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<p>It is possible to implement this model in the NEURON software (http://www.neuron.yale.edu/neuron/) to be able to simulate the transmembrane nodal currents. This software calculates the densities of the currents presented previously.</p> | <p>It is possible to implement this model in the NEURON software (http://www.neuron.yale.edu/neuron/) to be able to simulate the transmembrane nodal currents. This software calculates the densities of the currents presented previously.</p> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 4: </b>Result of the NEURON simulation of the electrical activity (evolution as a function of the time of the transmembrane current) of a Ranvier node of a typical axon of 8.7 | + | <div class="legend"><b>Figure 4: </b>Result of the NEURON simulation of the electrical activity (evolution as a function of the time of the transmembrane current) of a Ranvier node of a typical axon of 8.7 <FONT face="Raleway">μ</FONT>m diameter.<sup>[4]</sup></div> |
<p>The value of the electrical parameters of the model is based on the study of C. C. MCINTYRE and al.<sup>[5]</sup>. 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.</p> | <p>The value of the electrical parameters of the model is based on the study of C. C. MCINTYRE and al.<sup>[5]</sup>. 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.</p> | ||
<img src=""> | <img src=""> | ||
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<div class="block title"><h3 style="text-align: left;">2. Medium transfer function </h3></div> | <div class="block title"><h3 style="text-align: left;">2. Medium transfer function </h3></div> | ||
<div class="block full"> | <div class="block full"> | ||
− | <p>J. H. Meier and al. developed a nonhomogeneous and anisotropic model of a nerve [6]. 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 = <FONT face="Raleway">ρ</FONT> - a from the surface of the nerve and at a distance <FONT face="Raleway">ρ</FONT>0 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 ( | + | <p>J. H. Meier and al. developed a nonhomogeneous and anisotropic model of a nerve [6]. 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 = <FONT face="Raleway">ρ</FONT> - a from the surface of the nerve and at a distance <FONT face="Raleway">ρ</FONT>0 from the axon considered. The angle <FONT face="Raleway">θ</FONT> is the angle constructed from the radial position of the axon and the observation point M. The conductivity inside the nerve is different (<FONT face="Raleway">σ</FONT>z and <FONT face="Raleway">σ</FONT><FONT face="Raleway">ρ</FONT>) 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 <FONT face="Raleway">σ</FONT>s, and the outside of the nerve of conductivity <FONT face="Raleway">σ</FONT>e.</p> |
<img src=""> | <img src=""> | ||
<div class="legend"><b>Figure 6: </b>Model of the nerve fascicle, with perineural sheath labeled “s” and external surroundings labeled “e”.<sup>[6]</sup></div> | <div class="legend"><b>Figure 6: </b>Model of the nerve fascicle, with perineural sheath labeled “s” and external surroundings labeled “e”.<sup>[6]</sup></div> | ||
− | <p>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 | + | <p>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 <FONT face="Raleway">λ</FONT> of 1000 <FONT face="Raleway">μ</FONT>m is chosen. Current values correspond to the nodal currents of an active fiber of 10 <FONT face="Raleway">μ</FONT>m diameter at one instant of time.</p> |
<img src=""> | <img src=""> | ||
<div class="legend"><b>Figure 7: </b>The line represents the nodal current and the bars represent the currents of the active nodes. Each bar corresponds to one node.<sup>[6]</sup></div> | <div class="legend"><b>Figure 7: </b>The line represents the nodal current and the bars represent the currents of the active nodes. Each bar corresponds to one node.<sup>[6]</sup></div> | ||
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<img src=""> | <img src=""> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 8: </b>Spatial transfer function h2(z) and space-frequency H2(k) of the nonhomogeneous and anisotropic medium for two distances <FONT face="Raleway">ρ</FONT>0 = 200 and 500 | + | <div class="legend"><b>Figure 8: </b>Spatial transfer function h2(z) and space-frequency H2(k) of the nonhomogeneous and anisotropic medium for two distances <FONT face="Raleway">ρ</FONT>0 = 200 and 500 <FONT face="Raleway">μ</FONT>m between the observation point and the axon (depth of the axon in the nerve).<sup>6]</sup></div> |
<p>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.</p> | <p>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.</p> | ||
<p>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)<sup>[4]</sup>:</p> | <p>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)<sup>[4]</sup>:</p> | ||
<p>v(M,t) = h(z)∗i(z,t)</p> | <p>v(M,t) = h(z)∗i(z,t)</p> | ||
− | <p>We consider the typical case of a 8.7 | + | <p>We consider the typical case of a 8.7 <FONT face="Raleway">μ</FONT>m diameter axon near myelin gains (length lmy=1000 <FONT face="Raleway">μ</FONT>m) and diameter 2.8 <FONT face="Raleway">μ</FONT>m near the Ranvier’s nodes.</p> |
<p>The objective of this part is to study the spatial and spatio-frequency properties of the extracellular potential created by such an axon.</p> | <p>The objective of this part is to study the spatial and spatio-frequency properties of the extracellular potential created by such an axon.</p> | ||
− | <p>Two reference distances (<FONT face="Raleway">ρ</FONT>'=200 | + | <p>Two reference distances (<FONT face="Raleway">ρ</FONT>'=200 <FONT face="Raleway">μ</FONT>m and <FONT face="Raleway">ρ</FONT>'=500 <FONT face="Raleway">μ</FONT>m) 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: 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 <FONT face="Raleway">ρ</FONT>' distances, that is to say when the axon is close to the surface of the nerve, and this whatever the model used. </p> |
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 9: </b>Example of calculation of the extracellular action potential at the surface of the nerve for two reference distances (<FONT face="Raleway">ρ</FONT>0= | + | <div class="legend"><b>Figure 9: </b>Example of calculation of the extracellular action potential at the surface of the nerve for two reference distances (<FONT face="Raleway">ρ</FONT>0=200<FONT face="Raleway">μ</FONT>m and <FONT face="Raleway">ρ</FONT>0=500<FONT face="Raleway">μ</FONT>m) between the observation point and the axon. (1a and 1b) Distribution of nodal currents along the axon (identical). (2a and 2b) Transfer function of the medium according to models homogeneous isotropic model (2a) and nonhomogeneous anisotropic model (2b). (3a and 3b) Distribution of the extracellular action potential as a function of the position of the observation point along the nerve<sup>[4]</sup>. </div> |
