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Three-dimensional liquid metal-based neuro-interfaces for human hippocampal organoids – Nature Communications

Design and fabrication of 128-channel mMPC

Compared with the conventional electrodes utilized in various neural recordings and wearable devices, the fabrication of 3D mesh MEA poses significant challenges, namely, (1) the reduction of extra substrate and insulating material and (2) the precise encapsulation of the conductor, except for electrodes. In response to these challenges, we developed stretchable electronics by designing three poly(dimethylsiloxane) (PDMS) patterns for the conductor, the bottom substrate, and the top insulating layers, respectively, using the soft lithography process (Supplementary Fig. 1a–d). The conductor layer, which included electrodes and circuits, comprised MPC ink, where nano- and micro-meter GaIn particles were dispersed in a solvent. The MPC ink was not affected by the larger surface tension of pure GaIn and was easily manipulated to print on other substrates (Fig. 1a). Preparation and mechanism of the MPC ink have been described in our previous work30,31,32. To ensure precise exposure of the electrodes while encapsulating the circuits, we designed the PDMS patterns for the substrate and insulating layer differently. This difference was the addition of pillars in the top insulating layer, which matched the location of the electrodes (Supplementary Fig. 1e–h). These pillars prevented the insulating material from covering MPC electrodes.

The complete fabrication process is depicted in Fig. 1b. In brief, the process began with scraping the MPC ink into PDMS slab #1, which contains microchannels, to create the conductor layer (Step i). Following this step, we aligned PDMS slab #2, which also contains microchannels, on the surface of PDMS slab #1 and immersed them in the TPU solution. The TPU solution was allowed to completely fill the microchannels of PDMS slab #2 to produce mesh TPU, which served as the substrate after the solvent had evaporated (Steps ii and iii). These operations were then repeated to generate mesh PU as the insulation (Steps iv and v). Pillars in PDMS slab #3 for the PU layer effectively prevented the PU solution from covering these dots, thus enabling the proper exposure of electrodes (Step v). The mMPC was obtained after removing all PDMS slabs. In the end, the final device has no PDMS, only containing three components: TPU, PU, and liquid metal. To facilitate the easy connection of the mMPC with a signal acquisition instrument, two ends of the mMPC were bonded to the flexible printed circuit through an anisotropic conductive adhesive (Step vii). Notably, this fabrication approach is highly versatile and can produce other shapes of MPC electronics, depending on the design of PDMS patterns.

Morphology of mMPC

Considering the inevitable impacts of devices on the growth of hHOs, the balance between miniaturization and multi-channels should be considered. To achieve this balance, we employed a design strategy that involved reducing the width of a single MPC circuit to 15 µm while integrating two such circuits in a 50 µm-wide polymer structure to increase the channel number (Fig. 2a). A total of 64 electrodes, each with a diameter of 20 µm (Fig. 2b and c), distributed in four directions across a ~2*2 mm area, and located at different points within the mesh structure. Furthermore, our 128-channel mMPC was comprised of two layers of 64-electrode mesh, which enclosed the top and bottom hemispheres of the hHO, respectively. The two-layer design not only increased channels but also provided a stable holder for free-floating organoids. The mesh, featuring 150 µm gaps and 30 µm thickness (both 15 µm thickness in TPU and PU layer, Fig. 2b), weighed only ~500 µg. Given all these parameters, our extremely light, soft mMPC was conformal to the object surface (Fig. 2d).

Fig. 2: Characterization for the mMPC.
figure 2

a (Left) the single 64-electrode mMPC. Scale bar: 5 mm. (Middle) the distribution of 64 electrodes in the mesh structure. Scale bar: 500 µm. (Right) the structure of electrodes and encapsulation layers. Scale bar: 100 µm. b Optical image of the sandwich structure. Scale bar: 20 µm. c SEM images of electrodes. d Conformal attachment of the stretchable mMPC to the surface of a TPU ball. Scale bar: 1.5 mm. e The mMPC under 400% strain. Scale bar: 5 mm. f Two electrodes, circuits of the mMPC before and after 400% strain. Scale bar: 100 µm. g The bending test of 3 mMPCs. h Impedance of the mMPC across frequency before and after depositing PEDOT on electrodes and under 100% strain (n = 7, 7 independent electrodes randomly selected from 2 mMPCs; data are presented as median with maxima). mMPC mesh liquid metal-polymer conductor, TPU thermoplastic polyurethane, PU polyurethane. Images in c are representative of n = 4 independent measurement.

