When manipulating genetically engineered organisms, it is crucial to guarantee the confinement of these organisms. In our case, we want genetically modified bacteria to stay at the interface between the prosthesis and the external organic medium. At the same time, one of the main issues our project wants to tackle is the conduction of the neuron influx to the prosthesis. The answer to these questions came as a double solution: confinement of the bacteria by conductive nanoporous membranes. The membrane’s nanoporosity allows substances produced by our modified biofilm to pass through the membrane, but the bacteria remain confined. We tested the conductivity and biocompatibility of two types of membranes.
Sterlitech Polycarbonate Gold-Coated Membrane Filters represented one of the types of membranes we tested. The pores have a diameter of 0.4 micrometer, which is small enough to confine Escherichia coli bacteria, which diameter and size are respectively about 1 micrometer and 2 micrometers. These membranes were relatively easy to manipulate with a forceps because of their high flexibility. Scanning electron microscopy by courtesy of Bruno Bresson, Sciences et Ingénierie de la Matière Molle Physico-chimie des Polymères et Milieux Dispersés).
The other membranes were Sterlitech Alumina Oxide Membrane Filters with 0.2-micrometer pores. Their higher rigidity compared to the gold-coated membranes led to several membranes being broken while manipulating them with a forceps. We used these membranes as a support for different conductive and biocompatible polymers: PEDOT:PSS (poly(3,4-ethylenedioxythiophene) polystyrene sulfonate), PEDOT:Cl and PEDOT:Ts.
For PEDOT:PSS, an aqueous solution of PEDOT:PSS was prepared and alumina oxide membranes were dipped for 24 hours in this solution. Electron microscopy of the membranes before and after the experiment showed the deposit of a substance on their surface in a cluster-like fashion, indicating an incomplete coating.
Vapor-phase polymerization of PEDOT:Cl and PEDOT:Ts also induced a change in the surface of the membranes, in a more uniform way. The surface of the membrane seems to have thickened, but without blocking the pores either, which makes for a high quality homogenous coating.
The first issue to tackle was the confinement of the bacteria. For this purpose, we used microfluidic chips. Microfluidic chips are patterns molded in PDMS (polydimethylsiloxane), which can be used to design tiny circuits for liquid flow. We used Institut Curie's design of a microfluidic chip, which has 2 chambers connected by microchannels of 5 micrometers width and 2 micrometers height. We enhanced the design by integrating a membrane filter (gold-coated) to prevent bacteria to pass from one chamber to another. As this technique was quite improvised and new, we didn't had access to the needed equipement for better precision work, leading to many chips being leaky. We managed to conduct an experiment were the chip did not leak and the filter succesfully retained the bacteria introduced in the chip.
The second criterion for a fully functional interface is its ability to conduct a neuron’s influx. Thus, conductivity measurements were made for different types of membranes. Results indicated that bare alumina oxide and PEDOT:PSS-coated membranes showed similar conductivities, indicating the incomplete coating of PEDOT:PSS on alumina oxide membranes. On the opposite, PEDOT:Cl and PEDOT:Ts exhibit on average better conductivities, but in the same time, the coating of these membranes revealed by electron microscopy seemed to have covered the alumina oxide membranes in a more uniform way, ensuring enhanced conductive capabilities . These results can be criticized because of the high deviation and because the membranes conductivity was measured after several biofilms were grown on them, which may have affected the measurements.
One last important property of the membranes is the capability of bacteria to form a biofilm on them, as in our prosthesis system, the membrane is going to be directly in contact with the genetically modified biofilm, as well as the human body. We conducted multiple series of biofilm culture on special culture wells designed by our team. Biofilm growth was measured for each type of membrane.
Biocompatible polymers like PEDOT:PSS represent ideal materials for engineering biocompatible and conductive interfaces, that are also relatively easy to produce, thus making them our preferred choice in our project. However, it is worth mentioning that we are totally aware of the fact that we can’t just expect neuron axons to bind to our interface and produce an electric signal. The electric signal transmitted by a nerve is heavily limited to the interior of the nerve by myelin covering the axon, and the signal transmitted by the axon is purely chemical. So it requires special electrodes, like Fine or Cuff electrodes, to detect an electric signal. We might explore these solutions in the continuation of our project to enhance our interface’s ability to transmit neuron signals.
