High-Rate Anisotropic Properties in Human Infant Parietal and Occipital Bone

Each year, more than 650,000 children are victims of abuse and neglect, with most cases occurring in children less than three years of age [1]. Infants less than one year of age are the most vulnerable age group and have four times the fatality rate from abuse and neglect compared to older children [1]. Identifying child abuse early in this young age group is challenging because symptoms are often nonspecific, infants can't confirm or deny a history of trauma, and injury from abusive head trauma and accidental falls in young children can be similar [2–5]. Careful experimental and computational biomechanical investigations can illuminate subtleties or patterns of injury associated with accidental or inflicted trauma, but such studies require a thorough assessment of the mechanical properties of biological tissue.

Due to the commonality of skull fracture in both accidental and abusive head trauma, several computational studies have sought to identify probabilities of infant skull fracture from head impact [6–9] or to predict skull fracture patterns in simulations of individual cases of accidental falls in infants [10–12]. These studies rely heavily on limited pediatric animal [6] or human [11,13,14] data to formulate the models and make necessary assumptions about the anisotropic nature of pediatric cranial bone.

Human infant cranial bone is known to be region-dependent and anisotropic [15,16]. The anisotropy is in contrast to human adult cranial bone which is primarily isotropic [17]. These age-related differences are likely due to the trabecular features in infant human bone that disappear during development. Briefly, the cranial cavity begins as a membranous structure. Dermal intramembranous ossification centers form in the center of the bony plates and bone grows outward toward suture lines. The path of bone growth is dictated by trabecular fibers radiating outward from the ossification centers [18]. These fibers are visible to the naked eye in human infant cranial bone. As the bone develops and begins to differentiate into three layers, the trabecular fibers are absorbed. In quasi-static testing, McPherson and Kriewall report that the elastic modulus of human infant cranial bone from infants (24 weeks gestation—40 weeks gestation) is 4.9 times greater when tested along the direction of the fibers compared to perpendicular to the fibers [16]. It is unknown if this anisotropic ratio holds true for dynamic tests.

Previously, we performed three-point bending tests of human infant cranial bone at high strain-rates. We found no difference in elastic modulus or ultimate stress compared to the quasi-static tests of McPherson and Kriewall, suggesting infant cranial bone is not rate-dependent. However, we hypothesized there may be rate dependence when tested along the primary fiber direction of infant cranial bone. The objective of this study was to quantify the dynamic anisotropy of human infant cranial bone by measuring material properties of infant bone parallel to the trabecular fibers at high strain rates. We compare the data to our previous work measuring material properties of infant bone perpendicular to the trabecular fibers. Specimens from parietal and occipital cranial bones were included to assess region dependence on the anisotropy. The possibility of anisotropic rate-dependence of human infant cranial bone was evaluated by comparing dynamic data to quasi-static data in the literature. These data will be critical to the accurate development of computational models to predict skull fracture in infants and may provide insight into skull fracture patterns from accidental or inflicted trauma.

All human subject protocols were reviewed and approved by the Institutional Review Boards at the University of Utah and Primary Children's Hospital. Human cranial bone specimens were collected through autopsies performed by the Pathology Department at Primary Children's Hospital. Criteria for acceptance into the study were subjects ≤ 3 years old of age with no prior history of skull fracture, skull malformations, human immunodeficiency virus, or hepatitis. Two cranial specimens, occipital and parietal, with the trabecular fibers oriented along the long axis of the specimen (parallel) were removed from each subject according to Fig. 1 and frozen. On the day of testing, frozen cranial samples were thawed to room temperature (25 °C) in a phosphate buffered saline solution. Parietal bone samples were trimmed at the sagittal suture. Samples were lightly machined under a constant drip of phosphate buffered saline to produce a uniform thickness and shape and tested within 1 h of thawing. This freeze and thaw protocol does not significantly affect the material properties of cranial bone [19].

