Investigation of Loss of Consciousness Induced by Gravity Acceleration on the Human Brain

Abbas Shafiee^1*, Amirhossein Ahmadian², Mohammadali Alidoost³

¹School of Mechanical Engineering, Purdue University, West Lafayette, USA.
²Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA.
³Department of Bioengineering, University of California, Los Angeles, USA.

DOI: 10.4236/oalib.1107507                

Abstract

Traumatic Brain Injuries (TBI’s) are any disorder in a brain’s functionality that can be caused by numerous reasons, including motor-vehicle crashes, falls, and assaults. Impractical in-vivo head injury experiments compel bio- engineers to develop a robust, accurate, and efficient computer model. In this study, bovine brain samples were tested under a confined compression testing machine. Consequently, the result from unconfined compression tests, at quasi-static strain rates of ε=0.0004 s^-1, ε=0.008 s^-1, and ε=0.4 s^-1, and a stress relaxation test under unconfined uniaxial compression with a ε=0.67 s^-1 ramp rate were utilized for fitting brain tissue model. The tissue model employs Drucker stability criteria and conventional hyperelastic models. A finite element model was also developed and validated by experimental data to examine the experiments’ friction effect. Furthermore, the extracted brain tissue model was employed in a 3D head injury model. The 3D model was employed to examine the effect of +Gz acceleration on the human brain and present damage threshold based on loss of consciousness in HIC and Maximum Brain Pressure criteria. It is shown that the relative difference between simulation results at friction coefficient of μ=0.5 and μ=0.0 are less than 20%, and the ramp rate variation has a slight effect on normalized shear modulus. Moreover, Head modeling results revealed that the Maximum Brain Pressure ≥ 3.1 KPa and HIC ≥ 30 are a representation of loss of consciousness.

Keywords

Brain Tissue, Viscohyperelastic, Finite Element Analysis (FEA), TBI (Traumatic Brain Injury), G-Acceleration, Damage Criteria

1. Introduction

Introduction Traumatic Brain Injury (TBI) is a disruption in the brain’s normal function resulting from a blow or jolt to the head or an object penetrating brain tissue. TBI can have a wide range of physical and psychological effects including mild, moderate, and severe categories. The USA’s Centers for Disease Control and Prevention (CDC) reports that about 155 Americans die from Traumatic Brain Injuries (TBI)-related injuries each day in 2014 [1]. In a space mission where an astronaut’s brain is exposed to quasi-static and dynamic strain rates, the risk of TBI is increased. TBIs are one of the leading causes of death or disability [2] [3]. Pilots flying high-performance aircraft are exposed to loss of consciousness due to the +G_z forces and its consequent high acceleration. There are actual reports in the US and United Kingdom Royal Air Forces confirming such cases [4]. The importance of this matter compels bioengineers to predict the cause and effect of TBI. It is crystal clear that in-vivo experiments are not practical in the realm of TBI.

Ergo, the Finite Element Method (FEM) offers a cost-effective alternative [5] [6] [7] [8] [9] in bio-mechanical [10] - [17] and specifically human injury research [18]. Dynamic responses of brain tissues are required to model the head injury and foresee TBI accurately. Nevertheless, the relationship of skull kinematics and the tissue responses causing TBIs is not intuitional due to the fact that brain can deform with complicated and non-linear material properties as well as complex brain-skull boundary conditions [19] [20] [21].

Literature shows that the brain, like most tissues in our body, is a viscohyperelastic material, directionally changes [22] [23] and are time dependent [24].

There are a lot of researches to identify the complex mechanical behavior of structural materials, experimentally and analytically; however, there is not much in the area of biomechanics as to working with live tissues [25] - [33].

McCarty in her thesis tried to characterize the mechanical properties of brain tissues during and after blast induced TBIs in a stress relaxation experiment. The effect of blast impact and swelling were explored by exposing the porcine brains to a shock wave generated by an air pistol and soaking them in a container with saline solution, respectively. The results from this work extended the information about the dynamic mechanical behavior of brain tissue [34].

