CN103767686A - Method for positioning bioluminescence imaging light sources in small animal - Google Patents

Method for positioning bioluminescence imaging light sources in small animal Download PDF

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CN103767686A
CN103767686A CN201410025266.1A CN201410025266A CN103767686A CN 103767686 A CN103767686 A CN 103767686A CN 201410025266 A CN201410025266 A CN 201410025266A CN 103767686 A CN103767686 A CN 103767686A
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light sources
distribution
light source
toy
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CN103767686B (en
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陈多芳
梁继民
朱守平
陈雪利
张瑞
田捷
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Xidian University
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Abstract

The invention discloses a method for positioning bioluminescence imaging light sources in small animal. The method is characterized by comprising the following steps: building a relation between body surface measured data vectors and in-vivo unknown light source distribution of the small animal by utilizing a quantitative optical molecular tomography device and a finite element method; computing the in-vivo light source distribution of the small animal by adopting an algebraic iterative reconstruction method; determining a threshold value according to sparseness, and performing correction on the light source distribution, obtained by adopting the algebraic iterative reconstruction method, by utilizing the threshold value; circulating for multiple times to finally obtain the in-vivo light source distribution of the small animal to realize the positioning of the bioluminescence imaging light sources. The method disclosed by the invention has the beneficial effects that the L0 normalization item does not need to be added to a mathematic model of the reconstruction problem, and approximation analysis does not even to be performed on the L0 norm by adopting the L1 norm and the Lp (0< p&Lt; 1) norm, but the correction is performed on the light source distribution, obtained by adopting the algebraic iterative reconstruction method, directly by utilizing the sparseness. As norm approximation in the prior art is not adopted, the in-vivo light source positioning precision of the small animal is improved by the method provided by the invention.

Description

A kind of toy bioluminescence imaging source localization method
Technical field
The present invention relates to a kind of imaging source localization method, be specifically related to a kind of toy bioluminescence imaging source localization method, belong to optical imaging field.
Background technology
Luciferase gene labeled cell or DNA for bioluminescence imaging technique, utilize semiconductor refrigerating CCD collected by camera optical signalling, can directly monitor cellular activity and gene behavior in living body biological body.
Bioluminescence imaging technique can also be observed the biological processes such as the expression of the growth of living animal in-vivo tumour and transfer, infectious disease evolution, specific gene.
Bioluminescence imaging technique has without ionizing radiation, the feature such as highly sensitive, cost is low, in biological study, is widely used.
One of key problem of bioluminescence imaging technique is bioluminescence light source location in petty action object, and light source location can distribute and obtain according to the toy body surface fluorescence signal rebuilding body inner light source of measuring.Because measurement data number is less than unknown number number, the solution of bioluminescence imaging reconstruction problem is not unique.For obtaining and the true approaching solution that distributes of light source, can in the object function of Problems of Reconstruction, add regularization term.Consider the petty action object inner light source sparse feature that distributes, researcher proposes to adopt l 0norm retrains the regularization term adding.And on mathematics, l 0norm regularization problem is difficult to solve, and conventionally adopts l in reality 1norm or l p(0<p<1) norm is to l 0norm is similar to.
Chinese invention patent " a kind of bioluminescence tomography rebuilding method ", application number 201310259527.1, the applying date 20160626, open day 20130904, a kind of bioluminescence cross sectional reconstruction method is disclosed, in the object function of Problems of Reconstruction, add l 0.5regularization term, and adopt weighting interior point method by l 0.5regularization object function transforms to attach most importance to composes the l of power 1regularization minimization problem, then utilizes interior point method to solve minimization problem, obtains the three-dimensional localization quantitative information of fluorescence light source in organism.Due to l 0norm is similar to, and must introduce reconstruction error, causes locating inaccurate.
