Improved action potential detection

Abstract

For separating compound action potentials from artifacts in a neural recording. A memory stores a set of basis functions including at least one compound action potential basis function and at least one artifact basis function. A neural recording of electrical activity in neural tissue is decomposed by determining at least one of a compound action potential and an artifact based on the set of basis functions. An estimate of at least one of a compound action potential and an artifact is output.

Description

Technical Field

[0001] The present invention relates to electrical recording of neural activity, such as compound action potentials evoked by neural stimulation, and more particularly to systems and methods for improving detection of neural responses in the presence of stimulation artifacts, noise, and the like. Background of the Invention

[0003] Electrical neuromodulation is used or contemplated for the treatment of various diseases (including chronic pain, Parkinson's disease and migraines), as well as for the restoration of functions such as hearing and motor function. Neuromodulation systems apply electrical pulses to neural tissue in order to produce a therapeutic effect. Such systems typically include an implantable electrical pulse generator and a power source such as a battery that can be recharged by transcutaneous inductive transmission. An electrode array is connected to the pulse generator and positioned near the neural pathway (s) of interest. The electrical pulses applied to the neural tissue by the electrodes cause depolarization of the neurons, which produces a propagating action potential (reverse, forward, or both) to achieve a therapeutic effect.

[0004] When used, for example, to relieve chronic pain, electrical pulses are applied to the dorsal columns (DC) of the spinal cord, and the electrode array is positioned in the dorsal epidural space. The dorsal column fibers stimulated in this way inhibit the transmission of pain from that section of the spinal cord to the brain.

[0005] Generally speaking, the electrical stimulation generated in a neuromodulatory system triggers a neural action potential, which later has an inhibitory effect or a stimulatory effect. The inhibitory effect can be used to modulate an undesirable process such as pain transmission, or the stimulatory effect can be used to induce a desired effect such as muscle contraction or auditory nerve stimulation.

[0006] Action potentials generated in a large number of fibers are summed to form a compound action potential (CAP). The CAP is the sum of the responses caused by a large number of individual fiber action potentials. When the CAP is recorded electrically, the measurement includes the results of a large number of different fiber depolarizations. The propagation speed is largely determined by the fiber diameter and can exceed 60 ms for large myelinated fibers found in the dorsal root entry zone (DREZ) and nearby dorsal columns of the spinal cord. -1 The CAP produced by the excitation of a group of similar fibers is measured as a positive peak P1 of the recorded potential, followed by a negative peak N1, followed by a second positive peak P2. This is caused by the area of ​​activation passing through the recording electrode as the action potential propagates along the individual fibers, resulting in a typical three-peak response curve. Depending on the stimulation polarity and the sensing electrode configuration, the measured curve of some CAPs may have opposite polarity, i.e., two negative peaks and one positive peak.

[0007] In order to better understand the effects of neuromodulation and / or other neural stimulation, and, for example, to provide stimulators controlled by neural response feedback, it is desirable to accurately detect and record the CAP produced by stimulation. When the evoked responses occur later than the time when the artifact occurs, or when the signal-to-noise ratio is high enough, they are less difficult to detect. Artifacts are typically confined to a time of 1-2 ms after stimulation and therefore response measurements can be more easily obtained if the neural response is detected after this time window. This is the case in surgical monitoring, where the distance between the stimulating electrode and the recording electrode is large (e.g., for a 60 ms pulse). -1 conduction nerves, greater than 12 cm), so that the propagation time from the stimulation site to the recording electrode exceeds 2 ms.

[0008] However, in order to characterize the responses from the dorsal columns, high stimulation currents and close proximity between the electrodes are required. Similarly, any implantable neuromodulation device must be of compact size, so that in order for such a device to monitor the effects of the applied stimulation, the (multiple) stimulation electrode(s) must be in close proximity to the (multiple) recording electrode(s). In this case, the measurement process must directly overcome the artifacts. However, this can be a difficult task because the CAP signal component observed in the neural measurements will typically have a maximum amplitude in the microvolt range. In contrast, the stimulation applied to induce CAP is typically several volts and can result in electrode artifacts, which appear in the neural measurements as an attenuated output of several millivolts that occurs partially or completely simultaneously with the CAP signal, which poses a significant obstacle to separating or even detecting the much smaller CAP signal of interest.

[0009] For example, to resolve a 10μV CAP with a resolution of 1μV in the presence of, for example, a 5V input stimulus requires an amplifier with a dynamic range of 134dB, which is impractical in an implantable system. Because neural responses can occur simultaneously with stimulation and / or stimulation artifacts, CAP measurements present a difficult challenge to the design of the measurement amplifier. In practice, many non-ideal aspects of the circuit lead to artifacts, and because most of these have a decaying exponential appearance that can be either positive or negative, their identification and elimination can be laborious.

[0010] The difficulty of this problem is further exacerbated when attempting to implement CAP detection in an implantable device. The power budget of a typical implant allows for a limited number (e.g., a few hundred or a few thousand) of processor instructions per stimulus in order to maintain the desired battery life. Therefore, if a CAP detector for an implantable device is to be used regularly (such as on the order of once per second), care must be taken that the detector consumes only a small portion of the power budget.

[0011] Any discussion of documents, acts, materials, devices, articles and the like that has been included in this specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all of these matters formed part of the prior art base or were common general knowledge in the field relevant to the present invention by virtue of their existence before the priority date of each claim of this application.

[0012] Throughout this specification, the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or any other group of elements, integers or steps.

[0013] In the present specification, stating that an element may be “at least one of” a list of options will be understood that the element may be any one of the listed options, or may be any combination of two or more of the listed options. Summary of the invention

[0014] According to a first aspect, the present invention provides a system for separating compound action potentials from artifacts in neural recordings, the system comprising:

[0015] A memory storing a set of basis functions including at least one compound action potential basis function and at least one artifact basis function;

[0016] an input for receiving a neural recording of electrical activity in neural tissue; and

[0017] A processor is configured to decompose the neural recording by determining at least one of a compound action potential and an artifact based on the set of basis functions, and is further configured to output an estimate of at least one of the compound action potential and the artifact.

[0018] According to a further aspect, the present invention provides a method for separating compound action potentials from artefacts in neural recordings, the method comprising:

[0019] accessing a memory containing a set of basis functions, the set of basis functions including at least one compound action potential basis function and at least one artifact basis function;

[0020] receiving neural recordings of electrical activity in neural tissue; and

[0021] decomposing the neural recording by determining at least one of a compound action potential and an artifact from the set of basis functions, and

[0022] An estimate of at least one of a compound action potential and an artifact is output.

[0023] According to another aspect, the invention provides computer software for performing the method of the second aspect.