<p>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.</p> | <p>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.</p> | ||
<p>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.</p> | <p>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.</p> | ||
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<p>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).</p> | <p>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).</p> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 12: </b>Example of spatial extracellular action potential along a fascicle. For two distances: <FONT face="Raleway">ρ</FONT>0=200 | + | <div class="legend"><b>Figure 12: </b>Example of spatial extracellular action potential along a fascicle. For two distances: <FONT face="Raleway">ρ</FONT>0=200 <FONT face="Raleway">μ</FONT>m (solid line) and <FONT face="Raleway">ρ</FONT>0=500 <FONT face="Raleway">μ</FONT>m (dotted line)<sup>[9]</sup>.</div> |
− | <p>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 (<FONT face="Raleway">ρ</FONT>0=200 | + | <p>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 (<FONT face="Raleway">ρ</FONT>0=200 <FONT face="Raleway">μ</FONT>m), and the other being further away (<FONT face="Raleway">ρ</FONT>0=500 <FONT face="Raleway">μ</FONT>m).</p> |
− | <p>In this figure 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 (<FONT face="Raleway">ρ</FONT>0 = 200 | + | <p>In this figure 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 (<FONT face="Raleway">ρ</FONT>0 = 200 <FONT face="Raleway">μ</FONT>m). Then at greater distances (<FONT face="Raleway">ρ</FONT>0=500 <FONT face="Raleway">μ</FONT>m), 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 <FONT face="Raleway">μ</FONT>V (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.</p> |
</div> | </div> | ||
<div class="block title"><h1>VI. Neural information:</h1></div> | <div class="block title"><h1>VI. Neural information:</h1></div> | ||
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<p>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.</p> | <p>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.</p> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 7: </b>Extra-neural potential of monopolar action according to the position of the measuring point. The diagram at the top left shows the simulated situation. At the top right, the simulation corresponding to this configuration is represented: calculation of twice five monopolar potentials, for a typical axon (diameter of 8.7 | + | <div class="legend"><b>Figure 7: </b>Extra-neural potential of monopolar action according to the position of the measuring point. The diagram at the top left shows the simulated situation. At the top right, the simulation corresponding to this configuration is represented: calculation of twice five monopolar potentials, for a typical axon (diameter of 8.7 <FONT face="Raleway">μ</FONT>m, and lmy= 1 mm). The distances from this axon to the measurement points are <FONT face="Raleway">ρ</FONT>1=100 <FONT face="Raleway">μ</FONT>m for site A and <FONT face="Raleway">ρ</FONT>2=500 <FONT face="Raleway">μ</FONT>m for site B. Below, the monopolar signals at points “a” to “e” are shown for each of the measurement sites.</div> |
<p>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".</p> | <p>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".</p> | ||
</div> | </div> | ||
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<div class="block title"><h3 style="text-align: left;">5. Sensibility of a small:</h3></div> | <div class="block title"><h3 style="text-align: left;">5. Sensibility of a small:</h3></div> | ||
<div class="block full"> | <div class="block full"> | ||
− | <p>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 | + | <p>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 <FONT face="Raleway">μ</FONT>V 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.</p> |
<img src=""> | <img src=""> | ||
<div class="legend"><b>Figure 8: </b>Peak-to-peak amplitudes of the output action potential of a small tripole and of a big one</div> | <div class="legend"><b>Figure 8: </b>Peak-to-peak amplitudes of the output action potential of a small tripole and of a big one</div> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 9: </b> Peak-to-peak amplitudes measure at the output of a big tripole (left) or a small tripole (right) in function of the position of the active axon (diameter 8, 7 | + | <div class="legend"><b>Figure 9: </b> Peak-to-peak amplitudes measure at the output of a big tripole (left) or a small tripole (right) in function of the position of the active axon (diameter 8, 7 <FONT face="Raleway">μ</FONT>m, and lmy=1 mm) in a cylindrical nerve of 300 <FONT face="Raleway">μ</FONT>m in diameter.</div> |
</div> | </div> | ||
<div class="block title"><h3 style="text-align: left;">6. Selectivity study:</h3></div> | <div class="block title"><h3 style="text-align: left;">6. Selectivity study:</h3></div> | ||
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<p>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.</p> | <p>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.</p> | ||
<img src=""> | <img src=""> | ||
− | <div class="legend"><b>Figure 11: </b>FORTE electrode, h = 375 | + | <div class="legend"><b>Figure 11: </b>FORTE electrode, h = 375 <FONT face="Raleway">μ</FONT>m.</div> |
<img src=""> | <img src=""> | ||
<div class="legend"><b>Figure 12: </b>Two fascicles represented in the electrode. These disposition of the fascicles is the one used for the simulations made to obtain figure 13 and figure 14</div> | <div class="legend"><b>Figure 12: </b>Two fascicles represented in the electrode. These disposition of the fascicles is the one used for the simulations made to obtain figure 13 and figure 14</div> |
Revision as of 14:09, 16 October 2018
INTRODUCTION
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.
Membrane
Nerve modelisation
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 principaly based on the thesis of 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.