Graphically mapping rotors in a heart using Shannon entropy

1. A method for graphically indicating pivot points of rotors associated with atrial or ventricular fibrillation, comprising:

receiving, using a processor, an electrogram for each of a plurality of spatial locations in a heart, each electrogram comprising time series data including a plurality of electrical potential readings over time;

generating, from the time series data, an entropy dataset including a plurality of Shannon entropy values corresponding to the plurality of spatial locations in the heart; and

generating, from the entropy dataset, an entropy map including a plurality of graphical indications of the Shannon entropy values at the plurality of spatial locations in the heart, wherein the entropy map includes an image of the heart and graphical indications of locations of the pivot points of the rotors in the heart.

2. The method of claim 1 , further comprising physically changing the heart at one or more of the plurality of spatial locations in the heart according to the entropy dataset.

3. The method of claim 2 , wherein the changing of the heart includes catheter ablations at the one or more of the plurality of spatial locations in the heart.

4. The method of claim 1 , further comprising performing the plurality of electrograms at the plurality of spatial locations in the heart to obtain the time series data.

5. The method of claim 1 , further comprising displaying graphical indicators of the plurality of Shannon entropy values corresponding to the plurality of spatial locations in the heart using a display device.

6. The method of claim 5 , wherein the graphical indicators of the plurality of Shannon entropy values include a range of different colors, shades of a gray or another color, different symbols, or indexed values each of the range corresponding to a Shannon entropy value such that the displaying of the graphical indicators of the plurality of Shannon entropy values shows Shannon entropy levels at different locations in the heart.

7. The method of claim 1 , wherein the plurality of electrograms is derived from an optical mapping experiment on the heart.

8. The method of claim of claim 1 , wherein the generating of the entropy dataset includes:

binning the plurality of electrograms according to amplitude, which results in a plurality of bins per binned electrogram, wherein a bin of the plurality of bins represents an amplitude or amplitude range and includes a frequency of occurrences of the amplitude or amplitude range;

determining a probability density of each bin of the plurality of bins, per binned electrogram; and

determining a Shannon entropy value according to the determined probability densities, per binned electrogram,

wherein the determining of the Shannon entropy value includes using the following equation:

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and wherein N is a number of bins in the plurality of bins per binned electrogram, and p i is a probability of a sample reading falling within a particular bin of the plurality of bins.

9. A method for graphically indicating aspects of rotors associated with atrial or ventricular fibrillation, comprising:

receiving, using a processor, an electrogram for each of a plurality of spatial locations in a heart, each electrogram comprising time series data including a plurality of electrical potential readings over time;

binning the plurality of electrograms according to amplitude, which results in a plurality of bins per binned electrogram, wherein a bin of the plurality of bins represents an amplitude or amplitude range and includes a frequency of occurrences of the amplitude or amplitude range;

determining a probability density of each bin of the plurality of bins, per binned electrogram;

determining a Shannon entropy value according to the determined probability densities, per binned electrogram;

generating an entropy dataset including the Shannon entropy values corresponding to the plurality of spatial locations in the heart; and

generating, from the entropy dataset, an entropy map including a plurality of graphical indications of the Shannon entropy values at the plurality of spatial locations in the heart, wherein the entropy map includes an image of the heart and graphical indications of locations of the pivot points of the rotors in the heart.

10. The method of claim 9 , further comprising physically changing the heart at one or more of the plurality of spatial locations in the heart according to the entropy dataset.

11. The method of claim 10 , wherein the changing of the heart includes catheter ablations at the one or more of the plurality of spatial locations in the heart.

12. The method of claim 9 , further comprising performing the plurality of electrograms at the plurality of spatial locations in the heart to obtain the time series data.

13. The method of claim 9 , further comprising displaying graphical indicators of the plurality of Shannon entropy values corresponding to the plurality of spatial locations in the heart using a display device, wherein the graphical indicators of the plurality of Shannon entropy values include a range of different colors, shades of a gray or another color, different symbols, or indexed values, each of the range corresponding to a Shannon entropy value such that the displaying of the graphical indicators of the plurality of Shannon entropy values shows Shannon entropy levels at different locations in the heart.

14. The method of claim 9 , wherein the determining of the Shannon entropy value uses the following equation:

SE

=

-

∑

i

=

0

N

-

1

⁢

p

i

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log

2

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p

i

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wherein N is a number of bins in the plurality of bins per binned electrogram, and p i is a probability of a sample reading falling within a particular bin of the plurality of bins.

15. The method of claim 9 , further comprising:

generating a histogram of the plurality of bins;

communicating the histogram to a display device communicatively coupled to the processor; and

graphically displaying the histogram by the display device.

16. A non-transitory computer readable medium for graphically indicating aspects of rotors associated with atrial or ventricular fibrillation, comprising:

instructions executable by a processor to receive an electrogram for each of a plurality of spatial locations in a heart, each electrogram comprising time series data including a plurality of electrical potential readings over time;

instructions executable by a processor to generate, from the time series data, an entropy dataset including a plurality of Shannon entropy values corresponding to the plurality of spatial locations in the heart; and

instructions executable by a processor to generate, from the entropy dataset, an entropy map including a plurality of graphical indications of the Shannon entropy values at the plurality of spatial locations in the heart, wherein the entropy map includes an image of the heart and graphical indications of locations of the pivot points of the rotors in the heart.

17. The non-transitory computer readable medium of claim 16 , wherein the instructions to generate the entropy dataset include:

instructions executable by a processor to bin the plurality of electrograms according to amplitude, which results in a plurality of bins per binned electrogram, wherein a bin of the plurality of bins represents an amplitude or amplitude range and includes a frequency of occurrences of the amplitude or amplitude range;

instructions executable by a processor to determine a probability density of each bin of the plurality of bins, per binned electrogram; and

instructions executable by a processor to determine a Shannon entropy value according to the determined probability densities, per binned electrogram, and according to the following equation:

SE

=

-

∑

i

=

0

N

-

1

⁢

p

i

⁢

log

2

⁢

p

i

,

wherein N is a number of bins in the plurality of bins per binned electrogram, and p i is a probability of a sample reading falling within a particular bin of the plurality of bins.