This post looks at the possiblity of brain cells being waveguides for electromagnetic fields.
This post does not consider channel waveguides, such as optical fibres, but examines the more fundemental transverse waveguides where either the electric or magnetic field do not propagate along the tube in the axial direction. Channel waveguides only support hybrid modes, and are formed from composite transverse modes.
In three previous posts some basic facts about the size and behaviour of electrical fields and neurons were described :-
* Fields In Cylindrical Tubes – described waveguides in cylindirical tubes
* Diameter of Neurons – described the approximate diamter of neurons
* The Electrolytes – described the wavelengths of common ions in the brain
The previous post on Fields in Cylindrical Tubes looked at a number of conditions that were necessary to create a transverse waveguide.
The conditions necessary for brain cells to be waveguides were:-
1. The brain cell is a cylindrical tube
2. The brain cell acts as a dielectric waveguide
3. The source of fields is electromagnetic
4. The diameter of the tube is a low fraction of the wavelength of the fields
5. The source of the waves is important for different modes
The brain cell is a cylindrical tube
The first issue is reasonably straight forward. Brain cells are formed of cylindrical tubes. That is to say dendrites, axons, filopodia, astrocytes are composed of tubes of varying lengths. The soma in these cells are not straight as they form a multi-junctions. In later posts the behaviour of wave guides in multi-junctions will be examined. A further, subtle but important complexity, is that these tubes branch and pass though electric synapses. This has the effect of splitting the wave pattern.
The brain cell acts as a dielectric waveguide
Waveguides for high (microwave) frequencies are made of rigid metal with a high conductive inner surface and no sharp bends or holes. At the frequency of light waveguides are made of dielectric materials which “reflect” waves using a mechanism called total internal “reflection”. Howver this is not “reflection” in the sense of absorption and transmission, but a transformation of the co-ordinate system using evanescence waves. This point is important because it maintains a continuous field, which was a basic requirement listed in a previous post on whether the Cogito could be a scientific hypothesis.
Total internal “reflection” means the external and internal material of the fibre must be made of a dialectic material. The refractive index of the core must be higher than the refractive index of the cladding. The refractive index is calculated by dividing the speed of light in a vacuum by the speed of light in that material. A vacuum has a refractive index of 1. When light traveling in the dense core hits a less dense cladding it is turned totally back into the core. The light must hit the cladding at an angle that is greater than a critical angle, which s a function of the difference between the refractive index of the two materials.
In an optic fibre the index of the core is greater than the index of the cladding to prevent loss. In a neuron the membrane clads the intra cellular fluid. It must be remembered the membrane contains a hydrophobic pocket which will, naturally, have a lower refractive index than water.
The issue of refractive index neurons was addressed by Antonov (1984) who measured the refractive index of the myelin sheath to be 1.5, the membrane to have a refractive index of 1.3 and the intracellular water to have refractive index of 1.36 – 1.37. From this he speculated on the possibility of waveguide properties within the myelin sheath or the axon.
Rappaz (2005) also found the refractive index of the intra cellular content of neurons in living cells, with high precision, to be 1.375 – 1.385 in a standard cell and 1.365 in a hypotonic (swollen) cell. The lower value in the hypotonic cell was caused by influx of water into the cell.
Thus, based on the refractive indexes of the material there remains as possibility that neurons may be waveguides. Given the close refractive index between intra-cellular water and the membrane that angle of incidence would need to be be low. This low angle of incidence would required to the wavelength being similar to the diameter of the neuron.
The source of fields is electromagnetic
The third issue raises some problems. Brain cells do not apparently carry a large number electromagnetic fields, in Maxwelian sense, that industrial waveguides do.
“Very weak” bio luminescence of photons are produced from lipid peroxidation of Fe+2 ions, and much weaker production from reactive oxygen species (ROS) singlet oxygen production and reactive nitrogen species (RNS) tryptophan oxidation during a free radical interaction (Vladimirov 2009) . This production is sourced in mitochondria which tend to be found in cell somas.
