Abstract:
We disclose multi-electrode, energy-recycling, resonant stimulation circuits and strategies for energy-efficient blocking of action potentials in nerve. Our schemes increase the probability that most of the electrical stimulation is directed through the nerve rather than dissipated in ohmic extracellular solution alongside it via mechanical and electrical means; they use energy-recycling and resonant-amplification strategies that recycle and amplify capacitive nerve energy such that the nerve itself becomes an integral part of the circuit creating its oscillatory blocking waveform; they use traveling-wave strategies with distributed multi-electrode stimulation that alters the timing and intensity of stimulation at various points along the nerve to synchronize blocking stimulation with wave propagation in the nerve in an energy-efficient fashion. The schemes operate synergistically in a medical device to create advanced energy-efficient nerve-blocking stimulators whose operation may be altered and adapted in a feedback fashion to sensed action potentials in the nerve.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims benefit under 35 USC §119(e) of U.S. Provisional Patent Application Ser. No. 62/085,826 filed on Nov. 29, 2014, the contents of which are incorporated herein in their entirety by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not applicable. 
       REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISC APPENDIX 
       [0003]    Not applicable. 
       BACKGROUND 
       [0004]    Action potential propagation can be blocked in nerves by alternating current excitation, as is described for example in J. Tanner, “Reversible Blocking of Nerve Conduction by Alternating Current Excitation”, NATURE, Vol. 195, pp. 718-719, Aug. 18, 1962. Typically, a relatively large pair of neighboring cuff electrodes circumferentially surround the nerve with a small lateral distance between them. A high-frequency a.c. waveform, usually in the 1 kHz to 100 kHz frequency range creates an oscillatory current or voltage waveform between these electrodes. Due to the small impedance of the extracellular solution separating the two electrodes—for example, this impedance has a value of approximately 50Ω from a typical 5 V/100 mA measurement—these conventional stimulation systems dissipate a lot of energy as ohmic loss instead of directing the energy efficiently to induce nerve blocking. In fact, the energy consumption of current stimulation systems for nerve blocking is very high compared with those of even the most power-hungry FDA-approved stimulators for nerve excitation. Thus, for long-term clinical use in human beings, circuits and architectures for nerve-blocking a.c. stimulation with a much higher energy efficiency than that of the current systems are needed. 
         [0005]    Prior patent-granted work as described in S. Arfin and R. Sarpeshkar, “An Electrode Stimulator with Energy Recycling and Current Regulation”, U.S. Pat. No. 8,700,144 B2, Issued Apr. 15, 2014, has used an inductor to recycle capacitive energy in an electrode impedance, shuttling this energy back and forth between a storage capacitance and electrode capacitance to lower power dissipation in nerve stimulation. This strategy enables the creation of a switching power supply that adaptively and adiabatically adjusts its compliance voltage to be just a little bit higher than that of the electrode voltage, thus minimizing ohmic losses. The differential value between the power supply and electrode voltage is regulated via a feedback loop to maintain constant-current stimulation into the electrode. The savings in power are near the fundamental limits of physics set by ohmic solution resistance. In most nerve stimulators that excite the nerve, electrode impedances are dominant such that this power scheme is as nearly optimal as it can be: one cannot dissipate less power than that caused by current flowing through an ohmic solution resistance. However, in blocking nerve stimulators, electrode impedances are typically not dominant such that it is the nerve impedance energy itself that needs to be recycled, not the electrode impedance energy. Furthermore, the waveform required for stimulation needs to be an oscillatory a.c. waveform such that the adiabatic switching power-supply techniques are not a power-efficient method for creating such a waveform. 