Mechanical and electrical characterization of mMPC

Conformal attachment is a key issue to consider when applying electronics to neural organoids. The highly flexible and stretchable nature of the mMPC allowed for attachment to the surface of objects (Fig. 2d). The mechanical properties of the mMPC were attributed to the encapsulation materials, namely TPU and PU, which exhibit excellent elasticity, high resistance, and good biocompatibility, making them broadly used in the medical industry for biomedical devices33. The fluidity of GaIn alloy, combined with the properties of TPU and PU, enabled the mMPC to perform ideally in both flexibility and stretchability, allowing for free folding, bending, and twisting (Supplementary Movies 1 and 2).

The extension test demonstrated that the mMPC could stretch up to five times its original length (400% strain, Fig. 2e), while the strain of another mesh MPC with a width of 30 µm was up to 500% (Supplementary Fig. 2a). Remarkably, the GaIn alloy remained entirely enclosed within the sandwich TPU–PU structure without any leakage or fracture, both for the exposed electrodes and the fully encapsulated circuits (Fig. 2f and Supplementary Fig. 2b). While we concerned that the TPU and PU layers might separate under strain, exposing the conductor layer, these two layers remained tightly bonded with no split between them. Notably, the conductivity was maintained at ~4000 S/cm when elongating the mesh by 400% (Supplementary Fig. 2f), underscoring the mMPC’s superior mechanical and conductive properties. The bending test also performed great stretchability and easy deformation of the mMPC, and displacement of 500 µm requires only 0.005 N force (Fig. 2g, an average bending stiffness of 1.50 × 10−3 N m2).

Electrical characterization revealed that electrodes on the mMPC had relatively low impedance, which decreased as frequency increased (Fig. 2h and Supplementary Fig. 2c). Impedance measurements were taken across 7 electrodes in 2 mMPCs, ranging from 0.1 Hz to 100 kHz and revealed an initial mean impedance of 70.69–28.78 kΩ at 1–40 kHz (Fig. 2h). To improve the stability of the electrodes, we coated them with PEDOT on MPC electrodes using electrodeposition, as GaIn alloy at the electrodes might be degraded after culturing the hHO on the mMPC. PEDOT is a conductive polymer commonly used for preparing flexible electrodes due to its biocompatibility, conductivity, and stability. However, the conductivity of polymers is lower than that of metals. The current-time curve of the electrodeposition process showed an initial rapid increase in resistance (performing at a decrease in current value, Supplementary Fig. 2d), followed by a gradual decline as more PEDOT covered the electrode surface. The impedance of PEDOT-coated electrodes only increased to 95.83 kΩ at 40 kHz (Supplementary Fig. 2e). Furthermore, the impedance decreased slightly under 100% strain compared to that without any strain (Fig. 2h). The result can be attributed to the stretching force breaking the oxidation on the surface of GaIn particles, which allowed more liquid metal into the circuit to reduce the resistance. The average root mean square (RMS) noise of 32 electrodes at a single mMPC, was only 6.88 µV (Supplementary Fig. 2g), which was over 7 times lower than the range of neural spike (from ~50 µV to hundreds of microvolts). In summary, our mMPC presented excellent flexibility, stretchability, conductivity, and electrical stability, all crucial properties for a neuro-interface to acquire signals from neural organoids.

The formation of hHOs

Researchers have proved that some hippocampal neurons, accompanied by the ChP and CH regions, could be derived from DMT organoids (Supplementary Fig. 3a, b)29. However, in an in vitro environment, the expansion of ChP tissues in DMT organoid tissues might affect the development of hippocampal tissue. Specifically, it has been observed that the TTR+ ChP tissue became more abundant while the neural tissue became smaller after long-term culture of the DMT organoids (Supplementary Fig. 3c–e). This result might be attributed to the enriched expression of BMPs in the ChP, which induced ChP epithelial fate and promoted its proliferation34,35,36. To generate hHOs from DMT tissue, alternative growth factors were considered to inhibit the ChP expansion.