- Jikui Wang, Guofeng Cai, Xudong Zhu, Xiaping Zhou, Oxidative Chemical Polymerization of 3,4-Ethylenedioxythiophene and its Applications in Antistatic coatings, Journal of Applied Polymer Science, 2012, Vol. 124, 109-115 .
- Alexis E. Abelow, Kristin M. Persson, Edwin W.H. Jager, Magnus Berggren, Ilya Zharov, Electroresponsive Nanoporous Membranes by Coating Anodized Alumina with Poly(3,4ethylenedioxythiophene) and Polypyrrole. 2014, 299, 190-197.
Nerve and electrodes
As seen in the other parts of this wiki, we chose to use a nanoporous membrane in our device. The first goal of the membrane was to confine our biofilm, so it does not escape the prosthesis. Moreover, we also used our membrane as a conductive electrode. This solution was interesting since we didn’t have enough time to develop an entire electrical device which collects and treat the signal of the nerves. However, we know we still need to improve our interface if we want the patient to fully control his prosthesis. That is why we decided to look at what is already made in this field. So, first, we detailed how it is possible to model the electrical characteristics of a nerve. Then, we searched for information on electrodes and signal treatment.
This section is principally based on the thesis of Olivier Rossel: Dispositifs de measure et d’interprétation de l’activité d’un nerf. Electronique. Université Montpellier II - Sciences et Techniques du Languedoc, 2012. Français.
One of the goals of NeuronArch is to use or even develop a neural signal collection solution that is both non-invasive for the nerve and highly selective. In this context, we seek to develop an innovative architecture to significantly improve the selectivity of extraneural electrodes. In order to be able to develop such a solution, we must be able to estimate the electrical potential created on the surface of the nerve by the propagation of transmembrane currents at the level of the axons.
For this study, we are only interested in myelinated axons present in the peripheral nervous system. Models that represent the extracellular voltage produced by the passage of an action potential for this type of fiber already exist. The evolution of the extracellular voltage in the space separating two nodes of Ranvier can be described by these models.
First, we are going to detail the physiological characteristics of the human nervous system. Then, we are going to model the electrical currents of an axon. Finally, we will estimate the influence of such currents at the surface of a nerve and model an entire nerve.
I. physiological characteristics of the human nervous system
The nervous system is divided into two different parts: the central nervous system (CNS) and the peripheral nervous system (PNS). We will focus on the peripheral nervous system as it transports the information between the rest of the body and the central nervous system. Moreover, it includes the somatic nervous system which consists of afferent nerves, also called sensory nerves, and efferent nerves also called motor nerves. Afferent nerves are responsible for relaying sensation from the body to the central nervous system; efferent nerves are responsible for sending out commands from the CNS to the body, stimulating muscle contraction; they include all the non-sensory neurons connected with skeletal muscles and skin. Generally, the fibers of the somatic nervous system have an insulating sheath called a myelin sheath.
Nerve fibers, consisting of axons and associated Schwann cells are grouped together in fascicles, sheathed by the perineurium (Cf. Figure 1). It is composed of layers of perineural cells. About half of the fascicular surface is occupied by the fibers, the rest is composed of the endoneurium which segments the inside of the fascicle into several groups of nerve fibers which will then form new fascicles.
The fascicles are contained in an isolated connective tissue called the epineurium that contains fibroblasts, collagen, and fat in different proportions. This envelope allows the fixation of the nerve on the surrounding structures. It contains the lymphatic and vascular network which crosses the perineurium to communicate with the network of arterioles and venula of the endoneurium. The epineurium constitutes 30 to 70% of the total area of a nerve.
The fascicular architecture is ordered only distally, close to the emergence of a nerve trunk. Going up to the proximal part, fascicles divide and some fibers change their fascicles, the size of the fascicles decreases and their number increases. An orderly organization relative to the target organ is found only in the final branches that innervate a muscle, a group of muscles or sensory receptors.
