Stretchable, dynamic covalent polymers for soft, long-lived bioresorbable electronic stimulators designed to facilitate neuromuscular regeneration

Bioresorbable electronic stimulators are of rapidly growing interest as unusual therapeutic platforms, i.e., bioelectronic medicines, for treating disease states, accelerating wound healing processes and eliminating infections. Here, we present advanced materials that support operation in these systems over clinically relevant timeframes, ultimately bioresorbing harmlessly to benign products without residues, to eliminate the need for surgical extraction. Our findings overcome key challenges of bioresorbable electronic devices by realizing lifetimes that match clinical needs. The devices exploit a bioresorbable dynamic covalent polymer that facilitates tight bonding to itself and other surfaces, as a soft, elastic substrate and encapsulation coating for wireless electronic components. We describe the underlying features and chemical design considerations for this polymer, and the biocompatibility of its constituent materials. In devices with optimized, wireless designs, these polymers enable stable, long-lived operation as distal stimulators in a rat model of peripheral nerve injuries, thereby demonstrating the potential of programmable long-term electrical stimulation for maintaining muscle receptivity and enhancing functional recovery.


Supplementary Note 1. Electrical performance characterization of the wireless power transfer system
Schematic illustration of the wireless power transfer systems (Fig. S1a) shows the input, transmitting, and output voltage (or power). "Input" indicates the programmed voltage and frequency at the waveform generator. "Transmitting" corresponds to the transmitting voltage (or power) at the primary coil (i.e. transmission (Tx) coil). Depending on the circuit structure, the transmission voltage (or power) is the same or smaller than the input voltage (or power). The input and transmission frequencies are the same. "Output" corresponds to the applied voltage (or power) at the nerve with internal resistance (RLoad). Monophasic electrical pulses (alternative current (AC) with programmed duration) are generated by a waveform generator. The voltage can be further amplified with an amplifier. The generated waveforms pass to the Tx coil. This RF power (i.e. transmission power) wirelessly transfers to the implanted bioresorbable receiver (Rx) coil and rectifying circuit, including the RF diode. When the transmitting frequency is higher than 1 MHz, the received waveform transforms into an ACsignal on a DC offset via the rectifier to stimulate the targeted nerve tissue with internal resistance (RLoad). This system exhibits frequency dependent behavior that follows mainly from characteristics of the diode 1 . For the operating frequencies explored here, the diode capacitance its finite time response lead to approximately DC output without the need for a separate smoothing capacitor.
The size of the load resistance, associated with the internal resistance of the targeted nerve, changes the resonance frequency (i.e. input frequency) for the maximum output voltage (Fig. S1b). For example, the bioresorbable device without a load resistance (i.e. open circuit structure) yields the maximum output voltage (Voc,max) of 17.4 V at an input frequency of 14.8 MHz (transmitting voltage = 3.5 Vpp; coil-to-coil distance (z-height) = 1.5 mm) ( Fig. 1e and f), while the device with a load resistance of 5 kΩ produces the maximum output voltage of 3.0 V at an input frequency of 12.7 MHz (transmitting voltage = 3.5 Vpp; z-height = 1.5 mm) (Fig.  S1c). The design parameters of both the Tx and Rx coils can affect the resonance frequency of the system. In this context, the device is designed to offer maximum power transfer efficiency at the resistance of sciatic nerve (~5 kΩ) ( Fig. S1d and e). At a load resistance of 5 kΩ, the device shows a maximum power and efficiency of 43 mW and ~0.8 % (transmitting voltage = 16.6 Vpp; transmitting frequency = 12.7 MHz; z-height = 1.5 mm), respectively.
The vertical (i.e. z-height) and horizontal (i.e. misalignment) distance between the Tx and Rx coils are critical for the inductive coupling-based wireless energy transfer. Fig. S1f shows the changes in open circuit voltage (Voc) as a function of vertical distance. The influence of misalignment is represented in Fig. S1g. Under small misalignment (< 3 mm), the Voc (coil diameters = 12 mm; z-height = 1.5 mm) remains largely unchanged, but decreases significantly for misalignments larger than 4 mm. Increasing the z-height from 1.5 to 2.5 mm further reduces the overall Voc at a given degree of misalignment. Significant reductions occur for misalignments greater than 3 mm. For the in vivo rat model, and for other practical use cases, good alignment can be easily achieved by marking the position of the receiver coil during the implantation process and adjusting the transmitting coil appropriately.

