Mechanical Characterization of Immature Porcine Brainstem in Tension at Dynamic Strain Rates

Background

With a rapid rise in motor vehicle use around the world, large numbers of injuries and deaths due to road traffic accidents (RTAs) occur annually, as detailed in a report of World Health Organization (WHO) [1]. In some countries children account for a large proportion of traffic injuries. For example, although children aged 15 years and younger account for about 18% of the population in some developed countries, children injured in crashes account for about one-third of the pedestrian accident dataset [2].

Brain injury is still a leading cause of death and disability for children and adolescents involved in RTAs. A report by Langlois et al. [3] showed that approximately 475 000 TBIs occurred each year among children aged 0 to 1 years. It was suggested that trauma to the brainstem is a hallmark of severe head injury because of its important role in physiological function. The mechanism of brain injury has been discovered to substantially involve impact to or rotation of the head, causing deformation of the brain, in which brain injury is associated with strain and strain rate. Owing to the geometry of the central nervous system (CNS), the brainstem is vulnerable to the high strain induced by the combination of compression, tension, and shear, especially in rotational acceleration loading on the head [4].

Head computational models are powerful tools for use in studying adult traumatic brain injury (TBI) mechanisms and determining adult brain injury tolerance [5]. To discover age-pertinent mechanisms and estimate the injury threshold of children and young adults, models are needed for use in studying pediatric brain injuries [6]. Such tools depend heavily on knowledge of pediatric brain tissue material properties and anatomical structures. Owing to the paucity in basic data on the material properties of pediatric brain tissue and skull, the child head finite element model was developed, mostly by scaling the adult head models, in which the child model was regarded as a miniature adult model. However, recent studies show age-related differences in the brain [7,8], meaning that it is not reasonable to regard the child’s head as a miniature adult head.

There have been many studies concerning brain tissue properties. For example, compressive and tensile tests of brain tissue at quasi-static strain rates were done to study the tissue mechanical properties under surgical conditions owing to considerably lower strain rate [9,10]. Other studies were performed to address the mechanical properties of brain tissue during impact events with compression tests at strain rates of 1, 10, and 50/s and tension tests at strain rates of 0.9, 4.3, and 25/s [11,12]. In the experiments involving brain tissue compression and tension by Rashid et al. [13,14], the 30% strain rates were 30, 60, and 90/s. Numerous studies have reported the adult brain tissue mechanical properties associated with brain injury in experiments at over 20% strain at strain rats of between 1 and 100/s [13–18]. A few studies have reported on the material properties of immature brain tissue: Prange [19], Prange and Margulies [8], Duhaime et al. [20], Ning et al. [21], and Li et al. [22]. Consequently, the brain material properties of children are not well understood, especially the tensile behavior.

Due to ethics constraints, there is great difficulty in obtaining fresh brain tissue from children; therefore, in the present study we used immature porcine brain tissue to serve as a substitute to study pediatric brain tensile behavior. The aim of this study was to conduct tensile tests in immature brainstem specimens at high stretch velocity (i.e., dynamic strain rates) and then determine the mechanical behavior of the immature brainstem during traumatic events.

Material and Methods

SPECIMEN PREPARATION:

A total of 23 immature pigs from the same farm, aged 4 weeks (at a developmental stage similar to human toddlers), with an average weight of 16±0.5 kg, were killed at a local slaughter house (Chongqing BORN Biological Technology Co., Ltd.). The brain was harvested immediately from the pigs as byproduct, and then stored in a thermally insulated stainless steel vessel filled with a saline solution with 0.9% NaCl at 4–50°C to maintain ionic balance during transportation to our lab.

