AU2009217392A1 - Neural stimulation with varying amplitude - Google Patents

Description

I "Neural stimulation with varying amplitude" Technical Field The present invention relates to neural stimulation, and in particular provides for the 5 application of a current stimulus having a varying amplitude in order to better maintain a resulting electrode voltage at a desired level, in a desired range, or along a desired profile. Background of the Invention 10 Many implanted medical devices rely on electronic circuits to provide electric stimulation of nerves. Such devices include retinal implants and cochlear implants, where the electrical stimulation is used to transfer information to the brain, as well as devices for applications where the stimulation is used for motor control. For chronic use in patients, it is necessary that such devices transfer a zero net charge, and so the 15 use of charge-balanced rectangular biphasic current pulses for neural stimulation is well established. These pulses often comprise a constant current stimulating cathodic phase, followed by a brief interphase gap in which no stimulation is applied, and then a constant current charge-balancing anodic phase. 20 Various kinds of neural stimulation performance improvement have been sought by varying the waveform of the signal. For instance variations from the basic symmetric rectangular biphasic current pulse have been investigated for their effect on threshold, for selective recruitment of different sized fibres, and for increasing charge delivery capacity of electrodes. 25 Neural stimulation devices further face certain constraints upon the voltage which may appear on the stimulating electrodes. While miniaturization of neural stimulation devices is desirable, integrated circuit (IC) technologies with reduced device (transistor) size tolerate smaller voltages. Thus, devices using progressively smaller 30 feature semiconductor technologies face limits on the maximum supply voltage available to effect the electrical neural stimulation. While smaller feature semiconductor technologies may be adapted to provide larger electrode voltages, this 2 necessitates increased circuit complexity and power consumption to step up the voltage. Another approach is to use semiconductor fabrication technology which allows both high and low voltage transistors on the same die however such specialised devices add to the IC fabrication cost. 5 Another factor affecting electrode voltage is the need to avoid voltages rising above a certain threshold, to prevent the formation of undesirable chemical products in the tissue surrounding the electrode. One approach for limiting peak electrode voltage involves monitoring the electrode voltage and reducing the current when a prescribed 10 voltage limit is approached. Implanted devices are generally battery powered and thus have a tight power budget. To reduce the power dissipated in neural stimulation circuitry, careful attention has been paid to design of current sources, and a voltage drive waveform designed to 15 approximately match the electrode voltage under constant current drive has also been proposed. Nevertheless the power budget remains a significant factor in neural stimulation. Any discussion of documents, acts, materials, devices, articles or the like which has 20 been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application. 25 Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps. 30 3 Summary of the Invention According to a first aspect the present invention provides a device for neural stimulation, the device comprising: at least one electrode for delivering electrical stimulation to neural tissue; 5 a stimulus generator for delivering a stimulus current pulse, the current pulse being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and of distinct amplitude to each other step of the pulse, and each step being of an amplitude selected to control electrode voltage in a desired manner. 10 According to a second aspect, the present invention provides a method for neural stimulation, the method comprising: delivering a stimulus current pulse to at least one electrode in order to electrically stimulate neural tissue, the stimulus current pulse being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and 15 of distinct amplitude to each other step of the pulse, and each step being of an amplitude selected to control electrode voltage in a desired manner. According to a third aspect the present invention provides a computer program product comprising computer program code means to make a computer execute a procedure for 20 neural stimulation, the computer program product comprising: computer program code means for delivering a stimulus current pulse to at least one electrode in order to electrically stimulate neural tissue, the stimulus current pulse being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and of distinct amplitude to each other step of the pulse, and each 25 step being of an amplitude selected to control electrode voltage in a desired manner. In some embodiments, each step of the current pulse is of reduced current amplitude relative to a preceding step of the pulse. In some such embodiments, each step may be of a duration that is the same as the duration of each other step in the pulse. Current 30 steps of equal duration may be advantageous due to ready availability of suitable hardware to deliver stepped currents of constant step duration. Alternatively, each step 4 after the first step may be of a duration which is greater than a duration of a preceding step in the pulse. Current steps of differing duration may be advantageous in effecting greater charge transfer while