[0024] According to another aspect, the present invention provides a computer program product comprising computer program code means for causing a computer to execute a program for separating compound action potentials from artefacts in neural recordings, the computer program product comprising computer program code means for executing the method of the second aspect.

[0025] According to a further aspect, the present invention provides a non-transitory computer readable medium for separating compound action potentials from artifacts in neural recordings, the non-transitory computer readable medium comprising instructions which, when executed by one or more processors, cause the method of the second aspect to be performed.

[0026] The electrical activity in the neural tissue may include evoked compound action potentials evoked by electrical stimuli applied to the neural tissue. The artifact basis function may be matched to electrical artifacts known to be induced by one or more such electrical stimuli.

[0027] In some embodiments of the invention, one or more corresponding estimates of a base signal may be output, the base signal comprising a compound action potential signal component of the neural recording and an artifact component of the neural recording. In some embodiments, the base signal may further comprise one or more of: background neuronal activity, such as neuronal activity not induced by the electrical neural stimulation; and / or induced late responses that may be produced by induced myoelectric activity.

[0028] In some embodiments of the invention, the or each estimate of the basis signal(s) may be a deterministic estimate.

[0029] In some embodiments of the invention, evoked compound action potentials (ECAPs) and artifacts are estimated simultaneously. In such embodiments, the estimated ECAPs and estimated artifacts can be balanced to best represent the observed neural recordings.

[0030] In some embodiments, an estimate of the noise-free ECAP may be output. In some embodiments, a signal characteristic may be imposed on some or all of the output estimates. In some embodiments, a signal characteristic of zero DC may be imposed on the ECAP estimate.

[0031] In some embodiments, the computational efficiency of the computational process for separating the compound action potential from the artifact in the neural recording can reach a level such as O(n). In some embodiments, the computational process for separating the compound action potential from the artifact in the neural recording can be performed within a determined time. In some embodiments, the computational process for separating the compound action potential from the artifact in the neural recording can be implemented in firmware of an implantable device.

[0032] In some embodiments, each basis signal is represented as a linear combination of basis functions. In such embodiments, the basis functions may be derived in advance, such as empirically and / or from a model of the basis signals. In such embodiments, the basis functions may be constant or may be periodically updated, such as by a firmware upgrade.

[0033] In some embodiments, the ECAP can be modeled in the basis function by a function that matches the expected noise-free ECAP morphology. For example, the ECAP can be modeled in the basis function by a piecewise function consisting of a sine wave of one period and a subsequent exponential function so that the derivative is continuous at their boundaries. The ECAP can be modeled in the basis function by a function that is fitted to a simulated ECAP model. The ECAP can be modeled in the basis function by a parameterized function having parameters that allow time stretching, time offset, and / or DC offset. Such parameterization may be limited in order to maintain computational performance, minimize the effects of broadband noise, and limit interference from artifacts while containing all expected real-world ECAPs. The ECAP can be modeled in the basis function by two or more basis functions, including, for example, a first basis function optimized for single-ended neural recording and a second basis function optimized for differential neural recording. For example, the second basis function can be formed as the difference between two parameterized ECAP basis functions to reflect the properties of differential recording as the difference between the ECAP signals observed at each corresponding recording electrode.

[0034] In some embodiments, the artifacts may be modeled in the basis function by three basis functions, including a DC basis function, a linear basis function, and an exponential basis function. The exponential basis function may, for example, have φ3(t)=e (-at), where a is a constant that is modeled or empirically matched to the relaxation component of the artifact. For example, a can be determined empirically from a library of human neural stimulation artifact recordings associated with the device and stimulation paradigm in use. In one embodiment, a is in the range of 10,000 to 70,000, more preferably in the range of 30,000 to 50,000, more preferably in the range of 35,000 to 40,000, and for example in one embodiment, a=38,348.

[0035] In an alternative such embodiment, the exponential basis function may be replaced with a fractional pole scrubber.

[0036] Some preferred embodiments of the present invention further provide for the detection of recordings in which only artifacts are present without any ECAP. In such embodiments, the signal is modeled using a basis function of only the artifacts, and also using a basis function of the combined ECAP and artifacts. A set of signal features is derived from the estimates produced by these two models, and the set of signal features is combined with the signal features from the recorded signal. This embodiment analyzes a series of signals known to contain both ECAP and artifacts or only artifacts, and saves the derived set of features. Machine learning is used to train a classifier with the following categories: 'ECAP' or 'no ECAP'. After sufficient training, the resulting classifier is able to automatically determine the presence of ECAP in the signal.

[0037] According to a further aspect of the present invention, there is provided a method for removing artifacts from a neural recording, the method comprising:

[0038] Receiving neural recordings of electrical activity in neural tissue;

[0039] fitting a fractional polar model of the artifacts to the neural recordings; and

[0040] The fitted fractional polar model was removed from the neural recordings.

[0041] In some embodiments of the invention, the electrical stimulation applied to induce the neural response may include multipolar stimulation applied from three or more stimulation electrodes, the stimulation being configured to induce a neural response only in one phase of the stimulation and only at one site. For example, the multipolar stimulation may be configured according to the teachings of the applicant's international patent application number PCT / AU 2019 / 051151, the contents of which are incorporated herein by reference.

[0042] In some embodiments of the invention, neural recordings are obtained by an implantable spinal cord stimulator. Alternatively, neural recordings may be obtained by alternative neural stimulation devices.

[0043] References to estimation or determination herein should be understood to refer to an automated process performed on data by a processor operating to execute a predefined estimation or determination program. The method proposed herein can be implemented in hardware (e.g., using an application-specific integrated circuit (ASIC)) or software (e.g., using instructions tangibly stored on a computer-readable medium to enable a data processing system to perform the above steps), or a combination of hardware and software. The present invention can also be embodied as a computer-readable code on a computer-readable medium. The computer-readable medium may include any data storage device that can store data, which can then be read by a computer system. Examples of the computer-readable medium include a read-only memory ("ROM"), a random access memory ("RAM"), a CD-ROM, a DVD, a magnetic tape, an optical data storage device, a flash memory device, or any other suitable storage device. The computer-readable medium can also be distributed on a network-coupled computer system so that the computer-readable code is stored and executed in a distributed manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Examples of the present invention will now be described with reference to the accompanying drawings, in which:

[0045] Figure 1 An implantable spinal cord stimulator is schematically shown;

[0046] Figure 2 is a block diagram of an implantable neurostimulator;

[0047] Figure 3 is a schematic diagram showing the interaction of an implanted stimulator with a nerve;

[0048] Figure 4 The washing process is shown;

[0049] Figure 5 is a signal flow graph;

[0050] Figure 6 The ECAP basis functions and the pseudo basis functions and their products are shown;

[0051] Figure 7 A complete algorithm of an embodiment is presented;

[0052] Figure 8 is an alternative illustration of a system for stimulating tissue and recording ECAP;

[0053] Fig. 9 shows the stimulus waveform as seen on the recording electrode;

[0054] Fig.10 Shown Fig. 9 simplification;

[0055] Fig.11 Demonstrates separation of resistive and capacitive components of input impedance; and

[0056] Fig.12 is a further simplification of the circuit being analyzed. DETAILED DESCRIPTION

[0057] Figure 1 An implantable spinal cord stimulator 100 is schematically illustrated. The stimulator 100 includes an electronics module 110 implanted at a suitable location in the patient's lower abdominal region or upper posterior buttock region, and an electrode assembly 150 implanted in the epidural space and connected to the module 110 by suitable leads. Many aspects of the operation of the implantable neural device 100 can be reconfigured by an external control device 192. In addition, the implantable neural device 100 plays a data acquisition role, wherein the acquired data is communicated to the external device 192.

