Page 382 - IJB-10-4

International Journal of Bioprinting 3D cartilage induction and monitoring

ethanol, followed by UV irradiation inside the laminar 3.2. Acoustic pressure wave propagation model
hood. Thereafter, the BR was coupled and initialized with A complex and novel 2D model, applying Multiphysics FEM
a flow rate of ≤0.5 mL·min to prevent cell damage (Video (COMSOL Multiphysics®), was developed to understand
−1
S2, Supporting Information). the mechanical behavior of the BR ultrasound system.
Figure 2E represents the BR output flow varying the Figure 3 displays the representation of the model and the
input voltage of the peristaltic pump. This calibration physics behind its comportment. Figure 3A represents
curve was done to ensure the proper flow rate inside the the XY-plane visualization of the whole geometry, where
BR as function of the input voltage. Figure 2C corresponds the modeled plane corresponds to a transversal section in
to two arbitrary ultrasound signals recorded in Raspberry the middle of BR. This plane was selected in both models
Pi; the red line denotes a scaffold seeded with cells, whereas (P-wave propagation and fluidic dynamic models) because
the black signal line the blank control (i.e., functionalized flow channels have no axial symmetry.
scaffold without cells). The amplitude of the red line (cell In summary, the signal originated in the transducer
signal) was almost double that black line (blank signal). (transmitter) as a mechanical P-wave. Figure 3B displays
Rebounds closer to the primary signal (approximately 40– mechanical displacement in the X direction, with negligible
45 µs) were also more attenuated in the cell signal. Figure displacement in the Y direction. The total displacement
2D represents the incident pressure exerted by the P-waves ranges from −25 × 10 µm (Figure 3B-a) at t = T /2 to
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0
produced by the transducer (transmitter). As our wave 25 × 10 µm (Figure 3B-b) at t = T . Thereafter, the P-wave
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0
generator had a limit output amplitude of 20 V, to verify is propagated through the acoustic pressure module
the linear response of the exerted pressure on the input (Figure 3C), where the dependent variables are material
excitation voltage, a curve from 0 to 50 V was computed. density and speed of sound:
Figure 2F presents the microfluidic model through
scaffold fibers (represented as circles) with two different (XV)
flow rates. The scaffold was represented as a matrix of circles,
where each circle had a diameter of 200 µm. The scaffolds
were separated by a 600-µm space due to the printed layer where Q is the monopole domain source, q is the
d
m
pattern. Mesh element size was adapted to 100 µm, i.e., half dipole domain source, and p = p + p , where p is the
b
t
b
the fiber diameter. The cylindrical approximation of the background pressure field. The interior impedance, a
fibers was demonstrated in the previous work. The cell boundary condition that simulates reflection/transmission,
46
medium density (ρ = 1.009 g·cm ) and dynamic viscosity depends on both parameters. Thus, the attenuation of the
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(µ = 0.93 mPa·s) were retrieved from prior literature. Re signal will depend on the density and sound speed of the
49
was calculated as: scaffold domain. For the external boundaries that represent
the walls of the BR:
ρuD
Re = h (XIV)
µ  1 ∇ ( p − ) 
n • −  t q d  = 0 (XVI)
 ρ 
where u is the input flow speed (i.e., at 0.8 mL·min ,
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u = 106.1 µm·s ; at 0.5 mL·min , u = 66.31 µm·s ) and Figure 3C-a, which corresponds to t = T /2, displays
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−1
−1
D is the input diameter height, i.e., 4 mm. The obtained a partially developed P-wave. In Figure 3C-b, the P-wave
0
h
Re (i.e., 4.6) is <2300, which is regarded as the upper limit is fully developed and displays contacts with the scaffold
for laminar flow, whereas turbulent flow develops when Re domain at t = 15 µs (Figure 3C-c) and t = 18 µs (Figure
> 2900. 50
3C-d), in the middle of the scaffold domain, implying that
According to model results, the flow rate can be the primary wave travels through the scaffold domain in
translated into actual flow speeds over cells by weighing: approximately 6 µs. At t = 34 µs, the main wave reaches
(i) 0.5 mL·min corresponds to flows below 800 µm·s , the transducer (receiver) (Figure 3C-e). At t = 50 µs (last
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−1
and (ii) 0.8 mL·min to flow speeds below 1000 µm·s . experimental time), there are only rebounds obtained
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Although the flow speed is higher between fibers close from different boundary conditions (Figure 3C-f). Similar
to the fiber surface (i.e., cell location), the flow speed to the transducer (transmitter), Figure 3D displays the
decreased to less than half of the maximum value displacement in the X direction of the mechanical P-wave
(Figure 2F). From the model, the maximum shear rates are over the transducer (receiver) domains. The P-wave
10 mPa at 0.5 mL·min (Figure 2F-b) and 16 mPa at 0.8 is fully developed at t = 35 µs, and rebound waves are
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mL·min (Figure 2F-d). transmitted at t = 40 µs. Finally, Figure 3E represents an
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Volume 10 Issue 4 (2024) 374 doi: 10.36922/ijb.3389