         [0006]    The system described in Franke, Kilgore, and Bhadra, “Systems and Methods that Provide an Electrical Waveform for Neural Stimulation or Nerve Block” focuses on methods to achieve an oscillatory waveform with charge balancing but has little impact on energy: It creates an oscillatory waveform in one circuit component, ensuring that it is charge balanced in another circuit component, and then couples the final output of the second circuit component as an electrical waveform suitable for nerve stimulation or blocking. One embodiment described in Franke et al. uses an inductor. It is easy to create an oscillator with an inductor as is well known in elementary electrical engineering, physics, and in the public domain, for example, see R. Sarpeshkar, “Ultra Low Power Biolectronics: Fundamentals, Biomedical Applications, and Bio-inspired Systems”, Cambridge University Press, 2010. However, if the nerve and electrodes are separated from the waveform generators that create the oscillation, and not part of it, the nerve capacitive energy does not resonate with the inductor, just the capacitive energy of a circuit component in the oscillator. Thus, there is little energy benefit, and not surprisingly, none claimed. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    In this application, we disclose circuits and architectures for reducing energy and power consumption of nerve-blocking stimulation systems. These embodiments include but are not limited to i) the use of passive inductive, active inductive, active transconductor-capacitor, or piezoelectric strategies that serve to resonantly amplify and/or recycle capacitive nerve energy such that the nerve itself becomes an integral part of the circuit that creates its oscillatory blocking waveform; ii) mechanical multi-electrode configurations and stimulation paradigms that help increase the probability that most of the stimulation current is directed through the nerve rather than dissipated in ohmic extracellular solution alongside it; iii) the use of multi-electrode traveling-wave architectures that alter the timing and intensity of stimulation at various points along the nerve to synchronize blocking stimulation with traveling-wave propagation in the nerve in an energy-efficient and selective fashion; iv) the use of feedback or calibration loops to configure these stimulation systems such that they operate at resonance and with mechanical/electrical electrode configurations that maximize blocking effectiveness and energy efficiency. 
         [0008]    We disclose that one can actually use either passive or active inductors to recycle or resonantly amplify the reactive energy in the nerve itself, shuttling energy back and forth between inductive and capacitive forms, to create a resonant oscillatory system. The nerve itself becomes an integral and inseparable part of a low-energy circuit that creates its oscillatory blocking waveform. That is, our invention uses the nerve itself to make an oscillatory system, rather than making a separate high-energy-consuming oscillatory system to drive the nerve as in all prior work. We can thus aim to achieve energy efficiency set by the fundamental limits of physics of reactive nerve impedance, the best that is possible in any design. 
         [0009]    Some embodiments of our invention use gyrated-capacitance implementations of inductors with active transconductors rather than passive inductors to create a more compact implementation. Those of ordinary skill in the art will appreciate that other active transconductor-capacitor circuits as are well known in low-power circuit design can provide alternative energy-efficient active implementations as well. Adaptive versions of our embodiments sense action potentials in the nerve to alter the parameters or topology of our nerve stimulator to offer maximal energy efficiency and to ensure operation at resonance. 
         [0010]    These and still other advantages of the invention will be apparent from the detailed description and drawings. What follows is merely a description of some preferred embodiments of the present invention. To assess the full scope of the invention the claims should be looked to as these preferred embodiments are not intended to be the only embodiments within the scope of the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  shows the effective nerve impedances seen by a four-electrode bridge-cuff electrode with two cuff electrodes above the nerve, and two cuff electrodes below the nerve at a given blocking frequency of stimulation. 
           [0012]      FIG. 2  shows how an axon nerve fiber can be modeled as a cascade of lumped passive and active distributed circuit elements. 
           [0013]      FIG. 3A  shows a distributed axon nerve fiber with electrical stimulation that launches an action potential at its left end. Blocking stimulation in the center prevents action-potential propagation to the right of the blocking site. 
           [0014]      FIG. 3B  shows that action potentials that arise before blocking is initiated propagate to a distal location to the right of the blocking site. However, action potentials that arise after blocking is initiated do not. 
           [0015]      FIG. 4  shows how the nerve itself can form part of an energy-efficient resonant oscillator in a bridge-cuff blocking stimulator. The inductors recycle and build up the capacitive nerve energy over many cycles causing the capacitive nerve voltage to be a resonantly amplified version of the input drive voltage. 
           [0016]      FIG. 5  shows resonant amplification of the input drive voltage in a bridge-cuff blocking stimulator. 
           [0017]      FIG. 6  shows a bridge-cuff electrode stimulator in cross section along the nerve that has ‘wings’ (marked as 5 in the figure). The insulating wings minimize the probability that current will take an extracellular path between the top and bottom electrodes of the cuff rather than a current path through the nerve. 
           [0018]      FIG. 7  shows a multi-electrode traveling-wave blocking stimulator with inductive energy-recycling and resonant amplification at each electrode site. 
           [0019]      FIG. 8A  shows the stimulation paradigm in a traveling-wave blocking stimulator. When energy is minimized, the timing and intensity of electrical stimulation amongst the electrodes is correlated with the timing of the action potential wave propagating in the nerve. 