Supplementary Note 2. Limitation of existing bioresorbable encapsulation materials
b-DCPU is attractive due to its bioresorbable properties, adhesion characteristics, elastic mechanical response, negligible swelling behavior, and biocompatibility. Robust adhesion of the bioresorbable encapsulation material with itself and with other bioresorbable materials is crucial not only for ensuring mechanical integrity but also for preventing interfacial penetration of biofluids 2 . According to our previous studies of bioresorbable electronic systems 2,3 , a mechanical and electrical failure can originate not only from out-of-plane water permeation through the encapsulation materials but also from in-plane water penetration through weak interfacial bonds or gaps between material layers, leading to short functional lifetimes (< 6 days). As a result, increasing the thicknesses of bioresorbable encapsulants formed with poly(lactic-co-glycolic acid) (PLGA) or Candelilla wax 3,4 does not extend the lifespan of the device significantly since such approach cannot prevent the in-plane water penetration.
Mechanical properties and swelling behaviors in biofluids are also important aspects of bioresorbable encapsulation materials. Most bioresorbable inorganic encapsulation materials, such as silicon dioxide 5,6 , silicon nitride 6 and various metal oxides 7 , are of limited practical utility, due to mechanical rigidity and resulting fragility 8 . Bioresorbable organic alternatives, such as silk fibroin 9,10 , poly(L-lactide) 11 , polylactic acid (PLA), PLGA 3 , etc. 12 , often exhibit swelling from water uptake and/or weak interfacial adhesion. The former can lead to failure due to fracture of the underlying device components, while the latter results in delamination 2,3 . Although engineering strategies to impart stretchability to rigid inorganic-based semiconductors 13 can be considered, in-plane water penetration at weak interfaces can limit the lifetimes.

Supplementary Note 3. Characterization of b-DCPU
The cross-linking ratio of hard segments in this polymer system provides a means to tailor the properties of b-DCPU to meet application requirements. Synthesis of b-DCPU with four different cross-linking densities (i.e. ratio of isocyanate-hydroxyl = 70, 80, 90 and 100%), named b-DCPU 80, b-DCPU 90, and b-DCPU 100, illustrate the effects. Fig. S4a shows the results of Fourier-transform infrared spectroscopy (FTIR; Nicolet 5700) measurements on uncured b-DCPU 80 (transmission mode) and cured b-DCPU 80, 90 and 100 (reflection mode). Uncured b-DCPU 80 shows a peak at 2300 cm -1 associated with isocyanate groups (-NCO). No isocyanate groups are present in cured b-DCPU 80, 90 and 100, consistent with reactions that consume these groups. As shown in Fig. S4b, the results of differential scanning calorimetry (DSC; Q200; a heating rate of 10℃ min -1 ) on cured b-DCPU 80, 90 and 100 reveal an absence of phase transitions between 0 to 80℃ and no melting below 0℃, consistent with an amorphous character across the range of temperatures of biomedical interest (25 to 45℃). The glass transition temperature of b-DCPU increases with crosslinking density. Fig. S4c demonstrates thermal stability across the relevant temperature range through thermogravimetric analysis (TGA; a heating rate of 10℃ min -1 ). The temperature at which decomposition begins is ~300 ℃, and fast weight loss occurs at ~400℃ for all samples. Fig.  S4d presents the transmittance spectra for wavelengths between 200 and 800 nm for b-DCPU 80 (black), 90 (red) and 100 (blue), respectively, measured by a UV/Vis/NIR spectrophotometer (LAMBDA 1050, Perkin Elmer). The results show that transmittance for wavelengths larger than 400 nm exceeds > 80% through a sample with a thickness of 200 μm. b-DCPU films exhibit hydrophobicity character, with a water contact angle of ~100°, independent of cross-linking ratio (Fig. S4e).

