Switchless Multiplexing of Graphene Active Sensor Arrays for Brain Mapping

: S ensor arrays used to detect electrophysiological signals from the brain are of major importance in neuroscience and biomedical engineering. However, the number of sensors that can be interfaced with macroscopic data acquisition systems currently limits the bandwidth of these devices. This bottleneck originates in the fact that, typically, sensors are addressed individually, requiring a connection for each of them. Herein, we present the concept of frequency-division multiplexing (FDM) of neural signals by graphene active sensors. We demonstrate the high performance of graphene transistors as mixers to perform amplitude modulation (AM) of neural signals in-situ , which is used to transmit multiple signals through a shared metal line. This technology eliminates the need for switches, remarkably simplifying the technical complexity of state-of-the-art multiplexed neural probes. Besides, the scalability of FDM graphene neural probes has been thoroughly evaluated and their sensitivity demonstrated in-vivo. Using this technology, we envision the implementation of a new generation of conformal neural probes with over a thousand channels for high bandwidth brain machine interfaces. the high performance of g-SGFETs as mixers to perform on-site of signals. We have shown their high sensitivity for wide-band both in the beaker as well as in-vivo. Besides, we have also demonstrated the outstanding drain-source frequency response of solution-gated graphene sensors, validating their performance for high carrier frequencies, required for the operation of large-scale arrays. have the crosstalk among sensing sites, which could reach the same level as for TDM with switches when translating this technology to human scale neural probes. In order maintain the sensitivity of the system for large arrays, with up to 32 superposed carriers, have


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TEXT: Over the last decades, progress in neurotechnology has enabled a deeper understanding of brain functions such as motor control 1,2 or speech processing and synthesis 3,4 . In turn, these insights have prompted the realization of technological breakthroughs in the field of braincomputer interfaces (BCIs) such as partial restoration of movement 5 or decoding of speech from neural activity 6 . Cortical functions involved in such tasks often emerge from the integration of information in distinct brain regions, yet local activity from small groups of neurons carries essential information for neural coding 7 . Therefore, combining the coverage of large brain areas with high sensor density (i.e. high sensor count) is paramount for both neuroscientific and biomedical applications [8][9][10] . In this sense, one of the main limitations in current neurotechnologies originates in the need of individually connecting each sensing element to a signal amplifier. This constrain implies having as many conductive lines as sensors in the neural probes, which imposes a trade-off between sensor density and coverage area. One way to overcome this constrain is to perform multiplexing among sensors, which allows the transmission of multiple signals over a shared wire.
State-of-the-art sensing technologies for neuroscientific research are mostly based on intracortical electrode arrays [11][12][13][14] . Intra-cortical electrode arrays can be fabricated on rigid substrates 15 , therefore enabling to incorporate integrated-circuits on the probes 12 to amplify and multiplex the measured signals. However, intra-cortical probes cause serious tissue damage, limiting the mapping over large areas of the cortex, especially for biomedical applications. Alternatively, electrocorticography (ECoG) offers a minimally invasive way to acquire similar information 16,17 , by recording local field potentials 18 (LFP) from the surface of the brain. Nevertheless, planar µ-ECoGs must be fabricated on a flexible substrate to provide conformability to the surface 4 morphology of the brain 8,19 . This constrain strongly limits the use of nanofabrication methodologies and available materials to fabricate integrated circuits on the neural probe, thus restricting the implementation of in-situ signal amplification for time-division multiplexing (TDM) of neural signals 20 . Flexible materials have been proposed to perform switching among active sensors in an addressable array configuration, including organic semiconductors 21 or ultrathin silicon layers 22 . However, organic semiconductors present an insufficient mobility for highspeed operation, which is critical to achieve high sampling speed for large number of sensors, and the high complexity of ultra-thin silicon technology on flexible substrates limits its widespread application.
Herein, we present a novel approach that uses frequency-division multiplexing (FDM) of graphene solution-gated field-effect-transistors (g-SGFETs) in order to eliminate the need for onsite switches and to reduce the fabrication complexity of high-count neural probes. In this approach, neural signals detected by different graphene active sensors on the array are amplitude modulated (AM) by different carrier signals, allowing to transmit multiple signals through a shared communication channel. We present the fabrication of g-SGFET arrays on an addressable column/row matrix configuration to demonstrate their high performance for FDM operation invivo, sensing wide-band neural activity from the surface of the rat brain. Besides, we carefully assess the scalability of this technique, demonstrating its potential for simultaneously recording from over a thousand channels. The simplification of the technological complexity, achieved by the elimination of switches and the use of graphene electronics, opens the door to the implementation of high-count flexible neural probes as a readily available technology for neuroscientific studies as well as clinical applications.

