Development and global validation of a 1-week-old piglet head finite element model for impact simulations

Abstract

Purpose

Child head injury under impact scenarios (e.g. falls, vehicle crashes, etc.) is an important topic in the field of injury biomechanics. The head of piglet was commonly used as the surrogate to investigate the biomechanical response and mechanisms of pediatric head injuries because of the similar cellular structures and material properties. However, up to date, piglet head models with accurate geometry and material properties, which have been validated by impact experiments, are seldom. We aim to develop such a model for future research.

Methods

In this study, first, the detailed anatomical structures of the piglet head, including the skull, suture, brain, pia mater, dura mater, cerebrospinal fluid, scalp and soft tissue, were constructed based on CT scans. Then, a structured butterfly method was adopted to mesh the complex geometries of the piglet head to generate high-quality elements and each component was assigned corresponding constitutive material models. Finally, the guided drop tower tests were conducted and the force-time histories were ectracted to validate the piglet head finite element model.

Results

Simulations were conducted on the developed finite element model under impact conditions and the simulation results were compared with the experimental data from the guided drop tower tests and the published literature. The average peak force and duration of the guide drop tower test were similar to that of the simulation, with an error below 10%. The inaccuracy was below 20%. The average peak force and duration reported in the literature were comparable to those of the simulation, with the exception of the duration for an impact energy of 11 J. The results showed that the model was capable to capture the response of the pig head.

Conclusion

This study can provide an effective tool for investigating child head injury mechanisms and protection strategies under impact loading conditions.

Introduction

According to the statistics, among all injuries in children, head injury of child younger than 3 years old accounts for 50% or even higher.^1,2 Traffic accidents, falls, and mishandling are the main causes of head injuries in young children.³ The most effective way to investigate the injury mechanisms and threshold of child head is to conduct cadaver tests. However, due to ethical reasons, the subjects of child cadavers are very difficult to collect, and thus the resulting experimental data are very scarce. At present, researchers generally develop child head finite element (FE) models4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 to investigate the child head responses under impact conditions, which provide encouraging results for understanding the injury mechanism of child head trauma. However, the developed child head FE models still face the challenges of lacking both the tissues’ material properties and the aforementioned cadaveric biomechanical data for model validation.

Considering that the anatomical structure of piglet head is similar to that of children,¹⁸ and a lot of material properties for components of the piglet head have been obtained and attempted to correspond to children,19, 20, 21, 22, 23, 24, 25, 26 the piglet head was generally used as a surrogate to study the biomechanical response and mechanism of pediatric head injury. Compared with the experiments conducted on the piglet heads,27, 28, 29, 30 the FE model of a piglet head can capture more responses under different impact conditions, which can be considered as a supplement to the experiment.

Up to date, very limited piglet head FE models have been developed. Powell²⁸ established a simplified spherical FE model to represent the piglet head. The model was used to predict the skull fracture under impact scenarios. Wagner³¹ established 2 piglet head models at 7 and 21 days old to investigate the skull fracture under suspected child abuse conditions, while in this model, only the cranium/suture was constructed, the brain and other components were not included. Coats et al.³² developed a detailed 3-5 day-old piglet head model by scaling the head geometry of a 4-week-old piglet. This model was used to study the mechanical response and injury threshold of intracranial hemorrhage under rapid head rotation conditions. Yates et al.¹⁷ established a Göttingen miniature pig brain FE model to study the response of brain tissue under impact loading, in which the brain was developed according to MRI data with high biofidelic, but the skull was assumed rigid.

According to the above description, a piglet head model based on actual medical images and material properties, and validated by impact experiments is very rare. In this study, a 1-week-old piglet head FE model with detailed anatomical structures and high-quality meshes was established. The model was validated against the experimental data from both drop tower impact tests and free-fall drop tests, and it could predict the head global dynamic responses accurately.

