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 cardiac mapping system, comprising:
a plurality of electrodes configured to sense and/or record electrical activity of at least one heart chamber, including:
a first set of electrodes configured to record a first set of electric potentials when in contact with a surface of the at least one heart chamber; and
a second set of electrodes configured to record a second set of electric potentials when not in contact with a surface of the at least one heart chamber; and
at least one processor configured to:
transform the first and second sets of electric potentials into a continuum of cellular membrane dipole density data and/or surface charge data, and
generate information to display the continuum as a map of charge densities across an endocardium of the at least one heart chamber.
2. The system of claim 1 , wherein the first set of electrodes includes a plurality of electrodes arranged in an ellipsoidal geometry.
3. The system of claim 1 , wherein the first set of electrodes includes a plurality of electrodes arranged in a spherical geometry.
4. The system of claim 1 , wherein the second set of electrodes includes one or more electrodes adapted to be placed on a skin surface of a thorax.
5. The system of claim 1 , wherein the at least one processor is further configured to execute a set of transformation instructions stored in a computer memory.
6. The system of claim 5 , wherein the transformation instructions include rules to employ a boundary element method (BEM) to transform the first and second sets of electric potentials into cellular membrane dipole density data.
7. The system of claim 6 , wherein the at least one processor employs the BEM to perform a discretisation of the endocardium.
8. The system of claim 6 , wherein the at least one processor employs the transformation instructions to implement rules that transform 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 system of claim 6 , wherein the at least one processor employs the transformation instructions to implement rules that transform 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 system of claim 1 , wherein the at least one processor is configured to execute a set of map generation instructions stored in a computer memory.
11. The system of claim 1 , wherein the processor is configured to drive at least one display to render 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 system of claim 1 , wherein the processor is configured to drive at least one display to render a map of dipole densities and/or surface charge densities as a 2-dimensional image.
13. The system of claim 1 , wherein the processor is configured to drive at least one display to render a map of dipole densities and/or surface charge densities as a 3-dimensional image.
14. The system of claim 1 , wherein the processor is configured to drive at least one display to render a map of dipole densities and/or surface charge densities as a time-dependent sequence of images.
15. The system of claim 1 , wherein the continuum is a continuum of cellular membrane dipole density data.
16. The system of claim 1 , wherein the continuum is a continuum of cellular membrane surface charge data.
17. The system of claim 1 , wherein the at least one processor is configured to determine the continuum of 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 system of claim 1 , wherein the first set of electrodes and the second set of electrodes are configured to sequentially record their respective potentials.
19. The system of claim 1 , wherein the first set of electrodes and the second set of electrodes are configured to simultaneously record their respective potentials.
20. The system of claim 1 , further comprising:
a probe system configured to record the first and second sets of electric potentials at given positions P on a cellular membrane of the endocardium of the at least one heart chamber.