Influence of bone microstructure on the mechanical properties of skull cortical bone – A combined experimental and computational approach

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Abstract

The strength and compliance of the dense cortical layers of the human skull have been examined since the beginning of the 20th century with the wide range in the observed mechanical properties attributed to natural biological variance. Since this variance may be explained by the difference in structural arrangement of bone tissue, micro-computed tomography (µCT) was used in conjunction with mechanical testing to study the relationship between the microstructure of human skull cortical coupons and their mechanical response.

Ninety-seven bone samples were machined from the cortical tables of the calvaria of ten fresh post mortem human surrogates and tested in dynamic tension until failure. A linear response between stress and strain was observed until close to failure, which occurred at 0.6% strain on average. The effective modulus of elasticity for the coupons was 12.01 ± 3.28 GPa. Porosity of the test specimens, determined from µCT, could explain only 51% of the variation of their effective elastic modulus. Finite element (FE) models of the tested specimens built from µCT images indicated that modeling the microstructural arrangement of the bone, in addition to the porosity, led to a marginal improvement of the coefficient of determination to 54%. Modulus for skull cortical bone for an element size of 50 µm was estimated to be 19 GPa at an average. Unlike the load bearing bones of the body, almost half of the variance in the mechanical properties of cortical bone from the skull may be attributed to differences at the sub-osteon (< 50 µm) level. ANOVA tests indicated that effective failure stress and strain varied significantly between the frontal and parietal bones, while the bone phase modulus was different for the superior and inferior aspects of the calvarium. The micro FE models did not indicate any anisotropy attributable to the pores observable under µCT.

Introduction

In the last decade traumatic brain injury (TBI) has emerged as a major problem in the United States military, so much so that it has been called the signature wound of war (Snell and Halter, 2010). The etiology of this injury is still unclear, however a vast majority of these cases are closed head injuries where brain damage occurs without any fracture of skull bone (Fischer, 2010). FE models of the head are already playing a big role in the research of TBI and researchers have shown that skull bending may be as important as direct transmission of compressive stress waves in the context of blast brain injury (Moss et al., 2009). The human calvarium has a sandwich structure and it exhibits stiffer bending compared to its through-the-thickness deformation. To accurately model both bending and through-the-thickness deformation mode, it is essential to separate the different layers of the calvarium and use correct sub-failure mechanical properties for the three layers of the calvarium.

Historically the problem of head injury has been approached by various researchers using impact experiments conducted on the whole human head or skull (Nahum et al., 1968, Hodgson et al., 1970, Got et al., 1978). Since these studies related kinematic indicators such as velocity and acceleration to head injury, a physical model of the head was required for the assessment of the risk of head injury as a result of mechanical insult. Materials for construction of this physical model were selected by studying the mechanical response of the various components of the head, including the skull. Apart from this, these studies provided data for development of computational models of the head which can be used to study the response of the head to any mechanical input.

The first comprehensive study of tensile and compressive failure properties of cortical bone from the skull was published in Evans and Lissner (1957). More than a decade later, the mechanical stiffness at quasi-static and dynamic rates was reported by Robbins and Wood (1969) and Wood (1971) respectively. Wood had studied 120 skull cortical bone specimens from thirty subjects at various rates of loading. Although a large sample was tested, no objective distinction of the different layers of the calvarium was done. Moreover, material inhomogeneity within the skull cortical bone samples was not addressed in any of these studies. Therefore, it is unknown to what extent the mechanical properties found in these studies are representative of the cortical layer of the human calvarium.

Properties of cortical bone have also been derived from composite skull bone bending tests (Hubbard, 1971, Delille et al., 2007, Motherway et al., 2009, Auperrin et al., 2014, Rahmoun et al., 2014). Inhomogeneity and porosity in the material used in a composite skull bending study was accounted for using a three-layer model by Hubbard (1971) and the layer thicknesses were calibrated through visual inspection. Delille et al. (2007) and Auperrin et al. (2014) have used mineral (ash) percentage to calibrate the thicknesses of hollow beam models of samples from the calvarium in their bending study. Microstructure from micro-radiology was used in conjunction with bending tests only recently by Motherway et al. (2009). However, in all these cases, curvature of the skull was ignored and a simplified straight beam model was assumed. Ultrasound transmission was used by (Peterson and Dechow, 2002) to estimate the Young's modulus of human skull cortical bone.

Pores in the human calvarium cannot be resolved using clinical computed tomography, but they can be discerned using micro computed tomography (µCT). In the only studies of the mechanical properties of skull cortical bone where µCT was used (Motherway et al., 2009, Rahmoun et al., 2014), it was assumed, despite evidence to the contrary (Rho et al., 1997, Zysset et al., 1999), that the bone in the cortical layers and the cancellous diploe layer had equal modulus. It is also unknown if the mechanical properties vary with location on the skull.

There are many papers in the literature which investigate the mechanical properties of cortical bone obtained from the long bones of the human body, and several of them have analysed the effect of porosity in the microstructure (McCalden et al., 1993, Rho et al., 1993, Wang et al., 2002, Zioupos and Currey, 1998). Unlike coupons harvested from the skull, these samples are composed of continuous bone consisting of cemented osteons and they do not have pores except the haversian canal system. The structures inside the osteons have been examined under microscopy using staining techniques. Wang et al. (2002) have described the relationship of mechanical properties with mineralization and collagen cross-link density, which are nano scale phenomena. These topics are combined under bone material quality research, particularly in the context of fragility and aging. Due to the thinness of the cortical layers in the skull, it is difficult to obtain samples that do not have interstitial pores in the osteon matrix.

