2.4. Multimodal Stimulation

Finite element method analysis was performed using the AC/DC and CFD modules from COMSOL Multiphysics software (version 5.2a, www.comsol.com, Stockholm, Sweden). The Electric Current (ec) and Laminar Flow (spf) physics interfaces were selected, considering a stationary study. Our goal was to find which input stimulation values originate optimal experimental electrical and flow stimulation conditions according with the experimental studies performed by Mobini et al. [10] and Zhao et al. [9].

Mobini et al. [10] applied electrical stimulation with L-shape electrodes that are immersed in the culture chamber, the cell culture takes place in the region between the two electrodes. Using an input voltage of 2.2 V direct current (DC) resulted in the delivery of an E-Field of 100 mV/mm (100 V/m). The induced E-field magnitudes reported produced a 3-fold increase in the rate of osteogenic differentiation of mesenchymal stem cells in comparison with non-stimulated cells. Zhao et al. [9] work found that the optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5 to 5 mL/min (in terms of fluid velocity: 0.166–1.66 mm/s), considering different scaffold geometries and according to a mechano-regulation theory where extracellular matrix mineralisation would be stimulated when wall shear stress was in certain described ranges [9].

The CAD model of the bioreactor was imported into COMSOL where a physics-controlled mesh was generated with 1.9 × 10⁶ tetrahedral volume elements, and an average element quality of 0.65, as shown in Figure 2. The final geometry was composed of four distinct domains: one fluidic domain, made from culture medium material with electrical conductivity of 1.5 S/m and relative electrical permittivity of 80.1 [13]; one construction domain, consisting in PETG material with electrical conductivity 10⁻¹⁴ S/m (resistivity 10¹² Ohm/cm) and relative electrical permittivity of 2.5 [14]; and two electrode domains, made from Steel AISI 4340 material with electrical conductivity of 4.032 × 10⁶ S/m and relative electrical permittivity of 1. The temperature for this simulation was set at 37 °C.

Bioreactor geometry volume mesh created using COMSOL Multiphysics, with 1.9 × 10⁶ elements, and an average element quality of 0.65.

For the COMSOL laminar flow study, the fluidid domain representing the culture medium was assumed as an homogeneous and incompressible Newtonian fluid with a volume density of 1000 kg/m³ and dynamic viscosity of 8.1 × 10⁻⁴ Pa ·s. Considering that the ROI diameter is 0.010 m, and the fluid velocity in the same region is 0.0016 m/s [9], the calculated Reynolds number was 18.51, which is less than the 2300 turbulent threshold [15]), and a single-phase laminar flow regime was also considered. Physics model solver applies the incompressible form of the Navier–Stokes and continuity equations. Boundary conditions were set for all reactor’s walls with a no-slip condition, the outlet was set at a reference constant pressure of 0 Pa, the two inlets were set at the same value for inflow velocity and the velocity vector field was assumed normal to the inlet surface. To find the inlet velocity value that generates an optimal velocity inside the ROI chamber, we determined the external inlet and outlet conditions that produced the desired values that adequately translate the necessary flow conditions in the cell culture scaffold region. For this laminar flow study, the system initial condition was at rest, so the velocity field and pressure of the entire system was set to zero.

We have also determined the external electrical stimulation required to produce the optimal E-field distribution in the same ROI, according to Mobini et al. [10]. A stationary study was considered in COMSOL, as DC stimulation parameters do not change over time. This study solves the Laplace’s equation (∇·(σ∇ϕ))=0, where ϕ is the electrostatic potential and σ is the electric conductivity, and takes the gradient of the scalar potential to determine the induced E-field. This procedure assumes that the quasi-statics approximation holds [16]. In this approximation, tissues are considered to be purely resistive with no capacitive components, which is valid for DC stimulation (low frequency range) [16]. The following boundary conditions were imposed; an electric insulation condition was added to all external boundaries of the bioreactor walls, continuity of the normal component of the current density in all interior boundaries and electrical potential boundary conditions were added to each electrode interior boundary surfaces relative to the ROI. One electrode boundary surface was set at 0 V potential (ground electrode). The other electrode surface boundary potential was varied in order to find the value that resulted in a predicted E-field in the ROI of 100 mV/mm, according to Mobini et al. [10]. All other domains and boundaries were set at 0V at the beginning of the simulation, to establish an initial resting condition state of the entire system.