Motion tracking and strain determination

1. An apparatus, comprising one or more processors, wherein the one or more processors are configured to:

obtain a source image of an anatomical structure and a target image of the anatomical structure;

determine, in the source image, a first plurality of points on a first surface of the anatomical structure and a second plurality of points on a second surface of the anatomical structure, wherein the first plurality of points and the second plurality of points are determined based on a partial differential equation such that each point in the second plurality of points corresponds to a point in the first plurality of points;

determine, based on the source image and the target image, a motion field that indicates a motion of the anatomical structure from the source image to the target image;

estimate, based on the motion field and respective locations of the first plurality of points and the second plurality of points in the source image, respective locations of the first plurality of points and the second plurality of points in the target image;

determine one or more strain parameters associated with the anatomical structure, wherein:

the one or more strain parameters include at least one of a radial strain of the anatomical structure or a circumferential strain of the anatomical structure;

if the one or more strain parameters include the radial strain, the radial strain is determined based on a change in a radial distance between one of the first plurality of points and one of the second plurality of points from the source image to the target image; and

if the one or more strain parameters include the circumferential strain, the circumferential strain is determined based on a change in a circumferential distance from the source image to the target image, the circumferential distance being a projection of the radial distance in a circumferential direction of the anatomical structure.

2. The apparatus of claim 1 , wherein the partial differential equation comprises Laplace's equation.

3. The apparatus of claim 2 , wherein the first plurality of points and the second plurality of points are determined by solving Laplace's equation to determine one or more equal-potential surfaces and wherein each of the one or more equal-potential surfaces comprises at least one point from the first plurality of points and at least one point from the second plurality of points.

4. The apparatus of claim 1 , wherein the first surface of the anatomical structure comprises an inner surface of the anatomical structure and the second surface of the anatomical structure comprises an outer surface of the anatomical structure.

5. The apparatus of claim 1 , wherein the motion field is determined using one or more artificial neural networks and wherein the determination comprises deriving a first motion field based on respective features extracted from the source image and the target image, and refining the first motion field to obtain a refined motion field.

6. The apparatus of claim 5 , wherein the refinement of the first motion field is performed by at least:

deriving a warped image based on the source image and the first motion field;

determining a second motion field based on respective features extracted from the warped image and the target image; and

combining the first motion field and the second motion field.

7. The apparatus of claim 1 , wherein the source image of the anatomical structure comprises a source segmentation mask associated with the anatomical structure and wherein the target image of the anatomical structure comprises a target segmentation mask associated with the anatomical structure.

8. The apparatus of claim 1 , wherein the one or more strain parameters include the radial strain of the anatomical structure, and wherein the one or more processors are configured to:

determine, in the source image, a first radial distance between a first point on the first surface of the anatomical structure and a second point on the second surface of the anatomical structure, wherein the first point belongs to the first plurality of points and the second point belongs to the second plurality of points, and wherein the first point corresponds to the second point in accordance with the partial differential equation;

determine, in the target image, a second radial distance between the first point on the first surface of the anatomical structure and the second point on the second surface of the anatomical structure;

determine a change between the first radial distance and the second radial distance; and

determine the radial strain based on the change between the first radial distance and the second radial distance.

9. The apparatus of claim 1 , wherein the one or more strain parameters include the circumferential strain of the anatomical structure, and wherein the one or more processors are configured to:

determine, in the source image, a first circumferential distance in the circumferential direction of the anatomical structure that corresponds to a projection of a first radial distance in the source image between a first point and a second point that are respectively located on the first and second surfaces of the anatomical structure, wherein the first point and the second point are among the first plurality of points and the second plurality of points, respectively;

determine, in the target image, a second circumferential distance in the circumferential direction of the anatomical structure that corresponds to a projection of a second radial distance in the target image between the first point and the second point;

determine a change between the first circumferential distance and the second circumferential distance; and

determine the circumferential strain based on the change between the first circumferential distance and the second circumferential distance.