Development of a 1-week-old piglet head FE model

Construction of the piglet head anatomical geometry

Considering that this study focuses on head injuries of newborns or very young children, a 1-week-old piglet was chosen as the research subject. The piglet, medium size, was picked from a group of 1-week-old piglet samples on a local farm to conduct CT scan. The CT image sets were obtained with a slice thickness of 0.625 mm. The procedure for obtaining the piglet head's three-dimensional geometry is shown in Fig. 1. First, the CT image sets were conducted segmentation to extract the inner and outer surfaces of the cranial bone and the suture boundaries from the surrounding tissues by defining the threshold as “bone (CT)” mode in Mimics (21.0, Materialise, Leuven, Belgium). Second, the outer surface of the skin was extracted by using the “soft-tissue (CT)” mode. Third, the three-dimensional geometries of the skull and skin were obtained by reconstructing the segmented image sets and were further repaired and smoothed in Geomagic studio (2012, Geomagic, Carolina). Finally, the surface of the skull, the boundary of the suture, and the outer surface of the skin were grouped for further meshing.

Fig. 1.

The procedure of obtaining the piglet head three-dimensional geometry.

Meshing of the piglet head

The global procedure of meshing the piglet head is from inside to outside, as shown in Fig. 2. The meshing of the brain and cerebrospinal fluid (CSF) is according to the geometry of the inner surface of the skull. In view of the closed surface having irregular geometry and the conventional meshing method cannot automatically generate hexahedral solid elements, therefore, a structured butterfly meshing method was adopted in Truegrid software (3.1.3, XYZ Scientific Application Inc., CA) to generate high-quality solid elements. First, the block mesh with butterfly topology was constructed and placed at a suitable position on the closed surface. Then, the vertex, boundary, and face of the block were projected onto the corresponding point, curve, and surface of the target geometry. For example, some of the pre-designed block boundaries were projected onto the suture curves at the inner surface of the skull to provide a true trajectory for the suture. Finally, as the meshes were initially obtained, they were globally smoothed until higher quality meshes were obtained. To obtain CSF, the thickness of the outmost layer elements was adjusted to approximately coincide with the spacing size of the CSF region measured from CT scans. For the nasal cavity, it was meshed using the same butterfly meshing method as the brain.

Fig. 2.

The meshing procedure for the 1-week-old piglet head FE model.

Two layers of shell elements with the thickness of 0.5 mm, which were respectively extracted from the outer of the brain and CSF, were regarded as the pia mater and dura mater. The hexahedral solid elements of the skull and suture with non-uniform thickness were constructed by meshing the actual geometry of the skull reconstructed from CT scans. For the scalp and remained soft tissue (muscle and fat), several lays of solid elements were generated by filling the region from the outer surface of the skull and suture to the outer boundary of the soft tissue referring to CT reconstruction. A surface-to-surface contact type was defined between the skull and the dura, as well as the skull and the outer soft tissue. The node between brain and pia are shared, as well as the pia and CSF, the CSF and dura.

The final developed FE model is shown in Fig. 3. In total, the piglet head includes 500,001 elements, in which there are 491,041 solid elements and 8960 shell elements. The mesh quality assessment metrics are shown in Table 1. It is seen that the piglet head showed fairly high mesh quality. For example, the Jacobian (a comprehensive assessment metric of mesh quality) of 99% solid elements are greater than 0.6, and of 98.7% shell elements are greater than 0.7.

Fig. 3.

The FE model of the piglet head. (A) The skull and the interior components; (B) the scalp and the soft tissue.

Table 1.

The quality assessment metrics for the piglet head elements.

Element type	Jacobian	Warpage	Skew	Min quad angle	Max quad angle
Solid element	≥ 0.6	≤ 40	≤ 60	≥ 30	≤ 150
Proportion	99.0%	99.7%	98.7%	98.4%	98.2%
Shell element	≥ 0.7	≤ 30	≤ 50	≥ 30	≤ 150
Proportion	98.7%	99.9%	98.9%	99.3%	99.0%

Material properties of different components of piglet head

Skull, suture, CSF, dura and pia mater

The elastic constitutive model, incorporated with a maximum strain failure criterion, was used to represent the elastic and rupture behavior of the skull and suture. The elastic modulus and Poisson's ratio were from Coats and Margulies²⁶ and Margulies and Thibault,¹⁹ who measured the parameters by conducting three-bending tests on the cranium bones, and tensile tests on the sutures of 3–5 days old piglets. The failure of the skull and suture was controlled by the maximum strain from Coats and Margulies,²⁶ which was implemented in LS-DYNA (smp D R7.0.0. Livermore Software Technology Corporation, USA) through the keyword ∗MAT_ADD_EROSION. The CSF was modeled as fluid with a high bulk modulus used in a 3 – 5 days old piglet brain model developed by Coats et al.³² For the dura and pia mater, considering no direct material properties of young piglets were reported in the literature, thus, the material parameters used in a 1-year-old child head model by He et al.³³ were adopted in the current model.

