We have AE at home

By: Ethan Childerhose, Kevin Chung, Andy Kong, Brian Machado, Marley Xiong

The acoustoelectric effect (AE) allows us to precisely target tiny areas—as small as a millimeter—and use ultrasound to single out the electric field of a region. Our goal is to use it to make brain-computer interfaces with 27,000x more channels than EEG.

We built a setup at home and replicated the AE effect. Our system is sensitive enough to measure acoustoelectric signals down to 250 nV with SNR > 1, despite no shielding or noise cancellation.

Currently, noninvasive devices are extremely limited in their spatial resolution. EEG can localize brain activity to about 3cm spatial regions, due to the smearing of potentials*.

* The power in each spatial frequency decreases exponentially with frequency, and the varying conductivity of layers of the head (skull, scalp, brain) further blurs the potentials. See the textbook Electric Fields of the Brain for a mathematical description.

What if we could do a lot better, say, 1mm resolution?

Comparison of resolution with regular EEG and with acoustoelectric imaging. Figure is representative; we expect brain data to look very different!

We got together to test the effect and build a proof of concept for using AE in brain imaging. All this was done in 10 days of hacking.

Radio analogy of AE

Imagine each neuron is an FM radio station, and they’re all blasting their tunes on the same channel. By being closer to one station, you can tune in a bit better, but the noise from all the other ones is still there. This is the problem that we face when recording EEG signals — in order to make good neural prosthetics, we need to be able to read from a tiny subset of the neurons WITHOUT the noise of the others getting in the way. How can we do that?

Radio stations work by modulating their music with a reference signal, say 90.3 MHz. When you want to tune into that channel, you set your car radio to 90.3 MHz, and receive just that one station’s music.

Evidently, neurons don't normally "sing" at unique frequencies. But perhaps with external pertubation—ultrasound—we can make them do so.

The acoustoelectric effect

The acoustoelectric effect is a phenomenon where ultrasound interacts with electric fields by changing the conductivity of a material.

Sketch map of acousto-electric effect [source]

By applying ultrasound to a region and measuring electrical signals on the scalp, you can isolate signals from that particular region by looking for modulation at the ultrasound frequency — typically > 500 kHz.

Ultrasound can be focused down to a 1-mm focal point in the brain. By detecting the acoustoelectrically generated signals, we can in principle obtain the mm-level spatial resolution with the temporal resolution of EEG.

The main technical challenge is that the AE-generated signals are small; people recently worked out the governing equation for acoustoelectric fields (full derivation here):

The governing equation for acoustoelectric fields is:

where $k = 1 \times 10^{-9} \, \text{Pa}^{-1}$ . This corresponds to a modulation of 0.1% per MPa of pressure, in the case of a plane wave geometry.

This Nature paper published last year provided a theoretical foundation for AE. Other people have shown AE in brain phantoms [1], and imaging of electric currents in the heart [2].

Results

We were able to produce and measure the acoustoelectric effect in a tank at home. We generated an electric field to simulate a current in the brain and applied ultrasound at 500 kHz to the local current region.

We worked with continuous-wave ultrasound at very low pressures (~10 kPa). For context, the Nature paper also used continuous-wave ultrasound, and appeared to have SNR < 1 when they used pressures below 250 kPa (figure 4d in their supplementary). By using a lock-in detector, we were able capture acoustoelectric signals down to 250 nV.

The AE effect appears at the frequency of the electric field $\text{f}_E$ mixed with the frequency of the acoustic field $\text{f}_A$ , giving rise to sum and difference frequencies. We made measurements at the difference frequency, $\text{f}_{AE} = \text{f}_A - \text{f}_E$ .

Magnitude of acoustoelectric effect with varying pressures. Each color is a different location in the acoustic field.

Each data point is the magnitude of AE at the difference frequency (500 kHz minus 135.145 kHz*). We swept the lock-in frequency in a 10 Hz range around $\text{f}_{AE}$ , between 499,760 and 499,770 Hz.

* We chose this frequency arbitrarily, but also tested lower frequencies (200 Hz) later.

The AE signal is the size of the peak against the background noise of the surrounding frequencies.

Lock-in amplifier readout over repeated frequency sweeps.

