Systems, devices, and methods for diffusion tractography
View Patent ↗Certain exemplary embodiments comprise a method, which can comprise automatically causing a representation of body tissue to be rendered. The body tissue can be tracked via clusters. The clusters each can comprise a predetermined number of particles. Each particle of a particular cluster can be representative of a discreet path associated with the particular cluster in a tensor field.
1. A method comprising:
automatically causing a representation of an in-vivo bundle of brain fibers to be rendered, said in-vivo bundle of brain fibers tracked via clusters, said clusters each comprising a predetermined number of particles, each particle of a particular cluster representative of a discreet path associated with said particular cluster in a tensor field, said discreet path a set of locations in said tensor field, said tensor field computed via a magnetic resonance imaging sensor, said representation comprising a most likely fiber structure, said most likely fiber structure comprising a path followed by a subset of said particles, said subset associated with particle probabilities above a predetermined threshold, each of said predetermined number of particles iteratively sampled via a probability function:
p
tensor
(
x
t
|
x
t
-
1
)
=
1
(
2
π
)
3
/
2
exp
(
-
1
2
(
x
t
-
x
t
-
1
)
T
D
(
x
t
-
1
)
-
1
(
x
t
-
x
t
-
1
)
)
where:
D(x) is a normalized tensor at location x, said normalized tensor obtained from said magnetic resonance imaging sensor;
t is a time interval associated with tracking said in-vivo bundle of brain fibers; and
x is a location associated with tracking said in-vivo bundle of brain fibers;
each of said predetermined number of particles having an associated weight computed from an equation:
w
0
:
t
i
=
p
(
x
t
i
|
x
t
-
1
i
)
p
tensor
(
x
t
i
|
x
t
-
1
i
)
w
0
:
t
-
1
i
where:
w 0:t i is a weight associated with particle i at time t;
t is a time interval associated with tracking said in-vivo bundle of brain fibers;
x i is a location associated with tracking said in-vivo bundle of brain fibers associated with particle i;
p tensor is obtained from said probability function;
p ( x t |x t−1 )= p tensor ( x t |x t−1 )× p reg ( x t |x t−1 )× p fa ( x t |x t−1 )
where:
p reg is a probability derived from a distance between x t−1 −x t−2 and x t −x t−1 ; and
p fa is a fractional anisotropy probability computed from fractional anisotropy at location x t determined from said normalized tensor;
each of said clusters created from a first particle and via recursive additions of a next particle to a closest existing cluster if a determined distance between said next particle and a center of said closest existing cluster is smaller than said predetermined threshold;
and
iteratively sampling each of said predetermined number of particles via said probability function.
2. The method of claim 1 , further comprising:
obtaining said tensor field from said magnetic resonance imaging sensor.
3. The method of claim 1 , further comprising:
initializing a set of particles at a seed point, a count of said set of particles being predetermined; and
tracking said in-vivo bundle of brain fibers beginning at said seed point.
4. The method of claim 1 , further comprising:
for each of said predetermined number of particles, determining a projection direction based upon a probability distribution induced by p tensor and moving each particle by a predetermined step size in said projection direction.
5. The method of claim 1 , further comprising:
calculating each weight via said weight equation.
6. The method of claim 1 , further comprising:
calculating each weight via said weight equation; and
normalizing each weight.
7. The method of claim 1 , further comprising:
for each cluster, removing particles whose weights are below a predefined threshold.
8. The method of claim 1 , further comprising:
for each cluster, duplicating particles until each cluster contains said predetermined number of particles, said duplicated particles randomly selected according to their weights; and
maintaining said predetermined number of particles in each cluster to branch without a loss of tracking power.
9. The method of claim 1 , further comprising:
defining said predetermined distance.
10. The method of claim 1 , further comprising:
creating a new cluster if a distance between said next particle and said center of closest existing cluster is above said predetermined threshold.
11. The method of claim 1 , further comprising:
determining a center of each cluster.
12. The method of claim 1 , further comprising:
determining a center of each cluster based upon a mean number of particles comprised in each cluster.
13. The method of claim 1 , further comprising:
removing a predetermined cluster if a count of particles comprised in said predetermined cluster is below a predetermined count threshold; and
reassigning each particle from said predetermined cluster to a closest remaining cluster.
