US2005283071A1PendingUtilityA1
Imaging volumes with arbitrary geometries in contact and non-contact tomography
Est. expiryJun 4, 2022(expired)· nominal 20-yr term from priority
A61B 5/415A61B 5/4504A61B 5/0073A61B 5/4887A61B 5/0059G01N 33/49G01N 21/4795A61B 5/418A61B 5/0071A61B 5/4528
43
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Claims
Abstract
A method for tomographic imaging of diffuse medium includes directing waves into a diffusive medium, solving a surface-bounded inversion problem by forward field calculations through decomposition of contributions from the multiple reflections from an arbitrary surface within the diffusive medium or outside the diffusive medium into a sum of different orders of reflection up to an arbitrary order, and using contact or non-contact measurements of waves outside said diffusive medium to generate a tomographic image.
Claims
exact text as granted — not AI-modified1 . A method for tomographic imaging of medium comprising:
(a) directing waves into a medium having a boundary S; (b) detecting an intensity of waves emitted from the medium by using contact or non-contact measurements of waves outside the medium; and (c) processing the detected intensity to generate a tomographic image.
2 . The method of claim 1 wherein the medium is diffusive or non-diffusive.
3 . The method of claim 1 wherein the medium fills an object of volume V, at least partially bounded by the boundary surface S.
4 . The method of claim 1 wherein step (c) includes representing the contribution of each wave into the detected intensity as a sum of an arbitrary integer number N of terms in a series.
5 . The method of claim 4 wherein each term in the series is an intensity of a wave reflected from an arbitrary surface within or outside the medium.
6 . The method of claim 5 , wherein step (c) includes determining G DRBM (N) according to:
G
DRBM
(
N
)
(
r
s
,
r
p
)
❘
r
∈
S
=
G
DRBM
(
N
-
1
)
(
r
s
,
r
p
)
❘
r
∈
S
-
τ
g
(
κ
r
s
-
r
p
)
+
τ
1
4
π
∫
S
[
∂
g
(
κ
r
′
-
r
p
)
∂
n
′
+
1
C
nd
D
g
(
κ
r
′
-
r
p
)
]
G
DRBM
(
N
-
1
)
(
r
s
,
r
′
)
ⅆ
S
′
where G (N) DRBM (r p ) is the N-order Green function in the DRBM approximation, D is the diffusion coefficient inside the diffusive medium, n is a unity vector normal to boundary surface S and pointing into the non-diffusive medium, κ is a diffusive wave number κ=√{square root over (−μ a /D+iω/c)}, for a modulation frequency ω, c is a speed of light in the medium, Sa is an absorption coefficient, τ is an evolution step, and r s , and r p are source and detector positions respectively, and wherein the detector is located at the surface, and where g is the Green's function for an infinite homogeneous diffusive medium with a wave number κ. given by formula g(κ|r−r′|)=exp[iκ|r−r′|]/D|r−r′|, and N is an arbitrary integer not smaller than 1, and
where C nd is a total reflectivity of the boundary surface S, integrated over all angles, and expressed through the Fresnel reflection coefficients r as:
C
nd
=
2
-
R
J
1
->
0
-
R
J
0
->
1
R
U
0
->
1
where
R J 1→0 =∫ 0 1 [1−| r 10 (μ)| 2 ]μ 2 dμ R J 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μdμ R U 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μ 2 dμ
and where μ=cos θ for an incidence angle θ, r 01 and r 10 represent the reflection coefficients when the incident wave comes from the inner, diffusive medium having an index of refraction n in , or outer, non-diffusive medium having an index of refraction n out , respectively, and are defined in terms of the parallel and perpendicular polarization components as:
r
2
=
1
2
(
r
⊥
2
+
r
∥
2
)
,
r
∥
=
n
in
cos
θ
t
-
n
out
cos
θ
i
n
in
cos
θ
t
+
n
out
cos
θ
i
,
r
∥
=
n
in
cos
θ
i
-
n
out
cos
θ
t
n
in
cos
θ
i
+
n
out
cos
θ
t
,
and where cos θ t is the cosine of the transmitted angle, which is found from Snell's law n out sin θ t =n in sin θ i .