Soft tissue

One-term Ogden model was used to represent the hyper-elastic behavior of soft tissues (muscle and fat), in which the expression was written as the strain energy function form as Eq. (1),²⁵

$$W\left({\lambda }_1,{\lambda }_2,{\lambda }_3\right)=\frac{{\mu }_1}{{\alpha }_1}\left({\lambda }_1^{{\alpha }_1}+{\lambda }_2^{{\alpha }_1}+{\lambda }_3^{{\alpha }_1}-3\right)$$ (1)

in which ${\mu }_1$ and ${\alpha }_1$ are the one-term shear modulus and stiffening parameter, respectively. ${\lambda }_1,{\lambda }_2,\text{ and }{\lambda }_3$ are the 3 principal stretch ratios. In uniaxial tension or compression, ${\lambda }_1$ is the first principal stretch ratio in tension or compression direction. According to the incompressible assumption (${\lambda }_1{\lambda }_2{\lambda }_3=1$), the other 2 principal stretch ratios can be obtained as Eq. (2).

$${\lambda }_2={\lambda }_3={\lambda }_1^{-\frac{1}{2}}$$ (2)

The ground-state shear modulus μ is defined as Eq. (3).

$${\mu }_1=\frac{2\mu }{{\alpha }_1}$$ (3)

Taking Eqs. (2), (3) into Eq. (1), it was simplified as Eq. (4).

$$W\left({\lambda }_1,{\lambda }_2,{\lambda }_3\right)=\frac{2\mu }{{\alpha }_1^2}\left({\lambda }_1^{{\alpha }_1}+2{\lambda }_1^{-\frac{{\alpha }_1}{2}}-3\right)$$ (4)

The engineering stress ($s_1$) can be obtained through the derivative of the strain energy W with respect to ${\lambda }_1$.

$$s_1=\frac{\partial w}{\partial {\lambda }_1}=\frac{2\mu }{{\alpha }_1}\left[{\lambda }_1^{{\alpha }_1-1}-{\lambda }_1^{-\left(1+\frac{{\alpha }_1}{2}\right)}\right]$$ (5)

The experimental data of the soft tissues from Myers et al.³⁴ were used in this study. During the test, the sample was wrapped in gauze soaked with normal saline and heated with a heat lamp to maintain the physiological temperature. The stress-strain history in Myers et al.³⁴ was first converted into a stress-stretch ratio curve according to ${\lambda }_1=1+\mathrm{\epsilon }$. Then, the stress-stretch curve was fitted using Eq. (5) (Fig. 4) to obtain the values of parameters $\mu$ and ${\alpha }_1$. Finally, $u_1$ can be calculated according to Eq. (3).

Fig. 4.

Fitting results on the stress-strain curve using one term Ogden model.

Brain

Prange and Margulies³⁵ conducted shear tests on the brain of the 5-day-old piglets to obtain the mechanical properties. One-term Ogden model mentioned above was used to represent the behavior of the brain. Under the shear conditions, ${\lambda }_3=1$, the other 2 principal stretch ratios can be obtained as Eq. (6).

$${\lambda }_2=\frac{1}{{\lambda }_1}$$ (6)

Taking Eq. (6) into Eq. (1), it was simplified as Eq. (7).

$$\text{W}=\frac{2\mu }{{{\alpha }_1}^2}[{\left({\lambda }_1\right)}^{{\alpha }_1}+{\left({\lambda }_1\right)}^{-{\alpha }_1}-2]$$ (7)

The relationship between ${\lambda }_1$ and engineering shear strain γ (2ε₁₂) can be defined as,

$${\lambda }_1=\frac{\gamma }{2}+\mathrm{（}1+\frac{{\gamma }^2}{4}{\mathrm{）}}^{\frac{1}{2}}$$ (8)

