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International Journal of Bioprinting A computational model of cell viability and proliferation of 3D-bioprinted constructs

Santoni et al. . Significant effort is being put into the from the boundaries. This possibly leads to cell suffering
[3]
optimization of the 3D printing process and into the and limited growth, with eventual cell death in the long
material functionalization. term [10,11] . The implementation of vascular networks
within the bioprinted constructs is needed to allow for
Bioprinting generically refers to different additive
manufacturing (AM) techniques applied to the biological a more uniform distribution of nutrients to all cells;
therefore, it constitutes an important step toward the use
field. Bioprinting techniques are classified according to of bioprinting for clinical applications.
the technique of layer-wise deposition, similarly to the
polymer AM standards (ISO/ASTM 52900) [4,5] . Extrusion- Two main phenomena that drive cell viability and
based bioprinting is very common due to its flexibility maturation in 3D-bioprinted constructs are nutrient
and ease of use. It involves the deposition of a bioink diffusion and consumption, as well as cell proliferation as a
that is a biocompatible hydrogel embedded with cells, function of their spatial location in the 3D geometry. With
in a layer-by-layer fashion. A dispensing unit extrudes respect to the nutrient diffusion and consumption, the Fick’s
the bioink from the cartridge through the application law is usually considered the reference to represent these
of a pneumatic mechanical force, that can be piston- phenomena, which can be modeled as the mass transport
driven or screw-driven, or a solenoid-based force . The of a solute in a solution using diffusion partial differential
[6]
presence of multiple printheads enables the extrusion of equations (PDEs). An interesting example of a Fick’s law
different materials and cell types in a single print. A major model to represent nutrients diffusion was presented by
drawback of this technique is the poor resolution of the McMurtrey in 2016 , who developed a mathematical
[10]
printed samples and the impossibility to print features model of diffusion and metabolism in basic 3D constructs
at the micro scale. This technique is known to retain a applied to cerebral organoids. The consumption rates of
high percentage of cell viability, which is mainly affected different cell types and the concentration and diffusion
by shear stresses. Another technique for dispensing a coefficients of oxygen and glucose in basic biological
hydrogel is inkjet-based bioprinting. This method allows environments were investigated. However, the models were
for the dispensing of picoliter and nanoliter drops through applied to simple geometries, such as one-dimensional
a piezoelectric or thermic actuator. Droplet impact velocity (1D), planar, cylindric, or spherical structures, and can be
and droplet volume have been identified as the main factors solved analytically. Therefore, one of the main limitations
affecting cell viability . Another bioprinting technique of McMurtrey’s approach is the 1D and quasi-stationary
[7]
is vat polymerization. This method consists of the representation of the problem and the limiting assumption
photopolymerization of a photoink, i.e., a photoresponsive on nutrient consumption, being either neglected or
material embedded with cells. A light source is projected considered constant. Other works in the literature provided
to the points intended to be polymerized and the construct more complex descriptions of the oxygen consumption
is built layer-by-layer . This technique allows for the rate. The most common one is the Michaelis–Menten’s law,
[8]
fabrication of high-resolution features but requires that the which considers the actual consumption as the maximum
materials are photopolymerizable and cannot be used with consumption times the ratio between the current
different materials at the same time. Digital light processing concentration and the current concentration summed
and two-photon polymerization exploit the same concept to the Michaelis–Menten constant. The latter is defined
and enable higher printing speed and resolution. A crucial as the concentration at which 50% of the maximum
point of vat photopolymerization is the effect on cell consumption occurs. Ehsan and George applied and
[12]
viability of some photoinitiators and laser sources, which validated Michaelis–Menten’s law with reference to human
must be chosen accurately.
lung fibroblasts. Similarly, Magliaro et al. showed
[13]
Current applications of 3D bioprinting are focused that oxygen consumption rates are well described by
on the realization of pathological models, organ-on- Michaelis–Menten kinetics given that reaction parameters
chips, and microfluidic systems, which better replicate are not literature constants but depend on cell density.
the in vivo environment. The ultimate goal is the The authors of the latter investigated the consumption
production of tissues and organs starting from the phenomenon in detail, which was found to be dependent
patients’ own cells. Different organs have been addressed, on oxygen concentration, cell concentration, and variation
ranging from simple ones like skin and cartilage to of the parameters. They also compared consumption in
more complex and articulated structures, such as the 2D and 3D environments and developed a model for the
heart . One of the main unsolved issues in bioprinting diffusion and consumption of oxygen in 3D constructs. The
[9]
is the capability to develop constructs with embedded cooperative behavior of cells, which can adapt their oxygen
vascularization. Large tissues with high cell density are consumption according to cell concentration, represents
prone to a lack of nutrients, especially in the areas far one of the key novelty factors of this study. In both cited

Volume 9 Issue 4 (2023) 352 https://doi.org/10.18063/ijb.741