Method and system for analysis of 3D deformations and regional function of a heart with 3D SinMod
A system and method for analysis of 3D deformations and regional function of a heart includes: a magnetic resonance imaging (MRI) scanner configured to acquire three tagged volume data series with mutually perpendicular tag lines of a heart; a data storage device in communication with the MRI scanner and configured to store the three tagged volume data series; and an image processing machine in communication with data storage device. The image processing machine is configured to: model an intensity distribution around each voxel of each tagged volume data series as a moving sine wave front with a local frequency and an amplitude; and determine a phase and frequency for each voxel from the local frequency and amplitude and a displacement from a quotient of a phase difference and the local frequency.
1. A method for analysis of 3D deformations and regional function of a heart comprising:
receiving, by an image processing device, three sets of 3D plus time volumetric data with mutually perpendicular tag lines of a volume of a heart;
modeling in 3D, by the image processing device, using the three sets of 3D plus time volumetric data, a neighborhood around each voxel in the volume as a moving sine wave front with local frequency and amplitude, separately, in each of x, y, and z directions as:
V
1
(
x
,
y
,
z
)
=
A
1
cos
(
ω
x
(
x
+
u
2
)
+
φ
)
+
n
1
(
x
,
y
,
z
)
V
2
(
x
,
y
,
z
)
=
A
2
cos
(
ω
x
(
x
+
u
2
)
+
φ
)
+
n
2
(
x
,
y
,
z
)
where:
ωx and φ are the spatial frequency and phase of the wave, respectively;
A 1 and A 2 are wave magnitudes for a 3D volume V 1 and a short time later, a 3D volume V 2 ;
n 1 and n 2 are additive noise; and
u is the displacement between these two volumes at position (x, y, z) along the x direction; and
the displacements v and w in the y and z directions have a corresponding formulation; and further wherein the 3D plus time volumetric data comprises 3D plus time volumetric data of one or more mid-wall contour deformation of the heart at the beginning of systole, 3D plus time volumetric data of one or more mid-wall contour deformations of the heart at end-systole, or both, and further wherein the one or more mid-wall contour deformation of the heart at the beginning of systole, the one or more mid-wall contour deformations of the heart at end-systole, or both are tracked by 3D SinMod; and
determining, using the image processing device, phase and frequency of the moving sine wave front for each voxel directly from the local frequency and amplitude and a 3D displacement from a quotient of phase difference and local frequency, thereby resulting in 3D deformation information for each voxel, wherein at least some of the 3D deformation information indicates a heart deformation involving a twisting motion combined with longitudinal shortening and wall thickening.
2. The method of claim 1 , wherein each of the three sets of 3D plus time volumetric data is acquired, by a magnetic resonance imaging (MRI) scanner, using a 3D complementary spatial modulation of magnetization (3D CSPAMM) tagging technique.
3. The method of claim 2 , wherein the 3D CSPAMM tagging technique includes rotating, by the MRI scanner, a tagging gradient in such a way as to acquire 3D+t data with orthogonal tags.
4. The method of claim 1 , wherein determining the phase and frequency for each voxel and the displacement comprises:
Fourier transforming, by the image processing device, the 3D volume V 1 (x, y, z) and the 3D volume V 2 (x, y, z) in a first tagging direction;
applying, by the image processing device, identical 3D band-pass filters to the Fourier-transformed volumes to isolate corresponding spectral peaks and produce two complex volumes in the Fourier domain, V bf1 (ω x ; ω y , ω z ) and V bf2 (ω x , ω y , ω z );
applying, by the image processing device, a low frequency band-pass filter and a high frequency band-pass filter to the two complex volumes in the Fourier domain, followed by an inverse Fourier transform to produce four complex volumes, V bfLf1 (x, y, z), V bfHf1 (x, y, z), V bfLf2 (x, y, z), and V bfHf2 (x, y, z);
determining, by the image processing device, the power spectra and cross power spectrum given by:
P Lf ( x,y,z )=| V bfLf1 | 2 +|V bfLf2 | 2
P Hf ( x,y,z )=| V bfHf1 | 2 +|V bfHf2 | 2
P cc ( x,y,z )= V bfLf1 V bfLf2 +V bfHf1 V bfHf2
where V is the complex conjugate of V;
determining, by the image processing device, the local frequency ω x and local displacement u from:
ω
x
(
x
,
y
,
z
)
=
ω
c
P
Hf
P
Lf
u
(
x
,
y
,
z
)
=
arg
(
P
cc
)
ω
x
where ω c is the band-pass center-frequency;
up-sampling, by the image processing device, the local displacement to the initial size of the volume; and
repeating the same steps for the other tagging directions to produce full 3D displacements.
5. The method of claim 1 , wherein the one or more mid-wall contour deformation of the heart at the beginning of systole, the one or more mid-wall contour deformations of the heart at end-systole, or both are compared using a motion field from a 3D SinMod. algorithm with 3D HARP.