The presence of the peak helps us confirm the AE effect and reject spurious environmental signal. The peak appears if and only if both the ultrasound and electric field were on, and disappeared when the stimulating electrodes were moved out of the ultrasound focus.

We measured 120 mV at the frequency of the driving electric field, and 1625 nV at the difference frequency—the AE signal. This corresponds to a modulation percentage of 0.00135% at 50 kPa, or 0.027% per MPa.

Brain signals have a magnitude of 10-100 µV within the 0-10 Hz bandwidth at the surface of the scalp, so we expect the AE signal to have a magnitude of 2.7-27 nV per MPa. From the picture of the lock-in amplifier, our noise floor was about 100 nV, so about 1-2 orders of magnitude of noise reduction would be necessary to capture AE signals from the brain.

Is this doable? From an electronics perspective, very low-noise preamplifiers exist with less than $1 \, \text{nV}/\sqrt{\text{Hz}}$ noise*.

*Samuel Groner, A low noise laboratory-grade measurement preamplifier

The more fundamental bound of our noise floor comes from Johnson noise in the brain and skull itself. The skull has a resistivity of about

7500 \, \Omega \cdot \text{cm}

, which translates to a Johnson noise of about

5 \text{ nV}/\sqrt{\text{Hz}}

. Assuming a bandwidth of 10 Hz, this gives a noise floor of roughly 23 nV, which would make the AE signal just barely detectable.

One idea to lower the noise floor would be to average over many electrodes. The uncorrelated Johnson noise would decrease as $\sqrt{N}$ in the number of electrodes, while the correlated AE signal would increase linearly with N.

Methods

Overview

Our home setup was very... bare-bones. We had no Faraday cage, no filtering, no pre-amp, not even an amplifier for the driving the transducer or applied electric field. We were able to get by by using continuous-wave ultrasound and with the magic of a lock-in amplifier. This handsome boy that we got on Ebay for $5k:

SR865A — 4 MHz DSP lock-in amplifier

Pictured below are; a hydrophone, 4 copper wires in a 2x2 grid, and electrode pads. The hydrophone connects to an oscilloscope, and allows us to locate the highest pressure region. The four copper wires sticking through the holes are the applied electric field. Only two are powered at once using a signal generator. Having four allows us to pick any two and test different directions and locations. Most often the two closest to the hydrophone were used. The electrode pads pickup the modified electric field (due to the acousto-electric effect).

Acousto-electric setup. Custom probe close-up.

The ultrasound single element probe is held in a 3D printed structure which also holds the acoustic lens right above it. In the setup, it is positioned at the bottom of the tank facing upwards. This is so we can have our custom probe free to move around from the surface, to locate the point of highest pressure.

Water tank

We used a water tank to model the brain. We got a plastic container from Target and filled it with degassed, deionized water. Water is a good acoustic model of the brain (1524 m/s in water, 1540 m/s in soft tissue), and 0.3% saline is a good conductivity model of the brain.

Degassing water

It's important to remove dissolved gases to reduce the risk of cavitation damage of the hydrophone. We used this vacuum chamber from Amazon and let the water sit under vacuum for 2 hours.

More often than not we were too impatient to use the vacuum chamber, so we used the indie method of degassing: boiling the water.

Acoustic field

We used a 500 kHz transducer (50 mm diameter, unfocused; Olympus A301s-SU). The ultrasound was driven straight from an arbitrary function generator (Siglent SDG1032X).

We encased the transducer in a latex balloon full of mineral oil to isolate the transducer from the system electrically.

Electric field

The electric field was applied with a pair of copper wires, stripped bare for 5 mm at the ends, with 4.5 mm (1.5 wavelengths) inter-electrode spacing. Crucially, we had to use a second function generator to drive the electric field. When the same function generator was used for both driving the ultrasound and electric field, we saw coupling between the signals that gave rise to a “fake AE” effect, probably due to crosstalk between the function generator channels. The Siglent SDG1032X has -60 dBc of channel crosstalk which is greater than the AE effect that we observed. We also saw coupling from the signal generator to the lock in amplifier when they were powered on the same circuit, beyond just the manufacturer quoted -60dBc we also encountered some level of test setup related coupling and interference between wires. Steps were taken to mitigate this by twisting wires together to reduce EMI and shielding where appropriate.

