CN103767686B - Method for positioning bioluminescence imaging light sources in small animal - Google Patents
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Abstract
本发明公开了一种小动物生物发光成像光源定位方法,包括以下步骤:利用定量光学分子断层成像装置和有限元方法构建小动物体表测量数据向量与体内未知光源分布的关系;采用代数迭代重建方法计算小动物体内光源分布;根据稀疏度确定阈值,利用阈值对采用代数迭代重建方法得到的光源分布进行修正;多次循环后,最终得到小动物体内光源分布。本发明的有益之处在于:不需要在重建问题的数学模型中加入l0正则化项,更不需要采用l1范数或lp(0<p<1)范数对l0范数进行近似求解,而是直接利用稀疏度对代数迭代重建方法得到的光源分布进行修正,由于没有采用已有技术中的范数近似,所以本发明的方法提高了小动物体内的光源定位精度。
The invention discloses a light source positioning method for small animal bioluminescent imaging, which comprises the following steps: using a quantitative optical molecular tomography device and a finite element method to construct the relationship between a small animal body surface measurement data vector and the distribution of an unknown light source in the body; using algebraic iteration to reconstruct Methods The light source distribution in the small animal body was calculated; the threshold was determined according to the sparsity, and the light source distribution obtained by the algebraic iterative reconstruction method was used to correct the threshold; after multiple cycles, the light source distribution in the small animal body was finally obtained. The advantage of the present invention is that it is not necessary to add an l0 regularization term in the mathematical model of the reconstruction problem, and it is not necessary to use the l1 norm or the lp (0< p <1) norm to carry out the l0 norm Instead, the sparseness is directly used to correct the light source distribution obtained by the algebraic iterative reconstruction method. Since the norm approximation in the prior art is not used, the method of the present invention improves the light source positioning accuracy in small animals.
Description
技术领域technical field
本发明涉及一种成像光源定位方法,具体涉及一种小动物生物发光成像光源定位方法,属于光学成像领域。The invention relates to an imaging light source positioning method, in particular to a small animal bioluminescent imaging light source positioning method, belonging to the field of optical imaging.
背景技术Background technique
生物发光成像技术用荧光素酶基因标记细胞或DNA,利用半导体制冷CCD相机采集光学信号,能够直接监控活体生物体内的细胞活动和基因行为。Bioluminescent imaging technology uses luciferase gene to mark cells or DNA, and uses semiconductor cooling CCD camera to collect optical signals, which can directly monitor cell activity and gene behavior in living organisms.
生物发光成像技术还可以观测活体动物体内肿瘤的生长及转移、感染性疾病发展过程、特定基因的表达等生物学过程。Bioluminescent imaging technology can also observe biological processes such as tumor growth and metastasis, infectious disease development, and specific gene expression in living animals.
生物发光成像技术具有无电离辐射、灵敏度高、成本低等特点,在生物研究中被广泛使用。Bioluminescent imaging technology has the characteristics of no ionizing radiation, high sensitivity, and low cost, and is widely used in biological research.
生物发光成像技术的核心问题之一为小动物体内生物发光光源定位,光源定位可根据测量的小动物体表荧光信号重建体内光源分布得到。由于测量数据个数小于未知数个数,生物发光成像重建问题的解不唯一。为得到与光源真实分布接近的解,可在重建问题的目标函数中加入正则化项。考虑到小动物体内光源分布稀疏的特点,研究者提出采用l0范数对加入的正则化项进行约束。而数学上,l0范数正则化问题难以求解,实际中通常采用l1范数或lp(0<p<1)范数对l0范数进行近似。One of the core issues of bioluminescence imaging technology is the location of bioluminescent light sources in small animals, which can be obtained by reconstructing the distribution of light sources in vivo based on the measured surface fluorescence signals of small animals. Since the number of measured data is less than the number of unknowns, the solution to the bioluminescence imaging reconstruction problem is not unique. In order to obtain a solution close to the real distribution of the light source, a regularization term can be added to the objective function of the reconstruction problem. Considering the sparse distribution of light sources in small animals, the researchers proposed to use the l 0 norm to constrain the added regularization term. Mathematically, the l 0 norm regularization problem is difficult to solve. In practice, the l 1 norm or the l p (0<p<1) norm is usually used to approximate the l 0 norm.
