Reducing electrical sensation when treating subject using electric field by gradually increasing amplitude of rotating alternating electric field

Abstract

When an array of transducers (i.e., an array of electrode elements) is used to apply an alternating electric field (e.g., a tumor therapy electric field or TTFields) to the body of a subject, the subject may experience an electrical sensation. When an AC voltage is initially applied to the transducer array, the electrical sensation may be improved by varying the manner in which the voltage increases from zero to its peak.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of U.S. Provisional Application 63 / 456,104, filed March 31, 2023, the entire contents of which are incorporated herein by reference. Background Technology

[0003] Tumor therapeutic electric fields (TTFields) therapy is an effective method for treating tumors using alternating electric fields with frequencies between 50 kHz and 1 MHz (e.g., 150 kHz to 200 kHz). Since the effectiveness of TTFields depends on the orientation of the alternating electric field relative to the longitudinal axis of dividing tumor cells, it is preferable to apply the alternating electric field at different times and in different orientations during the treatment course.

[0004] In existing technology In the system, TTFields are delivered to the patient via four transducer arrays placed on the skin near the tumor. These transducer arrays are arranged in two pairs, with one pair positioned on the left and right sides of the tumor and the other pair positioned on the front and back sides. Each transducer array is connected to an AC signal generator via a multi-wire cable. The AC signal generator (a) delivers AC current for 1 second through the front / back (A / P) transducer array pair, generating an electric field with a first orientation within the tumor; then (b) delivers AC current for 1 second through the left / right (L / R) transducer array pair, generating an electric field with a second orientation within the tumor. The system then repeats steps (a) and (b) throughout the treatment duration, causing the orientation of the electric field to switch repeatedly.

[0005] U.S. Patent 7,565,206 (the entire contents of which are incorporated herein by reference) describes another method for altering the orientation of an alternating electric field. More specifically, when a first sine wave is applied to the pair of A / P transducer arrays and a second sine wave of the same frequency is applied to the L / R transducer arrays, and when the first and second sine waves are 90° out of phase with each other, the orientation of the electric field will rotate continuously 360° during the treatment.

[0006] Alternating electric fields can also be used to treat medical conditions other than cancer. For example, as described in U.S. Patent No. 10,967,167 (the entire contents of which are incorporated herein by reference), alternating electric fields can be used to increase the permeability of the blood-brain barrier, allowing, for example, chemotherapy drugs to reach the brain.

[0007] When subjects are treated with alternating electric fields, higher amplitude is closely associated with higher therapeutic efficacy. However, as the amplitude of the alternating electric field increases, and / or as the frequency of the alternating electric field decreases (e.g., to around 100 kHz), some subjects experience electrosensory effects. These electrosensory effects may include, for example, vibrational sensations, paresthesia, and / or twitching or contraction of muscle fibers, or flashes of light in the eyes (photophanosis). Electrosensory effects may prevent some subjects from continuing their treatment with alternating electric fields. Furthermore, electrosensory effects may limit the amplitude of the alternating electric field that can be comfortably applied to a given subject, which may in turn limit therapeutic efficacy. Summary of the Invention

[0008] One aspect of the invention relates to a first method for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body. The first method includes applying an AC electric field to the target region, the AC electric field having an electric field orientation that rotates relative to the target region. The electric field has a frequency between 50 kHz and 1 MHz and an amplitude that increases from an initial level to a final level over a period of at least 0.1 s.

[0009] In some instances of the first method, when the amplitude of the electric field is at the final level, the electric field has an electric field strength of at least 1 V / cm in at least a portion of the target region. In some instances of the first method, the electric field is applied to the target region via an insulating electrode. In some instances of the first method, the electric field has an amplitude that increases from the initial level to the final level over a period of at least 0.3 s.

[0010] In some instances, the electric field in at least a portion of the target region is generated by an applied voltage, and the applied voltage is at least 50 V RMS when the magnitude of the electric field is at the final level, and optionally the applied voltage is at least 100 V RMS.

[0011] In some instances of the first method, the electric field has an amplitude that increases from the initial level to the final level over a period of at least 1 second. Optionally, in these instances, when the amplitude of the electric field is at the final level, the electric field has an electric field strength of at least 5 V / cm in at least a portion of the target region.