10. The apparatus of claim 1 , wherein the anatomical structure comprises a myocardium.

11. A method for motion tracking and strain determination, the method comprising:

obtaining a source image of an anatomical structure and a target image of the anatomical structure;

determining, in the source image, a first plurality of points on a first surface of the anatomical structure and a second plurality of points on a second surface of the anatomical structure, wherein the first plurality of points and the second plurality of points are determined based on a partial differential equation such that each point in the second plurality of points corresponds to a point in the first plurality of points;

determining, based on the source image and the target image, a motion field that indicates a motion of the anatomical structure from the source image to the target image;

estimating, based on the motion field and respective locations of the first plurality of points and the second plurality of points in the source image, respective locations of the first plurality of points and the second plurality of points in the target image;

determining one or more strain parameters associated with the anatomical structure, wherein:

the one or more strain parameters include at least one of a radial strain of the anatomical structure or a circumferential strain of the anatomical structure;

if the one or more strain parameters include the radial strain, the radial strain is determined based on a change in a radial distance between one of the first plurality of points and one of the second plurality of points from the source image to the target image; and

if the one or more strain parameters include the circumferential strain, the circumferential strain is determined based on a change in a circumferential distance from the source image to the target image, the circumferential distance being a projection of the radial distance in a circumferential direction of the anatomical structure.

12. The method of claim 11 , wherein the partial differential equation comprises Laplace's equation.

13. The method of claim 12 , wherein the first plurality of points and the second plurality of points are determined by solving Laplace's equation to determine one or more equal-potential surfaces and wherein each of the one or more equal-potential surfaces comprises at least one point from the first plurality of points and at least one point from the second plurality of points.

14. The method of claim 11 , wherein the first surface of the anatomical structure comprises an inner surface of the anatomical structure and the second surface of the anatomical structure comprises an outer surface of the anatomical structure.

15. The method of claim 11 , wherein the motion field is determined using one or more artificial neural networks and wherein the determination comprises deriving a first motion field based on respective features extracted from the source image and the target image, and refining the first motion field to obtain a refined motion field.

16. The method of claim 15 , wherein the refinement of the first motion field is performed by at least:

deriving a warped image based on the source image and the first motion field;

determining a second motion field based on respective features extracted from the warped image and the target image; and

combining the first motion field and the second motion field.

17. The method of claim 11 , wherein the source image of the anatomical structure comprises a source segmentation mask associated with the anatomical structure and wherein the target image of the anatomical structure comprises a target segmentation mask associated with the anatomical structure.

18. The method of claim 11 , wherein the one or more strain parameters include the radial strain of the anatomical structure and wherein determining the one or more strain parameters associated with the anatomical structure comprises:

determining, in the source image, a first radial distance between a first point on the first surface of the anatomical structure and a second point on the second surface of the anatomical structure, wherein the first point belongs to the first plurality of points and the second point belongs to the second plurality of points, and wherein the first point corresponds to the second point in accordance with the partial differential equation;

determining, in the target image, a second radial distance between the first point on the first surface of the anatomical structure and the second point on the second surface of the anatomical structure;

determining a change between the first radial distance and the second radial distance; and

determining the radial strain based on the change between the first radial distance and the second radial distance.

19. The method of claim 11 , wherein the one or more strain parameters include the circumferential strain of the anatomical structure and wherein determining the one or more strain parameters associated with the anatomical structure comprises:

determining, in the source image, a first circumferential distance in the circumferential direction of the anatomical structure that corresponds to a projection of a first radial distance in the source image between a first point and a second point that are respectively located on the first and second surfaces of the anatomical structure, wherein the first point and the second point are among the first plurality of points and the second plurality of points, respectively;

determining, in the target image, a second circumferential distance in the circumferential direction of the anatomical structure that corresponds to a projection of a second radial distance in the target image between the first point and the second point;

determining a change between the first circumferential distance and the second circumferential distance; and

determining the circumferential strain based on the change between the first circumferential distance and the second circumferential distance.

20. The method of claim 11 , wherein the anatomical structure comprises a myocardium.