Page 102 - IJB-9-2

International Journal of Bioprinting Holistic charge-based MEW scaffold model

the periphery. The local effect (⊕) results in a relatively commonly encountered in most MEW studies. When the
high-energy state at the prescribed locations compared layer number N is small, the scaffold is negatively charged,
to their adjacent pores, while the local effect (⊖) results and the energy surface evolves as Mode 2. As N increases,
in a relatively low-energy state at the prescribed locations more positive charges are retained in the scaffold, and
compared to their adjacent pores. Compared to the duality Mode 1 becomes increasingly dominant. Since N in this
(⊕/⊖) of global and local effects, there is only one type study is large (150), which fall in the positive regime of the
of polarization effect, which is consistently represented by residual charge based on the previous studies , most of
[30]
an energy decrease at the prescribed locations. In other the analyses are developed based on Mode 1 (an exception
words, the global and local effects depend on the polarity is shown in section 3.5 based on Mode 2).
of the deposited fibers. In contrast, the polarization effect
is independent of the polarity of the deposited fibers and, 3.2.3. Lateral characteristic curve and characteristic
thus, is fundamentally different from the global and local surface
effect in nature. Since it is inconvenient to track the evolution of the energy

Among the stated three charge effects, the global effect surface with z, as shown in Figure 3 to represent the
is consistently initiated earliest and exists throughout the deposition process, a more intuitive approach is needed.
entire deposition process. However, whether and when Therefore, a simplified representation is advanced herein
the local effect or polarization effect will arise depends on based on the following mathematical property of the
the selection of ξ and η. As stated previously, an increment energy surface. By analyzing Equation (VI), it is not
in ξ and η helps to increase the observability of the local difficult to notice that the intersecting curves of the energy
effect and the polarization effect, respectively. By taking surface with any planes perpendicular to the x or y axis are
into account all possible permutations for these three kin curves, that is, they share the same shape and differ by
charge effects, seven distinct modes of evolution can be only a constant. This can be proven by the fact that ∂f is
observed and defined, including Mode 1 (1 global effect ∂f ∂x
st
[⊕], 2 local effect [⊕], 3 polarization effect), Mode independent of y and ∂y is independent of x based on
nd
rd
2 (1 global effect [⊖], 2 local effect [⊖], 3 polarization Equation (VI). Therefore, if the intersecting curves of the
rd
st
nd
effect), Mode 3 (1 global effect [⊕], 2 polarization effect, energy surface with the plane represented by x = 0 and
nd
st
3 local effect [⊕]), Mode 4 (1 global effect [⊕], 2 local y = 0 are Curve A and Curve B (Figure 4A), respectively,
st
rd
nd
effect [⊕]), Mode 5 (1 global effect [⊕], 2 polarization the energy surface can be obtained by translating Curve B
st
nd
effect), Mode 6 (global effect [⊕]), and Mode 7 (global effect along the path defined by Curve A or vice versa. Since x
[⊖]). Since the local effect (⊖) is indifferentiable from and y are interchangeable in Equation VI, Curve A and
polarization effect in terms of their effects on the energy Curve B are exactly the same. Considering the objective of
surface topology when the deposited fibers are negatively the energy curve is to predict the lateral deviation of the
charged (i.e., β<1), two other possible modes, including incoming jet segment, which will be deposited along the y
(1 global effect [⊖], 2 local effect [⊖]) and (1 global direction, Curve B is selected as the lateral characteristic
st
st
nd
effect [⊖], 2 polarization effect), are indifferentiable from curve (Figure 4B), which represents the lateral energy
nd
Mode 2, and not considered as separate cases. Examples of variation. Since it is the relative trend rather than the
Modes 3–7 and their corresponding typical parameters are absolute value of the energy that affects the lateral deviation
summarized in Figure S1 and Table S1, respectively. of the jet, the lateral characteristic curves at different z are
In light of a full consideration of all possible modes translated to coincide at both ends (Figure 4B) for
of evolution, it is now possible to identify the commonly illustration purposes. The lateral characteristic curves for
encountered modes in the current studies. In terms of the Mode 1 and Mode 2 are shown in Figure 3F and 3J. More
local effect, as shown in Mode 3, ξ needs to be smaller than intuitively, if z is continuously varied, the evolution of the
6 whereby the local effect emerges after the polarization lateral characteristic curve with z can be shown in a
effect. Since ξ > 6 is valid in most studies, the local effect characteristic surface, as shown in Figure 4C.
can be thought to not only exist but also initiated earlier It should be noted that the jet deposition process
than the polarization effect. In terms of the polarization is affected by the energy variation in both lateral and
effect, although η cannot be experimentally measured, vertical direction simultaneously. Although the lateral
the commonly observed “autofocusing phenomena” characteristic curve, which represents the lateral energy
[27]
in MEW process indirectly support the existence of the variation, affects the lateral deviation of the incoming
polarization effect. Considering these two observations jet segment significantly, this does not imply that the
that limit the selection of ξ and η, Mode 1 and Mode 2 are vertical energy variation should be neglected. In this
Volume 9 Issue 2 (2022) 94 https://doi.org/10.18063/ijb.v9i2.656