Electromechanical Design of Self-Similar Inspired Surface Electrodes for Human-Machine Interaction

Stable acquisition of electromyography (EMG)/electrocardiograph (ECG) signal is critical and challenging in dynamic humanmachine interaction. Here, self-similar inspired configuration is presented to design surface electrodes with high mechanical adaptability (stretchability and conformability with skin) and electrical sensitivity/stability which are usually a pair of paradoxes. Mechanical and electrical coupling optimization strategies are proposed to optimize the surface electrodes with the 2nd-order self-similar serpentine configuration. It is devoted the relationship between the geometric shape parameters (height-space ratio η, scale factor β, and line width w), the areal coverage α, and mechanical adaptability, based on which an open network-shaped electrode is designed to stably collect high signal-to-noise ratio signals. The theoretical and experimental results show that the electrodes can be stretched> 30% and conform with skin wrinkle. The interfacial strength of electrode and skin is measured by homemade peeling test experiment platform. The surface electrodes with different line widths are used to record ECG signals for validating the electrical stability. Conformability reduces background noises and motion artifacts which provides stable recording of ECG/EMG signals. Further, the thin, stretchable electrodes are mounted on the human epidermis for continuous, stable biopotential signal records which suggests the way to highperformance electrodes in human-machine interaction.


Introduction
Surface electrodes that can acquire electrophysiological (EP) signals have many applications ranging from diagnosing neuromuscular disorders [1,2], artificial muscle [3,4], to stimulation of hand rehabilitation [5].The conventional electrodes are fixed on the body surface by caps, belts, or tapes [6], which lead to inconvenient life of the people as their relatively thick and rigid nature, limited options in mounting locations, and discomfort in long-term usage on the soft, curved, and dynamic human body [7].The ideal surface electrode is desired to have excellent mechanical adaptability (stretchability > 30%, and conformability with skin wrinkles) and keep electrical stability in recording EP signals during body motion.
Material selection and structural design strategies for stretchable electrodes were proposed to improve the mechanical flexibility and the strength of EP signals [8][9][10][11][12][13].An electrode with adhesive patch of modulus-tunable composite was proposed to health monitoring [14][15][16].Epidermal strain sensor with improved PEIE-polydimethylsiloxane (S3-PDMS) elastomer substrate showed excellent compatibility with human skin [17,18].Optimized structural designs for large deformation were validated by experimental and theoretical results and applied in flexible/stretchable electronics [19][20][21].The "bridge-island" structure was proposed to enhance both the stretchability of bridge and the area coverage of island for the stretchable electronics [22,23].Optimal geometric parameters of filamentary serpentine structure of surface electrode, such as the thickness of substrate, interelectrode distance, line width, and radius of the microstructure, were considered to improve the electrical performance [8,24].Self-similar serpentine interconnects were adopted in network-shaped surface electrode of EP sensor, to satisfy large deformation as the skin motion [25][26][27].It was mainly attributed to the tremendous reduction of stiffness and increasing of length of the 2ndorder structure compared to the 1st-order one [21,28,29].The structural optimization of surface electrode was merely focused on the stretchability and conformability, respectively [8,25].However, the collaborative optimization of the mechanical and electrical properties has not been reported for stretchable surface electrodes.
This paper proposes a design strategy of the self-similar inspired biopotential electrode, which satisfies mechanical adaptability and electrical performance.The optimization model is to simultaneously improve the stretchability up to >30%, the conformability with skin wrinkles, the output signal gain, and the signal-noise-ratio (SNR) of surface electrodes used in electromyography (EMG)/electrocardiograph (ECG) signal recordings.The theoretical analysis and experimental results indicate that the self-similar design effectively improves the stretchability, conformability, areal coverage, and electrical performance of the surface electrode.Further, the signal stability is validated through the biological signal recordings in the case of walking and running.The surface electrodes which conformally contact with the skin surface can reduce the motion artifacts for stable biological signal recordings.It firstly provides a structural design method for stretchable electrodes with high deformability, conformability, areal coverage, and recording stability of EP signals.The Au layer locates at the neutral plane of the electrode for reducing the strain of Au layer.Figure 1(d) shows that the stretchable surface electrode follows the wrinkles of the skin surface.Figure 1(e) depicts the equivalent circuit for data acquisition of the surface electrode with a voltage follower.Higher signal gain is realized by using higher input impedance, and low-input capacitance is adopted to improve the signal quality.Figure 1(f) depicts the layout of wavy network-shaped with the 2nd-order self-similar serpentine electrode consisting of horseshoe building blocks.The node connection of the unit cells in the network-shaped electrode forms triangular lattices.Figure 1(g) illustrates the geometry parameters of microinterconnect for the 1st-and 2nd-order serpentine structure.The heights of the 1st-order and the 2nd-order serpentine interconnects are H 1 and H 2 , respectively.And the line width and the thickness are w and t, respectively.As the shape of the 1st-and 2nd-order serpentine geometries is almost the same, that is, height-space ratio η = 2H 1 /L 1 = 2H 2 /L 2 .The scale factor β = L 2 /L 1 represents the ratio of the 2nd-order serpentine space to the 1storder space.The geometry of the 2nd-order serpentine structure is characterized by base length (L 1 , w, t) and two nondimensional parameters (η, β), where t is usually determined by the magnetron sputtering process.Both the mechanical adaptability and electrical performance depend on the geometry parameters of the electrodes but usually show competing relationship.