Wnt3a and purmorphamine (the SHH signaling activator) were incorporated into the culture protocol to generate hHOs under the hypothesis that Wnt3a and SHH weakened the expansion of ChP in DMT organoids and promoted the hippocampal fate25,37. Hence, some modifications were made to the culture protocol, including reducing the duration of BMP4 exposure from 4 days to 2 days and supplementing the culture medium with Wnt3a and purmorphamine after DMT induction (Fig. 3a). Fortunately, the resulting hHOs maintained their spherical structures without loose ChP tissues throughout the growth period (Fig. 3b). Key biomarkers of the development process are summarized in Fig. 3c38,39,40. The expression of FOXG1, LEF1, and PAX6 in day-30 hHOs indicated successful induction into the DMT stage (Fig. 3d). Furthermore, the hippocampus marker ZBTB20 expressed in the hHO and NESTIN+ neural stem cell and beta III-tubulin+ cell suggested neuronal differentiation within the hHO (Fig. 3d).

Fig. 3: Generation of hHOs.
figure 3

a The overall strategy to generate hHOs. b The typical morphology of hHOs at different ages. Scale bar: 100 µm. c The significant markers in the developmental process of the hHO. d Staining images of day-30 hHOs. Upper: Lager-scale image of the whole hHO. Scale bar: 100 µm. Lower: Zoom-in greyscale view of the white box in the upper figures. Scale bar: 40 µm. e The hippocampal PAX6+ and HOPX+ progenitors in day-60 hHOs. Scale bar: (left) 100 µm and (right, zoom-in greyscale view of the white box in the left figures) 40 µm. f The hippocampal PROX1+ cells in day-60 hHO and day-90 hHO. Scale bar: 150 µm. g qPCR for genes expressed in day-117 hHOs, day-71 hHOs versus day-46 hHOs (n = 3, three independent measurements using three independent samples, one-tailed t-test). h, qPCR for genes expressed in day-45 hHOs versus day-45 DMT organoids (n = 3, 3 independent measurements using three samples from different organoids, one-tailed t-test). Images in df are representative of n = 3 independent experiments. Exact sample size and values for h and g are provided in Source Data. Source data are provided as Source data files. hHO human hippocampal organoid, DMT dorsomedial telencephalon.

In the resulting hHOs, two important hippocampal progenitors, HOPX+ and PAX6+ progenitors39, and ZBTB20+PROX1+ granule neurons were observed (Fig. 3e and Supplementary Fig. 4a). PAX6+ progenitors were even more early in the hHO (Fig. 3d). PROX1 induces neural progenitors to the granule cell fate, which is essential for developing the DG and adult hippocampal neurogenesis41,42. Furthermore, mature neuron markers TAU and MAP2 were expressed throughout the hHO (Supplementary Fig. 4b). Other hippocampal markers, SEMA5A (for DG) and SULF2 (for CA3 and DG) were also expressed in the hHOs (Supplementary Fig. 4c). These results suggested the presence of DG granule neurons within the hHOs. Cells dissociated from hHOs also expressed these markers (Supplementary Fig. 4d). Additionally, GFAP+ astrocytes and OLIG2+ oligodendrocyte progenitor cells were present (Supplementary Fig. 4e). These cells have been reported to play roles in maintaining the growth environment of neurons and support the signal transmission between nerves43,44,45.

Immunostaining showed increased PROX1 expression in the more mature hHO (Fig. 3f). Along with the hHO growing, the ZBTB20 and PROX1 mRNA expression gradually increased (Fig. 3g). Wnt3a mRNA expression did not, however, consistently increase (Fig. 3g). Compared with day-45 DMT organoids, we found a significant increase in PROX1 mRNA expression and a significant decrease in TTR mRNA expression in the day-45 hHO (Fig. 3h). Taken together, these results demonstrated successful induction of organoids into a hippocampal fate through supplementing Wnt3a and SHH signals.

Transcriptome analyses of hHOs

To further characterize cell identities, we performed droplet-based single-cell RNA-sequencing (scRNA-seq) to analyze the transcriptome of 7511 cells obtained from 4 organoids at day 70, and 6781 cells from 10 organoids at day 81, using 10x Genomics Chromium. The two samples were dissociated differently, and the specific process can be found in the methods section. By analyzing differentially expressed genes for each cluster, we further segregated cells into eight major groups, including excitatory neurons (ExN), inhibitory neurons (InN), immature neurons (ImmN), neural progenitor cells (NPCs), astrocytes, oligodendrocyte progenitor cells (OPCs) and oligodendrocytes, ChP cells and others (Fig. 4a, b and Supplementary Fig. 8a). Two samples of hHOs had similar cell types (Supplementary Fig. 5), but the hHO at day 81 was missing the population of cells co-expressing oligodendrocyte markers (Fig. 4a and Supplementary Fig. 8a, b). These identified groups closely resemble the cell types found in the human developmental hippocampus up to 22 gestational weeks (GW22)39.