The cerebrum, cerebellum, and brainstem were separated in the lab, and then the midbrain of the brainstem was cut into a plate with a thickness of 5 mm along the axis of the upper brainstem. A steel circular trephine of a diameter of 9 mm with sharp edges was used to cut the brainstem plate to produce a specimen with a length of 5 mm and a diameter of 9 mm. In this section the main fibers of the brainstem were considered to orient along the long axis of the cylinder, as illustrated in Figure 1. During the preparation, the samples were sprayed with the physiological solution to maintain the in vitro physical environment.

EXPERIMENTAL STUDY:

To perform the tensile experiment, we used a computer-controlled, high test precision Bose ElectroForce 3100 machine (Bose Corporation, Gillingham, UK), adapted for testing biological specimens. The instrument contains an electromagnetic motor with a stroke resolution of 0.0015 mm and a maximum stroke length of 5 mm, and a minimum load resolution of 6 mN with a 22N load cell. The equipment was designed to have a high response speed so that the configured loading speed can be achieved instantly. The history of stretch and force experienced by the tissue were recorded when performing tensile tests.

EXPERIMENTAL PROTOCOL:

Owing to the great challenge in gripping the very soft biological tissue in the tensile test [10,23], great care was taken during preparation and testing of the specimens. We used tensile grips and clips of the apparatus to rigidly fix 2 glass slides in which the one fixed to the stroke was considered as the top, and the one fixed to the load cell was regarded as the bottom. A thin layer of surgical glue (Cyanoacrylate, low-viscosity Z105880-1EA, Sigma-Aldrich) was used to firmly cover the surface of both slides. The prepared tissue specimen was carefully placed on the bottom slide, and then the stroke was slowly lowered to slightly touch the superior surface of the specimen. The stroke was stopped when the load reached 5 mN. To ensure proper adhesion of the specimen to the top and bottom platen, the stroke would stay for 1 min prior to the tensile test.

After super- and sub-surfaces of the tissue were fixed to both slides using the procedure detailed above, the tests were carried out at stroke velocities of 10, 100, and 500 mm/s, in which the strain rate of the specimen was 2, 20, and 100/s, respectively. For all the test specimens, no preconditioning was done, and each sample only experienced 1 loading cycle. The final status of the specimens was checked when finishing the test, and the data were not used in subsequent analysis if the glue between the slides and faces of the specimen failed. All the tests were finished at room temperature of 22°C within 6 h postmortem.

DATA PROCESSING AND ANALYSIS:

The nominal stress, S11, was calculated using Formula (1), in which F represents the tension force in newtons, and A was the cross-section area of tested tissue in m2.

From the conclusion drawn by Miller [23], the stretch ratio λ for the specimen in the tensile test with confined conditions is related to the height change of the tissue if a value of hH is within 1.0~1.3, so

The constitutive models of immature brainstem tissue may be developed based on quasilinear viscoelastic (QLV) theory [24,25], in which the relationship between stress and strain tensors was derived from a strain energy potential function. The function, W, is defined using the invariants (I1, I2, I3) of the strain tensor. The third strain (I3) is unity, as the tissue is incompressible. As a result, the function is described in simplified form using I1 and I2. The invariants, I1 and I2, are defined as:

In the formulas, the squares of the principal stretch ratios, λ21,λ32, and λ32, had the relationship of λ21λ32λ32=1, due to incompressibility [26]. As assumed homogeneous deformation conditions of the brain tissue under tension, the Eulerian and Lagrangian principal axes of strain and stress are aligned with the tensile directions, with any 2 orthogonal axes x2, x3. Hence, the stretch ratios are indicated by the formula:

In the extensional test, the value of λ is not less than 1, so I₁ and I₂ are expressed by the formula:

Then, the stresses derived from the experiments may be compared to the predicted using the hyperelastic models from the formula:

The material parameters of some common hyperelastic models (e.g., Fung, Gent, and Ogden) may be obtained from fitting the curves.

Widely used to model soft biological tissues in tension, the Fung isotropic energy function depends on the first strain invariant only:

yielding the following nominal stress component S₁₁ along the x₁-axis:

where infinitesimal shear modulus μ(>0) and stiffening parameter b(>0) are the 2o constant material parameters [27].

