System and method for simultaneously registering multiple lung CT scans for quantitative lung analysis
A method for simultaneously registering a plurality of computed tomography (CT) scans of a region of interest of a subject including a subject's lungs for quantitative lung analysis includes receiving a plurality of CT scans of the region of interest acquired with a CT imaging system, receiving a breathing surrogate data for the subject, the breathing surrogate data comprising an amplitude for each of the plurality of CT scans and determining a deformation based on the plurality of CT scans and the breathing surrogate data using an iterative optimization process of an objective function. The objective function can include a first term based on an approximation of local changes in Hounsfield Units (HU) adjusted for breathing of the subject and a second term based on error in the conservation of mass. At least one quantitative lung parameter may be determined based on the deformation.
1 . A method for simultaneously registering a plurality of computed tomography (CT) scans of a region of interest of a subject including a subject's lungs for quantitative lung analysis, the method comprising:
receiving a plurality of CT scans of the region of interest acquired with a CT imaging system;
receiving a breathing surrogate data for the subject, the breathing surrogate data comprising an amplitude for each of the plurality of CT scans; and
determining a deformation based on the plurality of CT scans and the breathing surrogate data using an iterative optimization process of an objective function having a first term based on an approximation of local changes in Hounsfield Units (HU) adjusted for breathing of the subject and a second term based on error in the conservation of mass.
2 . The method according to claim 1 , wherein the deformation is a deformation vector field (DVF).
3 . The method according to claim 1 , wherein the objective function is given by:
HU
i
′
-
HU
j
′
p
+
α
ΔΓ
ij
p
where HU are Hounsfield units of the CT scans within a lung boundary, α is a parameter used to adjust the relative importance of the first term and the second term, ΔΓ ij is a mathematical description of the conservation of mass, i and j refer to scans such that i≠j, and p is the p norm.
4 . The method according to claim 3 , wherein the first term is given by:
(
HU
i
′
-
HU
j
′
)
=
(
HU
i
-
HU
j
)
+
dHU
dA
(
A
j
-
A
i
)
where HU, is an HU value of scan i, HU j is an HU value of scan j, dHU/dA is a slope of a fit of all HUs to their respective amplitudes, A i is a surrogate amplitude of scan i, A j is a surrogate amplitude of scan j, and one of i and j is a reference scan.
5 . The method according to claim 3 , wherein the second term is given by one of:
ΔΓ
ij
=
J
ij
-
ρ
i
/
ρ
j
2
or the inverse relationship
ΔΓ
ij
′
=
1
/
J
ij
-
ρ
j
/
ρ
i
2
where J is the Jacobian of a deformation vector field (DVF), ρ i is a tissue density determined by scan i, and ρ j is a tissue density determined by scan j.
6 . The method according to claim 1 , further comprising determining at least one quantitative lung parameter based on the deformation.
7 . The method according to claim 6 , wherein the at least one quantitative lung parameter is ventilation.
8 . The method according to claim 7 , wherein the ventilation is determined as a parameterization of a Jacobian of a deformation vector field (DVF) as a function of the breathing amplitude.
9 . The method according to claim 7 , wherein the ventilation (V) is determined as a rate of change of the Jacobian (J) of the deformation vector field (DVF) with respect to breathing amplitude (A) as given by:
V
=
dJ
dA
.
10 . The method according to claim 1 , wherein each CT scan in the plurality of CT scans is acquired during free-breathing.
11 . The method according to claim 1 , wherein each CT scan in the plurality of CT scans is acquired during modified breathing.
12 . The method according to claim 1 , wherein the amplitude is calibrated based on a position of a diaphragm dome of the subject in at least one of the plurality of CT scans.
13 . The method according to claim 1 , wherein determining a deformation based on the plurality of CT scans and the breathing surrogate data using an iterative optimization process of the objective function comprises determining a deformation vector field that minimizes the objective function.
14 . A system for simultaneously registering a plurality of computed tomography (CT) scans of a region of interest of a subject including a subject's lungs for quantitative lung analysis, the system comprising:
a processor device; and
a non-transitory computer-readable memory storing instructions executable by the processor device, wherein the instructions, when executed by the processor device, cause the system to:
receive a plurality of CT scans of the region of interest acquired with a CT imaging system;
receive a breathing surrogate data for the subject, the breathing surrogate data comprising an amplitude for each of the plurality of CT scans; and
determine a deformation based on the plurality of CT scans and the breathing surrogate data using an iterative optimization process of an objective function having a first term based on an approximation of local changes in Hounsfield Units (HU) adjusted for breathing of the subject and a second term based on error in the conservation of mass.
15 . The system according to claim 14 , wherein the deformation is a deformation vector field (DVF).
16 . The system according to claim 14 , wherein the objective function is given by:
HU
i
′
-
HU
j
′
p
+
α
ΔΓ
ij
p
where HU are Hounsfield units of the CT scans within a lung boundary, α is a parameter used to adjust the relative importance of the first term and the second term, ΔΓ ij is a mathematical description of the conservation of mass, i and j refer to scans such that i≠j, and p is the p norm.
17 . The system according to claim 16 , wherein the first term is given by:
(
HU
i
′
-
HU
j
′
)
=
(
HU
i
-
HU
j
)
+
dHU
dA
(
A
j
-
A
i
)
where HU i is an HU value of scan i, HU j is an HU value of scan j, dHU/dA is a slope of a fit of all HUs to their respective amplitudes, A i is a surrogate amplitude of scan i, A j is a surrogate amplitude of scan j, and one of i and j is a reference scan.
18 . The system according to claim 16 , wherein the second term is given by one of:
ΔΓ
ij
=
J
ij
-
ρ
i
/
ρ
j
2
or the inverse relationship
ΔΓ
ij
′
=
1
/
J
ij
-
ρ
j
/
ρ
i
2
where J is the Jacobian of a deformation vector field (DVF), ρ i is a tissue density determined by scan i, and ρ j is a tissue density determined by scan j.
19 . The system according to claim 14 , wherein the instructions, when executed by the processor device, further cause the system to determine at least one quantitative lung parameter based on the deformation.
20 . The system according to claim 19 , wherein the at least one quantitative lung parameter is ventilation.
21 . The system according to claim 20 , wherein the ventilation is determined as a parameterization of a Jacobian of a deformation vector field (DVF) as a function of the breathing amplitude.
22 . The system according to claim 20 , wherein the ventilation is determined as a rate of change of a Jacobian (J) of a deformation vector field (DVF) with respect to breathing amplitude (A) as given by:
V
=
dJ
dA
.
23 . The system according to claim 14 , wherein each CT scan in the plurality of CT scans is acquired during free-breathing.