The Eq. (7) can be expressed as a function of the independent value of $\gamma$,

$$\text{W}=\frac{2\mu }{{{\alpha }_1}^2}[{\left(\frac{\gamma }{2}+\mathrm{（}1+\frac{{\gamma }^2}{4}{\mathrm{）}}^{\frac{1}{2}}\right)}^{{\alpha }_1}+{\left(\frac{\gamma }{2}+\mathrm{（}1+\frac{{\gamma }^2}{4}{\mathrm{）}}^{\frac{1}{2}}\right)}^{-{\alpha }_1}-2]$$ (9)

The relationship between shear stress and engineering shear strain can be obtained through the derivative of Eq. (9) with respect to γ, as Eq. (10).

$${\tau }_{12}=\frac{\partial W}{\partial \gamma }=\frac{2\mu }{{\alpha }_1}\left(\frac{1}{2}+\frac{\gamma }{4}{\left(1+\frac{{\gamma }^2}{4}\right)}^{\frac{-1}{2}}\right)[{\left(\frac{\gamma }{2}+1+{\frac{{\gamma }^2}{4}}^{\frac{1}{2}}\right)}^{{\alpha }_1-1}-{\left(\frac{\gamma }{2}+1+{\frac{{\gamma }^2}{4}}^{\frac{1}{2}}\right)}^{-{\alpha }_1-1}]$$ (10)

Taking Eq. (8) into Eq. (10), the relationship between shear stress and the first principal stretch ratio can be obtained as,

$${\tau }_{12}=\frac{\partial W}{\partial \gamma }=\frac{2\mu }{{\alpha }_1}\frac{{{\lambda }_1}^{{\alpha }_1}-{{\lambda }_1}^{-{\alpha }_1}}{{\lambda }_1+{{\lambda }_1}^{-1}}$$ (11)

Prange and Margulies³⁵ used Eq. (11) to fit the experimental data to obtain the values of $\mu$ and ${\alpha }_1$. According to Eq. (3), parameter $\mu$ was converted into ${\mu }_1$ for simulation.

Scalp

The mechanical properties of the scalp for 1-week-old piglets were obtained by conducting tensile tests, as shown in Fig. 5. The scalp cutting from the piglet is about 25 mm in length and 3 mm in width. The TA ElectroForce 5500 test instrument (New Castle, Delaware, USA) was used to conduct tensile tests. The experimental results showed that the stress-strain curve of the scalp was approximately linear, and the average elastic modulus of tests was 2.5 MPa.

Fig. 5.

Tensile tests on the piglet scalp.

The material properties of different components of the piglet head are summarized in Table 2.

Table 2.

Mechanical parameters of different components of piglet head.

Components	Material properties	Reference
Skull	$\rho =$ 2.15e −6 kg/mm3	Coats et al.26 Margulies et al.19
	$\nu =0.28$
	$E=$ 0.1589 GPa
	${\epsilon }_{ult}=$ 0.104 $\pm$ 0.011
Suture	$\rho =$ 1.13e −6 kg/mm3	Coats et al.26 Margulies et al.19
	$\nu =0.28$
	$E=$ 57.1 $\pm$ 8.2 MPa
	${\epsilon }_{ult}=$ 0.141 $\pm$ 0.0021
Pia	$\rho =$ 1.133e-6 kg/mm3,	He et al.33
	$\nu =0.45$
	$E=$ 11.5 MPa
Dura	$\rho =$ 1.133e-6 kg/mm3,	He et al.33
	$\nu =0.45$
	$E=$ 0.0315 GPa
CSF	$\rho =$ 1.0e-6 kg/mm3 K = 2.2 GPa	Coats et al.32
Brain	$\rho =$ 1.04e-6 kg/mm3	Prange et al.35
	$\nu =0.499$
	${\mu }_1$ = 1.056e-04 GPa
	${\alpha }_1$ = 0.01
Scalp	$\rho =$ 1.2e-6 kg/mm3,	Obtained by experiments
	$E=$ 2.5 MPa
	$\nu =0.42$
Soft tissue	${\mu }_1$ = 4.246e-05 GPa	Myers et al.34 Zhou et al.36
	${\alpha }_1$ = 9.78785
	$\rho =$ 1.2e-6 kg/mm3
	$\nu =0.42$

CSF: cerebrospinal fluid.