Supplementary Note 4. Adhesion mechanisms with b-DCPU
As a mechanism for interfacial bonding between polymers in bioresorbable electronics, permanently adjusted chemical cross-linking of thermoset materials with dynamic covalent network structure (i.e. dynamic covalent polymers) are preferred, in terms of mechanical and chemical stability 14,15 , to temporary reversible bonding, including hydrogen bonds, of thermoplastic or conventional self-healing materials 16 . Dynamic covalent polymers are the recently emerged polymers that able to change their bond arrangement via reversible reaction which results in covalent interfacial bonding between different parts 14,15,17,18 . The strong adhesion between two layers (i.e. interfacial self-bonding) of bioresorbable dynamic covalent polyurethane (b-DCPU) follows from thermally activated dynamic bond exchange reactions (Fig. S5a). First, applied pressure generates conformal contact between two layers of b-DCPU. Then, at an appropriate setting temperature (~200℃), Sn(Oct)2 promotes dynamic bond exchange reactions (transesterification and transcarbamoylation) and formation of new chemical bonds (ester and urethane bonds) among interfaced chains across the interfacial area (Fig. S6). The ratio of isocyanate to hydroxyl groups plays a vital role in the resulting adhesion (i.e. interfacial toughness) because the amounts of free hydroxyl groups and the relative concentration of ester moieties throughout the network matrix influence the transesterification bonding process.

Supplementary Note 5. Permeation behavior of b-DCPU
Studies of the time-dependent changes in the resistance of Mo traces (~15 µm thick) without encapsulation, encapsulated with b-DCPU 80 (~100 µm thick), and encapsulated with PLGA (65:35 (lactide:glycolide); Mw 40-75 K; ~100 µm thick), after immersion in PBS (pH 7.4; 37°C) ( Fig. 2e), confirm the importance of strong interfacial adhesion on the operational stability of bioresorbable devices in biofluids. The results show that b-DCPU encapsulated Mo yields negligible changes in electrical properties over 90 days. In contrast, the resistances of Mo, without encapsulation and with PLGA encapsulation, increase with a rate of 0.05 Ω/day (up to 30 days) due to its hydrolytic degradation 7,19 , and loses its conductivity after 80 and 60 days, respectively.
Gradual hydrolysis of serpentine thin-film traces of Mg (length 21.35 mm, width 150 μm, thickness ~300 nm) can be used to define the relative out-of-plane water permeability of encapsulation layers cast on top. Considering the similar level of out-of-plane water permeability between PLGA and b-DCPU 80 (Fig. S6), the resistance changes of fully encapsulated Mo (Fig. 2e) imply that the loss of conductivity in Mo with PLGA encapsulation originates not from out-of-plane water permeation but from in-plane water penetration at the interface. Much higher rate of resistance increase in PLGA encapsulated Mo than that of Mo without encapsulation after 30 days of immersion can be explained by accelerated degradation of Mo in the low pH environment created by-products associated with hydrolytic degradation of PLGA 19 . These results suggest the possibility of long-lived operation of a bioresorbable electronic devices with b-DCPU due to its strong interfacial adhesion. It must be noted that we only measure the resistance changes of polymer encapsulated Mo electrode to demonstrate the device stability in PBS (Fig. 2e), and the interconnection would not be considered in this experiment. Since biofluids affect extension and nerve contact electrodes dominantly in vivo, and the harvester unit, including electrical connection points, are placed in a subcutaneous pocket where much lesser biofluids exists. In vivo testing in rodent model shows the stability of the whole device, including b-DCPU encapsulated electrodes and interconnections. Fig. 2f shows stress-strain tensile measurements on b-DCPU 70 (black), 80 (red), 90 (orange), and 100 (olive). The corresponding Young's moduli are 0.51, 0.93, 3.12 and 3.76 ± 0.24 MPa, respectively. b-DCPU 70 and 80 exhibit elongation (i.e. strain at fracture point) of up to 340 and 230% respectively, while that of b-DCPU 90 and 100 are both larger than 170%. The results reveal an increase in elongation and a reduction in Young's modulus with a decrease in crosslink density.

Supplementary Note 6. Mechanical stretchability of b-DCPU
Additional tests define the mechanical and electrical properties of the integrated system. Sandwiching a thin layer of a serpentine shaped Mo electrode by two layers of b-DCPU yields a mechanically robust, stretchable interconnect (Fig. S8). As demonstrated in Fig. 2g, the resistances of the structure show stable values for stretching at up to 50% strain, just prior to mechanical fracture. Finite-element analysis (FEA) results illustrate relationships between geometrical designs of the serpentine structure and the limits of elastic deformation, and show that the maximum strain in Mo is significantly less than its yield strain (0.6%) under stretching of 50% (Fig. 1g inset and Fig. S9). Fig. S10 shows the electrical stability of a b-DCPU encapsulated Mo electrode under cyclic loading conditions. Tensile fatigue tests of b-DCPU samples show the almost consistent behaviour on stretching and releasing, with negligible hysteresis in the strain range from 0-20% during 2000 cycles (Fig. S10a). The resistances of b-DCPU encapsulated Mo electrodes in stretched and compressed states show stable values for 10,000 cycles (with a rate of 5 mm/s) to tensile strains of +20% (stretching) and -20% (compression involving buckling), similar to those expected in the muscle movement of a rat leg 21,22 (Fig. S10b).

