# Hole in One: an element reduction approach to modeling bone porosity in finite element analysis

- Published
- Accepted

- Subject Areas
- Computational Biology, Evolutionary Studies, Paleontology
- Keywords
- biomechanics, finite element analysis, functional morphology, bone modeling, material properties, porous structures, trabecular bone

- Copyright
- © 2019 Santaella et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.

- Cite this article
- 2019. Hole in One: an element reduction approach to modeling bone porosity in finite element analysis. PeerJ Preprints 7:e27909v1 https://doi.org/10.7287/peerj.preprints.27909v1

## Abstract

Finite element analysis has been an increasingly widely used tool in many different science and engineering fields over the last decade. In the biological sciences, there are many examples of its use in areas as paleontology and functional morphology. Despite this common use, the modeling of porous structures such as trabecular bone remains a key issue because of the difficulty of meshing such highly complex geometries during the modeling process. A common practice is to mathematically adjust the boundary conditions (i.e. model material properties) of whole or portions of models that represent trabecular bone. In this study we aimed to demonstrate that a physical, element reduction approach constitutes a valid protocol to this problem in addition to the mathematical approach. We tested a new element reduction modeling script on five exemplar trabecular geometry models of carnivoran temporomandibular joints, and compared stress results of both physical and mathematical approaches to trabecular modeling to models incorporating actual trabecular geometry. Simulation results indicate that that the physical, element reduction approach generally outperformed the mathematical approach. Physical changes in the internal structure of experimental cylindrical models had a major influence on the recorded stress values throughout the model, and more closely approximates values obtained in models containing actual trabecular geometry than solid models with modified trabecular material properties. Therefore, we conclude that for modeling trabecular bone in finite element simulations, maintaining or mimicking the internal porosity of a trabecular structure is recommended as a fast and effective method in place of, or alongside, modification of material property parameters to better approximate trabecular bone behavior observed in models containing actual trabecular geometry.

## Author Comment

This is a submission to PeerJ for review.

## Supplemental Information

### Scan numbers and filled volume of the CC

The high-resolution CT-scans were obtained with the GE v|tome|x s scanner at the American Museum of Natural History (AMNH).

### Code performance consistency

1 to 10 points refer to the sampled points. Being 1 at the top area of the cylinder and 10 at the bottom. I to V refer to the five coded modified cylinders. Beneath those values, we present some statistical information (Mean: average; Stdev: standard deviation; Sterr: standard error of the mean; 95% CI: Confident Interval at 95 percent).

### von Mises stress values and statistical analysis

1 to 10 points refers to the sampled points. Being 1 at the top area of the cylinder and 10 at the bottom. T1 to T4 refers to each transect (left column stress in MPa; right column node number). The final four columns present some statistical information (Mean: average; Stdev: standard deviation; Sterr: standard error of the mean; 95% CI: Confident Interval at 95 percent).

### von Mises stress values and statistical analysis

1 to 10 points refers to the sampled points. Being 1 at the top area of the cylinder and 10 at the bottom. T1 to T4 refers to each transect (left column stress in MPa; right column node number). The final four columns present some statistical information (Mean: average; Stdev: standard deviation; Sterr: standard error of the mean; 95% CI: Confident Interval at 95 percent).

### von Mises stress values and statistical analysis

1 to 10 points refers to the sampled points. Being 1 at the top area of the cylinder and 10 at the bottom. T1 to T4 refers to each transect (left column stress in MPa; right column node number). The final four columns present some statistical information (Mean: average; Stdev: standard deviation; Sterr: standard error of the mean; 95% CI: Confident Interval at 95 percent).