[0012] In some instances of this first method, the electric field has an amplitude that increases from the initial level to the final level over a period of at least 0.3 seconds. When the amplitude of the electric field is at the final level, the electric field has an electric field strength of at least 5 V / cm in at least a portion of the target region. The frequency of the electric field is between 80 kHz and 300 kHz.

[0013] In some instances of the first method, the frequency of the electric field is between 80 kHz and 300 kHz. In some instances of the first method, the electric field has an amplitude that remains at the final level for at least 100 seconds. In some instances of the first method, the rotation of the AC electric field is accomplished by simultaneously applying AC voltages with different phases to at least three electrodes. In some instances of the first method, the increase in amplitude from the initial level to the final level is linear.

[0014] Another aspect of the invention relates to a first device for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body. The first device includes: at least three electrodes, each having a surface configured to rest against the subject's body; and an AC voltage source having at least three output terminals, each electrically connected to a corresponding electrode. Each of the at least three output terminals has a frequency between 50 kHz and 1 MHz, and each of the at least three output terminals has an amplitude that increases from an initial level to a final level of at least 50 VRMS over a period of at least 0.1 s.

[0015] In some embodiments of the first device, each of the at least three output terminals has an amplitude that remains at the final level for at least 30 seconds. In some embodiments of the first device, each of the at least three electrodes includes a conductive substrate, and each of the surfaces configured to rest against the subject's body includes an insulating material having a dielectric constant of at least 20, the insulating material being disposed on the respective conductive substrate.

[0016] In some embodiments of the first device, each of the at least three output terminals has an amplitude that increases from the initial level to the final level over a period of at least 0.3 seconds, and the final level is at least 100V RMS.

[0017] In some embodiments of the first device, each of the at least three output terminals has an amplitude that increases from the initial level to the final level over a period of at least 1 second, and the final level is at least 100V RMS. Optionally, in these embodiments, each of the at least three output terminals has a frequency between 80kHz and 300kHz.

[0018] In some embodiments of the first device, each of the at least three output terminals has a frequency between 80 kHz and 300 kHz. In some embodiments of the first device, each of the at least three output terminals has an amplitude that remains at the final level for at least 100 seconds.

[0019] In some embodiments of the first device, the AC voltage source has a first output terminal at a given frequency, a second output terminal at the given frequency offset by 120° relative to the first output terminal, and a third output terminal at the given frequency offset by 240° relative to the first output terminal. In some embodiments of the first device, the AC voltage source has a first output terminal at a given frequency, a second output terminal at the given frequency offset by 90° relative to the first output terminal, a third output terminal at the given frequency offset by 180° relative to the first output terminal, and a fourth output terminal at the given frequency offset by 270° relative to the first output terminal.

[0020] In some embodiments of the first device, the AC voltage source simultaneously applies a sinusoidal signal at a first frequency to each of the at least three output terminals, wherein the signal applied to each of the at least three output terminals is modulated by a sinusoidal wave at a second frequency at least ten times lower than the first frequency, and the modulated sine wave exhibits a phase shift. In some embodiments of the first device, the increase in amplitude from the initial level to the final level is linear.

[0021] In another aspect of the invention, an AC electric field is provided for use in a method of selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body. The electric field is oriented and rotated relative to the target region. The electric field has a frequency between 50 kHz and 1 MHz. The electric field has an amplitude that increases from an initial level to a final level over a process of at least 0.1 s.

[0022] In another aspect of the invention, an AC electric field is provided for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body. The AC electric field has an electric field orientation that rotates relative to the target region. The electric field has a frequency between 50 kHz and 1 MHz. The electric field has an amplitude that increases from an initial level to a final level over a period of at least 0.1 s. Attached Figure Description

[0023] Figure 1 This is a block diagram of a system for applying TTFields to target areas in a subject's body.

[0024] Figure 2 Examples of amplitude trajectories that may induce a noticeable electrosensory sensation are depicted.

[0025] Figure 3 An example of an amplitude trajectory that can be used to improve electrosensory perception is depicted.

[0026] Figure 4 Another example of an amplitude trajectory that can be used to improve electrosensory perception is depicted.

[0027] Figure 5 Four examples of nonlinear amplitude-increasing trajectories that can be used to improve electrosensitivity are depicted.

[0028] Figure 6 This is a block diagram of another system for applying TTFields to target areas in a subject's body.