Menichetti et al. applied up to 35% strain at 10 s⁻¹ strain rate to 12 different regions of the human brain to assess the mechanical behaviors of several brain regions. Their results demonstrated that there are statistically significant differences between regions; however, age, sex, and time post-mortem had no effect [35].

A study has been done by Li et al., where a uniaxial compression tests at strain rates of 0.01 s⁻¹, 1 s⁻¹, and 50 s⁻¹ up to 50% strain were performed for the corona radiata, corpus callosum, thalamus, cortex, cerebellum, and brainstem. They concluded that there is no considerable difference in tissue strength among the cerebrum regions of cortex, thalamus, corona radiata, and corpus callosum. Moreover, outcomes show that the one-term Ogden constitutive model can well represent the compressive behavior of the brain tissue at different strain rates [36].

Mihai et al. conducted a myriad of multiaxial shear, tension, and compression tests to systematically delve into the brain’s mechanical behaviors’ time-dependent characteristics. They recognized that an isotropic modified one-term Ogden model is suitable for representing the hyperelastic behavior under a combined loading condition [37]. However, other alternative hyperelastic models could be adopted [38].

Teferra and Brewick conducted a study to specify parameter distributions of brain tissue data illustrating the mechanical properties by considering the hyperviscoelastic constitutive model as well as multiple loading configurations using a Bayesian calibration approach. Their results showed that by following this approach, a more in-depth parameter variation analysis and model calibration can be achieved [39].

From the head model perspective of this paper, some 3D head models were developed for different investigations and Targets. Ruan et al. applied an impact to Wayne State University Head Injury Model (WSUHIM) (introduced in 1993). They showed a relationship between contrecoup pressure, maximum shear stress, the severity of impact, and brain injury [40]. Using Simulated Injury Monitor (SIMon) human finite element head model, Zhang et al. to investigate head injury induced by linear and rotational acceleration. Rotational acceleration was found to play a significant role in the head injury mechanism [41].

Shi et al. employed the THUMS (Ver. 4.0.2) finite element model to reconstruct vulnerable road users’ kinematics vehicle collisions (ground impacts) using the video records to evaluate different head kinematics-based injury risks criteria by deriving various brain tissue severe injury thresholds. They concluded that angular acceleration, linear acceleration, head injury criterion (HIC), coup pressure (C.P.), maximum principal strain (MPS), and cumulative strain damage measure (CSDM) were able to predict 75% - 100% of the accident [42].

Stephanie A. Pasquesi et al. measured brain-skull displacements from a myriad of sagittally transected piglet heads subjected to sagittal plane rotations, developed a finite element model imitating the geometry of the sagittally transected piglet head, and determined a brain-skull boundary condition in the finite element model that was well in agreement with finite element displacements to experimentally extracted value [43].

To model a 3D human head and predict TBI at a quasi-static strain rate, one needs the accurate viscohyperelastic constitutive model based on the investigation’s application and targets. As literature shows, there are different reports for brain tissue’s mechanical properties, and no studies have been carried out, to our best knowledge, to investigate head damage due to pressure resulting from +G_z acceleration and report loss of consciousness based on Max. Brain Pressure and HIC criteria.

This study aims to present a suitable viscohyperelastic model with consideration of Drucker stability criteria and study the effect of friction coefficient and ramp rate on experimental results. In this paper, relaxation and unconfined compression tests are conducted on cylindrical specimens of bovine brain tissue under compression up to 30% strain at strain rates of $\stackrel{\dot{}}{\epsilon }=0.0004{\text{s}}^{-1}$, $\stackrel{\dot{}}{\epsilon }=0.008{\text{s}}^{-1}$, and $\stackrel{\dot{}}{\epsilon }=0.4{\text{s}}^{-1}$ for the compression and $\stackrel{\dot{}}{\epsilon }=0.67{\text{s}}^{-1}$ ramp rate with 80 s holding time for the relaxation. The hyperelastic parameters corresponding to Baltz-Co, Fung, Gent, Van Der Waals, Arruda-Boyce, Ogden, Polynomial, and Reduced Polynomial strain energy function are obtained, and viscoelastic parameters corresponding to the Prony series were extracted.