Fig. 4: Transcriptomic signature of hHOs.
figure 4

a UMAP visualization of 7 scRNA-seq clusters from day-81 hHOs. The cluster of oligodendrocytes and oligodendrocyte progenitor cells was presented in day-70 hHOs dataset in Supplementary Fig. 8a–c. b Violin plots of expression levels of markers in six clusters. c Feature plots of hippocampal ZBTB20+ cells, SOX2+HOPX+ progenitors, SOX2+PAX6+ progenitors and PROX1+ neurons. d UMAP visualization of the integrated dataset of the human hippocampus in GW22 and day-81 hHOs. (Left) All samples dataset. (Middle) The human hippocampus. (Right) Day-81 hHOs. The distribution of day-70 hHOs was present in Supplementary Fig. 8c. hHO human hippocampal organoid, GW gestational weeks.

The ventral telencephalon markers NKX2-1, GSX1, GSX2, and LHX6, were not expressed in the cell clusters, suggesting that hHO was fully oriented toward dorsal telencephalic development during this period (Supplementary Fig. 6). Although the hHOs did not display an obvious presence of ChP epithelial cells, a small subset of cells expressed ChP markers (Supplementary Fig. 7a). We further examined the expression of TTR in cryosections of hHOs and observed TTR+ cells surrounding some cavities within the hHOs (Supplementary Fig. 7b). The result suggested that although Wnt3a and SHH inhibited the growth of ChP, it did not eliminate its presence. This might explain why a few hHOs developed cavities after being culture longer (Supplementary Fig. 7c), a phenomenon also observed in ChP organoids46. To confirm the hippocampal identity, we observed ZBTB20 expression in almost all cells (Fig. 4c). The ZBTB20+SOX2+ cells were clustered as immature cells (progenitors) and were further divided into HOPX+ and PAX6+ progenitor subgroups (Fig. 4c). Notably, some ZBTB20+PROX1+ cells were located in the cluster of excitatory neurons, suggesting the presence of PROX1+ granule cells in the hHOs (Fig. 4c). These results were consistent with the earlier immunofluorescence staining results in Fig. 3.

We integrated our two samples with a published scRNA-seq dataset of the developing human hippocampus39 and compared cell types and their distributions (Fig. 4d and Supplementary Fig. 8c). Both had a similar distribution of cell clusters, but the sample in vivo had some unique ImmN and InN, in addition to separate cell populations of endothelial cells and microglia. The absence of endothelial and microglial cells, differentiated from mesodermal cells, was reasonable. This result also suggested that the in vitro differentiation of the hHO needed to be more finely regulated and even co-cultured with other cell types to more closely resemble the in vivo hippocampus. Cell clusters of day-81 hHOs were missing oligodendrocytes, consistent with Fig. 4a, b. We identified a subgroup of cells as ‘others’ that we could not define based on their differentially expressed genes. The ‘other’ group mainly presented in hHOs samples, close to the neuron clusters. The single-cell trajectory analysis also indicated that the identified cells in the ‘others’ subgroup were located at a separate termination of neuron branches that began from the NPCs (Supplementary Fig. 8d). They did not occur in the fetal hippocampus. The imperfect in vitro culture might lead to other neuronal cells in the hHO that did not belong to the hippocampus. But, more experiments will be required to confirm the causal relationship. Combining the immunofluorescence and scRNA-seq datasets, our results indicated the successful generation of hHOs.

