Nerve cuff electrodes represent a less invasive alternative to penetrating array electrodes. Individual neurons in peripheral nerves are separated into fascicles, ...
EXTRACTING COMMAND SIGNALS FROM PERIPHERAL NERVE RECORDINGS
by BRIAN WODLINGER
Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy
Thesis Adviser: Dr. Dominique M. Durand
Department of Biomedical Engineering CASE WESTERN RESERVE UNIVERSITY
January, 2011
Committee Signature sheet (typed version)-originals turned in with Final Materials
ii
To my family, friends, and colleagues
iii
Table of Contents List of Figures ..................................................................................................................... v List of Tables ..................................................................................................................... vi List of Abbreviations ........................................................................................................ vii Abstract ............................................................................................................................ viii Chapter I: Introduction ........................................................................................................ 1 Background ..................................................................................................................... 1 Methods of separating signals ......................................................................................... 6 Beamforming Algorithms to Recover Signals from Nerve Cuff Electrodes .................. 9 Chapter II: Modeling Studies ............................................................................................ 13 Abstract ......................................................................................................................... 13 Introduction ................................................................................................................... 14 Method .......................................................................................................................... 16 Results ........................................................................................................................... 22 Discussion ..................................................................................................................... 33 Conclusions ................................................................................................................... 37 Chapter III: High Density Recording Nerve Cuff Electrode Design ................................ 38 Abstract ......................................................................................................................... 38 Introduction ................................................................................................................... 39 Methods ......................................................................................................................... 43 Results ........................................................................................................................... 46 Discussion ..................................................................................................................... 50 Conclusion ..................................................................................................................... 52 Chapter IV: Separation of Individual Branch Signals in an Acute In Vivo Peripheral Nerve Cuff Recording ....................................................................................................... 53 Abstract ......................................................................................................................... 53 Introduction ................................................................................................................... 54 Methods ......................................................................................................................... 56 Results ........................................................................................................................... 64 Discussion ..................................................................................................................... 79 Conclusion ..................................................................................................................... 83 Chapter V: Conclusions and Future Work ........................................................................ 85 Evaluation of the Beamforming Algorithm .................................................................. 85 Electrode Fabrication .................................................................................................... 86
iv In Vivo Experiments ..................................................................................................... 87 Summary ....................................................................................................................... 89 Future Work .................................................................................................................. 91 Appendix A - Extensions to the Beamforming Algorithm ............................................... 93 Introduction ................................................................................................................... 93 Accounting for Baseline Noise Level ........................................................................... 93 Optimal Filter Selection ................................................................................................ 94 Minimum Variance Beamforming ................................................................................ 95 CHAMPAGNE.............................................................................................................. 96 Summary ....................................................................................................................... 96 Appendix B - Reversible Block of Pain Fibers ................................................................. 98 Abstract ......................................................................................................................... 98 Introduction ................................................................................................................... 99 Methods ....................................................................................................................... 101 Results ......................................................................................................................... 105 Discussion ................................................................................................................... 109 Conclusions ................................................................................................................. 109 Appendix C – Mechanisms of Desynchronized Stimulation .......................................... 111 Appendix D - Alternate High Contact-Density Electrode Fabrication Techniques ....... 113 References ....................................................................................................................... 119
v List of Figures Figure 1. Finite element models to test and train the beamforming algorithm. ................ 17 Figure 2. Creating Simulated Recordings. ........................................................................ 21 Figure 3. Localization Using Realistic Signals. ................................................................ 23 Figure 4. Paired Localization Accuracy............................................................................ 26 Figure 5. Separating Signals from Pairs of Simultaneous Active Fascicles ..................... 28 Figure 6. Separating Signals from Multiple Simultaneous Active Fascicles.................... 30 Figure 7. Functional Recovery Without True Source Locations ...................................... 33 Figure 8. Hot-Knife Fabrication Technique...................................................................... 44 Figure 9. Recording System for High Contact Density Nerve Cuff Electrodes ............... 45 Figure 10. Signals Recorded by High Density FINE. ....................................................... 48 Figure 11. Finished High Contact-Density Electrode. ...................................................... 49 Figure 12. Schematic of the experimental setup ............................................................... 57 Figure 13. The model used to generate the Transformation Matrix. ................................ 60 Figure 14. Examples of source localization in three sciatic rabbit nerves ........................ 61 Figure 15. 130Hz Sinusoidal stimulation produces CAP-like neural responses .............. 65 Figure 16. Generating Pseudo-spontaneous activity. ........................................................ 67 Figure 17. Separation of Peroneal and Tibial components from combined signal ........... 69 Figure 18. Cross-correlation of the recovered single-branch signals ............................... 71 Figure 19. Classification Accuracy for a simple 2-class system ...................................... 75 Figure 20. Box plot of estimated activity in Tibial and Peroneal ..................................... 77 Figure 21. Overlapping stimulation of the Peroneal and Tibial branches. ....................... 78 Figure 22. Experimental Setup and Reflex Path. ............................................................ 103 Figure 23. Effect of Pain on Sural-Gastrocnemius Reflex.. ........................................... 106 Figure 24. Effect of Blocking Stimulation ...................................................................... 107 Figure 25. Summary of Block Effectiveness. ................................................................. 108 Figure 26. Stochastic Axon Simulation Results ............................................................. 112 Figure 27. Schematic of electrode showing the laser-cut pattern .................................. 114 Figure 28. Laser-based Electrode Fabrication Method. .................................................. 115 Figure 29. Finished Laser-cut electrode.......................................................................... 117
vi List of Tables Table 1. Parameters Used In FEM Simulations ................................................................ 17 Table 2. Summary Of Localization Error ......................................................................... 24 Table 3. Fascicular Groupings for Functional Test .......................................................... 31 Table 4. Hot-Knife Fabrication Technique Results .......................................................... 48 Table 5. Summary Of Large Signal Recovery Accuracy ................................................. 73
vii
List of Abbreviations CAP – Compound Action Potential FEM – Finite Element Model FES – Functional Electrical Stimulation FINE – Flat Interface Nerve Electrode USEA – Utah Slanted Electrode Array SNR – Signal to Noise Ratio LIFE – Longitudinal Intrafascicular Electrode
viii Extracting Command Signals from Peripheral Nerve Recordings
Abstract by BRIAN WODLINGER
Despite great advances in many areas of medical technology over the past 20 years, the challenge of providing amputees a prosthesis with the intuitive control and functionality of a natural limb remains. Improvements in materials have made them lighter and stronger, but little headway has been made in giving amputees more functionality and easier control.
Recently, this problem has been addressed on a number of fronts,
including electrical control from the muscles of the residual limb, or techniques involving multi-contact neural interfaces and muscular reinnervation.
While these techniques
represent important future directions for the field, they have not been shown to provide the robust and intuitive control signals required to take full advantage of a dexterous hand prosthesis. Nerve cuff electrodes represent a less invasive alternative to penetrating array electrodes. Individual neurons in peripheral nerves are separated into fascicles, which are loosely spatially organized based on the location they innervate. This thesis leverages the spatial organization in order to separate and recover fascicular signals. Simulations of a human femoral nerve finite element model were used to validate the approach, and demonstrate source localization to 180±170μm.
The electrode and recording system built to
ix implement in vivo experiments provided a 2μVrms noise floor on 16-channels, allowing the reconstruction accuracy to be measured at R2=0.81±0.08 for large synchronized neural responses in an in-vivo rabbit sciatic nerve model. Smaller, pseudo-spontaneous signals generated with high-frequency sinusoidal stimulation were separated with crosstalk of 23±13%, and found to transmit 4±2 bits-per-second-per-source.
These
recovered fascicular sources correlate to individual muscle activities (even if the muscles have been amputated) and their activity may be used to drive corresponding motors in a limb prosthesis. Beyond prosthetic limbs, this same technique is applicable for recording and localizing sources within any large nerve trunk and may be useful for many other artificial sensors and organs.
Chapter I:
Introduction Background The main goal of prosthetics is to give amputees more functionality and easier control over their environment. In order to accomplish this, it is necessary to provide them with artificial limbs that have the same number of degrees of freedom as the physiological limbs they are replacing. This high number of degrees of freedom has so far been difficult to achieve, limiting the utility of modern dexterous prostheses. Interfacing with the nervous system provides the opportunity to sense movement intention directly, allowing the user natural, volitional control of the device. Recently, several techniques have been investigated to achieve this goal including electrical control from the muscles [6] or nerves [7, 8] of the residual limb, surgically reattaching severed nerves to new muscular endpoints [9], and attempting to decode intent directly from the brain using everything from electroencephalograms recorded from the surface of the scalp [10] to single unit activity recorded by penetrating cortical arrays [11, 12]. In general, it is necessary to consider two tradeoffs when approaching problems that require interfacing with the nervous system: the tradeoff between a central and peripheral interface, and the tradeoff between the invasiveness of the approach and the quality of the signals recorded [13].
In this thesis, reliability of the interface for future clinical
implementation was of primary importance, which led to the use of a Flat Interface Nerve cuff technique [14] in order to preserve all neural membranes. This choice implies a
2 potential loss of signal quality, since the recording sites are placed around the nerve, relatively far from the neural sources. A high contact density electrode was selected to obtain the neural signals from both the superior and inferior surfaces of the nerve. This high contact density allowed a beamforming algorithm to be applied in order to separate the individual fascicular signals mixed within the cuff. Since each group of fascicular signals corresponds to a particular muscle or muscle group, these recovered signals should in principle be able to control a prosthesis. The tradeoffs implicit in this approach will be discussed at a more general level first, along with a summary of previous work on the problem, as background for the approach taken. Central vs. Peripheral Interfaces As one moves closer to the source of the movement intention (from muscle, through lower motor neurons, to spinal cord and then motor cortex), the signals become increasingly difficult to decode and the pathways shared between many competing signals. This implies that if we are interested only in a muscle command signal it is more difficult to try to find it in the brain, where signals may instead correspond to more abstract concepts like absolute position in space and could be spread over a large population of cells [15].
However, restricting techniques to electromyography, or
peripheral nerve recording requires the peripheral nerves and CNS, respectively, to be intact, limiting the range of conditions a system is able to treat. This is an important consideration because in many cases, such as spinal cord injury, much of the peripheral nervous system cannot be used as a source of control signals. The case of prosthetic limbs for amputees is very different from other disorders involving damage to the central nervous system, like spinal cord injury, in terms of the level of impairment and amount of
3 dexterity required to improve quality of life. In order to improve current prosthetic limbs, amputees require a limb with significantly more dexterity than the 2 or 3 very slow degrees of freedom demonstrated so far by devices controlled by interfacing directly with the central nervous system [16]. Therefore, the scope of this thesis was restricted to recording from the peripheral nervous system. Invasiveness vs. Signal Quality The peripheral nervous system is protected by successive layers of membranes, from the perineurium which constitutes the blood-nerve barrier and binds nervous tissue together all the way to the skin which protects the entire body. As successive membranes are compromised, the likelihood of damage or care which must be taken to prevent damage increases.
