Page 128 - IJB-10-6

International Journal of Bioprinting Fluid mechanics of extrusion bioprinting

and survivability. Several factors affect cell survival and De = 1 – exp (–a τ ) (VII)
- b 2
2
e
viability in extrusion printing, including the viscosity of
the bioink, the pressure used to extrude the bioink, the –
size of the nozzle, and the printing speed. In addition to where τ is the magnitude of shear stress at the dispensing
1,64
s
–
shear stress, cells also experience extensional stress during needle with an exposure time of t , and τ represents the
e
s
the bioprinting process, which plays a crucial role in average extensional stress. The model parameters of a, b,
determining their overall viability. 63,66,67 Extensional stress and c for Schwann (RSC96) and myoblast (L8) cell lines,
as identified, are listed in Table 2. Cells are exposed to
66
arises due to the abrupt change in velocity experienced extensional stresses as they pass through the contraction
by the cell suspension as it passes through the contractive region of the nozzle at the needle entrance within a
region of the needle (Figure 3). Compared to shear stress, relatively short time compared to their exposure time to
extensional stress can cause more severe damage to shear stresses. Therefore, exposure time is not included in
63
cells. Therefore, it is important to examine both shear the cell damage law for extensional stress effects.
and extensional stresses when studying the relationship
between cell damage and the bioprinting process. 63,68,69 By focusing on shear stress as the main cause of cell
damage (in comparison with compressive stresses), a
Figure 3 illustrates the stresses exerted on cells and cell damage law based on one independent variable, i.e.,
cell deformation as they enter and then pass through the pressure work (W ), was developed: 73
needle of a chamfered nozzle. Given the parallel flow inside p
the cylindrical needle (i.e., the Poiseuille flow ), the shear D t = D max + (D max – D 0)exp (–a pW p) (VIII)
70
stress inside the needle can be calculated by
Pressure work is a combined index to indicate the
r   ∆ 
τ =     P  (III) accumulated energy of the flow pressure as bioink passes
s
2
   L  through the needle. 73
where DP is the pressure drop in the needle, and r W = 1 ∆ P AL
and L are the radius and length of the needle, respectively. p 2 n (IX)
Cogswell proposed a relation to calculate the average
71
–
extensional stress a magnitude τ based on the pressure where A denotes the dispensing nozzle cross-sectional
e
drop DP at the nozzle entrance region, area, and DP is the total pressure drop in the nozzle with
n
en a total length of L (Figure 3); D max and D are reference
0
measures as maximum DCR and DCR value at the needle
3
τ e = ( n + ) ∆1 P (IV) entrance (the contraction region); a is the parameter
p
8 en that governs the cell sensitivity to pressure. While the cell
damage model of Han et al. has not considered extensional
73
where n is the power-law index of the fluid. While the stress as an effective factor, its results are validated in a
analysis indicates that Cogswell’s relation is not accurate wide range of bioprinting conditions.
71
72
for high nozzle convergence angles, it has been widely used While various studies have demonstrated that cell
for estimating the extensional stress due to its simplicity. damage increases with the printing pressure for a given
The most accurate method for calculating extensional needle diameter, 63,73,75 the influence of needle diameter
stress involves measuring the extensional viscosity on cell damage varies, presenting two different scenarios.
(Section 3.3.3). For a given printing pressure, Han et al. and Ning et al.
63
73
A previous study used the Cogswell relation for revealed an increase in cell damage with the needle
63
75
extensional stress to formulate their empirical cell damage diameter (Scenario 1). In contrast, Li et al. reported a
law as follows: decrease in cell damage with needle diameter (Scenario 2).
Chirianni et al. proposed a generalized version of the
74
73
Dt = De + (1 – De)Ds (V) cell damage model Han et al. that can predict both
scenarios by defining equivalent pressure work based on
where D denotes total damaged cell ratio (DCR), the equivalent nozzle area. They also added the effect of
t
with D and D representing DCR values originating from extensional stresses to the cell damage model by replacing
e
s
extensional and shear stresses, respectively : the constant D with a non-constant term, describing the
63
0
cell damage at the entrance of the needle where the cells are
Ds = 1 – exp(–a τ 1 t 1 ) (VI) exposed to extensional stresses. 74
b
c
1 s s
Volume 10 Issue 6 (2024) 120 doi: 10.36922/ijb.3973