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Topology Optimized Locking Compression Plates to Minimize Stress Shielding
Table 5. Equivalent stiffness of optimized plate designs considering In addition, the optimized bone plates produced
torsion loading conditions. using TO present complex features which are impossible
Volume Equivalent stiffness (Nmm/Rad) to manufacture using conventional manufacturing but
[28]
reduction % Plate with Plate with Plate with possible through additive manufacturing . Researchers
4 holes 6 holes 8 holes previously reported the successful combination of TO,
Initial design 28550±602 26170±1336 24792±562 electron beam melting, and selective laser melting,
considering different conditions (i.e. low mesh density) ,
[29]
25 23550±496 24574±1258 15737±357 and similar conclusions were also obtained by other
45 15767±333 17539±898 13348±302 researchers .
[19]
75 3653±77 6932±355 7304±166
5. Conclusion
Table 6. Equivalent stiffness of optimized plate designs considering Stress shielding is a common problem in standard bone
combined loading conditions fixation plates, requiring new tools to redesign them and
Volume Equivalent stiffness (kN/mm) new fabrication methods to produce them. This paper,
reduction % Plate with Plate with Plate with extending previously reported results considering 3D
4 holes 6 holes 8 holes plates, shows that TO is a suitable tool to redesign bone
fixation plates with different geometries, considering
Initial design 306±6.45 247±12.65 237±5.38 different loading conditions and volume reduction,
25 237±5.00 214±10.96 145±3.29 allowing to obtain plates with reduced equivalent stiffness
45 158±3.33 101±5.17 123±2.79 that matches the mechanical properties of native bone in
75 22±0.46 20±1.02 28±0.63 case of eight-hole plate, and considering bending load and
75% volume reduction. A trend between volume reduction
significant findings of the possibility of optimizing the and equivalent stiffness was observed. A significant
bone plate’s stiffness considering physiological loads stiffness reduction was achieved for high volume
by reducing the design’s material volume. In addition, a reductions, preventing stress shielding and potentially
significant reduction of the stiffness is a major indication avoiding bone resorption and eventual plate failure.
of reduced risk of the stress shielding (i.e., bone loss), Previously reported results showed the ability of
thus promoting callus formation and bone formation [22-24] . topology-optimized fixation plates, obtained by different
Considering that the bone elastic bending modulus ranges conditions (i.e., low mesh density), to withstand stresses
between 9 to 15 GPa, the bending optimized plate with in a biomechanical setting. This study did not investigate
eight holes and 75% of volume reduction showed an the potential stress concentration regions resulting from
equivalent elastic bending modulus (11 GPa) within this the TO and the mechanical strength (yield stress) of the
region . This proves that using topology optimization optimized plates with high mesh density. Future studies
[25]
is possible to obtain designs that are able to match the must address this limitation by computationally assessing
mechanical properties of native bone and thus, and the optimized bone plate designs with high mesh density
eliminate the main cause to stress shielding. In addition, designs from a biomechanical perspective in a fractured
previous studies reported that using TO in designing bone configuration.
generic fixation plates and mandible fixation plates ,
[26]
[27]
which depends on the volume reduction and loading Acknowledgments
condition, is possible to reduce the plate’s stiffness while Researchers Supporting Project number (RSP-2021/299),
maintaining its mechanical stability to withstand stresses. King Saud University, Riyadh, Saudi Arabia.
Design symmetry is important when considering
design to manufacture and to eliminate the design Conflicts of interest
complexity for the surgeons during surgery. Symmetrical
designs were observed in the case of compression and The author declare no conflicts of interest.
torsion due to the considered symmetrical loading and References
boundary conditions. Bending optimized designs were
symmetrical in YZ plane but not in the XY plane due 1. Amin S, Achenback S, Atkinson E, et al., 2014, Trends in
to the bending load which compresses one side of the Fracture Incidence: A Population-based Study Over 20 Years.
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the designs were freely designed regardless of the
symmetry as the combination of compression, bending, https://doi.org/10.1002/jbmr.2072
and torsion loads result in asymmetric stress and strain 2. Kramer D, Xu S, Kesselheim A, 2012, Regulation of Medical
distributions. Devices in the United States and European Union. N Engl J

160 International Journal of Bioprinting (2021)–Volume 7, Issue 3