[0058] Figure 2 is a block diagram of an implantable neurostimulator 100. Module 110 includes a battery 112 and a telemetry module 114. In an embodiment of the present invention, telemetry module 114 may transmit power and / or data between an external device 192 and the electronics module 110 using any suitable type of transcutaneous communication 190, such as infrared (IR) transmission, electromagnetic transmission, capacitive transmission, and inductive transmission.

[0059] The module controller 116 has an associated memory 118 that stores patient settings 120, control programs 122, etc. The controller 116 controls the pulse generator 124 to generate stimulation in the form of current pulses according to the patient settings 120 and the control program 122. The electrode selection module 126 switches the generated pulses to the appropriate electrode(s) of the electrode array 150 for delivering the current pulses to the tissue surrounding the selected electrode(s). The measurement circuit 128 is configured to capture measurements of the neural responses sensed at the sensing electrode(s) of the electrode array as selected by the electrode selection module 126.

[0060] Figure 3 1 is a schematic diagram showing the interaction of the implantable stimulator 100 with the nerve 180, however, in this case, the spinal cord alternative embodiment can be positioned near any desired neural tissue (including peripheral nerves, visceral nerves, parasympathetic nerves, or brain structures). The electrode selection module 126 selects the stimulation electrode 2 in the electrode array 150 to deliver three-phase current pulses to the surrounding tissue including the nerve 180, but other embodiments can additionally or alternatively deliver biphasic tripolar stimulation. The electrode selection module 126 also selects the return electrode 4 in the array 150 for stimulation current recovery to maintain zero net charge transfer.

[0061] Appropriate stimulation is delivered to the nerve 180 to induce a neural response, which includes a compound action potential that will propagate along the nerve 180 as shown for therapeutic purposes, which in the case of a spinal cord stimulator for chronic pain may be to produce paresthesia at a desired location. To this end, the stimulating electrodes are used to deliver stimulation at 30 Hz. To assemble the device, the clinician applies stimulation that produces a sensation that the user experiences as paresthesia. When the paresthesia is in a location consistent with an area of ​​the user's body affected by pain and has a size consistent with the area, the clinician recommends continued use of the configuration.

[0062] The device 100 is further configured to sense the presence and electrical profile of a compound action potential (CAP) propagating along the nerve 180, whether such CAP is induced by stimulation from electrodes 2 and 4, or induced in other ways. To this end, the electrode selection module 126 can select any electrode of the array 150 to serve as the measurement electrode 6 and the measurement reference electrode 8. The stimulator housing can also be used as a measurement or reference electrode, or a stimulation electrode. The signals sensed by the measurement electrodes 6 and 8 are transmitted to the measurement circuit system 128, which can, for example, operate according to the teachings of the applicant's international patent application publication number WO2012155183, the contents of which are incorporated herein by reference. The present invention recognizes that in applications such as Figure 3 In cases where the recording electrode is close to the stimulation site as shown, stimulation artifacts pose a significant obstacle to obtaining accurate recordings of compound action potentials, yet reliable and accurate CAP recordings are a key enabler for a range of neuromodulation techniques.

[0063] The present invention provides a method for separating a composite signal when the signal components belong to a closed signal space that can be represented by different basis sets. In neuromodulation, this is used to separate the 'ECAP part' and the 'artifact part' of a recorded signal.

[0064] A composite signal is a signal consisting of the sum of other signals, which are referred to herein as basis signals. The basis signal separation method of the present invention estimates the basis signal of a composite signal given only the composite signal, without knowing the exact basis signal. The present embodiment provides a blind signal separation algorithm that can assume some knowledge about the basis signal. That is, the present embodiment recognizes that it can be assumed that each basis signal can be represented by a set of basis functions. Unlike a blind signal separation algorithm with multiple inputs and one output, the present invention generates a deterministic estimate of the basis signal by utilizing this assumption.

[0065] In the field of neurostimulation, mixed signals can be a combination of ECAP and stimulation artifacts. In some cases, it is necessary to decompose the signal and analyze the components. Analyzing the individual components can reveal the characteristics of the signal components that can be used in a variety of advantageous ways. In some cases, analyzing the components of the mixed signal can reveal errors in the system. Further, there may be situations where a mixed or composite signal has a main but redundant component that masks an important component. In such a case, it is necessary to decompose the mixed signal into its components, remove the redundant components, and analyze the important components and their characteristics.

[0066] The present invention decomposes a mixed signal by determining at least one of the multiple signals that make up the composite signal based on a set of basis functions. The present invention separates a composite signal into its basic components by modeling each basic component of the composite signal with a basis. The present invention can be applied to neuromodulation to separate ECAP waveforms from artifact waveforms (and noise) given a signal recording that is a mixture of these signals. This results in more robust feature extraction from the ECAP, including the ECAP amplitude, which is obtained by Figures 1 to 3 features used during operation of a closed-loop control system. Additional features such as the ECAP peak position may also be measured more robustly, which may have scientific and / or operational benefits. The present embodiment estimates both the artifact and the ECAP simultaneously, where the signal contributions of the ECAP and the artifact are balanced to "best" represent the recorded signal. The present embodiment produces a noise-free ECAP estimate, and depending on the definition of the ECAP basis set, certain signal characteristics may be imposed (e.g., a baseline of 0V). Further, the present embodiment is efficient (O(n)) and runs in deterministic time (unlike non-deterministic methods), which means that it can potentially be integrated into firmware, providing improved real-time ECAP amplitude estimates without the need for manually tuning filters.