Gent strain energy function, widely used to describe viscoelastic material, also depends on the first strain invariant only:

then,

in which infinitesimal shear modulus μ>0 and Jm>0) are the 2 constant material parameters [28].

Ogden strain energy function is given by:

producing the stress form:

in which μ>0 is the infinitesimal shear modulus, and α is a stiffening parameter [29].

In addition, an exponential model was used to fit the Lagrange stress-versus-stretch ratio shown by the following formula:

All operations for fitting were done using the software OriginPro^® 8.0. The t test was performed for infinitesimal shear modulus, μ, in which a value of p<0.05 was considered to be significant.

Results

The history curve of Lagrange stresses for the tested brainstem specimens determined according to the formula (1) are illustrated in Figure 2. The brainstem tissue stretch ratio λ was determined using equation (2) from the distance that the tissue was stretched. The curves of the stress-versus-stretch ratio shown in Figure 3 were convex in shape. The average Lagrange stress for the tested specimen at the 30% strain at the strain rates of 2, 20, and 100/s were 273.3±114, 515±107, and 1121±197 Pa, respectively.

From the curves of Lagrange stress-versus-stretch ratio illustrated in Figure 3, it was found that the material became stiffer with an increase in strain rate. An interesting phenomenon was that all curves indicated points of inflection at the tensile strain of about 2.5% in each test group.

The Lagrange stress-against-stretch ratio, λ, can be fitted with the strain energy function of Fung (0.820≤R2≤0.933), Ogden (0.774≤R2≤0.940), and Gent (0.650≤R2≤0.922), and the exponential model (0.852≤R2≤0.981), as shown in formulas (15–17). Figure 4 exhibits curve fitting of Fung, Ogden, and Gent strain energy function, and the exponential model for the average curve experimentally acquired. We noted that the change trend of stress increase at the 2.5% tensile strain did not agree well with the fitted models:

Table 1 lists the infinitessimal shear modulus, μ, derived from the fitted strain energy function, Fung, Ogden and Gent, in which the infinitessimal shear modulus, μ, was found to have a strong rate dependence. For Ogden model in the table, for instance, the infinitessimal shear modulus at the strain rate of 100/s seemed to be 4.2 times higher than that at the strain rate of 2/s.

Discussion

LIMITATIONS:

We attempted to describe the material properties of immature porcine brainstem tissue at dynamic strain rates to build a finite element model of the pediatric brain. However, our study has some limitations that need to be mentioned. First, the number of samples and valid data for studying the material properties of brainstem tissue from immature pigs was limited. Furthermore, pigs aged 4 weeks are similar to human infants, which only account for a small proportion of all children. In high-rate tests, there is a period in which the crosshead is ramping up to the specified speed, and it is not exactly clear how long it took to achieve this speed in our study. The brainstem is anisotropic and therefore may violate the assumption of Miller [23] that the materials are isotropic and incompressible. In this study, only tensile tests were done, and it would be better if the compression and shear tests could also be performed in discover the material properties of the brain. Finally, immature porcine brain tissue served as a substitute to study the pediatric material tensile behavior in the current study, but a significant difference may exist in material properties between pigs and humans.

Conclusions

To address the material properties of immature brainstem in tension, dynamic tensile tests at 3 stretch speeds were performed for the brainstem tissue specimens obtained from 4-week-old pigs in the present study. Although some limitations exist in our study, the results show that the immature brainstem is a rate-dependent material in dynamic tensile tests, and the tissue becomes stiffer with an increase of strain rate, with inflection points in all the test groups at the strain of about 2.5%. The function of Fung, Ogden, Gent, and exponential model may match well with the material behavior of the brainstem for immature pigs in dynamic tensile testing. The reported results may be useful in understanding brain injuries in children who have been in road traffic accidents.