The nature of the recorded signal also varies with the proximity of the
electrode to the neural source; an individual unit’s spiking activity is available only within several hundred microns of that unit’s nodes of Ranvier. This spiking activity is the raw format of information transmission in the nervous system and so, if properly decoded over a population, may contain a complete account of the transmitted signals. As the recording device is moved further from the neural sources only activity from an increasingly large group of cells is received: the local field potential. Signals from within this group are added with destructive interference, causing a loss of information. The power of the signal also declines with distance, requiring a larger number of cells to fire synchronously to maintain the same signal to noise ratio. In the case of motor control for amputees, for which the interface discussed in this work is designed, it is sufficient to know which muscles are active and approximately how strongly. It is not necessary to decode detailed information regarding precisely which motor units are recruited, or even
4 which types of motor units. In light of this resolution requirement, recording electrodes should be placed as close to the neural tissue as possible, without compromising any of the membranes directly protecting it. Nerve cuff electrodes provide such an interface with the nerve since they are wrapped around the nerve and record neural signals with contacts positioned close to the surface of the epineurium. Previous Art Having limited the scope of this work to non-penetrating electrodes in the peripheral nervous system, previous attempts to use these signals to reconstruct motor commands are reviewed. An interesting approach that has recently been tested in human subjects is Targeted Muscular Reinnervation (TMR) [9]. This technique involves surgically connecting the nerves of the amputated arm (brachial plexus) to various locations on the pectoral muscle in the chest. The original innervations of this muscle are cut and ligated to prevent the original motor signals from interfering with the desired volitional signals from the brachial plexus. This approach is interesting for two reasons – first, the natural amplifier provided by the muscles makes the signal to noise ratio higher than for direct nerve recording. Second, the patient may retain some feeling in the phantom limb that can be stimulated by touching the reinnervated area. This sensation recovery is the next logical step after motor recovery in prosthetics and no other approach has been able to mimic it. Unfortunately, the various volitional signals generated in the pectoral muscle still undergo significant mixing in the volume conductor between the muscle and the skin surface. This problem, combined with inconsistent and unpredictable innervation by
5 different functional groups has prevented the technique from having a wide clinical impact. Nerve cuff recordings are a much less surgically demanding way to record these signals, although the low signal-level requires amplifiers with low input noise levels (below 2µVrms) and high common mode rejection ratio to account for the high offset voltages found at low frequency. [17] used cuff electrodes to record from individual branches of the sciatic nerve in Rabbit, bypassing the need for separation and showed that a neurofuzzy decoding system was able to predict ankle angle from the sensory nerve responses during passive ankle movement. This demonstrates the utility of functionally distinct whole nerve recordings.
Unfortunately, many of these single-function branches are
missing in amputees, requiring recordings on nerve trunks often carrying opposing signals. The same group [18] has recently implanted a human amputee with thin-film Longitudinal Intrafascicular Electrodes (penetrating arrays) and shown up to 85% correct classification of 3 grip patterns. Another approach to recover nerve signals within cuff electrodes is blind source separation. [8] used simulation results from a multi-contact FINE cuff of a single nerve trunk in order to recover fascicular signals. The results showed promising signal separation with R2>0.9 for very high signal-to-noise ratio, which declined quickly with noise level, required extra computation to solve the permutation ambiguity and was sensitive to the statistical independence of the signals. These examples demonstrate both the utility of these signals, as well as the difficulty in separating signals mixed in the volume conductor of the body. The recorded signals are
6 generally linear combinations of signals related to various muscle groups or degrees of freedom. These signals must be separated, or demixed, before they can be used to control a prosthesis. The BSS technique presented above is one of several techniques in the literature which are discussed below.
Methods of separating signals Signal separation algorithms fall into four main categories: Inverse Problems (IP), Blind Source Separation (BSS) and Beamforming/Spatial Filtering (BF). These techniques are each reviewed below. Inverse problem solutions (IP) These algorithms require a mathematically rigorous (although likely approximate) model of the relationship between the potential signal sources and the measured outputs. This model is generally linearized and its input-output function inverted to map a given recording to the level of activity at each source. This inversion is often slow and may not be suitable for real time processing; however the results are often very precise and provide good resolution.
Solutions may be constructed iteratively (for example,
FOCUSS [19]) and may incorporate various advanced methods such as expectationmaximization, or Bayesian statistics. In general, there may be infinitely many solutions within some arbitrary level of accuracy, and additional information is needed to select the most probable, such as selecting solutions having fewer active sources, or a lower overall power level. IP algorithms have been successfully applied to magnetoencephalography (MEG)-based source localization [20], mapping epicardial potentials from chest surface recordings, and impedance spectroscopy [21].
7 Blind source separation (BSS) The weights with which the source signals are linearly combined in the volume conductor of the body is known as the mixing matrix. When no information (e.g. from known anatomy or conductivity) about this mixing matrix is available a priori, blind source separation methods must be used. These methods attempt to estimate the mixing matrix by maximizing the statistical independence (using any number of metrics) of linear combinations of the recorded signals.
These algorithms make two fundamental
assumptions, first that the original sources are statistically independent, and second that the mixing matrix is linear. In the quasi-static formulation of Maxwell’s electromagnetic laws, which applies specifically to the propagation of neural signals through the body’s volume conductor, the second assumption is reasonable. The first assumption, however, is not generally true when dealing with muscle activation signals due to correlation from muscle synergies. One of the key strengths of these algorithms is that they require no training or model estimation of any kind – which may be extremely useful in biological situations where anatomy and biological response to implants cannot be well modeled. However, BSS algorithms remove absolute amplitude information, reducing the data to relative or normalized signals. This can be a problem when changes in the signal are taking place with a time constant longer than the processing window length. Further, a permutation ambiguity exists between subsequent windows where the sources may be reordered by the algorithm. This permutation ambiguity was discussed in [8] and may be solved at the expense of extra computation by examining the correlations between the subsequent mixing matrices. Blind source separation has been applied to the problem of fascicular signal separation in nerve cuff recordings by [8] and is often combined with
8 other techniques (such as spatial filtering, below) to make them adaptive. See [22] for a complete and rigorous discussion of such adaptive spatial filtering techniques for MEG and EEG. Spatial Filtering or Beamforming Beamforming algorithms are closely related to the inverse problem methods discussed above, but with one important difference: they do not require the same level or accuracy of a priori knowledge in order to perform the model inversion. The model is generally inverted a priori, independent of the recorded signals, to give a set of filter coefficients that map future recordings to an estimate of their spatial origin. This makes spatial filtering methods faster and more robust than IP algorithms, at the expense of precision. Much as traditional frequency filters do in frequency-space, these algorithms can be viewed as an attempt to focus the sensitivity of an antenna array to a specific location in space, leading to the term spatial filters. In the case of nerve cuff electrodes, each recording site on the cuff is treated as an antenna in the array. Also like traditional filters, many trade-offs between pass-band stability, stop-band rejection, and transition-band size can be used to tune the resulting filter to a specific problem. These algorithms may also be combined with BSS techniques to adapt the filter weights depending on the current active sources, compensating for cross-talk and providing more accurate spatial information [22]. In all of the techniques discussed, the differences between signals recorded at each spatially distinct recording site are used to separate signals based on their spatial origins. This makes the distribution of the recording sites a critical design parameter of the nerve cuff electrode. The Flat Interface Nerve cuff Electrode (FINE) [14, 23] is an ideal
9 geometry to use. This design reshapes or maintains the nerve with an elongated crosssection, causing the fascicles to spread within the epineurium. This increases the spacing of the fascicular sources, while at the same time decreasing the distance between the recording sites and the sources. Having a high cross-sectional aspect ratio also ensures some recording sites will be much closer to certain sources than others, providing the necessary differences in spatial pattern for these separation algorithms to distinguish and recover the various signals.
Beamforming Algorithms to Recover Signals from Nerve Cuff Electrodes BSS and IP algorithms have been applied to Nerve cuff electrode signals in the past, however neither has attained clinical utility due to problems with accuracy, training time, and statistical dependence. Moreover, an accurate IP approach may not be possible due to imperfect knowledge of the anatomy, which can change over time due to swelling, immune response, age and weight. For these reasons, spatial filtering was selected as the most promising technique to investigate. Spatial filtering methods are particularly well suited to nerve cuffs because of the spatial separation between functional sources, and small internal area. Simulations described below show that by applying spatial filtering techniques to new high-contact density electrode arrays placed in cuffs around peripheral nerves, we can visualize and separate the activity of each group of neurons within the nerve. These groups correlate to individual muscle activities (even if the muscles have been amputated) and their activity can be used to drive corresponding motors in a prosthesis. Beyond prosthetic limbs, this same technique is applicable for recording from any large nerve trunk and may be useful for many other artificial sensors and organs.
10 This thesis examines the hypothesis that fascicular signals can be recovered from multicontact cuff electrode recordings using beamforming algorithms. This hypothesis was tested with three specific aims. Aim 1: To Develop a Nerve Model and Develop a Beamforming Algorithm The hypothesis was first tested in a computer simulation. First, a model was generated to approximate an implanted FINE on a human nerve trunk based on existing histology. This model was used to generate realistic multi-channel cuff electrode recordings from realistically placed sources and was developed using Finite Element Modeling tools as well as NEURON and MATLAB. A simpler FEM was used to identify the receptive fields of each contact on the recording cuff, in saline and with a rectangular epineurium only (no nerve model). A set of beamformers was derived from this simpler model and applied to data from the more realistic FEM. Simulation experiments were performed to determine whether the algorithm could successfully localize signals from each fascicular group and subsequently separate and reconstruct recordings when multiple groups were simultaneously active. A cross-correlation metric was used to assess the error in the reconstructions. This simulation work is presented in Chapter II. Aim 2: To Design and Build a System for High Contact-Density FINE Recording The setup to test the algorithm developed in the previous aim in vivo required both a new high contact-density FINE, as well as a 16-channel pre-amplifier and multiplexer with very low noise and high input impedance (to account for the large variation in electrode impedance). An electrode fabrication technique was developed to allow for inexpensive rapid prototyping of new designs, greater precision in the placement and size of contacts,
11 and much higher contact density than possible when contacts are placed by hand. Contact-density higher than current 0.5-1 contacts/millimeter was necessary for this project since preliminary work indicated that the recorded signals will have spatial frequencies on the order of 1 cycle/mm, thus requiring 2 contacts/mm to accurately reconstruct. The technique was evaluated based on yield, robustness of finished product, and impedance. A description of the fabrication technique and recording system is presented in Chapter III. Alternate techniques that may be useful for more complex designs are presented in Appendix D. Aim 3: Experimental Testing of Recovery Algorithms Data were collected from a rabbit sciatic model with the FINE built in Aim 2.
By
recording on the main trunk while stimulating the Peroneal and Tibial branches it was possible to compare the algorithm’s recovered signals with known stimuli from two distinct sources. As in Aim 1 the correlation coefficient metric was used to quantitatively assess the accuracy of these recovered signals. These data allowed estimation of the signal recovery accuracy under a variety of conditions and are discussed in Chapter IV. During the analysis of these data, techniques to improve the reconstruction algorithm were identified; these are presented in Appendix A. The following four chapters of this thesis discuss each of these specific aims in detail, with results supporting the overall hypothesis.
They are written as individual
manuscripts to be submitted to peer review journals as noted at the beginning of each chapter. Appendix B, details a technique to induce selective pain block particularly well suited for amputees with phantom limb pain. This technique is included here since it uses
12 the same stimulation paradigm as was developed for Chapter IV, and is intended for the same patient population. It was also written as an independent manuscript. Appendix C presents several brief modeling results in an attempt to elucidate the effects of the highfrequency stimulation paradigm used in Chapter IV. Appendix D discusses two alternate electrode fabrication techniques that were not pursued, but may be useful for more complex designs.
13
Chapter II:
Modeling Studies In this chapter, a variety of modeling techniques are used to approximate the in vivo human nerve cuff recording case and develop an algorithm for separating fascicular signals from these recordings. This chapter is a modified version of [3], used with permission. The work was supported by National Institutes of Health NINDS grant #5R01NS032845-11 to Dominique M. Durand.
Abstract The peripheral nervous system carries sensory and motor information that could be useful as command signals for function restoration in areas such as neural prosthetics and Functional Electrical Stimulation (FES). Nerve cuff electrodes provide a robust and safe technique for recording nerve signals. However, a method to separate and recover signals from individual fascicles is necessary. Prior knowledge of the electrode geometry was used to develop an algorithm which assumes neither signal independence nor detailed knowledge of the nerve's geometry/conductivity, and is applicable to any wide-band near-field situation. When used to recover fascicular activities from simulated nerve cuff recordings in a realistic human femoral nerve model, this beamforming algorithm separates signals as close as 1.5mm with cross-correlation coefficient, R>0.9 (10% noise). Ten simultaneous signals could be recovered from individual fascicles with only a 20% decrease in R compared to a single signal. At high noise levels (40%), sources were localized to 180±170μm in the 12x3mm cuff. Localizing sources and using the resulting positions in the recovery algorithm yielded R=0.66±0.10 in 10% noise for 5 simultaneous
14 muscle-activation signals from synergistic fascicles. These recovered signals should allow natural, robust, closed-loop control of multiple degree-of-freedom prosthetic devices and FES systems.