7 . The method of claim 5 wherein step (c) includes determining G DRBM (N) and U DRBM (N) according to:
G
DRBM
(
N
)
(
r
s
,
r
d
)
=
g
(
κ
r
s
-
r
d
)
+
1
4
π
∫
S
[
∂
g
(
κ
r
′
-
r
d
)
∂
n
′
+
1
C
nd
D
g
(
κ
r
′
-
r
d
)
]
G
DRBM
(
N
)
(
r
s
,
r
′
)
ⅆ
S
′
U
DRBM
(
N
)
(
r
d
)
=
∫
V
S
(
r
′
)
G
DRBM
(
N
)
(
r
′
,
r
d
)
ⅆ
r
′
where G (N) DRBM (r p ) is the N-order Green function in the DRBM approximation, D is the diffusion coefficient inside the diffusive medium, n is a unity vector normal to boundary surface S and pointing into the non-diffusive medium, κ is a diffusive wave number κ=√{square root over (−μ a /D+iω/c)}, for a modulation frequency ω, c is a speed of light in the medium, μ a is an absorption coefficient, τ is an evolution step, and r s , and r p are source and detector positions respectively, and wherein the detector is located at the surface, and where g is the Green's function for an infinite homogeneous diffusive medium with a wave number κ given by formula
g (κ| r−r ′|)=exp[ iκ|r−r′|]/D|r−r′|,
N is an arbitrary integer not smaller than 1, U DRBM (N) (r d ) is a wave intensity at point r d , and S(r′) is the strength of the light source at position r′ expressed in units of energy density, and
where C nd is a total reflectivity of the boundary surface S, integrated over all angles, and expressed through the Fresnel reflection coefficients r as:
C
nd
=
2
-
R
J
1
→
0
-
R
J
0
→
1
R
U
0
→
1
where
R J 1→0 =∫ 0 1 [1−| r 10 (μ)| 2 ]μ 2 dμ R J 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μdμ R U 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μ 2 dμ
and where μ=cos θ for an incidence angle θ, r 01 and r 10 represent the reflection coefficients when the incident wave comes from the inner, diffusive medium having an index of refraction n in , or outer, non-diffusive medium having an index of refraction n out , respectively, and are defined in terms of the parallel and perpendicular polarization components as:
r
2
=
1
2
(
r
⊥
2
+
r
∥
2
)
,
r
∥
=
n
in
cos
θ
t
-
n
out
cos
θ
i
n
in
cos
θ
t
+
n
out
cos
θ
i
,
r
∥
=
n
in
cos
θ
i
-
n
out
cos
θ
t
n
in
cos
θ
i
+
n
out
cos
θ
t
,
and where cos θ t is the cosine of the transmitted angle, which is found from Snell's law n out sin θ t =n in sin θ i .
8 . The method of claim 5 , wherein step (c) further comprises:
monitoring a gradient of the boundary surface to detect complex boundaries; and automatically increasing a density of local surface discretization and the number N of terms in a series, if the boundary is complex.
9 . The method of claim 5 , wherein step (c) further comprises:
monitoring relative change in a value of the calculated intensity added by each term of the series; and truncating the series by selecting a finite number N of terms in a series, when the relative change in a value of the calculated intensity meets convergence criteria.
10 . The method of claim 1 , wherein step (c) further comprises:
monitoring the gradient of a surface boundary to detect complex boundaries; automatically increasing a density of local surface discretization and the number N of terms in a series, if the boundary is complex; and optimizing an evolution step r by assigning a value, of about τ=2imag{κ}/√{square root over (W)}+1, wherein W is a mean diameter of the diffusive medium.
11 . The method of claim 3 wherein the volume V is of arbitrary geometry.
12 . The method of claim 11 , wherein the volume or object has a fixed geometry whose surface is defined in terms of a continuous function f[z(x,y)] in cartesian, polar or cylindrical coordinates.
13 . The method of claim 11 , wherein the object is an animal.
14 . The method of claim 11 , wherein the object is a human.
15 . The method of claim 1 further including a step of selecting a tomographic imaging method.
16 . The method of claim 15 , wherein the tomographic imaging method is selected from the group consisting of diffuse optical tomography, fluorescence-mediated tomography, near-field optical tomography and thermal tomography.
17 . The method of claim 1 , wherein the medium is biological tissue.
18 . The method of claim 1 , wherein the waves are waves of temperature.
19 . The method of claim 1 , wherein the waves are light.
20 . The method of claim 1 , wherein the wave is continuous wave (CW), time-resolved (TR), intensity modulated (IM) or a combination thereof.
21 . The method of claim 19 , wherein the light is near-infrared or infrared light.
22 . The method of claim 19 , wherein light is continuous wave (CW), time-resolved (TR) light, intensity modulated (IM) light or any combination thereof.
