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R5. Connectivity determination
Transmission Line Theory is required for High-Frequency Signals
Electromagnetic waves travel along a conductor close to the speed of light, but electrical signals propagate at a much lower speed because charge carriers (electrons) move slower. Electric potentials (V) are created by transcient changes in local charge carrier concentrations (for example as the result of chemical activities). Such disturbances are not experienced in the distance because of shielding by charge redistributions in the proximity. When a voltage signal travels along a wire it is actually an electron concentration gradient moving. The signal propagation velocity is not the same as the charge carrier's drift velocity which is even slower, but the 2 may be related. Propagation of the voltage signal is characterised by resistance (R), inductance (L), and capacitance (C). Figure 1 represents an infinitesimal segment of a transmission line. Voltage drop along the x direction is given by
If we assume the signal is a sinusoidal wave, propagation speed (also known as phase velocity) can be expressed as
where w is the angular frequency, and in the limit where R = G = 0 the velocity can be reduced to .
Extracellular Space (ECS) is a Low-Pass Filter
"The fact that action potentials do not participate to EEG-related activities indicate strong frequency-filtering properties of cortical tissue. High frequencies (greater than ~100 Hz), such as that produced by action potentials, are subject to a severe attenuation, and therefore are visible only for electrodes immediately adjacent to the recorded cell." [Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. Claude B´edard, Helmut Kr¨oger and Alain Destexhe 2003]
"The resting impedance of the brain depends on a number of factors. White matter has a resistivity many times that of grey matter. In addition, the brain is anisotropic, the transverse resistance being up to ten times greater than the longitudinal (Nicholson 1965). Also, the brain consists of approximately equal proportions of neurones and glial cells which each have different impedance properties. An accepted value for the mean resistivity of the brain at body temperature and low frequency is 5.8 Ohm-m (Geddes and Baker 1967)." [Two-dimensional finite element modelling of the neonatal head. A Gibson, R H Bayford and D S Holder 1999]
Some Numerical Values
|Relative Magnetic Permeability of Biological Tissue||µr = 1.000|
|Membrane Capacitance of Pure Lipid Bilayer||Cmem = 10 nF/mm2|
|per unit area Resistance of Neuron Cytoplasmic Membranes||Rmem = 2 Ohm•m2|
|per unit area Electrical Conductance of Cytoplasmic Membranes||Smem = 10 S/m2|
|Volume of Extracellular Space (ECS) / Total Brain Volume||15 - 25 %|
|Resistivity of Cerebrospinal Fluid (CSF) @ body temperature||RCSF = 0.56 Ohm•m|
|Average Resistivity of the Brain||Rbrain = 5.8 Ohm•m|
|Extraneuronal Resistance of Brain Tissue||Rneuropil = 300 Ohm•cm/cm2|
|Intracellular Resistivity of Neurons||Ri = 0.62±0.07 Ohm•m|
|Resistivity of Cytoplasm @ 26°C||Rcyto = 2.421±0.183 Ohm•m|
|Electrical Conductivity of Cu (copper)||KCu = 6.0 x 107 S/m|
This design is ruled out as insufficient for uploading purposes. For details see Hybrid DNI.
#2 may turn out to be the better design in the long run, because of its superior spatial, temporal, and digital resolution.
Currently polymer layers can be deposited on silicon with a uniform thickness less than 20nm (~ 5x thicker than the lipid bilayer). We suppose similar techniques can be applied to coat microwires.
Fluoropolymers such as Teflon (polytetrafluoroethylene, —(CF2—CF2)n—) has very high insulation resistance and low dissipation factor, and is chemically extremely inert. Capacitance of a Teflon layer per unit length is on the order of <1 nF/m.
Signal Transmission. Resistance of a copper microwire 2mm long, 1µm - 0.1µm in diameter, is ~ 10Ohm - 1KOhm. (Quantum effects are probably not important at this scale). Transmission line theory gives an estimation of the signal propagation velocity close to the speed of light in this range. [Impedance consideration needed, graph is problematic]
2 Problems with Extracellular Recording
Intracellular recording makes signal processing much easier but it requires a junction that directly couples the wire to a single neuron.
On the right is a schematic diagram showing the microwire with its tip inside the neuron's cell body. The yellow region represents the metal, coated with a polymer layer (blue). [Diagram must be revised to include impedance considerations and noise]
A simplified block diagram is shown below. The transmission line is the same RCLG configuration as analysed before.
On the right is a conceptual diagram of the head complex.
The Ejection Mechanism enables intracellular probing of the neuron.
The Thin Film Electrode contains regions for both voltage recording and chemical sensing, when it is inserted into the neuron's soma. [Disruption to the neuron is a potential problem.]
[smallest size of chemosensor (eg FET-based or?)]
[smallest size of microscopic Electromagnet?]
The Si Substrate contains a small electronic unit that controls 2 stages of the probe's function: 1) navigation and electrode insertion after finding target; 2) recording.
How much Force is required for Neuropil Penetration?
(Electron micrograph of a typical appearance of the neuropil: cortex with pyramidal cells (161Kb)).
When the microwire is inside the neuropil, it experiences interfacial frictional forces that will hinder further penetration. First we need to determine the rough order of magnitude of this friction. The cell-cell adhesion energy density Wad typically lies in the 10-5J/m2 range. Fluoropolymer films can be expected to have a lower adhesion. For a 2mm polymer-coated wire with 0.5µm diameter (area ~= 3 x 10-9m2) the adhesion energy would be below ~10-14J. Without friction, the mechanical energy required to move this wire (mass ~= 10-14g) by 10µm in 0.1ms would be ~10-16J which is much smaller than the adhesion energy.
A conducting wire of length L with current I in a magnetic flux density field B experiences a force F given by the Lorentz force equation F = (I x B) L. B of a big electromagnet is on the order of ~0.1 Tesla (N/A•m).
This diagram shows a scheme for determining which neurons (eg B) have synaptic connections with another neuron (A). The molecular tag (red) is unique for each probe and encodes a number from 1 to 100 billion, which is the upper estimate of the total number of neurons in the brain. 100 billion = 11 digits (in base 10).
Multiplicity: Multiple synapses from the same pair of source-target neurons may be inferred from the concentration of tags detected.
A=solved, B=optimistic, C=maybe, X=difficult, ?=no clue
|R1.1. 2-way transmission||A|
|R1.2. Read Vm||B|
|R1.3. Write AP||B|
|R1.4. Temporal & digital resolution||A|
|R1.5. Electrical insulation||A|
|R1.6. Chemical insulation||C|
|R1.7. Impedance matching||A|
|R2.1. Cell-type recognition||C|
|R2.2. Cell-type reporting||C|
|R3.2. Small volume displacement||B|
|R3.4. Even distribution||C|
|R3.7. Cell-type targeting||C|
|R3.8. Probing density||B|
|R3.9. Site targeting||C|
|R3.10. Junction formation||?|
|R4.1. Mechanical stability||A|
|R4.2. Biochemical stability||?|
|R4.3. Electrical stability||A|
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Dec/2003 Yan King Yin