ARTICLE IN PRESS JID: JJBE [m5G;March 15, 2018;9:19] Medical Engineering and Physics 000 (2018) 1–8 Contents lists available at ScienceDirect Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model Ifaz T Haider, John Goldak, Hanspeter Frei ∗ Department of Mechanical and Aerospace Engineering, Carleton University, 3135 Mackenzie Building 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada a r t i c l e i n f o Article history: Received 7 March 2017 Revised 21 November 2017 Accepted 25 February 2018 Available online xxx Keywords: Femoral fracture Finite element analysis Physiological loading Quasi-brittle damage a b s t r a c t Nonlinear finite element (FE) modeling can be a powerful tool for studying femoral fracture. However, there remains little consensus in the literature regarding the choice of material model and failure crite- rion. Quasi-brittle models recently have been used with some success, but spurious mesh sensitivity re- mains a concern. The purpose of this study was to implement and validate a new model using a custom finite element designed to mitigate mesh sensitivity problems. Six specimen-specific FE models of the proximal femur were generated from quantitative tomographic (qCT) scans of cadaveric specimens. Ma- terial properties were assigned a-priori based on average qCT intensities at element locations. Specimens were experimentally tested to failure in a stumbling load configuration, and the results were compared to FE model predictions. There was a strong linear relationship between FE predicted and experimentally measured fracture load (R 2 = 0.79), and error was less than 14% over all cases. In all six specimens, sur- face damage was observed at sites predicted by the FE model. Comparison of qCT scans before and after experimental failure showed damage to underlying trabecular bone, also consistent with FE predictions. In summary, the model accurately predicted fracture load and pattern, and may be a powerful tool in future studies. © 2018 IPEM. Published by Elsevier Ltd. All rights reserved. 1. Introduction Osteoporosis is a significant source of morbidity and mortal- ity, particularly among the elderly [1,2]. To develop effective in- tervention strategies for the prevention of osteoporotic fractures, it is necessary to identify individuals who are most at risk. This can be challenging, as the likelihood of suffering a fracture is de- pendent on a number of factors including bone strength, the likeli- hood of suffering a fall, and the severity of the fall. Finite element (FE) modeling can be a powerful tool to help further understand some of these factors. Linear FE models are computationally inexpensive, and com- monly used [3–6]. Linear models treat bone as a linear elastic solid, and failure is assumed to occur after a certain number of elements exceed the selected failure criterion. These models are able to ac- curately predict strains at low loads [7], and achieve strong correla- tions between FE predicted and experimentally determined failure load (R 2 > 0.77). Despite the strength of correlation, however, error magnitudes can remain quite large; some studies show that indi- vidual specimens have differences of up to 45% between predicted ∗ Corresponding author. E-mail addresses: ihaider@connect.carleton.ca (I.T. Haider), jgoldak@mrco2.carleton.ca (J. Goldak), hanspeter.frei@carleton.ca (H. Frei). and experimentally measured fracture loads [4,6]. To achieve bet- ter results, some FE studies incorporate nonlinear material proper- ties. In these studies, bone elements behave linear-elastically until a failure a condition is met, at which point the element’s proper- ties are degraded, i.e., the stiffness and/or stress in the element is adjusted to account for localized failure of the bone material [8–11]. However, there is currently little consensus regarding the best material model and failure criterion to use for modeling fail- ure of the proximal femur. Some very recent studies [12,13] have had success using a quasi-brittle damage model, where stiffness of elements degrades gradually as strain increases, and the crack is modeled as the re- gion of elements whose stiffness has been reduced to near zero. While the technique is powerful, there are important challenges that need to be addressed. FE models that include strain softening behavior have well documented issues with spurious mesh sensi- tivity [14,15]. The size of the damaged region corresponds to the size of the mesh used to solve the problem. As the mesh is refined, the size of the damaged region, and thus the energy dissipated, shrinks. This is a physically inadmissible result; the energy dissi- pated by crack formation is a property of the material and should not be dependent on mesh size [14,15]. To remedy this issue, some authors have proposed using a non- local constitutive model. For example, damage evolution can be driven by a weighted spatial averaging of strains near a point, https://doi.org/10.1016/j.medengphy.2018.02.008 1350-4533/© 2018 IPEM. Published by Elsevier Ltd. All rights reserved. Please cite this article as: I.T. Haider et al., Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model, Medical Engineering and Physics (2018), https://doi.org/10.1016/j.medengphy.2018.02.008