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Kolan, et al.
           Table 2. Scaffold porosity and pore size.

           Architecture        Designed versus apparent (%)              Measured average pore size (µm)
                             50       60        70       80         50          60          70          80
           Cubic            33±2     40±2      54±1     66±3      0.5±0.02    0.7±0.02    1.0±0.04    1.3±0.02
           Spherical        32±1     42±3      49±3     61±1      0.5±0.04    0.6±0.05    1.0±0.04    1.0±0.04
           X                28±2     35±3      43±2     55±0      0.5±0.03    0.6±0.02    0.7±0.03    1.2±0.10
           Diamond          34±2     40±1      47±1     61±1      0.8±0.01    0.9±0.01    1.0±0.04    1.2±0.05
           Gyroid           34±1     41±1      49±1     60±1      0.8±0.01    0.9±0.01    1.0±0.03    1.1±0.04

           between 0.5 and 1.3 mm. X architecture scaffolds    subtracted from the solid unit cube to obtain the
           had the smallest pores which are consistent with    unit  cell  of  spherical  architecture.  Figure  2A
           the  X  scaffolds  having  the  largest  difference   shows unit cells of spherical and cubic scaffolds
           between  the  designed  and  apparent  porosities.   and their pore shapes and pore sizes. Decreasing
           The difficulty in removing adhered powder from      sphere  diameter  to  lower  porosity  would  hinder
           the X scaffold pores of green bodies contributed    the removal of powder particles from the scaffold.
           to its lowest porosity and most reduced pore size.   Hence,  unit  cell  pores  were  designed  to  enable
           The average pore size of scaffolds designed with    fabrication and removal of powder particles. The
           80% porosity ranged from 0.9 mm to 1.3 mm, and      pore volume variation for cubic and spherical unit
           the scaffolds designed with 50% porosity ranged     cells is shown in Figure 2B.
           from 0.5 mm to 0.8 mm. In theory, unit cell pore
           size varies along the Z-height, with it being the   3.2  Effect  of  porosity  and  pore  geometry  on
           smallest at the end and the largest at the center of   mechanical strength
           the unit cell. Therefore, true scaffold pore size has   Compressive strengths of borate glass scaffolds
           a range of values instead of being a constant value.  with different porosities are shown in Figure 3A.
             Several  parameters  limit  the  accuracy
           of  fabricating  scaffolds,  including  scaffold    Among the five architectures investigated in this
           architecture, the resolution of the machine, layer   study, cubic scaffolds had the highest compressive
           thickness,  binder  content,  and  particle  size. The   strength (15.5 ± 1.9 MPa) and X scaffolds had the
           laser  spot  diameter  of  the  SLS  machine  was   lowest strength (4.9 ± 1.2 MPa) at low porosity
           0.45  mm  and  therefore,  it  was  not  feasible  to   (~35%). The biomimetic architectures (gyroid and
           fabricate  scaffolds  with  struts  smaller  than  this   diamond scaffolds) had compressive strengths of
           limit  (<0.45  mm).  The  laser  spot  could  have   9.5 ± 2.5 MPa and 6.8 ± 1.6 MPa, respectively.
           heated  and  melted  particles  adjacent  to  the   The  scaffold  compressive  strengths  at  low
           scanning  area,  effectively  reducing  the  designed   porosity were near the high end of the range of
           pore size. Smaller particles are easier to remove   compressive strength for human trabecular bone
           from  the  green  body  scaffold  pores,  causing   (~2 – ~12 MPa), whereas the strengths at high
           less  deviation  from  the  actual  design.  However,   porosity levels (>55%) were near the low end of
           smaller  particles  require  higher  binder  content   the spectrum [39] . Cubic architecture scaffolds have
           because of the increased surface area that could    pillars in the axial direction that carry a majority
           increase  the  shrinkage  and  deviations  between   of the load in compression tests before structural
           designed  and  fabricated  parts.  The  amount  of   failure,  while  the  other  architectures  lacked  a
           binder  and  the  particle  size  was  optimized  for   similar feature. X architecture scaffolds provided
           scaffold  fabrication  in  our  previous  work .    the  least  resistance  in  compression  because  of
                                                        [35]
           One  key  aspect  in  designing  the  architecture   the 45° oriented struts. The compressive strength
           was  considering  scaffold  manufacturability.      for  all  scaffold  types  was  ~4  MPa  or  less  at
           For  instance,  in  spherical  scaffolds,  porosity  is   high  porosities,  which  falls  at  the  lower  range
           a  function  of  the  diameter  of  the  sphere  that  is   of  the  trabecular  bone  compressive  strength [39] .

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