[0029] Various embodiments are described in detail below with reference to the accompanying drawings, wherein the same reference numerals denote the same elements. Detailed Implementation

[0030] Figure 1 This is a block diagram of a system for applying TTFields to a target area in a subject's body. The system includes an AC signal generator 20, which is designed to generate a first AC output and a second AC output at frequencies between 50 kHz and 10 MHz (e.g., 50 kHz to 1 MHz, 50 kHz to 500 kHz, 80 kHz to 300 kHz, or 150 kHz to 250 kHz). The AC signal generator 20 applies a first sine wave to a pair of A / P electrode elements 10A / 10P and also applies a second sine wave at the same frequency to L / R electrode elements 10L / 10R. The surface of each of these electrode elements is configured to rest against the subject's body. Applying an AC voltage to the electrode elements 10A / 10P / 10L / 10R will create an alternating electric field in the target area. When the electrode elements 10A / 10L / 10P / 10R are positioned around the target body part at 90° intervals and the first and second sine waves are 90° out of phase with each other, the orientation of the electric field in the target area will continuously and repeatedly rotate 360° during the treatment.

[0031] Because the first sine wave is applied between the 10A and 10P output terminals, the signal at 10P will be 180° out of phase with the signal at 10A. Similarly, because the second sine wave is applied between the 10L and 10R output terminals, the signal at 10L will be 180° out of phase with the signal at 10R. Furthermore, because the second sine wave is 90° out of phase with the first sine wave, the signal at 10L will be 90° out of phase with the signal at 10A, and the signal at 10R will be 270° out of phase with the signal at 10A.

[0032] In some embodiments, each of the electrode elements includes a conductive substrate, and each of the surfaces configured to rest against the subject's body includes an insulating material having a dielectric constant of at least 20, the insulating material being disposed on the respective conductive substrate.

[0033] Electrosensory sensation is thought to originate from the interaction between an alternating electric field and nerve cells or fibers (i.e., neurons or axons) located near or adjacent to the electrode elements. The inventors have determined that electrosensory sensation is not a problem during the application of a steady-state AC voltage to a given pair of electrode elements, or when the AC voltage is off or decreasing. Instead, electrosensory sensation appears to be a problem only when the AC voltage is on or rising. The inventors have also determined that when the AC voltage is on, electrosensory sensation depends largely on the trajectory of how the AC voltage increases from zero to its peak value.

[0034] More specifically, if the amplitude of the AC voltage applied to the subject's body when the system is turned on at t=0 is as follows: Figure 2 If the voltage applied to the subject's body rises immediately from zero to its peak level, the electrosensory sensation may be very noticeable. However, if the amplitude of the AC voltage is increased more slowly to its peak level, the electrosensory sensation may not occur (or at least will be significantly reduced).

[0035] The embodiments described herein utilize this phenomenon to avoid Figure 2 The system is configured to eliminate or reduce the electrosensory sensation, as described, so that the amplitude of the AC voltage applied to the subject's body does not rise too rapidly. More specifically, Figure 1 The trajectory of how the AC voltage increases from zero to its peak value in the embodiment is similar to... Figure 2 The different instantaneous activation trajectories depicted prevent electrosensory sensation or at least reduce its degree.

[0036] AC signal generator 20 is configured to generate two out-of-phase sinusoidal outputs, each having an amplitude that depends on the state of at least one control input. Controller 30 transmits sequential control signals to at least one control input, and these control signals cause AC signal generator 20 to adjust its output amplitude accordingly. Therefore, the combination of controller 30 and AC generator 20 can be used to generate any amplitude trajectory described herein. Note that although... Figure 1 The controller 30 and the AC signal generator 20 are described as two different blocks, but these two blocks can be integrated into a single hardware device.

[0037] Figure 3An example of an amplitude trajectory that can be used to improve electrosensory perception is depicted. In this example, controller 30 transmits a first series of control signals to AC generator 20. This first series of control signals instructs AC generator 20 to linearly increase its output amplitude over a two-second period until a final voltage is reached. In some embodiments, the final voltage is at least 50 VRMS (e.g., at least 100 VRMS or 100 VRMS to 200 V RMS), and this generates an electric field with an electric field strength of at least 1 V / cm (e.g., at least 5 V / cm, 1 V / cm to 10 V / cm, or 5 V / cm to 10 V / cm) in at least a portion of the target area. And because the AC voltage applied to the subject's body in this embodiment rises slowly to its final level, electrosensory perception does not occur (or is at least significantly reduced). After the rise period, the output of AC signal generator 20 remains constant for an extended period of time (e.g., at least 30 s, at least 60 s, at least 100 s, etc.).