Introduction Peripheral nerves of the body carry both command and sensory signals in more accessible forms than found in the central nervous system, and could provide signals necessary to control high degree-of-freedom prosthetics, and closed-loop Functional Electrical Stimulation (FES) systems. Nerve recording methods are relatively non-invasive and safe [24]. In theory, these signals could be recovered using Inverse Problem techniques for electromagnetic sources in volume conductors. However, these techniques require high levels of model accuracy and signal-to-noise ratios (SNR). In particular, the reliable recovery of fascicular sources from whole nerve recordings has presented an unsolved problem. While numerous studies have documented the selective stimulation properties of conventionally round (i.e., transverse geometry) and even self-sizing electrodes [25], there is little experimental data concerning the ability of such electrodes to record and distinguish between different active fascicles [26]. The Flat Interface Nerve Electrode (FINE) is ideally suited to this task since it minimizes the distance between the circumferential electrodes and the fascicles. Blind Source Separation techniques have already been demonstrated on these FINEs, but require that each signal is independent from the others [8, 27]. Muscle synergies are the clearest example of why this may not be a valid assumption. Several other methods have been described in the literature for localizing or separating nerve trunk signals such as Neuro-fuzzy algorithms that use prior knowledge implicit in
15 fuzzy systems with Artificial Neural Networks [17]. Good single subject performance was achieved, but with only small angular oscillations of the ankle joint. Inverse Problem methods have also been investigated including an application of Radial Basis Functions (Kansa’s method) by [28], and the sLORETA algorithm by [29]. However, Ling, et al. [28] required close initial guesses for convergence and no testing was done with realistic or varying geometry. Zariffa and Popovic have recently provided data on the accuracy of localization (but not recovery) of their approach in a single-fascicle simulated rat model [30] as well as their ability to perform forward model reduction [29]. Neither group discusses algorithm speed so it is unclear whether these methods would be appropriate for real-time control applications. This paper proposes a different approach that takes into account available a priori knowledge not previously utilized and does not rely on the specific anatomy of the nerve, avoiding poor generalization.
The proposed technique is based on antenna array
beamforming, or spatial filters [22], and can be applied to any near-field wide-band case, particularly where the signal propagates too fast for timing information to be helpful. Linear, time-invariant real-valued weights are applied to the voltage recorded at each contact on the FINE nerve cuff electrode to shape the receptive field within the nerve. Due to the low frequency components of the signals, and the very short distances between the contacts, it is not practical to include phase or time delays in these weights, as is common in traditional beamforming. The algorithm is based on a priori knowledge of the cuff geometry (a priori Finite Element Model), and was tested on a realistic nerve model with anisotropic conductances (realistic Finite Element Model). Moreover, no
16 assumptions on signal independence were required as is the case for blind separation methods. This work was previously presented in abstract form [31].
Method Beamforming Algorithm The algorithm is divided into 2 training stages: First, a transformation matrix is built from the a priori Finite Element Model (apFEM). The Transformation matrix requires no additional information about the nerve, and is time-invariant. It is built using only prior information about the electrode geometry and an estimate of the epineurial conductivity.
This matrix operates on the recorded voltages to produce an image of
estimated activity levels within a cross-section of the nerve. The second training step takes place following cuff implantation, or using the realistic FEM (rFEM) for the simulation.
Source localization is performed using a map of the estimated activity
produced by the transformation matrix. The source localization training must be done after the cuff is implanted and signals are recorded. Once these training stages are complete, the algorithm consists of multiplying the recorded voltage at each contact by the transformation matrix (created from the lead-field matrix of the a priori model) and averaging the values of the pixels selected for the fascicle of interest (identified during source localization) in the resulting image. In Chapter IV, this algorithm is referred to as the Single Pixel Filter algorithm, in contrast with the Source-based Filter described there to reduce cross-talk between sources.
17
Figure 1. Finite element models generated to test and train the beamforming algorithm. Parts a) and b) show isometric and cross-sectional views (respectively) of the a priori model (apFEM) containing an insulating cuff with 22 contacts (in addition to upper and lower tripoles) and a simple rectangular epineurium filling the cuff. This model was used to generate the spatial filters, or beamformers, for the transformation matrix. Parts c) and d) show isometric and cross-sectional views (respectively) of the realistic model (rFEM), which contains the same cuff but with anisotropic endoneuria, and perineuria around each of the 22 fascicles. Fascicles used in testing are numbered, and color-coded to correspond to functional group. The geometry for this model is obtained from realistic cross-sections of the human femoral nerve presented in [4]. TABLE I PARAMETERS USED IN FEM SIMULATIONS
Conductivity Material
Parameter
Length (mm)
(S/m) [1]
Epineurium
0.083
Cuff Height
3
Saline
2.000
Cuff Length
15
Endoneurium (trans.)
0.083
Cuff Width
12
Endoneurium (long.)
0.571
Saline Volume
150x200x150
Perineurium
0.002
Table 1. PARAMETERS USED IN FEM SIMULATIONS
The a priori Finite Element Model (apFEM) The a priori FEM consists only of the insulating cuff electrode, large saline volume conductor, and simple rectangular epineurium filling the cuff.
It was created in
18 MAXWELL 3D (Ansoft Corp.), and is shown in Figure 1a, b with lengths and conductances given in Table I. This model is used to calculate the sensitivity (or leadfield) matrix, which provides the calculated voltages on all recording channels due to sources placed throughout the epineurium (the “forward problem” we are attempting to invert) and is calculated using reciprocity similar to Weinstein et al. [32] by placing a source on each recording contact in turn and recording the resulting voltage throughout the epineurium.
It is calculated using only prior information about the electrode
geometry and an estimate of the epineurial conductivity, since this information is all that is present in the apFEM. Each of the 22 contacts was set to 1mV in turn, with the outer faces of the volume conductor grounded, and the voltage was calculated in the x-y plane in the middle of the cuff. The vectors corresponding to the voltage generated by each contact were concatenated into the sensitivity (or lead-field) matrix, S. It is known from Electromagnetic Reciprocity theorem that the measurement will not change if the field point and source point are interchanged [33]. Thus, this sensitivity matrix also gives the recorded voltage at each contact due to a source at each pixel (i.e. the lead-field matrix [32]). Since the system is linear and superposition applies, linear combinations of these sensitivities can be generated to optimize the sensitivity for each pixel and generate the transformation matrix. The Transformation Matrix To calculate the transformation matrix, the weights (ti) on the sensitivity vectors (S) for each contact are optimized for a source signal located in a single ideal pixel (δi). The following equation (1) is solved for each pixel i where,
Sti i
(1)
19 Assuming n recording contacts and m pixels in the desired reconstruction, the variables are S{mxn}, the sensitivity matrix, and ti{nx1} the linear coefficients of the transformation matrix. Note that this equation is entirely independent of time and considers only the static behavior of the model For increased efficiency, the reduced QR factorization of S{mxn} is first calculated so that for δi equal to the delta function at index i, the solution reduces to Equation 2, below, where q*i is the ith row of Q (since Q is orthogonal, the transpose acts as an inverse on the range). Normalization is performed for each set of weights, as in Equation 3. t i R \ q i*
ti
ti Sti
(2)
(3)
The column vectors ti can then be concatenated to form the transformation matrix T{mxn}, which operates on a single time point t of observed data (o{nx1}) to produce the estimated activity at each pixel (â{mx1}) at time t (4). This activity vector can then be displayed as an image of the estimated activity in the plane of interest. Repeated application of the Transformation matrix at different time points gives the time dependence to this procedure.
aˆ To
(4)
Source Localization When the transformation matrix is multiplied by the vector of voltages on each contact (Equation 4), an image is created providing an estimate of the activation of each pixel
20 within the cross-section of nerve. A simple local-maxima-based algorithm was used to locate sources in the estimate using automatic thresholding to remove areas of low activity (Otsu's method [34]). Morphological opening (erosion followed by dilation) which removes islands and peninsulas below a given size from a binary image was applied to prevent the algorithm from finding small sources near the periphery associated with noise.
Once the fascicle locations are determined, the beamformers for those
locations are applied to the full time-signal in order to reconstruct the fascicular activity. Post-processing techniques, such as RMS windowed averaging or BSS, can improve SNR and reduce cross-talk. Realistic Finite Element Model (rFEM) for Testing the Algorithm FEM simulations for validation of the recovery algorithm were performed with a realistic nerve model consisting of the same cuff as previously described but with the addition of realistic nerve geometry obtained from histological analysis of a human femoral nerve [4] (Figure 1c,d) with conductivities given in Table I. Ten fascicles, out of the 22 in the model, were chosen to contain active sources representing a broad distribution of location, diameter, and separation distance. Ten axons were placed in the center of each fascicle, and these axons were each assigned a random diameter between 5.5 and 12.5 µm. Nodes of Ranvier were placed corresponding to each diameter, starting from a random center position on each fiber. Each node of Ranvier was simulated separately to create a lead-field matrix. Axonal Activity Simulations The 1978 Moore model of the myelinated axon was used to generate diameter-specific space (node) – time action potential transmembrane currents [35], (Fig 2a).
This
21 waveform is similar in shape to the leaky patch clamp recordings of Meeks, et al. [2]. Due to the linearity of the medium, these transmembrane currents are proportional to the nodes’ extracellular voltages. The lead-field matrix from the rFEM is multiplied by the voltage at each node to calculate the voltage recorded due to that node. These voltages are then summed to generate a Simulated Single Unit Action Potential (SSUAP), shown in Figure 2b. A fixed number of SSUAPs were randomly distributed within given windows of activity for each active fascicle and summed to generate a simulated recording (SR) of a neural signal [36], shown in Fig 2c (top) along with a typical experimental recording (bottom). The sampling rate for all simulations was 20kHz. Gaussian white noise was added to a given percentage of the variance of the signal.
Figure 2. Creating Simulated Recordings. a) Simulated transmembrane current in space and time (compare to loose patch recordings in [2]). b) Simulated single unit action potential recording from tripolar cuff recording. c) Comparison of simulated (top) and experimental (bottom) recordings. The simulated recording is obtained from sources in fascicle 3, recorded from the closest contact, with 40% noise. The experimental recording is taken from [5].
22
Results Localization of Sources A propagating source simulating realistic neural signals made by summing a fixed density of randomly delayed action potentials over a 100ms window of activity (Figure 3a) was placed in a single fascicle. The signal power (RMS) at each contact was calculated in 10ms bins, the beamforming localization procedure was applied to each one (Figure 3b) and the mean of the resulting list of sources calculated. This estimated location (green cross, Figure 3c) was then compared to the known location (red square, Figure 3c) and overlaid onto the fascicle map of the nerve for reference. The estimated sources are found to be within the correct fascicle. This process was repeated 10 times, at 3 different noise levels, for each of the 10 fascicles tested. The results for one trial of all 10 fascicles at the highest noise case (40%) are shown in Figure 3d, where the estimated source is shown as a green circle and the true location a red square. Even at this noise level, the figure clearly shows that all 10 sources are located to within their respective fascicles. Without noise, the mean distance between recovered and actual source position over all trials and all sources was 0.14±0.03mm (N=100). As the noise level is raised, the mean and especially the standard deviation increase to 0.18±0.17mm (N=100). The results for all noise levels are presented in Table II. These results suggest that the location of single sources can be identified to 180±170µm even in the presence of significant noise in the signal.
