THE POWER OF CAD/CAM LASER BIOPRINTING AT THE SINGLE-CELL LEVEL: EVOLUTION OF PRINTING - 3D Bioprinting and Nanotechnology in Tissue Engineering and Regenerative Medicine - page 83

4.3.1 MODELING CELLULAR DROPLET FORMATION
External pressure and internal stresses are exerted on cells during rapid evaporation (normal boiling
and phase explosion) and thermoelastic expansion of viscous droplets. The transformation of a super-
heated liquid to an equilibrium state of mixed phases is called a “phase explosion,” which eventually
leads to a pressure pulse. The pressure pulses are systematically exploited by MAPLE-DW to generate
printable droplets on demand. Although necessary for the formation of cellular droplets, the pressure
pulse and thermoelastic expansion can injure printed cells, reducing viability after deposition. As such,
both bubble formation and thermoelastic stress should be investigated via computational modeling to
understand and minimize possible sources of damage to printed cells.
4.3.1.1 Modeling Bubble-Formation-Induced Process Information
Figures 4.3 and 4.4 are schematic representations of the laser-induced bubble formation and expansion
process in a typical MAPLE-DW setup. While the MAPLE-DW scheme is shown here, the proposed
modeling approach is applicable to other laser-based printing methods that utilize a sacrificial energy-
absorbing layer. The modeling assumes that the energy conversion thickness ( < 100 nm) at the ribbon-
hydrogel interface is negligible.
During the bubble expansion process, a high-pressure pulse is generated, which ejects a droplet vol-
ume containing the cells. The bubble expansion process can be modeled using a computational domain
as shown in Figure 4.4 . The materials involved consist of (1) vaporized gas bubble, (2) air, (3) hydrogel
(used here as a coating material), and (4) the cell. Typically, the cell is modeled as a solid type material
and applied a Lagrangian mesh for simplicity. The bubble, coating material, and air are modeled using
the Eulerian mesh to avoid any extreme element distortion of these materials during ejection. The cell/
hydrogel interaction is modeled using the appropriate Euler/Lagrange coupling to capture the effect of
viscosity at the cell boundary layer. In addition, the interaction among the hydrogel, bubble gas, and air
is modeled by defining the borders in a multimaterial grouping.
The pressure pulse accelerates resting cells from the ribbon until the droplet is ejected at a criti-
cal ejection velocity. Ejection velocity largely determines the initial velocity at which the cell droplet
encounters the receiving substrate, and should be controlled to minimize cell injury during landing.
Figure 4.5 shows the cell-center velocity evolution during the ejection process. It can be seen that the
cell velocity oscillates initially and then gradually smoothes out to a constant ejection velocity, in this
case 107 m/s. This velocity oscillation is attributed to the elasticity of the cell, implying a negative ac-
celeration. Due to the compressibility of hydrogel, there is a delay in the velocity response to the bubble
expansion as seen from Figure 4.5 . After approximately 2 m s, the cell droplet has a very weak connec-
tion with the coating material and starts to separate from the coating material with a constant velocity.
FIGURE 4.4