Supplementary Note 7. Degradation behavior of b-DCPU
The soft segment, PCL, and hard segment, aliphatic diisocyanate, in the b-DCPU are biodegradable 23,24 . The degradation of b-DCPU involves three stages: (1) water absorption; (2) chain scission by the hydrolysis of ester and urethane groups; and (3) dissolution of watersoluble entities 25 . During immersion in PBS (pH 7.4; 37°C), b-DCPU exhibits negligible swelling with water uptake of 2 ± 0.1% after one day of immersion. By comparison, PLGA 65:35 absorbs more than 8 wt% of water after 4 h of immersion (Fig. S11). Fig. S12a shows the storage modulus of 25-mm-diameter b-DCPU 80 disks (thickness: ~200 μm) immersed in PBS (pH 7.4) at 85℃ for 0, 2, 5, 10, 20 and 30 days, respectively. The storage modulus decreases with time of immersion (Fig. S12), consistent with gradual delinking of the polymer network and chemical degradation. Fig. S13 shows the degradation behavior of b-DCPU in PBS (pH 7.4) at temperatures of 23, 37, 60 and 80°C. The b-DCPU film degrades gradually in PBS at 37°C over a year and to completion in 80 days at 80°C. The b-DCPU 80 degrades with a rate of ~4.78×10 -5 g/day (for the first 24 days) in PBS (pH 7.4) at physiological temperatures (37°C). The dissolution rate of b-DCPU 80 for the first 7 days at 80°C (~1.28×10 -4 g/day) is approximately 4 times higher than that at 23°C (~3.34×10 -5 g/day). This timescale can also be controlled by manipulating the surface area to volume ratio.
The rate of degradation depends on the chemistry of its soft segment structure composed of the polyols. Hydrophilic PEG, as another possible soft segment, typically degrades more quickly than hydrophobic PCL under physiological conditions 26 . As a result, the degradation rate of the b-DCPU can be controlled by adding hydrophilic PEG and tuning its composition. Compared to the degradation behavior of b-DCPU 80, PEG containing b-DCPU with weight ratio (PCL:PEG) of 22-58 degrades much faster, showing complete degradation within 11 days in the same physiological condition (Fig. 2h).

Supplementary Note 8. Biocompatibility and toxicity of b-DCPU
The non-toxicity of PCL-triol, HDI, and resulting polyurethane network is wellestablished 27 . Although tin-based catalysts are FDA-approved, studies of long-term liberation and physiological effects of tin-ions from large tissue-embedded scaffold-matrices have not been previously performed. The following describes comprehensive biocompatibility and toxicity tests on Sn(Oct)2 containing b-DCPU. , as compared to tissue culture polystyrene (TCPS), indicating that b-DCPU and its degradation by-products do not have any influence on cell survival (Fig. 2i). Normalized in vitro viability assay data present no signs of cytotoxicity for all the groups with b-DCPU (Fig. 2j).
(2) In vivo biocompatibility Histological analysis shows that, after 4 weeks of implantation, the b-DCPU generates inflammatory reactions similar to those produced by high-density polyethylene (HDPE, FDAapproved nontoxic control) (Fig. S19). Hematoxylin and Eosin (H&E) stained sections of implant sites surrounding tissues show comparable levels of immune cell infiltration between b-DCPU and HDPE-implanted tissues at day 28. Masson Trichrome staining revealed identical tissue fibrosis around implanted material. Immunohistochemical staining of skin four weeks after implantation indicates identical monocyte (CD68) and leukocyte (CD45) inflammatory cell infiltration at the material-tissue interface. The results in Fig. S20a show that the changes in weight between mice with PLGA implants, as controls, and those with b-DCPU implants are similar throughout the 4-weeks period of observation. Following implantation, the mice behave normally with no substantial skin necrosis or swelling for up to 4 weeks. The result indicates minimal differences, consistent with the absence of toxic effects. The results of complete blood chemistry tests provide a comprehensive understanding of the health of the mice (Fig. S20b and c). Blood levels of enzymes and electrolytes, which serve as indicators of organ-specific diseases, fall within the confidence intervals of control values. For example, normal levels of alanine aminotransferase, cholesterol and triglyceride, phosphorus and urea nitrogen, calcium, albumin and total proteins indicate the absence of disorders in the liver, heart, kidney, bone and nerve, and good overall health, respectively.