Electromechanical Optimization Model
The surface capacitive electrodes are designed based on self-similar serpentine geometry.The electromechanical optimization model is built to improve the electrical performance for satisfying excellent output gain, deformation, and conformability with the skin.As the principle of capacitive electrode shown in Figure 1(e), the transfer function model for the output gain of the electrode is represented as where R in and C in are the resistance and capacitance of the voltage follower.As R E > >R B , the transfer function model can be represented as [30] where Interfacial mechanics model is built to analyze the contact behavior at the electrode-skin interface, and the critical criteria to guarantee the electrode conformal contact with the skin is provided as [19,31] where w is the line width of the surface electrode, and h rough and λ rough denote the characteristic amplitude and wavelength of the skin roughness, respectively.Here, the adhesion force γ at skin-electrode interface is measured by the homemade peeling platform, and the experiment process is discussed in (Appendix B).
The stretchability ε stretchability of the self-similar inspired microinterconnect unit depends on the geometry parameters η, β, w/L 1 , and t/L 1 , which is expressed with the scale law formula [32][33][34]: The mapping relationship between the stretchability of the network-shaped electrode ε electrode−stretchability and the self-similar inspired microinterconnect unit ε stretchability can be written as [35] ε electrode-stretchability = ε stretchability × 1 − α electrode 5 The electromechanical optimization model ( 2), ( 3), (4), and ( 5) that integrates the coupling mechanical and electrical properties of the electrode is built to improve the mechanical adaptability and electrical performance.It is observed that the model is related to the geometry structure parameters η, β, and w.Design strategies are provided to realize with high filling factors and stretchability of the surface electrode.It is difficult to solve the complicated optimization model with multiple objectives and constraints directly.Multistep method is proposed to solve the optimization model ( 2), ( 3), (4), and ( 5), where the flow chart is shown in Figure 2, mainly including three steps: (1) explaining the competing relationship between areal coverage and stretchability of the microinterconnect unit for providing a relatively larger feasible range; (2) the effects of the layout of surface electrode on the output gain for determining the area of the electrode; and (3) devoting the relationship between stretchability and conformability to providing the 3 Complexity higher electrical performance and determining the feasible geometry parameter range of the surface electrode.

Competing Relationship between Areal Coverage and
Stretchability.There are two important factors, areal coverage and stretchability, used to evaluate the electrical and mechanical performances of the stretchable surface electrode.Step 1 in Figure 2 depicts the solving process for the optimization of the microinterconnect unit.Given the space L 1 of the microstructure unit, the geometry parameters η, β, and w are optimized to balance the areal coverage and the stretchability.
Figure 3(a) illustrates the effect of line width w on the stretchability and the areal coverage of microinterconnect unit.The scatter points are from FEM simulation, and the red curve is from the theoretical analysis [20].Given η = 1 25 and β = 8, the areal coverage linearly increases with the line width w, and the stretchability monotonously decreases with the line width w.For areal coverage and ε stretchability > 35%, the line width w ranges from 30 μm to 72 μm. Figure 3(b) depicts that the stretchability and the areal coverage of microinterconnect unit vary with the height-space ratio η.The scatter points are from FEM simulation, and the red curve is from the theoretical analysis.The areal coverage decreases with η by theoretical analyses and experiments, and the stretchability of microstructure unit monotonically increases with η.Given β = 8 and w = 50 μm, for ε stretchability > 35%, height-space ratio η is larger than 1.2. Figure 3(c) depicts the relationship between the stretchability and areal coverage of microinterconnect unit with scale ratio β.The stretchability decreases with increasing β, and it approaches to 28% (the stretchability of the 1st-order serpentine structure).Given η = 1 25 and w = 50 μm, for ε stretchability > 35%, β is smaller than 20.