In order to validate viscohyperelastic parameters, Finite Element Analysis (FEA) was employed where it matches nicely with experimental findings. Activities in these regards serve the implication in neurosurgery, haptic device design, and human head modeling, where an accurate mechanical characterization of brain tissue is of crucial importance.

Hence, this paper’s next step is an investigation of the loss of consciousness threshold from +G_z acceleration using head damage criteria such as HIC and maximum brain pressure based on a developed 3D finite element head model. Results revealed that Max. Brain Pressure ≥ 3.1 KPa and HIC ≥ 30 represents loss of consciousness, and 3D plots are provided to depict the loss of consciousness based on Max. Brain Pressure and HIC criteria.

The paper is structured as follows: Section 2 introduces Material and Method, including the experiment procedure and the governing equations for hyperviscoelastic material. In addition, a 3D finite element head model is presented. In Section 3, results and discussions for unconfined compression tests and relaxation tests are presented, and required representative constants for brain tissue hyperviscoelasticity are extracted. A finite element simulation was conducted for brain specimens to compare the brain-behavior with experimental results under extracted hyperelastic constants. After validating this finite element model, we explored the friction coefficient’s effect on the unconfined compression tests and ramp rate variation on relaxations tests. In addition, a 3D finite element of the head model is presented in Section 2 and is tested under different +G_z accelerations. Loss of consciousness is expressed in terms of HIC criteria and Maximum Brain Pressure in a 3D domain afterward. And finally, the paper is concluded in Section 4.

2. Materials

2.1. Specimen Preparation

In vitro human brain tissue studies are hard to conduct; therefore, animal brain samples (such as monkey, porcine, bovine, and rat) are being used for the tests. Considering various animals’ brain tissue, studies have also showed that there is not any difference between the in vitro dynamic mechanical response [44] [45]. In this study, the fresh bovine brain is collected from the slaughterhouse. Brain sample preparation is in accordance with our previous work [46] [47]. Conducted experiments and sample preparations were within the animal welfare guidelines and regulations. The cylindrical specimen brain is shown in Figure 1.

The samples include a mixed white and gray matter. There is extensive work to look into the white and gray matter separately to differentiate white and gray matter properties and define accurate mechanical properties [48] [49] [50]. However, at low strain and strain rate, the white and gray matter can be assumed to be homogeneous and isotropic [51].

2.2. Experimental Setup

Unconfined compression tests were conducted on cylindrical cerebral specimens using a Hounsfield H10KS testing machine, equipped with a servomotor for displacement shown in Figure 2(a). The testing machine enables us to apply uniform velocity during the compression of tissue in the axial direction. This testing machine is directly connected to a computer. Force and displacement were recorded in real-time manner.

3. Methods

3.1. Unconfined Compression Tests

Unconfined compression tests are performed on bovine brain cylindrical specimens up to 30% strain. The velocity of the compression platen (top platen) is

Figure 1. (a) The prepared bovine brain; (b) Steel pipe for cutting brain specimen; and (c) The cylindrical Specimen brain [46] [47].

Figure 2. (a) Hounsfield H10KS testing machine; (b) The brain specimen under unconfined compression [46] [47].

adjusted to 0.6 mm/min (slow), 12 mm/min (medium), and 600 mm/min (fast) corresponding to approximate strain rates of 0.0004, 0.008, and 0.4, respectively. Ten unconfined compression tests were performed at strain rates of 0.0004 and 15 at strain rates of each 0.008 and 0.4. Some sample preservation measures taken before doing unconfined compression tests are listed in our previous studies [46] [47]. Figure 2(b) shows the brain specimen under unconfined compression [46] [47].

3.2. Relaxation Tests

A separate relaxation test was performed on bovine brain cylindrical specimens up to 30% strain. Also, ten relaxation tests were performed under finite step-and-hold uniaxial compression with 0.67 s⁻¹ ramp rate and 80 s hold time. The average rise time, measured from the force relaxation experiments, was 450 ms.