Supplementary Note 9. Conventional neuromuscular electrical stimulation systems
Programs of neuromuscular electrical stimulation (NMES) appear to be acceptable to patients and have led to improvements in muscle strength, increasing range of motion, reducing edema, decreasing atrophy, healing tissue, and decreasing pain 28 . The effects of NMES therapy are expected on neuromuscular function in 3 populations: (1) preservation of neuromuscular function in patients during disuse; (2) partial restoration of neuromuscular function in patients after disuse; and (3) improvement of neuromuscular function in able-bodied individuals with "normal" function 29 . For example, applying NMES directly over a nerve trunk increased motor unit compared with a muscle belly 30 . In addition, as a strategic therapy for neuromuscular disorders, direct NMES significantly increased the number and size of AChRs clusters available for neuromuscular junction formation 31 . It is also reported that denervated muscles that received daily electrical muscle stimulation for 3 months had significantly greater numbers of reinnervated motor units, and improved behavioral outcomes 32 . In large animals, daily NMES for 8 weeks reversed the muscle fiber atrophy produced by complete denervation while avoiding a shift to a slow (type 1) fiber type 33 .
NMES occurs through depolarization of the motor nerves (rather than the muscle fibers directly) via transcutaneous, percutaneous, and implantable electrodes. As a non-invasive method, transcutaneous electrical stimulation devices apply current to muscles through electrodes on the skin. Due to the high impedance of the skin, transcutaneous muscle stimulation requires voltages with magnitudes ten times larger than those of implantable electrodes 34 . Hence, transcutaneous devices require much higher levels of power to induce muscle contractions for cases of traumatic nerve injuries. Implantable devices provide a direct means for neuromuscular stimulation via nerve cuff electrodes. A major disadvantage is that the associated surgical retrieval procedures subject patients to distress and expose them to the potential for additional complication 35,36 . In addition, conventional NMES mainly focuses on innervated muscle rehabilitation. For cases of damage to lower motor neurons or neuromuscular junctions (i.e. partial or complete denervation), the therapeutic benefit of NMES to the denervated muscle via implantable electrodes remains unclear 34 .

Supplementary Note 10. Modeling of reactive diffusion for polymer encapsulated Mg
The reactive-diffusion model (Fig. S23) can be expressed as where the water concentration w is solved as a function of time t and position y. The diffusivity ( ) and reaction constant ( ) of water in Mg are considered for 0 ≤ ≤ ℎ 0 . Due to the slow reaction process between the polymer encapsulation and water, only the diffusivity of water in polymer ( ) is considered for ℎ 0 ≤ ≤ ℎ 0 + ℎ , thereby reducing the equation to standard diffusion.
When the specimen is submerged in the aqueous solution, the water concentration at the interface between the top surface of the polymer encapsulation and water is constant, i.e., the water flux at the bottom surface of Mg is zero and the water concentration w at time = 0 is zero.
At the polymer/Mg interface, the concentration and flux of water molecules follows a continuity condition such that The solution of the reactive-diffusion problem is obtained by following the method presented elsewhere 4,37 . The water concentration (w) as a function of time (t) and position (y) is obtained as Where the eigenvalues ( ) are determined from The mass of dissolved Mg (per unit volume) is 2 , where the term corresponds to the mass of water that reacts at a given location (per unit volume), and 2 are the molecular mass of Mg and water, respectively, and = 2 are the two water molecules that react with each Mg atom in the process. Integrating  a, Simulated frequency-dependent S11 parameter of the wireless system for a separation distance of 1.5 mm. b, Simulated S21 parameter (black) and phase (red) as a function of frequency for the wireless system with a separation distance of 1.5 mm and a load resistance R = 5000 Ω. c, The frequency-dependent impedance (Z). (red) The real part of the impedance is the resistance, whereas (blue) the imaginary part is the reactance of the wireless stimulator. Mechanical failure of Type II devices at receiver and nerve cuff parts, and Type III device without any mechanical failure. In this model, the single Mg layer thickness (ℎ 0 ) and the polymer/Mg specimen thickness (ℎ 0 + ℎ polymer ) , where ℎ 0 and ℎ polymer are the initial thicknesses of the Mg layer and polymer, respectively.