23
Figure 3. Localization Using Realistic Signals. a) Sample signal of single fascicle activity recorded on a single contact. The signal power (RMS) is shown as a dark thick line, while the raw signal is light and thin. b) Localization results for each of the 3 marked timepoints in (a). The estimated location is marked with a green circle, and the actual location with a red square. c) To locate the source, the mean location of all reconstructions is used. This final localization result is shown superimposed on the fascicle map, with the estimate marked by a cross and the true location by a square. d) Localization results for all fascicles (single trial at 40% noise). The fascicle map is shown in grey, with true source locations as red squares, and a green circle centered on the estimated location. 10 trials, each 100ms, were performed for each of the 10 fascicles modeled. The accuracy for the 40% noise trials, as pictured here, was 0.18±0.17mm (N=100). For full results see Table II.
24 TABLE II SUMMARY OF LOCALIZATION ERROR FOR BOTH SINGLE ACTIVE FASCICLES, AND PAIRS OF ACTIVE FASCICLES
Number of 0% Noise
10% Noise
40% Noise
(mm)
(mm)
(mm)
1 (N=100)
0.14±0.03
0.13±0.04
0.18±0.17
2 (N=225)
0.34±0.09
0.33±0.08
0.6±0.7
Active Fascicles
Table 2 - Summary Of Localization Error For Both Single Acti e Fascicles and Pairs of Acti e Fascicles
Pairs of Simultaneous Active Sources To determine the effect of two simultaneously active pairs of fascicles, a fixed density of action potentials from axons in two fascicles (Figure 5a) were randomly distributed over a 100ms window, with 80ms on-time for each fascicle, offset by 20ms, to account for the fact that source amplitudes are likely to vary with respect to each other (Figure 5b). Signal power (RMS) was calculated for each 10ms bin, and the beamforming algorithm applied (Figure 5c, green crosses mark actual source locations). Since the method used for localization in the previous section implicitly assumed a single source (by taking the center-of-mass), a modified version of the algorithm was used to estimate the locations of the two sources. Instead of using the center-of-mass to identify the final estimate, this version applied an unsupervised k-means classifier to group the putative sources from each time point into 2 groups, the centers of the 2 groups were then compared to the actual source positions. This procedure was repeated 5 times for each possible pairing of fascicles, in 0, 10, and 40% noise (see figure below).
25 On average, the error was 0.34±0.09mm (N=225) at 0% noise with little variation due to source separation. At 40% noise, the overall error was 0.6±0.7mm (N=225), although close source pairs showed much higher error than the others. When separation was greater than 3.5mm, the 40% noise results were similar to those at 0% noise. In high noise, close sources may be confused as a single source, causing the algorithm to mistakenly identify distant noise as the second source. More complex algorithms able to estimate the number of local-maxima to search for may perform better in these cases. Localization is an essential training stage in this algorithm, and while the results here show that sub-fascicular localization is possible for both single and paired fascicle time windows, it is clear that multiple active fascicles cause a significant increase in error. However, as this localization step only needs to be performed once during training, the restriction to 1 or 2 simultaneous fascicles or functional groups is reasonable. During this short training, specific movements or stimulation can be used to ensure only 1 or 2 fascicles are active at a given time. It is also often possible to judge from the resulting image both how many fascicles are active and their approximate locations.
26
Figure 4. Paired Localization Accuracy. This case was performed for all possible selections of 2 fascicles, with localization done using the k-means style algorithm described above for k=2. The main source of error for sources closer than 3mm is the algorithm mistaking the two sources for a single source and selecting peripheral noise as the second location.
Recovering Fascicular Activation in Time Recovery of two active sources To determine the ability of the algorithm to recover the signals in time once the localization of the source is known, simulated single fascicle recordings (SR) were summed, two at a time with 0, 10, or 40% added Gaussian noise. The beamforming algorithm was applied at each time point and the pixels corresponding to each fascicle were used to generate the Reconstructed Fascicle 1 (RF1) and Reconstructed Fascicle 2 (RF2) signals. In order to determine the accuracy of the recovery algorithm alone, the known fascicular locations were used. The same procedure was repeated 10 times for each possible pair of fascicles with Fascicular Activity (FA) signals regenerated randomly each time, and multiplied by the rFEM lead-field matrix to create new SRs. A 10ms RMS windowed average was applied to all signals, both to improve noise tolerance
27 and correct for differences in the shape of single unit activity at the individual nodes of Ranvier (in the FA signals) and the recording contacts (in the SR and RF signals), as shown in Figure 2a and b. An example of the RMS averaged actual (FA) and recovered signals (RF) is shown in Figure 5a. These signals show very low cross-talk and each pair is highly correlated (R>0.9). Each possible pairing of the 10 fascicles was tested 10 times for each of the 3 noise levels, for a total N=1350. The cross-correlation coefficients are plotted in Figure 5b versus the distance between the fascicle centers. The figure shows R exponentially increasing towards 1 with increasing separation distance, as expected since less mixing occurs between sources that are farther apart. Recovery with R>0.9 was achieved for sources separated by a minimum distance of approximately 1.5 mm, or about twice the diameter of a typical fascicle and half the height of the cuff. Note that for some pairs of close fascicles, the cross-correlation is still very high compared to others with similar separations, suggesting that the geometry of the surrounding fascicles plays a significant role in the quality of recovery.
28
Figure 5. Separating Signals from Pairs of Simultaneous Active Fascicles. a) Example recovered signal when fascicles 1 and 5 are active, including the actual activity level for each fascicle. Fascicles 1 and 5 are 5.5mm apart and this trial resulted in R= 0.97. b) Correlation coefficients and standard deviations for each fascicular separation distance at three noise levels. 10 trials were performed for each noise level and each trial included every possible pair of fascicles. Recovery with negligible cross-talk is seen at R=0.9, which for 10% noise occurs at approximately 1.5mm – half the height of the cuff, and about twice the average fascicular diameter.
Effect of Multiple Active Fascicles In a physiological situation, there would likely be more than two fascicles from which to record (depending on the nerve and location). Therefore, we tested the ability of the algorithm to recover signals from n simultaneously active fascicles, for n from 1 to 10, again assuming the true source locations were known. In each trial, exactly n fascicles were active at all times, and all possible combinations of n active fascicles were used in
29 each trial. An example showing the input Fascicular Activity (FA) signals for n=2 is given in Figure 6a, where each plot shows the RMS activity of a single fascicle for the duration of the test. Note that exactly 2 fascicles are active at each time point, and over the course of the trial, all fascicle pairs are tested. Ten trials were performed for each value of n (1 to 10) at each of the three noise levels, for a total N=300.
The
reconstruction accuracy as a function of both the number of active fascicles and the noise level is shown in Figure 6b.
For up to 5 simultaneously active fascicles, the
reconstruction accuracy is unchanged with a mean value of R=0.74±0.18 (N=50). The accuracy decreases steadily as the number of active fascicles grows larger than 5, reaching 80% of the single fascicle value for 10 simultaneously active fascicles. Recording noise has a strong effect on the reconstruction, lowering the mean value of the
n=1…5 trials to R=0.61±0.18 (N=50), and dropping to 65% of the noisy single fascicle value for 10 simultaneously active fascicles.
30
Figure 6. Separating Signals from Multiple Simultaneous Active Fascicles. a) Input fascicular activity signals for the n=2 test, when all possible combinations of 2 fascicles are active. The ten figures each show the input signal for a single fascicle. b) Correlation coefficient as the number of active sources increases. The overall effect is a 20% drop in R when 10 sources are active, compared to 1. Up to 5 simultaneously active fascicles, the mean accuracy was R=0.74±0.18 (N=50) at 0% noise and R=0.61±0.18 (N=50) at 40% noise.
Functional Recovery In order to test the ability of the algorithm to recover meaningful muscle activation data in a realistic case, the fascicles were grouped by the muscles they innervate, and the localization algorithm was used to determine recording pixels, instead of the known locations. Due to the distributed nature of the sources, the final averaging step was omitted from the localization algorithm, leaving the full list of putative sources. Each group was then activated simultaneously (each action potential was assigned to a unique
31 axon in a single fascicle within the group while the group was active). The pattern of stimulation was similar to the one shown in Figure 6a except that combinations of muscle groups were tested instead of individual fascicles. However, contrary to the previously presented experiments, localization was performed on each signal, and the resulting source locations used for the recovery throughout the test. Thus, these results combine the localization and recovery sections of the algorithm to show how the system could be used in a real application. The groups used and their relationship to muscles innervated by the femoral nerve cross-section above are shown in Table III. TABLE III FASCICULAR GROUPINGS FOR FUNCTIONAL TEST AND THEIR CORRESPONDING MUSCLES FROM REALISTIC FEM
Muscle
Fascicle Number(s) (see Fig. 1)
Rectus Femoris
1
Vastus Lateralis
2, 10
Vastus Medialis
3, 7, 8
Saphenous
4, 5, 6
Sartorius
9
Table 3. FASCICULAR GROUPINGS FOR FUNCTIONAL TEST AND THEIR CORRESPONDING MUSCLES FROM REALISTIC FEM
As shown in Figure 7, correlation coefficients for the functional recovery tests are higher than for the multiple active fascicle tests above, as may be expected due to the proximity of the grouped sources. Figure 6a shows that increasing the number of groups results in a decrease in correlation coefficient from 0.80±0.18 (N=10) with a single group active to 0.70±0.11 (N=10) with all 5 groups active in the noise-free case. Figure 7b shows the
32 coefficients separated by group number; the quality of recovery is not consistent across groups. Group 1 (Rectus Femoris) has by far the lowest R values, having a mean 0.42±0.10 (N=50) compared to 0.87±0.09 (N=200) for the other 4 groups.
This
difference could be explained by the location of group 1, a small single fascicle, close to the edge of the nerve almost directly centered between the contacts and directly beside the large superficial fascicle 9. The signal from fascicle 9 was picked up as cross-talk in the recordings of group 1. The group 1 signal was also observed in fascicle 9 recordings, although to a lesser degree. All other groups except 5 (Sartorius) contained multiple fascicles. These results indicate that it may be possible to recover meaningful muscle activation signals in vivo, without knowing the locations of the relevant fascicles a priori. Figure 7c shows the estimated locations of each group for a single trial of the test. Due to the distributed nature of the groups the mean position was not used, simply the aggregate of all identified pixels. The estimated locations are shown as dark dots overlayed on the lighter fascicle map. All fascicles in the nerve are outlined and those that were active are shaded with a separate color for each group. This distributed nature of the sources also makes it difficult to infer any quantitative results, but qualitatively the estimates are distributed over the general area of the source fascicles.
In group 2 the estimated
locations mainly cluster around the more superficial of the two fascicles, and in both groups 1 and 5 there is a considerable offset towards the center of the nerve, possibly due to the higher-conductivity saline around the far right contact compared to the apFEM.
33
Figure 7. Functional Recovery Without True Source Locations. a) Correlation coefficient for 1 to 5 groups of active fascicles. Fascicles were grouped by terminal muscle enervation. Each bar represents 10 trials. b) Correlation coefficient for each group during testing, each bar represents 50 trials (10 repetitions for n active groups, for n from 1-5). Every possible combination of active groups was tested. Note that group 1 consists of a single small fascicle at the extreme center and side of the nerve, and so exhibited poorer recovery. Fascicles were grouped by terminal muscle enervation and unlike previous experiments the true source locations were not used. Instead, the localization algorithm was used during the n=1 trial to identify source locations. Thus this experiment simulates what may be possible to achieve during in vivo experiments. c) Estimated group locations from Localization algorithm. Note that the final center-of-mass step was removed because of the distributed nature of the sources, thus leaving the raw pixels identified by the algorithm. The estimated locations are the dark pixels, shown overlayed onto the nerve cross section. All fascicles are outlined and those active during the tests are shaded. Each group is shaded with a different color.