           [0020]      FIG. 8B  shows how constructive interference amongst electrodes stimulated with appropriate phase delays can serve to sequentially build up signal strength within an axon. 
           [0021]      FIG. 8C  shows that stimulation voltages can be sequentially lowered in a traveling-wave stimulator without causing the sequential membrane-potential buildup within the nerve to fall, thus saving energy. 
           [0022]      FIG. 9  shows a diagonal traveling-wave stimulation paradigm that helps spread current both laterally and across the nerve to increase the probability that unknown low-threshold sites are targeted by the stimulation but that the overall paradigm is still energy efficient. 
           [0023]      FIG. 10  shows how an active inductance implemented with a capacitance and active transconductors can replace passive inductances in all embodiments. 
           [0024]      FIG. 11  shows a discrete circuit embodiment of an active inductance, which is used to perform resonant amplification on a nerve impedance with a capacitive reactance. 
           [0025]      FIG. 12A  shows resonant amplification in the embodiment of  FIG. 11 . 
           [0026]      FIG. 12B  shows the output stimulation voltage in the embodiment of  FIG. 11 . 
           [0027]      FIG. 13  shows how the resonant frequency of operation of a blocking stimulator can be adapted via a feedback and calibration loop. 
           [0028]      FIG. 14  shows the architecture of a highly-configurable, closed-loop, multi-electrode, resonant blocking system. 
       
    
    
     DETAILED DESCRIPTION 
     The Bridge-Cuff Blocking Stimulator 
       [0029]    The ‘bridge cuff blocking stimulator’, which represents one embodiment of our invention, has two partially circumferential electrodes above the nerve, separated from each other by a small lateral distance as in current blocking stimulators. In addition, it has two partially circumferential electrodes below the nerve in symmetric locations, also separated from each other by the same lateral distance. Unlike a current blocking stimulator, we ensure that the lateral voltage drop across neighboring electrodes either below or above the nerve is always small. Thus, the lateral impedance of approximately 50Ω (estimated from 5V/100 mA measurements in traditional blocking stimulators) always develops little voltage across it and does not dissipate power by design. A feedback loop in a current-stimulation strategy can enforce this adiabatic voltage constraint across two electrodes through various means. In a voltage-stimulation strategy, two electrode voltage drives architected to always have a small differential voltage between them can enforce this constraint more easily. 
         [0030]    To help steer current through the nerve, we intentionally architect larger voltages across vertically separated electrodes by driving these electrodes in an anti-phasic fashion (via current or voltage). If the electrode impedances are designed to be small, as in current high-frequency blocking stimulators, then the impedance across two vertically separated electrodes in the bridge will be dominated by the actual electrical impedance of nerve and the solutions surrounding it. Thus, it can be modelled by an effective R nrv  and C nrv  in series that represent the complex impedance of the fascicles, epineuria, intra and extracellular solutions, nerve-membrane capacitance and other components, for example, as described in A. R. Kent and W. M. Grill, “Model-based analysis and design of nerve cuff electrodes for restoring bladder function by selective stimulation of the pudendal nerve”, Journal of Neural Engineering, (3), June 2013. Regardless of the complexity of the actual nerve, or even if electrode impedances are not negligible, at a given amplitude and frequency of oscillation, the overall electrical impedance can still be represented by a Thevenin equivalent of the net reactance and net resistance at this frequency, due to contributions from all sources. The Thevenin equivalent is valid for small deviations around the oscillation amplitude, and described by an effective describing function. Similarly, the lateral ohmic solution resistance between horizontal electrodes either at the top or bottom may be represented by R lat . These impedances are shown in  FIG. 1 . They bridge the top-left (V topL ), top-right (V topR ), bottom-left (V botL ), and bottom-right (V botR ) corners at which the four cuff electrodes are located. 
         [0031]    Driving vertically-separated electrodes anti-phasically helps steer the stimulation current through the nerve and, as a result, through the axons inside the nerve:  FIG. 2  shows a standard Hodgkin-Huxley model of the axon; the cylindrical-shaped axon is divided into small compartments, each one with a length of Δx. If Δx is sufficiently small, we can represent each compartment using a lumped circuit model. We can then model each compartment with two half membranes: the top membrane and the bottom membrane, each one having a separate membrane potential (V mt  and V mb ) to control the dynamics of its ion channels. The circuit model of each compartment is shown in on the bottom right of  FIG. 2 ; C mt  and C mb  represent the membrane capacitances of the top and bottom half membranes, respectively; I i,nt  and I i,nb  are the voltage-controlled current sources that represent the effective total ionic currents that flow out of the compartment through the top and bottom half membranes, respectively. I i,nt  is controlled by the top membrane&#39;s potential V mt  while I i,nb  is controlled by the bottom membrane&#39;s potential V mb . Each axon compartment is coupled to the adjacent compartments with the resistance R a /2 where R a  is the total longitudinal resistance of the compartment due to intracellular fluid inside the axon. 
