Page 186 - IJB-7-4

Support-Vector-Machine-Guided Parameter Selection for Extrusion-Based Bioprinting
then loaded into the printer for testing. In all temperature A Gaussian kernel was used in the model to
tests, the material was given an additional 10 min in the transform the feature parameters into high dimensional
printer to reach the set temperatures before printing. For space so that the nonlinear probability hyperplanes
each combination of parameters, three samples were can be constructed. Given m data set (x , y ), y =
(i)
(i)
(i)
printed. On each sample, five horizontal line width {−1,1}, i=1,2,…m, for a certain data sample x , the
(i)
measurements were taken at random around the grid. transformation is done by:
Data on vertical lines and pore width were also taken in
the same manner. These were taken by imaging the grids  i () j () 2 
under a microscope, then importing the images into Fiji f = exp − x − x  (2)

for assessment. Images were converted to 8-bit (black i   2 2  
and white) and then sharpened automatically using Fiji’s
(i)
(i) ,
(i)
(i)
automatic threshold adjustment. After sharpening, the so that x is constructed as (f , f ), f ) Here, σ
3
2
1
previously mentioned measurements were taken using is a scaling parameter and also a hyperparameter to tune
the line and automatic area selection tools. For each set in the SVM model. The optimization objective is to
of parameter tests, data from all three samples were then maximize the geometric margins of the hyperplane that
combined into one larger, 15-item set to calculate the separates the two classes. The optimization problem is to
mean and standard deviation. find the weight w and bias b that minimizes:
For a few variables, printing the originally selected
grid was not possible due to the effects of the parameters. m
1
The 21G nozzle and 20% PL 127 were unable to form a min w + C ∑  () i (3)
2
three-layer grid and were instead printed as a one-layer set wb  i
,, 2
of lines. In addition, 15% PL 127 was not viscous enough
to form any kind of grid and produced no useful data. subject to
2.8. Quantifying prints quality
)
T ()
i ()
To characterize prints a line width index was assigned y i () ( w f i + b ≥−1  �� m (4)
fori =…1
to each print using a method similar to prior research .
[17]
This allowed for an easy view of how accurate a print
was and what kind of error occurred in it. All averaged where ξ is a slack variable and C is the regularization
[29]
line values were divided by the theoretical line width, parameter .
following the formula: In this study, an open source SVM software
LIBSVM was used on MATLAB to train the model and
[30]
Experimental Line Experimental Line acquire the parameters w and b . A grid search on two
Width index = Width = Width (1) hyperparameters (C and g) was conducted with a threefold
Theoretical 0.4 mm cross-validation. C is the regularization parameter applied
on the slack variable SVM and g is the gamma parameters
2
2.9. SVM implementation in Gaussian kernel (1⁄(2σ )). The data set is labeled as “1”
class (good print) if the calculated width index in method
Uniform Design (UD) technique was used to select 2.8 is between 0.9 and 1.1, while labeled as “−1” class
[28]
12 experiment data points (Table 1) based on a three (bad print) otherwise (Table 2). 3D process map was
parameter four level data space U (P ). Concentration generated based on the pairwise probability estimates on
4
3
12
of PL 127 was set at 15, 20, 25, and 30 w/v%. The a 3D parameter space .
[31]
temperature of the nozzle was selected at 16, 23, 30, and
37°C, and the path height as 0.3, 0.35, 0.4, and 0.45 mm. 2.10. Statistical analysis
Twelve data points were normalized before being used as n = 3 prints were made for each parameter test, with
training set. n = 5 line measurements taken from each. Mean and
standard deviation were measured, and statistical analysis
Table 1. Uniform design with three parameters and four levels
Concentration 1 1 1 2 2 2 3 3 3 4 4 4 was performed based on original line data. Statistical
significance was investigated using data analysis tools
(Parameter 1) within Microsoft Excel. A t-test for two samples assuming
Temperature 4 2 1 3 1 3 4 2 2 1 3 4 equal variances was applied where P < 0.05 showed a
(Parameter 2) significant difference between tests. Results displayed in
Path height 4 3 1 3 1 2 2 4 3 2 4 1 Figure 2 are of line index data for clarity and insight. A *
(Parameter 3) symbol denotes significance.
182 International Journal of Bioprinting (2021)–Volume 7, Issue 4