3.3. Phenomenological Constitutive Models

3.3.1. Hyperelastic Constitutive Models

Mechanical properties of some materials, such as modulus of elasticity, strongly depend on the rate of applying load. Usually, these materials have non-linear behavior with strain and strain rate dependence. These materials are categorized as hyperelastic.

Preliminaries

An elastic-free energy potential can derive a constitutive response called Hyperelasticity which can be utilized for the materials experiencing sizeable elastic deformation. Applications for elastomers such as vulcanized rubber and synthetic polymers, along with some biological materials, often fall into this category [52]. There are several strain energy potentials associated with hyperelastic materials, namely: Arruda-Boyce, Ogden, polynomial, reduced polynomial, Van der Waals, Fung, Gent, and Baltz-Ko hyperelastic models. These models are going to used and fitted to experimental results to reveal which one can be a best hyperelasticity description of the brain tissue for our experiments. Four our future use, the 2^nd order reduced polynomial hyperelastic model is described here.

Second-order Reduced Polynomial Strain Energy Function

The hyperelastic 2^nd order reduced polynomial strain energy function U for the incompressible isotropic material is as follows:

$U={\displaystyle \underset{i=1}{\overset{N}{\sum }}}{C}_{i0}{\left(I_1-3\right)}^i$ (1)

In Equation (1), where $C_{i0}$ is a temperature-dependent material parameter which should be positive (for the satisfaction of Drucker stability), $I_1$ first strain invariant, and ${\mu }_0$ is the initial shear modulus. $I_1$ and ${\mu }_0$ are:

$I_1={\lambda }_1^2+{\lambda }_2^2+{\lambda }_3^2={\lambda }_U^2+2{\lambda }_U^{-1}$ (2)

${\mu }_0=2C_{10}$ (3)

where ${\lambda }_U$ is a stretch. Then the nominal stress $T_U$ is [53]:

$T_U=2\left({\lambda }_U-{\lambda }_U^{-2}\right){\displaystyle \underset{i=1}{\overset{N}{\sum }}}i{C}_{i0}{\left(I_1-3\right)}^{i-1}$ (4)

It should be noted that the Drucker stability criterion is a strong condition on the incremental internal energy of a material, which states that the incremental internal energy can only increase [54].

3.3.2. Prony Series for Viscoelastic Material

The Prony series can express the shear relaxation modulus (G(t)) of a viscoelastic material.

$G\left(t\right)=G_{\infty }+{\displaystyle \underset{i=1}{\overset{N}{\sum }}}{G}_i\exp \left(-\frac{t}{{\tau }_i}\right)$ (5)

where ${\tau }_i$, $G_i$, and $G_{\infty }$ are relaxation times, relaxation modulus constants, and

long-term shear modulus, respectively. If $G\left(0\right)=G_0=G_{\infty }+{\displaystyle {\sum }_{i=1}^N}{G}_i$, $g_i=\frac{G_i}{G_0}$, then:

where is normalized shear modulus $g\left(t\right)$ can be written as:

$g\left(t\right)=g_{\infty }+{\displaystyle \underset{i=1}{\overset{N}{\sum }}}{g}_i\exp \left(-\frac{t}{{\tau }_i}\right)$ (6)

since,

$1=g_{\infty }+{\displaystyle \underset{i=1}{\overset{N}{\sum }}}{g}_i$ (7)

the Equation (6) can be arranged to look like

$g\left(t\right)=1+g_{\infty }+{\displaystyle \underset{i=1}{\overset{N}{\sum }}}\left[g_i\exp \left(-\frac{t}{{\tau }_i}\right)-1\right]$ (8)

Specifically for two terms of viscoelastic Prony series, we have:

$g\left(t\right)=1-\left(g_1+g_2\right)+g_1\exp \left(-\frac{t}{{\tau }_1}\right)+g_2\exp \left(-\frac{t}{{\tau }_2}\right)$ (9)

3.4. Three Dimensional Finite Element Head Model Development

In this section, a 3D finite element head model is presented. Our model is composed of three parts, including skull, meningeal layer, and brain.We have used the 3D human head model developed in our previous work [55] [56].