[0038] Figure 4 Another example of an amplitude trajectory that can be used to improve electrosensory sensation is depicted. In this example, controller 30 transmits a second series of control signals to AC generator 20. This second series of control signals instructs AC generator 20 to set its output amplitude to a relatively low initial level at t=0, and then to linearly increase its output amplitude over a two-second period until a final voltage is reached. This initial level is selected to be below a threshold that induces electrosensory sensation (e.g., below 20 VRMS). In some embodiments, the final voltage is at least 50 VRMS (e.g., at least 100 VRMS or 100V RMS to 200V RMS), and this generates an electric field with an electric field strength of at least 1V / cm (e.g., at least 5V / cm, 1V / cm to 10V / cm, or 5V / cm to 10V / cm) in at least a portion of the target area. And here, because the AC voltage applied to the subject's body rises slowly to its final level, electrosensory sensation does not occur (or is at least significantly reduced). After the rise period, the output of AC signal generator 20 remains constant for an extended period of time, as described above. Figure 3 As described.

[0039] It should be noted that, although Figure 3 and Figure 4 The examples depicted all have a 2-second rise time, but this rise time can be different (e.g., at least 0.1s, at least 0.3s, at least 1s, at least 3s, at least 10s, etc.). Furthermore, Figure 3 and Figure 4The depicted linear ramp is not the only amplitude trajectory that can be used to prevent or improve electrosensory sensation. Instead, any amplitude trajectory from a wide variety of amplitude trajectories can be used, provided that the AC voltage applied to the subject's body increases slowly enough to avoid or at least minimize electrosensory sensation.

[0040] Figure 5 Four examples of nonlinear amplitude amplification trajectories that can be used to improve electrosensory perception are depicted. In the first example 51, the amplitude increases during interval 1, then remains constant during interval 2, then increases further during interval 1', then remains constant during interval 2', and then increases further during interval 1"". To generate this amplitude trajectory, controller 30 sequentially transmits control signals to AC signal generator 20 (e.g., every 1 ms, 2 ms, 5 ms, 10 ms, 20 ms, 50 ms, or 100 ms). When AC signal generator 20 receives these control signals, it produces an output with an amplitude trajectory similar to trace 51. Each of the intervals 1, 1', 1"', 2, 2' can be, for example, between 10 ms and 10 s in length. The basic principle of including intervals 2, 2' in the trajectory is to allow the subject to adapt to a given voltage setting before the voltage increases further. In some embodiments, each of these intervals is at least 20 ms, at least 50 ms, or at least 100 ms in length. After the amplitude increase trajectory has occurred, the output of AC signal generator 20 remains constant for an extended period of time at its final value (e.g., at least 50V RMS, at least 100V RMS, etc.), as described above. Figure 3 As described.

[0041] The second example 52 is similar to the first example 51, except that the amplitude of the AC signal generator 20 decreases during intervals 2 and 2' instead of remaining constant during intervals 2 and 2'. To generate this amplitude trajectory, the controller 30 sequentially sends control signals to the AC signal generator 20 (e.g., every 1ms, 2ms, 5ms, 10ms, 20ms, 50ms, or 100ms). When the AC signal generator 20 receives these control signals, it produces an output with an amplitude trajectory similar to that of trace 52. Each interval in intervals 1, 1', 1'', 2, 2' can be, for example, between 10ms and 10s in length. After the amplitude increase trajectory has occurred, the output of the AC signal generator 20 remains constant at its final value for an extended period of time, as described above in conjunction with trace 51.

[0042] In the third example 53, the controller 30 sequentially transmits control signals to the AC signal generator 20, such that the amplitude of the AC signal generator 20 increases linearly at a first rate during interval 1 (which may be, for example, between 100 ms and 10 s), and increases linearly at a second rate during interval 2 (which may also be, for example, between 100 ms and 10 s). After the amplitude increase trajectory has occurred, the output of the AC signal generator 20 remains constant at its final value for an extended period of time, as described above in conjunction with trajectory 51.

