- Email: [email protected]
The mechanical and morphological properties of 6 year-old cranial bone
Journal of Biomechanics 45 (2012) 2493–2498
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The mechanical and morphological properties of 6 year-old cranial bone Matthew T. Davis, Andre M. Loyd, Han-yu Henry Shen, Maura H. Mulroy, Roger W. Nightingale n, Barry S. Myers, Cameron Dale Bass Department of Biomedical Engineering, Duke University, Box 90281, Durham, NC 27708-0281, United States
a r t i c l e i n f o
abstract
Article history: Accepted 6 July 2012
Traumatic Brain Injury (TBI) is a leading cause of mortality and morbidity for children in the United States. The unavailability of pediatric cadavers makes it difficult to study and characterize the mechanical behavior of the pediatric skull. Computer based finite element modeling could provide valuable insights, but the utility of these models depends upon the accuracy of cranial material property inputs. In this study, 47 samples from one six year-old human cranium were tested to failure via four point bending to study the effects of strain rate and the structure of skull bone on modulus of elasticity and failure properties for both cranial bone and suture. The results show that strain rate does not have a statistically meaningful effect on the mechanical properties of the six year-old skull over the range of strain rates studied (average low rate of 0.045 s 1, average medium rate of 0.44 s 1, and an average high rate of 2.2 s 1), but that these properties do depend on the growth patterns and morphology of the skull. The thickness of the bone was found to vary with structure. The bending stiffness (per unit width) for tri-layer bone (12.32 75.18 Nm2/m) was significantly higher than that of cortical bone and sutures (5.58 71.46 Nm2/m and 3.70 7 1.88 Nm2/m respectively). The modulus of elasticity was 9.87 7 1.24 GPa for cranial cortical bone and 1.10 7 0.53 GPa for sutures. The effective elastic modulus of tri-layer bone was 3.69 7 0.92 GPa. Accurate models of the pediatric skull should account for the differences amongst these three distinct tissues in the six year-old skull. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Bone Cranial bone Pediatric Biomechanics Strength Skull Mechanical properties Injury Structure
1. Introduction Traumatic brain injury (TBI) is the leading cause of death for the population under 24 years old, accounting for an estimated 30% of all accidental deaths (James, 1999; Schneier et al., 2006). Additionally, it is estimated that as many as 5.3 million people in the United States are currently living with a TBI-related long-term disability (Bushnik et al., 2003). Owing to the limited number of postmortem pediatric cadavers available (Prange et al., 2004), pediatric head biomechanics has not been investigated in congruity with its societal impact (Langlois et al., 2005). Computational finite element models (FEMs) are commonly used in place of direct mechanical investigations of pediatric head injury (Coats, 2007; Coats et al., 2007; Klinich et al., 2002; Margulies and Thibault, 2000). FEMs have been used in the analysis of child safety restraints, seatbelts, and airbags. Accurate predictions, however, require accurate material properties. Among the most critical material properties needed are those of cranial bone, such as elastic modulus and ultimate stress and
n
Corresponding author. Tel.: þ1 919 660 5451; fax: þ1 919 660 5362. E-mail address: [email protected].(R.W. Nightingale)
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.07.001
strain. These properties drive the overall mechanical response of the head including skull fracture and brain response. Other methods, including inverse finite element optimization, couples experimentally observed force–deflection curves with computational models to reverse engineer the material properties of a given material (Guan et al., 2011). The mechanical properties of adult bone have been obtained in the past using a variety of methods (Evans and Lissner, 1956; McElhaney et al., 1970; Roberts and Melvin, 1968; Wood, 1971). More recent efforts to publish data on pediatric specimens have focused on neonates and infants (Coats and Margulies, 2006; Margulies and Thibault, 2000; McPherson and Kriewall 1980a, 1980b). Margulies and Coats analyzed the properties’ dependence on strain rate, region, and age for a collection of specimen ranging from 21 weeks gestation to 13 months old. Baumer et al. reported properties obtained via four-point-bending of infant porcine parietal bone to propose a correlation to human tissue (Baumer et al., 2009; Coats and Margulies, 2006. These studies found that the constitutive properties of pediatric cranial bone are age sensitive but not strain rate dependent for the rates tested. Prior research on the adult, however, has shown that these mechanical properties vary weakly with strain rate for bone (Carter and Hayes, 1976; McElhaney, 1966; Wood, 1971). Unfortunately,
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no data has been published on rate dependency in calvaria in or near the six year-old cohort used in this study. Extensive cranial growth occurs between the ages of 13 months and 18 years, however, the effect that this growth has on the mechanical properties of the pediatric skull during this transitional period remains largely undocumented. Although Kriewall and McPherson published data on the elastic modulus of a six year-old skull (7.1 GPa, mean thickness of 3.33 mm) they did not discuss the structure of the bones tested (Kriewall et al., 1980). As periosteal tissues expand in response to the developing brain, the bones of the cranium move apart, straining the sutures and simultaneously creating space for and signaling for the growth of new bone. Thus, the primary direction of bone growth in the pediatric skull is toward the sutures (Cohen and Maclean, 2000; DuterLoo and Enlow, 2005). The bone also transitions from the single layered structure observed in early childhood to the trilayer bone present in adults, which is comprised of a cortical table on both the ecto- and endo-cranial surface separated by a porous trabecular layer. This occurs by the simultaneous deposition of new bone on both the ectocranial and endocranial surfaces and resorption of the inner layer (Cohen and Maclean, 2000). These two modes of growth, resulting in the non-uniform development of the pediatric skull, may create regional variation in mechanical properties (Fig. 1). The purpose of this paper is to study the mechanical properties of a six year-old skull to better understand how the child calvarium differs from that of both adults and neonates. One hypothesized difference is that modulus of elasticity and ultimate stress and strain of the cranial tissue will vary with region due to the growth pattern of the pediatric skull. Finally, it is also hypothesized that modulus and failure properties will not vary significantly with strain rate for the range of loading rates studied.