The material properties implemented in the model are presented in Table 1. In order to describe the hyperelastic and viscoelastic mechanical behavior of the

Table 1. The implemented mechanical properties of the skull, meningeal layer, and brain tissues in our 3D FE model.

tissue, the 2^nd order reduced polynomial hyperelastic model and the Prony series were used.

The parameters of the 2^nd order reduced polynomial viscohyperelastic model used for three dimensional head model will be presented in the results section, as a finding from unconfined compression tests.

Our previous work [55] explains well the mesh properties, boundary conditions between the skull, meningeal layer, and brain and provides model validation using literature [60] [61] [62] [63].

4. Results and Discussion

4.1. Unconfined Compression Tests

The experimental data for slow, medium and fast strain rate are shown in Figures 3(a)-(c), respectively. In these figures and similar figures in this paper, solid

Figure 3. Experimental results for the compression of brain tissue at various loading velocities. (a) Loading velocity of 0.6 mm/min (slow), corresponding to a strain rate of 0.0004. (b) Loading velocity of 12 mm/min (medium), corresponding to the strain rate of 0.008. (c) Loading velocity of 600 mm/min (fast); corresponding to the strain rate of 0.4.

curves are the mode of experimental results, and vertical lines are scattering line at the specific axial strain. The stress-strain curves are concave upward for all compression rates, and by increasing strain rate, the brain tissue becomes stiffer.

4.2. Relaxation Experimentation

Stress versus time for relaxation test with 0.67 s⁻¹ ramp rate and 80 sec. Hold time is shown in Figure 4.

As can be seen in Figure 4, stress increases in a short period and relaxes afterward.

4.3. Fitting of Constitutive Hyperelastic Models to Unconfined Compression Test Result

The material coefficients of the hyperelastic models are calibrated by lsqcurvefit function in MATLAB^® from experimental stress-strain data at a slow rate. This function minimizes the relative error in stress [64]. For the nominal stress-nominal strain data pairs, the relative error E was minimized, where:

$E={\displaystyle \underset{i=1}{\overset{N}{\sum }}}{\left(1-\frac{T_i^U}{T_i^{test}}\right)}^2$ (10)

$T_i^{test}$ ’s are stress value from the test data and $T_i^U$ ’s come from one of the nominal stress expressions derived in Section 2. 2^nd order reduced polynomial hyperelastic model was found to be the most suitable with the highest accuracy, fewer parameters, and shorter computational time requirements. The experimental data and fitted model of 2^nd order reduced polynomial is shown in Figure 5. An agreement exists between the two shown curves as the following.

Figure 4. Experimental results for relaxation of brain tissue with 0.67 s⁻¹ ramp rate and 80 sec. hold time.

Figure 5. Experimental (green dotted line) and theoretical (solid red line) engineering stresses at each stretch.

The parameters of 2^nd order reduced polynomial hyperelastic model, and the coefficient of determination (R²) is tabulated in Table 2.

Using Equation (3), the initial shear modulus is $G_0=1.0162\text{kPa}$. In similar research by Miller and Chinzei (2002) [65] and Rashid et al. (2013) [60], the initial shear modulus is shown to be $G_0=0.842\text{kPa}$ and $G_0=1.038\text{kPa}$, respectively. In the present study, Drucker stability criteria are considered in the parameters extraction of strain energy function while most previous studies such as Refs. [44] [65] [67] [68] [69] have not considered this important criterion.

Table 2. The parameters of 2^nd order reduced polynomial hyperelastic model.

4.4. Fitting of Prony Series Model to Relaxation Test Result

According to Quasi-linear viscoelastic (QLV) theory, the normalized shear modulus is independent of strain up to 30% strain [70]. In this research, the linear viscoelastic theory was used, and it was shown that at least two terms of the In fact, the Prony series (Equation (6)) are needed to capture the material relaxation behavior accurately. Two terms of the Prony series parameters and coefficient of determination (R²) are tabulated in Table 2 and calibrated by lsqcurvefit function.

The parameters in Table 2 and Table 3 can be directly used in finite element commercial software such as ABAQUS^® or ANSYS^®.