The hippocampal cyb-organoid platform

To enable the integration of the mMPC with the hHO and facilitate the connection with the Plexon instrument, we assembled the mMPC and culture dishes. To prevent the two-layer meshes from severely squeezing on the soft hHO, the bottom mMPC was designed as a ‘bowl’ to hold the hHO when we assembled this device (Supplementary Fig. 9a). We placed a TPU ball of ~3 mm when assembling the device to reserve the space the hHO may need (Supplementary Fig. 9a, b). After sterilization, the cultured medium was added to the dish, and the TPU ball was removed from the side; the hHO was inserted into the space between the top and bottom mMPCs. The oblique view and the side view showed that the top mMPC varies with the undulation of the hHO surface without causing significant compression on the hHO and the hHO assembly (Fig. 5a, b and Supplementary Fig. 9b). More details about the process can be found in Supplementary Movie 3. Comparisons before and after the attachment of the top mMPC showed that the top mMPC could slightly squeeze the hHO, resulting in an area enlargement of <5% in the bottom view and a reduction of <5% in the side view (Supplementary Movie 4 and Supplementary Fig. 10a–c). Micro-computed tomography (micro-CT) images showed the hHO changes in height within 1% compared to its suspended state (Supplementary Fig. 10d and Supplementary Movie 5). This squeeze did not severely affect the morphology of the hHO or cause damage to the hHO.

Fig. 5: The hippocampal cyb-organoid platform.
figure 5

a Integration of the 128-channel mMPC and the hHO. (Upper) The hHO was stayed in a low-attachment dish. (Lower) The hHO was enveloped in two-layer mMPC. Scale bar: 1 mm. Notably, there was no significant deformation when the hHO was inserted between two layers of mMPC. b The bottom view captured by a microscope. Scale bar: (Left) 500 µm, (right) 100 µm. c Confocal images of cells from suckling mice hippocampus culturing in the mMPC for 30 days. Scale bar: 100 µm. d Confocal images of MAP2+ neurons, GFAP+ astrocytes and EGFP+ cells in the cyb-organoid platform. Scale bar: 100 µm. e The cross-sectional view of the attachment between the mMPC and the hHO. The arrowhead points to the mMPC. Scale bar: 100 µm. Images in ce are representative immunofluorescence staining cross-independent experiments: c (n = 4), d (n = 3), and e (n = 3).

Because of the concern about the potential risk of leakage of liquid metal on the electrode locations and possible toxicity, we cultured cells from suckling mice hippocampus on the mMPC to verify its long-term biocompatibility. After placing the mMPC in a Petri dish, cells could proliferate and grow stably on the mMPC for more than 30 days (Supplementary Fig. 9c). The cell density was not significantly different from that of the control group without the mMPC (Supplementary Fig. 9d). A large number of axonal structures were present at electrode spots (Fig. 5c), indicating that the mMPC possessed excellent biocompatibility.

The mMPC offered distinct advantages over the 2D MEA. Specifically, the two-layer mMPCs supported hHOs directly, while fixing hHOs on the 2D MEA was challenging. Additionally, we observed that cells from the hHO gradually migrated in the 2D MEA, leading to a contribution to the signal from these migrated cells rather than the neural network of hHOs (Supplementary Fig. 11a). In contrast, without coating poly-l-lysine (PLL) -laminin, the mMPC allowed for the clear boundary of the hHO to be maintained for 30 days without significant migration of cells away from the hHO (Supplementary Fig. 11b). Cell migration also occurred in the PLL-laminin-coated mMPC, leading to fusion locally between the hHO and the mesh structure (Supplementary Fig. 11b).

That transparent mMPC facilitated direct imaging by confocal microscopy. Figure 5 shows confocal microscope images of hHOs enveloped inside the mMPC. The attachment of the mMPC to the surface of the hHO, spanning most of its surface without any noticeable tissue damage, was highlighted in Supplementary Movie 4 and the cross-sectional view in Fig. 5e and Supplementary Fig. 11e. Fluorescence immunostaining of the hHO which was removed from the mMPC revealed no obvious tissue or cellular damage on the hHO surface (Supplementary Fig. 11d). In addition, the deposition of PEDOT was critical for long-term integration. In the control group, electrodes without PEDOT coating displayed gradual degradation of GaIn alloy within 2 weeks, resulting in transparent electrodes in bright-field images, whereas PEDOT-coated electrodes maintained their original appearance (Supplementary Fig. 11c).

Electrical activity recording through the mMPC

Spontaneous spikes from hHOs were successfully recorded across the mMPC (Fig. 6a, b). The uniform spike waveform with an amplitude of ~50 to 150 µV and an average duration of ~800 µs, was similar to the waveform of extracellular action potential (Fig. 6c). Furthermore, the same electrode could capture multiple signals, and 2–4 spike types were displayed after sorting (Fig. 6d).

