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 database table of surface charge densities ρ(P′,t) that embody an ionic nature of cellular membranes across a cardiac wall of at least one given heart chamber, the cellular membrane surface charge density information comprising a table ρ(P′, t) wherein:
i) a position P′=(x′,y′,z′) of a point on the cellular membrane of the cardiac wall of a heart chamber is defined in x, y, z-coordinates,
ii) t is a time of measurement for said cellular membrane surface charge density, and
iii) ρ is the cellular membrane surface charge density at said time t and said position P′ derived from a measured electric potential,
the method comprising the following steps:
a) determining electric potential data V e at locations P at a given time t using a plurality of electrodes,
b) transforming the electric potential data V e into said cellular membrane surface charge density ρ(P′,t) at positions P′ on the cardiac wall using a processor executing a set of conversion instructions stored in a computer memory, and
c) storing each cellular membrane surface charge density in the computer memory as a table of cellular membrane surface charge densities,
wherein transforming the electric potential data V e into the cellular membrane surface charge density (ρ) in step b) employs a boundary element method (BEM).
2. The method according to claim 1 , where the electrical potential data V e is determined by contact mapping.
3. The method according to claim 1 , where the electrical potential data V e is determined by non-contact mapping.
4. The method according to claim 1 , where a geometry of the plurality of electrodes used in determining the electrical potential data V e is ellipsoidal.
5. The method according to claim 1 , where a geometry of the plurality of electrodes used in determining the electrical potential data V e is spherical.
6. The method according to claim 1 , wherein said electric potential data V e is transformed into the cellular membrane surface charge densities ρ using the following equation:
V
e
(
P
)
=
-
1
4
π
∫
S
e
ρ
(
P
′
)
P
′
-
P
ⅆ
σ
(
P
′
)
Wherein:
S e =surface of the cardiac wall;
P′=integration variable running over the entire cardiac wall; and
P=position of the measuring electrode.
7. A method for generating a database table of dipole densities ν(P′,t) that embody an ionic nature of cellular membranes across a cardiac wall of at least one given heart chamber, the cellular membrane dipole density information comprising a table ν(P′, t) wherein:
i) a position P′=(x′,y′,z′) of a point on the cellular membrane of the cardiac wall of a heart chamber is defined in x, y, z-coordinates,
ii) t is a time of measurement for said cellular membrane dipole density, and
iii) ν is the cellular membrane dipole density at said time t and said position P′ derived from a measured electric potential,
the method comprising the following steps:
a) determining electric potential data V e at locations P at a given time t using a plurality of electrodes;
b) transforming the electric potential data V e into said cellular membrane dipole density ν(P′,t) at positions P′ on the cardiac wall using a processor executing a set of conversion instructions stored in a computer memory; and
c) storing each cellular membrane dipole density in the computer memory as a table of cellular membrane dipole densities,
wherein transforming the electric potential data V e into the cellular membrane dipole density (ν) in step b) employs a boundary element method (BEM).
8. The method according to claim 7 , wherein the electrical potential data V e is determined by contact mapping.
9. The method according to claim 7 , wherein the electrical potential data V e is determined by non-contact mapping.
10. The method according to claim 7 , wherein a geometry of the plurality of electrodes used in determining the electrical potential data V e is ellipsoidal.
11. The method according to claim 7 , wherein a geometry of the plurality of electrodes used in determining the electrical potential data V e is spherical.
12. The method according to claim 7 , wherein said electric potential data V e is transformed into the cellular membrane dipole densities ν using the following equation:
V
e
(
P
)
=
1
4
π
∫
S
e
υ
(
P
′
)
∂
∂
n
P
′
1
P
-
P
′
ⅆ
σ
(
P
′
)
Wherein:
S e =surface of the cardiac wall,
P′=integration variable running over the entire cardiac wall, and
P=position of the measuring electrode.
13. A system that generates a table of surface charge densities ρ(P′,t) that embody an ionic nature of cellular membranes across a cardiac wall of a given heart chamber, comprising:
a) a measuring and recording unit that measures and records electrical potential data V e at given positions P;
b) an a/d-converter that converts the electrical potential data V e into digital voltage data;
c) processor that transforms the digital voltage data into digital cellular membrane surface charge density data; and
d) a memory that stores the electrical potential data V e and the transformed digital cellular membrane surface charge density data.
14. The system of claim 13 , wherein the measuring and recording unit comprises electrodes configured to measure the electrical potential data V e when brought into contact with at least one part of the heart chamber.
15. The system of claim 13 , wherein the measuring and recording unit comprises electrodes configured to measure the electric potential data V e when not in contact with at least one part of the heart chamber.
16. The system of claim 13 , further comprising:
an imaging unit that represents the cellular membrane surface charge densities ρ(P′,t) as a 2-dimensional image or time-dependent sequence of images.
17. The system of claim 13 , further comprising:
an imaging unit that represents the cellular membrane surface charge densities ρ(P′,t) as a 3-dimensional image or time-dependent sequence of images.
18. A system that generates a table of dipole densities ν(P′,t) that embody an ionic nature of cellular membranes across a cardiac wall of a given heart chamber, comprising:
a) a measuring and recording unit that measures and records electrical potential data V e at given positions P;
b) an a/d-converter that converts the electrical potential data V e into digital voltage data;
c) processor that transforms the digital voltage data into digital cellular membrane dipole density data; and
d) a memory that stores the electrical potential data V e and the transformed digital cellular membrane dipole density data.
19. The system of claim 18 , wherein the measuring and recording unit comprises electrodes configured to measure the electrical potential data V e when brought into contact with at least one part of the heart chamber.
20. The system of claim 18 , wherein the measuring and recording unit comprises electrodes configured to measure the electric potential data V e when not in contact with at least one part of the heart chamber.
21. The system of claim 18 , further comprising:
an imaging unit that represents the cellular membrane dipole densities ν(P′,t) as a 2-dimensional image or time-dependent sequence of images.
22. The system of claim 13 , further comprising:
an imaging unit that represents the cellular membrane dipole densities ν(P′,t) as a 3-dimensional image or time-dependent sequence of images.