*3.4. Theoretical Modeling of NG-Cell Interaction*

To estimate the expected behavior of the effective voltage and current applied to the cell membrane by NG, an equivalent circuit was used to model the interaction of the piezoelectric nanofiber NG and cells. Figure 6a shows the diagram of NG-cell and corresponding equivalent circuit model [54,55]. Under external mechanical vibration, the NG deformation produced an external voltage excitation that could be modeled as a voltage source (*VNG*). The voltage reached the cell membrane through the culture medium, the conductivity of the medium would affect the voltage that stimulated the cell. The cell membrane is composed of a phospholipid bilayer, which can be regarded as an insulator. The extracellular fluid, cell membrane and intracellular fluid constitute a capacitor (*Cm*) [56]. The initial potential of ion channel is represented as *Vm* [57]. Figure 6b shows the simulation results of voltage and current transmitted to the cell membrane through the circuit due to sinusoidal voltage stimulation. When an excitation of 1.3 V was input, the voltage and current delivered to the cell was ~0.8 V and 0.4 mA, respectively. According to the basic principles of the circuit, when *VNG* is active, the capacitor *Cm* is charged (corresponding to the current that is stimulating cell growth), and the voltage across the capacitor (the voltage applied to the cell) *Vc* (t) (t is time, hereinafter abbreviated as *Vc*), which is expressed as

$$V\_{\mathfrak{c}} = -\frac{R\_{\mathfrak{m}}V\_{\mathrm{NG}}}{R\_{\mathrm{cm}} + R\_{\mathrm{m}}} \cdot e^{-\frac{R\_{\mathrm{cm}} + R\_{\mathrm{m}}}{R\_{\mathrm{cm}}R\_{\mathrm{m}}C\_{\mathrm{m}}}t} + \frac{R\_{\mathcal{L}m}V\_{\mathrm{m}} + R\_{\mathrm{m}}V\_{\mathrm{NG}}}{R\_{\mathrm{cm}} + R\_{\mathrm{m}}}$$

The result calculated by the formula of the voltage applied to the cell was consistent with that of the circuit simulation.

**Figure 6.** Electrical model of the NG-cell and FEM model of NG. (**a**) The diagrammatic sketch of NG-cell and corresponding equivalent circuit model. (**b**) The voltage (yellow) and current (black) applied to the cell membrane due to sinusoidal voltage stimulation (blue). (**c**) FEM stimulation of deformation distribution of nanofibers on NG at the stress amplitude of 0.5 Mpa.

Since a large deformation of the substrate will hinders cell adhesion, the deformation of aligned nanofibers based on NG under 0.5 MPa stress was analyzed by using finite element model (Figure 6c). The resulting maximum deformation was ~7 μm.