FREQUENCY-DIVISION MULTIPLEXING OF G-SGFET ARRAYS
G-SGFETs have been proposed as signal transducers in the field of biosensing and bioelectronics 19,[23][24][25] , presenting unique properties for the detection of full-band neural signals, from infra-slow to high-frequency components, with a high spatial resolution 26 . Besides, as active sensors, G-SGFETs provide an intrinsic pre-amplification of the signal and can be arranged in a column/row addressable matrix due to their two terminal (i.e. drain and source) configuration (see Fig. 1a and 1b). These properties, combined with their remarkable frequency response 27 , make g-SGFETs an ideal technology for the implementation of frequency-division sensor arrays.
In g-SGFETs, the graphene channel is placed in contact with an electrolyte gate, i.e. the brain tissue in the case of neural sensing applications. Electrical potential fluctuations in the environment influence the conductivity of the transistor channel through the gate capacitance. The constant of proportionality between drain-source conductance ( ) and the electrical potential at the interface ( ) is referred to as the transconductance 28 ( ). g-SGFETs can be modelled by the equivalent circuit shown in Fig. 1a. Its stationary response to a constant bias ( − ) is described by the voltage dependent term − , while its dynamic response to a small-amplitude, timedependent signal ( ) is characterised by the term . In the typical operation mode (DC mode), the drain-source bias is constant; thus, the only time variations in the drain-source current ( ) are caused by variations in (Fig. 1c). On the other hand, in FDM (or amplitude modulation-AM mode), the drain-source bias is typically a pure tone signal ( ( )).
The multiplication of and produces the folding of their frequencies. In the frequency-domain representation of ( ) * ( ) (Fig. 1d-left), a peak at the carrier frequency ( ) can be observed, which is proportional to − . In addition, two side bands (at

IN-VITRO CHARACTERIZATION OF FDM GRAPHENE NEURAL PROBES
In order to validate the suitability of g-SGFETs for frequency-division multiplexing, their sensitivity in the AM mode must be characterized and compared with the sensitivity in the DC mode. The characterization of can be performed following two approaches: from the derivative of the stationary − curve or from the dynamic response of g-SGFETs to signals with various frequency components applied at the gate (see Fig. 1c).  The magnitude of over frequency of the signal applied at the gate is shown for the two modes.
The response was measured in a 2x2 g-SGFET array. c. − for an integration bandwidth of In the DC mode, the g-SGFETs are operated at a stationary point in the − plane, but in the AM mode the drain-source bias oscillates along the axis. In this way, non-linearities in the − curves will lead to distortion of the carrier signal, introducing harmonics at frequencies multiple of (see Fig. 2g and supporting information). Harmonic distortion constrains the selection of carrier frequencies that can be used for AM: high order harmonics must not lie within the frequency band of operation dedicated to the carrier signals.
Thereby, the frequency of all carriers must be below the 2 nd order harmonic of the carrier of lowest frequency (see Fig. 2g). In addition, the Nyquist frequency ( /2) must be above the 2 nd order harmonic of the highest carrier frequency in order to prevent folding of 3 rd order harmonics into the band of operation by aliasing.
Another important aspect affecting the selection of carrier frequencies is the frequency response of g-SGFETs. The graphene-electrolyte interface exhibits a capacitive response, which at high frequencies allows a displacement current to flow from drain to source through the electrolyte 27 , degrading the device performance. The characteristic cut-off frequency of this phenomenon appears at relatively high frequencies due to the high ratio between mobility and interface capacitance in graphene. Other active sensors, such as organic electrochemical transistors, which present a lower mobility and a larger interface capacitance 29 , are expected to present a worse frequency response 27 . Fig. 4e shows the frequency response of g-SGFETs for multiple channel lengths, demonstrating an approximately constant response for channels shorter than 100 and frequencies below 500 at least.

SCALABILITY OF FDM GRAPHENE NEURAL PROBES
Considering the ultimate goal of enabling high-density, large-area sensor arrays, the scalability of the FDM graphene neural probes has to be thoroughly explored. Important aspects limiting the scalability of FDM are the crosstalk in the g-SGFET array, the constrains in the selection of carrier frequencies, and the requirements for the electronics used to operate the arrays.
In FDM, no switching among sensing sites is required. Although this feature bears a clear advantage for ease of fabrication of the neural probes, it prevents from doing on-site switching of the sensors, and can therefore lead to an increased susceptibility to crosstalk. Crosstalk can appear between g-SGFETs in the same row (i.e. sharing a readout channel) as well as in the same column (i.e. biased by the same carrier) due to common-mode voltage ( ) oscillations in the resistance of metal tracks in series with the drain ( ) and source ( ). Analysing the equivalent circuit in Fig. 3a, an analytical expression can be derived, which indicates that crosstalk among rows and among columns is proportional to and respectively (see Fig. 3a and supporting information). Additionally, crosstalk signals couple with g-SGFETs that are out of the same column and row, causing a second order crosstalk (see supporting information S4). In order to experimentally determine the crosstalk level, we have patterned multiple polyelectrolyte gates on the graphene sensor arrays by inkjet printing (see Fig. 3a and supporting information S5). Fig. 3b shows the signal measured by an individually gated g-SGFET (black) and the crosstalk it induced on sensors in the same column (orange), the same row (blue) and on the rest of g-SGFETs (red), together with the fitting of the experimental data using the analytical expression presented in the supporting information. A crosstalk of ~36dB/~73dB is observed for g-SGFETs within/outside the same column or row, which corresponds to a ≈ = 50 . In order to reduce the crosstalk to the level achieved using on-site switches (~65dB) 30 , the resistance of the tracks should be reduced to the range of few ohms. This target could be met by increasing the width of the metal lines, which can be implemented easily when translating this technology from rodents research into human clinical applications. .