2. Methods 2.1. Specimen preparation A single six year-old female cadaver (COD: germ cell malignancy, Weight: 60l bs, Height: 40 600 Ethnicity: Caucasian) was obtained in compliance with federal, state, local and institutional regulations. The calvarium was removed and 71 samples were cut from the frontal and parietal regions of the skull using a
table mounted Dremel tool (Robert Bosch Tool Corporation, Mount Prospect, Illinois) with a 1/1600 grinding bit. The suture samples were harvested perpendicular to and across the suture lines, and the bone samples were taken from the parietal and frontal regions of the calvaria. The samples were cut so that their dimensions were 30–35 mm in length and 3–5 mm in width. The bone was moistened with a saline drip during the process. Each sample was then fixed into ABS plastic containers of rectangular geometry using polymethylmethacrylate (PMMA), leaving approximately 12 mm of bone exposed. Each of the bone samples was then wrapped in gauze soaked in saline (0.9% NaCl) to keep the bones moist throughout the testing process and stored separately in a refrigerator at 5 1C for 1– 3 days while testing was carried out. During this time each sample was scanned using micro-CT at 50 m resolution. 2.2. Testing procedure Bending tests were performed using a custom-built four-point-bending apparatus attached to a Bose ElectroForce 3200s linear actuator (Bose, Framingham, Massachusetts). The rig was designed to minimize friction by the use of steel roller pins mounted in ABEC-7 ball bearings as supports. Displacement control failure tests were run at three different displacement rates (4 mm/s, 40 mm/s, 400 mm/s). Because the relationship between displacement of the beam supports and the angle of beam deflection is non-linear, the corresponding average strain rates were approximately 0.045 s 1, 0.44 s 1, and 2.2 1, with some variation due to the variation in specimen size. The force during testing was recorded using a Honeywell Model-31 222.5 N load cell (Morristown, New Jersey). End brackets were lubricated with light machine oil and placed onto the stainless steel roller supports of the fourpoint-bending apparatus. High speed digital imaging data from a Phantom video camera (Vision Research, Inc., Wayne, NJ) was recorded for each failure test (2000 frames per second for low rate, 7700 frames per second for medium and high rate) and later used to determine the angle of displacement undergone by each specimen using TEMA tracking software (Photo-Sonics, Inc., Burbank, CA). 2.3. Analysis The geometry of the specimen was determined using the micro-CT scans taken before testing and photographs taken after failure. To avoid the uncertainties of stress-concentrations and other end-effects, we did not analyze any samples that broke in or near the PMMA-bone interface. The cross-sectional dimension of each bone was obtained by measurement of the smallest cross-sectional area of each specimen. Stress was estimated by assuming that the samples behave like solid beams of constant cross-section as:
s¼
ð1Þ
where M is the bending moment, y is the half-thickness of the sample at the location of failure, and I is the moment of inertia of the rectangular cross section (I ¼ bh3/12). Using the same assumptions, an estimate of the tensile strain on the outer surface of the bone was obtained by considering the radius of curvature of the sample in bending and from tracking the angle of rotation of the end pieces by the equation:
e¼
Fig. 1. An image of the cross-section of the intact skull showing the distribution of tri-layer and uni-layer bone. The oblique coronal view of the left and right parietal regions shown above indicates that the bone is thickest and most mature in the area surrounding the sagittal suture. The bone nearer the sides and the apexes are comprised of only cortical bone.
My I
2yF L
ð2Þ
where y is the same half-thickness measurement as the stress equation above, L is the original length of the beam exposed, and F is the angle of rotation of the end pieces (Fig. 2). The modulus of elasticity was obtained by a constrained minimization of the residuals of a Ramberg–Osgood piecewise linear and power law curve fit to the stress–strain data using a 0.2% offset as the cutoff for linearity. For the case of the sandwich structure specimens and the suture specimens we use the simplifying assumption that the bone has a homogeneous cross section to simplify the analysis and because we are interested in the bulk load response of the specimens. For this reason, the modulus of elasticity of these samples should be considered to be an effective modulus of a composite structure model of the tissue, and does not reflect the true modulus of any one constituent material of the bone. The bending stiffness is the product of this modulus of elasticity and the area moment inertia (EI) and used as a metric of bending stiffness. This was calculated for each specimen base on the effective elastic modulus and the microCT crosssection. Because the width of each specimen varied as a result of the harvesting procedure, the bending stiffnesses were normalized by the width and are thus reported in units of Nm2/m. The categorization of samples based on structure was performed using the micro-CT scans and Avizo imaging software (VSG, Burlington, MA). The crosssectional profiles of the beam were captured at the location of failure and the mean grayscale value in each pixel row within the bone was plotted against thickness. A local minimum in these plots indicated the presence of a porous layer or the beginnings of a resorptive process, and thus indicated that the bone was not
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suture specimens (3.7071.88 Nm2/m), but that the latter two are not significantly different from one another (p¼0.47) (Fig. 5). Lastly, because thickness was seen to co-vary with type, its contribution to mechanical properties was tested in a general linear regression for cortical, sandwich, and suture specimens, as well as the specimens in the transient region (Fig. 6, Supplementary material Table B). No statistically significant variation with thickness was observed for the mechanical properties of cortical, sandwich, or suture specimens. The modulus of elasticity of the transitional specimens, however, varied significantly with thickness (R2 ¼0.93, R2adj ¼0.90, p o0.01), and the ultimate stress of the same specimens, though not significant, showed a decreasing trend as well (R2 ¼0.43, R2adj ¼0.24, p¼0.23). All the suture specimens failed at the suture but remained physically connected on the compression side. The majority of the tri-layer and cortical bone specimens completely separated at failure. Furthermore, cortical bone specimens were found only in the left and right parietal regions near the parietal eminence of each plate. Fig. 2. Photographs showing the progression of a bending test from top to bottom. Parameters used in calculating the stress–strain relationship from the force– displacement data are overlain on the images.