[0067] A scrubber is an algorithm that estimates the ECAP classification and artifact components of a composite signal. A composite signal is defined as a signal that is composed of the sum of multiple different components. In the context of ECAP measurements, the components of the composite measurement are the artifacts, the neurophysiological response to the stimulus (ECAP), and everything else. The main goal of the scrubber is to isolate the ECAP. However, artifact estimation is often a byproduct of this task and is useful in itself, as insights into the artifact mechanisms will help us minimize them in future designs. The rest includes noise from the electronics and neurophysiology that is not related to the stimulus. Figure 4 shows this process.

[0068] This embodiment adopts the following process. Each basis signal is represented as a linear combination of basis functions. Consider a composite signal with two basis signals:

[0069]

[0070] The basis functions are derived empirically based on experience and surrogate models of the basis signal. For the purposes of explanation, they are treated as constants. Computing the pairwise inner products of the basis functions and the inner product between each basis function and the composite signal, one can write a set of linear equations that can be solved by matrix inversion to obtain a set of coefficients α and β. Given the α coefficient, one can then write down a basis representation of f(x), thereby estimating f(x). Similarly, g(x) can be estimated given the β coefficient. The method is not limited to composite signals containing two components, but rather the problems to which it is applied in the described field of neuromodulation have only two components.

[0071] The basic element signal separation method of this embodiment is a mathematical tool for deconstructing composite signals. Consider a signal containing an ECAP component f(t) and an artifact component g(t). Therefore, the signal σ(t) measured on the patient can be expressed as:

[0072] σ(t)=f(t)+g(t)+e(t)

[0073] Where e(t) is some noise. Since the ECAP component of the given signal has a regular shape (similar to two damped oscillation cycles), closed-loop stimulation works. Likewise, if the artifact component of the signal does not have a regular shape, closed-loop stimulation will not work. To measure the ECAP amplitude, we use a detector to filter out most of the artifacts, which assumes that the artifacts have a regular exponential shape.

[0074] This embodiment operates on the assumption that the ECAP signal component and the artifact signal component belong to different function families. That is, the ECAP is always a short-lived oscillatory event, while the artifact is an exponential signal. For each different function family, we can predefine a basis to represent it. For a suitable basis function, the basis coefficients can be calculated, and the ECAP basis expansion and the artifact basis expansion can be isolated separately. The ECAP basis expansion then provides us with an artifact-free estimate of the ECAP component.

[0075] The calculation of the basis coefficients balances the contribution of each basis function in a way that approximates the overall signal as best as possible. In other words, the estimated ECAP contribution and the artifact contribution are balanced so that the recorded signal is optimally modeled. In order to achieve better performance, the present embodiment assumes that all ECAPs belong to a certain function family and that there are no ECAP shapes outside of the family. At the time of writing this article, ECAPs with late reactions (such as those described in WO 2015070281) are outside the ECAP function family used in this embodiment and therefore cannot be correctly estimated. Therefore, when working with signals that are not adequately modeled by the ECAP basis used at the time, it may be more appropriate to use other scrubbers. Alternative embodiments of the present invention may combine basis functions that include ECAPs with late reactions within the ECAP basis function family to provide late reaction estimates.

[0076] The above method forms Figure 5 . In some embodiments, pre-processing 502 and post-processing 506 are used to improve the signal estimate. For example, pre-processing 502 can be used to reduce high frequency noise in the signal. However, a feedback mechanism 510 is used to improve the construction of the basis set. A rough 'initial estimate' basis can be used to approximate the signal, and the resulting estimate can be used to refine the basis set in subsequent passes. For example, the first pass can guess the ECAP basis in order to make a good estimate of the artifacts. Subtracting the artifacts from the signal and using signal correlation methods can be used to refine the choice of the ECAP basis. Re-running the algorithm with the improved basis will produce better estimates of the ECAP and artifacts.

[0077] This embodiment uses the following three basis functions to model the artifacts:

[0078] φ1(t)=1φ2(t)=t

[0079] The unit basis function φ1 captures the DC component of the measured signal. The linear basis function φ2 captures the component of the artifact due to amplifier drift. The exponential basis function φ3 captures the chemical charge relaxation component of the artifact. The decay constant of the exponential component can be any suitable variable, and the values ​​above are empirically determined based on model performance against a library of human artifact records. Different devices may present different artifacts and / or ECAP results, and therefore may require different constants, which can similarly be obtained empirically.

[0080] Once the algorithm of the present embodiment is applied, the artifact component of the signal is expressed as:

[0081] A(t)=αφ1(t)+βφ2(t)+γφ3(t)

[0082] Although simple, the model has been applied to thousands of representative neural recordings from human patients. Combined with the ECAP basis functions, the combined model accurately estimates the recorded signals.

[0083] Unusual neurological artifacts (such as background neuronal activity or delayed responses) are not modeled in this embodiment, but may be incorporated according to alternative embodiments of the invention. The estimates obtained from the method of this embodiment will remove such features, so at least in this embodiment, the results cannot be relied upon when measuring non-ECAP neurological features.

[0084] The ECAP basis function is defined using the product of the γ probability density function with parameters k = 1.7 and θ = 0.60,

[0085]

[0086] This is a piecewise function consisting of a period of a sine wave followed by an exponential function such that the derivative is continuous at their boundaries:

[0087]

[0088] Where C = 0.37. These two components and their product are Figure 6 There is only one morphological parameter in this FPAP model; the frequency of the sinusoidal component: f. As can be seen above, the time scale of the γPDF is scaled accordingly. The model was obtained by manually fitting elementary functions to the simulated ECAP model.

[0089] By scaling the time axis by a factor of ν and applying an offset t0: ν(t-t0), we can stretch and shift the ECAP basis function in time. Such a stretched and scaled ECAP is called a parameterized ECAP basis function:

[0090] There are two different ECAP models, one for single-ended measurements (where recordings are made from a single electrode with respect to a neutral reference such as device ground) and one for differential measurements (where recordings are made from two recording electrodes exposed to neural signals). The single-ended ECAP basis consists of a parameterized ECAP basis function, and ECAP E is represented as:

[0091]

[0092] The differential ECAP basis is formed by the difference of two parameterized ECAP basis functions, giving the following ECAP model

[0093]

[0094] In either model, the time stretch (corresponding to the ECAP oscillation frequency) and the time offset are chosen so that κ or κ + is positive, and κ - is negative. This embodiment tests sweeps of ECAP frequencies and offsets to ensure that this condition holds. The frequencies and offsets chosen to model the ECAP component of the recorded signal are chosen so that the fit to the recording using the ECAP model and the artifact model is as good as possible.

[0095] It should be noted that the single-ended ECAP model assumes that the ratio of peak height to peak time is fixed. Neurophysiological parameters such as the half-width or the ratio n1:p2 are completely determined by the time stretch ν applied to the parameterized basis function.

