Fluorescence intensity compensation method and fluorescence intensity calculation device
A fluorescence intensity compensation method, includes: receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths; collecting detected values for the photodetectors; and obtaining a measurement spectrum, by approximating, from the linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes; wherein approximation of the measurement spectrum by the linear sum of the single-stain spectrums is performed using the restricted least-square method.
1. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (3) through (5)
Minimize
Sx
-
p
2
(
3
)
subject
to
Ax
≤
b
(
4
)
x
≥
0
(
5
)
A
=
(
-
1
0
…
0
0
-
1
0
⋮
⋱
⋮
0
0
…
-
1
)
(
6
)
b
=
(
-
U
1
-
U
2
⋮
-
U
M
)
(
7
)
where S represents an N×M order matrix with s ij as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, A is set as an M×M order matrix and b as an M×1 order matrix, and U 1 through U M represent said lower limit value;
wherein in said Expression (2), an undyed average value V j of the j'th fluorochrome obtained from an average value of detection values from each of said photodetectors, obtained by irradiating light on microparticles not marked with the j'th fluorochrome, is used as said lower limit value U j .
2. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (3) through (5)
Minimize
Sx
-
p
2
(
3
)
subject
to
Ax
≤
b
(
4
)
x
≥
0
(
5
)
A
=
(
-
1
0
…
0
0
-
1
0
⋮
⋱
⋮
0
0
…
-
1
)
(
6
)
b
=
(
-
U
1
-
U
2
⋮
-
U
M
)
(
7
)
where S represents an N×M order matrix with s ij , as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, A is set as an M×M order matrix and b as an M×1 order matrix, and U 1 through U M represent said lower limit value;
wherein in said Expression (2), a random number generated following an undyed probability density function F j (U j ) of the j'th fluorochrome obtained from a probability density function of detection values from each of said photodetectors, obtained by irradiating light on microparticles not marked with the j'th fluorochrome, is used as said lower limit value U j .
3. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (3) through (5)
Minimize
Sx
-
p
2
(
3
)
subject
to
Ax
≤
b
(
4
)
x
≥
0
(
5
)
A
=
(
-
1
0
…
0
0
-
1
0
⋮
⋱
⋮
0
0
…
-
1
)
(
6
)
b
=
(
-
U
1
-
U
2
⋮
-
U
M
)
(
7
)
where S represents an N×M order matrix with s ij as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, A is set as an M×M order matrix and b as an M×1 order matrix, and U 1 through U M represent said lower limit value;
wherein in said Expression (2), an undyed average value V j and undyed standard deviation ρ j of the of the j'th fluorochrome are obtained from an average value and dispersion of detection values from each of said photodetectors, obtained by irradiating light on microparticles not marked with the j'th fluorochrome, and a random number, generated following a probability density function F j (U j ) in Expression (9) is used as said lower limit value U j :
F
j
(
U
j
)
=
1
2
π
ρ
j
ⅇ
-
(
U
j
-
V
j
)
2
2
ρ
j
2
.
(
9
)
4. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (12) and (13), and executing the following Expression (14)
Minimize ∥ Sx ′−( p−u )∥ 2 (12)
subject to x′≧ 0 (13)
x=x′+U (14)
where S represents an N×M order matrix with s ij as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, u represents an N'th order vector with an average value v i of detected values from the i'th photodetector, obtained by irradiating light on microparticles unmarked with the j'th fluorochrome, as elements, and U represents an M'th order vector with an undyed average value V j of the j'th fluorochrome obtained from the average value v, as elements.
5. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (15) and (16), and executing the following Expression (17)
Minimize ∥ Sx ′−( p−u )∥ 2 (15)
subject to x′≧ 0 (16)
x=x′+U (17)
where S represents an N×M order matrix with s ij as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, u represents an N'th order vector with random numbers u i generated following a probability density function f i (u i ) of a detection value of the i'th photodetector, obtained by irradiating light on microparticles unmarked with the j'th fluorochrome, as elements, and U represents an M'th order vector with random numbers U j generated following an undyed probability density function F i (U i ) of the j'th fluorochrome obtained from the probability density function f i (u i ) as elements.
6. A fluorescence intensity compensation method, comprising:
receiving, with photodetectors having different input wavelength bands, fluorescence emitted from fluorochromes excited by irradiating light on microparticles multiply-labeled by a plurality of fluorochromes with overlapping fluorescence wavelengths;
collecting detected values for the photodetectors; and
obtaining a measurement spectrum, by approximating, from a linear sum of single-stain spectrums obtained from microparticles individually labeled with the fluorochromes;
wherein approximation of said measurement spectrum by the linear sum of said single-stain spectrums is performed using a restricted least-square method;
wherein the intensity of fluorescence emitted from each fluorochrome is calculated by obtaining a parameter x j (j=1 through M) where an evaluation function shown in the following Expression (1) satisfies the following Expression (2) and also is a smallest value
χ
2
=
∑
i
=
1
N
(
p
i
-
∑
j
=
1
M
s
ij
·
x
j
σ
i
)
2
(
1
)
x
j
≥
U
j
(
2
)
where S ij represents a detected value of the i'th photodetector in the single-stain spectrum of the j'th fluorochrome, p i represents a detected value of the i'th photodetector in the measurement spectrum, σ i represents an inverse number of a weight as to a detected value of the i'th photodetector, and U j represents a lower limit value of the fluorescence intensity of each fluorochrome to be calculated;
wherein said parameter x j (j=1 through M) is obtained by solving the quadratic programming problem in the following Expressions (20) and (21), and executing the following Expression (22)
f
i
(
u
i
)
=
1
2
π
σ
i
ⅇ
-
(
U
i
-
V
i
)
2
2
σ
i
2
(
18
)
F
j
(
U
j
)
=
1
2
π
ρ
j
ⅇ
-
(
U
j
-
V
j
)
2
2
ρ
j
2
(
19
)
Minimize
Sx
′
-
(
p
-
u
)
2
(
20
)
subject
to
x
′
≥
0
(
21
)
x
=
x
′
+
U
(
22
)
where S represents an N×M order matrix with s ij as elements, x represents an M order matrix with x j as elements, p represents an N'th order vector with p i as elements, u represents an N'th order vector with a random number u j generated by obtaining an average value V j and dispersion σ i of the of the i'th photodetector, obtained by irradiating light on microparticles not marked with the j'th fluorochrome, and generating a random number u j following a probability density function f j (u j ) in Expression (18), as the elements, and U represents an M'th order vector having as the elements a random number U j generated by obtaining the undyed average value V j and undyed standard deviation ρ j of the j'th fluorochrome from an average value v i and dispersion σ i and generating the random number U j following a probability density function F j (U j ) in Expression (19).