Model validation

The developed piglet head FE model was validated against the experimental data from 2 types of impact tests. The first type test is the guided drop tower test, in which a drop hammer impacts the piglet head from different heights. The other type test is the free-fall drop test conducted by Powell et al,²⁸ in which the piglet head freely drops toward the ground at different energy levels. Simulations were performed on the piglet head FE model according to the aforementioned test conditions. The LS-DYNA was used as the solver to conduct the simulation. The force-time histories from simulations were compared with the tests to verify the model.

Validation on the piglet head model according to the guided drop tower tests

Ethical approval for this research was obtained from the Institutional Review Board of School of Science, Beijing Jiaotong University. Four dead piglets at around 1week old were used to conduct drop tower tests, in which 2 samples were respectively used in 30 cm and 50 cm drop tower tests. A custom-designed guided drop tower is shown in Fig. 6, in which the drop hammer can drop freely along the guided rails. The drop hammer is 45 mm in diameter and 8 mm in thickness. As equipped with the load cell, the total mass is 2.92 kg. A load cell with capacity of 0.2 t and accuracy of 0.1% was fixed on the central location of the hammer to record the impact force. According to the testing on the equipment, the movement of the hammer can be equivalent to free fall. Before testing, the posture of the piglet head was adjusted to make sure the drop hammer can approximately impact the central location of the parietal bone, then the piglet head was fixed to the plate with straps. In testing, the hammer impacted the piglet heads from the heights of 20 cm and 50 cm, and the force-time histories were collected and slightly smoothed.

Fig. 6.

The testing apparatus and guided drop tower test on piglet head. (A) Testing setup and (B) guided drop tower test on piglet head.

Simulations were conducted on the piglet head FE model according to the test conditions. For the drop hammer, only the degree in Z-direction was kept since it can only move along the vertical direction in testing. Due to the constraint of the straps, some soft tissues at the bottom of the head were slightly compressed. To fulfill this in simulation, 2 loading steps were exerted on the FE model. The first equivalent loading step was to slowly compress the head to make the bottom soft tissues deform to a degree similar to that in the tests, and then the second loading step was triggered, in which the drop hammer impacted the piglet head FE model at a certain velocity. The drop heights of 20 cm and 50 cm were converted to the corresponding velocities according to $\nu =\sqrt{2gh}$, with the values of $1.98m/s$ and $3.1m/s$. The contact between the drop hammer and the piglet head model, as well as the contact between the piglet head model and the plate, were defined as surface-to-surface contact type.

The comparisons of force-time histories between the simulations and the experiments are shown in Fig. 7. The simulation results generally agree with the experiments at the aforementioned two impact velocities. The peak forces in simulations are fairly close to the experimental results, while the time durations are slightly longer. The comparisons of peak force between the simulations and the experiments are shown in Fig. 8. The average peak force of the 20 cm impact test is 611 N, and that of simulation is 645 N, with an error of 5.6%. The average peak force of the 50 cm impact test is 989 N, and that of simulation is 979 N, with an error of 1.0%. The comparisons of duration between the simulations and the experiments are shown in Fig. 9. Under the 20 cm impact condition, the experimental average duration is 25 ms, and the simulation duration is 24 ms, with an error of 4.0%. Under the 50 cm impact condition, the experimental average duration is 25 ms, and the simulation duration is 27 ms, with an error of 8.0%. The results show that the developed piglet head FE model exhibits a relatively high accuracy in predicting the dynamic response caused by the impact of a drop hammer.

Fig. 7.

The comparisons of force-time histories between the simulations and the experiments under hammer impact condition. (A) An impact velocity of 1.98 m/s and (B) an impact velocity of 3.13 m/s.

Fig. 8.

The comparisons of peak force between the simulations and the experiments under hammer impact condition. (A) An impact velocity of 1.98 m/s and (B) an impact velocity of 3.13 m/s.

Fig. 9.

The comparisons of duration between the simulations and the experiments under hammer impact condition. (A) An impact velocity of 1.98 m/s and (B) an impact velocity of 3.13 m/s.