Discussion While the beamforming idea presented here is similar to non-adaptive algorithms applied previously in other fields [22, 37], these results show that it could also be helpful for recovering neural signals. Since the training of the algorithm is independent of the nerve
34 anatomy, this method should be robust for realistic changes in conductivity and anatomy when moving from in silico to in vivo models. The simulation results presented span a broad range of situations, from simple single source localization, to a realistic functionalgroup localization-then-recovery, with 5 active groups each with up to 3 independent fascicles. With 40% Gaussian noise, the beamforming algorithm is able to locate sources with a sub-fascicular accuracy of 0.18±0.17mm (N=100).
This accuracy is reduced when
multiple fascicles are active, but even when a window of single fascicle activity cannot be found, pair-wise tests showed localization was accurate to 0.33±0.08mm (N=225) in 10% noise. The algorithm could be further improved by modifying the unsupervised classifier so that the number of sources does not have to be estimated a priori. Perhaps more important than localization, the algorithm shows excellent (R>0.9) signal reconstruction for fascicles whose centers are only 1.5mm apart. As expected due to the effect of mixing in the volume conductor, the fidelity of recovery increases asymptotically as source separation increases. This is promising for functional recovery, since fascicles innervating the same muscle are often located close to each other [4]. In tests with the fascicles grouped by muscle enervation, recovered muscle activities with all 5 test groups active showed correlation coefficients of 0.70±0.11 (N=10) in the noiseless case and 0.66±0.10 (N=10) in 10% noise.
Moreover, the pixels of interest in this
recovery were determined by localization on the simulated recordings themselves, showing that the combination of the two components of the algorithm provide a coherent solution to the recovery problem. In tests designed to recover simultaneous activity in 10
35 active fascicles, with no assumptions made regarding the independence of their activity, correlation values dropped only 20% from the single fascicle case. The correlation coefficient presented above is a metric of reconstruction accuracy; however it is difficult to extend this value to assess the utility of a reconstruction. The correlation coefficient does provide a convenient way of comparing accuracy with other groups, and when squared, provides a measure of the proportion of variance in the signal explained by the reconstruction. Clearly, reconstructions with higher R-values will be more useful than those with low values; however the necessary and sufficient values will depend strongly on the application and difficulty of the control problem to which they are applied. The values of R >0.95 at 10% noise and 1.5mm separation from this algorithm are higher than results published in other studies including [8] where correlation coefficients of 0.8 with Blind Source Separation were achieved at the same noise level, and the small ankle oscillation results of [17] who obtained R=0.93±0.09 from in vivo recordings using two ENG cuffs. Each of these algorithms applies a different constraint to analyze the recorded data. BSS assumes independence, and because it does not require amplitude information it is able to extract signals from arbitrarily placed sources with no training. The neuro-fuzzy algorithm of [17] requires fully online training, and was used only for small perturbations of the ankle joint with constant velocity. The beamforming algorithm presented here uses a very different constraint: the known geometry of the electrode. This allows most of the training to be done ahead of time with no assumptions made on the signals of interest, neither that they are small perturbations, that related variables are held constant, nor that they are statistically independent. The method does require that sources be spatially separated in order to achieve good reconstruction. This
36 lower spatial resolution (compared to some techniques) is similar to the philosophy behind sLORETA, one of the more popular and successful inverse problem algorithms for EEG and cardiac surface potential mapping.
However, sLORETA involves a
regularized matrix inversion at each data point and is generally slower (for the same level of detail) than the initial training matrix inversion, followed by single matrix multiplications at each data point required here [38]. As a benchmark, the Beamforming algorithm required 0.19ms of calculation time per time point in MATLAB on a dual-core 2.4GHz Intel PC with 4GB of RAM.
Still, a comparison of sLORETA with the
beamforming algorithm would be interesting, and will be investigated as part of future work. We have shown that the required separation is on the order of fascicular diameter and so should allow for fascicle-level signal reconstruction. The most interesting property of this algorithm is its robustness. The algorithm was trained without any information on the nerve anatomy. It was tested with a complex, anatomically realistic model comprised of conductivities far different from the empty rectangular epineurium it was trained on, including anisotropic endoneurium and highly resistive perineurium.
Thus the addition of fascicles and epineurium appears as a
perturbation from the empty a priori model. Despite this large perturbation, and high noise levels, the beamforming algorithm still shows good reconstruction and localization. The beamforming algorithm requires only a single matrix multiplication, and therefore may be applied in real-time. Several post-processing techniques have been developed in the literature which could be used to improve the resolution of the algorithm, and subsequently improve recordings.
Iterative Inverse problem techniques may be
particularly well suited since they derive the most benefit from the close initial guess the
37 beamformer generates.
The FOCal Underdetermined System Solver (FOCUSS), in
particular, seems promising due to the focal nature of the fascicular sources [19]. Blind Source Separation may also be applied to the individual pixel sources – the results could then be correlated with position in the image to solve the permutation ambiguity and localize the activity in one step [8]. Adaptive beamforming has also been investigated for far-field, narrow-band situations [39]. With some modifications, for example replacing the steering matrix with a lead-field matrix and using the transformation matrix as an initial weight set, they may be able to improve noise tolerance and multi-source reconstruction.
Conclusions In 10% noise, the beamforming algorithm separates signals as close as 1.5mm with R>0.9, with a drop in accuracy of only 20% when simultaneously recovering 10 active signals. No assumptions on the independence of these signals were necessary. This distance is on the order of fascicular diameter and should be sufficient for functional separation of motor signals. The localization algorithm showed sub-fascicular accuracy, even in 40% noise for segments of single fascicle activity as short as 100ms. Postprocessing techniques to improve the resolution, noise tolerance and multiple-source recovery will be investigated, primarily FOCUSS [19], BSS [8], and adaptive beamforming [39]. In the following chapter, an electrode and recording system are developed, in order to finally test the algorithm in vivo in Chapter IV.
38
Chapter III:
High Density Recording Nerve Cuff Electrode Design
In this chapter, a technique for the fabrication of a suitable Flat Interface Nerve Electrode is presented, along with results from testing various electrodes. This chapter will be submitted as a short paper or communication in a peer-reviewed journal. This work was supported by National Institutes of Health NINDS grant #5R01NS032845-11 to Dominique M. Durand.
Abstract New techniques for processing whole nerve recordings require higher contact-density than traditional Flat Interface Nerve Electrodes possess (see Chapter II). Flat Interface Nerve Electrodes have the potential for large numbers of contacts but are difficult to make with precision and with biocompatible materials. A 16-ch FINE device was made using only silicone and metal wires. These electrodes were fabricated without the use of photolithography or other specialized techniques and so represent a low-cost, short production time, and high accuracy (contact spacing of 238±9μm) alternative to traditional techniques.
Although other metals may be used, the electrode was
implemented with stainless steel and shown to have 45±9kΩ impedance at 1 kHz, approximately one order of magnitude higher than similarly sized silver/silver chloride contacts. A 16-channel recording system suitable for future inclusion on the electrode cuff itself was realized based on a single IC preamplifier/multiplexer from Intan
39 Technologies LLC. Recordings were made on the rabbit sciatic nerve during activity evoked using a variety of stimulation techniques and show clear compound action potentials as well as much smaller desynchronized pseudo-spontaneous evoked activity. Averaging of the 16 recorded channels led to a 6±4 fold reduction in noise, without sacrificing temporal precision. These high contact-density electrodes provide additional information on the spatial positions of the neural sources which can be used to separate and recover fascicular signals, or reduce the noise level of whole nerve recordings.
Introduction The peripheral nervous system transmits a large amount of information, from both distal sensors and central command centers, which could be very useful to medical science. For example, lower motor neurons carry muscle activation signals which do not require decoding – a large advantage compared to their complex cortical equivalents. Similarly, nerves provide a connection between various biological sensors and their associated control systems, a suitable peripheral neural interface would allow robust monitoring of a large variety of biological signals such as blood sugar, blood pressure, as well as a variety of sensory modalities. These signals could be used to augment failing or insufficient biological effectors and control systems. Creating biocompatible, safe electrodes capable of recovering these signals without damaging the nerve is an ongoing challenge. Many different techniques have been used to interface with the peripheral nervous system including Utah Slanted Electrode Arrays (USEA) [40], Longitudinal Intrafascicular Electrode Arrays (LIFEs) [13], Flat Interface Nerve Electrodes (FINEs) [8], and Spiral Cuff Electrodes [41].
However, only the FINE and Spiral cuff preserve all neural
membranes (epineurium and perineurium) and so may have superior long-term stability.
40 However, this decreased invasiveness comes at the cost of a decrease in selectivity. While the more invasive electrodes are capable of distinguishing individual units, cuff electrodes are only able to record ensemble activity – much the same as the difference between penetrating cortical electrodes and Electrocorticography (ECoG). While the FINE improves the selectivity of the spiral cuff by reshaping the nerve cross-section to spread the fascicles, recent work shows that its selectivity can be further improved by recording simultaneously from closely-spaced contacts transverse to the nerve [3]. Therefore, the FINE can achieve fascicle-selective recording and since it is sensitive to the entire functional group the results may be easier to interpret and more stable. Need for a New Electrode Design In many fields of biomedical engineering, there is a constant trade-off between the invasiveness of a device and its specificity. This is also true of interfaces with the peripheral nervous system where a range of approaches have been demonstrated from the invasive penetrating electrode array [40], which provides excellent sensitivity and selectivity, to cuff electrodes [24], which are generally unable to provide single-unit signals. However, the chronic stability of penetrating electrode recordings remains to be determined. These devices may be more sensitive to micromotion due to their position extremely close to nodes of Ranvier, and may damage the nerve by piercing the perineurium which maintains positive pressure in the fascicles and may represent part of a peripheral blood-nerve barrier. In contrast, cuff electrodes are in current clinical use (e.g. Victhom’s Neurostep) and their long term safety has been established [42]. Recent work suggests that by reshaping or maintaining the nerve in a flat cross-section, and including multiple contacts, the selectivity of nerve cuffs can be improved for both
41 recording and stimulation [4, 14, 23], possibly down to the fascicular level. While lower density FINE cuffs have been commercially produced by Point Medical [43], they have typically contained 8 contacts per cuff, approximately half of the 2 contacts / mm density simulated in [3]. It is unclear what density is achievable given their current processing techniques, and the cost to redesign the device is relatively high. This suggests a need for a robust FINE with a large number of contacts spread across the nerve to maximize selectivity. High Contact Density Electrodes in Literature Many examples of electrodes with a high contact-density and contact-number appear in the literature. In general, these are mostly produced using expensive photolithography techniques and specialized materials and machines. Some examples are discussed below. MultiElectrode Arrays (MEAs) Commercial electrode fabrication with this level of contact density (2 contacts/mm) is usually done using photolithography, and has typically been used for penetrating electrode arrays [44-46]. These devices have been used extensively both in the peripheral nervous system and cortex, in some cases implanted chronically for years. As these are generally penetrating arrays, they separate signals based on spike sorting techniques not applicable to local field potential recordings. When silicon is used as the base for these devices they are very stiff relative to the neural tissue, and this mismatch may cause micro-motion relative to the surrounding tissue and potentially exacerbate encapsulation of the device.
Since single unit recordings are sensitive to small distances, these
movements may cause instability in the recorded signals and require frequent retraining.
42 As an alternative to silicon, more flexible polyimide has been used; however this polymer does not provide sufficient resistance to water penetration for long term implantation. The Matrix Electrode The matrix electrode, used by Popovic, et al. [30] is simply a spiral cuff electrode with a two dimensional array of contacts. technique on polyimide.