remaining within a given maximum electrode voltage level, or in effecting transfer of a given amount of charge while minimising a peak 5 electrode voltage value. In a fourth aspect, the invention concerns a method of generating a neural stimulus electrical waveform for the delivery of charge through a pair of electrodes to stimulate surrounding neural tissue, the method comprising: 10 parameterising an electrode current waveform as a sequence of piecewise constant steps, each step having substantially the same duration as all other steps and each step having a calculatable amplitude; identifying electrode-tissue interface (ETI) parameters; and for each step calculating the respective step amplitude using the identified ETI parameters to 15 optimise the electrode voltage. Further embodiments may comprise specifying algorithms to directly identify electrode-tissue interface parameters. In one such embodiment, in which the current pulse comprises n current steps of equal duration T,, an excitation current is applied to 20 the tissue for a period of T,, and the voltage across the electrodes is measured at times T,, 2.T,, ... n.T,. Transfer function coefficients may be estimated from such voltage measurements, from which an optimised amplitude of each current step may be calculated. 25 Embodiments of the fourth aspect may further comprise, prior to the calculating, defining an optimum electrode voltage, and specifying preferable ranges for the step duration. Brief Description of the Drawings 30 An example of the invention will now be described with reference to the accompanying drawings, in which: 5 Figure 1 is a circuit diagram of a model of the electrode-tissue interface; Figure 2 illustrates a conventional electrode current pulse; Figure 3 illustrates the voltage profile arising on the stimulating electrodes when the conventional current pulse of Figure 2 is delivered to tissue; 5 Figure 4 illustrates an electrode current pulse in accordance with one embodiment of the present invention, consisting of five current steps of decreasing amplitude optimised to maximise delivered charge while minimising electrode voltage; Figure 5 illustrates the voltage profile arising on the stimulating electrodes when the current pulse of Figure 4 is delivered to tissue; 10 Figure 6 illustrates a current waveform of a charge balanced biphasic pulse with interphase gap, in accordance with an embodiment of the present invention; Figure 7 illustrates an electrode current pulse in accordance with another embodiment of the present invention, consisting of two current steps of differing duration and amplitude, each step amplitude being optimised to minimise electrode 15 voltage for a given charge transfer; and Figure 8 illustrates the voltage profile arising on the stimulating electrodes when the current pulse of Figure 7 is delivered to tissue. Description of the Preferred Embodiments 20 The embodiment described here relates to the design of electrical current waveforms for the delivery of electric charge from an electronic circuit through a pair of electrodes into neural tissue for the purpose of evoking stimuli. In particular this embodiment takes an analytical approach to designing electrode stimulation current waveforms in such a way as to reduce the maximum voltage between the two electrodes while 25 delivering a given charge in a specified time. Conventionally, the first phase, also called the stimulation phase, of a biphasic stimulation current waveform has constant amplitude for the total duration of the stimulation phase, as shown in Figure 2. 30 6 Instead, this embodiment of the invention provides for piecewise constant (stepped) current waveforms to replace the constant current stimulation phase, wherein the step durations are given and equal, and the step sizes (current amplitudes) are calculated in a manner to minimise the peak voltage between the electrodes, while delivering the 5 required specified amount of electric charge through the tissue. This invention recognises that reducing the maximum electrode voltage is desirable for several reasons. First, it allows the supply voltage to the current generating electronic circuits to be reduced, thereby reducing power loss in the stimulation circuitry. 10 Second, devices using small feature semiconductor technologies face limits on the allowed size of supply voltage. Third, limiting the maximum electrode voltage can prevent the formation of undesirable chemical products. In this embodiment, optimised stepped current levels are determined from (a) a 15 specification of a stepped electrode current for the stimulation phase, where the steps are of given and equal duration as shown in Figure 4, and (b) a representation of the electrode-tissue interface by an equivalent linear electric circuit, as set out in Figure 1. Together, these allow engineering design techniques to be used to determine the optimal amplitudes of the current steps which will both minimise peak electrode 20 voltage and ensure that the required electric charge is delivered. The basic formulation of the waveform design problem presented here uses an assumed known electric circuit equivalent model of the electrode-tissue interface, as shown in Figure 1. In a practical in-vitro or in-vivo situation, modifications enabling more direct 25 modelling of the electrode-tissue interface may be used without going through the intermediate step of an equivalent circuit model. This embodiment is particularly advantageous in that the electrode current design problem can be approached using techniques used for control system design, since 30 zero-order-hold sampled signals are widely used in digital control systems where a digital computer is used to compute signals to drive an analog device in order to 7 achieve desired performance. With the framework used here, the problem of delivering given charge with minimum electrode voltage is closely related to that of designing a current waveform which maximizes charge delivered under the constraint of not exceeding a designated voltage level. 