Catheter localization system

1. A method for localizing a catheter, the method comprising:

providing a catheter electrode, C, and a plurality of reference electrodes, R 1 , R 2 , R 3 , and R 4 ;

determining distance values between R 1 and C, R 2 and C, R 1 and R 2 , R 3 and C, R 4 and C, and R 3 and R 4 ;

identifying first and second triangles based on the distance values between (1) R 1 and C, R 2 and C, R 1 and R 2 , and (2) R 3 and C, R 4 and C, and R 3 and R 4 , respectively;

determining first and second orthogonal distances within the first and second triangles, respectively;

identifying a first circle having a radius equal to the first orthogonal distance and a second circle having a radius equal to the second orthogonal distance;

determining a position of the catheter electrode where the first and second circles substantially coincide or are within a minimum distance between the first and second circles;

applying a transformation to the first and second circles to express the first and second circles in a global coordinate system; and

displaying an image as a function of the position of the catheter electrode.

2. The method of claim 1 , wherein the transformation is an Euler transformation.

3. The method of claim 1 , wherein determining the distance values includes determining the distance values based on an impedance or voltage potential.

4. The method of claim 1 , further comprising:

translating origins of the first and second circles to the position of the catheter electrode before applying the transformation.

5. The method of claim 1 , further comprising:

repositioning the first and second circles, after applying the transformation; and

solving for a global coordinate value of the catheter electrode based on where the first and second circles substantially coincide or the minimum distance between the first and second circles.

6. The method of claim 1 , further comprising:

registering the plurality of reference electrodes in the global coordinate system.

7. A system for localizing a catheter, the system comprising:

an electrode, C, on a catheter;

a plurality of reference electrodes, comprising at least reference electrodes R 1 , R 2 , R 3 , and R 4 , each reference electrode of the plurality of reference electrodes configured to transmit or receive a signal to or from the electrode, respectively; and

a processor operable to determine distance values between R 1 and C, R 2 and C, R 1 and R 2 , R 3 and C, R 4 and C, and R 3 and R 4 , and determine a position of the electrode by identifying first and second circles based on the distance values and applying a transformation to the first and second circles to express the first and second circles in a global coordinate system,

wherein the electrode is located at a position where the first and second circles substantially coincide or within a minimum distance between the first and second circles, and

wherein identifying the first and second circles comprises determining first and second orthogonal distances within first and second triangles, respectively, dimensions of the first and second triangles being associated with the distance values between (1) R 1 and C, R 2 and C, R 1 and R 2 , and (2) R 3 and C, R 4 and C, and R 3 and R 4 , and the first and second orthogonal distances being the radius for the first and second circles, respectively.

8. The system of claim 7 , wherein the transformation is an Euler transformation.

9. The system of claim 7 , wherein the plurality of reference electrodes further comprises reference electrodes R 5 , R 6 , R 7 , and R 8 , and wherein the plurality of reference electrodes comprises six reference electrodes positioned on a body surface and two reference catheter electrodes.

10. The system of claim 7 , wherein the processor is operable to determine the distance values based on an electrical characteristic associated with the respective signal.

11. The system of claim 10 , wherein the electrical characteristic comprises an impedance or voltage potential.

12. The system of claim 7 , wherein the processor is further operable to determine the position of the electrode of the catheter by translating origins of the first and second circles to the position of the electrode of the catheter before the transformation.

13. The system of claim 7 , wherein the processor is further operable to determine, after applying the transformation, the position of the electrode of the catheter by repositioning the first and second circles and solving for a global coordinate value of the electrode of the catheter.

14. In a computer-readable medium having stored therein instructions executable by a processor, the instructions comprising:

providing a catheter electrode, C, and a plurality of reference electrodes, R 1 , R 2 , R 3 , and R 4 ;

determining distance values between R 1 and C, R 2 and C, R 1 and R 2 , R 3 and C, R 4 and C, and R 3 and R 4 ;

identifying first and second triangles based on the distance values between (1) R 1 and C, R 2 and C, R 1 and R 2 , and (2) R 3 and C, R 4 and C, and R 3 and R 4 , respectively;

determining first and second orthogonal distances within the first and second triangles, respectively;

determining first and second circles based on the first and second orthogonal distances, respectively;

determining a position of the catheter electrode where the first and second circles are the closest; and

applying a transformation to the first and second circles, the transformed first and second circles being in a global coordinate system.

15. The instructions of claim 14 , wherein the transformation is an Euler transformation.

16. The instructions of claim 14 , further comprising:

translating origins of the first and second circles to the position of the catheter electrode before the transformation.

17. The instructions of claim 14 , further comprising:

repositioning the first and second circles, after the transformation; and

solving for a global coordinate value of the catheter electrode based on where the first and second circles are the closest.

18. The system of claim 7 , further comprising:

a catheter generator configured to generate a first signal having a first signal frequency and transmit the first signal from the electrode on the catheter;

a reference generator configured to generate a second signal having a second signal frequency and to transmit the second signal from a first reference electrode of the plurality of reference electrodes,

wherein the second signal frequency is substantially similar to the first signal frequency but is phase shifted relative to the first signal, such that a current is created between the electrode on the catheter and the first reference electrode.

19. The system of claim 18 , wherein the processor is operable to determine the distance values based on a voltage potential difference, created by the current, measured between the electrode on the catheter and the first reference electrode.

20. The instructions of claim 14 , wherein determining the first orthogonal distance comprises determining a first shortest distance, r 1 , between a point between R 1 and R 2 , and the catheter electrode; and

wherein determining the second orthogonal distance comprises determining a second shortest distance, r 2 , between a point between R 3 and R 4 , and the catheter electrode.

21. The method of claim 1 , wherein R 2 and R 4 represent a same reference electrode.

22. The system of claim 7 , wherein R 2 and R 4 represent a same reference electrode.

23. The instructions of claim 14 , wherein R 2 and R 4 represent a same reference electrode.