Fig. 6: Electrical activity recording.
figure 6

a (Upper) Raster plots of neural spikes, and (lower) the continuous signal in a channel of the mMPC. b Continuous recording for a spike. c The uniform spike waveforms and the average waveform in a channel of the mMPC. d Two different spikes appeared in the same channel (upper) and the sorting results (lower). e The comparison of spike rates detected by the mMPC and the 2D MEA (these channels covered by the hHO). f The synchronous signals between two channels. (Upper) Raster plots of neural spikes in these two channels and (lower) continuous recording for two spikes. The time interval was <1 ms. g The oscillatory network activity of the hHO. (Upper) the population activity histogram and (lower) the raster plot (black) identified bursts of spiking detected on 32 channels and coordinated bursts (red) of activity across channels. h Raster plots before and after Glutamine supplement. i 3D visualization plot showing average spike numbers throughout 128 channels. mMPC mesh liquid metal-polymer conductor, MEA multi-electrode array.

A similar signal was observed using the 2D MEA (Supplementary Fig. 12a). After placing hHOs on the 2D MEA for ~3 days, cells migrated away from the hHOs and formed a monolayer on the MEA surface (Supplementary Fig. 11a), and some neural signals were detected from this area. The higher spike rates were concentrated on these electrodes covered by the hHOs (Supplementary Fig. 12b, c). These results suggested that neurons in tissues might maintain higher nerve activity than monolayer neurons. Even after removing the data of the extended nerves which were not integrated into the hHO, we compared the spike rates detected by the electrodes covered by hHO in the 2D MEA with the mMPC, showing more active neural activities in the mMPC (Fig. 6e). The comparison highlighted the necessity to develop 3D MEAs.

In a series of experimental tests, we detected signals from the single hHO or hHO-fused assemblies, and the number of active channels was listed in Supplementary Table 1. The number of active channels was mainly affected by the hHO size. For signal acquisition of an individual hHO, we detected signals in a maximum of 54 channels, whereas when we used fused assemblies of 2 hHOs, the maximum number of active channels increased to 85. Simultaneous signals always appeared in pairs in two channels. We found that the time interval of these paired signals was <1 ms. They always appeared one after the other (Fig. 6f). This observation suggested that neurons on the hHO formed functional synapses capable of transmitting signals. In addition, neural activity was detected on the hHO (Fig. 6g). As potential evidence of neural network maturation, the synchrony was proposed to reflect a balance between ExN and InN and coordinate neuronal communication in the hHO47. We further confirmed the capability of mMPCs by examining the signal of hHOs response to 10 mM glutamine, a precursor of the neurotransmitter glutamate. The spike raster before and after the supplement of glutamine showed a significant glutamine-induced increase in spikes (Fig. 6h). We found no significant difference in spike amplitude (only a slight increase in the average spike waveform, +6.23 µV, Supplementary Fig. 13a). Electrophysiological activity was distributed throughout the 128 channels and was able to be visually represented in 3D plots based on the location of the electrodes (Fig. 6i and Supplementary Movie 6). These visualizations have the potential for future spatial and temporal mapping of electrical activities across neural organoids.

Concerned that pressure from the top mMPC could affect the electrical activity of the hHO, we compared the neural signals before and after cutting the top mMPC. A comparison of the average spike rates of multiple active channels over 2 min showed no significant difference, with only a few channels showing slightly higher spike rates (Supplementary Fig. 14a). However, as in the absence of top mMPC, we placed the hHO at the bottom mMPC directly and found that only a few electrodes were able to detect the signal when the hHO was sunk onto the bottom mMPC by its gravity alone (Supplementary Fig. 14b). When the top mMPC was used simultaneously, more electrodes at bottom mMPC detected the signal. Pressure from the top mMPC can improve the contact between the hHO and the mMPC, allowing more channels to work. Following one month of integration, we measured the electrode impedance after removing the hHO from the mMPC. At 40 kHz, impedance increased from 95.83 to 196.03 kΩ compared with the initial stage (Supplementary Fig. 13b). This increase in impedance might have resulted from the degradation of some GaIn alloy from the electrodes, leading to a reduction in the conductivity.