Reducing the thickness of the substrate decreases the bending rigidity, thereby improving conformal contact. Unfortunately, clinical arrays and even the thinnest devices designed for research have thicknesses (700 μm and >10 μm^{9, 10}, respectively) that are larger than desired to ensure conformal contact. Analogous systems based on stretchable substrates have also been explored in other neural interfaces^{11, 12} but typically with similar or larger thicknesses. In conventional designs, ultrathin geometries (i.e. < 10 μm) are impractical, because the films are not sufficiently self-supporting to be manipulated effectively during fabrication or implantation.

Silk is an appealing biopolymer for this application because it is optically transparent^{13, 14}, mechanically robust and flexible in thin film form^15–17, compatible with aqueous processing^{18, 19}, amenable to chemical and biological functionalization^{13, 20}. The silk, in both the non-treated and ethanol treated formats, is biocompatible^{21, 22}, bioresorbable²³, and water soluble with programmable rates of dissolution^{15, 16}. In addition, recent work demonstrates the ability of silk films to serve as a platform for transistors²³ and various classes of photonic devices^{24, 25}. The process of preparing silk substrates for the purposes reported here began with material derived from Bombyx mori cocoons, and followed published procedures^{18, 19}. Briefly, boiling the cocoons in a 0.02 M aqueous solution of sodium carbonate for 60 minutes removed sericin, a water-soluble glycoprotein that binds fibroin filaments in the cocoon but can induce undesirable immunological responses^{21, 26}. An aqueous solution of lithium bromide at 60°C solubilized the fibers and subsequent dialysis removed the lithium bromide. Centrifugation followed by micro-filtration eliminated particulates to yield solutions of 8–10 % silk fibroin with minimal contaminants. Casting a small amount of the solution on a flat piece of poly(dimethylsiloxane) (PDMS) followed by crystallization in air (~12 h) yielded uniform films (thickness of 20–50 μm) (Fig 1a) that were subsequently removed from the PDMS for integration with separately fabricated electronics.

For the systems described in the following, polyimide (PI) served as a support for arrays of electrodes designed for passive neural recording. Control devices consisted of otherwise similar layouts, but formed using standard photolithographic procedures applied directly on commercial PI films (Kapton, DuPont, USA) with thicknesses of 25 and 75 μm (Fig S1). Anisotropic conductive film (ACF) bonded to electrode pads at one end of the arrays provided electrical connection to external data acquisition systems (Fig S2). Ultrathin PI films, with or without mesh layouts, cannot be manipulated effectively for processing, interconnecting or implanting onto the brain due to their extreme flexibility and mechanical fragility. For these cases, the fabrication process exploited layers of PI spin cast onto silicon wafers coated with sacrificial films of poly(methylmethacrylate) (PMMA) (left frame of Fig 1b). After electrode fabrication, the mesh structure devices underwent further etching to remove unwanted parts of the PI. The processing was completed by dissolving the PMMA layer with acetone, transfer printing the entire assembly to a film of silk and connecting the ACF, yielding easily manipulated bioresorbable neural recording systems. See schematic illustrations and images of Fig. 1b. In all cases, the electrode arrays consisted of 30 measurement electrodes (Au, 150 nm) in a 6 × 5 configuration, each with dimensions of 500 μm × 500 μm and spaced by 2 mm. Interconnection wires to each electrode were protected by a thin (~1.2 μm) overcoat of PI to prevent contact with the tissue or surrounding fluids. Choosing the thickness of the PI passivation layer to match that of the PI substrate locates the gold electrode at the neutral mechanical plane, thereby minimizing the potential for bending-induced mechanical fracture. Details of the fabrication steps appear in the methods section. Electrode arrays were implanted by placing them on the exposed brain (after craniotomy) and then flushing with saline to dissolve the silk, simulating immersion in cerebral spinal fluid. This procedure induced spontaneous, conformal wrapping of the device, as illustrated schematically for the mesh design in Fig. 1c. After the required measurement, the electrode array can be easily removed, due to attachment of the electrodes to the ACF.

The sequence of images in Fig. 2a shows the dissolution process for a representative case (7 μm thick PI film, connected to ACF on a silk substrate with thickness of ~25 μm) inserted into warm water (~35 °C). As the silk substrate disappears, the total bending stiffness, EI, diminishes dramatically due to its cubic dependence on thickness. Computed results appear in Fig 2b and Fig S3c for PI thicknesses of 2.5 and 7 μm. To highlight the benefits of reduced thickness, the inset shows the ratio of EI for these two cases. Through programmed control of the dissolution rate via modifications of the silk protein secondary structure^{15, 16}, these changes in EI can be designed to occur over periods of time ranging from seconds to years, depending on requirements. Figure 2c shows, as an example, the dissolution rate of silk film slightly treated with ethanol (left frame) and computed time dependence of EI in devices that employ more thorough ethanol treatment (right frame). The error range for silk thickness measurement is ± 7%. See SI for detailed conditions. This dissolution time can be lengthened even more by extending the treatment time to days or weeks¹⁵; the corresponding time dependence of EI appears in Fig S4.

