Device and method for the geometric determination of electrical dipole densities on the cardiac wall
Disclosed are devices, a systems, and methods for determining the dipole densities on heart walls. In particular, a triangularization of the heart wall is performed in which the dipole density of each of multiple regions correlate to the potential measured at various locations within the associated chamber of the heart.
1. A method of generating a database of dipole densities d(y) at the surface of one or more cardiac chambers of a patient, comprising:
inserting an electrode array including multiple electrodes into a cardiac chamber of a patient;
placing at least one skin electrode onto the patient;
recording mapping information from the electrode array and the at least one skin electrode;
creating a database of dipole densities d(y) at the surface of the cardiac chamber based on mapping information and a geometrical depiction of the cardiac chamber, wherein creating the database of dipole densities d(y) includes determining a dipole density for individual triangle-shaped projections onto the cardiac chamber wall; and
choosing a number of triangle-shaped projections so that the dipole density d(y) of each triangle-shaped projection is substantially constant.
2. The method according to claim 1 , wherein each triangle-shaped projection at a location y contributes {acute over (ω)}(x,y) times the dipole density d(y) to a potential V(x) at a point x, wherein {acute over (ω)}(x,y) is the solid angle for that triangle projection, and where:
a) x represents a series of locations within one or more cardiac chambers; and
b) V(x) is a measured potential at point x, said measured potential recorded by the multiple electrodes.
3. The method according to claim 1 , wherein electrode array includes a three-dimensional array of electrodes.
4. The method according to claim 1 , wherein generating the database d(y) of dipole densities includes mapping the dipole densities d(y) to the one or more surfaces of the one or more cardiac chambers.
5. The method according to claim 4 , further comprising creating maps of the dipole densities d(y) at different time intervals.
6. The method according to claim 5 , further comprising synthesizing the maps of dipole densities d(y) at different time intervals to create an activation sequence of cardiac activity over a plurality of time intervals.
7. The method according to claim 1 , further comprising:
updating the database of dipole densities d(y) at a plurality of time intervals during the cardiac activity.
8. The method according to claim 7 , wherein the plurality of time intervals includes at least one time interval per cardiac cycle.
9. The method according to claim 7 , wherein the plurality of time intervals includes a plurality of time intervals per cardiac cycle.
10. The method according to claim 7 , wherein the plurality of time intervals includes a time interval of about a millisecond.
11. The method according to claim 1 , wherein the multiple electrodes of the electrode array are included in a single catheter.
12. The method according to claim 1 , wherein the multiple electrodes of the electrode array are included in two or more catheters.
13. The method according to claim 1 , further comprising:
generating a computer display of dipole density information based on the database of dipole densities d(y); and
updating the computer display of the dipole information based on updating the database of dipole densities d(y).
14. The method according to claim 1 , wherein the database of dipole densities d(y) represents a distribution and activity of dipole charge densities on one or more cardiac walls.
15. The method according to claim 1 , wherein the mapping information recorded from the at least one skin electrode is used to recalculate the database of dipole densities.
16. The method according to claim 1 , wherein the at least one skin electrode comprises more than one skin electrode.
17. The method according to claim 1 , wherein the at least one skin electrode is placed on the thorax.
18. A method of generating a database of dipole densities d(y) at the surface of one or more cardiac chambers of a patient, comprising:
inserting an electrode array including multiple electrodes into a cardiac chamber of a patient;
placing at least one skin electrode onto the patient;
recording mapping information from the electrode array and the at least one skin electrode; and
creating a database of dipole densities d(y) at the surface of the cardiac chamber based on mapping information and a geometrical depiction of the cardiac chamber, wherein creating the database of dipole densities d(y) includes determining a dipole density for individual triangle-shaped projections onto the cardiac chamber wall, and wherein the number of triangle-shaped projections is at least 1,000.
19. A method of generating a database of dipole densities d(y) at the surface of one or more cardiac chambers of a patient, comprising:
inserting an electrode array including multiple electrodes into a cardiac chamber of a patient;
placing at least one skin electrode onto the patient;
recording mapping information from the electrode array and the at least one skin electrode;
creating a database of dipole densities d(y) at the surface of the cardiac chamber based on mapping information and a geometrical depiction of the cardiac chamber; and
one or more computer processors calculating and/or recalculating the dipole densities d(y) using the following equations:
W
k
=
∑
l
=
1
L
A
kl
V
l
.
(
1
)
wherein a small sinusoidal voltage V l is applied to each electrode l=1, . . . L on the electrode array in the heart, and the resulting voltages W k , k=1, . . . K is measured at the surface electrodes, which yields the K×L transition matrix A kl ;
V
l
=
∑
n
=
1
N
B
ln
d
n
.
(
2
)
wherein calculating solid angles produces the linear transformation B ln between the electrode array potentials V l and the dipole densities d n , n=1, . . . N of N regions of the cardiac chamber wall; and
W
k
=
∑
l
=
1
L
∑
n
=
1
N
A
kl
B
ln
d
n
.
(
3
)
where equation (2) above is substituted into equation (1) to form equation (3).
20. The method according to claim 19 , further comprising the one or more computer processors solving equations (2) and (3) using regularization techniques.
21. The method according to claim 20 , wherein the regularization technique is Tikhonov regularization.