Only 100 bio photons per cm2 per second can be detected from the cortex surface, and therefore bioluminescence has been called “very weak”. However, it is estimated that 100 bio photons per second are produced in a visual neuron by mitochondria’ free-radical reactions (Bokkon 2010). This equates to 10^8 bio photons per second across the 10^6 neurons activated in the visual cortex when viewing an object.
However, as photons travel in water at 3/4 of their speed in a vacuum, or 225 million meters per second, (5.8 times around the the earth per second) they are very transient within brain cells. This might provide a fast signalling mechanism, however unless the photons could somehow create a standing wave then they could not provide a continuous field.
There is also a question that bioluminescence is a bio-product of energy production and not an intrinsic information carrier. As such bioluminescent could be a very transient and weak epiphenomena.
Having said this, it is worth examining how brain cells could be waveguides to see if it reveals any evidence for how consciousness might work.
Another possibilty is that the wavelengths of The Electrolytes that were described in a previous post could create energy of the correct wavelength. The suggestion is that whilst ions do not emit photons they may produce near fields that do not fully radiate but have wavelength properties.
Given the intracellular refractive index is c. 1.38 the wavelengths are as follows:-
* Mg+2 202 nm
* Ca+2 286 nm
* Na+ 426 nm
* K+ 555 nm
The diameter of the tube is a low fraction of the wavelength of the fields
The Diameter of Neurons, were described in a previous post as follows:-
* Pyramidal axons 500-900nm
* Pyramidal basal dendrites 500-1000nm
* Pyramidal apical dendrites 250-1000nm
* Filopodia. 220nm
* Star Astrocytes. 220nm
It is now possible to see that if wavelength-like-properties were emitted from ions whether any transverse modes could be supported in brain cells. These patterns are determined by the cut off wavelength, which is usually calculated as, λ=(2πr)÷Xmn. However to figure out which transverse mode would be created for different brain cells diameter for different electrolyte ion wavelengths, it is calculated as (λXnm)÷π=d.
The table showing the cut off diameters for the electrolyte ion wavelengths in a material with a refractive index, of a neurons intracellular fluid, of 1.38, as follows:-
| Nm | Magnesium Mg+2 | Calcium Ca+2 | Sodium Na+ | Potassium K+ |
| Wavelength | 202 | 286 | 426 | 555 |
| TM11 (1.84) | 118 | 168 | 250 | 325 |
| TE01 (2.40) | 155 | 220 | 327 | 425 |
| TM21 (3.05) | 197 | 279 | 415 | 540 |
| TE11 (3.83) | 247 | 350 | 521 | 677 |
| TM01 (3.83) | 247 | 350 | 521 | 677 |
| TM31 (4.20) | 270 | 384 | 571 | 742 |
| TE21 (5.13) | 330 | 469 | 698 | 907 |
| TM12 (5.33) | 343 | 487 | 724 | 942 |
| TE02 (5.52) | 355 | 504 | 750 | 975 |
| TE31 (6.39) | 411 | 584 | 868 | 1129 |
| TM21 (6.79) | 437 | 620 | 922 | 1200 |
| TE12 (7.01) | 451 | 640 | 952 | 1239 |
| TM02 (7.01) | 451 | 640 | 952 | 1239 |
| TM32 (8.01) | 515 | 732 | 1088 | 1415 |
| TE22 (8.41) | 541 | 768 | 1143 | 1486 |
| TM13 (8.53) | 549 | 779 | 1159 | 1507 |
| TE03 (8.65) | 557 | 790 | 1175 | 1528 |
| TE32 (9.76) | 628 | 891 | 1326 | 1724 |
| TM23 (9.9) | 637 | 904 | 1345 | 1749 |
| TE13 (10.17) | 654 | 929 | 1382 | 1797 |
| TM03 (10.17) | 654 | 929 | 1832 | 1797 |
| TM33 (11.34) | 730 | 1036 | 1541 | 2004 |
The importance here is that given the material properties of membranes and water, and the wavelengths of electrolytes photon emission, and the diameters of diameters of axons, dendrites, filopodia and astrocytes means brain cells could would act as waveguides if they were transmitting electromagnetic radiation from ions. In other words the diameters of neurons and the wavelengths of ions in the brain are in the same ball park.