         [0032]    To emulate the blocking mechanism seen in nerves, we chain  410  axon compartments together to form a long axon as shown in  FIG. 3A . In this model, we terminate the two ends of the axon with R T , which is equal to the input resistance into an infinitely-long axon with the same diameter. With Δx=100 μm, the total length of our axon is 4.1 cm. We then stimulate one end of the axon with the pulse source V gen  to generate spikes that propagate through the axon. A high-frequency sinusoidal blocking waveform is differentially applied across V top  and V bot  nodes on the compartments n 201  to n 210 -these compartments are 2 cm away from the origin of the spikes as in many typical research or clinical applications. Our simulations show that, for an axon with a diameter of 50 μm, we only require |V top -V bot |≈200 mV pp  to make the latter compartments refractory and to thus block the action potential propagation in the axon; the stimulation waveform is a 20-kHz sinusoidal voltage.  FIG. 3B  shows the intracellular potentials in the n 150  and n 300  compartments. The blocking stimulation waveform is applied at t=25 ms. Before the blocking stimulation is applied, spikes from n 150  reach n 300  in an unblocked fashion. However, once the blocking stimulation is applied, spikes from the n 150  compartment can no longer reach the n 300  compartment, indicating that the axon is blocked at the stimulation site. 
         [0033]    One key to being energy efficient in blocking stimulation is to develop this axonal excitation with as little stimulation voltage as possible.  FIG. 4  shows how we can achieve resonant amplification and energy recycling within a bridge cuff: Inductors L ind    1  resonate with C nrv    2  in each vertical series resonance circuit, driven by anti-phasic voltage sources V topL  and V botL  and V topR  and V botR  respectively. The lateral voltages |V topL -V topR | and |V botL -V botR | are always maintained to have a relatively small magnitude. The inductive energy recycling of capacitive energy and vice versa over many cycles of stimulation can amplify the voltage drop across C nrv    2  to be significantly higher than that across R nrv    3 , thus enabling blocking via refractory nerve stimulation more easily. Indeed,  FIG. 5  shows even 100 mV voltages on all four bridge cuff electrodes can amplify the effective voltage across C nrv  by about a factor of 10 compared with that across R nrv  to create a 1 V amplitude. To do so, L ind    1  and the frequency of stimulation are appropriately chosen. Furthermore, we always maintain a low lateral voltage drop across the ohmic solution resistance R lat  (top and bottom traces are nearly identical w.r.t. corresponding voltages). 
         [0034]    With this embodiment of the invention, by forcing the voltage drop across R lat  to be small through the amplitude and timing control of the stimulation voltages, a value of R nrv  of 1 kΩ already saves 20× power over a conventional two-electrode blocking cuff. In addition, it can save about 10× power via resonant effects: a 100 mV stimulation yields 1 V reactive excitation across C nrv  that would otherwise need 10× larger voltages in the conventional scheme. Thus, an overall savings of 200× in power may be achievable. 
         [0000]    A Bridge Cuff with Insulating Wings 
         [0035]      FIGS. 4 and 5  indicate that we want the effective R nrv  across vertical cuff electrodes to be small to get maximum resonant amplification and low loss. There is not much that we can do w.r.t. resistance within the nerve except for attempting to get multi-electrode arrays closer to regions of interest; furthermore, the small distance between the top and bottom cuff vertical electrodes minimizes this resistance anyway. However, we may want to minimize ohmic shunting loss through extracellular solution outside the nerve between top and bottom electrodes.  FIG. 6  shows a mechanical topology in one embodiment in cross section along the nerve that helps in this regard: Mechanical wings  5  that extend the grey insulating substrate on which the black metallic electrodes normally reside and a small electrode-to-nerve distance  6  lengthen shunting paths outside the nerve between vertical cuff electrodes compared to paths within the nerve, thus reducing their contribution to R nrv . 