Specimen collection, testing, and analysis are based on ASTM standard D790 [21] and are largely unchanged from our previous study [15]. Details are repeated here for completeness. To collect high strain-rate material properties, the drop tower load frame from our previous study [15] was refurbished with the following features: dual dampers with hard stops (SC 190-1-BP, Ace Controls, Farmington Hills, MI), high-resolution laser displacement sensor (LK-G152, Keyence, Osaka, Japan), and a new 25-lb load cell (Honeywell, Morris Plains, NJ) and amplifier (IAA100, Futek, Irvine, CA). The drop tower shown in Fig. 2 was revalidated with a rate independent copolymer (n $≤$ 15; Copolymer, Boston O&P, Avon, MA) tested in three-point bending using the drop tower and compared to three-point bending on an Instron 5943-100N (Instron, Norwood, MA). An unpaired Student's t-test was used to statistically compare the drop tower data to the Instron data.

Due to the limited availability of human specimens, only drops from 20.5 centimeters (0.67 feet) were used in this study. The average impact rate was 1.68 m/s, matching our previous study. Displacement (δ) and force (F) data were collected via laptop (MSI, New Taipei City, Taiwan) using a data acquisition system (Labview Signal Express 2015, National Instruments, Austin, TX) sampled at 10,000 Hz. A fourth order Butterworth low pass filter with a cutoff frequency of 800 Hz was used on each dataset.

where $(F/δ)$ is the force–displacement ratio during the linear elastic region of the three-point bending test, $L$ is the span of the test, and $I$ is the moment of inertia of the rectangular cross section of the beam [22]. Span to thickness ratios were maintained at greater than 14:1 to satisfy conditions of ASTM standard D790.

In this equation, $F$ is the measured force, $w$ is the specimen width, $c$ is half the specimen thickness, and $y$ is the location of interest on the outer surface of the specimen $(y=±c)$⁠. Ultimate stress $(σult)$ was calculated using the maximum force (⁠$Fpeak)$ in Fig. 3 for $F$ in Eq. (2).

where $δ$ is the deflection of the specimen, $t$ is the thickness of the specimen. Ultimate strain $(εult)$ was selected as the flexural strain corresponding to the ultimate stress. Modulus of toughness, $Ut$⁠, was calculated by integrating the stress–strain curve using a trapezoidal approximation.

A correlation analysis was used to identify significant increases in $E$⁠, $σult$⁠, $εf$⁠, and $Ut$ with age. A paired Student's t-test identified significant differences in material properties with region (parietal/occipital). One-way ANOVAs were used to identify significant differences in age, orientation (parallel versus perpendicular), and region (parietal/occipital) when combined with data from our previous study [15]. Due to limited sample size, interaction effects could not be explored. For all tests, significant differences were defined as $p<0.05$⁠.

There were no significant differences in elastic modulus (E) and ultimate strain (⁠$ϵult$⁠) between three-point bending tests of copolymer on an Instron and three-point bending tests with our drop tower. $σult$ from the drop tower (59.06$±$0.727 MPa) overestimated $σult$ from the Instron (54.94$±$2.48 MPa) by 7.2%, and was significant with $p=0.042$⁠.

Fifteen human pediatric cranial bone specimens were collected from nine infant donors ranging from 32 weeks gestation to 10 months of age (Table 1). The variation in thickness across all specimens was small due to the light machining performed on each specimen (1.0592 ± 0.1801 mm). A statistical linear regression analysis found no significant effect of thickness on any of the material properties, verifying no geometric effects in testing. Bending modulus $(E)$ significantly increased with donor age $(p=0.008;n=15;Fig. 4)$⁠. Ultimate stress $(σult)$ also increased with age, but variation was large, and it did not reach significance $(p=0.067;Fig. 4)$⁠. Ultimate strain $(εult)$ and modulus of toughness (⁠$Ut)$ were not significantly correlated with age. $E$ and $σult$ were generally higher in the parietal bone (⁠$E$⁠: 4807 ± 2976 MPa; $σult$⁠: 108.5 ± 42.28 MPa; $n=9$⁠; Fig. 5) compared to the occipital bone (⁠$E$⁠: 3884 ± 3016 Mpa; $σult$⁠: 84.54 ± 36.09 MPa; $n=6$⁠), but this was not significant in the paired t-test analysis $(p>0.08;Fig. 5)$⁠. $εult$ and $Ut$ were not significantly different between parietal bone (0.0448 ± 0.0154 mm/mm; 2.802 ± 0.9673 MPa) and occipital bone (0.0393 ± 0.0116 mm/mm; 2.004 ± 0.6355 MPa).

