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 86

FIGURE 4.7
A representative pressure profile below the laser spot center (z = 50 m m) ( Wang et al . , 2011 ).
4.3.2 MODELING OF DROPLET LANDING PROCESS
During landing, cell droplets undergo significant deceleration and impact(s), surviving a much higher
external force than they are capable of surviving under steady state conditions. This landing process
and its induced impact can be modeled using the mass, momentum, and energy conservation equations
( Wang et al., 2007, 2008 ). These equations hold true for cells, hydrogel in the droplet, and the substrate
coating. In addition to boundary and initial conditions, proper material models, which include the equa-
tion of state, constitutive model, and failure criteria, are also indispensable in solving these equations.
The equation of state is used to define the functional relationship between pressure, density, and internal
energy. The constitutive model defines the stress dependence of related strain, strain rate, and tempera-
ture. Generally, a material model also includes a failure criterion to determine whether and when the
material fails and loses its ability to support certain stress/strain.
A representative result of simulated landing is presented in Figures 4.8 and 4.9 , when a cell drop-
let with a velocity of 50 m/s hits a rigid substrate coated with a 30 m m thick layer of hydrogel. A cell
droplet with a cell in the center is modeled using a mesh-free smooth particle hydrodynamic (SPH)
method. It can be seen that there are two different impacts during the process under the specified condi-
tions. The first impact is between the cell droplet and the hydrogel coating, and the second impact is
between the cell and the rigid substrate after the cell passes through the coating after the first impact. As
the landing progresses, the hydrogel-enclosed cell droplet gradually merges into the substrate coating.
After the cell is immersed in the coating ( Figure 4.8 ), the outside hydrogel enclosure and the coating
bear relatively less stress even though the cell experiences more stress.