II. Propagation of nerve impulses:
The nerve impulse is initiated by action potentials that are created by successive openings and closings of the ion channels. The membrane current due to ionic flux creates an electric field in the nerve that produces a potential difference outside the nerve called extracellular voltage. It is this extracellular voltage that a measuring electrode will perceive. For a myelinated axon, these ionic currents appear only at the nodes of Ranvier.
III. Modelisation of the currents of a axon’s membrane
Although our objective is the measurement of the extracellular action potential, it is necessary to know the currents produced at the level of an axon.
From an electrical point of view, the myelin sheath of the axon acts as an insulator, preventing the appearance of transmembrane currents elsewhere than at Ranvier's nodes. In fact, seen from the outside of the axon, the action potential seems to jump from one node of Ranvier to the other. Let us now consider how to model this propagation, in order to extract the transmembrane currents at the nodes of Ranvier.
1. Electric model of an axon
We used the model of Hodgkin-Huxley to describe the flow of electric current through the surface membrane of a giant nerve fiber. The electrical behavior of the membrane may be represented by the network shown in Figure 2. Current can be carried through the membrane either by charging the membrane capacity or by movement of ions through the resistance in parallel with the capacity. The influence of membrane potential on permeability can be summarized by stating: first, that depolarization causes a transient increase in sodium conductance and a slower, but maintained, increase in potassium conductance; secondly, that these changes are graded and that they can be reversed by repolarizing the membrane.
Thanks to this model, we are able to determine the evolution of the membrane’s potential (V), ionic current (Ji) and capacitive (JCM) densities as a function of time (Cf. Figure 3).
2. Simulation of the transmembrane nodal currents
It is possible to implement this model in the NEURON software (http://www.neuron.yale.edu/neuron/) to be able to simulate transmembrane nodal currents (Cf. Figure 4). This software calculates the density of the currents presented previously.
The value of the electrical parameters of the model is based on the study of C. C. MCINTYRE and al.. The simulations make it possible to generate a large database comprising, for each of the nodes of Ranvier of each of the fibers, the representation of the transmembrane current as a function of time. For the study of electrode selectivity, it is the distribution of these nodal currents in the space that must be defined. In other words, we need to know at a fixed time t0 the distribution of the currents generated by the nodes of Ranvier. In fact, Figure 5 represents the total activity of forty nodes of Ranvier. It can be noted that of these forty nodes of Ranvier, only a few are active simultaneously. The envelope of the generated currents is represented in dashed lines.
If we take into account realistic data of characteristic and propagation of an action potential (duration between 0.1 and 0.2ms and propagation speed between 50 and 100 ms-1) we find a wavelength of the order of 10mm. This wavelength value is characteristic of the propagation of action potential in a peripheral nerve, it is used to size the spacing between the poles of a conventional electroneurogram measuring electrode.
IV. Calculation of the potential at the surface of the nerve
The purpose of this part is to know the potential “seen” by an electrode wrapped around the nerve. For this, we will study the extracellular potential at the surface of the nerve by considering an axon parallel to the longitudinal axis of the nerve. Each Ranvier node is considered as a point current source. To estimate the potential at a point M at the periphery of the nerve, it is necessary to determine a transfer function linking this potential to each of the transmembrane currents of the axon. The simulation of the membrane current of the axone we developed previously is used as the input of the nerve model.
2. Medium transfer function
J. H. Meier and al. developed a nonhomogeneous and anisotropic model of a nerve . We consider a cylindrical nerve of radius a and an axon at a distance r from the axis of the nerve (figure 6). The nodes of Ranvier are separated by a distance lmy. The point M, where the extracellular potential will be calculated, is located at a distance d = ρ - a from the surface of the nerve and at a distance ρ0 from the axon considered. The angle θ is the angle constructed from the radial position of the axon and the observation point M. The conductivity inside the nerve is different (σz and σρ) depending on the direction, longitudinal or radial. We consider two media other than the interior of the nerve: the perineural sheath that surrounds the nerve, of conductivity σs, and the outside of the nerve of conductivity σe.