Data were combined with our previous study [15] to look at the effects of fiber orientation (Fig. 6). E and $σult$ significantly increased when tested parallel to fibers (⁠$n=15$⁠) compared to perpendicular to fibers $(n=29; p<0.0001)$⁠. This significant effect was stronger in infants < 1 month old $(p<0.0001;n=22)$ than in infants ≥ 1 month old $(p=0.025;n=22)$⁠. $E$ in infants < 1 month old was 13.4 times greater and $σult$ 5.1 times greater when tested parallel to the trabecular fibers (⁠$E$⁠:3471 ± 1729 MPa; $σult$⁠: 90.12 ± 22.35 MPa) compared to perpendicular to the trabecular fibers (⁠$E$⁠: 259.0 ± 189.9 MPa; $σult$⁠: 17.65 ± 20.43 MPa). Trabecular fiber orientation had no significant effect on ultimate strain.

In this study, we evaluated the material properties of human infant parietal and occipital bone at high strain-rates and assessed age, region, and fiber direction dependence. This study tested samples with parallel trabeculae (Fig. 1) and a correlation analysis showed bending modulus significantly increased with age. This is in agreement with other studies [15,16,23] and further supports the use of age-specific data when investigating pediatric head injury. Ultimate strain and stress tended to increase with age but did not achieve significance $(εult p=0.185;σult p=0.067;n=15)$⁠, likely due to the large variation inherent to biological samples combined with the low sample size of the study. Specifically, for ultimate stress one cranium from a 5-month old infant (Cranium 4) had ultimate stress values 1.59 times lower than the mean (or 1.15 standard deviations below the mean). It is possible there were defects in the bone that weakened it. If this value is removed from the analysis, the p-value decreases to $(p=0.0023)$⁠. A posthoc power analysis indicates statistical powers of 93% and 81% for ultimate stress and strain, respectively. Therefore, it's unclear that increased sample size will overcome these variations.

During the validation of modified drop tower, we found $σult$ was significantly (p = 0.042) underestimated using our drop tower apparatus. The significance was primarily due to the very small variability from the drop tower (1.1%) and equates to a difference of 4 MPa (7.2%) between the methods of analysis. Applying this percentage to our human data suggests that ultimate stress in our study may be underestimated by 7.8 MPa and 6 MPa in parietal and occipital bone, respectively. This magnitude is well within the natural variability of both bone regions (standard deviation: 42 MPa for parietal and 36 MPa for occipital) and would not alter the comparative statistical evaluations within this study. However, when developing predictive metrics of failure using $σult$⁠, researchers should consider this underestimation.