To examine the ability of these systems to conform to relevant surfaces, we performed experiments using a human brain model, following the basic steps shown in Fig. 1c. Figure 3 provides images for various cases after washing with saline, including relatively thick control devices that do not incorporate silk. Clearly, the extent of conformal coverage increases with decreasing thickness; the mesh design provides further improvements, as shown in Fig. 3d, S5 and S6. To reveal the underlying mechanics, we performed systematic and quantitative studies on well defined surfaces that capture certain basic features of the curvature of the brain. The first set of experiments explored wrapping the devices on isolated and overlapped cylindrical surfaces. Figure 4a shows the simplest case of a device with bending stiffness EI, thickness h, width b and length 2L, wrapped on a cylinder with radius R. Analytical expressions for EI can be written for the multilayer structures of Fig. 1 in terms of material properties and geometries, as described in the SI. For the wrapped state to be energetically favorable,

where γ is the adhesion energy per unit area. The bottom frame of Fig. 4a compares the above relation with a series of experiments (Fig. S7). The data, whose error range is ± 5%, are consistent with γ ~10 mJ/m², which is comparable to reported values for wet interfaces²⁷. Reducing the thickness provides clear benefits, e.g. wrapping cylinders using only capillary adhesion forces is possible for R ~1 cm when h < ~15 μm.

A pair of overlapped cylinders represents a simple model for a gyrus of the brain. Figure 4b shows cylinders with radii R, a center-to-center separation of 2d and connected by a smooth arc of radius r₀, at the angular position θ₀ = sin⁻¹[d/(R + r₀)]. The contact angle of thin film with one cylinder θ can be shown to be

where γ_c is given in Eq. (1). The solution of equation (2) takes the form θ = θ(d/R, γ/γ_c). For γ < γ_c, the energy has a minimum at θ = 0, and the film does not wrap around the cylinders. Partial wrapping occurs to a contact angle of θ (i.e. contact for angles between 0 and θ < θ₀) for , where is obtained from Eq. (2) with θ = θ₀ as given in SI. For , wrapping is complete (i.e. conformal contact for angles between 0 and θ₀). By comparing Eq. (2) with the experiment in Fig. S8, the extracted adhesion energy per unit area is γ = 10mJ m². Results appear in the bottom frame of Fig. 4b, where the parameters correspond roughly to features on the brain model: R=6.14 mm, d=5.93 mm and r₀=1.72 mm. The error range of the data is ± 5%. (Experimental images appear in Fig. S8) By substituting θ with θ₀ in Eq. (2), the critical thickness for conformal contact is obtained as h₀ = 4.9μm for the current system, i.e., devices thinner than ~4.9 μm achieve conformal contact on this surface. The experimental results are consistent with this calculation.

Cylindrical surfaces like those of Fig. 4a and 4b are developable; the brain is not. As a model of non-developable surface, we examined the case of a hemispherical substrate. Figure 4c shows results for electrode arrays with sheet designs at thicknesses of 7 and 2.5 μm and with an open mesh layout²⁸ at 2.5 μm, each on a glass hemisphere with radius of curvature of 6.3 mm. With only water capillarity as the adhesion force, the mesh electrode array achieves excellent conformal contact. The sheets show comparatively poor contact, with large wrinkles, even for the thinnest case (i.e. 2.5 μm). Mechanical analysis of a simple model reveals the underlying physics. The left frame of Fig. 4d shows the mechanics model for the sheet design, which consists of a circular film with radius r+w wrapped onto a sphere with radius R. The central green part denotes a PI plate of radius r, tension stiffness (Eh)_PI and equi-biaxial bending stiffness (EI)_PI. The yellow ring corresponds to a multilayer structure of PI and Au, of width w, tension stiffness (Eh)_composite and equi-biaxial bending stiffness (EI)_composite. For the film to wrap around the sphere, the required minimum adhesion energy per unit area is obtained analytically as

A mechanics model for the mesh design appears in the right frame of Fig. 4d, which consists of only a circular strip of a corresponding multilayer of PI and Au. In this case, the minimum adhesion energy per unit area is

For the case that w r, in Eq. (3) is always larger than in Eq. (4), i.e., . The inference is that the open mesh design requires much lower adhesion energy than the corresponding sheet, thereby leading to greatly improved ability for conformal coverage, as shown in the Fig. S9a. Figure S9c shows critical adhesion energies for films with thicknesses up to 80 μm. For a thickness of 2.5 μm and w/r = 4, for the sheet, which is more than 12 times larger than the mesh . In addition, the mesh design involves membrane strains that are smaller, by roughly a factor of w/r, compared to sheets with similar thickness. For the experimental mesh systems, this ratio is on the order of 1/4. As a result, for a representative critical wrinkling strain of 0.1%, nearly two thirds of the sheet will wrinkle. Under the same conditions, the entire mesh gives perfect, conformal contact. Finally, the normal (peeling) interfacial stresses for the mesh is only 1/4 of that for the sheet (Fig. S9b and Fig. S9d), leading to improved adhesion and reduced forces applied to the substrate. See SI for details.