Layout of Surface Electrodes.
Step 2 in Figure 2 illustrates how to determine the layout of the self-similar inspired surface electrode based on the triangular lattices.The voltage follower with the input impendence R B = 1 GΩ and C in = 100 pF is shown in Figure 1(e).The output gain of the surface electrode depends on the capacitance C E at skin-electrode interface, as shown in (2). Figure 4(a) reflects the effect of area (the area of metal film) on the electrical performance (normalized gain) of the surface electrode, where the areal coverage α = 0 1, 0.2, 0.3, 0.4, and 0.5, respectively.The output gain increases with the effective area of the electrode.When the areal coverage α = 0 1, it is difficult to reach the objective of the output gain G (>0.95).Figure 4(b) shows that the output gain increases with the increasing area with different η, and it reaches capacity with S > 25 mm 2 , which provides a guideline to determine the electrode area.As the surface electrode with the second-order serpentine interconnect forms into the triangular lattice structure, Areal coverage E skin EI electrode π 3   3   Signal gain Optimized structural electrode 4 Complexity number of nodes are also computed for the electrode with the given area of the surface electrode, and so is the layout of the surface electrode.

Competing Relationship between Stretchability and
Conformability.The feasible range of geometry parameters of microinterconnect under the constraints of stretchability and areal coverage given in Figure 3 provides a selection range for structural optimization of the surface electrode.The effect of line width w on the stretchability and conformability is presented in Figure 5(a).It can be observed from (3) the surface electrode conformally contacts with the skin when the width w is smaller than 72 μm.When it is smaller than 65 μm, the stretchability is larger than 30% by the scale formula (4).For the electrode with high filling factor to detect biological signals, the line width w should be larger than 30 μm.So the feasible range of line width w is (30 μm, 65 μm).
Figure 5(b) depicts the effect of height-space ratio η on the stretchability and conformability.The stretchability and the total energy (sum of the bending and elastic energy of the electrode, skin energy, and the adhesion energy) at the electrode-skin interface increase with η.The surface electrode can conformally contact with the skin surface at the case of η < 2 25, and the stretchability is larger than 30% by (4) when η > 1.2.For the conformal contact and stretchability, the feasible range of η is (1.2, 2.25).
Figure 5(c) is a depiction on the effect of scale factor β on the stretchability and conformability.When it is smaller than 16, the stretchability is larger than 30% by (4).When β is smaller than 10, the electrode conformally contacts with the skin.As the space of the 2nd-order structure is four times larger than the space of the first order, β is larger than 4. For the conformal contact behavior and stretchability, the feasible range of geometry parameter β is (4, 10).7 Complexity 4.2.Conformability.Conformal contact between the electrode and the skin improves SNR of EMG signal measurement and reduces the motion artifacts and background noise.The surface electrode adhered onto the skin surface is driven only by van der Waals interactions.Conformal contact occurs when the adhesion energy is larger than the sum of the bending and elastic energy [19,36,37].Figure 7(a) depicts the relationship between the conformability and the line width w via theoretical analysis and experiments, and the total interfacial energy at electrode-skin interface increases with the line width of electrode.The critical line width is 72 μm where U total = 0, that is, the electrodes with line width smaller than the critical width 72 μm can contact with the skin conformally.The scatter data in Figure 7(a) are the experimental results with line width w = 30μm, 50 μm, 70 μm, and 90 μm, respectively.The electrodes with w = 30μm and 50 μm conformally contact with the skin, and the electrodes with w = 90μm cannot conform with the skin.The experiment data agree well with the theoretical results of (3). Figure 7(c) depicts that the areal coverage of the surface electrode increases with the line width w.The line width is smaller than 70 μm to keep conformal contact with the skin surface shown in Figure 7(a).For the stretchability ε elec- trode > 30%, the line width is less than 65 μm (Figures 5(a) and 6).To provide enough areal coverage to collect biological signals, the line width is larger than 30 μm.Considering the conformability, stretchability, and areal coverage of the surface electrode, the feasible range of line width is in (30, 65) μm, which agrees well with optimization results in Figure 5.