The active fiber is simulated as an array of active point current sources along the fiber bundle. Each source represents a node of Ranvier. A nodal distance λ of 1000 μm is chosen. Current values correspond to the nodal currents of an active fiber of 10 μm diameter at one instant of time.
From this model, the calculation of the extracellular potential is based on the calculation of the electric field in a cylindrical medium. J. H. MEIER and al. established an analytic expression of the extracellular action potential using the medium transfer function in the spatio-frequency domain . With the simplifications we have chosen, this transfer function is the sum of the series presented below by separating, for each term, a factor depending on the respective positions of the axon and the point of observation, and two factors dependent on the physical characteristics of the nerve considered.
From this expression, it is possible to determine the "spatial" transfer function h2(z). To do this, it suffices to calculate the inverse Fourier transform of Hω2, which is done numerically as it can not be practiced analytically . The behavior of these two views of the transfer function is shown in Figure 8 for two reference distances ρ0 between the observation point M and the axon.
It is of course possible to go from the nonhomogeneous and anisotropic model to the homogeneous isotropic model by considering in the nonhomogeneous and anisotropic model that the conductivities of the media are equal to each other and that the perineurium is infinite. It is clear that the nonhomogeneous and anisotropic model is more realistic but the two models give relatively close medium transfer function variation trends.
We have described the two models in order to calculate the potential extracellular created by the presence of nodal currents generated at Ranvier nodes. This extracellular potential at a point M and at a time t can be expressed as the convolution product in the spatial domain between the nodal current i(z, t) and the transfer function of the medium h(z):
v(M,t) = h(z)∗i(z,t)
We consider the typical case of a 8.7 μm diameter axon near myelin gains (length lmy=1000 μm) and diameter 2.8 μm near the Ranvier’s nodes.
The objective of this part is to study the spatial and spatio-frequency properties of the extracellular potential created by such an axon.
Two reference distances (ρ'=200 μm and ρ'=500 μm) are considered between the observation point and the axon. The action potential at the surface and along the nerve is represented figure 9 for the two previous models. Whatever the model used, the low-frequency component - space current envelope (see Figure 9) - is found on the action potential generated. It can be concluded that the action potential has the same wavelength as the nodal currents at Ranvier's node. The nonhomogeneous and anisotropic model, closer to reality, gives a greater amplitude than the homogeneous isotropic model. This phenomenon - due partly to the insulating effect of the extraneural electrode - allows to expect a more easily measurable amplitude at the electrode. We also note that the extracellular action potential has a high frequency ripple, we will call this ripple a High Spatial Frequency component (HSF). This ripple is due to the spatial discretization of transmembrane current sources due to the nodes of Ranvier. The position of each peak is related to the location of a Ranvier node and the period of the ripple is directly related to the distance between two Ranvier nodes. Finally, it is interesting to note that the amplitude of these peaks is significant for the low ρ' distances, that is to say when the axon is close to the surface of the nerve, and this whatever the model used.
Whatever the model, the transfer functions behave like low-pass filters whose slope depends on the depth of the axon within the nerve. The high frequencies are all the more attenuated that the axon is far from the point of observation.
The high frequencies are attenuated according to the depth of the axon. The amplitude of the peaks decreases rapidly according to the depth of the axon, while that of the low frequency component is only slightly affected.
The low frequency component is a global phenomenon. It is interesting to note that conventional extra-neural electrodes are sized to be sensitive to the low frequency component of extracellular potential, and therefore measure the overall activity of the nerve. In this type of conventional measurement, the position of the axon will not influence enormously the measurement.
V. Extracellular potential generated by a fascicle
The purpose of this section is to ensure that axon studies can be generalized to fascicles. It is a question of understanding the evolution of the high frequency component of the signal during the superposition of action potentials. Finally, the extracellular action potential will be estimated using the homogeneous and isotropic model.
It can be observed that the fascicles are roughly elliptical. Our nerve model is therefore based on an assembly of elliptical fascicles. The shape (round, rectangular, etc.), the dimensions of the nerve and the number of fascicles being determined, the forms and positions of the fascicles inside the nerve are fixed randomly. A fascicle is itself built by placing many fibers close to each other, positions and types of these fibers are also generated randomly (according to a uniform law).