4.5. Finite Element Analysis

In this section, the results of the finite element analysis are compared with experimental data. In order to carry out finite element analysis, two parts include top and lower rigid parts as top and lower platens, and a deformable part as a brain specimen is created in ABAQUS^® Finite Element Analysis (FEA) software. The property of deformable part (brain specimen) was assigned according to Table 2 and Table 3. The number of nodes and the number of elements are 3990 and 3380, respectively, and element type are C3D8R (a 8-linear node brick reduced integration hourglass energy). Meshed assembly parts in ABAQUS^® FEA are shown in Figure 6. Mesh convergence tests were performed to validate the mesh density used, and hourglass energy analysis was conducted to evaluate all FE simulations’ integrity.

It is noticeable in all FE simulations for unconfined compression tests, relaxation tests, and ramp rate variation on the relaxation test, the friction coefficient hypothesized to be $\mu =0.1$ [69] [71]. The effect of friction coefficient and ramp rate in the relaxation test are studied. FE simulations of unconfined compression tests at three velocities are depicted in Figures 7(a)-(c).

As shown in this Figure 8, the relative error between experimental and FE simulation decreases as strain rate increases. These phenomena can be owing to the elimination of the viscoelastic effect at a high strain rate. FE simulation of relaxation test is presented in Figure 10. This figure indicates that a reasonable agreement exists between experimental and FE simulations.

Figure 9(b) and Figure 9(a) present the variation of ramp rate on the relaxation test using finite element analysis. FE simulation was conducted for three ramp rates of 1, 10, and 450 ms.

From Figure 9, it is evident that the ramp rate has little effect on normalized shear modulus. The relative difference between ramp rates of 1 and 450 ms is about 4.6%. Effect of the friction coefficient between the top and bottom platen

Table 3. Two terms of the Prony series parameters.

Figure 6. Meshed assembly parts in ABAQUS^® FEA.

Figure 7. Comparisons of experimental (green dotted line) and finite element simulation (red solid line) engineering stress vs strain: (a) Loading velocity 0.6 mm/min (slow), (b) Loading velocity 12 mm/min (medium), (c) Loading velocity 600 mm/min (fast).

Figure 8. Results of experimental (solid black line) and FE simulation (red dotted line) engineering stresses vs. time.

with cylindrical brain specimen at a speed of 600 mm/min in unconfined compression test are investigated using finite element analysis. The findings of the simulation and experiment are shown in Figure 10. As can be seen in Figure 10, as the friction coefficient increases, the difference between numerical and experimental results for the associated stress reduces. The relative difference between simulation results at a friction coefficient of $\mu =0.5$ and $\mu =0$ is less than 20%.

Figure 11 presents stress distribution in the cylindrical brain specimen at a speed of 600 mm/min in an unconfined compression test for two different friction coefficients.

Figure 9. Effect of ramp rate variation on relaxation test.

Figure 10. Effect of friction coefficient on stress-strain curve at strain rate of 600 mm/min in unconfined compression test.

Figure 11. The influence of friction coefficient on stress and displacement distribution (a) frictionless (b) mu = 0.1.

It is clear that as friction coefficient increases, stress and displacement distribution become non-uniform.

4.6. +G_z Accelerations

Brain damage criteria such as HIC and Maximum Brain Pressure are evaluated at different +G_z acceleration using the 3D model. Developed 3D FE model was subjected to +G_z that is a squared sinusoidal pulse (sin²) with an amplitude of a₀ and duration of T. The equation of the pulse may be written as:

$a=a_0\left({\sin }^2\frac{\pi }{T}t\right)$ (11)

The maximum velocity $V_{\max }$ occurs at time T and $V_{\max }=\frac{a_{0}T}{2}$. The HIC criteria may be defined as follows [72] in Equation (12):

$\text{HIC}=\max \left(\left[t_2-t_1\right]{\left[\frac{1}{t_2-t_1}{\displaystyle {\int }_{t_1}^{t_2}}a\left(t\right)\text{d}\left(t\right)\right]}^{2.5}\right)$ (12)

then:

$\text{HIC}=T{\left(\frac{a_0}{2}\right)}^{2.5}=T{\left(\frac{v_{\max }}{T}\right)}^{2.5}=v_{\max }{\left(\frac{a_0}{2}\right)}^{1.5}$ (13)

Scott et al. (2012) presented the threshold of +G_z-induced Loss of Consciousness (G-LOC) curve from physiologist’s perspective (Figure 12) [73]. While G-LOC was induced by +G_z stress, the G-LOC curves were developed for prediction according to a theoretical concept in which acceleration influences underlying physiological mechanisms affording tolerance to acceleration, their limitations, and what happens when they are exceeded. A minimal dataset of sign and symptom endpoints led to the basis of previous +G_z-time tolerance curves [74]. In order to express G-LOC threshold based on HIC and Maximum Brain Pressure criteria, Equation (13) and 3D FE model simulations were used, respectively. At selected points (Red points) of acceleration and time (Figure 12), the related maximum brain pressure was evaluated by our 3D FE model simulations.

4.7. Three-Dimensional Configuration of Loss of Consciousness Threshold

Critical points of loss of consciousness at a specific amplitude and time duration (Figure 12) are specified based on maximum brain pressure as indicated on third axes of loss of consciousness threshold domain (Figure 13). Similarly, loss of consciousness threshold may be presented in a 3D domain with HIC criteria as the third axis (Figure 14).

From Figure 13 and Figure 14, it is evident that Max. Brain Pressure 3.1 KPa and HIC 30 are a representation of loss of consciousness. For example, pressure on the entire brain at the time of t = 3 Sec. at point F (acceleration of 4G and time duration of T = 6 Sec.) is shown in Figure 15.

Figure 12. G-LOC tolerance curve [73].

Figure 13. Maximum brain pressure induced +G_z acceleration.

Figure 14. HIC criteria for GLOC.

A study of the previous investigations indicates a loss of consciousness addressed qualitatively by the researchers and rarely quantifies through an engineering perspective. In the present study, two 3D dimensional domains are developed for Max. Brain Pressure and Loss of consciousness criteria.

Figure 15. Pressure (KPa) in the entire brain at the time of t = 3 s on point F (acceleration of 4G and time duration of T = 6 Sec.).

5. Conclusions

This study highlights the importance of strain rate effects on brain trauma under finite deformation. In this regard, experimental setup on brain tissue was developed to perform unconfined compression tests at quasi-static strain rates of $\stackrel{\dot{}}{\epsilon }=0.0004{\text{s}}^{-1}$, $\stackrel{\dot{}}{\epsilon }=0.008{\text{s}}^{-1}$, and $\stackrel{\dot{}}{\epsilon }=0.4{\text{s}}^{-1}$ and a stress relaxation test under unconfined uniaxial compression with a $\stackrel{\dot{}}{\epsilon }=0.67{\text{s}}^{-1}$ ramp rate. We found that the 2^nd order reduced polynomial hyperelastic model is favorable among different hyperelastic models due to its accuracy, fewer parameters, and shorter computational time requirements. Drucker stability criterion has been utilized to extract parameters of the strain energy function. Also, the obtained parameters can be directly used in any commercial finite element software. Finite element simulation is conducted based on an experimental setup. Conducting ramp rate effects on the relaxation test indicates that the ramp rate variation has a slight effect on normalized shear modulus. Finally, it has been shown that the relative difference between simulation results at a friction coefficient of $\mu =0.5$ and $\mu =0$ is less than 20%.

Moreover, a 3D head model, constructed based on a human head’s real data, was used to apply +G_z accelerations, thus obtaining maximum brain pressure. The threshold of loss of consciousness arising from +G_z acceleration considering brain damage criteria such as HIC and maximum brain pressure is presented. Results revealed that the Maximum Brain Pressure ≥ 3.1 KPa and HIC ≥ 30 are a representation of loss of consciousness. Finally, two 3D domains were developed for the loss of consciousness, according to Max. Brain Pressure and the HIC criteria.

Acknowledgements

The first author would like to sincerely thank Dr. M.T. Ahmadian. This work would not have been possible without his scientific supports.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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