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Error Correction for Bioprinting
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           Figure 7. (A-C) The error between the printing helix trajectory and the reference trajectory was mapped to the helix trajectory; the darker
           blue represents higher level of error. The error value of each helix was shown in the color column on the right. Each helix model was tested
           3 times repeatedly.

           the correct printing helix trajectory, and the surrounding   curves, which induce much greater  challenges  in the
           blue line mapped the errors at different positions. The   error correction stage.  Figure  5 shows  the deviation
           depth  of  the  color  reflected  the  error  value  between   error between the printed helix trajectory and the ideal
           the  corrected  printing  helix  trajectory  and  the  ideal   reference  trajectory.  Therefore,  the  significance  of  this
           reference trajectory. The error value corresponded to the   study is to correct this deviation value and to improve
           error color column on the right, which was consistent   the resolution of extrusion-based bioprinting. The error of
           with the color column, as shown in Figure 7. Obviously,   each helix reference trajectory is compensated according
           the error value of the corrected printing helix trajectory   to  the normal  vector  approach, and  the  printed  helix
           had been reduced dramatically by algorithm processing   trajectory  is  overlapped  with  the  ideal  helix  trajectory
           and a high error range represented by dark blue hues   as much as possible. Furthermore, the printing error is
           for each helix compared with the original printing helix   reduced to an acceptable range.
           trajectory was absent.                                  Figure  7 shows that the errors are not similar
                                                               at  different  positions  between  the  printing  helix
           3.3. Repeatability                                  trajectory  and  the  ideal  reference  trajectory  in  the
                                                               same Cartesian coordinate system. The dark blue area
           To ensure that the error statistics of the corrected helix   with high error is concentrated on the top curvature
           print  trajectory  maintained  high  repeatability,  three
           repeated  corrected  printing  helix  trajectories  for  each   position for each helix, which indicates that the error
           helix were tested independently. Figure 10 illustrates the   value at the curvature position is higher than the error
                                                               at the other positions, and the highest error reaches
           error distribution state in three printings for each helix.   2.53 mm in the second helix calculated by Euclidean
           The value of the overall error in the low error range (light   norm (1) [36] .  The error level shows a decreasing
           blue) was less than 1.0 mm, while there was no high error   tendency  due  to  the  helix  trajectory  changes  from
           range  (dark blue) in the  three  printing  experiments  of   curve to straight, which dropped to the blue and light
           each helix.                                         blue middle error range. Furthermore, compared with
           4. Discussion                                       straight trajectory, relying on single-axis control, the
                                                               curved trajectory requires two axes to control the print
           Many studies have indicated that bioprinting resolution   head during the printing process, and the error level is
           is a crucial printing parameter. However, the number of   also higher than the straight trajectory because of the
           studies aiming to improve printing resolution, including   low accuracy of multiple axis motion.
           printing error detection  and correction, is still limited.   For the new printing helix trajectory resulting from
           Most  of  the  printing  helix  trajectories  contain  large   the modified reference trajectory, the errors are all located in

           180                         International Journal of Bioprinting (2022)–Volume 8, Issue 2
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