The extracellular action potentials for the configuration described in figure 11 are presented in figure 12 for observation sites (M1 and M2). One being close to the fascicle (ρ0=200 μm), and the other being further away (ρ0=500 μm).
We can verify some similarities with the study done on a single fiber. We can first see the existence of high spatial frequency components for small distances (ρ0 = 200 μm). Then at greater distances (ρ0=500 μm), these variations are substantially attenuated, and to a lesser extent the low frequency component of the action potential. This observation validates our proposal to observe the effect of Ranvier nodes for action potentials of fascicles. We can see that the peak-to-peak amplitude of the HSF component of this signal is of the order of 10 μV (noted VppHF in figure 12). These considerations lead us to believe that this HSF component, a consequence of the activity of the fascicles, will be measurable on the surface of the nerve.
VI. Neural information:
The neural information is coded by the frequency of the impulses of the action potentials and the number of fibers recruited. The shape and amplitude of the action potentials collected do not convey any neural information but only information on the distance where the nerve fiber is located in the nerve.
In the same nerve, several types of information transit. The nerve carries efferent neuronal signals, from the central nervous system to the peripheral nervous system, which regulates and control the body's natural functions through muscle recruitment. But nerves also carry information from natural sensors (mechanoreceptors, proprioceptive, etc.) and transiting to the central nervous system by activation of the afferent nerve fibers. Generally, muscle recruitment and sensory fiber activation are not coded in the same way.
In the case of motor or efferent fibers, the number of active motor units, as well as their discharge frequencies, vary at the same time as the force produced by the muscle.
We presented the calculation of the spatial action potential at the surface of the nerve. Based on these results, we exposed the construction of a nerve model for which the fascicles are generated randomly. This model allows us to represent a fascicular activity on the surface of the nerve. We show that the high spatial frequency component can be present at the surface of the nerve, but only for fascicles close to the point of measurement.
Finally, we have shown that the amplitude of this component is of the order of ten microvolts.
All the information presented can be used to realize an extraneural electrode having the desired performances.
- Rigoard, P., Buffenoir, K., Wager, M., Bauche, S., Giot, J.-P., Robert, R., and Lapierre, F. (2009). Organisation anatomique et physiologique du nerf périphérique. /data/revues/00283770/v55sS1/S0028377008004025/.
- Hodgkin, A.L., and Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117, 500–544.
- Olivier Rossel. Dispositifs de mesure et d’interprétation de l’activité d’un nerf. Electronique. Université Montpellier II - Sciences et Techniques du Languedoc, 2012. Français.
- McIntyre, C.C., Richardson, A.G., and Grill, W.M. (2002). Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. J. Neurophysiol. 87, 995–1006.
- H. Meier, J., Rutten, W., and B K Boom, H. (1998). Extracellular potentials from active myelinated fibers inside insulated and noninsulated peripheral nerve. Biomedical Engineering, IEEE Transactions On 45, 1146–1153.
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- Rossel, O., Soulier, F., Coulombe, J., Bernard, S., and Cathébras, G. (2011a). Fascicle-selective multi-contact cuff electrode. Conf Proc IEEE Eng Med Biol Soc 2011, 2989–2992
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Electrodes and signal treatment
The more selective an electrode is the simpler the extraction of information. Thus, the maximum selectivity, being reduced to the activity of a single fiber, is required for the measurement interfaces. Unfortunately, this search for selectivity will lead to a search for proximity between the electrode and the fibers, at the detriment of the nerve’s physical integrity. Indeed, the risk of infection or trauma to the body increases with the invasiveness of the electrodes. Electrodes can therefore be classified according to criteria such as selectivity and invasiveness. The ideal electrode is one that has the highest selectivity while remaining the least invasive possible. To make a choice, a compromise must be made between the selectivity and the degree of invasiveness of the electrode. The "secondary" criteria are stability and repeatability. We will present the neural electrodes by exposing their performances in terms of selectivity and level of invasiveness.