[0096] As with the artifact, this assumption has been verified by fitting parameterized basis functions to real-world single-ended measurements.

[0097] In the case of a differential model, such neurophysiological parameters can be independent of ν + and ν - and additionally depends on the composition of the ECAP estimate. That is, κ + and κ - Additional degrees of freedom are provided. Although relative neurophysiological parameters can vary, their degrees of freedom are restricted compared to more free-form ECAP models. As with the single-ended ECAP assumption, this model constraint has been validated by fitting the differential ECAP basis to real-world differential measurements.

[0098] The range of parameterized ECAP frequencies is limited to a set of linearly spaced frequencies between 500 Hz and 2 kHz. The upper limit of 2 kHz was chosen to minimize interference of broad spectrum (up to 8 kHz) noise on the parameter selection procedure. The lower limit of 500 Hz was chosen to limit interference of artifacts on the parameter selection procedure. A sufficiently slow parameterized ECAP will closely resemble the artifact within a limited time window. The range of offsets tested was chosen to be wide enough to simulate real-world ECAPs, but reasonably limited to maintain computational performance.

[0099] So far, we have assumed that every recorded signal contains ECAP. However, in practice, this is not the case for subthreshold signals. Including ECAP basis functions in the model of subthreshold signals is problematic because the ECAP will fit into the noise in the signal and the estimate will be meaningless. Additionally, since the ECAP features and the artifact features are balanced in the combined model, the artifact component of the signal will be incorrectly represented.

[0100] Therefore, it is desirable to include a mechanism for detecting the presence of ECAP in a signal so that the ECAP basis can be included in the overall model only when the underlying ECAP is real. The present embodiment incorporates such a mechanism. The signal is modeled using an artifact-only basis and a combined ECAP and artifact basis. A set of signal features is derived from the estimates produced by the two models, and the set of signal features is combined with signal features from the recorded signal. The present embodiment analyzes a series of signals known to contain both ECAP and artifacts or only artifacts, and saves the derived set of features. Machine learning is used to train a classifier with the following categories: 'ECAP' or 'no ECAP'. After sufficient training, the resulting classifier is able to automatically determine the presence of ECAP in a signal. The present embodiment is rated as detecting ECAP in a signal containing ECAP with 85% accuracy and rejecting ECAP in a signal containing only artifacts with 95% accuracy.

[0101] Combining these concepts together, we arrive at the complete algorithm of this embodiment, as Figure 7 As depicted in .

[0102] First, the recorded signal is modeled at 702 using an artifact-only basis 704, under the assumption that the recording does not contain ECAP. Whether or not ECAP is present, this will provide an estimate of the artifacts via the basis coefficients. If ECAP is present, the estimate can be improved by also including the ECAP basis. At 706, the initial artifact estimate is subtracted from the recorded signal to help better determine the parameterized ECAP basis. The estimated artifacts and derived features from 702 are also passed to an 'ECAP presence classification' (or ECAP detector) block 712 for later use.

[0103] Once the parameters of the parameterized ECAP basis are determined at 708, the coefficients of the combined ECAP and artifact basis are determined at 710. The resulting estimate and feature set are passed to the ECAP detector 712.

[0104] The ECAP detector 712 now has everything it needs to classify the presence of ECAP in the recorded signal.Based on its decision, the estimate selection block 714 returns either the ECAP and artifact estimate, or only the artifact estimate.

[0105] The steps of the method are as follows:

[0106] a. Capturing / recording a composite signal, where the composite signal has two or more additional components.

[0107] b. Selecting a first basis set corresponding to the first signal component from a basis set pool. Selecting a second basis set corresponding to the second signal component from a different basis set pool.

[0108] c. Determine a first component and a second component of the composite function based on the basis functions. Determine an estimate of the first component as a linear expansion of the first basis set, and determine an estimate of the second component as a linear expansion of the second basis set.

[0109] d. Iteratively improve the basis set using the estimated components from the previous iteration.

[0110] The following explanation delves into the math behind this embodiment. The coefficients are determined as follows. Let σ(t) be our recorded signal, and f(t) and g(t) be the fundamental ECAP component and the fundamental artifact component, respectively. The problem we are trying to solve is to use the recorded signal σ(t) we know to find estimates for f(t) and g(t) that we do not know. For simplicity, we assume that there is no noise in the signal. Therefore,

[0111] σ(t)=f(t)+g(t)

[0112] Now assume that f(t) can be represented by a finite set of basis functions Similarly, assume that g(t) can be represented by a finite set of basis functions {φ j (t): j∈{1, 2, ...m}}, which is different from the group used to represent f(t). Then f(t) and g(t) can be expanded on their respective bases,

[0113]

[0114]

[0115] Then, by simply replacing:

[0116]

[0117] At this stage in the problem, the basis set is known, but the coefficients of the specific signal σ(t) are unknown. Using these coefficients, we can recover estimates of f(t) and g(t). We will now recover them.

[0118] For any basis function f, consider the following inner product of functions: And by linearizing the inner product, we have:

[0119]

[0120] Similarly, consider the inner product of any basis function g: l (t)

[0121]

[0122] Equations (4) and (5) provide us with a system with n+m unknowns (coefficients a k and b j ). Therefore, determining the coefficients is an important problem in solving the following linear equations:

[0123] Hv=b

[0124] in,

[0125]

[0126] Therefore, the coefficients can be obtained by H -1 b to solve. The matrix H is invertible if and only if none of the basis functions from the ECAP basis belongs to the range of the imaginary basis (and vice versa), and the basis functions with respect to the ECAP basis and the imaginary basis are different. The basis functions should be scaled to unit powers so that relatively large or small inner products do not introduce computational errors in the inversion of H.

[0127] In practice, there is noise in the signal that is not modeled by any basis. However, since the inner product of an independent noise source with any signal is zero for an infinite time interval, the error introduced will be small. Restricting the inner product to a finite number of samples in the computation of b will propagate some error, but the error is not significant.

[0128] The ECAP parameters are determined as follows. The parameterized ECAP basis is determined using the recorded signal from which the initial artifacts have been removed and any residual baseline has been subtracted. This signal is referred to as the "perfected recording". The correlation grid is determined by scanning a series of base ECAP frequencies and offsets and taking the dot product between the perfected recording and each parameterized basis function.

[0129] The present embodiment samples 16 linearly spaced frequencies between 800 Hz and 2 kHz for both single-ended and differential modes, and the offset varies from -7 samples to -1 sample, inclusive. This frequency range and offset have been found to work well for test signals observed in human subjects, but these ranges can be extended. Extending them too far will allow the parameterized ECAP to lock onto noise or artifacts, so proceed with caution. The highest positive stationary point of the correlation grid determines the parameters of the first ECAP basis element. If the measurement is single-ended, this is the only ECAP basis element.