4. Discussion 4.1. Mechanical properties and previous research
purely cortical in nature (Fig. 3). Minimum to maximum grayscale ratios were calculated for each specimen and cutoffs for the cortical group ( 485%) and the sandwich structure group (o55%) were determined based on inspection of the gross morphological features of the bone samples and the bimodal distribution of grayscale ratios. Those specimens that fell between 85 and 55% were classified as transitional. ANOVA with Tukey–Kramer means comparison testing was used to examine the effect of structure and loading rate on effective modulus, ultimate stress and ultimate strain. Linear regressions were used to examine the relationships between sample thickness and mechanical properties.
3. Results A total of 47 of the 71 specimens tested met the inclusion criteria. Of these, seven were comprised of only cortical bone, seventeen exhibited a layered cross-section of both cortical and trabecular bone, and eighteen included a closed suture. Five were determined to be in the transition stage from a one layered structure to a tri-layered structure and were thus not analyzed with either group. There was a significant relationship between thickness by bone structure (po0.01). Cortical-only specimens (1.88 mm70.16 mm) were significantly thinner than sandwich structure specimens (3.3870.45 mm, p o0.01) or suture specimens (3.60 70.71 mm, po 0.01), but sandwich and suture specimens were not significantly different from one another (p ¼0.49). For this reason, thickness and structural type were not included in the same ANOVAs. The effective modulus of elasticity was not affected by loading rate (p ¼0.71), but was significantly affected by structure (Fig. 4). The effective modulus of elasticity of cortical (9.8771.24 GPa), sandwich (3.69 70.92 GPa), and suture (1.1070.53 GPa) specimens were all different from one another (Fig. 4, all po0.01). The relationship between loading rate, structure, and ultimate stress was significance for structure (p o0.01) and not for rate (p¼ 0.54). Cortical specimens had the highest ultimate strength (184.49725.19 MPa), followed by sandwich specimens, (82.877 22.00 MPa), followed by the suture specimens (27.1879.23 MPa). Ultimate strain was not dependent on either rate (p ¼0.71) or structure (p ¼0.87). The analysis of bending stiffness indicates that the sandwich specimens (12.3275.18 Nm2/m) are significantly stiffer (po0.01) than either the cortical-only (5.5871.46 Nm2/m) or
The results of this study indicate that the mechanical properties of the six year-old calvarium are both distinct from and intermediate to those of infants and adults (Fig. 7). Kriewall and McPherson reported an elastic modulus of 7.1 GPa for one six year-old subject and a range of moduli spanning from 1.7 GPa for pre-term bone to 3.9 GPa for term bone (McPherson and Kriewall, 1980a,1980b). Margulies and Thibault reported the elastic modulus of a range of pediatric specimens from 19 days to 13 months old in the markedly lower range of 0.3–1.3 GPa (Margulies and Thibault, 2000). The elastic modulus of adult bone has been estimated to be above 12 GPa for the cortical component (Wood, 1971). The finding that cortical-only specimens have an average modulus of elasticity of 9.87 GPa and sandwich specimens have an effective modulus of 3.69 GPa is consistent with previous results and suggests a progressive increase in the stiffness of the cortical bone with age. It also supports the hypothesis that intra-cranial variations exist in children due to cranial development. Previous research suggests that there is little rate dependency in the tissue of pediatric specimen, but that the mechanical properties of adult bone are rate sensitive. However, a review of the literature suggests that this reflects the range of rates of loading used in each study. Margulies and Coats aggregated results from previous research (Coats and Margulies, 2006) and reported that for young pediatric specimens, ultimate strain varied significantly over a wide range of strain rates from 0.000001 to 100 s 1. For adults, Carter, McElhaney, and Wood all found evidence to support the rate dependency of ultimate stress, and the latter two also conclude that the modulus of elasticity of adult bone increases with loading rate (Carter and Hayes, 1976; McElhaney, 1966; Wood, 1971). The current study, however, only tests loading rates spanning two decades (0.01– 1 s 1) while the aforementioned authors studied strain rates over many orders of magnitude (Wood from below 0.01 to above 100 s 1, McElhaney from 0.001 to 1500 s 1, and Carter from 0.001 to over 100 s 1). Moreover, the rate sensitivity observed in previous research is usually found to be weakly log-linear with strain rate, so such sensitivity may not be meaningful over a two decade range. In this regard, the choice of inclusion of loading rate in constitutive modeling should depend on the domain over which loading rate varies. For example, head-impact onto rigid
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Fig. 3. Seen above are the axial (I) and cross-sectional (II) CT images of 3 specimens. Mean grayscale value was plotted as a function of depth (III) and the minimum to maximum grayscale ratio was used to categorize specimen as either purely cortical (a), sandwich (c), or in transient (b) in structure. Cortical specimens were significantly thinner than either the sandwich or suture specimens.
and padded surfaces varies by significantly less than two orders of magnitude and as such rate effects may not be important to consider (Nightingale et al., 1997). By contrast, damping as a result of viscoelastic effects may indeed modulate the response and should be considered (Camacho et al., 2001). 4.2. Morphological effect Skull morphology has a direct and significant effect on the mechanical properties of the skull tissue. As a result of cranial growth, both the geometry and structure of the six year-old calvaria are unique; both adult and neonatal subjects exhibit more uniform structure and thickness than the six year-old. The tendency of growth to occur preferentially near and in the direction of the suture interfaces makes the spatial variation of mechanical properties predictable, and the correlation between bone thickness and structure makes the intracranial variation in mechanical properties feasible to model. The finding that bending stiffness is highest for the tri-layer specimens is well aligned with the teleological intuition that the human cranium grows in such a way that the stiffness of the skull
increases as the bone matures. The invariance between the bending stiffness of the cortical bone and sutures suggests that at the age of six the skull utilizes thickness and structure as compensatory mechanisms for the relative weakness and lower elastic modulus of the sutures. Strain to failure does not vary between bone and suture samples, and sutures fail under significantly lower stresses than bone samples. Moreover, the sutures are surrounded by tri-layer bone that are over three times as stiff and with similar thickness. These findings might suggest that the sutures of the six year-old skull are the region most susceptible to fracture, and that due to their tendency to remain connected beyond the point of failure, diastatic fracture may be clinically under-diagnosed (Mulroy et al., 2011). 4.3. Limitations The principal limitation of this study is that the data was obtained from a single subject. Although there are no data to suggest the donor is not representative of the broader population, the true utility of this study is to highlight intracranial variation in
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Fig. 5. Sandwich structure specimens are the most stiff of the three specimen types found in the six year-old cranium.