In this study, we tested specimens with the trabeculae parallel to the long axis (Fig. 1). In this orientation, a t-test showed that region (parietal $n=9$/occipital $n=6$⁠) had no significant effect on $E, σult, εult$⁠, or $Ut$⁠. This is similar to limited data within McPherson and Kriewall [16] that show minimal differences in modulus between parietal and frontal bone when tested parallel to the long axis of the specimen (parietal: 3510 MPa versus frontal: 3060 MPa with an average 21% coefficient of variability). However, our previous study and a more recent study by Wang et al. found significant regional effects in infant cranial bone when specimens were tested perpendicular to trabeculae [15,24]. Therefore, it may be the bone matrix rather than the collagen trabecular fibers that varies between regions. To our knowledge, the regionality of infant cranial bone mineralization composition and structure has not been evaluated in depth. Kriewall et al. [25] evaluated ash content in a small sample of infant frontal bones (⁠$n=10$ from 1 subject) and found they were on average 2% lower than infant parietal bones (⁠$n=10$⁠) from the same subject. However, in a larger study, the ash content in adult cranial cortical bone ranged 63%–68% [26], suggesting 2% may be within the natural variability of the bone. Therefore, the microstructure of the bone matrix may influence the differences in regional properties more than the material composition of the bone matrix. Additional studies will be needed to identify and confirm microstructural regional differences in infant cranial bone. These studies could utilize micro-CT or histological techniques and may also be able to link specific features to bone quality and material strength.

The lack of regional statistical significance may also be due to small sample sizes. We had 15 specimens from nine infants in our study. Craniums with paired comparisons were limited to six donors. To evaluate this, we performed a posthoc power analysis on the paired t-tests (G*Power 3.1.9.4, Universitat Kiel, Germany). $E$ and $σult$ had statistical powers greater than 99%, indicating that there was sufficient power to identify statistical differences. The power for $εult$ and $Ut$⁠, however, was lower (27% and 77%, respectively), suggesting there may have been insufficient samples sizes to detect significant differences. These findings, combined with the statistical differences in $E$ and $σult$ between parietal and occipital bone when tested perpendicular to the fiber orientation, highlights that regional differences can still exist within the infant skull and should be carefully considered in computational models simulating infant head trauma.

At high strain rates, E in infants < 1 month old was 13.4 times greater and $σult$ 5.1 times greater when tested parallel (⁠$n=9$⁠) to the trabecular fibers than when tested perpendicular (⁠$n=13$⁠) to the trabecular fibers (Fig. 6). For infants > 1 month of age, these increases were reduced to 11.9 and 4.1 (parallel $n=6$⁠; perpendicular $n=16$⁠), respectively. This suggests the infant cranial skull is becoming more isotropic with age, likely due to trabecular fiber absorption with development of the pediatric skull. By the age of 4 years old, the radial growth of the bony plates is reduced and layer differentiation through the thickness begins and continues into adulthood [27]. The decrease in fibers likely reduces the anisotropic properties of bone. In adults, the skull has been characterized as isotropic [17], but there is currently no data to establish timelines for the transition from anisotropic to isotropic skull.

The transverse anisotropy of human infant skull has been reported by McPherson and Kriewall [16] at quasi-static rates. They found bending modulus was 4.9 times greater parallel to the trabeculae compared to perpendicular, about 2.7 times lower than our measurements at high rates. This suggests the trabeculae fibers cause a rate-dependent effect on the material properties of the infant skull. To further investigate this potential rate dependence, the material properties found in this study (⁠$n=6$⁠) and our previous study (⁠$n=6$⁠) [15] were compared with the material properties from McPherson and Kriewall (⁠$n=12$⁠) [16] and Margulies and Thibault (⁠$n=8$⁠) [23]. The effect of strain rate on bending moduli from infant parietal bone < 1 month old across all three studies is shown in Fig. 7. Bending modulus in specimens tested parallel to the trabeculae fibers increased with strain rate but was not significantly rate dependent when data were placed in a linear regression model. This is in contrast with adult skull, which exhibits a significant rate effect [17,28,29]. However, limited specimens and methodological differences confound the statistical comparison. Therefore, the rate dependence of human skull through development is something that still requires continued study.