We drove the function generator with 20V peak-to-peak, giving rise to a potential of 19.5V peak-to-peak across the electrodes. Our function generator has a finite output impedance of 50 Ohm and given the voltage drop would suggest the electrical resistance of the solution is around 1kOhm at 100 Hz.

Pressure Recording

We used an 0.5 mm needle hydrophone (Onda HNR 0500) to measure the incident pressure wave generated from the transducer. Given the hydrophone’s small size profile at the recording tip, we could localize where in space the pressure reached its maxima, and place our AE pickup electrodes at this position.

Interlude: speed of sound

As a side-note, our setup also allowed us to measure the speed of sound in our saltwater medium. By recording from both the transducer’s driving signal generator and the hydrophone simultaneously, you can see the time delay between the start of the transducer sending out its acoustic waves and the hydrophone receiving this signal. By measuring the distance between the hydrophone and the transducer, and dividing this distance by the time delay, we can determine the speed of sound.

Speed of sound measurement — Purple: transducer driving signal. Yellow: hydrophone pickup signal. Time is along the x-axis.

Acoustic Lenses

Surprisingly, acoustic lenses are hard to obtain. They’re one of those things that are offered on websites with a button that says “Contact us to request a quote”. Lame 😩

Thankfully, you can just make your own. The ideal acoustic lens has the same impedance as water, but a different speed of sound. PDMS is perfect, but takes 3 weeks to ship on Amazon. So we went on a hunt for household materials that could be shaped into a sphere. Things we tried:

a grape (nothing happened)
orbeez (too well-matched to water)
silicone caulking shaped by the bottom of an aluminum can (hard to handle, takes days to set)

After none of the simple options worked, we designed our own to be 3D printed, both out of PLA and resin. Before the 3d prints came in we made molds and casted the lens out of candle wax.

The resin printed lenses were the best. The wax casted ones were difficult to make, and were very dependant on the type of wax used. The FDM printed PLA lenses had some air gaps between the 100% printed infill which causes lots of acoustic reflection.

Lock-in amplifier

Analog signals are riddled with noise—namely, thermal noise, line noise, and 1/f noise. We expect the acoustoelectric signal to be very small (on the order of nanovolts to microvolts), so naive, direct measurements will result in our signal being drowned out by noise.

By using the acoustoelectric effect, we've shifted our signal to 500 kHz, away from most sources of noise. We can use filters to get rid of noise contributions outside of this band. Within the bandwidth of interest, we expect the noise to be mostly thermal (white noise).

Lock-in amplifiers are extreme examples of frequency-selective filters. Say our signal of interest occurs around a particular frequency f with some bandwidth b, but that this signal is polluted by lots of noise from various regions of the frequency spectrum. Our AE signal is such a signal, occurring only around the ultrasound frequency with bandwidth determined by EEG signal bandwidth. If we multiply this signal with another sinusoidal signal with frequency f through the use of an analog mixer, then we are able to produce a modulated signal. In this modulated signal, a large principal component of the signal would be in the original frequency band around f, but two side bands would also occur: one at the difference of the two input frequencies, and another at the sum (recall trig identities of multiplying two sinusoids!), which in this case are around 0 and 2f. By using a low-pass filter on this modulated output, we can strictly select for the component of the modulated signal around 0Hz.

In total, what the above operation achieves is a very tight band-pass filter that gets rid of noise from everywhere but around the frequency of our interest. This in turn greatly boosts our SNR and allows us to confidently detect signals down to the low-nanovolt range, around where we expect to see the AE signal. Furthermore, in the specific context of AE, recall how we added the ultrasound frequency f to our EEG signal, only to subtract it again through the use of the lock-in amplifier. We have effectively demodulated our AE signal back into the normal EEG frequency range, but this time with minimal noise (thanks to the lock-in amplifier) AND with spatial specificity (thanks to the AE effect)! Double wow!

Functional ultrasound through the skull

Check out our other post, Functional ultrasound through the skull!

Acknowledgements

A big thank you to:

Protocol Labs for sponsoring the project
Hunter Davis, David Garrett, Simon Tartakovsky, and Jean Provost for technical advice
Leo Zaroff for lending us his hydrophone and for advice
Keith Murphy and Attune Neurosciences for lending us their transducer

CAD Models

You can find our CAD models in our GitHub repository.