23 . The method of claim 1 , wherein contact measurements are made using optical guides, fiber guides, optical matching fluids, lenses or any combination thereof.
24 . The method of claim 1 , wherein non-contact measurements are made using a system of lenses, pinholes, apertures or any combination thereof.
25 . A method of obtaining a tomographic image of a target region within an object, the method comprising:
(a) directing light waves from multiple points into an object; (b) detecting light waves emitted from multiple points from the object, wherein the light is emitted from an intrinsic absorber, fluorochrome, or scatterer; (c) processing the detected light by representing the contribution of each wave into the detected intensity as a sum of an arbitrary number N of terms in a series and wherein each term in the series is an intensity of a wave reflected from an arbitrary surface within or outside a diffusive medium; and (d) forming a tomographic image that corresponds to a three-dimensional target region within said object and to a quantity of intrinsic absorber, fluorochrome, or scatterer in the target region.
26 . The method of claim 25 , wherein the intrinsic absorber, fluorochrome, or scatterer is selected from the group consisting of hemoglobin, water, lipid, myoglobin, tissue chromophores and organelles.
27 . A method of obtaining a tomographic image of a target region within an object, the method comprising:
(a) administering to an object a fluorescent imaging probe; (b) directing light waves from multiple points into the object; (c) detecting fluorescent light emitted from multiple points from the object; (d) processing the detected light by representing the contribution of each wave into the detected intensity as a sum of an arbitrary number N of terms in a series and wherein each term in the series is an intensity of a wave reflected from an arbitrary surface within or outside a diffusive medium; and (e) forming a tomographic image that corresponds to a three-dimensional target region within the object and to a quantity of fluorescent imaging probe in the target region.
28 . The method of claim 27 , wherein steps (a)-(e) are repeated at predetermined intervals thereby allowing for evaluation of emitted signal of the fluorescent imaging probe in the object over time.
29 . The method of claim 27 , wherein the presence, absence or level of fluorescent signal emitted by the fluorescent imaging probe is indicative of a disease.
30 . The method of claim 27 , wherein the method is used in the early detection, or staging of a disease.
31 . The method of claim 27 , wherein the method is used to assess the effect of one or more pharmacological therapies on a disease.
32 . The method of claim 30 , wherein the disease is selected from the group consisting of cancer, cardiovascular diseases, neurodegenerative diseases, immunologic diseases, autoimmune diseases, infectious diseases, dermatologic diseases, and bone diseases.
33 . The method of claim 27 , wherein the tomographic image is co-registered with an image obtained by another imaging modality.
34 . A tomographic imaging system comprising:
(a) a wave source block to direct waves into an object; (b) a wave detector block to detect the intensity of waves emitted from the object and to convert the intensity of the waves into a digital signal representing waves emitted from the object; (c) a processor to control the detector block and, optionally, the source block and to process the digital signal representing waves emitted from the object into a tomographic image on an output device, wherein the processor is programmed to process the digital signal by representing the contribution of each wave into the detected intensity as a sum of an arbitrary integer number N of terms in a series and wherein each term in the series is an intensity of a wave reflected from an arbitrary surface within or outside a medium.
35 . The system of claim 34 wherein the processor is programmed to determine G DRBM (N) according to:
G
DRBM
(
N
)
(
r
s
,
r
d
)
|
r
∈
S
=
G
DRBM
(
N
-
1
)
(
r
s
,
r
p
)
|
r
∈
S
-
τ
g
(
κ
r
s
-
r
p
)
+
τ
1
4
π
∫
S
[
∂
g
(
κ
r
′
-
r
d
)
∂
n
′
+
1
C
nd
D
g
(
κ
r
′
-
r
p
)
]
G
DRBM
(
N
-
1
)
(
r
s
,
r
′
)
ⅆ
S
′
where G (N) DRBM (r p ) is the N-order Green function in the DRBM approximation, D is the diffusion coefficient inside the diffusive medium, n is a unity vector normal to boundary surface S and pointing into the non-diffusive medium, κ is a diffusive wave number κ=√{square root over (−μ a /D+iω/c)}, for a modulation frequency ω, c is a speed of light in the medium, μ a is an absorption coefficient, τ is an evolution step, and r s , and r p are source and detector positions respectively, and
wherein the detector is located at the surface, and where g is the Green's function for an infinite homogeneous diffusive medium with a wave number κ. given by formula g(κ|r−r′|)=exp[iκ|r−r′|]/D|r−r′|, and N is an arbitrary integer not smaller than 1, and
where C nd is a total reflectivity of the boundary surface S, integrated over all angles, and expressed through the Fresnel reflection coefficients r as:
C
nd
=
2
-
R
J
1
→
0
-
R
J
0
→
1
R
U
0
→
1
where
R J 1→0 =∫ 0 1 [1−| r 10 (μ)| 2 ]μ 2 dμ R J 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μdμ R U 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μ 2 dμ
and where μ=cos θ for an incidence angle θ, r 01 and r 10 represent the reflection coefficients when the incident wave comes from the inner, diffusive medium having an index of refraction n in , or outer, non-diffusive medium having an index of refraction n out , respectively, and are defined in terms of the parallel and perpendicular polarization components as:
r
2
=
1
2
(
r
⊥
2
+
r
∥
2
)
,
r
∥
=
n
in
cos
θ
t
-
n
out
cos
θ
i
n
in
cos
θ
t
+
n
out
cos
θ
i
,
r
∥
=
n
in
cos
θ
i
-
n
out
cos
θ
t
n
in
cos
θ
i
+
n
out
cos
θ
t
,
and where cos θ t is the cosine of the transmitted angle, which is found from Snell's law n out sin θ t =n in sin θ i .