中国发明专利《一种生物发光断层成像重建方法》,申请号201310259527.1,申请日20160626,公开日20130904,公开了一种生物发光断层重建方法,重建问题的目标函数中加入l0.5正则化项,并采用加权内点法将l0.5正则化目标函数转化为重赋权的l1正则化极小化问题,然后利用内点法求解极小化问题,获取生物体内荧光光源的三维定位定量信息。由于对l0范数进行了近似,必然引入重建误差,导致定位不准确。Chinese invention patent "A Bioluminescence Tomography Reconstruction Method", application number 201310259527.1, application date 20160626, publication date 20130904, discloses a bioluminescence tomography reconstruction method, adding l 0.5 regularization term to the objective function of the reconstruction problem, and The l 0.5 regularized objective function is transformed into a reweighted l 1 regularized minimization problem by using the weighted interior point method, and then the minimization problem is solved by using the interior point method to obtain the three-dimensional positioning and quantitative information of the fluorescent light source in the organism. Due to the approximation of the l 0 norm, the reconstruction error must be introduced, resulting in inaccurate positioning.
发明内容Contents of the invention
为解决现有技术的不足,本发明的目的在于提供一种小动物生物发光成像光源定位方法,该方法先采用代数迭代重建(ART)方法计算光源分布,再利用阈值对上述光源分布进行修正,使修正后的光源分布的稀疏度满足给定的条件,然后以修正后的光源分布作为初值,继续采用ART方法计算新的光源分布,多次重复,直到根据光源分布计算得到的小动物体表荧光信号与CCD探测到的荧光信号之间的误差小于给定误差值,计算结束,最后根据光源分布计算光源位置,实现对小动物体内的光源的准确定位。In order to solve the deficiencies of the prior art, the purpose of the present invention is to provide a method for locating the light source for bioluminescence imaging of small animals. The method first uses the algebraic iterative reconstruction (ART) method to calculate the light source distribution, and then uses the threshold value to correct the above light source distribution. Make the sparsity of the corrected light source distribution meet the given conditions, then use the corrected light source distribution as the initial value, continue to use the ART method to calculate the new light source distribution, and repeat it many times until the small animal object calculated according to the light source distribution When the error between the surface fluorescence signal and the fluorescence signal detected by the CCD is less than a given error value, the calculation ends, and finally the position of the light source is calculated according to the distribution of the light source, so as to realize the accurate positioning of the light source in the small animal body.