The device is built using a photolithography
Depending on the materials and technique used, this device
may not be suitable for long term implantation due to water penetration. Also, as this is a spiral cuff, it will reshape most large nerves into a round shape which reduces signal separation accuracy. The Lasercut Electrode Schuettler, et al. [47] developed a simple technique that has promising applications for prototyping because no expensive photolithography masks are used. By electro-spinning thin layers of PDMS, and sputtering platinum, they were able to create multilayered electrodes that could be patterned using an Nd:YaG laser. The technique is fast, and certainly has the required resolution, however the machinery required is very specialized, and a significant portion of the work is still completed by hand (removal of excess material). The authors investigated several interconnection strategies and settled on parallel gap welding or microflex ball bonding [48], which require additional specialized equipment. Several groups have proposed designs and fabrication techniques for new high contact density arrays to extend the utility of conventional neural recording and stimulation systems, however none have achieved standard use in the peripheral nerve recording
43 field. This is primarily due to high cost, especially for new designs, and a lack of longterm biocompatibility. Here we demonstrate a relatively low-cost technique, which is easily modified so that electrodes of varying size can be made with trivial adjustments to the process. A recording system small enough for integration within the cuff is also presented and is capable of simultaneous recording from 16 channels at 15kHz with 2μVrms noise. These electrodes are tested for impedance, noise level, precision, and robustness during multiple in vivo implantations.
Methods Electrode Fabrication Technique Each contact and lead wire in this design is a single piece of braided stainless steel wire, coated in PTFE (Fort Wayne Metals, IN). A certain number of these wires, depending on the number of contacts needed, are tightly packed in a single row and heat is applied to fuse their insulation together. A hot knife can then be used to strip the insulation from a narrow band perpendicular to the wires, forming a set of small, evenly spaced contacts. These contacts form the basis of the electrode and a schematic of the procedure is given in Figure 8. Depending on the use, a number of housings for this array of contacts are possible. In the simplest case, silicone adhesive may be used to attach the array to a sheet of silicone with some form of stiffener (shown in Figure 8). A piece of silicone tubing on either side of the wires may be attached the same way to create the cuff lumen. For a more complex cuff design, the array may be included in a silicone injection mold containing the cuff form. In this work, a simple sheet of silicone with a polyimide stiffener was used on
44 either side of the cuff, with a stainless steel wire tripolar reference on the top and bottom at each of the anastamoses. A magnet was glued to one side of the cuff, so that a second, removable magnet could act as a closure, however a more traditional closure (such as suture or post-socket) will be required when this electrode is used beyond acute experiments.
Figure 8. Hot-Knife Fabrication Technique. From top to bottom on left, PTFE coated stainless steel medical wires are first arranged tightly next to each other as a ribbon cable. A heat gun or the flat side of a hot knife is then used to fuse the insulation, locking the wires in place. A hot knife or wire with a guide is then used to cut a slit in the insulation, exposing the metal underneath. The unwanted end is then sealed in silicone to prevent current leakage. On the right, silicone adhesive is used to attach the finished bare wire array to a sheet of silicone with polyimide stiffener, along with the tripolar references. Finally, the free ends of the wires are crimped into gold pins with conductive epoxy to ensure a good connection to the amplifier. Silicone tubes of blocks parallel to and on either side of the wires may be added to form the cuff lumen.
Recording System The signals from the electrode were amplified by a single IC from Intan Technologies LLC. This 16-channel capacitively coupled multiplexer/preamplifier was combined with
45 a counter and National Instruments Data Acquisition (DAQ) card to form the full recording system. The signal was low-pass filtered at 5kHz, then sampled at 15kHz per channel with the multiplexer control on the amplifier connected to a counter driven by the DAQ convert clock. In this way a single 240 kHz recording contained interleaved samples from each of the 16 channels and could be demultiplexed in Labview. Digital filters were applied offline to limit the recording bandwidth to 800Hz-3kHz. A schematic of the system is shown in Figure 9. Noise in the system was kept to a minimum by connecting a large braided copper cable from the surgical table to building ground, isolating all electrical equipment through an isolation transformer, and running the preamplifier off of battery power.
Figure 9. Recording System for High Contact Density Nerve Cuff Electrodes. An Intan RHA1016 preamplifier/multiplexer was connected directly to the electrode and a counter was used to control the multiplexer channel input. The counter was clocked by the Convert Clock on an NI DAQ card connected to a PC running labview, so that the active channel was incremented by 1 after each sample.
Validation Methods Noise measurements were obtained across the frequency range of electroneurogram recordings (800Hz-3kHz) in physiological saline and during acute implantation on a
46 rabbit sciatic nerve. The contact spacings were also measured across two finished 16channel electrodes, in addition to the impedance of each channel in physiological saline at 1kHz. Impedance was measured using a Protek Z580 LCR meter with a 3x3” stainless steel plate as a return. In Vivo Experiments Four New Zealand White Rabbits were used for this study. Anesthesia was induced with 20-50 mg/kg IM ketamine and 5 mg/kg IV diazepam and maintained with 60 mg/kg IV alpha-chloralose (followed by one quarter dose every 2 hours or as needed) and .02 mg/kg IM buprenex.
All protocols were approved by the Case Western Reserve
University IACUC. The animal was monitored using the toe pinch reflex, eye blink reflex, as well as heart rate and SPO2 to maintain surgical anesthetic depth throughout the experiment. Body temperature was maintained at 38ºC with a heating pad. The animal was fixed in the prone position, and an incision made along the thigh from the hip to the knee. The biceps femoris muscle was separated and retracted to expose the sciatic nerve and its branches over a length of 3–4 cm. The sciatic, tibial and peroneal nerves were carefully isolated from the surrounding soft tissue for about 3 cm and were kept moist with sterile saline. The high contact-density FINE was placed around the sciatic nerve and one tripolar FINE was placed on each of the tibial and peroneal nerves. Stimulation was applied from these distal cuffs and the antidromic activity recorded using the highcontact density FINE.
Results The electrodes fabricated using this technique proved reliable and robust, with a yield very near 100% (depending on skill, and tolerances for the contact size). Two electrodes
47 were fabricated and their contact spacing measured under optical microscopy.
The
impedance of these electrodes was then tested in saline after 180 seconds in an ultrasonic cleaner. Following these tests, the electrodes were used in 8 acute experiments on the Rabbit sciatic nerve, during which their noise properties were investigated. The results of these tests are summarized in Table 4.
The impedance of single contacts on the
electrodes in saline was 45±9kΩ (n=16), which is approximately one order of magnitude larger than similarly sized platinum contacts and still extremely small compared to the input impedance of the Intan preamplifier (1012 Ω). More importantly, the electrodeamplifier setup demonstrated a noise floor of 2.2±0.5μVrms (n=26), which corresponded to a CAP signal-to-noise ratio of 12±5 (n=14) and was suitable for recording pseudospontaneous evoked electroneurograms. A sample compound action potential recorded with this electrode is shown in Figure 10a. Also in Figure 10, a histogram of the noise from a baseline recording during the same experiment. This baseline recording had a noise level of 3µVrms consistent across the 16 channels.
48
Figure 10. Signals Recorded by High Density FINE. (A) A single compound action potential-like event is shown, recorded by a 16-channel stainless steel FINE on the sciatic nerve of rabbit during 130Hz stimulation of the peroneal branch. All 16 voltage traces are shown, demonstrating the uniformity of the signal during the neural response and the noise before and after. In this recording the signal to noise ratio was approximately 8. (B) A histogram of the noise during a typical baseline recording with noise level of 2.9µVrms.
Finally, the contact spacing (calculated under light microscopy) was 238±9μm (n=30), providing approximately 4 contacts/mm. Three photographs of the electrode are shown in Figure 11, on the left showing the bare wire array alone, on the right embedded in a FINE with platinum foil tripolar references, and below a close-up of the bare wire array showing an inter-contact distance measurement. TABLE IV HOT-KNIFE FABRICATION TECHNIQUE RESULTS
T bl
Impedance (1kHz)
45±9kΩ (n=16)
Noise Level (800-3kHz)
2.2±0.5μVrms (n=26)
Contact Spacing
238±9μm (n=30)
4
FASCICULAR
GROUPINGS
FOR
49
Figure 11. Finished High Contact-Density Electrode. (Left) Array of 16 contacts produced by the technique in Figure 8. The array is 4mm wide. (Right) Completed electrode with FINE structure made from silicone sheeting and tubing and platinum tripolar references. (Below) Expanded view of stainless steel electrode array before inclusion in cuff, the scale bar is 1 mm and a sample inter-contact distance measurement is shown
Since the noise on each channel of the electrode is independent (the amplifier noise, not the “neural noise” or interfering biopotential signals) it should be possible to improve the signal to noise ratio by averaging in space across the contacts. Over 11 experiments, a 6±4 fold reduction in noise level, to as low as 0.2 μVrms, was measured. This result suggests a way to improve the noise floor in cases where spatial information is not needed (for example providing two modes, a spatially selective recording or stimulation mode and more sensitive precision recording mode).
50
Discussion This electrode design technique improves on current handmade Flat Interface Nerve Electrodes in a number of ways. Primarily, it allows smaller and more reliable contact spacing. This spacing is easily varied using wire with different insulation thickness and diameter, and can be made with a large variety of wire types, from stainless steel to platinum-iridium. Secondly, this technique is simple and repeatable, allowing electrodes to be built with little equipment by one technician. Even when stainless steel is used, these electrodes show impedance levels typical of contacts this small and when combined with a low-noise preamplifier (Intan Technologies) the noise floor is low enough to permit recording of compound action potentials and high frequency induced activity. These electrodes are built using only FDA approved methods and materials (silicone, silicone adhesive, stainless steel medical wire with PTFE insulation), and can have up to 4 contacts/mm. This density is competitive with electrodes built using photolithography techniques such as used in [30], which had a contact density of 2.5 contact/mm. In this work, only half of the contacts were used due to limitations in the sampling rate of the recording system resulting in 16 contacts per electrode (8 on top and 8 on bottom). When the two 16-contact electrodes were tested on the rabbit sciatic nerve, all 32 channels functioned properly and allowed spatially selective recording to be performed as in [3] (see Chapters II,IV). One of these electrodes has lasted 16 implantations with no obvious damage to the main recording contacts, although the tripolar references at the anastamoses of the cuff have delaminated and required reattachment. Two additional electrodes were fabricated with twice as long an exposure of stainless steel (along the length of the wire), they were not included in this test set as their impedance was
51 approximately half and their larger contacts precluded them from use with the beamforming algorithm, however all 32 combined channels were functional so they may be counted towards the yield of this technique (100% yield, n=4). A simplified version of an alternate technique proposed by [47] was also used to fabricate two 16-channel FINE. This technique involves using an Nd:YaG laser to cut gold foil on silicone sheeting.
While potentially useful for more complex designs, the resulting
electrodes were frail and difficult to connect lead wires to.
In a second alternate
technique, gold wire was heated to create evenly sized spheres on the ends. These wires could then be threaded through a sheet of silicone so that the spherical-contacts rested on the surface. Unfortunately, connecting lead wires was again an unsolved issue, however if the preamplifier can be included on the electrode cuff this technique may be convenient as the entire process could be performed with a modified wire-ball bonder. Neither technique produced electrodes suitable for these experiments, but they are presented in Appendix D for future reference. In general, high-contact density cuffs were found to provide significant benefit over more traditional tripolar designs. For example, the noise floor may be dramatically reduced by averaging in space across the various contacts. In one experiment where the baseline noise was on average 1.6µVrms, the noise level was improved to 0.2µVrms if the 16 channels were averaged together (overall, a 6±4-fold reduction in noise was seen, n=11). Interestingly, the noise level of this amplifier is largely insensitive to input impedance, suggesting that the noise level of one large contact with the same surface area as 16 regular contacts would be the same as a single regular contact.
Therefore this
improvement should hold even over large single-contact electrodes with 1/16th of the
52 impedance. If simple averaging of independent randomly distributed signals is involved, one would expect an improvement of 4 (=√16), which is well within 1 standard deviation of the result measured. The spatial information generated by this electrode is used in Chapters IV to separate signals originating from different fascicles or fascicle groups. A beamforming approach based on the a priori known geometry of this cuff electrode was able to separate evoked pseudo-spontaneous tibial and peroneal signals with 23±13% cross talk (n=10) (Chapter IV).
