Multiphysics 5.2a

We used COMSOL Multiphysics 5.2a to compute the transmembrane potential in the LEPD system. Simulations were performed using the AC/DC electric currents module. The schematic of the geometry and the details of the material properties and that of the pulse applied are specified in fig. S4 of the Supplementary Materials. The governing equations of the current conservation and boundary condition that were used are $$\nabla .(\mathrm{\sigma }\nabla V)+\nabla .\mathrm{\epsilon }\frac{\mathrm{\partial }\nabla V}{\mathrm{\partial }t}=0$$ $$\mathbf{n}.\mathbf{J}=0$$ where σ is the conductivity (siemens per meter), V is the potential (volts), ε is the permittivity of the relevant domain, n is the surface unit normal vector, and J (ampere per meter squared) is the electric flux vector. The boundary condition of Eq. 2 was used for emulating insulating interfaces in the system, while a nonzero electric potential was applied to the dipped electrode, and ground was applied to the bottom gold electrode (fig. S4). We modeled the cell membrane in Eq. 3 as a thin resistive material with an effective contact impedance $$\mathbf{n}.\mathbf{J}=\frac{1}{d}(\mathrm{\sigma }+\mathrm{\epsilon }\frac{\mathrm{\partial }}{\mathrm{\partial }t}) V_m$$ where V_m (volts) is the transmembrane potential and d is the thickness of the cell membrane (meters). A physics-controlled mesh of COMSOL was used to discretize the entire geometry. The simulation was carried out for the entire duration of the pulse, and a backward Euler scheme was used for the time discretization.

COMSOL Multiphysics®5.2a was used to perform finite element simulations for the interstitial flow inside a developed microvascular network. Thresholded vessel images were smoothed and processed into outlines using ImageJ software, then converted into a .dxf file using Img2cad software. After the vessel outline was closed, and redundant fragments were removed using AutoCAD software, the complete vessel outline was scaled and integrated into the geometry of a microfluidic device. The refined CAD vessel diagram was then built into a 2D free and porous media flow model in COMSOL Multiphysics. Water was chosen to model the flow of culture media through the vascular network. The porosity and permeability of fibrin gel were estimated to be 0.99 and 1.5 × 10⁻¹³ m², respectively, based on our published result.^{18 (link)} Inlet/outlet were designated at the media reservoir boundaries, with pressure specified as 98 and 0.001 Pa, respectively, based on calculated gravity-driven pressure difference in the device, as previously described.^{18 (link)}