**2. Head injuries**

The human head consists of three components [9],


Injuries to the skin may be categorized as superficial or deep, and include contusion (bruise), laceration (cut), and abrasion (scrape). Injuries to the skull may break one or more of the bones of the skull in which case the skull is said to have been fractured (broken). Two aspects of a skull fracture are 1) whether it is open, or 2) depressed [10]. Injuries to the brain and associated soft tissue are the result of either head impact or abrupt head movement (e.g., deceleration injury) or some combination of the two. Injuries may be due to the skull fracturing and being pushed inward (a depressed fracture), or from the brain impacting the interior of the skull, or from internal stressing of the brain (i.e., shear, tension and/or compression). The complexities of the head and brain systems are reflected in head injury consequences, Figure 3.

**Figure 2.** Anatomy of the human head [10]

96 Injury and Skeletal Biomechanics

**2. Head injuries** 

**P**eriosteum

consequences, Figure 3.

**Figure 1.** Scope of traumatic brain injury in comparison to other modalities [13]

2. The skin and other soft tissue covering the skull. Which consists of layers known as the SCALP (**S**kin, **C**onnective Tissue, **A**poneurosis (Galea), **L**oose connective tissue and

3. The contents of the skull. Most notably the brain, but also including the brain's protective membranes (meninges) and numerous blood vessels, shown in Figure 2 Injuries to the skin may be categorized as superficial or deep, and include contusion (bruise), laceration (cut), and abrasion (scrape). Injuries to the skull may break one or more of the bones of the skull in which case the skull is said to have been fractured (broken). Two aspects of a skull fracture are 1) whether it is open, or 2) depressed [10]. Injuries to the brain and associated soft tissue are the result of either head impact or abrupt head movement (e.g., deceleration injury) or some combination of the two. Injuries may be due to the skull fracturing and being pushed inward (a depressed fracture), or from the brain impacting the interior of the skull, or from internal stressing of the brain (i.e., shear, tension and/or compression). The complexities of the head and brain systems are reflected in head injury

The human head consists of three components [9],

1. The bony skull - Cranial and facial bones

**Figure 3.** Flowchart of TBI injury assessment criteria development

The injury to the brain may be categorized in terms of, 1) The cause of injury, either contact vs. non-contact, 2) The type of injury, either primary in which the injury occurs at the time of initial injury producing event, or secondary where the injury results from some injury producing event but does not develop until somewhat later (through an intermediate process such as a metabolic effect), and 3) the type of injury, either focal (i.e. fairly localized) or diffuse (rather distributed) as shown in Figure 3.

Comparison of Intracranial Pressure by Lateral and Frontal Impacts – Validation of Computational Model 99

The shell was assumed to be filled with an inviscid fluid of density (f) and Bulk modulus (B) [5]. The impact mass, contact stiffness, impact velocity, angular velocity, accelerations, young's modulus, poison's ratio, time duration, height of the head(projectile) and an impactor influence severity of external forces were incorporated in the model. Effect of impact mass, contact stiffness and impact velocity on pressure-time histories have been

(Rf- inviscid fluid of density, B- Bulk modulus, Esol; Esh and nsol; nsh are the Young's moduli and Poisson's ratio of solid and shell (Sphere), respectively. At occipital side of skull msh-mass of spherical shell-1.96 kg, h - thickness -0.00561, Rsh- radius of spherical shell-

The maximum acceleration of either projectile or head, assuming a quasi-static global response of the system, can be obtained by dividing the maximum force transmitted by the mass of the projectile or head, respectively [5]. For t>6ms impact time duration, neck force also needs to be considered, Figure 5, while calculating the resultant head accelerations. For short duration impacts (<6ms), the neck does not influence the kinematic head response [35,

Load or force to fracture/failure of the skulls of 12 unembalmed cadavers heads were reported by Yoganandan [19]. Using a hemispherical impactor with a 48 mm radius, they carried out impacts to various locations on the skull at a rate of 7.1–8.0 m/s. Failure loads ranged between 8.8 and 14.1 kN, with an average of 11.9 kN. Allsop [20] carried out temporo-parietal impacts on 31 unembalmed cadaver heads with two types of flat rigid impactors––one circular and 2.54 cm in diameter, the other a rectangular plate 5x10 cm. Fracture force for the small circular plate ranged between 2.5 and 10 kN with an average of 5.2 kN. Fracture force for the rectangular plate ranged between 5.8 and 17 kN with an

0.0725m, Msol- mass of solid, Rsol- outer radius of solid, Dv- velocity)[5]

�∗�����1����

��3����ℎ�

� �

�� � ���

**Figure 4.** Illustrative representation of the analytical shell model.

described in [6].