6. The method of claim 1 , further comprising generating average radial, circumferential, and longitudinal strain curves during systole.
7. The method of claim 6 , wherein the average radial, circumferential, and longitudinal strain curves comprise strain curves for one or more regions of the heart selected from the group consisting of mid-ventricular anterior, mid-ventricular antero-septal, mid-ventricular infero-septal, mid-ventricular inferior, mid-ventricular posterior, and mid-ventricular lateral, or any combination thereof.
8. The method of claim 7 , wherein the average radial, circumferential, and longitudinal strain curves comprise strain curves for each of the mid-ventricular anterior, mid-ventricular antero-septal, mid-ventricular infero-septal, mid-ventricular inferior, mid-ventricular posterior, and mid-ventricular lateral regions of the heart.
9. A system for analysis of 3D deformations and regional function of a heart comprising:
a magnetic resonance imaging (MRI) scanner configured to acquire three sets of 3D plus time volumetric data with mutually perpendicular tag lines of a volume of a heart;
a data storage device in communication with the MRI scanner and configured to store the three sets of 3D plus time volumetric data; and
an image processing device in communication with data storage device and configured to:
model in 3D, using the three sets of 3D plus time volumetric data, a neighborhood around each voxel in the volume as a moving sine wave front with local frequency and amplitude, separately, in each of x, y, and z directions as:
V
1
(
x
,
y
,
z
)
=
A
1
cos
(
ω
x
(
x
+
u
2
)
+
φ
)
+
n
1
(
x
,
y
,
z
)
V
2
(
x
,
y
,
z
)
=
A
2
cos
(
ω
x
(
x
+
u
2
)
+
φ
)
+
n
2
(
x
,
y
,
z
)
where:
ωx and φ are the spatial frequency and phase of the wave, respectively;
A 1 and A 2 are wave magnitudes for a 3D volume V 1 and a short time later, a 3D volume V 2 ;
n 1 and n 2 are additive noise; and
u is the displacement between these two volumes at position (x, y, z) along the x direction; and
the displacements v and w in the y and z directions have a corresponding formulation; and further wherein the 3D plus time volumetric data comprises 3D plus time volumetric data of one or more mid-wall contour deformation of the heart at the beginning of systole, 3D plus time volumetric data of one or more mid-wall contour deformations of the heart at end-systole, or both, and further wherein the one or more mid-wall contour deformation of the heart at the beginning of systole, the one or more mid-wall contour deformations of the heart at end-systole, or both are tracked by 3D SinMod; and
determine phase and frequency of the moving sine wave front for each voxel directly from the local frequency and amplitude and a 3D displacement from a quotient of phase difference and local frequency, thereby resulting in 3D deformation information for each voxel, wherein at least some of the 3D deformation information indicates a heart deformation involving a twisting motion combined with longitudinal shortening and wall thickening.
10. The system of claim 9 , wherein the MRI scanner acquires each of the three sets of 3D plus time volumetric data using a 3D complementary spatial modulation of magnetization (3D CSPAMM) tagging technique.
11. The system of claim 10 , wherein the MRI scanner, performing the 3D CSPAMM tagging technique, rotates a tagging gradient in such a way as to acquire 3D+t data with orthogonal tags.
12. The system of claim 9 , wherein the image processing device determines the phase and frequency for each voxel and the displacement by:
Fourier transforming the 3D volume V 1 (x, y, z) and the 3D volume V 2 (x, y, z) in a first tagging direction;
applying identical 3D band-pass filters to the Fourier-transformed volumes to isolate corresponding spectral peaks and produce two complex volumes in the Fourier domain, V bf1 (ω y , ω y , ω z ) and V bf2 (ω x , ω y , ω z );
applying a low frequency band-pass filter and a high frequency band-pass filter to the two complex volumes in the Fourier domain, followed by an inverse Fourier transform to produce four complex volumes, V bfLf1 (x, y, z), V bfHf1 (x, y, z), V bfLf (x, y, z), and V bfHf2 (x, y, z);
determining the power spectra and cross power spectrum given by:
P Lf ( x,y,z )=| V bfLf1 | 2 +|V bfLf2 | 2
P Hf ( x,y,z )=| V bfHf1 | 2 +|V bfHf2 | 2
P cc ( x,y,z )= V bfLf1 V bfLf2 +V bfHf1 V bfHf2
where V is the complex conjugate of V;
determining the local frequency ω x and local displacement u from:
ω
x
(
x
,
y
,
z
)
=
ω
c
P
Hf
P
Lf
u
(
x
,
y
,
z
)
=
arg
(
P
cc
)
ω
x
where w c is the band-pass center-frequency;
up-sampling the local displacement to the initial size of the volume; and
repeating the same steps for the other tagging directions to produce full 3D displacements.