relationship is converted into the minimization problem of Prescribed Properties, algebraic reconstruction technique and the steepest descent method of alternately carrying out weighting solve, thereby obtain distributed in three dimensions and the concentration of the fluorescent target of reconstructed object inside.

2. according to claim 1 based on the fluorescent molecule tomography rebuilding method of interative computation alternately, it is characterized in that:

Comprise the following steps:

(1) obtain measurement data

A, excitation source carry out the transmission-type tomoscan of multi-angle to being fixed on reconstructed object on automatically controlled turntable;

B, use optical detecting instrument obtain measurement data, obtain pharosage Φ _m

(2) obtain anatomical information and the optical property parameter of reconstructed object;

(3) based on light mode and finite element theory, the anatomical information of reconstructed object and optical property parameter, as prior information, are set up the measurement data on surface and the linear relationship of the inner fluorescent target distribution of reconstructed object;

(4) above-mentioned linear relationship is converted into the minimization problem of Prescribed Properties:

min||X|| ₂，s.t.|AX-Φ _m|≤ε，X≥0

ε is a non-negative error coefficient, and this is the least norm of the 2-with a Prescribed Properties problem;

(5), to the minimization problem of belt restraining in step (4), adopt the algebraic reconstruction technique of weighting to solve constraints: | AX-Φ _m|≤ε, X 〉=0,2-least norm problem solves with steepest descent method; The algebraic reconstruction technique of weighting is following form:

$X=X+\mathrm{\&beta;}{\stackrel{\&RightArrow;}{A}}_i\frac{{\mathrm{\&Phi;}}_m-{\stackrel{\&RightArrow;}{A}}_{i}X}{{\stackrel{\&RightArrow;}{A}}_i{\stackrel{\&RightArrow;}{A}}_i}$

Wherein

The i that is matrix A is capable, and β is positive weights;

(6) utilize fluorescent target distribution results in step (5) to calculate pharosage With pharosage value Φ on the border of measuring _mWith value of calculation

Poor

Stopping criterion as reconstruction algorithm; If Finish reconstruction algorithm, obtain target distribution X; Otherwise, carry out next step;

(7) with the initial solution of the solution of step (5) as steepest descent method, iterative 2-least norm problem, and make solution meet nonnegativity:

$X=X-\mathrm{grad}\_d{x}^{*}\frac{{\&dtri;}_X\left|\right|X|{|}_2}{\left|{\&dtri;}_X\right|\left|X\right|{|}_2|};$

Wherein grad_dx is the iteration step length size,

The gradient of 2-least norm problem,

It is the mould value of gradient;

(8) utilize fluorescent target distribution results in step (7) to calculate pharosage

With pharosage value Φ on the border of measuring _mWith value of calculation Poor Stopping criterion as program; If Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (9);

(9) the solution X that step (7) is obtained, conversely again as the initial solution of carrying out algebraic reconstruction technique, goes to step (5);

(10) show result, the anatomical structure of last reconstructed results and imageable target is carried out image co-registration, with Tecplot software, show.

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