5 The problem considered in this embodiment is the design of the stimulation current phase, the first part of a biphasic waveform (shown in full in Figure 6), for the delivery through a pair of electrodes of a specified charge Q coulombs over a specified stimulation phase duration T seconds. For convenience of presentation, the charge is 10 specified positive ie Q > 0, while it is known that the stimulation phase is usually negative. The actual negative stimulation phase would be obtained by changing the signs of the currents from the calculated values. Voltages and currents which are functions of time t are denoted by lower case letters 15 such as v(t). Samples of v(t) taken at time intervals t = kT, where k = 0, 1, 2, . . . are denoted Vk, shorthand for v(kTs). The z-transform of a sequence h = { k}=O is denoted h(z) and is given by b.(z) = Z . k=O (1) With this convention, a stable transfer function has all its poles at values of z : Izi > 1. 20 Also the symbol z denotes the unit delay. The electrode-tissue interface is modelled with the circuit of Fig. I comprising access resistance Ra ohms, double layer capacitance C Farads and Faradaic resistance R ohms. It is assumed the values of these three parameters are known. With constant electrode 25 current i(t) = io applied for t > 0, the internal voltage w(t) and the electrode voltage v(t), both for t > 0 are given by w(t) = w(0)e /IRC + ioR( - e-fRC) (2) v(t) = w(t) + ioRa. (3) 8 Parametrization of stimulation current follows. Firstly, the stimulation phase duration T is broken up into a whole number, n, of discretization time intervals each of duration Ts. In alternative embodiments within the scope of the present invention, the stimulation phase duration may be broken into intervals of varied duration. Thus in this 5 embodiment T = nTs, where n is a positive integer. Setting n = 1 specifies the standard constant current stimulation phase. The current i(t) is parametrized to be piecewise constant over time intervals T, as follows: 0; t < 0. i (t) = ik; kT, < t < (k + 1)T,; k = 0, 1,.,n - 1, 0; it > nT,. (4) 10 The desired charge Q of the stimulation phase is obtained by setting n-1 k=0 .(5) From (4), i(t) takes on n values ik, which are constrained to satisfy (5). If the current has the form (4), then over each time interval given by kTs < t 5 (k + I)T, where k = 0, 1, . . . , n - 1, voltage w(t) is given by 15 w(Q) = w(kTs)e-(t-kTs)/RC +ikR(I-e-(t-kTs)/RC) (6) and v(t) is given by v(t) = w(t) + ikRa. (7) This embodiment takes a linear programming approach to minimizing peak electrode 20 voltage, as follows. From (2) and (3), the maximum value of v(t) in response to a current step occurs either at the beginning or the end of that current step. Thus the problem of minimizing the peak electrode voltage in response to a current of the form (4) requires consideration of v(1) only at sample times t = kTs. This allows the electrode-tissue dynamics to be represented by discrete-time versions of (2) and (3) 25 namely Wk Wk- 1 ± k-1R(l - a), (8) k Wk ± ik-1Ra (9) where k = 1, 2, . . . , n and a = e-T. (10) 9 Denoting the minimum peak value of v(t) by J, the problem of calculating J can be formulated as the following finite linear program where y is a variable introduced to bound Vk. J = mi ly 5 subject to ik 2 0; k 0, 1,..., n - 1, (12) n-1 k=O T. ,(13) WO = 0, (14) Wk = aWA.-1 + ik-1R(1 - a); k 1, 2,..., n, (15) 10 Vk = Wk + ik-IRa; k =1, 2, ... ,n, (16) vk5 9y; k = 1, 2,. .. ,n. (17) This optimization problem can be solved numerically to determine the current step sizes and the minimized peak electrode voltage. The voltages w(t) and v(t) between the 15 sample values can be calculated from (6) and (7). There is scope to modify the problem by the addition of further inequality or equality constraints on variables ik, Vk, Wk. For example bounds could be placed on the values of some of the ik or on their rate of change. 20 It is noted that, in an alternative approach to obtaining the solution to the problem (11) (17). direct calculation of stimulation current may occur. This alternative approach occurs without solving a numerical optimization. It can be shown that the solution to the optimization problem (11)-(17) has the property that the electrode voltage satisfies vt = V2 = . . . = V > 0. This enables the values of io, . . . , i,-,. and v;, . . . , v, to be 25 constructed directly. The procedure involves three steps. Firstly, the discrete-time transfer function h(z)of the electrode-tissue equivalent circuit voltage response at times t = kU, to a unit step current applied over one sample time 0 < t < T, is determined. Then the relation between the electrode voltage samples and the 30 current values is given by 10 i:(z) = h(z)i(z). (18) Eliminating Wk from (8) and (9) gives S I - az (19) where 5 bi =Ra+ R(l - a), (20) b2 = - a Ra. (21) Secondly, a stepped electrode current denoted f(z) with the form of (4) which would give an electrode voltage satisfying vo=0, v = 1; k = 1,2,... (22) 10 or equivalently z (1-z) (23) is calculated. Now f(z) such that a~)= f(z)ht(z) = Z (1 - z) (24) is given by I z 15 (0 - 7) h(z) (25) 1 1/1j(1 - nz) (I - z) (1 + (b2/bj)z) (26) Thirdly f(z) is truncated to n terms and then scaled to give a current (z) which satisfies the charge constraint (5): W(z = * o l .