EMG Signal
Recording.The EMG signals are recorded by the stretchable capacitive electrodes to diagnose neuromuscular disorders and study muscle pain [38].To minimize the motion artifacts during movement, the electrodes should keep conformal contact with the skin surface when the external load is applied to the electrode.The ground electrode, located in the center of the measurement and reference electrodes (16 mm apart at center-to-center distance), determines the common-zero potential.A customized PCB is used to collect the EMG data from different parts of the body.It yields analog data, converted to digital signals for recording using LabView software and analysis using MATLAB software.4.4.Electrical Performance.The electrical performances (capacitance C E at skin-electrode interface, output gain, SNR, and background noise) are related to the geometry parameters of the electrode [39,40].Capacitance C E determines SNR through its effect on the gain of the preamplifier.As expected, the output gain G is also improved as the C E is increased with increasing effective area of the electrodes [41].Figure 10(

Conclusion
Electromechanical optimization method for the stretchable capacitive electrodes with self-similar configuration was studied to realize excellent mechanical (large deformation > 30% and conformal contact with skin) adaptability and simultaneously improve the electrical performance (high SNR and signal stability).Feasible range of the geometry parameters of the 2nd-order self-similar serpentine structure was determined by solving the optimization model.

Appendix A. Solving Process Chart for the Optimization Model
The electrical performance of the surface electrode is related to the geometric parameters η, β, and w.It is  3), (4), and (5) with the coupling mechanical and electrical properties of the surface electrode.Three-stage solving method is proposed to solve the optimization model.Figure 2 depicts the detailed solving process for optimized structural design of the electrodes, mainly including three steps: parameter optimization of the microinterconnect unit, geometry size and layout of surface electrode, and structure optimization of surface electrode.

B. Experiment Setup for Adhesion Energy Measurement
The homemade experimental platform with motion and velocity adjusted part is shown in Figure 8(a).The peeling velocity is adjusted from 0.05 mm/s-100 mm/s, and the peel force is obtained using load cell (222-N LCM300, FUTEK, USA) with an accuracy of 1 mN.Test samples of the electrodes with different line widths w = 30 μm, 50 μm, 70 μm, and 90 μm are prepared for the peeling experiments which are used to measure the critical energy at electrode-skin interface.The peeling force per unit has been measured for the electrode peeling from skin surface by the peeling experiment platform with the peeling velocity v peel = 0.02, 0.05, 0.1 mm/s, 0.2 mm/s, 0.5 mm/s, 1 mm/s, and 2 mm/s.It is plotted in Figure 8(b) with scatter point, and exponential function is used to fit the scatter data.

Figure 1 ( 1 L 2 H 1 H 2 Figure 1 :
Figure 1(a) depicts the optical image of the surface capacitive electrode conformally mounted on the human skin.The surface capacitive electrode measures EP signals by embedding

Figure 2 :
Figure 2: Solving process chart for the optimized structural design of surface electrode.

Figure 3 :Figure 4 :
Figure 3: The effects of geometry parameters of the microinterconnect structure on the areal coverage and stretchability.(a) Line width w; (b) height-space ratio η; and (c) scale ratio β.

Figure 5 :
Figure 5: The feasible range of geometric parameters for the stretchability and conformability of the network-shaped electrode: the effects of (a) line width w, (b) height-space ratio η, and (c) scale ratio β.

Figure 7 :
Figure 7: Conformability analysis for the electrodes with different line widths.(a) Theoretical and experiment results of the network-shaped electrode contact with the skin with different line widths.(b) Optical images of the electrodes contact with the skin surface (I) 30 μm; (II) 50 μm; (III) 70 μm; and (IV) 90 μm.(c) Feasible range of the line width of the electrode with given stretchability and conformability.

Figure 8 : 9 ComplexityFigure 9
Figure 8: (a) The peeling test experiment platform and the local enlarged graph and (b) experiment data and analysis from the experiment platform at skin-electrode interface with different line widths.
a) depicts the experimental and theoretical results of the output gain and the area of the electrode at areal coverage α = 0 2. The scatter points in Figure10(a) are the experimental results with area = 20 mm 2 , 30 mm 2 , and 40 mm 2 , respectively.It is seen that experimental results agree well with the theoretical results.The output gain of the electrode increases with the area of the electrode.Figure 10(b) depicts SNR from the capacitive EMG electrode with line width w = 30 μm, 50 μm, 70 μm, and 90 μm, respectively.Signal voltage and noise voltage represent the amplitude of the EMG signal and background noise signal.The histogram shows that SNR from the electrode with line width w = 50 μm is larger than line width w = 30 μm, 70 μm, and 90 μm.

Figure 10 :
Figure 10: Electrical performance of the capacitive biological electrode.(a) The experimental and theoretical results between the output gain and the area.(b) SNR from the capacitive biological electrode with different line widths.(c) Contact impedance versus with the scanning frequency.(d) The leakage current at the skin/electrode interface.
εα η, β, w S electrode /h PI is the capacitance of the electrode-PI-skin capacitor, R B is a bias resistance between the ground and the operational amplifier.The output signal gain G depends on the capacitance C E with given voltage follower.The 2-norm of the transfer function (1) is represented as