Most current finite element models of the infant head consider the infant skull to be isotropic and linear elastic [9,14,30,31], but data by McPherson and Kriewall [16] and data in this study clearly indicate the infant skull is transversely isotropic. Only a handful of infant finite element models have considered this anisotropy [7,8,12,31]. In these simulations, the anisotropy of the skull is represented with linear elastic parameters. The parallel trabeculae fibers are estimated based on the anisotropic relationships reported by McPherson and Kriewall [16] and our previous high-rate study on the linear elastic material properties of cranial bone perpendicular to the fiber orientation [15]. Poisson's ratio is typically estimated to be 0.19–0.22, similar to adult cranial bone [9,12,14,29–31]. The shear moduli transverse to the fibers is determined from linear elastic theory, and assumed to be equal to the shear moduli parallel to the fibers. In this study, we fill one of the important gaps in the literature by directly measuring the linear elastic parameters of infant cranial bone parallel to the trabecular fibers. These parameters can be input explicitly into finite elements models using a linear elastic transversely isotropic model. Additional work still needs to be performed to determine whether the use of adult Poisson's ratio values can be used to represent the pediatric skull, and to directly measure shear moduli in infant cranial bone.

As can be seen in Fig. 3, the stress–strain response of the infant cranial skull is not entirely linear. Like many biological materials, there is a nonlinear toe region, followed by a linear elastic region, followed by a nonlinear region. It is not known whether this later nonlinear region is elastic or includes permanent damage to the microstructure. Future models may want to consider incorporating the nonlinearity and anisotropy into a more advanced constitutive model. However, it first needs to be determined whether to model this later nonlinear region with hyperelasticity or damage-based models, and whether this additional complexity is needed in infant head impact simulations.

The bending modulus of human infant skull significantly increased with age when tested parallel to the trabecular fibers. The ultimate stress followed the same trend but did not reach significance. At dynamic test rates, bending modulus of cranial bone in infants < 1 month of age was 13.4 times greater and ultimate stress 5.1 times greater when tested parallel (⁠$n=9$⁠) to the trabeculae fibers compared to perpendicular (⁠$n=13$⁠). We did not find a statistically significant effect of region (parietal bone; $n=9$ versus occipital bone; $n=6$⁠) on modulus or ultimate stress when tested parallel to trabecular fibers, but we previously showed significant regional effects when tested perpendicular to trabecular fibers. This could suggest that regional differences in the infant cranial bone are due to the mineralization of bone instead of the collagen structure. Future work on regional variations in structure and composition in the infant skull would be valuable to better understand regional mechanical differences and similarities. Elastic moduli at the high strain-rates in this study were 2.7 times greater than quasi-static data reported previously, but this finding may be confounded by methodological differences. Anisotropic rate dependence should be evaluated further within a single study.

The anisotropic high strain rate data in this study fill an important gap in the literature and indicate that the material properties of human infant skull are age-dependent and transversely anisotropic at rates similar to low height falls. These data are vital to building accurate computational models when investigating accidental and inflicted pediatric head injury, and will contribute to the prediction, detection, and evaluation of traumatic head injury in children.

We would like to thank Dr. Candice Fike and her lab at the University of Utah for the donation of neonate porcine skulls which were used in the initial evaluation of the methods and instruments prior to human testing. The opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect those of the Department of Justice.

• National Institute of Justice, Office of Justice Programs, U.S. Department of Justice (Award No. 2016-DN-BX-0160; Funder ID: 10.13039/100005289).

$c$ =

half the specimen thickness or $(t2)$

$E$ =

elastic modulus

$F$ =

force measured by load cell during test

$Fpeak$ =

max force during a test

L =

span of three-point bend test

$I$ =

moment of inertia of the rectangular cross section of the specimen

$n$ =

number of samples

$p$ =

p-value or probability value

$t$ =

specimen thickness

$Ut$ =

modulus of toughness

$w$ =

specimen width

$y$ =

location of interest on the outer surface of the specimen $(y=±c)$

$δ$ =

crosshead displacement with $δ=0$ at impact

$εf$ =

flexural strain

$εult$ =

ultimate Strain

$σult$ =

ultimate stress

$σxx$ =

in-plane stress