Summary of the invention
For solving the deficiencies in the prior art, the object of the present invention is to provide a kind of toy bioluminescence imaging source localization method, the method first adopts algebraically iterative approximation (ART) method to calculate distribution of light sources, recycling threshold value is revised above-mentioned distribution of light sources, make the degree of rarefication of revised distribution of light sources meet given condition, then using revised distribution of light sources as initial value, continue to adopt ART method to calculate new distribution of light sources, repeatedly repeat, until the error between the fluorescence signal that the toy body surface fluorescence signal calculating according to distribution of light sources and CCD detect is less than given error, calculate and finish, finally calculate light source position according to distribution of light sources, realize the accurate location to the light source in petty action object.
In order to realize above-mentioned target, the present invention adopts following technical scheme:
A kind of toy bioluminescence imaging source localization method, is characterized in that, comprises the following steps:
(1) obtain toy body surface optical signalling and internal structural information
1.a utilizes quantitative optical molecular tomographic device to obtain the two-dimentional bioluminescence image of toy body surface and the three-dimensional computer faultage image of internal structure;
The bioluminescence image collecting is arranged in data vector by 1.b, and utilize the relation of unknown distribution of light sources in Finite Element Method structure data vector and body, as shown in the formula:
y=Ax+n (1)
In formula, y is obtained by bioluminescence image, and size is listed as for M capable 1,
A is the coefficient matrix being obtained by computed tomography image, and size is the capable N row of M,
X is the unknown distribution of light sources in petty action object, and size is listed as for N capable 1,
N is noise, and size is listed as for M capable 1;
(2) initialization
Set primary light source distribution x, initial threshold β, initial degree of rarefication wherein, x>=0, β>=1,
Figure BDA0000458940250000032
(3) iteration is upgraded distribution of light sources
3.a gets the 1st row of coefficient matrix, is designated as A 1, the 1st element of the vectorial Y that fetches data, is designated as y 1, calculate increment:
&Delta; = &gamma; A 1 ( y 1 - A 1 x ) | | A 1 | | 2 2 - - - ( 2 )
In formula,
Figure BDA0000458940250000034
for A 1l 2norm square,
γ is weights, γ <1;
3.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':
x'=x+△ （3）
The x' substitution formula (2) that 3.c obtains step 3.b, gets the 2nd row A of coefficient matrices A 2the 2nd the element y with vectorial y 2, calculate new increment △, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M the element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x new;
(4) threshold value correction distribution of light sources
4.a gets the x that step 3.c obtains newgreatest member, be designated as x_max, calculate &alpha; = x _ max &beta; ;
4.b is by x newthe 1st element compare with the α of step 4.a successively to N element, if aforementioned elements is less than α, aforementioned elements is made as to zero, obtain revise distribution of light sources, be designated as
Figure BDA0000458940250000042
4.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction
Figure BDA0000458940250000043
degree of rarefication:
&psi; = N - | | x &OverBar; new | | 1 / | | x &OverBar; new | | 2 N - 1 - - - ( 4 )
In formula,
Figure BDA0000458940250000045
be respectively
Figure BDA0000458940250000046
l 1norm and l 2norm;
The degree of rarefication ψ that 4.d obtains step 4.c and initial degree of rarefication
Figure BDA0000458940250000047
compare, if
Figure BDA0000458940250000048
change threshold value beta and return to step 4.a, 4.b and 4.c calculates and judges; If
Figure BDA0000458940250000049
the distribution of light sources of the threshold value obtaining and correction is designated as respectively
Figure BDA00004589402500000410
with
Figure BDA00004589402500000411
execution step (5); ε is error;
(5) error of calculation and judge stop condition
According to the distribution of light sources of revising in step 4.d calculate
Figure BDA00004589402500000413
and will
Figure BDA00004589402500000414
compare with the y in formula (1), if
Figure BDA00004589402500000415
obtain with step 4.d
Figure BDA00004589402500000416
with
Figure BDA00004589402500000417
distribute as initial threshold and primary light source, with return to step (3) and step (4), iteration is upgraded distribution of light sources and threshold value correction distribution of light sources again; If
Figure BDA00004589402500000420
as final distribution of light sources, be designated as x opt, execution step (6);
(6) light source location
The final distribution of light sources x obtaining according to step (5) opt, find the greatest member position of aforementioned final distribution of light sources, complete light source location.