14. The method of claim 1 , further comprising:
recalculating said center of said closest existing cluster based upon a mean number of particles comprised in said closest existing cluster.
15. The method of claim 1 , further comprising:
terminating said method when a particle probability is determined to be below a predetermined probability threshold.
16. A machine-readable medium comprising machine instructions for activities comprising:
automatically causing a representation of an in-vivo bundle of brain fibers to be rendered, said in-vivo bundle of brain fibers tracked via clusters, said clusters each comprising a predetermined number of particles, each particle of a particular cluster representative of a discreet path associated with said particular cluster in a tensor field, said discreet path a set of locations in said tensor field, said tensor field computed via a magnetic resonance imaging sensor, said representation comprising a most likely fiber structure, said most likely fiber structure comprising a path followed by a subset of said particles, said subset associated with particle probabilities above a predetermined threshold, each of said predetermined number of particles iteratively sampled via a probability function:
p
tensor
(
x
t
|
x
t
-
1
)
=
1
(
2
π
)
3
/
2
exp
(
-
1
2
(
x
t
-
x
t
-
1
)
T
D
(
x
t
-
1
)
-
1
(
x
t
-
x
t
-
1
)
)
where:
D(x) is a normalized tensor at location x, said normalized tensor obtained from said magnetic resonance imaging sensor;
t is a time interval associated with tracking said in-vivo bundle of brain fibers; and
x is a location associated with tracking said in-vivo bundle of brain fibers;
each of said predetermined number of particles having an associated weight computed from an equation:
w
0
:
t
i
=
p
(
x
t
i
|
x
t
-
1
i
)
p
tensor
(
x
t
i
|
x
t
-
1
i
)
w
0
:
t
-
1
i
where:
w 0:t i is a weight associated with particle i at time t;
t is a time interval associated with tracking said in-vivo bundle of brain fibers;
x i is a location associated with tracking said in-vivo bundle of brain fibers associated with particle i;
P tensor is obtained from said probability function;
p ( x t |x t−1 )= p tensor ( x t |x t−1 )× p reg ( x t |x t−1 )× p fa ( x t |x t−1 )
where:
P reg is a probability derived from a distance between x t−1 −x t−2 and x t −x t−1 ; and
p f , is a fractional anisotropy probability computed from fractional anisotropy at location x t determined from said normalized tensor;
each of said clusters created from a first particle and via recursive additions of a next particle to a closest existing cluster if a determined distance between said next particle and a center of said closest existing cluster is smaller than a predetermined threshold
and
iteratively sampling each of said predetermined number of particles via said probability function.
17. A method comprising:
via a magnetic resonance imaging sensor, transforming sensed molecular placement data into a tensor field that is associated with a physical structure of a body tissue, said transforming comprising:
calculating a discreet path associated with a particular cluster in said tensor field, said particular cluster one of a plurality of clusters, said clusters each comprising a predetermined number of particles, said discreet path a set of locations in said tensor field, said tensor field comprising a most likely fiber structure, said most likely fiber structure comprising a path followed by a subset of said particles, said subset associated with particle probabilities above a predetermined threshold, each of said predetermined number of particles iteratively sampled via a probability function:
p
tensor
(
x
t
|
x
t
-
1
)
=
1
(
2
π
)
3
2
exp
[
-
1
2
(
x
t
-
x
t
-
1
)
T
D
(
x
t
-
1
)
-
1
(
x
t
-
x
t
-
1
)
]
where: D(x) is a normalized tensor at location x, said normalized tensor obtained from said magnetic resonance imaging sensor; t is a time interval associated with tracking said in-vivo bundle of brain fibers; and x is a location associated with tracking said in-vivo bundle of brain fibers;
each of said predetermined number of particles having an associated weight, said weight calculated using:
a previous weight calculated at an earlier time,
said time interval,
a probability derived from a distance, and
a fractional anisotropy probability computed from a fractional anisotropy at said location;
each of said clusters created from a first particle and via recursive additions of a next particle to a closest existing cluster if a determined distance between said next particle and a center of said closest existing cluster is smaller than a predetermined threshold.