Arrangement of osteons in cortical bone may lend anisotropy to its macroscopic mechanical behavior, making it stiffer under deformation along the grain as compared to the transverse directions. Dempster (1967) concluded that on the surface of the skull vault, away from the forehead and internal sagittal markings, osteonal grain patterns were randomly oriented. This observation concurs with all research about the mechanical response of skull cortical bone: although osteonal bone is inherently anisotropic, because of the randomly oriented osteons, the macroscopic mechanical response of the cortical layers of the skull may be considered to be transversely isotropic about the axis perpendicular to the surface.

Finite element (FE) models of the head typically use a single isotropic material for the entire skull thickness. These models cannot simultaneously exhibit the stiffened bending response and softer through-the-thickness deformation response that is characteristic of the skull sandwich structure. Models that do include multiple materials (Horgan and Gilchrist, 2003, Panzer et al., 2012, Asgharpour et al., 2014) use a fixed ratio of thicknesses of the three layers of the skull using material properties taken from mechanical testing of cortical tensile coupons. Because of the lack of objective delineation of the three layers of the calvarium, it is not certain if the material properties used for the different layers actually represent the material in those layers. In a bid to match the bending response, these models exhibit increased stiffness under through-the-thickness deformation (Boruah et al., 2013).

The objective of this study was to examine the Young's modulus of cortical bone from the skull, specifically the calvarium, at a sub-osteon element size (50 µm), under the assumption that the bone behaves in an isotropic fashion at this length scale. Despite this assumption, at the macroscopic scale, the porous bone samples may behave in an anisotropic fashion depending on the existence of any directionality in the bone scaffold. A three-step approach was designed. First, tensile coupons were harvested from the outer cortical layer of the calvarium and imaged using µCT to analyze the bone micro-structure. Second, the coupons were tested under dynamic tension. Third, coupon specific FE models were developed to account for the micro-structural arrangement of osteons and to identify the mechanical properties of bone at a microscopic scale. Explosive blast events associated with conventional explosive devices typically last a few milliseconds (Moss et al., 2009, Panzer et al., 2012). The rate of tensile loading of the coupons was chosen to represent quasi-static rates compared to blast rates. The properties found using this approach will be suitable for application to a head FE model which uses layer thicknesses of the calvarium that were determined using µCT (Boruah et al., 2015).

In addition to the assessment of influence of microstructure on the mechanical properties of the cortical layers of the calvarium, the statistical difference in these properties between subjects and between the frontal and parietal bones and between the superior and inferior aspects of the calvarium within subjects was also determined.

Section snippets

Materials and methods

Cortical coupon samples were obtained from the outer cortical tables of ten adult male post-mortem human surrogates (PMHS), with an upper age limit of 70 years (Table 1). All test subjects were frozen post-mortem and thawed for use. Torimitsu et al. (2014) found that freezing-thawing cycles have no significant effect on the mechanical properties of bone. All subjects were screened for hepatitis A, B, C, and HIV and for pre-existing pathology that may influence bone properties, such as trauma

Results

The results for 97 successfully tested calvarium coupon samples are presented here. Eighteen coupons were damaged during mounting on the test setup.

A few coupons before and after testing are shown in Fig. 6a and b. The strain field was measured on both coupon surfaces (Fig. 6c and d). Typically engineering stress varied linearly with engineering strain (Fig. 7), and the effective linear elastic modulus of the coupon was estimated from linear regression of stress vs. strain data within 20% to

Discussion

It is known that biomaterials undergo elastic as well as plastic deformation when they are quasi-statically loaded. Consequently, their elastic modulus can only be assessed upon unloading the specimen (Luczynski et al., 2013). Plastic effects have been found to be dependent on the stress level and strain-rate. Permanent plastic deformation of bone from the human femur was found to occur at stress greater than 80 MPa (Fondrk et al., 1988). Zioupos et al. (2008) found that plastic behavior was

Conclusions

  • 1.

    Effective mechanical properties including failure characteristics of outer cortical layer of the adult human calvarium under tension in the tangential direction were reported (Table 3).

  • 2.

    Bone phase modulus was calculated using both empirical correlation between effective modulus and BVF, and micro FE models of coupons (Table 4).

  • 3.

    Small improvement in predictability from micro FE models compared to the BVF based power law model may indicate lack of consistent directionality in osteonal grain pattern.

Acknowledgement

This research was sponsored by contract no. N00421-11-C-0004 from the U.S. Naval Air Warfare Center, Aircraft Division, Patuxent River, MD.

References (38)

  • C.H. Turner

    On Wolff's law of trabecular architecture

    J. Biomech.

    (1992)
  • X. Wang et al.

    Age-related changes in the collagen network and toughness of bone

    Bone

    (2002)
  • J.L. Wood

    Dynamic response of human cranial bone

    J. Biomech.

    (1971)
  • P. Zioupos et al.

    Changes in the stiffness, strength, and toughness of human cortical bone with age

    Bone

    (1998)
  • P. Zioupos et al.

    Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure

    J. Biomech.

    (2008)
  • P.K. Zysset et al.

    Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur

    J. Biomech.

    (1999)
  • A. Ascenzi et al.

    The tensile properties of single osteons

    Anat. Rec.

    (1967)
  • Boruah, S., Henderson, K., Subit, D.L., Salzar, R.S., Shender, B.S., Paskoff, G.R., 2013. Response of human skull bone...
  • R. Delille et al.

    Experimental study of the bone behaviour of the human skull bone for the development of a physical head model

    Int. J. Crashworth.

    (2007)
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    This work was done at Center for Applied Biomechanics, Department of Mechanical and Aerospace Engineering, University of Virginia, 4040 Lewis & Clark Drive, Charlottesville, VA 22911, USA.

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