Aforesaid toy bioluminescence imaging source localization method, is characterized in that, in step (2), and when initialization, x=0, β=2,
Figure BDA0000458940250000051
Aforesaid toy bioluminescence imaging source localization method, is characterized in that, in step (3), and when iteration is upgraded distribution of light sources calculating increment, γ=0.25.
Aforesaid toy bioluminescence imaging source localization method, is characterized in that, in step (4) and step (5), and error ε=1e -6.
Aforesaid toy bioluminescence imaging source localization method, is characterized in that, while utilizing quantitative optical molecular tomographic device to obtain the bioluminescence image of toy body surface and the computed tomography image of internal structure, toy attitude remains unchanged.
Usefulness of the present invention is: light source localization method of the present invention need to not add l in the mathematical model of Problems of Reconstruction 0regularization term, does not more need to adopt l 1norm or l p(0<p<1) norm is to l 0norm is carried out approximate solution, but the distribution of light sources of directly utilizing degree of rarefication to obtain ART method is revised, thereby realize, the bioluminescence light source in petty action object is positioned, owing to not adopting, the norm in prior art is approximate, method of the present invention has improved the light source positioning precision in petty action object, can be used for tumor earlier detection and treats the research fields such as tracking.
Accompanying drawing explanation
Fig. 1 is the flow chart of toy bioluminescence imaging source localization method of the present invention.
The specific embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is done to concrete introduction.
With reference to Fig. 1, toy bioluminescence imaging source localization method of the present invention, comprises the following steps:
1, anesthesia and fixing toy
The toy that has bioluminescence light source in body is anaesthetized, and the extremity of toy, head and afterbody are all fixed on sample holder.
2, obtain toy body surface optical signalling and internal structural information
2.a, in darkroom, utilizes the disclosed quantitative optical molecular tomographic device of Chinese invention patent ZL201010173473.3, first gathers the fluorescence signal of toy body surface, and every 90 degree collections once, toy rotates a circle and can collect 4 width fluoroscopic images; Under the prerequisite remaining unchanged in toy attitude, then the data for projection of collecting computer fault imaging, every 1 degree collection once, toy rotates a circle and gathers 360 data for projection, utilizes backprojection algorithm to obtain the three-dimensional computer faultage image of toy.
The 4 width fluoroscopic images that collect are arranged in data vector by 2.b, utilize professional software Amira to carry out subdivision to the three-dimensional computer faultage image of toy, adopt diffusion equation to light the transmitting procedure in petty action object carry out modeling, utilize Finite Element Method, can build the relation of data vector and the interior unknown light source of petty action object of toy body surface fluorescence signal, as shown in the formula:
y=Ax+n (1)
In formula, y is obtained by bioluminescence image, and size is listed as for M capable 1,
A is the coefficient matrix being obtained by computed tomography image, and size is the capable N row of M,
X is the unknown distribution of light sources in petty action object, and size is listed as for N capable 1,
N is noise, and size is listed as for M capable 1.
3, initialization
Set primary light source distribution x, initial threshold β, initial degree of rarefication
Figure BDA0000458940250000061
wherein, x>=0, β>=1,
Figure BDA0000458940250000062
preferably, x=0, β=2,
Figure BDA0000458940250000063
4, iteration is upgraded distribution of light sources
4.a gets the 1st row of coefficient matrix, is designated as A 1, the 1st element of the vectorial Y that fetches data, is designated as y 1, calculate increment:
&Delta; = &gamma; A 1 ( y 1 - y 1 x ) | | A 1 | | 2 2 - - - ( 2 )
In formula,
Figure BDA0000458940250000072
for A 1l 2norm square,
γ is weights, and γ <1 is preferred, γ=0.25.