Interestingly different ions would produce different wave patterns in neurons of the same diameter and the same ion would produce different wave patterns in neurons of different diameters.
The source of the waves is important for different modes
The source of electric and magnetic waves in brains comes from moving ions which transmit through either ion channels, chemical synapses, electric synapses or along astrocytes or filopodia. The sources of these waves are found on the sides of neurons, or along astrocytes or filopodia. The previous post on waveguides showed how waves whose radiation was sourced on the sides of cylindrical tubes would encourage the creation different wave patterns.
These sources can be descibed, very generally, as follows. Ion channels generally tend to generate the electrical potentials that sum to form action potentials. Chemical synapses generally block the electric fields that flow down axons, but trigger a further electric field that originates in astrocyte cells and flows through arrays of channels in the post-synaptic cleft and into dendritic spines. This is the so called tripartate synapse. Electric synapses are formed of “connexion plaques”, which are large arrays of channels, which can be uni- or bi-directional. The nature of these channels and the ions that flow through them and their location is therefore very important and will be subject of further posts.
Neurons as waveguides
In the literature axons, axon membranes and microtubles have been considered as potential waveguides to transmit information. However, there are problems with all three of these of these structures being uses as a the basis of consciousness.
(Xue 2012) said due to resistance in the inner part of axon, axons were not suitable as a waveguides as the inner part of the axon strongly scattered electromagnetic fields due to its non uniformity. Axons rely on phospholipid bi layer which is uniform and could create an electromagnetic wave guide in the inner fluidic environment, which may not scatter the electromagnetic wave.
Scattering in wave guides was a key issue in early optic fibres, “if one has a sufficiently “clean” type of glass, one should be able to see through a slab as thick as several hundred meters.” (Kao 2009). However the distances being covered in brain cells is in the order of micrometers.
The potential scattering of energy in the inner parts of neurons, due to filaments and proteins, offer a challenge to explain waveguides. However the location of fields patterns, in higher modes tends to move energy to the outside of the cylinder which would avoid the filaments and proteins.
A question also needs to be raised about which wavelength would be transmitted down the membrane. There would need to be a wavelength less than 20nm to transmit a transverse mode. Alternatively the membrane could acts as an optic wave guide and transmit in the hybrid mode of HE11 (not yet defined) which would transmit most of the energy outside the membrane.
An objection to membranes acting as waveguides for consciousnes is that the membranes are enclosed and a wave could not be continous between them.
Kuma (2016) speculated that axons may act as waveguides for biophotons from mitochondrial respiration or lipid oxidation. The paper suggested that waveguides needed to be straight. However Nockel (1996) showed resonant modes exist in dielectric cylinders despite deformations of between 1% to 50% as long as the cavity remained convex.
An objection to axons acting as waveguides for consciousness is that most (but not all axons) are effectively simple one dimensional tube structures that hit an electrical dead end at the pre-synapse. In terms of signal processing axons can be viewed as carrying packets of signals to synapses (Luczak 2015, 2016) rather than maintaing a continuous field present.
Microtubles have been suggested as waveguides (Salari 2010) as wave guides. An objection of that their internal diameters of 15nm is similar to membranes and would need similar wavelengths and modes as membranes.
An objection to microtubles acting as waveguides for consciousness is that they are cylindrical detached from each other, so would not be continuous.
Dendrites as conscious waveguides
Surprisingly dendrites have not been considered as waveguides for consciousness, which is where the neurology would suggest complex patterns could interact. Future posts will follow this idea.
The earlier key statement was that the electrolytes in the brain could possibly transmit wavelength properties in the near field. This should be considered for a few reasons. The brain would not want to use energy transmitting information as photons. If the brain has evolved it would prefer a low energy rather than a high energy solution. We know that brain cells transmit a great deal of electrical and magnetic energy from slow moving ions. The seperation between static electric and static magnetic fields and electromagnetic fields is not a simple immediate transformation. Slow moving, or quasi-static electic and magnetic fields are a poorly understood area of physics, which are often treated as short-cuts by engineers, rather than being first class phenomena.
Fields of Consciousness 