Systems, apparatuses and methods for delivery of ablative energy to tissue

1. A system, comprising:

a pulse waveform generator operatively coupled to an ablation device, the pulse waveform generator configured to:

select electrode sets from a plurality of electrodes of the ablation device, each electrode set including a first subset of electrodes configured as one or more anodes and a second subset of electrodes configured as one or more cathodes;

generate voltage pulses in the form of pulsed waveforms, each pulsed waveform including:

(a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses;

(b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and

(c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and

apply the voltage pulses to the electrode sets according to a predefined sequence with at least one pulsed waveform being applied across the first and second subsets of electrodes of each electrode set.

2. The system of claim 1 , wherein the pulse waveform generator is configured to apply the voltage pulses to the electrode sets by applying the pulsed waveforms to successive electrode sets within the predefined sequence offset by a fourth time delay.

3. The system of claim 2 , wherein the fourth time delay is at most about 5 milliseconds.

4. The system of claim 2 , wherein the pulse waveform generator is configured to generate and apply the voltage pulses such that a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of the electrode sets within the predefined sequence, the first time delay, the second time delay, and the fourth time delay are jointly constrained by a Diophantine inequality.

5. The system of claim 1 , wherein the plurality of electrodes is 4 electrodes.

6. The system of claim 1 , wherein the pulse waveform generator is configured to apply the voltage pulses to the electrode sets during refractory periods of cardiac cycles of a heart.

7. The system of claim 1 , wherein each pulse of the first set of pulses is a biphasic pulse with a voltage amplitude of at least 500 Volts and a pulse time duration being in the range from about 0.5 nanosecond to about 20 microseconds.

8. The system of claim 1 , wherein the first time delay is greater than a pulse time duration of each pulse of the first set of pulses.

9. The system of claim 1 , further comprising a cardiac stimulator configured to generate pacing signals for cardiac stimulation of a heart,

the pulse waveform generator further operatively coupled to the cardiac stimulator and configured to apply the voltage pulses to the plurality of electrodes in synchrony with the pacing signals.

10. A system, comprising:

a pulse waveform generator operatively coupled to an ablation device, the pulse waveform generator configured to:

receive a set of parameters for a pulsed waveform;

generate voltage pulses in the form of pulsed waveforms according to the set of parameters, each pulsed waveform including:

(a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses;

(b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and

(c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and

apply the voltage pulses to an ablation device operatively coupled to the pulse waveform generator.

11. The system of claim 10 , wherein the pulse waveform generator is configured to apply the voltage pulses to the ablation device by applying the pulse waveforms over a sequence of electrode sets and with a fourth time delay offsetting application of the pulsed waveforms to successive electrode sets in the sequence.

12. The system of claim 11 , wherein the set of parameters is a first subset of parameters, the pulse waveform generator further configured to:

determine a second subset of parameters for the pulsed waveform such that the first and second subsets of parameters collectively satisfy a Diophantine inequality.

13. The system of claim 12 , wherein the first and second subsets of parameters collectively include: a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of electrode sets within the sequence, the first time delay, the second time delay, and the fourth time delay.

14. The system of claim 13 , wherein the Diophantine inequality is j[m 2 (m 1 w+t 1 (m 1 −1))+t 2 (m 2 −1)]+t d (j−1)<T r , where j is the number of electrode sets within the sequence, m 1 is the number of pulses in each first set of pulses, m 2 is the number first sets of pulses in the plurality of first set of pulses of each second set of pulses, t 1 is the first time delay, t 2 is the second time delay, t d is the fourth time delay, w is a pulse width of each pulse in each first set of pulses, and T r is a time period of a refractory period of a cardiac cycle.

15. The system of claim 12 , wherein the pulse waveform generator is configured to determine the second subset of parameters by:

identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality;

presenting the plurality of second subsets to a user; and

receiving a selection indicative of the second subset from the plurality of second subsets to be used to generate the voltage pulses.

16. The system of claim 12 , wherein the pulse waveform generator is configured to determine the second subset of parameters by:

identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; and

selecting the second subset from the plurality of second subsets to be used to generate the voltage pulses based on a predefined criterion.