Conclusion A FINE with up to 32 channels was realized for a 4x2mm nerve, using only FDA approved methods and materials, as well as a fabrication process that is both low cost and extremely robust to repeated in vivo implantation. These electrodes had extremely precise contact spacing (238±9μm n=30) and signals were obtained from 16 contacts using a 16-channel recording system at 15 kHz/channel with 2.2±0.6μVrms (n=26) noise. The electrode is suitable for validating the fascicular signal separation algorithm presented in [3] (see Chapter II) and is used in the next chapter to obtain and recover fascicular signals from the rabbit sciatic nerve. Future work with the design of the cuff will involve the inclusion of the preamplifier and multiplexer directly on the cuff, in order to reduce wire tethering forces and make the system suitable for chronic implantation. Improving the design of the preamplifier stage, and the surface or material of the electrode may help further reduce the noise level to improve SNR.
53
Chapter IV:
Separation of Individual Branch Signals in an Acute In Vivo Peripheral Nerve Cuff Recording In this chapter, in vivo experiments are performed to determine the ability of the algorithm first presented in Chapter II to reconstruct signals from individual fascicular groups.
These tests are made possible by the high contact density electrode and
recording system presented in Chapter III. Two useful neural stimulation paradigms novel to this application are also described. This chapter will be submitted to a peerreviewed journal with authors Brian Wodlinger, and Dominique M. Durand. This work was supported by National Institutes of Health NINDS grant # 5R01NS032845-11 to Dominique M. Durand.
Abstract Despite great advances in many areas of medical technology over the past 20 years, the challenge of providing amputees a prosthesis with the intuitive control and functionality of a natural limb remains. The peripheral nerves of the residual limb should provide the robust and natural control signals needed, but these signals generally have low signal to noise ratios (SNR) are mixed in the volume conductor of the body, and extracting them represents an unsolved problem. Individual axons in peripheral nerves are separated into fascicles, which are loosely spatially organized based on the location they innervate. This spatial organization could allow the mixed signals from each fascicle to be separated using inverse problem or spatial filtering techniques and provide estimates of the signals
54 responsible for driving the missing limb. Once separated, these signals could allow voluntary control of a robotic prosthesis. A beamforming algorithm was applied to acute in vivo recordings obtained using a high contact-density Flat Interface Nerve Electrode on rabbit sciatic nerve proximal to the popliteal fossa during stimulation of the two major distal branches. Electrical stimulation was applied to individual branches to generate synchronized compound action potentiallike signals, as well as desynchronized pseudo-stochastic activity within the fascicles. The beamforming algorithm separated the fascicular signals better than the best pair of channels in every case (n=14) using a 16 channel nerve cuff electrode on the rabbit sciatic nerve (approximately 4mm x 2mm). Large compound action potential signals were separated with R2=0.81±0.08 (n=14) and during pseudo-spontaneous activity. The stimulated branch was classified with 98±4% accuracy (n=12) in 100ms bins (when at least 50% above of the motor activation threshold). These results show that this technique can recover selective fascicular signals and could be useful for providing voluntary natural and robust command signals for advanced prosthetic limbs for amputees.
Introduction Recent advances in the fields of electronics and robotics have made possible the design and manufacture of sophisticated anthropomorphic prosthetic arms and hands, each of which possess a large number of possible degrees of freedom. However, there are a limited number of ways for amputees to voluntarily control such devices. Some use
55 EMG signals from residual muscles, mechanical connections to the contralateral shoulder, or even a simple mode switch. None of these techniques provides a sufficient number of signals to take advantage of all the degrees of freedom available in these devices. In order to properly make use of this technology and advance the quality of life of amputees, it is necessary to develop a set of robust and natural voluntary command signals. Recently, Targeted Muscle Reinnervation [9] has been shown to provide these types of signals, but the surgery required is very invasive and the systems require daily electrode placement and have significant cross-talk. Penetrating electrodes have also been employed, such as the Utah Slanted Electrode Array (USEA) [40] and the Longitudinal Intrafascicular Electrode (LIFE) [13]. Both of these devices must penetrate the perineurium in order to place their contacts very close to axons and as a result have shown good signal to noise ratio and single-unit recording capability. Unfortunately, these results have not yet translated into robust, long-term command signals and the stability of these penetrating devices has not been established. Nerve cuff electrodes do not compromise the perineurium or the epineurium and have been shown to be both a safe and robust means of recording from the peripheral nervous system [24]. However, as they are much farther from the axons in the nerve, the signal to noise ratio is lower compared to penetrating devices, and they are only able to record field potential activity from a large number of units. This may be acceptable in the case of peripheral nerves as functional units of axons tend to be bundled within the same fascicles. This suggests that recovering fascicular level activity may be sufficient to reconstruct a muscle command signal. Several efforts have been made to use cuff
56 electrodes to separate recorded signals into the functional components controlling each muscle, using statistical [8, 27], neural network [17] and inverse problem methods [28, 30]. While all of these techniques have shown some level of selectivity, none take advantage of an important piece of a priori knowledge: the geometry of the cuff itself. In [3], a novel method based on Antenna Array techniques [22], where linear weights are used to focus the sensitivity of an array of recording electrodes to the broadband, nearfield nerve signal was presented. The simulation results showed that training the system on a homogeneous, rectangular epineurium and testing it on a finite element model of a human femoral nerve, localization was accurate to 180±170μm and mixed signals from fascicles separated by more than 1.5mm were separated with R2>0.8 using a single-pixel filter algorithm. Here, we extend that algorithm to reduce cross-talk between sources and test the modified algorithm in an in vivo rabbit preparation in order to determine its performance for both high-SNR low-frequency evoked activity and more physiological pseudo-spontaneous neural signals.
Methods Data Collection Six New Zealand White Rabbits were used for this study. Anesthesia was induced with 20-50 mg/kg IM ketamine and 5 mg/kg IV diazepam and maintained with 60 mg/kg IV alpha-chloralose (followed by one quarter dose every 2 hours or as needed) and .02 mg/kg IM buprenex every 9 hours. All protocols were approved by the Case Western Reserve University IACUC. Recordings were made from a novel 16-channel tripolar Flat Interface Nerve Electrode (FINE) placed on the sciatic trunk near the popliteal fossa. The signals were AC coupled, amplified, multiplexed and low-pass filtered at 5kHz by an
57 RHA1016 preamplifier chip (Intan Technologies, Utah). A National Instruments data acquisition card was used to perform A-to-D conversion and sampling at 15 kHz/channel. Tripolar stimulating FINE cuffs were placed on the Tibial and Peroneal branches of the Sciatic, distal to the recording cuff. Stimulation was applied to the cuffs using 130Hz, 5kHz, or 10kHz sinusoids. Signals were post-processed using an 800Hz – 3kHz bandpass filter to ensure removal of any remaining EMG or stimulation artifacts. A schematic of the setup is shown in Figure 12. These stimulation paradigms allow both high-SNR synchronized activity and lower-SNR pseudo-spontaneous activity to be generated and used for several offline experiments. The methods used to generate the test signals, the beamforming algorithm applied to them, and the metrics for analysis are all described below.
Figure 12. Schematic of the experimental setup. A 16-channel quasi-tripolar FINE is placed on the main sciatic trunk, and two tripolar stimulating cuffs are placed on the peroneal and tibial branches, distally. Stimulation is provided through isolated voltage-to-current stimulators and recording done using an Intan RHA1016 preamplifier.
58 Fascicular Signal Generation
Low Frequency Evoked Activity: In order to localize sources with as much accuracy as possible, a high SNR signal was generated. Traditional pulse-evoked Compound Action Potentials (CAPs) contain very large stimulation artifacts. Since anatomical constraints made moving the stimulating and recording cuffs farther apart difficult, we applied 130Hz sinusoidal stimulation which was found to generate CAP-like synchronized neural activity with high SNR and an easily filtered artifact.
Pseudo-random neural activity: Traditional methods of eliciting more realistic neural activity (i.e. sensory stimulation) were found to be difficult to control and ill-suited for the task of generating consistent, repeatable, and finely controlled neural signals. Similar to the technique described in [49] for more physiological cochlear implant stimulation, 5 or 10 kHz sinusoids were used to elicit pseudo-spontaneous activity at a variety of amplitudes. The timing and amplitude of this activity could be controlled by modulating the amplitude of the stimulation waveform. The artifact could be easily removed and the statistical properties of the neural signals were similar to those observed during sensory activity Beamforming and Sourcebased Filters Described more completely in [3], Beamforming involves the generation of a large number of spatial filters from a priori knowledge of the cuff geometry. These filters can then be used to map the instantaneous voltage on each contact to an image of the activity within the nerve cross-section. The differences in spatial location of the sources make it possible to recover the voltage signals from each source. The full algorithm is divided into three steps. First, a finite element model of the cuff to be implanted containing an
59 empty, rectangular epineurium and volume conductor is created. This model is used to calculate the lead-field matrix representing the sensitivity of each contact to each pixel in the nerve cross-section. This lead-field matrix is used to calculate the Transformation matrix described below (and in Chapter II) which integrates the a priori knowledge of the cuff geometry and epineurium conductivity. Second, after the cuff has been implanted, functionally distinct sources are localized by activating single fascicles or functional groups. The recorded responses during this activity are multiplied by the transformation matrix (training phase) to localize the signal within the nerve cross-section. A short 100ms segment of nerve activity has been shown to be sufficient to localize the sources (see Chapter II). Once the sources have been localized, the spatial filters associated with each source are calculated. In Chapter II, each pixel was associated with a single Pixel Filter (SPF). Here source-based filters (SBF) are designed to select signals from the full spatial extent of a particular source, while rejecting signals from interfering sources (see section below) Transformation Matrix First, a lead-field matrix (S) is generated [32] using a finite element model of the cuff electrode including a homogeneous, rectangular epineurium (Figure 13). The lead-field matrix provides the sensitivity of each contact on the electrode to each pixel in the nerve cross-section and is used with Equation 5 to calculate the least-squares optimal filter (t) for each pixel (i), where δ is the Kronecker delta function.
60
Figure 13. The model used to generate the Transformation Matrix. The cuff has a 5mm x 1.5mm lumen and 8 recording contacts per side. Recording is performed using a quasi-tripolar technique by referencing the large outer electrodes at the openings of the cuff. Note that this model includes no nerve geometry, and so can be solved before cuff implantation. The cuff is made of silicone and enclosed in a large saline bath. [3]
These filters are normalized using Equation 6, and then concatenated to form a transformation matrix which when multiplied by the contact voltages gives an instant-byinstant estimate of the activity at each pixel in the cross-section. Please see [3] for details on these equations, including the technique used to solve Equation 5.
(5) (6)
Localization of sources The second step in the signal recovery is the determination of the location of the source within the cuff in order to optimize the spatial filters, t. 130Hz current-controlled sinusoidal stimulation was used to elicit compound action potentials (CAPs) on each branch in separate trials which were then averaged over 30 iterations to improve the SNR. The RMS power was calculated on each channel over the duration of the CAP and the transformation matrix was applied to the resulting 16x1 vector producing an estimate of the location of the source within the nerve cross-section. Figure 14 shows the results of three localization experiments on three separate nerves. In each case, the top 10% of
61 the beamforming activity map for the tibial and peroneal sources are shown (tibial in red, peroneal in green). The accuracy of the source localization has been previously studied using computer simulations and is 180±170μm [3]. To obtain experimental verification, the images for each source are superimposed on histological nerve cross sections (Methylene Blue stain) showing the fascicles and a scale illustration of the cuff and contact positions. In all three cases, the position of the nerve in the cuff is centered and the separation between the sources and relevant fascicle groups are consistent with the location of the source. Further quantification of these data is not possible since neither the position of the cuff relative to the fascicles, nor the exact origin of the signals within their respective fascicular groups, is exactly known.
Figure 14. Examples of source localization in three rabbit sciatic nerves. These images show the locations estimated using the beamforming algorithm, with nerve histology overlayed and a schematic of the cuff, for reference. The tibial branch signals are in red, while peroneal branch signals are in green – in every case they overlap the correct group of fascicles. Note that the position of the nerve histology within the cuff is approximate.