Fig. 4. Both modulus of elasticity and ultimate stress differed significantly between specimens of different structures, but the same pattern was not observed for ultimate strain. Varying strain rate from 0.045 to 2.2 s 1 had no effect on any of the mechanical properties. (An asterisk means p o 0.01).
mechanical properties which will be present in any child or adolescent skull in which both pediatric single-layer and mature tri-layer bone is present. The assumptions that were made about the geometry of each bending specimen are a second limitation. The analysis method used in this paper assumes each specimen behaved like a linear beam of uniform cross section. Though it was observed that the
Fig. 6. Elastic modulus and ultimate stress did not depend on thickness within groups except for the group of specimens undergoing the transition from single layer to sandwich structure. Within this group E and ultimate stress decrease with increasing thickness.
bone samples were curved in the longitudinal direction, the initial radius of curvature was greater than five times the thickness of each specimen, and thus not large enough to be significant
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bone and suture samples. In particular, Dr. Allan Johnson and Dr. Cristian Badea Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech. 2012.07.001.
References
Fig. 7. Comparison of current data with previously published studies showing upper and lower bounds or error bars where known.
(Hibbeler, 2003). It was also assumed that the cross section of each sandwich structure specimen was uniform, but this approximation has only a minor effect on mechanical properties because the porous layer surrounds the neutral axis. Still, the effective modulus of elasticity and ultimate stress reported here likely underestimates the true elastic modulus and ultimate stress of sandwich structure specimens due to the overestimation of the area moment of inertia.
5. Conclusions This paper presents an analysis of the effect of morphology on the mechanical properties of the pediatric skull. The effective modulus of elasticity and strength to failure vary widely intracranially amongst cortical bone (E¼9.87 GPa, sult ¼185 MPa), trilayer bone (E¼3.69 GPa, sult ¼82.9 MPa), and sutures (E¼1.10 GPa, sult ¼27.18 MPa) in the six year-old skull while ultimate strain is not significantly different amongst the various structures. Furthermore, these traits covary with thickness and the tri-layer bone develops first near the sutures as a result of the growth mechanism of the skull leading up to early adolescence. This combination of factors leads to the tri-layered bone being the stiffest and the thin cortical and thick sutures exhibiting lower stiffness. These findings suggest that accurate finite element models of the pediatric skull need to account for this intracranial variation in mechanical properties and that geometrical data may be used as a useful indicator of bone structure.
Conflict of interest statement None of the authors have a conflict of interest.
Acknowledgments NHTSA Cooperative Agreement no. DTNH22-94-Y-07133. We would like to acknowledge the help from Duke’s Center for In Vivo Microscopy for providing the micro-CT scans for our cranial
Baumer, T.G., Powell, B.J., Fenton, T.W., Haut, R.C., 2009. Age dependent mechanical properties of the infant porcine parietal bone and a correlation to the human. Journal of Biomechanical Engineering, 131. Bushnik, T., Hanks, R., Kreutzer, J., Rosenthal, M., 2003. Etiology of traumatic brain injury: characterization of differential outcomes up to 1 year postinjury. Archives of Pysical Medicine and Rehabilitation 84 (2), 255–262. Camacho, D.L.A., Nightingale, R.W., Myers, B.S., 2001. The influence of surface padding properties on head and neck injury risk. Journal of Biomechanical Engineering 123, 432–439. Carter, D.R., Hayes, W.C., 1976. Bone compressive strength: the influence of density and strain rate. Science 194 (4270), 1174–1176. Coats, B., 2007. Mechanics of head impact in infants. Dissertation. University of Pennsylvania, Philadelphia. Coats, B., Margulies, S.S., 2006. Material properties of human infant skull and suture at high rates. Journal of Neurotrauma 23 (8), 1222–1232. Coats, B., Margulies, S.S., Ji, S., 2007. Parametric study of head impact in the infant. Stapp Car Crash Journal 51, 1–15. Cohen, M.M.J., Maclean, R.E. (Eds.), 2000. Evaluation and Management, second ed. Oxford University Press, Oxford. DuterLoo, H.S., Enlow, D.H., 2005. A comparative study of cranial growth in Homo and Macaca. American Journal of Anatomy 127 (4), 357–368. Evans, F.G., Lissner, H.R., 1956. Tensile and compressive strength of human parietal bone. Journal of Applied Physiology 10 (3), 493–497. Guan, F., Han, X., Mao, H., Wagner, C., Yeni, Y.N., Yang, K.H., 2011. Application of optimization methodology and specimen-specific finite element models for investigating material properties of rat skull. Annals of Biomedical Engineering 39 (1), 85–95. Hibbeler, 2003. Bending, Mechanics of Materials. Pearson Education, Inc., Upper Saddle River, NJ, pp. 324–329. James, H., 1999. Pediatric head injury: what is unique and different. Acta Neurochirurgica Supplement (Wien) 73, 85–88. Klinich, K.D., Hulbert, G.M., Schneider, L.W., 2002. Estimating infant head injury criteria and impact response using crash reconstruction and finite element modeling. Stapp Car Crash Journal 46, 165–194. Kriewall, T.J., McPherson, G.K., Tsai, A.C., 1980. Bending properties and ash content of fetal cranial bone. Journal of Biomechanics 14, 73–79. Langlois, J.A., Marr, A., Mitchko, J., Johnson, R.L., 2005. Tracking the silent epidemic and educating the public: CDC’s traumatic brain injury-associated activities under the TBI Act of 1996 and the Children’s Health Act of 2000. Journal of Head Trauma Rehabilitation 20 (3), 196–204. Margulies, S.S., Thibault, K.L., 2000. Infant skull and suture properties: measurements and implications for mechanisms of pediatric brain injury. Journal of Biomechanical Engineering 122, 364–371. McElhaney, J.H., 1966. Dynamic response of bone and muscle tissue. Journal of