*2.1.3. Accelerations* 

*2.1.4. Contact area* 

43].

3 4 � 16 15� � � �∗ � �

�∗ � ��<sup>∗</sup> � ��� � � +

In injury producing events, there are generally 3 collisions which occur [2]:


### **2.1. Parameters that control head injury**

A number of publications [17-43] discuss modeling and analyses of TBI using specific tools [44- 45]. Gong [16] recently proposed a simple head-striker model to simulate the contact between a human head and a foreign-object striker. Based on the head-striker model, they formulated a contact force function, which is a function of time, impact mass, contact stiffness, impact velocity, and material properties of the head and neck. The contact force function was used for the estimation of the contact force between the human head and the foreign striker [5, 16].

### *2.1.1. Force*

The contact force can be approximated [16] from the equation below. Then the estimated contact force may be used in two ways: 1) for the assessment of the exterior head injury, such as scalp damage, skull fracture, and 2) as input to the head model to predict the inner head injury, such as hematoma and brain injury [5].

$$Fmax = \frac{R \ast^{\frac{1}{5}} E \ast^{\frac{2}{5}} m \ast^{\frac{3}{5}} \Delta \nu^{\frac{6}{5}} E\_{sh}^{\frac{1}{2}} h}{\left(\frac{1}{\sqrt{2.3}}\right) R \ast^{\frac{1}{5}} E \ast^{\frac{2}{5}} m \ast^{\frac{1}{10}} \Delta \nu^{\frac{1}{5}} R\_{sh}^{\frac{1}{2}} (1 - \nu\_{sh}^2)^{\frac{1}{4}} + \left(\frac{\sqrt{3}}{2}\right) \left(\frac{16}{15}\right)^{\frac{1}{10}} E\_{sh}^{\frac{1}{2}} h}$$

The terminologies are explained in the original reference [16].

$$\frac{1}{R\_{R^\*}} = \frac{1}{R\_{\rm sol}} + \frac{1}{R\_{\rm sh}}, \ \frac{1}{m^\*} = \frac{1}{m\_{\rm sol}} + \frac{1}{m\_{\rm sh}} \quad and \ \frac{1}{E^\*} = 1 - \frac{\nu\_{\rm sol}^2}{E\_{\rm sol}} + 1 - \frac{\nu\_{\rm sh}^2}{E\_{\rm sh}}$$

### *2.1.2. Time duration*

An analytical model [17] was proposed the impact of a fluid-filled spherical shell of mass (msh), thickness (h) and outer radius (Rsh) with a solid homogeneous isotropic elastic sphere of mass (msol) and outer radius (Rsol) at a relative velocity( Dv) as shown in Figure 4.

$$Tp = \pi \sqrt{\frac{\frac{3}{4} \left(\frac{16}{15}\right)^{\frac{1}{5}} m^{\*\frac{4}{5}}}{R^{\*\frac{2}{5}} E^{\*\frac{4}{5}} \Delta \nu^{\frac{2}{5}}}} + \frac{m^\* R\_{sh} \sqrt{\left(1 - \nu\_{Sh}^2\right)}}{2.3 \, E\_{sh} h^2}$$

The shell was assumed to be filled with an inviscid fluid of density (f) and Bulk modulus (B) [5]. The impact mass, contact stiffness, impact velocity, angular velocity, accelerations, young's modulus, poison's ratio, time duration, height of the head(projectile) and an impactor influence severity of external forces were incorporated in the model. Effect of impact mass, contact stiffness and impact velocity on pressure-time histories have been described in [6].

**Figure 4.** Illustrative representation of the analytical shell model.

(Rf- inviscid fluid of density, B- Bulk modulus, Esol; Esh and nsol; nsh are the Young's moduli and Poisson's ratio of solid and shell (Sphere), respectively. At occipital side of skull msh-mass of spherical shell-1.96 kg, h - thickness -0.00561, Rsh- radius of spherical shell-0.0725m, Msol- mass of solid, Rsol- outer radius of solid, Dv- velocity)[5]

### *2.1.3. Accelerations*

98 Injury and Skeletal Biomechanics

within the occupant.

