Methods for providing diagnostic information using endocardial surface data for a patient's heart

1. A method for providing diagnostic information using endocardial surface data for a patient's heart, the method comprising:

receiving endocardial surface data for the left ventricle of a heart, wherein the endocardial surface data represents the endocardial surface of the left ventricle at multiple times over a heartbeat, the multiple times comprising end diastole and end systole of the heartbeat, and wherein the endocardial surface data is obtained using a volumetric imaging application;

generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle at end diastole and end systole using the endocardial surface data, wherein the prolate spheroidal coordinates comprise a longitudinal angular coordinate μ, a circumferential angular coordinate θ, and a coordinate λ as a function of longitudinal angular coordinate μ and circumferential angular coordinate θ, and wherein λ ED represents the value of coordinate λ at end diastole and λ ES represents the value of coordinate λ at end systole; and

computing three-dimensional fractional shortening (“3DFS”) of the left ventricle as 3DFS=(λ ED −λ ES )/λ ED , wherein the three-dimensional fractional shortening identifies an ischemic region of the left ventricle.

2. The method of claim 1 , further comprising:

providing an indication of the three-dimensional fractional shortening on a map of the left ventricle, such that the ischemic region of the left ventricle is identified on the map.

3. A method for providing diagnostic information using endocardial surface data for a patient's heart, ‘the method comprising:

receiving endocardial surface data for the left ventricle of a heart, wherein the endocardial surface data represents the endocardial surface of the left ventricle at multiple times over a heartbeat, and wherein the endocardial surface data is obtained using a volumetric imaging application;

generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle at least a portion of the multiple times using the endocardial surface data, wherein the prolate spheroidal coordinates comprise a longitudinal angular coordinate μ, a circumferential angular coordinate θ, and a coordinate λ as a function of longitudinal angular coordinate μ and circumferential angular coordinate θ;

computing a measure based at least in part on the value of coordinate λ at the at least a portion of the multiple times, wherein the measure provides diagnostic information related to the left ventricle; and

wherein the multiple times over the heartbeat comprise end diastole and end systole of the heartbeat, wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises generating a representation at end diastole and end systole, such that λ ED represents the value of coordinate λ at end diastole and λ ES represents the value of coordinate λ at end systole and wherein the measure comprises three-dimensional fractional shortening (“3DFS”) of the left ventricle computed as 3DFS=(λ ED −λ ES )/λ ED .

4. The method of claim 3 , further comprising:

providing an indication of the measure on a map of the left ventricle.

5. The method of claim 4 , wherein the map comprises an area-preserving map of the left ventricle.

6. The method of claim 4 , wherein the map comprises a circumferential polar plot of the left ventricle.

7. The method of claim 3 , further comprising:

providing the measure to a mapping application, such that an indication of the measure can be provided on a map of the left ventricle by the mapping application.

8. The method of claim 3 , wherein the multiple times over the heartbeat comprise end diastole of the heartbeat.

9. The method of claim 3 , wherein the multiple times over the heartbeat comprise end diastole and end systole of the heartbeat.

10. The method of claim 3 , wherein the volumetric imaging application is selected from the group consisting of real-time three-dimensional echocardiography, magnetic resonance imaging; x-ray ventriculography, and computed tomography.

11. The method of claim 3 , wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises:

converting the endocardial surface data into the prolate spheroidal coordinates; and

fitting the prolate spheroidal coordinates to a finite element mesh representing the endocardial surface of the left ventricle.

12. The method of claim 11 , wherein the finite element mesh is constructed from polynomial basis functions.

13. The method of claim 3 , wherein the endocardial surface data for the left ventricle of the heart corresponds to spatial coordinates in a spatial coordinate system defining the endocardial surface of the left ventricle, and wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises:

converting the spatial coordinates in the spatial coordinate system to Cartesian coordinates X 1 , X 2 , and X 3 in a Cartesian coordinate system; and

converting Cartesian coordinates X 1 , X 2 , and X 3 to the prolate spheroidal coordinates.

14. The method of claim 3 , wherein the endocardial surface data for the left ventricle of the heart corresponds to Cartesian coordinates X 1 , X 2 , and X 3 defining the endocardial surface of the left ventricle, and wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises:

converting Cartesian coordinates X 1 , X 2 , and X 3 to the prolate spheroidal coordinates, wherein the prolate spheroidal coordinates are defined by transformation equations

X 1 =d ·cos h λ·cos μ,

X 2 =d ·sin h λ·sin μ·cos θ, and

X 3 =d ·sin h λ·sin μ·sin θ; and

wherein the variable d comprises a focal length of the prolate spheroidal representation.