Applied Physiology 21, 1231–1236. McElhaney, J.H., Fogle, J.L., Melvin, J.W., Haynes, R.R., Roberts, V.L., Alem, N.M., 1970. Mechanical properties of cranial bone. Journal of Biomechanics 3, 495–511. McPherson, G.K., Kriewall, T.J., 1980a. The elastic modulus of fetal cranial bone: a first step towards an understanding of the biomechanics of fetal head molding. Journal of Biomechanics 13, 9–16. McPherson, G.K., Kriewall, T.J., 1980b. Fetal head molding: an investigation utilizing a finite element model of the fetal parietal bone. Journal of Biomechanics 13 (1), 17–26. Mulroy, M.H., et al., 2011. Evaluation of Pediatric Skull Fracture Imaging Techniques. Duke University. Nightingale,R.W., McElhaney, J.H., Camacho, D.L., Winkelstein, B.A., Myers, B.S., 1997. The dynamic responses of the cervical spine: the role of buckling, end conditions, and tolerance in compressive impacts. In: Proceedings of the 41st Stapp Car Crash Conference Proceedings, vol. 41(973344), pp. 451–471. Prange, M., Luck, J., Dibb, A., Van Ee, C., Nightingale, R., Myers, B., 2004. Mechanical properties and anthropometry of the human infant head. Stapp Car Crash Journal 48, 279–299. Roberts, V.L., Melvin, J., 1968. Study of mechanical properties of human calvarium, Accident Pathology. Schneier, A.J., Shields, B.J., Hostetler, S.G., Xiang, H., Smith, G.A., 2006. Incidence of pediatric traumatic brain injury and associated hospital resource utilization in the United States. Pediatrics 118 (2), 483–492. Wood, J., 1971. Dynamic response of human cranial bone. Journal of Biomechanics 4, 1–12.
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
The mechanical and morphological properties of 6 year-old cranial bone Matthew T. Davis, Andre M. Loyd, Han-yu Henry Shen, Maura H. Mulroy, Roger W. Nightingale n, Barry S. Myers, Cameron Dale Bass Department of Biomedical Engineering, Duke University, Box 90281, Durham, NC 27708-0281, United States
a r t i c l e i n f o
abstract
Article history: Accepted 6 July 2012
Traumatic Brain Injury (TBI) is a leading cause of mortality and morbidity for children in the United States. The unavailability of pediatric cadavers makes it difficult to study and characterize the mechanical behavior of the pediatric skull. Computer based finite element modeling could provide valuable insights, but the utility of these models depends upon the accuracy of cranial material property inputs. In this study, 47 samples from one six year-old human cranium were tested to failure via four point bending to study the effects of strain rate and the structure of skull bone on modulus of elasticity and failure properties for both cranial bone and suture. The results show that strain rate does not have a statistically meaningful effect on the mechanical properties of the six year-old skull over the range of strain rates studied (average low rate of 0.045 s 1, average medium rate of 0.44 s 1, and an average high rate of 2.2 s 1), but that these properties do depend on the growth patterns and morphology of the skull. The thickness of the bone was found to vary with structure. The bending stiffness (per unit width) for tri-layer bone (12.32 75.18 Nm2/m) was significantly higher than that of cortical bone and sutures (5.58 71.46 Nm2/m and 3.70 7 1.88 Nm2/m respectively). The modulus of elasticity was 9.87 7 1.24 GPa for cranial cortical bone and 1.10 7 0.53 GPa for sutures. The effective elastic modulus of tri-layer bone was 3.69 7 0.92 GPa. Accurate models of the pediatric skull should account for the differences amongst these three distinct tissues in the six year-old skull. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Bone Cranial bone Pediatric Biomechanics Strength Skull Mechanical properties Injury Structure
1. Introduction Traumatic brain injury (TBI) is the leading cause of death for the population under 24 years old, accounting for an estimated 30% of all accidental deaths (James, 1999; Schneier et al., 2006). Additionally, it is estimated that as many as 5.3 million people in the United States are currently living with a TBI-related long-term disability (Bushnik et al., 2003). Owing to the limited number of postmortem pediatric cadavers available (Prange et al., 2004), pediatric head biomechanics has not been investigated in congruity with its societal impact (Langlois et al., 2005). Computational finite element models (FEMs) are commonly used in place of direct mechanical investigations of pediatric head injury (Coats, 2007; Coats et al., 2007; Klinich et al., 2002; Margulies and Thibault, 2000). FEMs have been used in the analysis of child safety restraints, seatbelts, and airbags. Accurate predictions, however, require accurate material properties. Among the most critical material properties needed are those of cranial bone, such as elastic modulus and ultimate stress and
n
Corresponding author. Tel.: þ1 919 660 5451; fax: þ1 919 660 5362. E-mail address: [email protected].(R.W. Nightingale)
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.07.001
strain. These properties drive the overall mechanical response of the head including skull fracture and brain response. Other methods, including inverse finite element optimization, couples experimentally observed force–deflection curves with computational models to reverse engineer the material properties of a given material (Guan et al., 2011). The mechanical properties of adult bone have been obtained in the past using a variety of methods (Evans and Lissner, 1956; McElhaney et al., 1970; Roberts and Melvin, 1968; Wood, 1971). More recent efforts to publish data on pediatric specimens have focused on neonates and infants (Coats and Margulies, 2006; Margulies and Thibault, 2000; McPherson and Kriewall 1980a, 1980b). Margulies and Coats analyzed the properties’ dependence on strain rate, region, and age for a collection of specimen ranging from 21 weeks gestation to 13 months old. Baumer et al. reported properties obtained via four-point-bending of infant porcine parietal bone to propose a correlation to human tissue (Baumer et al., 2009; Coats and Margulies, 2006. These studies found that the constitutive properties of pediatric cranial bone are age sensitive but not strain rate dependent for the rates tested. Prior research on the adult, however, has shown that these mechanical properties vary weakly with strain rate for bone (Carter and Hayes, 1976; McElhaney, 1966; Wood, 1971). Unfortunately,