���� = 

� �<sup>∗</sup> <sup>=</sup> � ���� <sup>+</sup> � ��� , � �<sup>∗</sup> <sup>=</sup> � ���� <sup>+</sup> � ���

*2.1.2. Time duration* 

*2.1.1. Force* 

or diffuse (rather distributed) as shown in Figure 3.

subsequent contact with the vehicle interior.

head injury, such as hematoma and brain injury [5].

� <sup>1</sup> √2.3��∗�

**2.1. Parameters that control head injury** 

In injury producing events, there are generally 3 collisions which occur [2]:

The injury to the brain may be categorized in terms of, 1) The cause of injury, either contact vs. non-contact, 2) The type of injury, either primary in which the injury occurs at the time of initial injury producing event, or secondary where the injury results from some injury producing event but does not develop until somewhat later (through an intermediate process such as a metabolic effect), and 3) the type of injury, either focal (i.e. fairly localized)

1. The "first collision" is where injury producing event occurs, e.g. the vehicle strikes another car or object and as a result the vehicle is rapidly decelerated and/or rotated. 2. The "second collision" is the movement of the occupants in the vehicle and their

3. The "third collision" is when the internal organs of the occupant collide and/or move

A number of publications [17-43] discuss modeling and analyses of TBI using specific tools [44- 45]. Gong [16] recently proposed a simple head-striker model to simulate the contact between a human head and a foreign-object striker. Based on the head-striker model, they formulated a contact force function, which is a function of time, impact mass, contact stiffness, impact velocity, and material properties of the head and neck. The contact force function was used for the estimation of the contact force between the human head and the foreign striker [5, 16].

The contact force can be approximated [16] from the equation below. Then the estimated contact force may be used in two ways: 1) for the assessment of the exterior head injury, such as scalp damage, skull fracture, and 2) as input to the head model to predict the inner

> � ∗� � � ∗ � � � ∗ � � �� � � ��� � � ℎ

> > �� ��� ���� �

An analytical model [17] was proposed the impact of a fluid-filled spherical shell of mass (msh), thickness (h) and outer radius (Rsh) with a solid homogeneous isotropic elastic sphere

of mass (msol) and outer radius (Rsol) at a relative velocity( Dv) as shown in Figure 4.

� �1−��� � � � � + �√3

> �<sup>∗</sup> =1− ���� � ����

 ��� �

<sup>2</sup> � �<sup>16</sup> 15�

+1− ��� � ���

� �� ��� � � ℎ

� � ∗ � � � ∗ �

The terminologies are explained in the original reference [16].

The maximum acceleration of either projectile or head, assuming a quasi-static global response of the system, can be obtained by dividing the maximum force transmitted by the mass of the projectile or head, respectively [5]. For t>6ms impact time duration, neck force also needs to be considered, Figure 5, while calculating the resultant head accelerations. For short duration impacts (<6ms), the neck does not influence the kinematic head response [35, 43].

### *2.1.4. Contact area*

Load or force to fracture/failure of the skulls of 12 unembalmed cadavers heads were reported by Yoganandan [19]. Using a hemispherical impactor with a 48 mm radius, they carried out impacts to various locations on the skull at a rate of 7.1–8.0 m/s. Failure loads ranged between 8.8 and 14.1 kN, with an average of 11.9 kN. Allsop [20] carried out temporo-parietal impacts on 31 unembalmed cadaver heads with two types of flat rigid impactors––one circular and 2.54 cm in diameter, the other a rectangular plate 5x10 cm. Fracture force for the small circular plate ranged between 2.5 and 10 kN with an average of 5.2 kN. Fracture force for the rectangular plate ranged between 5.8 and 17 kN with an

��

given degree of injury the logarithmic slope of the exposure time and acceleration graph is approximately –2.5. This relationship proposes the Severity Index (SI) as a measure of the injury potential of an impact [25]. SI is the integral of the acceleration time curve, weighted

> �� � � � ���� �

> > �

Where *a (t)* is the acceleration-time pulse of the impact and *T* is its duration. An SI score of 1000 approximates the limit of human tolerance. Impacts with a higher score have a non-

Severity Index SI [25] calculates distress of an impact in a way that quantifies the risk of head injury. In practice, SI scores are logical predictors of the injury potential of impacts that produce focal brain injuries. For impacts of lower intensity but longer duration, the SI calculation produces unreasonably high values that predict more severe injuries than those actually observed in cadaver experiments. The Head Injury Criterion (HIC) is an alternative measure of impact severity that is not subject to these errors. The HIC score is given by:

��� � ���

values

Where *t0* and *t1* are the beginning and end times of the portion of the acceleration-time pulse being examined. The integral account for the duration of the acceleration and an iterative

� ��� ��

value or gmax score.

the area under the curve

�������

(A) Acceleration-time pulse from an impact between a surrogate head and an artificial turf surface, showing the peak

(B) The same pulse with acceleration

exponentiated to power 2.5. The SI score is

(C) As (B) but showing the time limits, t0 and t1, that maximize the HIC score.

����

by the 2.5 factor observed in the Wayne State Tolerance Curve and calculated as

zero probability of causing a life-threatening brain trauma [7].

��� � ��� ���� � ��� � <sup>1</sup>

search found the time interval (t0, t1) to maximize the HIC score [7], Figure 7.

**Figure 7.** Example of SI and HIC calculations [7]

**Figure 5.** Force mechanism for head-neck [48]

average of 12.4 kN. The authors concluded that there is a significant relationship between contact area and fracture force. Thus, impacts with the ground are likely to require higher forces than with a smaller impactor [4].

### **2.2. Head injury criteria**

Prior experiments on the capability of the human brain to hold impact forces were performed at Wayne State University using human cadavers and animal models [21, 22] as shown in Figure 6. This work led to the publication of the Wayne State Tolerance Curve [23, 24], a generally logarithmic curve that describes the relationship between the magnitude and duration of impact acceleration and the onset of skull fractures [7].

**Figure 6.** Wayne State Tolerance Curve [23, 24]

The relationship is nonlinear – the head can tolerate high accelerations for very brief periods but a longer exposure to a lower acceleration level may be damaging as well, Fig. 6. For a given degree of injury the logarithmic slope of the exposure time and acceleration graph is approximately –2.5. This relationship proposes the Severity Index (SI) as a measure of the injury potential of an impact [25]. SI is the integral of the acceleration time curve, weighted by the 2.5 factor observed in the Wayne State Tolerance Curve and calculated as

$$SI = \int\_0^{\tau} a^{2.5} \, dt$$

Where *a (t)* is the acceleration-time pulse of the impact and *T* is its duration. An SI score of 1000 approximates the limit of human tolerance. Impacts with a higher score have a nonzero probability of causing a life-threatening brain trauma [7].

Severity Index SI [25] calculates distress of an impact in a way that quantifies the risk of head injury. In practice, SI scores are logical predictors of the injury potential of impacts that produce focal brain injuries. For impacts of lower intensity but longer duration, the SI calculation produces unreasonably high values that predict more severe injuries than those actually observed in cadaver experiments. The Head Injury Criterion (HIC) is an alternative measure of impact severity that is not subject to these errors. The HIC score is given by:

$$HIC = \max\left( (t\_1 - t\_0) \left[ \frac{1}{(t\_1 - t\_0)} \int\_{t = t\_0}^{t\_1} a\_t \, dt \right]^{2.5} \right)$$

Where *t0* and *t1* are the beginning and end times of the portion of the acceleration-time pulse being examined. The integral account for the duration of the acceleration and an iterative search found the time interval (t0, t1) to maximize the HIC score [7], Figure 7.

100 Injury and Skeletal Biomechanics

**Figure 5.** Force mechanism for head-neck [48]

mhead a = FI

So, a = (FI

+ FN

/ mhead) + (FN/ mhead )

forces than with a smaller impactor [4].

**Figure 6.** Wayne State Tolerance Curve [23, 24]

**2.2. Head injury criteria** 

average of 12.4 kN. The authors concluded that there is a significant relationship between contact area and fracture force. Thus, impacts with the ground are likely to require higher

Prior experiments on the capability of the human brain to hold impact forces were performed at Wayne State University using human cadavers and animal models [21, 22] as shown in Figure 6. This work led to the publication of the Wayne State Tolerance Curve [23, 24], a generally logarithmic curve that describes the relationship between the magnitude

The relationship is nonlinear – the head can tolerate high accelerations for very brief periods but a longer exposure to a lower acceleration level may be damaging as well, Fig. 6. For a

and duration of impact acceleration and the onset of skull fractures [7].

