Transcranial Magnetic Stimulation

Enthalpy

And here's the fourth picture needing a second message: Biot and Savart's law for the vector potential. You know, A, from B = rot(A). And mu/4pi is 10^-7 in S.I.

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Enthalpy

Greater numbers of shorter pulses need even less power. Here the current shall increase for 5ns and decrease for adjustable 50ns.

The coil can keep the same shape as for 1µs but now thick rod or tube is good enough. The turns are now in parallel to reduce the voltage to 100V; or several generators can feed each a part of the coil; or the coil can consist of one single very broad conductor, preferably broader at the return leg, and accept a slightly smaller voltage. Over 5ns, the total current increases to 3.6A only.

The outer turns will swallow more current than the inner ones, which isn't bad for the induction pattern; to avoid this, put the turns on a square pattern (or hexagonal, etc) near the target zone, instead of side-by-side.

The fast main switch is a dual MOS meant for RF transmitters, like the BLF884P. Their supply is at most 50V, brought to 100V by a 1:2 transformer which also produces bipolar pulses. Braking through the diodes reinjects power in two special lines; the one that shall not brake is just fed over twice the supply voltage - this better design works for longer pulses as well. Some diode-capacitor pump can preload the braking lines, while voltage regulation defines the braking time. A few Zener chosen by transistors could dissipate the small power.

The diodes could be SiC Schottky like the C3D08060A. These would contribute 4W of the 7W switching losses at 70ns period, and to nearly all 4W conduction losses. These diodes begin at 600V in a LF package; a better fit would be welcome.

The HF electronics is at the coil, and the power and control cable is now easy and lightweight.

Marc Schaefer, aka Enthalpy

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Enthalpy

With pulses like 70 ps long we leave the simpler near-field operation and magnetic coils. This is electromagnetic wave with antennas.

A strong short pulse followed by a weaker and longer compensation needs a wide band antenna, nevertheless directive and powerful. I sketch one possibility below (click to enlarge), where the rectangles are conducting elements meant to radiate.

The antenna comprises many dipoles side by side and butt, together with driving electronics. The shape should better approximate a section of a sphere; the dipoles can be driven with a slight time difference only, for fine steering, to compensate small tolerances, or to compensate diffraction at the target. The antenna has no reflector but can be backed by an absorber at some distance.

The dipoles are charged before each pulse; here resides the emitted energy. Each dipole has locally its own fast transistors to discharge it, for instance two BFG425W. The switch could also be behind a line, and possibly shared among several dipoles, but bigger transistors are uncommon at that speed.

Take dipoles 2* 20 mm long, wide to have 80 ohm wave impedance, charged at +-4 V. The transistors can reach the 50 mA in 30 ps; this constant current widens to 2* 20 mm within 70 ps, which defines the duration of the strong short plateau of induced electric field at the target.

10*12 dipoles at 200 mm distance would create in air the same field as present TMS apparatus with 3 GA/s. Permittivity at the brains and the cranial liquid reduces the field, and so do reflections at the scalp and the skull, but R² times more dipoles, R times more distant, create a field R times stronger.

When the current pulse reaches the ends of a dipole, fast diodes (for instance three BAT62 per dipole) allow the current to continue flowing, due to the antenna's inductance, this time between butt dipoles. The current decreases more slowly, first due to losses in the transistors and diodes, say 1.2 V versus 8 V accelerating voltage, and second due to the finite length cumulated by butt dipoles. This defines the weaker longer plateau of induced electric field, maybe 6 times weaker here than the strong plateau. Less asymmetric than before, but still better than present TMS apparatus.

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The dipole width or diameter can adjust the wave impedance a bit to match the components' current capability. They can't be too close, or their interaction will limit the current. The examples given are not optimum, especially the old diode is capacitive and slow (which cancels out partially). Stronger voltages would be very useful but MOS seem unavailable at this speed. I haven't checked other FET.

Driving the bipolars is difficult. I expect no charge gain per stage at 30ps, so the gain of the driving tree shall result from impedance transformation, but on a wide band and with floating voltages... Striplines similar to a gamma match, with ferrite for the bandwidth, and tapered to match the impedance?