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no data has been published on rate dependency in calvaria in or near the six year-old cohort used in this study. Extensive cranial growth occurs between the ages of 13 months and 18 years, however, the effect that this growth has on the mechanical properties of the pediatric skull during this transitional period remains largely undocumented. Although Kriewall and McPherson published data on the elastic modulus of a six year-old skull (7.1 GPa, mean thickness of 3.33 mm) they did not discuss the structure of the bones tested (Kriewall et al., 1980). As periosteal tissues expand in response to the developing brain, the bones of the cranium move apart, straining the sutures and simultaneously creating space for and signaling for the growth of new bone. Thus, the primary direction of bone growth in the pediatric skull is toward the sutures (Cohen and Maclean, 2000; DuterLoo and Enlow, 2005). The bone also transitions from the single layered structure observed in early childhood to the trilayer bone present in adults, which is comprised of a cortical table on both the ecto- and endo-cranial surface separated by a porous trabecular layer. This occurs by the simultaneous deposition of new bone on both the ectocranial and endocranial surfaces and resorption of the inner layer (Cohen and Maclean, 2000). These two modes of growth, resulting in the non-uniform development of the pediatric skull, may create regional variation in mechanical properties (Fig. 1). The purpose of this paper is to study the mechanical properties of a six year-old skull to better understand how the child calvarium differs from that of both adults and neonates. One hypothesized difference is that modulus of elasticity and ultimate stress and strain of the cranial tissue will vary with region due to the growth pattern of the pediatric skull. Finally, it is also hypothesized that modulus and failure properties will not vary significantly with strain rate for the range of loading rates studied.
2. Methods 2.1. Specimen preparation A single six year-old female cadaver (COD: germ cell malignancy, Weight: 60l bs, Height: 40 600 Ethnicity: Caucasian) was obtained in compliance with federal, state, local and institutional regulations. The calvarium was removed and 71 samples were cut from the frontal and parietal regions of the skull using a
table mounted Dremel tool (Robert Bosch Tool Corporation, Mount Prospect, Illinois) with a 1/1600 grinding bit. The suture samples were harvested perpendicular to and across the suture lines, and the bone samples were taken from the parietal and frontal regions of the calvaria. The samples were cut so that their dimensions were 30–35 mm in length and 3–5 mm in width. The bone was moistened with a saline drip during the process. Each sample was then fixed into ABS plastic containers of rectangular geometry using polymethylmethacrylate (PMMA), leaving approximately 12 mm of bone exposed. Each of the bone samples was then wrapped in gauze soaked in saline (0.9% NaCl) to keep the bones moist throughout the testing process and stored separately in a refrigerator at 5 1C for 1– 3 days while testing was carried out. During this time each sample was scanned using micro-CT at 50 m resolution. 2.2. Testing procedure Bending tests were performed using a custom-built four-point-bending apparatus attached to a Bose ElectroForce 3200s linear actuator (Bose, Framingham, Massachusetts). The rig was designed to minimize friction by the use of steel roller pins mounted in ABEC-7 ball bearings as supports. Displacement control failure tests were run at three different displacement rates (4 mm/s, 40 mm/s, 400 mm/s). Because the relationship between displacement of the beam supports and the angle of beam deflection is non-linear, the corresponding average strain rates were approximately 0.045 s 1, 0.44 s 1, and 2.2 1, with some variation due to the variation in specimen size. The force during testing was recorded using a Honeywell Model-31 222.5 N load cell (Morristown, New Jersey). End brackets were lubricated with light machine oil and placed onto the stainless steel roller supports of the fourpoint-bending apparatus. High speed digital imaging data from a Phantom video camera (Vision Research, Inc., Wayne, NJ) was recorded for each failure test (2000 frames per second for low rate, 7700 frames per second for medium and high rate) and later used to determine the angle of displacement undergone by each specimen using TEMA tracking software (Photo-Sonics, Inc., Burbank, CA). 2.3. Analysis The geometry of the specimen was determined using the micro-CT scans taken before testing and photographs taken after failure. To avoid the uncertainties of stress-concentrations and other end-effects, we did not analyze any samples that broke in or near the PMMA-bone interface. The cross-sectional dimension of each bone was obtained by measurement of the smallest cross-sectional area of each specimen. Stress was estimated by assuming that the samples behave like solid beams of constant cross-section as:
s¼
ð1Þ
where M is the bending moment, y is the half-thickness of the sample at the location of failure, and I is the moment of inertia of the rectangular cross section (I ¼ bh3/12). Using the same assumptions, an estimate of the tensile strain on the outer surface of the bone was obtained by considering the radius of curvature of the sample in bending and from tracking the angle of rotation of the end pieces by the equation:
e¼
Fig. 1. An image of the cross-section of the intact skull showing the distribution of tri-layer and uni-layer bone. The oblique coronal view of the left and right parietal regions shown above indicates that the bone is thickest and most mature in the area surrounding the sagittal suture. The bone nearer the sides and the apexes are comprised of only cortical bone.