为了实现上述目标,本发明采用如下的技术方案:In order to achieve the above object, the present invention adopts the following technical solutions:
一种小动物生物发光成像光源定位方法,其特征在于,包括以下步骤:A method for positioning a light source for bioluminescence imaging of small animals, comprising the following steps:
(1)获取小动物体表光学信号与内部结构信息(1) Acquisition of optical signals and internal structure information on the body surface of small animals
1.a利用定量光学分子断层成像装置获取小动物体表的二维生物发光图像和内部结构的三维计算机断层图像;1.a Use quantitative optical molecular tomography to obtain two-dimensional bioluminescence images on the surface of small animals and three-dimensional computed tomography images of internal structures;
1.b将采集到的生物发光图像排列成数据向量,并利用有限元方法构建数据向量与体内未知光源分布的关系,如下式:1.b Arrange the collected bioluminescent images into data vectors, and use the finite element method to construct the relationship between the data vectors and the distribution of unknown light sources in the body, as follows:
y=Ax+n (1)y=Ax+n (1)
式中,y由生物发光图像得到,大小为M行1列,In the formula, y is obtained from the bioluminescence image, and the size is M rows and 1 column,
A为由计算机断层图像得到的系数矩阵,大小为M行N列,A is the coefficient matrix obtained from computed tomography images, the size of which is M rows and N columns,
x为小动物体内的未知光源分布,大小为N行1列,x is the unknown light source distribution in the small animal body, the size is N rows and 1 column,
n为噪声,大小为M行1列;n is noise, the size is M rows and 1 column;
(2)设定初值(2) Set the initial value
设定初始光源分布x,初始阈值β,初始稀疏度其中,x≥0,β≥1, Set the initial light source distribution x, the initial threshold β, and the initial sparsity Among them, x≥0, β≥1,
(3)迭代更新光源分布(3) Iteratively update the light source distribution
3.a取系数矩阵的第1行,记为A1,取数据向量Y的第1个元素,记为y1,计算增量:3.a Take the first row of the coefficient matrix, denoted as A 1 , take the first element of the data vector Y, denoted as y 1 , and calculate the increment:
式中,为A1的l2范数的平方,In the formula, is the square of the l 2 norm of A 1 ,
γ为权值,γ<1;γ is the weight, γ<1;
3.b利用上述增量△更新x,更新后的x用x'表示,有:3.b Utilize the above increment △ to update x, and the updated x is denoted by x', which has:
x'=x+△ (3)x'=x+△ (3)
3.c将步骤3.b得到的x'代入式(2),取系数矩阵A的第2行A2和向量y的第2个元素y2,计算新的增量△,继续利用式(3)更新x;直到利用系数矩阵A的第M行和向量y的第M个元素计算增量并更新x完毕,更新完毕后的光源分布记为xnew;3.c Substitute the x' obtained in step 3.b into formula (2), take the second row A 2 of the coefficient matrix A and the second element y 2 of the vector y, calculate the new increment △, and continue to use the formula ( 3) Update x; until the increment is calculated using the Mth row of the coefficient matrix A and the Mth element of the vector y and the update of x is completed, the light source distribution after the update is recorded as x new ;
(4)阈值修正光源分布(4) Threshold correction light source distribution
4.a取步骤3.c得到的xnew的最大元素,记为x_max,计算
4.b将xnew的第1个元素到第N个元素依次与步骤4.a的α进行比较,若前述元素小于α,则将前述元素设为零,得到修正的光源分布,记为 4.b Compare the first element to the Nth element of x new with α in step 4.a in turn. If the aforementioned element is smaller than α, then set the aforementioned element to zero to obtain the corrected light source distribution, which is denoted as
4.c利用下式计算上述修正的光源分布的稀疏度:4.c Use the following formula to calculate the above corrected light source distribution The sparsity of:
式中,分别为的l1范数和l2范数;In the formula, respectively The l 1 norm and l 2 norm of ;
4.d将步骤4.c得到的稀疏度ψ与初始稀疏度进行比较,如果则改变阈值β并返回步骤4.a、4.b和4.c再进行计算和判断;如果则将得到的阈值和修正的光源分布分别记为和执行步骤(5);ε为误差;4.d Compare the sparsity ψ obtained in step 4.c with the initial sparsity To compare, if Then change the threshold β and return to steps 4.a, 4.b and 4.c for calculation and judgment; if Then the obtained threshold value and the corrected light source distribution are recorded as and Execute step (5); ε is the error;
(5)计算误差和判断停止条件(5) Calculation error and judgment stop condition
根据步骤4.d中修正的光源分布计算并将与式(1)中的y进行比较,如果则以步骤4.d得到的和作为初始阈值和初始光源分布,即和返回步骤(3)和步骤(4),再次迭代更新光源分布和阈值修正光源分布;如果作为最终光源分布,记为xopt,执行步骤(6);According to the corrected light source distribution in step 4.d calculate and will Compare with y in formula (1), if then get from step 4.d and As the initial threshold and the initial light source distribution, ie and Return to step (3) and step (4), iteratively update the light source distribution and threshold correction light source distribution again; if As the final light source distribution, denoted as x opt , perform step (6);
(6)光源定位(6) Light source positioning
根据步骤(5)得到的最终光源分布xopt,找到前述最终光源分布的最大元素位置,完成光源定位。According to the final light source distribution x opt obtained in step (5), the maximum element position of the aforementioned final light source distribution is found to complete the light source positioning.
