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Biomechanical Study of Different Plate Configurations for Distal Humerus Osteosynthesis

Authors:

M. Bogataj1, F. Kosel1, R. Norris2, M. Krkovic3, M. Brojan1,*

  1. Laboratory for Nonlinear Mechanics, Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000, Ljubljana, Slovenia.
  2. University Hospitals Coventry and Warwickshire, Clifford Bridge Road, Coventry, CV2 2DX
  3. Consultant Orthopaedic Trauma Surgeon, Addenbrookes Hospital, Cambridge University Hospitals, NHS Foundation Trust, Cambridge Biomedical Campus, Hills Road, Cambridge, CB2 0QQ, UK.

* Corresponding Author

Miha Brojan,

e-mail:

phone: +386 1 4771 604

Fig. S1.Cortical bone thickness in humerus of a 45 years old male patient was measured in Mimics 10.01 from the CT images (blue line). For the purposes of our study humerus was divided into three parts along the length, in which the thickness was approximated (red line) by a constant along the epiphysis (2.5 mm) and the diaphysis (6.5 mm) and a linear function in-between.This enabled us to model the cortical bone simply with an offset from the outer surface of the point cloud in each of the three parts.

Fig. S2. CAD models of bone plates (units in mm). Plating system was “normalized”, so that all plates have the same cross section (4x10 mm) at the fracture site, the same material properties and the same configuration of screws (there is a difference in the most proximal screw position, between medial and lateral plates where crossing of screws in the bone had to be avoided). Such “normalization” of plates eliminated the differences between designs from different manufacturers and enabled us to investigate the plate configuration effect on the system response alone.

Fig. S3.Density of trabecular bone was measured in Mimics 10.01. Young's modulus was calculated using thefollowing expression:Etr = 2915 03. Elastic modulus Etrvaried from 0 to 1000 MPa (blue line). Sensitivity test showed (see the material below) that the mechanical properties of trabecular bone have limited effect on the results of our study. For the sake of simplicity, the trabecular bone was modeled as a solid and further approximated to be constant Etr = 500 MPa (red line).

Table S1. Sensitivity analysisresults: Influence of trabecular bone Young's modulus on global displacements results.

# of elements / Young's modulus
cortical bone / trabecular bone / sum / Cortical bone [GPa] / Trabecular bone [Mpa] / Max displacement [mm]
1 / 307675 / 0 / 307675 / 20 / 0 / 2,037 / <- Max value
2 / 307675 / 57058 / 364733 / 20 / 250 / 2,035
3 / 307675 / 57058 / 364733 / 20 / 500 / 2,033
4 / 307675 / 57058 / 364733 / 20 / 750 / 2,032
5 / 307675 / 57058 / 364733 / 20 / 1000 / 2,031 / <- Min value

Fig. S4.Sensitivity analysis of the Young's modulus in trabecular bone was performed. We varied Etr between 0 MPa (trabecular bone removed from the model = bone is hollow, only cortical shell) and 1000 MPa (maximumvaluemeasured). We subjected the bone to one of the load cases during flexion and maximum bone displacement was recorded. Results showed that the difference in maximum recorded bone displacement using Etr = 0 and Etr = 1000 MPa, was well within 0.5 %. Sensitivity test thus shows that trabecular bone properties have little (practically negligible) effect on the results of our study. Complete removal of the trabecular bone from the model would result in even more decreased computing times. However, trabecular bone could not be removed entirely because of the need of contact surfaces (i.e. contact surfaces between the bone and screw, fragments,...).

Fig. S5. In the sensitivity analysis humerus was subjected to one of the loading cases during flexion. Maximum bone displacement was recorded. Figure shows displacement state of a loaded humerus (coloured) and humerus in initial/unloaded state (shadowed). Note that displacement is scaled for easier representation.

Fig. S6. Mesh convergence test was performed on simplified geometry, including only the cortical part of the bone. Quadratic tetrahedral elements C3D10 give better results within coarse mesh, whereas linear tetrahedral elements C3D4 require finer mesh for good results.