       Traveling-Wave Multi-Electrode Stimulation 
       [0036]    Nerve conduction block from high-frequency stimulation occurs from the modulation of the axon&#39;s membrane potential, which alters the dynamics of the voltage-gated ion channels on the membrane and prevents the propagation of the action potentials. In myelinated axons, ion channels are clustered at the nodes of Ranvier (NRV)-gaps in the myelin sheath that play important roles in speeding up the action potential propagation—whose internode distance can be quite large (sometimes up to 1.5 mm). One important question arises regarding our proposed vertical driving scheme using the bridge cuff electrodes: How do we surgically place the top and bottom cuff electrodes right on top of a NRV such that the ion channels underneath are directly modulated? Due to the random nature of NRV&#39;s internode distance, it is likely that the placed cuff electrodes may miss the NRV, reducing the effectiveness of the stimulation, especially when the electrodes are placed very close to the nerve to minimize R nrv . Conventional blocking schemes avoid the issue by directing a very large stimulation current along the lateral distance of the nerve, thus increasing the probability that some small fraction of the stimulation current may get to the ion channels located between the two lateral electrodes. As we have discussed, this conventional scheme incurs high power dissipation due to high ohmic loss. 
         [0037]    The embodiment disclosed in  FIG. 7 , termed “Traveling-wave multi-electrode stimulation”, aims to maximize the effectiveness of stimulation while avoiding high ohmic loss. The scheme enables one to maximize the amplitude of the membrane potentials along the lateral distance of the axon with low overall stimulation power. In  FIG. 7 , if we stimulate the E 1t -E 1b  electrode pair  11 , the amplitude of the membrane potential of the axons right under the E 1t -E 1b  pair  11  is maximized but decays exponentially along the lateral distance of the axon. We may consider the membrane potential as a wave that propagates along the axonal cable. Being lowpass in nature, the axonal cable attenuates the membrane potential wave as it moves away from the origin, thus reducing the effect of stimulation on the ion channels away from the stimulation site. However, at optimal distances along the nerve away from the E 1t -E 1b  electrode pair, if we place other pairs of electrodes (E 2t -E 2b , . . . , E nt -E Nb    12 ) and stimulate them anti-phasically with the right timing V diff2 , . . . , V diffN    13  introducing proper phase delays with respect to V diff1    14 —we can create constructive interference with the membrane potential wave that travels from the E 1t -E 1b  pair  11 . Thus, with lower stimulation levels (and lower power consumption) compared to that applied to the E 1t -E 1b  pair  11 , the other electrode pairs  12  may still elicit the same membrane potential amplitude in the axons underneath them, increasing the probability of modulating ion channels along the lateral distance of the axons. 
         [0038]      FIG. 8A  illustrates the key features of this embodiment in more detail. We applied stimulation voltages at the top membranes of the compartments n 25  to n 28  and recorded their bottom membrane potentials.  FIG. 8B  shows the result when we set V t25 -V t28  to have the same amplitude while we chose their phases such that the stimulation voltage from each source is synchronized with the membrane potential wave that is propagating through the axon. Notice that the compartments further along the axon have their membrane potentials built up w.r.t their preceding compartments.  FIG. 8C  shows the result when we progressively decreased the amplitudes of V t25 -V t28  but kept their phases synchronized with the propagating membrane potential wave; the top window shows the stimulation voltages on the n 25 -n 28  compartments while the bottom window shows the potentials on their bottom membranes. Compared to the preceding compartments, the further compartments—with lower stimulation voltages on them—still exhibit similar levels of axonal excitation, thanks to the membrane potential wave that propagates from preceding compartments. Thus, with proper amplitude and timing control, the traveling-wave multi-electrode stimulation scheme allows us to excite a larger patch of axon, to increase the probability of blocking, with a low overall stimulation power. 