My I
2yF L
ð2Þ
where y is the same half-thickness measurement as the stress equation above, L is the original length of the beam exposed, and F is the angle of rotation of the end pieces (Fig. 2). The modulus of elasticity was obtained by a constrained minimization of the residuals of a Ramberg–Osgood piecewise linear and power law curve fit to the stress–strain data using a 0.2% offset as the cutoff for linearity. For the case of the sandwich structure specimens and the suture specimens we use the simplifying assumption that the bone has a homogeneous cross section to simplify the analysis and because we are interested in the bulk load response of the specimens. For this reason, the modulus of elasticity of these samples should be considered to be an effective modulus of a composite structure model of the tissue, and does not reflect the true modulus of any one constituent material of the bone. The bending stiffness is the product of this modulus of elasticity and the area moment inertia (EI) and used as a metric of bending stiffness. This was calculated for each specimen base on the effective elastic modulus and the microCT crosssection. Because the width of each specimen varied as a result of the harvesting procedure, the bending stiffnesses were normalized by the width and are thus reported in units of Nm2/m. The categorization of samples based on structure was performed using the micro-CT scans and Avizo imaging software (VSG, Burlington, MA). The crosssectional profiles of the beam were captured at the location of failure and the mean grayscale value in each pixel row within the bone was plotted against thickness. A local minimum in these plots indicated the presence of a porous layer or the beginnings of a resorptive process, and thus indicated that the bone was not
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suture specimens (3.7071.88 Nm2/m), but that the latter two are not significantly different from one another (p¼0.47) (Fig. 5). Lastly, because thickness was seen to co-vary with type, its contribution to mechanical properties was tested in a general linear regression for cortical, sandwich, and suture specimens, as well as the specimens in the transient region (Fig. 6, Supplementary material Table B). No statistically significant variation with thickness was observed for the mechanical properties of cortical, sandwich, or suture specimens. The modulus of elasticity of the transitional specimens, however, varied significantly with thickness (R2 ¼0.93, R2adj ¼0.90, p o0.01), and the ultimate stress of the same specimens, though not significant, showed a decreasing trend as well (R2 ¼0.43, R2adj ¼0.24, p¼0.23). All the suture specimens failed at the suture but remained physically connected on the compression side. The majority of the tri-layer and cortical bone specimens completely separated at failure. Furthermore, cortical bone specimens were found only in the left and right parietal regions near the parietal eminence of each plate. Fig. 2. Photographs showing the progression of a bending test from top to bottom. Parameters used in calculating the stress–strain relationship from the force– displacement data are overlain on the images.
4. Discussion 4.1. Mechanical properties and previous research
purely cortical in nature (Fig. 3). Minimum to maximum grayscale ratios were calculated for each specimen and cutoffs for the cortical group ( 485%) and the sandwich structure group (o55%) were determined based on inspection of the gross morphological features of the bone samples and the bimodal distribution of grayscale ratios. Those specimens that fell between 85 and 55% were classified as transitional. ANOVA with Tukey–Kramer means comparison testing was used to examine the effect of structure and loading rate on effective modulus, ultimate stress and ultimate strain. Linear regressions were used to examine the relationships between sample thickness and mechanical properties.
3. Results A total of 47 of the 71 specimens tested met the inclusion criteria. Of these, seven were comprised of only cortical bone, seventeen exhibited a layered cross-section of both cortical and trabecular bone, and eighteen included a closed suture. Five were determined to be in the transition stage from a one layered structure to a tri-layered structure and were thus not analyzed with either group. There was a significant relationship between thickness by bone structure (po0.01). Cortical-only specimens (1.88 mm70.16 mm) were significantly thinner than sandwich structure specimens (3.3870.45 mm, p o0.01) or suture specimens (3.60 70.71 mm, po 0.01), but sandwich and suture specimens were not significantly different from one another (p ¼0.49). For this reason, thickness and structural type were not included in the same ANOVAs. The effective modulus of elasticity was not affected by loading rate (p ¼0.71), but was significantly affected by structure (Fig. 4). The effective modulus of elasticity of cortical (9.8771.24 GPa), sandwich (3.69 70.92 GPa), and suture (1.1070.53 GPa) specimens were all different from one another (Fig. 4, all po0.01). The relationship between loading rate, structure, and ultimate stress was significance for structure (p o0.01) and not for rate (p¼ 0.54). Cortical specimens had the highest ultimate strength (184.49725.19 MPa), followed by sandwich specimens, (82.877 22.00 MPa), followed by the suture specimens (27.1879.23 MPa). Ultimate strain was not dependent on either rate (p ¼0.71) or structure (p ¼0.87). The analysis of bending stiffness indicates that the sandwich specimens (12.3275.18 Nm2/m) are significantly stiffer (po0.01) than either the cortical-only (5.5871.46 Nm2/m) or
The results of this study indicate that the mechanical properties of the six year-old calvarium are both distinct from and intermediate to those of infants and adults (Fig. 7). Kriewall and McPherson reported an elastic modulus of 7.1 GPa for one six year-old subject and a range of moduli spanning from 1.7 GPa for pre-term bone to 3.9 GPa for term bone (McPherson and Kriewall, 1980a,1980b). Margulies and Thibault reported the elastic modulus of a range of pediatric specimens from 19 days to 13 months old in the markedly lower range of 0.3–1.3 GPa (Margulies and Thibault, 2000). The elastic modulus of adult bone has been estimated to be above 12 GPa for the cortical component (Wood, 1971). The finding that cortical-only specimens have an average modulus of elasticity of 9.87 GPa and sandwich specimens have an effective modulus of 3.69 GPa is consistent with previous results and suggests a progressive increase in the stiffness of the cortical bone with age. It also supports the hypothesis that intra-cranial variations exist in children due to cranial development. Previous research suggests that there is little rate dependency in the tissue of pediatric specimen, but that the mechanical properties of adult bone are rate sensitive. However, a review of the literature suggests that this reflects the range of rates of loading used in each study. Margulies and Coats aggregated results from previous research (Coats and Margulies, 2006) and reported that for young pediatric specimens, ultimate strain varied significantly over a wide range of strain rates from 0.000001 to 100 s 1. For adults, Carter, McElhaney, and Wood all found evidence to support the rate dependency of ultimate stress, and the latter two also conclude that the modulus of elasticity of adult bone increases with loading rate (Carter and Hayes, 1976; McElhaney, 1966; Wood, 1971). The current study, however, only tests loading rates spanning two decades (0.01– 1 s 1) while the aforementioned authors studied strain rates over many orders of magnitude (Wood from below 0.01 to above 100 s 1, McElhaney from 0.001 to 1500 s 1, and Carter from 0.001 to over 100 s 1). Moreover, the rate sensitivity observed in previous research is usually found to be weakly log-linear with strain rate, so such sensitivity may not be meaningful over a two decade range. In this regard, the choice of inclusion of loading rate in constitutive modeling should depend on the domain over which loading rate varies. For example, head-impact onto rigid
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Fig. 3. Seen above are the axial (I) and cross-sectional (II) CT images of 3 specimens. Mean grayscale value was plotted as a function of depth (III) and the minimum to maximum grayscale ratio was used to categorize specimen as either purely cortical (a), sandwich (c), or in transient (b) in structure. Cortical specimens were significantly thinner than either the sandwich or suture specimens.
