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International Journal of Bioprinting                               Nozzle geometry for enhanced cell viability




            fitting a modified expression for cell damage under shear   in modulating mechanical stresses that affect cells.
            and extensional stresses. These expressions consider an   Optimizing these parameters can minimize extensional
            exponential dependence on Ca , Ca , and τ : s      stress, thereby improving post-printing viability.
                                    e
                                        s
                                                                  The findings indicate that extensional stress, rather
                                     b c
                           D 1  e  aCa s s         (XI)    than shear stress, is a primary cause of cell damage,
                            s
                                                               particularly in the contraction region of the nozzle. Based
                                                               on the results, it is recommended that nozzle designs with
                                                               intermediate θ (30–60°) be used to balance extensional and
                           D 1  e  dCa e e         (XII)    shear stresses, thus optimizing cell viability. Furthermore,
                             e
                                                               reducing capillary length and  d  can decrease exposure
                                                                                         2
                                                               time to mechanical stress, thereby improving cell survival.
               where a, b, c, d, and e are fitting parameters determined   These parameters should be prioritized when designing
            by fitting Equations XI and XII to all experimental data.  nozzles for sensitive or high-density cell bioinks.
               As illustrated in Figure 7B, an increase in Ca  resulted   The  proposed  model helps  to understand the
                                                   e
            in a higher D  for a given τ . This is consistent with the   relationship between nozzle geometry and stress-induced
                       t
                                   s
            understanding that higher values of  Ca   correspond to   cellular damage, offering another perspective that can
                                             e
            greater cell deformation in extensional flows, leading to   guide future nozzle designs to improve bioprinting results.
            increased cell damage. The color gradient representing τ   s  From an application standpoint, engineering customized
            further highlights that lower residence times are associated   nozzles with optimized geometries holds great promise
            with reduced fractions of damaged cells.           for enhancing bioprinting outcomes, ultimately advancing
               In  Figure 7A, the effect of increasing  τ   is apparent,   regenerative medicine and tissue engineering. The findings
                                               s
            with transitions between nearly parallel planes in the   from this study provide critical insights that can inform
            parameter space of Ca , Ca , and τ . Conversely, the impact   the design of next-generation bioprinters capable of
                                       s
                                 s
                             e
            of shear stress was significantly less pronounced, as shown   producing high-fidelity, cell-rich constructs with enhanced
            in Figure 7C. The data reveal a weak dependence of D  on   biological functionality.
                                                       t
            Ca  for a given τ . However, an increase in τ  still leads to   In conclusion, this study highlights the crucial role of
                                               s
                         s
              s
            a notable increase in cell damage. This weak correlation   nozzle design in bioprinting. By systematically refining
            between D  and Ca  can explain the observed behavior of   nozzle geometry, it can reduce mechanical stress, enhance
                    t
                           s
            D  with varying d , as seen in Figure 5. A reduction in d    cell viability, and improve the overall quality of bioprinted
                          2
             t
                                                          2
            increases Ca  and, consequently, the shear stress. However,   tissues, bringing bioprinting closer to clinical applications
                      s
            this increase in shear stress is relatively ineffective in   in regenerative medicine. With the rise of innovative
            deforming  and  damaging  cells,  as  shown in  Figure  7C.   bioprinting techniques—such  as printing within a  self-
            Simultaneously, a decrease in d  reduces the residence time   healing support bath that can be subsequently washed
                                    2
            in the capillary, thereby limiting the exposure of cells to   away to enable the fabrication of complex structures—it
            shear stress and ultimately reducing cell damage.
                                                               would be highly beneficial to develop long needles capable
               The  non-linear  dependence  of cell  deformability  on   of penetrating deeply into the support material. Long
            Ca , Ca , and τ  is highly influenced by the specific response   needles—whose extended capillary length could increase
              e
                  s
                       s
            of cells to these flow conditions, making accurate modeling   cell exposure to mechanical stress—are increasingly
            challenging. The introduction of fitting parameters helps   necessary for support-bath-based printing strategies.
            address this complexity. Notably, the greater effectiveness   The current findings on the role of needle length offer a
            of extensional flows in deforming particles compared to   valuable starting point for optimizing such designs.
            shear  flows  has  been  previously  highlighted  by  Grace,
                                                         19
            also emphasizing the importance of exposure time to shear   Acknowledgments
            conditions in determining particle deformation.
                                                               None.
            4. Conclusion                                      Funding
            This study comprehensively examines the influence of
            nozzle design on cell viability in extrusion-based 3D   None.
            bioprinting. Through experimental observations and   Conflict of interest
            theoretical  modeling,  it is  demonstrated that  nozzle
            geometry—particularly  θ and  d —plays a critical role   The authors declare they have no competing interests.
                                       2
            Volume 11 Issue 4 (2025)                       325                            doi: 10.36922/IJB025190182
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