I. Extra-neural electrodes
1. Helicoidal electrode interface:
Helicoidal electrodes are placed surrounding the nerve and are made of flexible metal ribbon in a helical design. This design allows the electrode to conform to the size and shape of the nerve to minimize mechanical trauma. The structural design causes low selectivity. Helicoidal electrodes are currently used for functional electrical stimulation, to control intractable epilepsy, sleep apnea, and to treat depressive syndromes.
2. Cuff electrode :
Considered as extraneural electrodes, cuff electrodes are widely used to perform basic and applied electro-neurophysiology studies and are particularly interesting for their ability to achieve good nerve recruitment with low thresholds. The cuff-style electrode provides a cylindrical electrode contact with a nerve for each of an arbitrary number of contacts, is easy to place and remove in an acute nerve preparation, and is designed to fit on the nerve (Cf. Figure 1). For each electrode, the electrical contacts were cut from metal foil as an array so as to maintain their positions relative to each other within the cuff. Lead wires were soldered to each intended contact. The structure was then molded in silicone elastomer, and individual contacts were electrically isolated. The final electrode is curved into a cylindrical shape with an inner diameter corresponding to that of the intended target nerve. These electrodes have been successfully used for nerve stimulation, recording, and conduction block in a number of different acute animal experiments by several investigators.
The activity recorded by the cuff electrode represents the simultaneous activity of a large number of active axons. The potential of action seen by the electrode is overlapped, allowing only a "global" image of the activity inside the nerve. As a result, the selectivity of the recording is limited by the number of axons undergoing simultaneous discharge and by the position and surface of the contact of the cuff electrode. This type of measurement, therefore, does not allow the identification of fiber activity alone.
Increasing the number of electrode poles allows increasing the selectivity of this type of electrode. A multi-pole cuff electrode is then called a cuff electrode having more than three contacts. These contacts can be rings or segments of rings.
3. FINE electrode:
The flat-interface nerve electrode (FINE) was designed for selective nerve recording by realigning the fascicles and reshaping the nerve into a more flattened cross section which increases the surface area of the exposed nerve and offers greater access to fascicles. This kind of electrode is particularly interesting as it was possible to achieve more than 90% selectivity  (Cf. Figure 2)
II. Information extraction:
1. Extraction of the discharge frequency:
The most relevant information to extract is the discharge frequency of active fibers because it represents the means of coding information by the nervous system. Significantly, such processing must be applied to signals representing the activity of a limited number of fibers. In fact, the published examples relate exclusively to intra-neural collection: the only method, today, which allows to observe the activity of fibers alone. However, since we don’t want to use intra-neural electrode in our device we will not detail how to extract the discharge frequency.
2. Envelope extraction :
Rectification and Bin-Integration (RBI) of the nerve raw signal is widely used in rehabilitation application. This point of RBI ENG is found by calculating the average of the absolute value of ENG samples spread over a given period of time. This period is called “bin” and its value depends on the application. It ranges from 10 ms to 200 ms. The smoothed envelope-like signal created by RBI makes it easy to extract information about the innervated organ.
III. Improvement of the electroneurogram records selectivity
1. ENG-EMG selectivity :
The body is made so that a nerve is never very far from a muscle. However, the triggering and control of muscle contractions use a similar mechanism to the propagation of nerve impulses. Thus, the vicinity of a muscle is the seat of important extracellular currents because of the large number of muscle fibers excited simultaneously. The potential differences associated with these currents are called EMG, for electromyogram. Action potentials in muscle have mV amplitude, larger than a neural signal, and their spectra overlap. Minimizing these forms of interference is there for essential.
In order to attenuate the EMG signal, tripolar cuff electrode are used (Cf. Figure 3). For the nerve signal, the main point of the cuff is that it reduces the volume of tissue in which the action currents flow and, therefore, increases the potential differences between the electrodes. For the EMG interference, the fact that the cuff is a tube of uniform cross-sectional area means that the gradient inside, due to each external source, is approximately constant and, therefore, the potential differences between the pairs of electrodes are equal and cancel. How they are canceled depends on the amplifier configuration but the principle is that out-of-cuff signals are canceled while neural signals do not.