(A) Acceleration-time pulse from an impact between a surrogate head and an artificial turf surface, showing the peak value or gmax score.

(B) The same pulse with acceleration values

exponentiated to power 2.5. The SI score is the area under the curve

(C) As (B) but showing the time limits, t0 and t1, that maximize the HIC score.

**Figure 7.** Example of SI and HIC calculations [7]

A HIC score of 1000 represents the "safe" limit of human tolerance, above which the risk of a serious head injury is non-zero. In the sports surfacing world, HIC scores are the primarily determinant of playground surfacing, shock attenuation performance. Other terms of surfacing shock attenuation use a 200 g max limiting performance criterion, on that basis it approximates the HIC limit [7].

Comparison of Intracranial Pressure by Lateral and Frontal Impacts – Validation of Computational Model 103

**Head Injury Criteria AIS Code Level Of Brain Concussion And Head Injury**

520 – 899 2 Unconscious less than 1 hour – linear fracture 900 – 1254 3 Unconscious 1 – 6 hours – depressed fracture 1255 – 1574 4 Unconscious 6 – 24 hours – open fracture

*2.2.1. Injury criteria for Subarachnoid haematoma, contusion and skull fracture* 

create conditions necessary for the production of bridging vein ASDH [4].

**Figure 9.** Injury tolerance curve for ASDH in rhesus monkeys [4]

will thus be subjected to the same accelerations [4].

1575 – 1859 5 Unconscious greater than 25 hours – large haematoma

Tolerance curves for ASDH due to rupture of bridging veins were experimentally produced in monkeys [28] and compared with human clinical data. It was concluded that bridging veins are highly sensitive to strain-rate and tend to rupture during impacts associated with high rates of increasing acceleration. As the duration of the pulse increases, higher levels of angular acceleration will be required in order to maintain the high strain rate necessary for rupture of bridging veins. Figure 9 shows tolerance curves for rhesus monkeys. For humans, a fall resulting in head acceleration of over 200 g and pulse duration of 3.5 ms or less would

Figure 10 shows the tolerance curves [29], derived for 5% critical strain, below which there is no axonal injury, and 10% critical strain, below which mild injury such as concussion could be expected and above which DAI can be expected. For impacts with very stiff contacts and short durations, the brain will move relative to the skull at impact, and thus a change in angular velocity of the skull will be of prime importance and causation of injury, Fig. 10. However, for impacts with softer structures, the brain will tend to move with the head, and

135 – 519 1 Headache or dizziness

> 1860 6 Non survivable

**Table 1.** Levels of Consciousness In Relation To Head Injury Criteria [46]

Empirically determined relationships between HIC scores and the probability of head injury [26, 27] are widely used in the automotive industry to estimate the risk of injury. Figure 8 shows examples of Expanded Prasad-Mertz Curves. Each curve estimates the possibility that an impact with a given HIC score will result in a specified level of head trauma [7]. Figure 8, also shows the relationship between the HIC score of a head impact and the probability of an injury.

**Figure 8.** Expanded Prasad-Mertz Curves [7]

Computational simulation of real life head injury accidents has been used for various purposes. Some have compared AIS (abbreviated injury scale) scores for real life injuries to HIC scores or other indices of injury calculated from the reconstruction [4, 30-32]. HIC and tolerance levels have been explained [46-47] and tabulated in Table 1. Also, moderate and severe neurological injuries can only be distinguished with a criterion that is computed using intracranial variables and not with the sole global head accelerations [1]. More recently, there has been a move away from this approach of looking for a parameter that correlates well with overall severity of injury, and many are now focusing on determining tolerance limits of the head to specific lesion types, for example, acute subdural hematoma (ASDH), diffuse axonal injury (DAI) or skull fracture [4].


**Table 1.** Levels of Consciousness In Relation To Head Injury Criteria [46]

102 Injury and Skeletal Biomechanics

approximates the HIC limit [7].

probability of an injury.

**Figure 8.** Expanded Prasad-Mertz Curves [7]

(ASDH), diffuse axonal injury (DAI) or skull fracture [4].