(27) 20 Moreover the value of vi, v 2 ,... , v, is given by the scaling factor above, so that .JQ 1 Is Ejo /j.(28) This approach can be used to calculate numerical solutions, identical to those from (1 1)-(17). Furthermore a closed-form solution for the minimum value of the peak electrode voltage can be obtained by resolving (26) into two partial fractions, followed 25 by truncating the individual series expansions and scaling to obtain: l1 Q ( R + R,)2( _ a) Ts (Ra + R)(1 - a)nt + R H(1 - ( _ )"). (29) The above can even give more general results. Suppose the solution to (11)-(17) for given parameters and charge Qo has a minimum peak electrode voltage of value J(Qo). 5 Then the following hold: 1) Scaling with charge: If only the charge is changed to Q = cQo where c > 0, the solution to (I 1)-(17) becomes J(cQo) = cJ(Qo); c > 0, (30) 2) Maximizing charge with given bound on electrode voltage: Given # > 0 axQ= Qo 3 10 s J(Qo) (31) Example 1 This example uses electrode-tissue interface parameter values Ra = 11000, C = 0.98piF, R = 1OkfQ, with charge parameters Q = IpC, T = 5ms. A constant-current stimulation 15 phase is obtained by setting n = 1. For this case, there is no scope for optimization. The electrode voltage is obtained by evaluating (6) and (7) with initial condition w(0) 0 and current io given by (5). Plots are shown in Figs. 2 and 3. To illustrate the approach shown in this paper, a five-step current waveform is obtained 20 by setting T, = Ims and n = 5. Solving (1 1)-(17) gives the sampled voltages Wk and Vk and the currents ik. The voltage values between time samples are obtained from (6) and (7). Electrode current and voltage plots are in Figs. 4 and 5. Results for various values of n and T, chosen to keep the stimulation phase duration T 25 nT, constant at 5ms are shown in Table I, obtained using (29). For this example, the maximum electrode voltage can be reduced by approximately 21% through the use of this approach. Most of the performance improvement is achieved with 5-10 steps. TABLE I: Values of minimized peak electrode voltage for a 5ms stimulation phase.