[0043] In the fourth example 54, the controller 30 sequentially transmits control signals to the AC signal generator 20, such that the amplitude of the AC signal generator 20 increases at a first linear rate during interval 1 (which may be, for example, between 100 ms and 10 s), and at a second non-linear rate during interval 2 (which may also be, for example, between 100 ms and 10 s). Here, after the amplitude increase trajectory has occurred, the output of the AC signal generator 20 remains constant at its final value for an extended period of time, as described above in conjunction with trace 51.

[0044] The four examples 51 to 54 provided above are not exhaustive. Instead, a variety of alternative amplitude amplification trajectories can be readily envisioned to prevent the amplitude from increasing too rapidly in order to improve electrosensory perception.

[0045] Figure 6 This is a block diagram of another system used to apply TTFields to target areas in a subject's body. This system is similar to the one described above. Figure 1 The systems are similar, the difference lies in Figure 6 The embodiments use a three-phase approach instead of the combination of the above. Figure 1 The described sine-cosine method is used to achieve electric field rotation. Figure 6 The embodiment uses an AC signal generator 20, which is designed to generate three AC outputs with frequencies between 50 kHz and 10 MHz (e.g., 50 kHz to 1 MHz, 50 kHz to 500 kHz, 80 kHz to 300 kHz, or 150 kHz to 250 kHz). These three outputs are 120° out of phase with each other and are applied to three sets of electrode elements 10X / 10Y / 10Z, which are configured for placement against the subject's body. When the electrode elements 10X / 10Y / 10Z are positioned around the target body part at 120° intervals, applying the tri-phase signal to those electrode elements will apply an alternating electric field with an orientation that rotates continuously and repeatedly 360° during the treatment session to the target area.

[0046] In addition to Figure 6 The embodiment uses a three-phase electric field rotation instead of the above combination. Figure 1The described distinction is based on the rotation of the electric field between sine and cosine. Figure 6 The operation of the embodiment is the same as described above. Figure 1 The operation of the embodiment is similar.

[0047] Finally, in some anatomical locations, the electrode elements are not positioned on the subject's skin. Instead, the electrode elements are implanted into the subject's body (e.g., just below the subject's skin) such that applying an AC voltage between the electrode elements will create an alternating electric field in a target area of ​​the subject's body.

[0048] While the invention has been disclosed with reference to certain embodiments, various modifications, alterations, and changes can be made to the described embodiments without departing from the scope and domain of the invention as defined by the appended claims. Therefore, the invention is intended to be limited to the described embodiments, but rather to have the full scope defined by the language of the appended claims and their equivalents.

Claims

1. A device for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body, the device comprising: At least three electrodes, each of the at least three electrodes having a surface configured to rest against the subject's body; and An AC voltage source having at least three output terminals, each output terminal being electrically connected to a corresponding electrode among the electrodes. Each of the at least three output terminals has a frequency between 50 kHz and 1 MHz, and Each of the at least three output terminals has an amplitude that increases from an initial level to a final level of at least 50V RMS over a period of at least 0.1s.

2. The apparatus of claim 1, wherein each of the at least three output terminals has an amplitude that is maintained at the final level for at least 30 seconds.

3. The apparatus of claim 1 or claim 2, wherein each of the at least three electrodes comprises a conductive substrate, and wherein each of the surfaces configured to rest against the subject's body comprises an insulating material having a dielectric constant of at least 20, the insulating material being disposed on the respective conductive substrate.

4. The apparatus according to any of the preceding claims, wherein each of the at least three output terminals has: an increase in magnitude from the initial level to the final level over a period of at least 0.3 s, wherein the final level is at least 100 V RMS; and optionally an increase in magnitude from the initial level to the final level over a period of at least 1 s, wherein the final level is at least 100 V RMS.

5. The apparatus according to any of the preceding claims, wherein each of the at least three output terminals has a frequency between 80 kHz and 300 kHz.

6. The apparatus according to any of the preceding claims, wherein the AC voltage source has a first output terminal at a given frequency, a second output terminal at the given frequency offset by 120° relative to the first output terminal, and a third output terminal at the given frequency offset by 240° relative to the first output terminal.