62 SourceBased Filter (SBF) Generation The transformation matrix contains ideal filters for each pixel in the nerve cross-section and this technique (the “single pixel filter” or SPF) was used in the simulation experiments of Chapter II [3]. However, this matrix does not account for the finite spatial extent of the source or the locations of interfering sources. To improve the determination of the spatial extent of the sources, new filters are generated to take into account information from other locations. The filters from each pixel are weighted by the value of the source image at that pixel and averaged. This method places more emphasis on locations where the source is stronger, and provides some spatial averaging to reduce noise.
(7)
Where n is the number of contacts, m is the number of pixels, fi{1 x n} is the filter for the ith source, Si{m
x 1}
is the source image for that source, and M{m
x n}
is the transformation
matrix. In order to reduce sensitivity to areas with high interference, the spatial locations causing interference are iteratively subtracted from each filter using the following: 1. Calculate the interference (Iij) due to source j picked up by the filter for source i | (8) 2. Subtract or add the difference between the images, multiplied by the amount of incorrect signal in each to reduce the amount of interfering signal ∑ | (9) 3. Repeat, also recalculating the filters as in equation 7, until: threshold reached, or previous iteration was ineffective at removing inference
See Appendix A for a discussion of other techniques for improving the beamforming algorithm.
63 Analysis Metrics Correlation Coefficient The correlation coefficient was used as a metric of similarity between signals in order to be consistent with previous work [3, 8, 17]. In particular, recordings of single-branch activity were filtered using the Source-Based Filter (SBF) scheme, and correlated with multiple-branch activity, filtered using the same SBFs in order to determine how well the filters rejected interfering activity.
Correlation coefficients were calculated as in
Equation 10 ,
,
(10)
Best a posteriori Single Channel In order to compare these high-contact density techniques with more traditional techniques, the channels most highly correlated with each recovered single-source signal were selected after each trial. The correlation coefficients obtained with these channels which take into account interference as well as SNR, were compared with the correlation coefficients produced by the beamforming algorithm. Calculation of Information Transfer Rate In order to determine the feasibility of using this system for controlling a prosthetic limb, a bit-rate calculation was performed.
The signals from each source were treated
independently, and the range of amplitudes recorded was broken down into a set of classes. A linear discriminant analysis was performed to determine the accuracy with which these data could be classified according to the strength of stimulation (and so expected level of neural activity). 10% of the data were used for training and the
64 remaining 90% for testing. Equation 11 [50] was used to calculate the throughput or bitrate where TP is the throughput in bits-per-second, R is the classification rate (in this case fixed at 10 classifications/second or 100ms bins), N is the number of classes, and P is the classification accuracy. 1
log
P N
(11)
Results Results are first presented demonstrating the techniques used to elicit activity on the branches of the Sciatic nerve as these techniques are not standard and provide very interesting opportunities for further work. Second, large SNR recordings of synchronized activity are investigated, and the SBF algorithm applied to separate them.
Having
investigated the accuracy of the algorithm on high SNR signals, pseudo-spontaneous signals are then applied and used in progressively more difficult tests from simple 2-state classification, to amplitude recovery, and finally separation of low-SNR pseudospontaneous signals. In each of these experiments except the last, signals are recorded in vivo and then mixed or compared offline under the assumption that the volume conductor is linear. This final result therefore also provides validation of the linearity of the volume conductor. Fascicular Signal Generation In order to test the fascicular recovery algorithm, low frequency and pseudo-spontaneous neural activity were obtained from a 16-channel FINE. In both cases the stimulation artifact was a single frequency outside the signal band, and so easily removed. The low frequency signals provide synchronized neural activity with high signal to noise ratio
65 while the pseudo-spontaneous signals were similar to physiological neural or motor activity. Low Frequency Evoked Activity 130Hz sinusoidal stimulation applied to each fascicle was found to elicit CAP-like discharges from the nerve superimposed on the artifact (Figure 15A). Since the artifact was sinusoidal, it could easily be removed using notch or high-pass filters by a minimum of 100dB as shown in Figure 15B. These signals increased in amplitude and complexity with increasing stimulation amplitude and had a signal to noise ratio of 12±5 times. Recent work also demonstrates that these waveforms may be able to block C-fiber activity (chronic pain sensation) in vivo. Since this stimulation may activate large motor fibers at the same time, it would be ideal for an amputee population suffering from phantom limb pain.
The experiments used to demonstrate this selective blocking
capacity are presented in Appendix B.
Figure 15. 130Hz Sinusoidal stimulation produces CAP-like neural responses with variable amplitude, delay, and complexity as the stimulation intensity is raised. (A) Recording high-pass filtered at 100Hz, (B) the same signal high-pass filtered at 800Hz. (C) A sample spike from the 170μApp stimulation level. Note that the filter has effectively removed all traces of the stimulus artifact (119dB rejection).
66 Pseudospontaneous Activity The signals generated by the sinusoidal stimulation described above produce neural responses with a good SNR but they are significantly different from spontaneous signals [41] which are unsynchronized and display stochastic properties.
In order to elicit
activity resembling natural signals while maintaining control of the timing and amplitude, 5 or 10kHz sinusoids were applied. Since the neuronal refractory periods are longer than a single period of this stimulation, axons are unable to fire synchronously and the activity becomes pseudorandom [49]. The recorded signals were digitally filtered between 8003000Hz to remove any artifact or EMG contamination and are shown in Figure 16B, along with spontaneous natural activity in Figure 16A and a comparison of the power spectra in Figure 16C. See Appendix C for preliminary work on the mechanism of this desyncronization.
67
Figure 16. Generating Pseudo-spontaneous activity. (A) Experimentally recorded hypoglossal nerve signal (from Mesut Sahin PhD thesis ‘Chronic Recordings of Hypoglossal Nerve in a Dog Model of Upper Airway Obstruction’ 1998) shown here for comparison with the 5kHz evoked neural signals recorded during these experiments. (B) ENG signals during 5 KHz stimulation of the peroneal branch, filtered 800-3000Hz at three different intensities. Each intensity was recorded during a separate but sequential trial and a segment from each is shown side-by-side here for comparison. The power of the signal increases as the stimulation intensity (given in white at the center of each segment) increases. (C) Comparison of power spectral densities from ENGs recorded during 5kHz peroneal stimulation at increasing intensity with recordings during spontaneous inspiration, using data from A. (D) Box and whisker plot of power in recorded signal for each stimulation intensity applied. Points above each column represent outliers.
Recovery of Low Frequency Evoked Activity In order to test the ability of the algorithm to recover signals from the high-SNR lowfrequency evoked activity, the Tibial and Peroneal fascicles were stimulated with a 130Hz sinusoidal stimulus independently and recorded signals were then mixed off-line. Due to the linearity of the volume conductor, no generality is lost with the off-line mixing
68 and it does provide single-source references for evaluating the separation quality. However, adding these signals offline does have the side effect of reducing the signal to noise ratio up to √2. In order to validate the procedure mixed signals are recorded directly and studied in a later section. The artifact was removed and the transformation matrix was applied to localize the activity within the nerve (see methods). An example of the recovered signals from the two identified sources is shown in Figure 17. Two sets of 30s 16-channel recordings were obtained separately (one during stimulation of each branch) in order to have a true single-branch reference available to quantitatively assess the separation.
These two 16-channel signals were normalized to eliminate the
confounding effect of sensitivity differences in the recordings before being added together to create a mixed 2-branch signal. The tibial and peroneal filters were first calculated using the beamforming algorithm (equations 3-5) then applied to the data. An example of the recovered signals from the two identified sources is shown in Figure 17B,C.
69
Figure 17. Separation of Peroneal and Tibial components from combined signal using Beamforming filters. (A) The mean of all 16-channels (for clarity) for a signal created by adding a normalized recording during tibial stimulation with a normalized recording during peroneal stimulation. The beamformers were applied to this signal to generate an estimate for each branch, shown in the B,C (Recovered signal). The two signals can easily be distinguished based on the shape of the responses, and the separation is nearly complete. The equivalent single-branch signals (calculated by applying the filters to the single-branch recordings directly) are shown as a thick line for reference.
Since the original recordings contained only single-branch activity and therefore could be used as a reference to gauge separation quality calculated using the correlation coefficient between the output of the filter on the single-branch signal and the output of the filter on the mixed 2-branch signal. For comparison, the correlation was calculated between each of the 16 channels in the combined signal and the output of the filter on the single-branch signal. Figure 18 shows the correlation coefficients obtained for both the SBF and SPF beamforming filters along with the correlation coefficient obtained from the “best” contact, defined as the single contact with the highest correlation to the filtered singlebranch recording, for each branch for all nerves tested. The results from seven animal experiments (14 branches) show the signals recovered by the source based filter
70 beamforming algorithm were highly correlated with the single-branch recordings, R2=0.81±0.08 (n=14). This represents an improvement of 30±14% over the best single channels in the mixed recording and 22±11% better than the single pixel filter. Note that while the SBF results (light bar) are always better than the best single channel (dark bar), the SPF algorithm (grey circles) shows much higher variation and can be better than the SBF algorithm, or worse than the best single channel. The results also show that even a posteriori when the true single-branch signal is known, it is not possible to select a channel that is a better estimate than the beamforming filter. This is true even though the beamformer is calculated without knowledge of the reference signal. The normalization of the signals, which makes the noise floor uneven between the two branches, was done so that the accuracy of each separation would not depend on the relative magnitudes of the CAPs (as this can be modified by stimulation intensity anyway, but is difficult to match perfectly). It is unclear how much this increased noise floor has degraded the results, but even so these results are still valid as a lower bound.
71
Figure 18. Cross-correlation of the recovered single-branch signals with the recovered mixed-branch signals (light) and the best single channels in the mixed-branch recording (dark). The R2 for each of the 16 channels compared to each recovered single-branch signal was calculated and the highest value is shown here compared to the value from the beamforming estimate. Note that despite the fact that the best channel was calculated a posteriori and the beamforming filters a priori, the beamformers still outperform by 0.24±0.11. Grey circles represent the performance of the beamforming approach in [3], without the source-based filter selection algorithm described in this work. The beamforming algorithm accuracy was R2=0.81±0.08 (n=14).
Effect of Contact Density and Position on Signal Recovery In order to determine the role of contact density the above experiments were repeated with 8 instead of 16 contacts. Other recording configurations were produced by removing rows from the transformation matrix and recorded data. Two different configurations were tested 1) top half of the electrode only, and 2) evenly numbered contacts only. The transformation matrix was recalculated using equations 1 and 2 with the appropriate rows of the lead-field matrix removed; the Tibial and Peroneal filters were then recalculated using the SBF algorithm. The correlation coefficient was calculated between the output of these reduced tibial or peroneal filters on the mixed-branch signal and the full tibial or
72 peroneal filter (ie, all 16 channels active) operating on the single branch signal to determine the relative quality of the techniques. The results indicate that any decrease in the contact density produced a significant decrease in the cross-correlation coefficients. For the 7 animal experiments, with 2 sources for each nerve, reducing the number of contacts to 8 from the full 16 contacts (2/mm) reduced R2 value from 0.81±0.08 to 0.47±0.28 when only the top half of the electrode was used and to 0.59±0.19 when only the evenly numbered contacts were used. The reduction in accuracy when using the best single-channel recordings (best channel chosen based on the highest correlation coefficient) instead of the SBF algorithm with 16 contacts is lost when only 8 contacts are available, suggesting a certain contact density is required to achieve the full benefits of the algorithm. A full comparison of all of the different test configurations is available in Table 5, for all values n=14 and single-sided paired t-tests were used to determine statistical significance.
73 TABLE V SUMMARY OF LARGE SIGNAL RECOVERY ACCURACY
Number Filter
Configuration of
Test Case
R2
of Calculation
Contacts
Reduction in
Statistical
Performance
Significance
Contacts
Source
based
Source-based
16
Full
0.81±0.08
0
Single row of
16
Full
0.64±0.14
0.18±0.09
p