Figure 4| Scalability of g-SGFET arrays multiplexed in the frequency-domain: a.
Equivalent circuit of a 3x3 g-SGFET array. The metal track resistance of the columns and rows is modelled by and respectively. Each column is biased with a different carrier Another important aspect related to the scalability of FDM graphene neural probes is the selection of the carrier frequencies, which is constrained by the frequency response of g-SGFETs and the harmonic distortion of the carrier signals. The ( ) was characterized by sweeping and measuring the dynamic response of the graphene sensors to pure tone signals applied at the gate. Fig. 3c shows that remains approximately constant for carrier frequencies up to at least 600 and a channel length of 50 . Sampling at four times this frequency limit (i.e. /2 ≥ 2 = 1.2 ) allows to use carriers of up to ~600 . Fig. 3c shows a combination of carrier frequencies which meets all the requirements to allow the operation of 32x32 graphene sensor arrays. In this configuration, operation in quadrature AM 31 can be used to maximize the frequency bandwidth of each sensor to 10 (see Fig. 3c). Above this bandwidth, the signal will be filtered in the digital domain to eliminate any components corresponding to other carriers. The discrete electronics system designed for the validation of the technology in-vivo is limited to operate arrays of up to 4x8 g-SGFETs. This limitation comes from the constrained scalability of discrete electronics, in opposition to application specific integrated circuits (ASIC).

IN-VIVO EVALUATION OF FDM GRAPHENE NEURAL PROBES
Previous works have shown that g-SGFETs operated in the DC mode present a high sensitivity for the recording of neural activity 19,23 . Moreover, g-SGFETs have demonstrated a unique capability for the recording of infra-slow neural activity with a high spatial resolution 26 .
The FDM operation of g-SGFETs is not only expected to preserve their sensitivity for infra-slow signals, but to enhance their performance by eliminating flicker noise from the amplifiers due to the lock-in amplification in the AM mode. To validate the in-vivo functionality of FDM graphene probes, we have recorded electrical activity from the cortex of a Long Evans rat in an acute setting using a 4x8 FDM graphene neural probe (see Fig. 4a-b and supporting information). The optimum which maximizes and the highest carriers amplitude ( ), which fills the dynamic range of the amplifiers were determined in-vivo (see Fig. 4c).
The sensitivity of the sensors to high-frequency LFP activity was evaluated by measuring visually evoked potentials 33 triggered by a blue LED emitting light-pulses of 100 ms every 5s. The sensors directly placed on the primary visual cortex V1 (lower left) exhibit a sharp response with 50 ms delay and 250 µV peak amplitude lasting until 100 ms after the initial trigger (Fig. 4d).
Sensors placed further away from the V1 show a distance-dependent suppressed response of smaller amplitude and extended delay (Fig. 4e). This result is in full agreement with previously reported values 33 , demonstrating the preserved sensitivity of g-SGFETs in this frequency band in the FDM operation mode.
Similarly, the distortion-free recording of infra-slow activity using g-SGFET has been previously shown in the DC mode by the recording of cortical spreading depression (CSD) events 26 . CSDs are a slowly propagating wave of depolarizing neurons and astrocytes, which has been clinically related to stroke, brain injury and migraine 34,35 . CSDs can be easily triggered by injecting KCl into the brain cortex and present a propagation speed of approximately 5 mm per minute across the cortex. Fig. 4f shows the spontaneous activity under anaesthesia where highly coherent transitions from up to down-states can be observed. Fig. 4g shows the signal from channel in position (1,5) filtered in the 1-50Hz frequency band (blue) together with the signal filtered in the 0.001-50Hz band. This spontaneous activity is strongly suppressed during the depolarization wave, which results in a large infra-slow signal drift with a duration over 70s. Fig.   3h shows the propagating front of the CSD wave across the array, demonstrating the capabilities 17 of FDM graphene neural probes to study topography of wide-band oscillatory dynamics in the brain.