Validation on the piglet head model according to the free-fall drop tests

Powell²⁸ conducted free-fall drop tests on the piglet heads at the age of 2 – 17 days. Considering the variability of different subjects, the experimental data for the subjects at the age of 3—12 days were used to verify the piglet head FE model. Simulations were conducted on the piglet head model under drop loading conditions. Two energy levels of 6.5 J and 11 J were involved in the drop tests in this age group. Based on these 2 energy levels and the piglet head mass, the free-fall velocities exerted on the FE model can be calculated according to $v=\sqrt{2W/m}$, with the corresponding values of 5.4 m/s and 7 m/s respectively.

The entire impact force-time histories were not provided in Powell,²⁸ thus the peak forces and time durations from simulations were compared with the experimental results (Noted that: in Powell's study, the time duration was defined as the total time taken until the impact forces began to decrease). As shown in Fig. 10, the simulated peak force and time duration generally lied within the corridor of the experimental ones at 2 impact energy levels, except the time duration at the impact energy of 11 J. It illustrates that the developed model can predict the global biomechanical responses of piglet head under drop loading conditions.

Fig. 10.

The comparisons of peak forces and time durations between the simulations and the experiments under drop loading condition. (A) Peak force and (B) time duration.

Discussion

Child head injury under impact scenarios (e.g. falls, vehicle crashes, etc.) is an important topic in the field of injury biomechanics. To study the head injury mechanism, biomechanical response, and the injury criterion, the gold standard is to conduct cadaver experiments, however, due to ethical reasons, the availability of the child cadavers and the experimental data are very scarce. Therefore, most developed FE models of child head at different ages cannot be validated against the corresponding experimental data.4, 5, 6^,10

Considering the physiological structures and the material properties of some animals, e.g. pigs, are similar to the corresponding parts of human, it is common to use piglet head as the surrogate of children. A piglet head FE model that validated against experimental data can investigate the biomechanical response. In this study, a detailed piglet head FE model was developed and validated against the experimental data under drop tower impact and free-fall drop conditions. It can provide insights on finite element modeling of pediatric head and injury prediction. In the meantime, it should be pointed out that the present model is still a preliminary model. Several limitations still exist, which need to be improved in future studies. One limitation is that the brain was constructed as a whole component in this model based on the CT scans; however, according to previous experimental studies on the material properties of different components of piglet brain,^22,25 the stiffness of the brainstem is much higher than those of the cerebrum and cerebellum. Therefore, the brain should be further divided into multiple parts using MRI data and assigned different material properties, and then a piglet head FE model including accurate regions of the brain can be developed to investigate the brain injury. The other limitation is that only a few drop tower impact tests were conducted on the piglet head to obtain the head global dynamic responses, and the information of skull fracture and brain response/injury was not taken into consideration. Next step, a more complicated and detailed test procedure should be designed to conduct more impact tests. The information of skull injury (fracture location, pattern, etc.) and brain injury (tissue strain, contusion, etc.) should be collected and analyzed besides the global force-time histories. These detailed experimental data can help to examine and improve the biofidelity of the developed FE model. Once the model was comprehensively verified by the experiments, it can be applied to investigate the skull and brain injury under real-world impact conditions.

In conclusion, a one-week-old piglet head FE model, as a surrogate of the pediatric head, has been developed in this study. The detailed anatomical structures of the head (skull, suture, brain, scalp, soft tissue, etc.) were reconstructed through actual CT scans, and they were respectively meshed by a structured butterfly method to obtain high-quality elements. The developed model was verified against the experimental data from both drop tower impact tests and free-fall drop tests. The results show that the model has fairly high accuracy in predicting head global dynamic responses under impact loading conditions.

Funding

This study was supported by the National Natural Science Foundation of China (Grant No. 51975041; No. 51505024), and Funding of Ministry of Industry and Information Technology for Civil Aircraft (Grant No. MJ-2018-F-18).

Ethical statement

The design is in compliance with ethical standards.

Declaration of competing interest

The authors declare that they have no competing interest.

Author contributions

Zhong-Qing Su and Rui Li conducted the simulation and drafting the manuscript; Da-Peng Li, Guang-Liang Wang and Lang Liu developed the FE model. Ya-Feng Wang and Ya-Zhou Guo conducted the guide drop tower tests. Zhi-Gang Li designed the study and polished the manuscript.