12 n | T, (ms) J (volts) | Voltage reduction(%) | 1 5 1.019 0 2 2.5 0.906 11 5 1 0.843 17 10 0.1 0.823 19 100 0.05 0.807 21 1000 0.005 0.806 21 This embodiment thus provides for a neural stimulation current design approach using a current waveform comprising piecewise constant segments with regular time intervals 5 between transitions, in place of the often used single constant current. The use of numerical optimization using a finite linear program to compute the current step sizes to minimize peak electrode voltage has been demonstrated. A direct approach for synthesizing the optimal current steps is also given. Table I shows that this approach gives current waveforms which can deliver a given charge to a specified load with 10 useful voltage headroom reduction below that required with conventional rectangular current pulses. This technique thus attempts to directly control the electrode voltage. The approach presented here has the advantage of reducing the peak electrode voltage. It is to be noted that in alternative embodiments each current step may be of a duration 15 which differs from the duration of one or more other steps of the current pulse. One such alternative embodiment is shown in Figures 7 and 8. Figure 7 illustrates an electrode current pulse in accordance with another embodiment of the present invention, consisting of two current steps of differing duration and amplitude, optimised to minimise electrode voltage for a given charge transfer. Figure 8 illustrates 20 the voltage profile arising on the stimulating electrodes when the current pulse of Figure 7 is delivered to tissue. It will be appreciated that in alternative embodiments the current pulse may comprise more than two steps, each of differing duration to the other steps. 25 It is further noted that step amplitude and/or duration may be optimised in vivo, rather than relying upon a modelled equivalent circuit of the electrode-tissue interface. Provided below is a discussion of one example for determining optimised current step 13 amplitudes in an embodiment comprising n current steps of equal duration. This algorithm is for identifying the electrode tissue interface (ETI) transfer function coefficients and shows how they are used to determine the optimal current waveform. 5 The problem is first defined . The charge to be delivered is Q coulombs. Let n be the number of steps in the stimulation phase. The total stimulation phase duration is seconds. The duration of each step is then T, = Tin seconds. Define a reference current I,,f given by /,,f= Q / T. (101) 10 The aim is to determine the current i(t) which is parametrized to be piecewise constant over time intervals T, as follows: 0; t < 0. i(t) = ik; k T, < t < (k + 1)T,; k = 0, 1, .. ,n-1, 0; t > nT. (102 15 and also the minimised peak voltage which is the value of v(Ts), v(2T,), . . . v(nTs) when these are made equal to each other. The currents calculated should satisfy: n- Q k=0, (103) and the measured values of v(T,), v(2T,), . . . v(nT) should be equal to each other. 20 The next step is identification of E T I transfer function coefficients. The electrode tissue interface transfer function coefficients to be identified are hl, h 2 , . . . , hn. The excitation current i(t) is 0: t < 0, i(.t) = I,; 0 < t <; Ts; 0; t > .(104) 25 14 Apply this excitation current to the electrodes. Measure the voltages v(Ts), v(2T), . v(nTs). Then the estimated transfer function coefficients are lk = v(kTs) k = 1,2,..., n. Ire f (105) 5 For the scheme to work, the voltage response should be monotonic decreasing and positive for t > T. It is then possible to calculate optimal current levels, by solving the following triangular linear system of n equations in n unknowns: 10 1 = 10 h 1 (106) 1 X012 + 1 (107) 1 = 0 31 h 112 + 2 11 (108) 15 1 = 0oh?, 1 -1 - + r-1hl. (109) Solving these from the top, xo = 1/h, > 0, x1 = l1/h,( - xoh 2 ) > 0, x2 = l/h;(l-xoh3-xth2) n-2/ give allx\ > 0. Continuing till n-1 -. - i) > 0 gives all xt. Calculate = = The optimal currents are then 20 s,; (110) and the predicted minimised peak voltage is Q A numeica exa k = e 1 2. o .v A numerical example of implementation of this in vivo optimisation technique follows.

