THE ROLE OF THE DEAD ZONE IN PREDICTIONS OF TRABECULAR BONE TOPOLOGY AND CONTINUUM LEVEL MECHANICAL PROPERTIES
Authors: Radukic Branimir , Phillips Andrew 
Published: November 2023

1.0 Objectives

Predictive structural models resulting in a trabecular bone topology closely resembling real bone would be a step toward 3D printing of sympathetic prosthetics. This study modifies an established trabecular bone structural adaptation approach, with the objective of achieving an improved adapted topology, specifically connectivity, compared to CT imaging studies; whilst retaining continuum level mechanical properties consistent with those reported in experimental studies. Strain driven structural adaptation models successfully identify trabecular trajectories, although tend to overpredict connectivity and skew trabecular radii distribution towards the smallest radius included in the adaptation. Radius adaptation of each trabecula is driven by a mechanostat approach with a target strain (1250 µɛ) below which radius is decreased (resorption), and above which radius is increased (apposition). Simulations include a lazy zone, in which neither resorption nor apposition takes place (1000 to 1500 µɛ); and a dead zone (<250 µɛ) in which complete resorption of trabeculae with the smallest included radius takes place. This study assesses the impact of increasing the dead zone threshold from <250 µɛ to <1000 µɛ, the lower limit of the lazy zone.

2.0 Methods

In-silico structural models with an initial connectivity (number of trabeculae connecting at each joint) of 14 were generated using a nearest neighbour approach applied to a random cloud of points. Trabeculae were modelled using circular beams whose radii were adapted in response to normal strains caused by the axial force and bending moments due to a vertical pressure of 1 MPa applied to the top of the lattice, with the bottom of the lattice fixed in the vertical direction. Lattices in which nodes are either able (rigid jointed) or unable (pin jointed) to transmit bending moments were considered. Five virtual samples of each lattice type were used, and each simulation repeated twice: with a dead zone of either <250 µɛ or <1000 µɛ.

3.0 Results

In pin jointed lattices the increase in dead zone threshold resulted in reduction of predicted Young's Modulus from 580 MPa (95% CI [577 MPa, 583 MPa]) to 408 MPa (95% CI [397 MPa, 419 MPa]) whilst in rigid jointed lattices it increased form 839MPa (95% CI [832 MPa, 846 MPa]) to 933 MPa (95% CI [931 MPa, 936 MPa]). Mean connectivity decreased from 10.2 to 5.8 in pin jointed simulations and from 9.6 to 3.8 in fixed joined simulations. Topological studies of trabecular bone CT images report a mean connectivity of around 3.4. Pin jointed lattice mean radius increased from 33mm to 45mm, and rigid jointed lattice mean radius increased from 33mm to 64mm. Prevalence of smallest included radius beams decreased in both.

4.0 Conclusion

Improved in-silico representations of trabecular bone can be achieved in structural adaptions by increasing the dead zone threshold and adopting a bending dominated (rigid jointed) lattice structure.

Declaration of Interest

(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.