The variation of the ENG is not linear over the entire length of the electrode, it is at a maximum in the center of the cuff. Moreover, the average value of the EMG potential is zero or close.
Thus, the impact of EMG on the measurement is significantly attenuated, while the ENG is preserved
The electronic realization of this treatment is very simple, it can be done in two different ways using either one or three differential amplifiers, these structures are named respectively "quasi-tripole" and "true-tripole" (Cf. Figure 4)
2. Type of nerve fiber selectivity :
Nerves carry a lot of different neural signals, with both afferent and efferent traffic. However, by recording the signal we reduce it to only one artificial signal and we lose a lot of information. As the different types of signals are transmitted by fibers of different diameters, it should be interesting to select the fiber we record according to its diameter.
The method (Cf. Figure 5) uses a double differential array of amplifiers ('tripole amplifiers') and, for each selected velocity (of either sign), artificial time delays, as well as an adder and a narrow-band filter. An action potential transiting the nerve will be perceived in the same way by each tripole, but with delays inversely proportional to the speed of propagation of the action potential. If this time offset is compensated by the delay added by the measurement system, the action potentials appear simultaneously at the output of the delay stages. Thus, summing them to each other, the amplitude of the action potential is amplified. This system makes it possible to amplify the measurement for this particular action potential. Whereas, for another action potential having a different speed or direction of propagation, the amplification will not take place because the delay implemented in the system does not correspond to the delay due to the propagation of the action potential. This system is therefore selective for a given propagation speed.
3. Spatial selectivity :
Methods aim to increase the spatial selectivity of extra-neural electrodes to discriminate active fascicles, in order to determine the activity of each nerve branch.
One way to increase the spatial selectivity is to increase the number of measurement points. The issue is to separate the sources. In this context, in order to increase the spatial selectivity of the extra-neural electrodes, the multipolar cuffs or FINE electrode have been designed. These structures make it possible to increase the number of contacts, thus the number of measured signals.
Another way is to use algorithms. Blind source separation techniques are able to decompose fascicular signals from FINE electrodes. Several other methods have been described in the literature. They aim to localize or separate nerve trunk signals. For instance, Neurofuzzy algorithms use an artificial neural network.
We can also mention the method based on antenna array beamforming. This seems to be one of the most advanced methods to distinguish fascicular activity inside a nerve. It would be possible to distinguish up to five active fascicles at the same time.
IV. An example of the development of a multi-channel acquisition device 
Olivier Rossel, in his thesis, chose to work on improving the selectivity of the cuff electrodes. He chose this type of electrode because they respect the integrity of the nerve and its fascicles membranes and that they make it possible to limit both the number of implants and the complexity surgical gesture. The electrode need reject the EMG signals and to measure local ENGs at multiple sites around the nerve.
In this part, all the results use the electrical models of the nerve developed in the previous part.
1. Tripolar electrode
As we saw previously, it is possible to reject the EMG signal by using a tripolar cuff electrode (Cf. Figure 6). A tripolar cuff and the adapted electrical treatment is used.
2. Tripolar treatment analysis
The tripolar cuff electrode is considered as a spatial filter with a 1/h periodic frequency response, where h is the distance between the poles. For the spatial frequencies inferior at 1/h, the filter is a bandpass filter with a gain of 2 and a bandwidth of -6 dB between 1/4h and 3/4h.
If we consider the larger “d” of the electrode poles (Cf. Figure 6), the impulse response associated with each of the poles of the electrode is then a gate function of width d and amplitude 1/d.
3. Electrode sizing
n order to increase neural information relative to the noise, it is vital to optimize the cuff dimensions. The literature suggests that the best compromise between cuff length and the available place is a cuff length close to the wavelength of the transmembrane action potential. This one is approximately linear with fiber diameter .
According to Struijk , the action potential propagation velocity can be approximated as 55.800 nodes/s and the duration, of the transmembrane action potential, is approximately 0,4 ms.