15. The method of claim 3 , wherein the multiple times over the heartbeat comprise end diastole of the heartbeat, wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises generating a representation at end diastole and two or more additional times over the heartbeats such that λ ED represents the value of coordinate λ at end diastole and λ MIN represents the minimum value of coordinate λ over the heartbeat, and wherein the measure comprises four-dimensional fractional shortening (“4DFS”) of the left ventricle computed as 4DFS=(λ ED −λ MIN )/λ ED .

16. The method of claim 15 , wherein the minimum value of coordinate λ over the heartbeat λ MIN is determined by fitting the prolate spheroidal coordinates to a finite element mesh representing the endocardial surface of the left ventricle.

17. The method of claim 3 , wherein the measure comprises a derivative of coordinate λ selected from the group consisting of ∂λ/∂μ, ∂λ/∂θ, ∂λ/∂t, ∂ 2 λ/∂μ∂t, and ∂ 2 λ/∂θ∂t.

18. The method of claim 3 , wherein the measure comprises maximum systolic ∂λ/∂t for the heartbeat.

19. The method of claim 3 , wherein the diagnostic information related to the left ventricle comprises an indication of size of one or more ischemic regions of the left ventricle.

20. The method of claim 3 , wherein the diagnostic information related to the left ventricle comprises an indication of location of one or more ischemic regions of the left ventricle.

21. The method of claim 3 , wherein the diagnostic information related to the left ventricle comprises an indication of severity of one or more ischemic regions of the left ventricle.

22. The method of claim 3 , wherein the diagnostic information related to the left ventricle comprises an indication of synchrony of contraction of the left ventricle.

23. A non-transitory computer readable medium storing computer executable instructions for providing diagnostic information using endocardial surface data for a patient's heart, the executable instructions comprising:

generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle of a heart at multiple times over a heartbeat using endocardial surface data, wherein the endocardial surface data is obtained using a volumetric imaging application, and wherein the prolate spheroidal coordinates comprise a longitudinal angular coordinate μ, a circumferential angular coordinate θ, and a coordinate λ as a function of longitudinal angular coordinate μ and circumferential angular coordinate θ;

computing a measure based at least in part on the value of coordinate λ at the multiple times, wherein the measure provides diagnostic information related to the left ventricle; and

wherein the multiple times over the heartbeat comprise end diastole and end systole of the heartbeat, wherein generating a representation in prolate spheroidal coordinates of the endocardial surface of the left ventricle comprises generating a representation at end diastole and end systole, such that λ ED represents the value of coordinate λ at end diastole and λ ES represents the value of coordinate λ at end systole, and wherein the measure comprises three-dimensional fractional shortening (“3DFS”) of the left ventricle computed as 3DFS=(λ ED −λ ES )/λ ED .

24. A method for providing diagnostic information using endocardial surface data for a patient's heart, the method comprising:

receiving endocardial surface data for the left ventricle of a heart, wherein the endocardial surface data represents the endocardial surface of the left ventricle at multiple times over a heartbeat, and wherein the endocardial surface data is obtained using a volumetric imaging application;

generating a three-dimensional representation of the endocardial surface of the left ventricle at least a portion of the multiple times using the endocardial surface data, wherein the three-dimensional representation comprises a coordinate λ, that identifies a position of the endocardial surface with respect to a central axis of the left ventricle;

computing a measure based at least in part on the value of coordinate λ, at the at least a portion of the multiple times, wherein the measure provides diagnostic information related to the left ventricle; and

wherein the multiple times over the heartbeat comprise end diastole and end systole of the heartbeat, wherein generating a three-dimensional representation of the endocardial surface of the left ventricle comprises generating a three-dimensional representation at end diastole and end systole, such that λ ED represents the value of coordinate λ at end diastole and λ ES represents the value of coordinate λ at end systole, and wherein the measure comprises three-dimensional fractional shortening (“3DFS”) of the left ventricle computed as 3DFS=(λ ED −λ ES )/λ ED .

25. The method of claim 24 , wherein generating a three-dimensional representation of the endocardial surface comprises generating a three-dimensional representation in prolate spheroidal coordinates, the prolate spheroidal coordinates comprising a longitudinal angular coordinate μ, a circumferential angular coordinate θ, and the coordinate λ as a function of longitudinal angular coordinate μ and circumferential angular coordinate θ.

26. The method of claim 24 , wherein the multiple times over the heartbeat comprise end diastole of the heartbeat, wherein generating a three-dimensional representation of the endocardial surface of the left ventricle comprises generating a three-dimensional representation at end diastole and two or more additional times over the heartbeat, such that λ ED represents the value of coordinate λ at end diastole and λ MIN represents the minimum value of coordinate λ over the heartbeat, and wherein the measure comprises four-dimensional fractional shortening (“4DFS”) of the left ventricle computed as 4DFS=(λ ED −λ MIN )/λ ED .