       Diagonal-Bridge Traveling-Wave Multi-Electrode Stimulation 
       [0039]    To further increase the probability of blocking the action potential propagation in the nerve, we can extend the traveling-wave stimulation concept by exploiting the mechanical configurations of cuff electrodes on the nerve. The embodiment disclosed in  FIG. 9 , termed the diagonal-bridge traveling-wave multi-electrode stimulation, aims to maximize the effectiveness of the stimulation while avoiding high ohmic loss encountered in conventional schemes. Presented in  FIG. 9  with only six electrodes without loss of generality, this diagonal-bridge stimulation scheme can be generalized to a higher number of electrodes to cover a larger patch of the nerve. Instead of applying anti-phasic stimulation waveforms across the vertically-separated electrodes as discussed in the original bridge-cuff stimulation of  FIG. 4 , we apply stimulation voltages ‘diagonally’: the E 1top -E 2bot  electrode pair  7  is stimulated differentially with the voltage source V diff1    8  while the E 2top -E 3bot  pair  9  is stimulated differentially with the voltage source V diff2    10 . The stimulation current between each electrode pair is thus steered diagonally through the nerve, instead of laterally through the solution resistance, increasing the probability of modulating the ion channels of axons to elicit blocking. If the phase difference between V diff1    8  and V diff2    10  are controlled with sufficient resolution to keep the voltage differences between the top electrodes and between the bottom electrodes small, ohmic loss in the lateral solution resistance is minimized. In addition, if the phases of the stimulation voltage sources further along the nerve are synchronized with the membrane potential wave propagating along the axon, we can achieve the same traveling-wave amplification effect as discussed in the traveling-wave embodiment in the previous section. 
       Voltage Driver Design 
       [0040]    A classic Class-E RF amplifier can be designed such that the transistor switches architect square-wave drives that are filtered by the resonant circuits. The switching is timed carefully to ensure that it always occurs when there is either zero voltage or zero current across the transistor thus minimizing loss. Such amplifiers can be nearly 100% efficient. An adaptive circuit described in M. Baker and R. Sarpeshkar, “Feedback Analysis and Design of RF Power Links for Low-Power Bionic Systems,” Invited Paper,  IEEE Transactions of Biomedical Circuits and Systems , Vol. 1, No. 1, pp. 28-38, April 2007 also ensures that the timing of the circuit adapts to changing load conditions preserving efficiency via pulsatile and clocked inputs. Thus, if we can record and decode from action potentials while stimulating, we can architect energy-efficient, adaptive, closed-loop stimulators including partial blocking. The use of clocks with phase delays allows digitally programmable control in actual experimental settings for bridge, traveling-wave, and other embodiments. 
       Multi-Electrode Resonant Stimulation Using Active Inductance 
       [0041]    The use of passive inductors in our proposed resonant stimulation schemes enables energy recycling, shuttling energy back and forth between the capacitive and inductive forms. However, if the nerve presents a small capacitive loading to the electrode, the required passive inductance to achieve resonance at our targeted frequency (1 kHz-100 kHz) sometimes does not allow for a small-form-factor implementation. 
         [0042]    One popular technique to realize a large effective inductance is to electrically gyrate a capacitance using low-power operational transconductance amplifiers (OTA) to realize an active inductor. This technique is very attractive for low-power integrated circuit implementations as the entire stimulation circuitry can be integrated onto a single miniature chip. A fully-differential resonant stimulation circuit using an active inductor is shown in  FIG. 10  to illustrate this embodiment. The active inductance  15  is realized by the G m1    16 , G m2    17  OTAs and the two capacitors C ind &#39;s  18 . This effective inductance appears in parallel with the nerve which can be modeled as a parallel R p -C p  network  19  using a standard series-to-parallel conversion of the effective nerve impedance. The local oscillator LO  20  generates a reference sinusoidal waveform from which the G m0  OTA  21  converts into current to drive the RLC network. At the resonance frequency, the active inductance resonates with C p  leaving only R p  as the load of the G m0  OTA. The voltage across the nerve thus depends on the amplitude of the G m0  OTA&#39;s output current and the value of R p , which can be made efficient via our cuff electrode design. Note that the LO  20  used in this scheme just provides amplitude and timing references for the stimulation voltage and does not drive the load directly. Due to the low frequency of the stimulation voltage relative to today&#39;s standards, the LO can be implemented in modern IC technologies with negligible power consumption compared to the stimulation power. For example, in  FIG. 9 , the LO is implemented with a direct digital synthesizer (DDS), a digital-to-analog converter (DAC), and a lowpass filter (LPF)  22  to provide very accurate amplitude and timing controls. As will be discussed below, the high-Q nature of the system and the inherent properties of the OTAs used for realizing the active inductor provide several benefits for the design of low-power multi-electrode blocking stimulation systems:
       i) The active inductor helps resonantly amplify the stimulation voltage on the nerve, thus making it more likely to induce the nerve conduction block from a high-frequency current stimulator. With the active inductor absent, the nerve behaves as a parallel RC circuit and acts as a lowpass filter for stimulation currents, reducing stimulation effectiveness at high frequencies.   ii) It has been shown that a sinusoidal waveform is often more effective at inducing nerve conduction block. The active inductor makes the stimulator a narrowband circuit. If the ohmic loss in the electrode-nerve network is low through the careful electrode design, we can make the stimulator a very “high-Q” system. As a result, we can achieve a relatively pure sinusoidal stimulation waveform on the nerve from a “dirty” reference waveform of the LO  20  and let the high-Q stimulator filter out the unwanted harmonics. The DDS in the LO can be designed with a small memory while the DAC can be designed with low resolution and modest linearity, thus reducing the complexity and the overall power consumption of the LO.   iii) With a fixed bias current in each OTA, the stimulator is current limited, thus providing an automatic safety feature in the case of electrode shorting.       