15 With n = 3, Q = 40nC, T = 400ps, then T, = 133p s. Then If = Q / T = 1OOuA. The excitation current is: 0; t < 0, i(t) 100pA 0 < t < 133is; 0; t > 133ps. (112) 5 The measured voltage response was vt = 0.121V , v 2 = 0.042V , v 3 = 0.035V . Then the optimal stimulation current waveform is io = 140.383kA, i, = 91.6549kA, i 2 = 67.9622pA. The predicted value of vt, v 2 , v 3 is v= 0.169863V. It will be appreciated by persons skilled in the art that numerous variations and/or 10 modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive. 15

Claims (14)

1. A device for neural stimulation, the device comprising: at least one electrode for delivering electrical stimulation to neural tissue; a stimulus generator for delivering a stimulus current pulse, the current pulse 5 being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and of distinct amplitude to each other step of the pulse, and each step being of an amplitude selected to control electrode voltage in a desired manner.

2. The device of claim 1, wherein the current pulse comprises a plurality of current steps, each step being of substantially constant current amplitude. 10

3. The device of claim 2, wherein each step is of reduced current amplitude relative to a preceding step of the pulse.

4. The device of claim 2 or claim 3, wherein each step is of a duration that is the same as the duration of each other step in the pulse.

5. The device of claim 2 or claim 3, wherein each step after the first step is of a 15 duration which is greater than a duration of a preceding step in the pulse.

6. A method for neural stimulation, the method comprising: delivering a stimulus current pulse to at least one electrode in order to electrically stimulate neural tissue, the stimulus current pulse being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and 20 of distinct amplitude to each other step of the pulse, and each step being of an amplitude selected to control electrode voltage in a desired manner.

7. The method of claim 6, wherein the current pulse comprises a plurality of current steps, each step being of substantially constant current amplitude.

8. The method of claim 7, wherein each step is of reduced current amplitude 25 relative to a preceding step of the pulse.

9. The method of claim 7 or claim 8, wherein each step is of a duration that is the same as the duration of each other step in the pulse.

10. The method of claim 7 or claim 8, wherein each step after the first step is of a duration which is greater than a duration of a preceding step in the pulse. 30

11. A computer program product comprising computer program code means to make a computer execute a procedure for neural stimulation, the computer program product comprising: 300529_3 17 computer program code means for delivering a stimulus current pulse to at least one electrode in order to electrically stimulate neural tissue, the stimulus current pulse being a stepped current pulse comprising a plurality of current steps which are each of constant amplitude and of distinct amplitude to each other step of the pulse, and each 5 step being of an amplitude selected to control electrode voltage in a desired manner.

12. A method of generating a neural stimulus electrical waveform for the delivery of charge through a pair of electrodes to stimulate surrounding neural tissue, the method comprising: parameterising an electrode current waveform as a sequence of piecewise 10 constant steps, each step having substantially the same duration as all other steps and each step having a calculatable amplitude; identifying electrode-tissue interface (ETI) parameters; and for each step calculating the respective step amplitude using the identified ETI parameters to optimise the electrode voltage. 15

13. The method of claim 12 further comprising specifying algorithms to directly identify electrode-tissue interface parameters.

14. The method of claim 12 or claim 13 further comprising, prior to the calculating, defining an optimum electrode voltage, and specifying preferable ranges for the step duration. 20 300529_3