In-vivo neural monitoring experiments on a feline animal model demonstrated the practical implications of this favorable mechanics. The tests involved an anesthetized cat head fixed in a stereotaxic apparatus with its eyes focused on a monitor that subtended 28 × 22 degrees of space. An initial craniotomy and durotomy exposed a 2 × 3 cm region of cortex. The electrode arrays covered much of visual cortex as shown in the left frames of Fig 5a, b and c. Visual stimuli consisted of full-field drifting gratings presented for 1 second at 2 Hz with a spatial frequency of 0.5 cycles/degree. Gratings were presented at 2 different directions over 8 different orientations (16 unique stimuli). However, the responses obtained from all 16 unique stimuli were averaged to obtain the largest possible signal to noise ratio.

Three kinds of electrode arrays were used for comparison: 76 μm and 2.5 μm thick sheets and a 2.5 μm thick mesh. The second two included dissolvable silk supports. The left images of Fig 5a, b and c illustrate the progressively improved conformal contact with reduced thickness (i.e. 76 μm to 2.5 μm, in Fig. 5a and b, respectively) and with introduction of the mesh (i.e. Fig. 5c). The right frames of Fig 5a, b and c demonstrate the effectiveness of decreasing the electrode thickness and the mesh structure on physiological measurements of brain activity.

In particular, these frames show the average evoked response measured at each electrode, each plotted in a spatial arrangement that corresponds to the images in the left frames. Prominent visually evoked potentials are observed, particularly a strong P100 response. The P100 response is a “positive” evoked response typically occurring at 100 ms after the stimulation onset²⁹. The P100 responses shown in Figure 5 appear in the negative direction because they have been plotted negative down as opposed to the neuroscience convention of plotting negative up. The background color of each plot illustrates a quantitative measure of the evoked response signal quality. This measure of signal quality was calculated by dividing the root mean square (RMS) amplitude of each average electrode response in the 200 ms window immediately after the presentation of the visual stimulus by the RMS amplitude of the average 1.5 second window immediately preceding the stimulus presentation. The color bar at the bottom of Fig. 5c provides the numerical scale for all of the colors used in Fig 5a, b and c. This measurement serves as a quantitative metric of the electrode performance, because the uniform nature of the stimulation is expected to evoke similar responses across the entire visual cortex.

In each case, 28 of the 30 electrode channels were recorded and evaluated for evoked potential response, as colored in green through red. Two channels, indicated in grey, were reserved as local references, as required by the recording apparatus, and were not evaluated. The channels with high and low RMS amplitude ratios are colored green and red, respectively. The 76 μm (Fig 5a) electrode array exhibited the lowest performance with a mean RMS amplitude ratio of all 28 channels of 3.6 ± 1.8. This was due to poor contact at many of the electrodes. The 2.5 μm array (Fig 5b) showed better conformal contact and correspondingly a higher mean RMS amplitude ratio of 5.2 ± 3.9. However the higher standard deviation and correspondingly wide spectrum of red and green channels on the array indicate that while many electrodes recorded excellent signals, approximately half of the electrodes still had poor contact with the brain and recorded weak responses. The 2.5 μm mesh electrode (Fig 5c) showed the best performance, with nearly all channels in good contact and a still higher mean RMS amplitude ratio of 5.7 ± 3.0. The lower standard deviation the 2.5 μm array illustrates that the majority of the electrodes recorded good responses.

Figure 5d shows representative single channel data from one of the 2.5 μm mesh electrodes. A sleep spindle is observed with good signal amplitude and signal to noise ratio. This collective set of observations is consistent with the systematic mechanics studies described previously. We did not observe any evidence of immune response. Histology data from related types of devices implanted under the skin exhibited no inflammation after 4 weeks, as shown in Fig. S10.

Although purely passive electrode systems serve to demonstrate the advantages and underlying aspects of these systems, the same approaches are compatible with fully active electronics and optoelectronics. This technology allows intimate integration of finely spaced electrode systems with living tissue, enabling the kind of reliable biotic/abiotic interface with moving, biological structures that will be required for chronically implanted, high resolution medical devices. This improved electrode-tissue interface has the potential for positive impact on human health in many modes of use.

Supplementary data including Figures S1-S11 and their captions