 
         [0046]      FIG. 11  shows an example discrete implementation of our active-inductor embodiment. The nerve  19  at the blocking frequency is represented by an equivalent impedance of 400-pF capacitance in parallel with a 50-kΩ resistance (a series impedance equivalent can also be used). All the OTAs are implemented with Bipolar Junction Transistors (BJT) from Analog Devices, Inc. (MAT14ARZ for NPN and SSM2220 for PNP). The bias currents I B0    23 , I B1    24 , and I B2    25  are 20 μA and the capacitance C ind    26  is 200 pF. The transconductance values of G m0    21 , G m1    16 , and G m2    17  OTAs are controlled by the degeneration resistances, R 0    27 , R 1    28 , and R 2    29 , respectively, all with a value of 15 kΩ in this design. The capacitance C c    30  is added in parallel with R 2    29  to stabilize the overall feedback loop. Only the current of G m2  OTA  17  needs to be sufficiently high to provide the stimulation current to the nerve. Since they are well known to those of ordinary skill in the art, Common-mode-feedback (CMFB) circuits are not shown in  FIG. 11  to avoid clutter. 
         [0047]      FIG. 12A  shows the magnitude response from V LO    31  to V stim    32 . A sharp peak in the response at the resonance frequency of f c =34.5 kHz is evident.  FIG. 12B  shows a differential voltage on V stim  whose amplitude is 466 mV pp . Due to the high-Q (high quality factor) nature of the resonant stimulator, V stim  exhibits very little harmonic distortion. In cases where a larger V stim  is needed, we can achieve a larger amplitude of V stim  simply by increasing the input linear range of the G m1    16  OTA with well-known linearization techniques. 
         [0048]    Active implementations of resonant blocking systems are not limited to the example embodiment that uses an active inductor, which is implemented with a gyrated capacitance and active transconductors as in  FIG. 10 . For example, other highly energy-efficient active transconductor-capacitor filter topologies that can achieve sharp resonances with large linear range in subthreshold circuit technology are explained in chapter 13 of R. Sarpeshkar, “Ultra Low Power Biolectronics: Fundamentals, Biomedical Applications, and Bio-inspired Systems”, Cambridge University Press, 2010. 
       A Closed-Loop Architecture for Resonant Frequency Configuration 
       [0049]    The proposed resonant stimulator is a high-Q system which raises an important question: how do we stimulate right at the resonant frequency for the maximum blocking effectiveness? The nerve represents an unknown load to the stimulator, thus making it difficult to determine the resonant frequency of the system apriori. The embodiment of  FIG. 13  reveals how we may detect the resonant frequency and configure the stimulator to operate at the optimum point for the blocking effectiveness and power consumption. 
         [0050]    The architecture consists of an LO  33  and the resonant stimulator similar to the one in  FIG. 10 . We then add the calibration circuitry which consists of a mixer  35 , a lowpass filter  36 , a low-resolution/low-speed analog-to-digital converter (ADC)  37  and a digital control unit (DCU)  38 . During calibration, the mixer  35  multiplies together the LO&#39;s reference waveform V LO    39  and the stimulation waveform V stim    40  to produce the signal V o,mix    41 . At resonance, V stim    40  has the maximum amplitude and is in phase with V LO    39 , thus producing the largest low-frequency component on V o,mix    41 . The lowpass filter then extracts this low-frequency component (V res    42 ) and passes it, through the ADC  37 , to the DCU  38 . The DCU  38  then performs a search algorithm to find the optimum setting for the reference frequency of the LO and the resonant frequency of the stimulator—through setting the value of the freq_set bus  43  and the value of res_set bus  44 —such that the closed-loop system produces the maximum value of V res    42 . Assuming that the condition of the load changes slowly, we can heavily duty cycle the calibration (i.e., turning the calibration circuitry off when not in use): for instance, if the calibration is needed once every 10 seconds and each calibration takes approximately 10 ms, the duty-cycle ratio is only 1:1000, making the power required for the calibration circuit negligible compared to the actual stimulation power. In addition, for multi-electrode stimulation which consists of many nerve stimulators, the extra circuitry required for calibration (e.g. mixer, LPF, ADC, and DCU) can be time shared among all the stimulators, incurring only small area overhead per stimulator. 
