Micromechanical modeling of calcifying human costal cartilage using the generalized method of cells Anthony G. Lau a,⇑ , Matthew W. Kindig b , Rob S. Salzar b , Richard W. Kent b a Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA b Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, USA article info Article history: Received 22 August 2014 Received in revised form 10 February 2015 Accepted 13 February 2015 Available online 21 February 2015 Keywords: Micromechanical modeling Calcifying cartilage Generalized method of cells Effective modulus abstract Various tissues in the human body, including cartilage, are known to calcify with aging. There currently is no material model that accounts for the calcification in the costal cartilage, which could affect the overall structural response of the rib cage, and thus change the mechanisms and resistance to injury. The goal of this study is to investigate, through the development of a calcifying cartilage model, whether the calcification morphologies present in the costal cartilage change its effective material properties. A calcified cartilage material model was developed using the morphologies of calcifications obtained from microCT and the relaxed elastic modulus of the human costal cartilage obtained from indentation testing. The homogenized model of calcifying cartilage found that calcifications alter the effective material behavior of the cartilage, and this effect is highly dependent on the microstructural connectivity of the calcification. Calcifications which are not contiguous with the rib bone and constitute 0–18% of the cartilage volume increase the effective elastic modulus from its baseline value of 5 MPa to up to 8 MPa. Calcifications which are attached to the rib bone, which typically constitute 18–25% of the cartilage volume, result in effective moduli of 20–66 MPa, depending on the microstructure, and introduce marked anisotropy into the material. The calcifying cartilage model developed in this study can be incorporated into biomechanical models of the aging thorax to better understand how calcifications in the aging thorax affect the structural response of the rib cage. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 1. Introduction Throughout a lifetime, soft tissues of the human body exhibit forms of calcification or ossification. Skeletal development is the major period of endochondral ossification, where a cartilage model is turned into bone [1–3]. Other biological soft tissues can calcify and in certain cases this can result in pathological conditions. Cal- cification of biological tissues can alter their material properties thus their physiological behavior. Regions of the human body that are known to calcify include: vertebral disks, ligaments, aorta, heart valves, articular cartilage, and costal cartilage [4–10]. The degree of calcification in the costal cartilage is known to increase with age [11–13]. The costal cartilages link the sternum to the ribs and thus serve an important structural role within the thoracic cage during respiration [14]. Calcifications of the costal cartilage, along with other physiological thoracic changes associat- ed with aging (e.g. osteoporosis of the ribs), also alter the mechan- ical response of the thorax under external loading such as restraining forces during an automotive crash [15]. Older drivers are more prone to sustain chest injuries in automotive crashes [16] and are more likely to die from chest injuries [17]. Rib cage mechanics likely play a role in both of these negative outcomes. Because the aging thorax is also a calcifying thorax, it is important to know the material properties of the calcifying costal cartilage, which in turn, allows for a better understanding of the aging thorax during respiration, under external loading, and following injury. The material properties of the costal cartilage have been studied at the micrometer [18] and nanometer [19] length scales, and at the whole-structure level during calcification up to 24% volume fraction [20,21]. However, no studies have quantified how the specific morphologies and connectivity of calcifications [10] alter the effective modulus of the costal cartilage at the millimeter length scale—the scale at which typical finite elements of the entire thorax are developed. Micromechanical analysis, in particular, the method of cells, was developed in the composites field to predict the effective behavior of a multi-phased material when the material properties http://dx.doi.org/10.1016/j.actbio.2015.02.012 1742-7061/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: National Space Biomedical Research Institute: First Award Postdoctoral Fellow, University of North Carolina – Chapel Hill, Department of Biomedical Engineering, USA. Tel.: +1 919 966 4276. E-mail address: ALau@unc.edu (A.G. Lau). Acta Biomaterialia 18 (2015) 226–235 Contents lists available at ScienceDirect Acta Biomaterialia journal homepage: www.elsevier.com/locate/actabiomat