4.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':
x'=x+△ （3）
The x' substitution formula (2) that 4.c obtains step 4.b, gets the 2nd row A of coefficient matrices A 2the 2nd the element y with vectorial y 2, calculate new increment △, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M the element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x new.
5, threshold value correction distribution of light sources
5.a gets the x that step 4.c obtains newgreatest member, be designated as x_max, calculate &alpha; = x _ max &beta; .
5.b is by x newthe 1st element and the α of step 5.a compare, if described the 1st element is less than α, described the 1st element is made as to zero; If described the 1st element is more than or equal to α, described the 1st element remains unchanged.
Compare successively, until x newlast element, obtain revise distribution of light sources, be designated as
Figure BDA0000458940250000074
5.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction
Figure BDA0000458940250000075
degree of rarefication:
&psi; = N - | | x &OverBar; new | | 1 / | | x &OverBar; new | | 2 N - 1 - - - ( 4 )
In formula,
Figure BDA0000458940250000082
be respectively l 1norm and l 2norm,
Figure BDA0000458940250000084
in 1 fewer, degree of rarefication ψ more approaches 1,
Figure BDA0000458940250000085
only having an element is 1 o'clock, ψ=1.
The degree of rarefication ψ that 5.d obtains step 5.c and initial degree of rarefication compare, if
Figure BDA0000458940250000087
change threshold value beta and return to step 5.a, 5.b and 5.c calculates and judges; If
Figure BDA0000458940250000088
the distribution of light sources of the threshold value obtaining and correction is designated as respectively
Figure BDA0000458940250000089
with
Figure BDA00004589402500000810
execution step 6.
ε is error, is an a small amount of, preferred, ε=1e -6.
6, the error of calculation and judgement stop condition
According to the distribution of light sources of revising in step 5.d
Figure BDA00004589402500000811
calculate and will
Figure BDA00004589402500000813
compare with the toy body surface fluorescence signal data vector y in formula (1), if
Figure BDA00004589402500000814
obtain with step 5.d
Figure BDA00004589402500000815
with
Figure BDA00004589402500000816
distribute as initial threshold and primary light source,
Figure BDA00004589402500000817
with
Figure BDA00004589402500000818
return to step 4 and step 5, iteration is upgraded distribution of light sources and threshold value correction distribution of light sources again; If
Figure BDA00004589402500000819
as final distribution of light sources, be designated as x opt, execution step 7.
7, light source location
The final distribution of light sources x obtaining according to step 6 opt, find the greatest member position of described final distribution of light sources, complete light source location.
Light source localization method of the present invention need to not add l in the mathematical model of Problems of Reconstruction 0regularization term, does not more need to adopt l 1norm or l p(0<p<1) norm is to l 0norm is carried out approximate solution, but the distribution of light sources of directly utilizing degree of rarefication to obtain ART method revises, and owing to not adopting, the norm in prior art is approximate, so method of the present invention has improved the light source positioning precision in petty action object.
Light source localization method of the present invention, can be used for tumor earlier detection and treats the research fields such as tracking.
It should be noted that, above-described embodiment does not limit the present invention in any form, and all employings are equal to replaces or technical scheme that the mode of equivalent transformation obtains, all drops in protection scope of the present invention.