前述的小动物生物发光成像光源定位方法,其特征在于,在步骤(2)中,设定初值时,x=0,β=2, The aforementioned small animal bioluminescence imaging light source positioning method is characterized in that, in step (2), when setting the initial value, x=0, β=2,
前述的小动物生物发光成像光源定位方法,其特征在于,在步骤(3)中,迭代更新光源分布计算增量时,γ=0.25。The aforementioned light source positioning method for small animal bioluminescence imaging is characterized in that, in step (3), γ=0.25 when iteratively updating the light source distribution and calculating the increment.
前述的小动物生物发光成像光源定位方法,其特征在于,在步骤(4)和步骤(5)中,误差ε=1e-6。The aforementioned light source positioning method for small animal bioluminescence imaging is characterized in that, in step (4) and step (5), the error ε=1e -6 .
前述的小动物生物发光成像光源定位方法,其特征在于,利用定量光学分子断层成像装置获取小动物体表的生物发光图像和内部结构的计算机断层图像时,小动物姿态保持不变。The aforementioned light source positioning method for bioluminescent imaging of small animals is characterized in that when using a quantitative optical molecular tomography device to acquire bioluminescent images of the body surface of small animals and computed tomographic images of internal structures, the posture of the small animals remains unchanged.
本发明的有益之处在于:本发明的光源定位方法不需要在重建问题的数学模型中加入l0正则化项,更不需要采用l1范数或lp(0<p<1)范数对l0范数进行近似求解,而是直接利用稀疏度对ART方法得到的光源分布进行修正,从而实现对小动物体内的生物发光光源进行定位,由于没有采用已有技术中的范数近似,本发明的方法提高了小动物体内的光源定位精度,可用于肿瘤早期检测与治疗跟踪等研究领域。The benefit of the present invention is that: the light source positioning method of the present invention does not need to add an l0 regularization term in the mathematical model of the reconstruction problem, and does not need to use the l1 norm or the lp (0< p <1) norm The l 0 norm is approximated, but the light source distribution obtained by the ART method is directly used to correct the sparsity, so as to realize the positioning of the bioluminescent light source in the small animal body. Since the norm approximation in the prior art is not used, The method of the invention improves the positioning accuracy of the light source in the small animal body, and can be used in research fields such as early tumor detection and treatment tracking.
附图说明Description of drawings
图1是本发明的小动物生物发光成像光源定位方法的流程图。FIG. 1 is a flow chart of the method for positioning a light source for small animal bioluminescence imaging of the present invention.
具体实施方式detailed description
以下结合附图和具体实施例对本发明作具体的介绍。The present invention will be specifically introduced below in conjunction with the accompanying drawings and specific embodiments.
参照图1,本发明的小动物生物发光成像光源定位方法,包括以下步骤:Referring to Fig. 1, the positioning method of the light source for small animal bioluminescence imaging of the present invention comprises the following steps:
1、麻醉与固定小动物1. Anesthetizing and immobilizing small animals
对体内有生物发光光源的小动物进行麻醉,并将小动物的四肢、头部和尾部都固定在样品支架上。Anesthetize a small animal with a bioluminescent light source in its body, and fix the limbs, head and tail of the small animal on the sample holder.
