Page 379 - IJB-10-4

International Journal of Bioprinting 3D cartilage induction and monitoring

Transition layers were marked as interior impedances: will mostly depend on the scaffold’s speed of sound and
density. By substituting the equation with bulk modulus
Z = ρ • C m (VI) (K) (Equation (9)), P-wave propagation can be defined as
m
i
Equation (10).
where ρ and c are parameters from the reflective
m
m
(1
material. K = E − v) (IX)
Finally, a boundary probe was attached to the (1 + v)(1 −2 v)
transducer to obtain the final electrical modeled signal. No
initial potential was computed for the piezo; instead, the
floating potential was selected as the outer potential. C = K (X)
p
A 2D model was selected as it could drastically ρ
reduce the computational time, memory requirements,
and representation complexity. All previous parameters With that in mind, a set of signals were synthetically
−1
are essential to compute inverse problem studies where created, with varying C from 1300 to 1600 m·s and ρ −3
SD
SD
parametric sweeps are performed. Contrasting the (density of the scaffold domain) from 1000 to 1400 kg·m .
previous model that describes the microfluidic flow, the Thereafter, empirical signals obtained from the BR ex vivo
porosity of this model has not been computed due to the experiments were compared with the set of signals.
higher wavelength of the ultrasound P-wave through the
scaffold domain than the PS: 47 (XI)

C
λ = SD f (VII) Each empirical signal was cross-correlated, with each
SD
0
synthetical signal generated using the computational model.
Every synthetic signal was tagged with its corresponding
where the speed of sound of the scaffold domain (c ) > ρ and C . It was estimated that the maximum cross-
SD
SD
1480 m·s , cutoff frequency (ƒ ) = 1 MHz, and thus, λ > correlation (>80%) correlated with optimal density and
−1
SD
SD
0
1.48 mm, resulting in PS < 400 µm. Mesh element size speed of sound.
was selected through parameter sweep to verify model
convergence (Figure S3, Supporting Information). It was To validate the present model, BR was assembled in
established that an element size below 400 µm is sufficient two different manners: without any scaffold (and filled
to acquire a stable signal. In Figure S3G–J, Supporting with water) and with a solid disk of PLA (and filled with
Information, no significant variance over amplitudes in water). In previous literature, both the density and speed
48
mesh sizes below 400 µm can be appreciated. The rest of sound of the materials have been disclosed. The speed
of the parameters (i.e., c PMMA , c H2O , ρ PMMA , and ρ H2O ) was of sound of PMMA was empirically calculated to be 2630
−1
−
−1
6
reconstructed through the inverse problem. m·s , with an acoustic impedance of 3 × 10 kg·m ²·s .
Figure S2, Supporting Information, represents the level
Further, P-wave propagation models should consider of correlation between the water model (Figure S2A and
the mechanical behavior of three different materials C, Supporting Information) and the PLA model (Figure
(PMMA, water, and bTPUe). Thus, the final electrical S2B and D, Supporting Information). A signal correlation
signal, representing the ultrasonic pulse, envelops all such (comparing synthetic and experimental signals) higher
parameters, thereby complicating the data extraction than 80% was obtained in both cases.
process. Additionally, the computer model focused on the
reconstructive parameters that had more variability over 3. Results
time. Therefore, P-wave propagation can be presented
based on the speed of the longitudinal wave: 3.1. Perfusion bioreactor with pulsed ultrasound
characterization
A novel BR was designed to promote perfusion flow and
(1
E − v)
C = ρ (1 + v)(1 −2 v) (VIII) exert direct shear stress on the cell surface among scaffold
p
fibers to induce chondrogenesis (Figure 1A). PMMA
was selected for this study, owing to its effortless sterility,
where E denotes the Young’s modulus. This equation transparency, and economical manufacturing cost. The BR
estimates that the final signal obtained by the transducer is mainly composed of three different pieces: the culture
Volume 10 Issue 4 (2024) 371 doi: 10.36922/ijb.3389