7. The apparatus according to any one of claims 1 to 5, wherein the AC voltage source has a first output terminal at a given frequency, a second output terminal at the given frequency offset by 90° relative to the first output terminal, a third output terminal at the given frequency offset by 180° relative to the first output terminal, and a fourth output terminal at the given frequency offset by 270° relative to the first output terminal.

8. The apparatus according to any of the preceding claims, wherein the AC voltage source simultaneously applies a sinusoidal signal at a first frequency to each of the at least three output terminals, wherein the signal applied to each of the at least three output terminals is modulated by a sinusoidal wave at a second frequency at least ten times lower than the first frequency, and the modulated sine wave has a phase shift.

9. The apparatus according to any of the preceding claims, wherein the increase in amplitude from the initial level to the final level is linear.

10. An AC electric field used in a method for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body, the method comprising the steps of: The AC electric field is rotated within the target region, wherein the orientation of the electric field is rotated relative to the target region. The electric field described therein has a frequency between 50 kHz and 1 MHz, and The electric field therein has an amplitude that increases from an initial level to a final level over a period of at least 0.1 s.

11. An AC electric field for selectively disrupting or inhibiting the growth of rapidly dividing cells located in a target region of a subject's body, wherein the AC electric field has an electric field orientation that rotates relative to the target region, wherein the electric field has a frequency between 50 kHz and 1 MHz, and wherein the electric field has an amplitude that increases from an initial level to a final level over a process of at least 0.1 s.

12. The AC electric field used in claim 10 or the AC electric field according to claim 11, wherein the electric field in at least a portion of the target region is generated by an applied voltage, and wherein the applied voltage is at least 50 V RMS when the amplitude of the electric field is at the final level, and optionally the applied voltage is at least 100 V RMS.

13. The AC electric field used in claim 10 or claim 12, or the AC electric field according to claim 11 or claim 12, wherein the electric field is applied to the target region via an insulating electrode.

14. The AC electric field used in claim 10, 12, or 13, or the AC electric field according to claim 11, 12, or 13, wherein the electric field has an amplitude that increases from the initial level to the final level in a process of at least 0.3 s and optionally in a process of at least 1 s.

15. The AC electric field used in claim 10 or any one of claims 12 to 14, or the AC electric field according to any one of claims 11 to 14, wherein when the amplitude of the electric field is at the final level, the electric field has an electric field strength of at least 1 V / cm and optionally at least 5 V / cm in at least a portion of the target region.

16. The AC electric field used according to claim 10 or any one of claims 12 to 15, or the AC electric field according to any one of claims 11 to 15, wherein the frequency of the electric field is between 80 kHz and 300 kHz.

17. The AC electric field used in claim 10 or any one of claims 12 to 16, or the AC electric field according to any one of claims 11 to 16, wherein the rotation of the AC electric field is accomplished by simultaneously applying AC voltages with different phases to at least three electrodes.

18. The AC electric field used according to claim 10 or any one of claims 12 to 17, or the AC electric field according to any one of claims 11 to 17, wherein the increase in amplitude from the initial level to the final level is linear.

19. The apparatus according to any one of claims 1 to 8, or the AC electric field used according to claim 10 or any one of claims 12 to 17, or the AC electric field according to any one of claims 11 to 17, wherein the increase in amplitude from the initial level to the final level is non-linear, and includes one or more of the following: a) A first interval, during which the amplitude increases at a constant rate; followed by a second interval, in which the amplitude is constant; followed by a third interval, in which the amplitude increases at the constant rate; b) A first interval during which the amplitude increases at a first constant rate; followed by a second interval during which the amplitude decreases at a second constant rate; followed by a third interval during which the amplitude increases at the first constant rate. c) A first interval during which the amplitude increases at a first constant rate; followed by a second interval during which the amplitude increases at a second constant rate, wherein the second constant rate is different from the first constant rate; d) A first interval during which the amplitude increases at a constant rate; followed by a second interval during which the amplitude increases at a non-constant rate.

20. The apparatus according to any one of claims 1 to 8, or the AC electric field used according to claim 10 or any one of claims 12 to 17, or the AC electric field according to any one of claims 11 to 17, wherein the increase in amplitude from the initial level to the final level comprises: a) Setting the amplitude to an intermediate level between the initial level and the final level, wherein the intermediate level is below a threshold that causes inductance, and b) The amplitude is then increased from the intermediate level to the final level. Optionally, the intermediate level is 20V RMs.

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