Systems, devices, and methods for bundle segmentation in diffusion tensor magnetic resonance imaging
View Patent ↗Certain exemplary embodiments can comprise a method that can comprise automatically causing a representation of body tissue to be rendered. The representation of the body tissue can comprise a plurality of voxels located in an interior region of the body tissue. Each of the plurality of voxels can have a negative value of an energy change function.
1. A method comprising:
via an information device comprising a graphical user interface, said information device communicatively coupled to a magnetic resonance imaging (MRI) machine:
automatically causing a representation of a brain fiber bundle to be rendered, said representation of said brain fiber bundle comprising a plurality of voxels located in an interior region of said brain fiber bundle, each of said plurality of voxels having a negative value of ΔE(x) when ΔE(x) is calculated via:
Δ
E
(
x
)
=
log
σ
1
σ
2
+
1
2
d
2
(
I
1
(
x
)
,
I
0
(
x
)
)
σ
1
2
-
1
2
d
2
(
I
2
(
x
)
,
I
0
(
x
)
)
σ
2
2
+
∇
d
I
1
(
x
)
2
-
∇
d
I
2
(
x
)
2
+
Δ
a
(
x
)
where:
ΔE(x) is an energy change function;
σ 1 is a variance of tensor distances for voxels located in said interior region;
σ 2 is a variance of tensor distances for voxels located in an exterior region;
I 0 is an initial approximation of a tensor image;
I 1 is a tensor image defined in said interior region;
I 2 is a tensor image defined in said exterior region;
d is a distance measurement between a pair of tensors;
∇ d is an intrinsic gradient under a metric of a tensor image function
Δa(x) is a change in surface area caused by promoting a particular voxel to said interior region; and
x represents three dimensional coordinates of a point in Euclidean space, the point directly related to said particular voxel.
2. The method of claim 1 , further comprising:
promoting a voxel to said interior region based upon a negative value of ΔE(x).
3. The method of claim 1 , further comprising:
not promoting a voxel to said interior region based upon a positive value of ΔE(x).
4. The method of claim 1 , further comprising:
initializing said interior region to a single voxel located inside said brain fiber bundle.
5. The method of claim 1 , further comprising:
defining a band comprising neighboring voxels that approximately surround said interior region.
6. The method of claim 1 , further comprising:
computing a mean tensor, said mean tensor a local average of tensors inside said interior region.
7. The method of claim 1 , further comprising:
automatically updating statistical parameters σ i according to equations
σ
1
2
=
∫
Ω
ⅆ
2
(
I
1
(
x
)
,
I
0
(
x
)
)
H
(
x
)
ⅆ
x
∫
Ω
H
(
x
)
ⅆ
x
σ
2
2
=
∫
Ω
ⅆ
2
(
I
2
(
x
)
,
I
0
(
x
)
)
(
1
-
H
(
x
)
)
ⅆ
x
∫
Ω
(
1
-
H
(
x
)
)
ⅆ
x
,
where:
Ω denotes an image domain (union of said interior region and said exterior region);
d is a distance measurement between two tensors;
H(x)={1, xεΩ 1 ; 0, xεΩ 2 };
Ω 1 denotes said interior region; and
Ω 2 said exterior region.
8. The method of claim 1 , further comprising:
repeatedly computing ΔE(x) for voxels in a band at least partially surrounding said interior region until all voxels associated with a negative energy change have been promoted to said interior region.
9. The method of claim 1 , further comprising:
automatically updating I 1 based upon a local average of tensors inside said interior region.
10. The method of claim 1 , further comprising:
automatically updating I 2 based upon a local average of tensors inside said exterior region.
11. The method of claim 1 , further comprising:
automatically computing d according to an equation:
d ( I i ( x ), I 0 ( x ))=| {right arrow over (y)} i −{right arrow over (y)} 0 |
where:
{right arrow over (y)} i is a vector that points in a principal orientation of a first tensor and has magnitude proportional to an anisotropy of said first tensor in said interior region; and
{right arrow over (y)} 0 is a candidate vector that points in a principal orientation of a second tensor and has magnitude proportional to an anisotropy of said second tensor in said exterior region.
12. The method of claim 1 , wherein I is piecewise smooth.
13. A machine-readable medium storing machine-implementable instructions for activities comprising:
automatically causing a representation of a brain fiber bundle to be rendered, said representation of said brain fiber bundle comprising a plurality of voxels located in an interior region of said brain fiber bundle, each of said plurality of voxels having a negative value of ΔE(x) when ΔE(x) is calculated via:
Δ
E
(
x
)
=
log
σ
1
σ
2
+
1
2
d
2
(
I
1
(
x
)
,
I
0
(
x
)
)
σ
1
2
-
1
2
d
2
(
I
2
(
x
)
,
I
0
(
x
)
)
σ
2
2
+
∇
d
I
1
(
x
)
2
-
∇
d
I
2
(
x
)
2
+
Δ
a
(
x
)
where:
ΔE(x) is an energy change function;
σ 1 is a variance of tensor distances for voxels located in said interior region;
σ 2 is a variance of tensor distances for voxels located in an exterior region;
I 0 is an initial approximation of a tensor image;
I 1 is a tensor image defined in said interior region;
I 2 is a tensor image defined in said exterior region;
d is a distance measurement between a pair of tensors;
∇ d is an intrinsic gradient under a metric of a tensor image function;
Δa(x) is a change in surface area caused by promoting a particular voxel to said interior region; and
x represents three dimensional coordinates of a point in Euclidean space, the point directly related to said particular voxel.