2、获取小动物体表光学信号与内部结构信息2. Obtain the optical signal and internal structure information of the small animal body surface
2.a在暗室中,利用中国发明专利ZL201010173473.3公开的定量光学分子断层成像装置,先采集小动物身体表面的荧光信号,每隔90度采集一次,小动物旋转一周可采集到4幅荧光图像;在小动物姿态保持不变的前提下,再采集计算机断层成像的投影数据,每隔1度采集一次,小动物旋转一周采集360次投影数据,利用反投影算法得到小动物的三维计算机断层图像。2.a In the darkroom, using the quantitative optical molecular tomography device disclosed in Chinese invention patent ZL201010173473.3, first collect the fluorescent signals on the body surface of small animals, and collect them every 90 degrees. Four fluorescent images can be collected when the small animal rotates once. Image: Under the premise that the posture of the small animal remains unchanged, the projection data of the computerized tomography imaging is collected once every 1 degree, and the projection data is collected 360 times when the small animal rotates a circle, and the three-dimensional computed tomography of the small animal is obtained by using the back projection algorithm image.
2.b将采集到的4幅荧光图像排列成数据向量,利用专业软件Amira对小动物的三维计算机断层图像进行剖分,采用扩散方程对光在小动物体内的传输过程进行建模,利用有限元方法,可以构建小动物体表荧光信号的数据向量与小动物体内未知光源的关系,如下式:2.b Arrange the four collected fluorescence images into data vectors, use the professional software Amira to segment the three-dimensional computed tomography images of small animals, and use the diffusion equation to model the light transmission process in small animals. The meta-method can construct the relationship between the data vector of the fluorescent signal on the surface of the small animal and the unknown light source in the small animal, as follows:
y=Ax+n (1)y=Ax+n (1)
式中,y由生物发光图像得到,大小为M行1列,In the formula, y is obtained from the bioluminescence image, and the size is M rows and 1 column,
A为由计算机断层图像得到的系数矩阵,大小为M行N列,A is the coefficient matrix obtained from computed tomography images, the size of which is M rows and N columns,
x为小动物体内的未知光源分布,大小为N行1列,x is the unknown light source distribution in the small animal body, the size is N rows and 1 column,
n为噪声,大小为M行1列。n is noise, the size is M rows and 1 column.
3、设定初值3. Set the initial value
设定初始光源分布x,初始阈值β,初始稀疏度其中,x≥0,β≥1,优选的,x=0,β=2, Set the initial light source distribution x, the initial threshold β, and the initial sparsity Among them, x≥0, β≥1, Preferably, x=0, β=2,
4、迭代更新光源分布4. Iteratively update the light source distribution
4.a取系数矩阵的第1行,记为A1,取数据向量Y的第1个元素,记为y1,计算增量:4.a Take the first row of the coefficient matrix, denoted as A 1 , take the first element of the data vector Y, denoted as y 1 , and calculate the increment:
式中,为A1的l2范数的平方,In the formula, is the square of the l 2 norm of A 1 ,
γ为权值,γ<1,优选的,γ=0.25。γ is a weight, γ<1, preferably, γ=0.25.
4.b利用上述增量△更新x,更新后的x用x'表示,有:4.b Utilize the above increment △ to update x, and the updated x is denoted by x', which has:
x'=x+△ (3)x'=x+△ (3)
4.c将步骤4.b得到的x'代入式(2),取系数矩阵A的第2行A2和向量y的第2个元素y2,计算新的增量△,继续利用式(3)更新x;直到利用系数矩阵A的第M行和向量y的第M个元素计算增量并更新x完毕,更新完毕后的光源分布记为xnew。4.c Substitute x' obtained in step 4.b into formula (2), take the second row A 2 of the coefficient matrix A and the second element y 2 of the vector y, calculate the new increment △, and continue to use the formula ( 3) Update x; until the increment is calculated using the Mth row of the coefficient matrix A and the Mth element of the vector y and the update of x is completed, the light source distribution after the update is recorded as x new .