17. The system of claim 10 , wherein each pulse of the first set of pulses is a biphasic pulse with a voltage amplitude of at least 500 Volts and a pulse time duration being in the range from about 0.5 nanosecond to about 20 microseconds.

18. The system of claim 10 , wherein the first time delay is greater than a pulse time duration of each pulse of the first set of pulses.

19. A method, comprising:

selecting electrode sets from a plurality of electrodes of an ablation device, each electrode set including a first subset of electrodes configured to be anodes and a second subset of electrodes configured to be cathodes;

generating voltage pulses in the form of pulsed waveforms, each pulsed waveform including:

(a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses;

(b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and

(c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and

applying the voltage pulses to the electrode sets according to a predefined sequence with at least one pulsed waveform being applied across the first and second subsets of electrodes of each electrode set.

20. The method of claim 19 , wherein applying the voltage pulses to the electrode sets includes applying the pulsed waveforms to successive electrode sets within the predefined sequence offset by a fourth time delay.

21. The method of claim 20 , wherein a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of the electrode sets within the predefined sequence, the first time delay, the second time delay, and the fourth time delay are jointly constrained by a Diophantine inequality.

22. The method of claim 19 , wherein applying the voltage pulses to the electrode sets is during refractory periods of cardiac cycles of a heart.

23. The method of claim 19 , wherein applying the voltage pulses to the electrode sets is in synchrony with pacing signals generated by a cardiac stimulator.

24. A method, comprising:

receiving a set of parameters for a pulsed waveform;

generating voltage pulses in the form of pulsed waveforms according to the set of parameters, each pulsed waveform including:

(a) a first level of a hierarchy of the pulsed waveform that includes a first set of pulses and a first time delay separating successive pulses of the first set of pulses;

(b) a second level of the hierarchy of the pulsed waveform that includes a plurality of first sets of pulses as a second set of pulses and a second time delay separating successive first sets of pulses, the second time delay being at least three times the duration of the first time delay; and

(c) a third level of the hierarchy of the pulsed waveform that includes a plurality of second sets of pulses as a third set of pulses and a third time delay separating successive second sets of pulses, the third time delay being at least thirty times the duration of the second level time delay; and

applying the voltage pulses to an ablation device.

25. The method of claim 24 , wherein applying the voltage pulses to the ablation device includes applying the pulse waveforms over a sequence of electrode sets and with a fourth time delay offsetting application of the pulsed waveforms to successive electrode sets in the sequence.

26. The method of claim 24 , wherein the set of parameters is a first subset of parameters, the method further comprising

determining a second subset of parameters for the pulsed waveform such that the first and second subsets of parameters collectively satisfy a Diophantine inequality.

27. The method of claim 26 , wherein the first and second subsets of parameters collectively include: a number of pulses in each first set of pulses, a number of first sets of pulses in the plurality of first sets of pulses of each second set of pulses, a number of electrode sets within the sequence, the first time delay, the second time delay, and the fourth time delay.

28. The method of claim 27 , wherein the Diophantine inequality is j[m 2 (m 1 w+t 1 (m 1 −1))+t 2 (m 2 −1)]+t d (j−1)<T r , where j is the number of electrode sets within the sequence, m 1 is the number of pulses in each first set of pulses, m 2 is the number first sets of pulses in the plurality of first set of pulses of each second set of pulses, t 1 is the first time delay, t 2 is the second time delay, t d is the fourth time delay, w is a pulse width of each pulse in each first set of pulses, and T r is a time period of a refractory period of a cardiac cycle.

29. The method of claim 26 , wherein determining the second subset of parameters includes:

identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality;

presenting the plurality of second subsets to a user; and

receiving a selection indicative of the second subset from the plurality of second subsets to be used to generate the voltage pulses.

30. The method of claim 26 , wherein determining the second subset of parameters includes:

identifying a plurality of second subsets of parameters that each with the first subset of parameters satisfies the Diophantine inequality; and

selecting the second subset from the plurality of second subsets to be used to generate the voltage pulses based on a predefined criterion.