[0130] In case of differential ECAP measurements, a new correlation grid is calculated, sampling frequencies at 16 linear intervals between 500 Hz and the frequencies of the previously determined basis elements. It is assumed that the reference is always further away from the stimulus than the recording electrode. This allows us to exploit human neurophysiology, as the ECAP frequency decreases monotonically with recording distance. Likewise, offsets are tested between the previous ECAP basis offset and 12 samples. Again, these ranges were chosen empirically to work well with good signals from humans. Instead of using the highest positive stagnation point of the correlation grid, the most negative stagnation point determines the parameters of the secondary basis functions. If there are no negative stagnation points, only the primary basis functions are exploited.

[0131] Most blind signal separation algorithms assume that the basis signals are statistically independent and use statistical signal processing techniques to estimate the basis signals. The problem of ECAP and artifact estimation cannot be solved in this way because the basis signals are fundamentally interdependent. Instead, this embodiment assumes that each basis signal can be expressed as a linear combination of basis functions (a stronger assumption), which limits its application to processes where some knowledge of the basis signals already exists before recording them in the form of a composite signal.

[0132] Artifact Models lists the basis functions used to model the artifacts present in our hardware / recordings. The FPAP model is the single basis function used in the overall ECAP basis set. In practice, we use one FPAP for single-ended measurements, and two FPAPs for differential measurements to handle reference electrode effects that arise when making differential measurements between two recording electrodes.

[0133] An alternative embodiment is further provided. In this embodiment, Figure 4 The process is changed to be implemented as follows.

[0134] Artefact Estimation Scrubber is a scrubber that attempts to estimate only the artifact component of the signal g(t) and derives the ECAP estimate using σ(t)-g(t). Exponential Scrubber models the artifact as a sum of exponential functions. Three such models are contemplated here:

[0135]

[0136] Table 1: Index Scrubber Artifact Model

[0137] A nonlinear optimization is performed using the simplex hill climbing Nelder Mead algorithm, where the parameters a; b; c; d; e; f; g and h are adjusted to minimize the value of the cost function. The nonlinear optimization minimizes the sum of the squared errors between the estimated artifact samples and the samples of the recorded signal. Mathematically, the cost function is defined as:

[0138]

[0139] Nonlinear optimizations are non-deterministic algorithms, meaning that they do not terminate in a predictable or predeterminable amount of time. This means that it is possible to provide such a scrubber with a signal that cannot be scrubbed within a reasonable time frame. Further, nonlinear optimizations may get stuck in a local minimum, making it impossible to find the true optimal solution. In practice, this scrubber works well, but has limitations that should be known before using it widely. Regardless, such an embodiment does have some uses in certain applications.

[0140] A further embodiment is a fractional pole scrubber, which works on the same principle as the exponential scrubber, where nonlinear optimization is used to determine the parameters a; k; α and h of the following artifact model:

[0141] g(t)==a exp(-kt)·t 1.()-α +h

[0142] In more detail, the inventors have noted that electrode impedance variations are commonly observed clinically in humans, and that such electrode impedance variations can affect the behavior of the electrode-tissue interface and produce artifacts. Indeed, such variations can affect the constant phase element model of the electrode-tissue interface more than the resistive portion of the impedance. Accordingly, the present embodiment recognizes that artifacts caused by such characteristics can be best handled by understanding the impact of electrode impedance differences between one electrode and the next. To this end, we consider a segmented electrode model of a constant phase element as set forth in the applicant's International Patent Application No. PCT / AU2019 / 051160, the contents of which are incorporated herein by reference.

[0143] Electrode-tissue is the interface between the body's ion-rich aqueous environment and the charged metal lattice of the implanted electrode. In fact, aqueous ions show unique behavior in response to the rapid charging and discharging of the metal lattice, mainly characterized by the rapid formation and diffusion of a double layer of ions on the electrode surface. This is called an ionic double layer, which has both capacitive and resistive properties. In an ideal system, the aggregation and diffusion of ions from the metal surface is purely capacitive. However, it is also known that reversible modification of ion species and electrode exchange at the metal surface occurs at a voltage-dependent rate. In this way, we electrically characterize the electrode-tissue interface using a concept called the constant phase element (CPE), which is actually a leaky capacitor. The CPE is formed when the metal contacts the ionic fluid in the tissue. In a saline bath, the entire electrode surface contributes to conduction, but when implanted, adjacent materials such as bone or encapsulating tissue reduce the effective size of the contact, thereby increasing the CPE component of the impedance. The impedance of individual electrodes along an implanted lead can differ by more than 2:1.

[0144] Figure 8 shows a system for stimulating tissue and recording ECAP, similar to Figure 1 The organization is shown as a resistor grid to which the electronics are connected via a constant phase element (CPE). The representation is explained in detail in International Patent Application No. PCT / AU 2019 / 051160. In this figure, the system stimulation electrodes are represented by CPE3 and CPE4, and the recording electrodes are represented by CPE1 and CPE2. On the electronics, the connections to CPE1, CPE2, etc. will be referred to as electrode 1, electrode 2, etc.

[0145] The stimulator in this system can generate stimulation with one or more phases through the operation of switches and current sources. The current amplitude and switching timing are controlled by the stimulator and are known before the stimulation occurs. The switch operation connecting the tissue to Vdd or ground causes current to flow through CPE1 and CPE2 and into the resistive and capacitive input impedances of the amplifier.

[0146] The method described in the present disclosure is relevant to the following situation: the recording electrodes associated with CPE1 and CPE2 are far enough away from the stimulation site that they can be considered to be at the same potential, at least on the tissue connection side. That is, the current through the resistor grid near these electrodes is effectively zero. When the system is delivering anodal stimulation to electrode 3, it connects electrode 3 to ground and connects electrode 4 to a positive current source. The voltage on recording electrodes 1 and 2 will be between the voltage on electrodes 3 and 4, depending on the details of the grid. For convenience, assume that the fraction is one-half, that is, halfway between the two. If the impedance between the stimulation electrodes is R, then the voltage will be IR / 2.

[0147] When the system is delivering cathodic stimulation to electrode 3, it connects electrode 3 to Vdd, and connects electrode 4 to a negative current source. Again, the tissue voltage is assumed to be somewhere in between these two. When the tissue is not being driven, the tissue can be connected to either Vdd or ground, in which case ground will be chosen (although it is arbitrary). Choosing ground is the preferred approach because it does not require maintaining a high voltage power supply when no stimulation is being performed.

[0148] In the case of biphasic stimulation, the waveform is as Fig. 9 The second sub-figure of , which shows the stimulus waveform seen at the recording electrode, will be observed to be the sum of the electrode-to-supply voltage and the electrode-to-electrode voltage.