       Highly-Configurable Closed-Loop Multi-Electrode Resonant Blocking System 
       [0051]    To efficiently block action potential propagation in practical medical devices, we need to optimize several parameters of the stimulation system such as the characteristics of the stimulation waveforms (e.g. amplitudes, phases, and frequencies) and the stimulation schemes (e.g., traveling-wave, diagonal-bridge traveling-wave). Therefore, an efficient blocking stimulator should be highly-configurable with the ability to calibrate itself for an optimum stimulation setting in terms of blocking effectiveness and power consumption. Towards this aim,  FIG. 14  shows a highly-configurable closed-loop multi-electrode resonant blocking stimulation system. The system consists of three sets of electrodes—the Action Potential Generating Electrode (APGE)  45 , the Blocking Electrodes (BE)  46 , and the Recording Electrode (RE)  47 )—the LO bank  48 , the stimulator bank  49 , the switch matrix  50 , and the calibration circuitry  51 . The main function of the switch matrix  50  is to determine the connection between each stimulator and a pair of electrodes. With proper network design, the switch matrix allows the system to be configured as either a conventional bridge-cuff stimulator, a traveling-wave stimulator, or a diagonal-bridge traveling-wave stimulator—the choice of which is determined by the blocking effectiveness and power consumption. 
         [0052]    During calibration, the stimulator Stim_0  51  stimulates the nerve through the APGE  45  and causes action potentials to propagate along the nerve. At the same time, the stimulators Stim_1-Stim_N  58  stimulate the nerve through the BE to block the action potential propagation. Located at a sufficient distance away from the BE  46  to minimize stimulation artifacts, the RE  47  records, via the nerve amplifier  52  and the ADC  53 , action potentials that propagate from the APGE  45 . The ADC  53  then digitizes the output of the nerve amplifier and identifies the presence of action potentials to the digital control unit (DCU)  54 . The DCU  54  then applies a search algorithm to find the optimum setting of the stimulation system; it sets the characteristics of the waveforms via the LO_set bus  55 , sets the drive strengths and resonant frequencies of the stimulators via the stim_set bus  56 , and sets the electrode configurations via the elec_set bus  57  that controls the switch matrix  50 , to identify the setting at which the action potential propagation is blocked with minimum power consumption. 
         [0053]    Since conduction velocities of action potentials vary between nerve fibers of different diameters and amongst fascicles within larger nerves, the timing and intensity of traveling-wave stimulation can be adapted to block only certain desired fibers or at least lower the threshold for such blocking. Thus, our closed-loop multi-electrode systems can be not only energy efficient but also selective in targeting particular nerves, an important feature in many medical indications. 
       Embodiments of the Invention that Use Electromechanical Devices Such as Piezo-Electrets 
       [0054]    The innovations disclosed here can be generalized to other embodiments: For example, the inductor disclosed in our embodiments can be replaced with a piezo-electret, thus recycling nerve capacitive energy via mechanical energy and vice versa. Piezoelectrets are well-known devices to those in the art and form the basis for many energy-efficient quartz crystal oscillators. For example, they are described in Hillenbrand, J. and Sessler, G. M., “Piezoelectricity in cellular electret films,” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 7, No. 4, pp. 537-542, August 2000. 
         [0055]    Piezo-electrets may also be used to electrically actuate electrodes in synchrony with the stimulation such that either or both fluid flow and distance to the nerve are also oscillatory, further maximizing the chance that current flows into the nerve: Electrodes nearer to the nerve are more likely to send current into it; pushing fluid into the nerve while pulling it out elsewhere can dynamically modulate extra-cellular ohmic solution resistance in an advantageous configuration such that current is steered across the nerve rather than alongside it. 
         [0056]    The mechanical, circuit, and stimulation strategies that we have disclosed serve to reduce power and energy dissipation for nerve-blocking stimulators in synergistic circuits and architectures.