5、阈值修正光源分布5. Threshold correction light source distribution
5.a取步骤4.c得到的xnew的最大元素,记为x_max,计算
5.b将xnew的第1个元素与步骤5.a的α进行比较,若所述第1个元素小于α,则将所述第1个元素设为零;若所述第1个元素大于或等于α,则所述第1个元素保持不变。5.b Compare the first element of x new with α in step 5.a, if the first element is less than α, set the first element to zero; if the first element greater than or equal to α, the first element remains unchanged.
依次比较,直到xnew的最后一个元素,得到修正的光源分布,记为 Compare sequentially until the last element of x new to obtain the corrected light source distribution, which is denoted as
5.c利用下式计算上述修正的光源分布的稀疏度:5.c Use the following formula to calculate the above-mentioned corrected light source distribution The sparsity of:
式中,分别为的l1范数和l2范数,中的1越少,稀疏度ψ越接近1,只有一个元素为1时,ψ=1。In the formula, respectively The l 1 norm and l 2 norm of The less 1 in , the closer the sparsity ψ is to 1, When only one element is 1, ψ=1.
5.d将步骤5.c得到的稀疏度ψ与初始稀疏度进行比较,如果则改变阈值β并返回步骤5.a、5.b和5.c再进行计算和判断;如果则将得到的阈值和修正的光源分布分别记为和执行步骤6。5.d Compare the sparsity ψ obtained in step 5.c with the initial sparsity To compare, if Then change the threshold β and return to steps 5.a, 5.b and 5.c for calculation and judgment; if Then the obtained threshold value and the corrected light source distribution are recorded as and Go to step 6.
ε为误差,是一个小量,优选的,ε=1e-6。ε is an error, which is a small amount, preferably, ε=1e -6 .
6、计算误差和判断停止条件6. Calculate the error and judge the stop condition
根据步骤5.d中修正的光源分布计算并将与式(1)中的小动物体表荧光信号数据向量y进行比较,如果则以步骤5.d得到的和作为初始阈值和初始光源分布,即和返回步骤4和步骤5,再次迭代更新光源分布和阈值修正光源分布;如果作为最终光源分布,记为xopt,执行步骤7。According to the corrected light source distribution in step 5.d calculate and will Compared with the small animal body surface fluorescence signal data vector y in formula (1), if then get from step 5.d and As the initial threshold and initial light source distribution, ie and Return to step 4 and step 5, iteratively update the light source distribution and threshold value correction light source distribution again; if As the final light source distribution, denoted as x opt , go to step 7.
7、光源定位7. Light source positioning
根据步骤6得到的最终光源分布xopt,找到所述最终光源分布的最大元素位置,完成光源定位。According to the final light source distribution x opt obtained in step 6, the maximum element position of the final light source distribution is found to complete the light source positioning.
本发明的光源定位方法不需要在重建问题的数学模型中加入l0正则化项,更不需要采用l1范数或lp(0<p<1)范数对l0范数进行近似求解,而是直接利用稀疏度对ART方法得到的光源分布进行修正,由于没有采用已有技术中的范数近似,所以本发明的方法提高了小动物体内的光源定位精度。The light source positioning method of the present invention does not need to add an l0 regularization term in the mathematical model of the reconstruction problem, and does not need to use the l1 norm or the lp (0< p <1) norm to approximate the l0 norm , but directly uses the sparsity to correct the light source distribution obtained by the ART method. Since the norm approximation in the prior art is not used, the method of the present invention improves the positioning accuracy of the light source in the small animal body.
本发明的光源定位方法,可用于肿瘤早期检测与治疗跟踪等研究领域。The light source positioning method of the present invention can be used in research fields such as early tumor detection and treatment tracking.
需要说明的是,上述实施例不以任何形式限制本发明,凡采用等同替换或等效变换的方式所获得的技术方案,均落在本发明的保护范围内。It should be noted that the above embodiments do not limit the present invention in any form, and all technical solutions obtained by means of equivalent replacement or equivalent transformation fall within the protection scope of the present invention.
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