Method and device for determining and presenting surface charge and dipole densities on cardiac walls
The invention discloses a method, a system, a computer program and a device for determining the surface charge and/or dipole densities on heart walls. Using the foregoing, a table of dipole densities ν(P′, t) and/or a table of surface charge densities ρ(P′, t) of a given heart chamber can be generated.
1. A method for generating a map of charge densities across an endocardium of a heart chamber, the method comprising:
(i) recording a first set of electric potentials by at least one electrode in contact with a surface of the heart;
(ii) recording a second set of electric potentials by at least one electrode not in contact with a surface of the heart;
(iii) transforming the first and second sets of electric potentials into a continuum of cellular membrane dipole density data and/or surface charge data using a special purpose computer; and
(iv) generating a display of the continuum.
2. The method of claim 1 , including performing the recording in step (i) using a plurality of electrodes that includes electrodes arranged in an ellipsoidal geometry.
3. The method of claim 1 , including performing the recording in step (i) using a plurality of electrodes that includes electrodes arranged in a spherical geometry.
4. The method of claim 1 , including performing the recording in step (ii) using one or more skin electrodes on a thorax.
5. The method of claim 1 , including performing step (iii) using a processor executing a set of transformation instructions stored in a computer memory.
6. The method of claim 5 , wherein the transformation instructions include rules to employ a boundary element method (BEM) in transforming the electric potential data into cellular membrane dipole density in step (iii).
7. The method of claim 6 , including employing the BEM for performing a discretisation of the endocardium.
8. The method of claim 6 , wherein the transformation instructions implement rules for transforming measured potentials V e from the first and/or second sets of electric potentials into surface charge densities ρ according to the following equation:
V
e
(
P
)
=
-
1
4
π
∫
S
e
ρ
(
P
′
)
P
′
-
P
d
σ
(
P
′
)
wherein:
Se=surface of endocardium;
P′=integration variable running over an entire cardiac wall; and
P=Position of the at least one electrode in contact with a surface of the heart or the at least one electrode not in contact with a surface of the heart.
9. The method of claim 6 , wherein the transformation instructions implement rules for transforming measured potentials V e from the first and/or second sets of electric potentials into dipole densities ν according to the following equation:
V
e
(
P
)
=
1
4
π
∫
S
e
υ
(
P
′
)
∂
∂
n
P
′
1
P
-
P
′
d
σ
(
P
′
)
wherein:
Se=surface of endocardium;
P′=integration variable running over an entire cardiac wall; and
P=Position of the at least one electrode in contact with a surface of the heart or the at least one electrode not in contact with a surface of the heart.
10. The method of claim 1 , including performing step (iv) using a processor executing a set of map generation instructions stored in a computer memory.
11. The method of claim 1 , wherein generating the display of the continuum in step (iv) includes generating a graphical representation of the cellular membrane dipole density data and/or surface charge data in association with a graphical representation of the heart.
12. The method of claim 1 , wherein generating a display of the continuum in step (iv) includes generating a display of a map of dipole densities and/or surface charge densities as a 2-dimensional image.
13. The method of claim 1 , wherein generating a display of the continuum in step (iv) includes generating a display of a map of dipole densities and/or surface charge densities as a 3-dimensional image.
14. The method of claim 1 , wherein generating a display of the continuum in step (iv) includes generating a display of a map of dipole densities and/or surface charge densities as a time-dependent sequence of images.
15. The method of claim 1 , wherein the continuum is a continuum of cellular membrane dipole density data.
16. The method of claim 1 , wherein the continuum is a continuum of cellular membrane surface charge data.
17. The method of claim 1 , wherein transforming the first and second sets of electric potentials into the continuum of cellular membrane dipole density data and/or surface charge density data in step (iii) and generating a display of the continuum in step (iv) includes determining cellular membrane dipole density data and/or surface charge density data at a set of positions P′ as a 3-dimensional image, a 2-dimensional image, or a time-dependent sequence of images, or a combination of one or more thereof.
18. The method of claim 1 , wherein the recording in steps (i) and step (ii) includes sequentially contact and non-contact by the at least one electrode in contact with a surface of the heart and the at least one electrode not in contact with a surface of the heart.
19. The method of claim 1 , wherein the recording in steps (i) and step (ii) includes simultaneous contact and non-contact by the at least one electrode in contact with a surface of the heart and the at least one electrode not in contact with a surface of the heart.
20. The method of claim 1 , including performing steps (i) and (ii) with a probe system for recording the first and second sets of electric potentials at given positions P on a cellular membrane of an endocardial wall in a heart chamber to produce the first and second sets of electric potentials.