36 . The system of claim 34 wherein the processor is programmed to determine G DRBM (N) and U DRBM (N) according to:
G
DRBM
(
N
)
(
r
s
,
r
d
)
=
g
(
κ
r
s
-
r
d
)
+
1
4
π
∫
S
[
∂
g
(
κ
r
′
-
r
d
)
∂
n
′
+
1
C
nd
D
g
(
κ
r
′
-
r
d
)
]
G
DRBM
(
N
)
(
r
s
,
r
′
)
ⅆ
S
′
U
DRBM
(
N
)
(
r
d
)
=
∫
V
S
(
r
′
)
G
DRBM
(
N
)
(
r
′
,
r
d
)
ⅆ
r
′
wherein where G (N) DRBM (r p ) is the N-order Green function in the DRBM approximation, D is the diffusion coefficient inside the diffusive medium, n is a unity vector normal to boundary surface S and pointing into the non-diffusive medium, κ is a diffusive wave number κ=√{square root over (−μ a /D+iω/c)}, for a modulation frequency ω, c is a speed of light in the medium, μ a is an absorption coefficient, τ is an evolution step, and r s , and r p are source and detector positions respectively, and wherein the detector is located at the surface, and where g is the Green's function for an infinite homogeneous diffusive medium with a wave number κ given by formula g(κ|r−r′|)=exp[iκ|r−r′|]/D|r−r′|, N is an arbitrary integer not smaller than 1, U DRBM (N) (r d ) is a wave intensity at point r d , and S(r′) is the strength of the light source at position r′ expressed in units of energy density, and
where C nd is a total reflectivity of the boundary surface S, integrated over all angles, and expressed through the Fresnel reflection coefficients r as:
C nd = 2 - R J 1 → 0 - R J 0 → 1 R U 0 → 1
where
R J 1→0 =∫ 0 1 [1−| r 10 (μ)| 2 ]μ 2 dμ R J 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μdμ R U 0→1 =∫ 0 1 [1−| r 01 (μ)| 2 ]μ 2 dμ
and where μ=cos θ for an incidence angle θ, r 01 and r 10 represent the reflection coefficients when the incident wave comes from the inner, diffusive medium having an index of refraction n in , or outer, non-diffusive medium having an index of refraction n out , respectively, and are defined in terms of the parallel and perpendicular polarization components as:
r 2 = 1 2 ( r ⊥ 2 + r ∥ 2 ) , r ∥ = n in cos θ t - n out cos θ i n in cos θ t + n out cos θ i , r ∥ = n in cos θ i - n out cos θ t n in cos θ i + n out cos θ t ,
and where cos θ t is the cosine of the transmitted angle, which is found from Snell's law n out sin θ t =n in sin θ i .
37 . The system of claim 34 wherein are selected from the group consisting of waves of light, waves of sound and waves of temperature.
38 . An apparatus comprising:
a machine executable code for a method of tomographic imaging of medium including the steps of: (a) directing waves into a medium having a boundary S; (b) detecting an intensity of waves emitted from the medium by using contact or non-contact measurements of waves outside the medium; (c) processing the detected intensity to generate a tomographic image by representing the contribution of each wave into the detected intensity as a sum of an arbitrary integer number N of terms in a series and wherein each term in the series is an intensity of a wave reflected from an arbitrary surface within or outside the medium.Cited by (0)
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