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70 ps make a pulse 20 mm long in air, which relates to the best field concentration at the target. This speed is difficult for components, and isotonic water has only 49 mm penetration depth at 5 GHz and 22 mm at 10 GHz.

Operation immersed in a water-like (or brain-like) material would improve a lot. It could use a liquid gel at the hair and a solid gel on the way from the antenna. 2 to 5 GHz limit the losses; the ~150 ps pulse is easier to produce even if stronger and is only 5.5 mm long in water, which improves the field concentration at the target and the size of the dipoles.

Immersed operation also reduces reflections, as only the skull has strong interfaces, and reduces imprecision due to refraction. Subtle beam synthesis by electronic steering can compensate the aberrations due to the skull, but this difficult option is more futuristic.

If the antenna doesn't touch the skull, the beam can follow the optically observed head's movements, by limited electronic steering, or by automatic control of the antenna's position.

Marc Schaefer, aka Enthalpy

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Enthalpy

A V antenna is wideband, and it can produce naturally the asymmetric pulse. Please refer to the sketch below; log in and click to magnify.

The source injects a current whose longitudinal components in both arms of the V compensate another's effect, and transverse components add. As only a fraction of the current radiates, the V antenna is much a transmission line; its line impedance should better be kept uniform so the current is as well: the conductors on the sketch are thicker where wider apart - or they can be sheet of variable width, or several wires packed closely at near the source and spread at the far end.

Inject a current pulse that raises in 70 ps for instance - easier than the previous 30 ps. It propagates in the conductors essentially at the medium's transverse electromagnetic speed, say 350 ps for some 100mm length, so the A field (magnetic vector potential) emitted near the source arrives at the on-axis target retarded by that additional delay, while near the tips, the field is emitted later but without the additional delay. The radiation cumulates over the length, with the net effect on-axis to radiate a 70 ps pulse as would the same current do over the width of the antenna, but over a broad band. Off-axis, the delays compensate badly so radiation is weaker. This is very similar to an ultra-relativistic particle that radiates when deflected. If the V is 2*10 mm wide for instance over 100 mm, the discrepancy is less than 2 ps.

After some 350 ps for 100 mm length, the pulse arrived at the open conductor tips is reflected and the current stops, beginning at the tips and extending to the source over the 100 mm in 350 ps more. Because the reflected pulse travels away from the target, its effect created near the source arrives at the target 2*350 ps later than the effect created near the tips, or 700 ps, so the A field takes this time to decrease. The induced electric field, which is the variation speed or A, is made asymmetric here, again more easily than with the butt dipoles.

Other antennas have a wide band (log-periodic, cigar) or rather wide (helical, Uda-Yagi...) but the V has naturally the uniform propagation time that takes care of a pulse's shape.

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The electronics can preload the antenna and discharge it with the 70 ps current rise time in a switch transistor near the antenna, where the current lasts for 700 ps - or the pulse can be produced by other wideband means. A propagation line can also reach a more distant component, say one output of an integrated circuit, but not too far since this prolongs the conduction time and worsens the achievable repetition rate. A distributed amplifier is an option.

An array of such antennas and sources brings the needed signal strength to the target. Arranging them on a section of a sphere remains good, and as the V antennas are much more independent, electronic steering and beam forming fits better here, especially if the integrated circuits can make the variable delays. Now the focus can follow the patient's movements.

Or if one (or few) source has enough power, a single antenna can feed a concentrating reflector or lens. With individual or collective lens, the antenna V can be wider and still focus to a narrow target.

Immersing the array in a water-like or brains-like material brings the advantages described for the butt dipoles. Electronic steering eases the compensation of diffraction at the skull to achieve full resolution in the very permittive medium: very few mm, even deep in the brains.

Marc Schaefer, aka Enthalpy

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Enthalpy

The V antenna is more directive than a dipole, hence the wave that leaves it is wider than a half wavelength. Consequently, synthetic beam formation alone can't achieve the narrowest focus; something like a lens, individual or collective, is necessary, possibly in addition to phasing the array.