Claims (5)

1. a toy bioluminescence imaging source localization method, is characterized in that, comprises the following steps:
(1) obtain toy body surface optical signalling and internal structural information
1.a utilizes quantitative optical molecular tomographic device to obtain the two-dimentional bioluminescence image of toy body surface and the three-dimensional computer faultage image of internal structure;
The bioluminescence image collecting is arranged in data vector by 1.b, and utilize the relation of unknown distribution of light sources in Finite Element Method structure data vector and body, as shown in the formula:
y=Ax+n (1)
In formula, y is obtained by bioluminescence image, and size is listed as for M capable 1,
A is the coefficient matrix being obtained by computed tomography image, and size is the capable N row of M,
X is the unknown distribution of light sources in petty action object, and size is listed as for N capable 1,
N is noise, and size is listed as for M capable 1;
(2) initialization
Set primary light source distribution x, initial threshold β, initial degree of rarefication
Figure FDA0000458940240000011
wherein, x>=0, β>=1,
Figure FDA0000458940240000012
(3) iteration is upgraded distribution of light sources
3.a gets the 1st row of coefficient matrix, is designated as A 1, the 1st element of the vectorial Y that fetches data, is designated as y 1, calculate increment:
&Delta; = &gamma; A 1 ( y 1 - A 1 x ) | | A 1 | | 2 2 - - - ( 2 )
In formula, for A 1l 2norm square,
γ is weights, γ <1;
3.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':
x'=x+△ （3）
The x' substitution formula (2) that 3.c obtains step 3.b, gets the 2nd row A of coefficient matrices A 2the 2nd the element y with vectorial y 2, calculate new increment △, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M the element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x new;
(4) threshold value correction distribution of light sources
4.a gets the x that step 3.c obtains newgreatest member, be designated as x_max, calculate &alpha; = x _ max &beta; ;
4.b is by x newthe 1st element compare with the α of step 4.a successively to N element, if described element is less than α, described element is made as to zero, obtain revise distribution of light sources, be designated as
Figure FDA0000458940240000022
4.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction
Figure FDA00004589402400000214
degree of rarefication:
&psi; = N - | | x &OverBar; new | | 1 / | | x &OverBar; new | | 2 N - 1 - - - ( 4 )
In formula, be respectively
Figure FDA0000458940240000025
l 1norm and l 2norm;
The degree of rarefication ψ that 4.d obtains step 4.c and initial degree of rarefication
Figure FDA0000458940240000026
compare, if change threshold value beta and return to step 4.a, 4.b and 4.c calculates and judges; If
Figure FDA0000458940240000028
the distribution of light sources of the threshold value obtaining and correction is designated as respectively
Figure FDA0000458940240000029
with
Figure FDA00004589402400000210
execution step (5); ε is error;
(5) error of calculation and judge stop condition
According to the distribution of light sources of revising in step 4.d
Figure FDA00004589402400000211
calculate
Figure FDA00004589402400000212
and will
Figure FDA00004589402400000213
with formula
(1) y in compares, if
Figure FDA0000458940240000031
obtain with step 4.d
Figure FDA0000458940240000032
with
Figure FDA0000458940240000033
distribute as initial threshold and primary light source,
Figure FDA0000458940240000034
with
Figure FDA0000458940240000035
return to step (3) and step (4), iteration is upgraded distribution of light sources and threshold value correction distribution of light sources again; If
Figure FDA0000458940240000036
as final distribution of light sources, be designated as x opt, execution step (6);
(6) light source location
The final distribution of light sources x obtaining according to step (5) opt, find the greatest member position of described final distribution of light sources, complete light source location.
2. toy bioluminescence imaging source localization method according to claim 1, is characterized in that, in step (2), and when initialization, x=0, β=2,
Figure FDA0000458940240000037
3. toy bioluminescence imaging source localization method according to claim 1, is characterized in that, in step (3), and when iteration is upgraded distribution of light sources calculating increment, γ=0.25.
4. toy bioluminescence imaging source localization method according to claim 1, is characterized in that, in step (4) and step (5), and error ε=1e -6.
5. toy bioluminescence imaging source localization method according to claim 1, it is characterized in that, while utilizing quantitative optical molecular tomographic device to obtain the bioluminescence image of toy body surface and the computed tomography image of internal structure, toy attitude remains unchanged.
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