Thus, to have an optimal measurement, the cuff electrode must cover 22 nodes of Ranvier. The inter-pole distance must, therefore, be adjusted to h = 11 lmy (lmy is the length of myelin separating two nodes of Ranvier). So, for a typical fiber, the inter-electrode distance h should be about 1 cm, which is used in most ENG measuring electrodes.
Knowing the characteristics of the electrode we want, it is possible to evaluate the distance h between the poles. This distance is of the order of a hundred micrometers which is much lower than that of a classical tripole which is of the order of a centimeter. This is why we will call, in the rest of this work, the tripole proposed a "small tripole".
4. Local variations of the potential
The spatial low frequencies of the electric field generated by an active axon, has almost the same amplitude at each point of the nerve surface, regardless of the location of the axon inside the nerve. Conversely, the amplitudes of the high-frequency components of this electric field depending on the distance between the axon and the point of observation.
It was possible for several poles placed online, to determine the depth of the axon. Indeed, for axons close to the surface of the nerve, there is a difference in amplitude (as a function of the relative position of each pole relative to that of Ranvier's nodes), while for those who are far from the surface the measured amplitude is the same for each of the poles (Cf. Figure 7). Thus, it is necessary to suppress the common mode and amplify only the difference of the signals collected on several poles.
5. Sensibility of a small:
For the small tripole, we have a fast attenuation depending on the distance compared to big tripole (Cf. Figure 8). As figure 8 confirms it, the small tripole is much more selective than the big tripole. Moreover, figure 9 shows that despite the low power level of the targeted signals and the spatial filtering performed, the peak-to-peak amplitude of the output signals of the tripole can reach 6 μV for a single active fiber. Considering the superposition of signals - the simultaneous activity of several fibers - we can hope to reach larger amplitude. Even if it is the case, the output signals of a small tripole remain of very low amplitude and it will thus be necessary to be very attentive to the sources of noise to maintain an acceptable signal-to-noise ratio.
6. Selectivity study:
Olivier ROSSEL developed a new electrode architecture he compared to the FINE electrode. The FINE electrode used is the one developed by Paul YOO and Dominique DURAND (Cf. Figure 7).
Olivier ROSSEL tried to improve this electrode replacing each measure point by a small tripole and by deleting two external ring. He called this electrode the FORTE electrode for “FINE with Original Recording Tripolar Electrode” (Cf. Figure 11). The main difference between these two electrodes is the inter-poles distance in the longitudinal way.
The activity of two fascicles is simulated (Cf. Figure 12) and the peak-to-peak amplitudes of the output signals are compared (Cf. Figure 13). The first difference we see is the signal from the FORTE electrode is attenuated 20 dB compared to the FINE electrode. In figure 13, we see that when only one fascicle is active, the FORTE electrode makes it possible to locate the active fascicle much more easily than the FINE electrode.
Moreover, in the general case of a simultaneous activity of different fascicles, the signals from the different active fascicles are summed at the level of each tripoles (Cf. Figure 14). We can see that for the FINE electrode the amplitude measured makes it impossible to differentiate the active fascicles. However, for the FORTE electrode, since the small tripole is locally sensitive, we can’t see the difference between the figure 13 and the figure 14. It is easy to differentiate the active fascicles.
Finally, we see the FORTE electrode can surpass in selectivity the FINE electrode. The FORTE electrode is a great example of an electrode we could use for our device.
Thus, thanks to this example, we understand that it is possible to develop our own type of electrode. We gathered a lot of different information. First, having a good electrical model of the nerve is crucial to understand what are the parameters we need to take into account to develop our electrode. Moreover, it is primordial in order to be able to simulate the performance of an electrode. We now know that different algorithms that improve the output signal of an electrode already exist. We would like to test and use such algorithms for our device. Finally, thanks to the example of the FORTE electrode, we have already thought about how it will be possible to incorporate such an electrode in our device.
- MicroProbes for Life Sciences, « Nerve Cuff Electrodes ». Retrieved Oct. 14th, 2018 from https://microprobes.com/products/peripheral-electrodes/nerve-cuff
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