[0149] Because the voltage on electrodes 2 and 3 is the same, and the waveform is as Fig. 9 As described in Figure 8 can be simplified to Fig.10 If we assume that R is controlled by careful design and componentsI1 =R I2 And C I1 =C I2 , then if P B1 ! =P B2 , there will only be non-zero voltages at the amplifier output. This is to be expected in practice, since the electrodes are placed in the tissue and are not homogenous, so it would be expected that the impedances would not be the same.

[0150] If we now calculate the impedance at each amplifier input, call it Z i is the impedance of the input circuit and Z c is the impedance of the CPE, so as a simple voltage divider:

[0151]

[0152] Because Z i >>Z c1 , using Newton's approximation: (1+p) q =1+pq, if pq<<1, then we can write it as:

[0153]

[0154] The voltage between the amplifier input terminals is

[0155]

[0156] That is, the voltage is proportional to the difference in impedance. C1 and Z C2 It is a fractional pole, so the impedance will also have the characteristics of a fractional pole.

[0157] Fig.11 The separation of the resistive and capacitive components of the input impedance is demonstrated. Because the current applied to the system is zero during recording, and also because Z i >>Z c1 , Fig.11 The transformation of decomposes the current through the CPE into a resistive component and a capacitive component. Since the waveform is rectangular, the voltage pulse generates a current pulse into the CPE under the action of the resistor, and the edge generates a pulse through the capacitor.

[0158] The impulse response of the CPE is the inverse Laplace transform of the fractional pole and is given by

[0159] i(t)=kt -α , t≥0 and the equation

[0160] i(t)=0,t<0

[0161] From this, the step response can be simply calculated as

[0162]

[0163] The step response can be expanded to describe the impulse response of a pulse of width T as

[0164] p(t, T) = s(t) - s(tT) Equation 2

[0165] This can be equivalently extended to more complex waveforms, such as biphasic and triphasic pulses.

[0166] Fig. 9 The waveform has two components: a biphasic stimulus pulse and a rectangular tissue-return pulse. The response of the CPE can be separated into a resistive (pulse) and a capacitive (pulse) response from the amplifier input impedance term. Therefore, the artifact produced at the amplifier output is the sum of the resistive and capacitive components, as well as the biphasic pulse and the supply-return pulse.

[0167] Naming the pulse associated with the biphasic pulse "b", the pulse associated with the stimulus return pulse "s", the pulse from the rectangular resistive pulse "r", and the pulse from the pulse capacitor pulse "c", the four terms are:

[0168]

[0169]

[0170] y(r,s)=k(r,s)[s(t-pw-ipg)-s(t-2.pw-ipg)] Equation 5

[0171] y(c,s)=k(r,s)[i(t-pw-ipg)-i(t-2.pw-ipg)] Equation 6

[0172] Total Illusion

[0173] y=y(r,b)+y(c,b)+y(r,s)+y(c,s) Equation 7

[0174] Each of these terms has a proportionality constant, such as k(r, b). These will depend on the impedance difference of the CPE (Z c2 -Z c1 ), the (variable) amplitude of the stimulus and the fixed amplitude of the supply voltage, and the resistor R i and capacitor C i The value of .

[0175] However, the present embodiment recognizes that these four terms may be used in a scrubber that finds the most likely match between the sum of these components and the ECAP.

[0176] If the input impedance of the amplifier is purely capacitive, then y(r, s) = y(r, b) = 0. In this case, there is no need to find a corresponding value of "k", leaving only two unknowns to be solved.

[0177] The relationship between the capacitive and resistive impedance parts of a CPE is described in International Patent Application No. PCT / AU2019 / 051160. This can be used to allow y(r,b) to be calculated from y(c,b), thereby reducing the number of variables that must be evaluated.

[0178] Finally, if tissue impedance is measured, stimulation current and supply voltage are known, the tissue voltage can be calculated and used in place of the four equations described previously.

[0179] It has been observed that the term α varies with the electrode geometry. Therefore, the washing process may also require varying this parameter during its optimization.

[0180] The true washout properties of the mathematical basis underlying the origin of stimulation artifacts were investigated using mixed ECAP and artifact signals recorded in human SCS patients. The washout properties of the artifact basis described below were investigated by implementing a modified version of the basis element signal separator described previously.

[0181] As mentioned above, we can describe the voltage response of the CPE with two component voltage signals having fractional-pole characteristics.

[0182] Each of these time-varying components represents one of the different capacitive and resistive behaviors of the amplifier input impedance. One component has a positive slope and represents the voltage produced by the resistive component of the amplifier input impedance. We call this the step component:

[0183]

[0184] The other component has a negative slope and represents the interaction of the CPE with the capacitive component of the amplifier input impedance. We call this the impulse component:

[0185] i(t)=k i t -α

[0186] The fractional pole time constant α is considered to depend on the geometry of the electrode-tissue interface. For this analysis, we assumed a constant value:

[0187] α=0.364

[0188] Assume that the step (k s) and the scalar component of the pulse (ki) depend on the amplitude of the stimulation current delivered to the stimulation electrode and the characteristics of the tissue between the stimulation site and the recording site, which we do not control for here. Importantly, we assume that k s and k i For a given source (ie, stimulation and recording electrode set), the γ is kept constant.

[0189] For a given biphasic or triphasic stimulation paradigm, the stimulus waveform and return voltage waveform will contain multiple steps. Each edge of the voltage step acts as a singularity at which we can define a set of independent step and pulse components. The number and timing of these edges / singularities can be precisely defined based on the stimulus waveform and depends on the following adjustable parameters of the system:

[0190] Number of phases (two-phase or three-phase).

[0191] The polarity of the first phase (negative or positive).

[0192] Pulse width

[0193] Phase gap

[0194] The recorded artifact is the scaled sum of all time-shifted step and pulse components produced by the stimulus and return voltage waveforms. We can define general equations for these time-shifted stimulus and return step and pulse responses that use these known parameters of the stimulus waveforms:

[0195] The above artifact basis is also used to construct an embodiment of the artifact scrubber by modifying the basis element signal separator described above. As described above, the basis element signal separator uses three basis functions to model the artifacts:

[0196] Exponential fixed time constant

[0197] Linear slope

[0198] DC offset

[0199] This example modifies this by replacing the exponential artifact basis with the fractional polar model described above. The K value is fitted to a representative artifact, then resolved to a basis element signal separator and held fixed to wash all signals for a given activation map.

[0200] Note that the basis element signal separator performs linear operations on the artifact and ECAP basis to optimize the fit to the base signal. That is, for this embodiment, the fractional polar artifact basis does not require precise specification of the amplitude and polarity of the artifact basis, only its temporal characteristics and shape characteristics, because the basis element signal separator performs additional scaling as part of the fit.