and padded surfaces varies by significantly less than two orders of magnitude and as such rate effects may not be important to consider (Nightingale et al., 1997). By contrast, damping as a result of viscoelastic effects may indeed modulate the response and should be considered (Camacho et al., 2001). 4.2. Morphological effect Skull morphology has a direct and significant effect on the mechanical properties of the skull tissue. As a result of cranial growth, both the geometry and structure of the six year-old calvaria are unique; both adult and neonatal subjects exhibit more uniform structure and thickness than the six year-old. The tendency of growth to occur preferentially near and in the direction of the suture interfaces makes the spatial variation of mechanical properties predictable, and the correlation between bone thickness and structure makes the intracranial variation in mechanical properties feasible to model. The finding that bending stiffness is highest for the tri-layer specimens is well aligned with the teleological intuition that the human cranium grows in such a way that the stiffness of the skull
increases as the bone matures. The invariance between the bending stiffness of the cortical bone and sutures suggests that at the age of six the skull utilizes thickness and structure as compensatory mechanisms for the relative weakness and lower elastic modulus of the sutures. Strain to failure does not vary between bone and suture samples, and sutures fail under significantly lower stresses than bone samples. Moreover, the sutures are surrounded by tri-layer bone that are over three times as stiff and with similar thickness. These findings might suggest that the sutures of the six year-old skull are the region most susceptible to fracture, and that due to their tendency to remain connected beyond the point of failure, diastatic fracture may be clinically under-diagnosed (Mulroy et al., 2011). 4.3. Limitations The principal limitation of this study is that the data was obtained from a single subject. Although there are no data to suggest the donor is not representative of the broader population, the true utility of this study is to highlight intracranial variation in
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Fig. 5. Sandwich structure specimens are the most stiff of the three specimen types found in the six year-old cranium.
Fig. 4. Both modulus of elasticity and ultimate stress differed significantly between specimens of different structures, but the same pattern was not observed for ultimate strain. Varying strain rate from 0.045 to 2.2 s 1 had no effect on any of the mechanical properties. (An asterisk means p o 0.01).
mechanical properties which will be present in any child or adolescent skull in which both pediatric single-layer and mature tri-layer bone is present. The assumptions that were made about the geometry of each bending specimen are a second limitation. The analysis method used in this paper assumes each specimen behaved like a linear beam of uniform cross section. Though it was observed that the
Fig. 6. Elastic modulus and ultimate stress did not depend on thickness within groups except for the group of specimens undergoing the transition from single layer to sandwich structure. Within this group E and ultimate stress decrease with increasing thickness.
bone samples were curved in the longitudinal direction, the initial radius of curvature was greater than five times the thickness of each specimen, and thus not large enough to be significant
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bone and suture samples. In particular, Dr. Allan Johnson and Dr. Cristian Badea Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech. 2012.07.001.
References
Fig. 7. Comparison of current data with previously published studies showing upper and lower bounds or error bars where known.
(Hibbeler, 2003). It was also assumed that the cross section of each sandwich structure specimen was uniform, but this approximation has only a minor effect on mechanical properties because the porous layer surrounds the neutral axis. Still, the effective modulus of elasticity and ultimate stress reported here likely underestimates the true elastic modulus and ultimate stress of sandwich structure specimens due to the overestimation of the area moment of inertia.
5. Conclusions This paper presents an analysis of the effect of morphology on the mechanical properties of the pediatric skull. The effective modulus of elasticity and strength to failure vary widely intracranially amongst cortical bone (E¼9.87 GPa, sult ¼185 MPa), trilayer bone (E¼3.69 GPa, sult ¼82.9 MPa), and sutures (E¼1.10 GPa, sult ¼27.18 MPa) in the six year-old skull while ultimate strain is not significantly different amongst the various structures. Furthermore, these traits covary with thickness and the tri-layer bone develops first near the sutures as a result of the growth mechanism of the skull leading up to early adolescence. This combination of factors leads to the tri-layered bone being the stiffest and the thin cortical and thick sutures exhibiting lower stiffness. These findings suggest that accurate finite element models of the pediatric skull need to account for this intracranial variation in mechanical properties and that geometrical data may be used as a useful indicator of bone structure.
Conflict of interest statement None of the authors have a conflict of interest.
Acknowledgments NHTSA Cooperative Agreement no. DTNH22-94-Y-07133. We would like to acknowledge the help from Duke’s Center for In Vivo Microscopy for providing the micro-CT scans for our cranial
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