[0201] Results using nonlinear methods to fit bounded values ​​of k show that the model artifacts are able to match the temporal and shape properties of the representative artifacts in all cases, but lack some linear properties of the recorded signals.

[0202] The model artifacts were resolved into basis element signal separators and the resulting fits to the artifacts were of consistently high quality and minimal error, indicating that only linear properties were missing from the model.

[0203] We tested the performance of our modified basis element signal separator implementation as an artifact scrubber when processing mixed ECAP and artifact signals. As described above, for each input activation map, the artifact basis is parameterized using a representative artifact. The signal from the activation map is then scrubbed using the parameterized model and the results are visualized. The scrubber demonstrates effective removal of artifacts and the residual ECAP signal is flat and clean. Additionally, the scrubbed activation map has no subthreshold offset or slope present in the original.

[0204] The circuit we are considering can be distilled into Fig.12 , which can help understand the relationship between variables.

[0205] There are two stimulus waveforms:

[0206] 1. The voltage formed by the current source output multiplied by the tissue impedance. This varies with tissue impedance and stimulation current; the former is unique to the electrode, while the latter is known from the programming system (an unknown).

[0207] 2. Return voltage (VddHV). This is known from the programming system.

[0208] Both waveforms have an amplitude component and a shape component. The shape component is known from the programming system. The tissue voltage is the sum of the return voltage and the stimulus voltage:

[0209] V T =V R R T I S css

[0210] The CPE stores charge that flows into the amplifier input impedance and this redistribution of charge causes the artifact.

[0211] The capacitance provides a path for the impulse response from the stimulus waveform, differentiating the tissue voltage to provide the impulse component.

[0212] This boils down to the following equation, which has a small number of variables and, if implemented in a scrubber, can be used to find the parasitic component Z CPE , R A and C A The physical value of .

[0213]

[0214] Finally, it has been noted that the term (1 / R A )(V RrS +R TIScSS ), since this term has been observed to be negligible in the data considered so far. Therefore, a minimum impedance is observed. In this case, only C A d / dt(V RrS +R T I s css) component may have almost the same performance. Note that for any given implant, C A Probably constant.

[0215] Overall, the evaluated modified scrubber works well and has too many degrees of freedom, which provides opportunities for further optimization.

[0216] Yet another embodiment is a complex pole scrubber. If we assume that the artifact is a second order response (double exponential is a subset of this response), then we can estimate the parameters of the second order response that fits the original signal. For discrete signals, the artifact g follows the following model:

[0217] g[n]=b·g[n-1]]+c·g[n-2]

[0218] Given a sample sequence, we can write the matrix equation:

[0219]

[0220] in,

[0221]

[0222] Therefore, the coefficients b and c can be determined by the following calculation:

[0223]

[0224] Those skilled in the art will appreciate that, without departing from the spirit or scope of the invention as broadly described, many changes and / or modifications may be made to the invention as shown in the specific embodiments. Therefore, the present embodiments should be considered in all aspects as illustrative rather than restrictive or limiting.

Claims

1. A system for separating at least one of compound action potentials and artifacts from neural recordings, the system comprising: A memory storing a set of basis functions including at least one compound action potential basis function and at least one artifact basis function; an input terminal for receiving neural recordings of electrical activity in neural tissue; as well as A processor is configured to separate at least one of the compound action potential and the artifact from the neural recording by determining at least one of the compound action potential and the artifact in the neural recording using the set of basis functions, and is further configured to output at least one of the compound action potential and the artifact.

2. The system of claim 1, wherein: The electrical activity includes evoked compound action potentials, which are evoked by electrical stimulation applied to the neural tissue.

3. The system of claim 2, wherein: The at least one artifact basis function is matched to electrical artifacts known to be induced by one or more such electrical stimuli.

4. The system according to any one of claims 1 to 2, wherein: One or more base signals are output, wherein the one or more base signals include compound action potentials recorded from the nerve and artifacts recorded from the nerve.

5. The system of claim 4, wherein: The one or more basal signals further include one or more of: background neuronal activity; and evoked late responses.

6. The system according to any one of claims 1 to 2, wherein: Both the compound action potential and the artifacts are separated simultaneously.

7. The system according to any one of claims 1 to 2, wherein: Output pairs are noise-free compound action potentials.

8. The system according to any one of claims 1 to 2, wherein: The amount of computation used to separate the compound action potential and at least one of the artifacts from the neural recording follows the order O(n), where n is the number of samples in the neural recording.

9. The system according to any one of claims 1 to 2, wherein: A computational process for separating at least one of the compound action potential and the artifact from the neural recording is performed within a predetermined time.

10. The system according to any one of claims 1 to 2, wherein: A computational process for separating at least one of the compound action potential and the artifact from the neural recording is implemented in firmware of the implantable device.

11. The system according to any one of claims 1 to 2, wherein: Each basis signal is represented as a linear combination of basis functions.

12. The system of any one of claims 1 to 2, wherein: The compound action potential is an evoked compound action potential ECAP, and the ECAP is modeled in the basis function by a function that matches an expected noise-free ECAP morphology.

13. The system of claim 12, wherein: The ECAP is modeled in the basis function by a piecewise function consisting of a one-period sine wave followed by an exponential function such that the derivatives are continuous at their boundaries.

14. The system of claim 12, wherein: The ECAP is modeled in the basis function by two or more basis functions.

15. The system of claim 14, wherein: The two or more basis functions include a first basis function optimized for single-ended neural recording and a second basis function optimized for differential neural recording.

16. The system of any one of claims 1 to 2, wherein: Artifacts are modeled in the basis functions by three basis functions, including a DC basis function, a linear basis function, and an exponential basis function.

17. The system of any one of claims 1 to 2, wherein: Artifacts are modeled in the basis functions by three basis functions, including a DC offset basis function, a linear basis function, and a fractional pole function.

18. The system of any one of claims 1 to 2, further configured to detect recordings in which only artifacts are present without any compound action potentials.

19. A method for separating at least one of compound action potentials and artifacts from a neural recording, the method comprising: accessing a set of basis functions contained in a memory, wherein the set of basis functions includes at least one compound action potential basis function and at least one artifact basis function; receiving neural recordings of electrical activity in neural tissue; and separating at least one of the compound action potential and the artifact from the neural recording by determining at least one of the compound action potential and the artifact in the neural recording using the set of basis functions, and At least one of the compound action potential and the artifact is output.

20. A computer program product comprising computer program code means for causing a computer to execute a program for separating at least one of compound action potentials and artefacts from neural recordings, the computer program product comprising computer program code means for executing the method of claim 19.

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