A HIC score of 1000 represents the "safe" limit of human tolerance, above which the risk of a serious head injury is non-zero. In the sports surfacing world, HIC scores are the primarily determinant of playground surfacing, shock attenuation performance. Other terms of surfacing shock attenuation use a 200 g max limiting performance criterion, on that basis it

Empirically determined relationships between HIC scores and the probability of head injury [26, 27] are widely used in the automotive industry to estimate the risk of injury. Figure 8 shows examples of Expanded Prasad-Mertz Curves. Each curve estimates the possibility that an impact with a given HIC score will result in a specified level of head trauma [7]. Figure 8, also shows the relationship between the HIC score of a head impact and the

Computational simulation of real life head injury accidents has been used for various purposes. Some have compared AIS (abbreviated injury scale) scores for real life injuries to HIC scores or other indices of injury calculated from the reconstruction [4, 30-32]. HIC and tolerance levels have been explained [46-47] and tabulated in Table 1. Also, moderate and severe neurological injuries can only be distinguished with a criterion that is computed using intracranial variables and not with the sole global head accelerations [1]. More recently, there has been a move away from this approach of looking for a parameter that correlates well with overall severity of injury, and many are now focusing on determining tolerance limits of the head to specific lesion types, for example, acute subdural hematoma

### *2.2.1. Injury criteria for Subarachnoid haematoma, contusion and skull fracture*

Tolerance curves for ASDH due to rupture of bridging veins were experimentally produced in monkeys [28] and compared with human clinical data. It was concluded that bridging veins are highly sensitive to strain-rate and tend to rupture during impacts associated with high rates of increasing acceleration. As the duration of the pulse increases, higher levels of angular acceleration will be required in order to maintain the high strain rate necessary for rupture of bridging veins. Figure 9 shows tolerance curves for rhesus monkeys. For humans, a fall resulting in head acceleration of over 200 g and pulse duration of 3.5 ms or less would create conditions necessary for the production of bridging vein ASDH [4].

**Figure 9.** Injury tolerance curve for ASDH in rhesus monkeys [4]

Figure 10 shows the tolerance curves [29], derived for 5% critical strain, below which there is no axonal injury, and 10% critical strain, below which mild injury such as concussion could be expected and above which DAI can be expected. For impacts with very stiff contacts and short durations, the brain will move relative to the skull at impact, and thus a change in angular velocity of the skull will be of prime importance and causation of injury, Fig. 10. However, for impacts with softer structures, the brain will tend to move with the head, and will thus be subjected to the same accelerations [4].

The types of lesions examined were subdural haematoma, subarachnoid haematoma and brain contusions. While the authors did not elaborate on the relationship between the mechanical parameters and the lesions observed, they concluded that reconstructing pedestrian accidents could be a useful means of estimating tolerance limits for discrete brain injuries. However, due to lack of certainty about input variables, these are still very approximate estimations [4].

Since all head injury criteria are generally explained in terms of the resultant head accelerations, the resultant head acceleration are determined by placing an accelerometer to the desired points. The impact mechanisms are related with stresses, strain and pressure induced by the impact in the head which produce injury. Besides all these parameters affecting TBI with the resultant head accelerations, the following human head injury mechanisms and tolerance limits

A brain pressure reaching 200 kPa is an indicator for brain contusions, oedema and

A brain Von Mises stress reaching 18 kPa is an indicator for moderate neurological injuries. A brain Von Mises stress reaching 38 kPa is an indicator for severe neurological injuries. A global strain energy of the brain skull interface reaching 5.4 J is an indicator for subdural

Finite element modeling and simulation of the human head biomechanics remain scarce in the literature. Only models that exist in the literature were reported by Ruan [18], and Willinger [35] and validated with limited experimental data. As FEM of the head finds wider applications in a diversity of fields, experimental validation is a critical key element [3]. Therefore, one of the objectives of this paper was to construct a 3D model of the head from Magnetic Resonance Imaging and validate FE analysis with available experimental data on stress induced by frontal and lateral impacts. Two sets of experimental data were

Previous research used various computational software: ULP models, ScanFE/RP (Simpleware Ltd.), FEA packages MSC/PATRAN; MSC/DYTRAN; ABAQUS; LS-DYNA3D (LS-DYNA3D, LSTC), MADYMO (Mathematical Dynamic Models) - may combine both multibody and FEM techniques, Test dummy- human body models to reconstruct the accident especially vehicle/car crash, Vtk and SUDAAN (based on CT scan sets).

MIMICS software used in this study allows user to process and edit 2D image data (CT, μCT, MRI, etc.) to construct 3D models with accuracy, flexibility and user-friendliness, Figure 12. Besides smoothening, FEA, wide variety of boolean functions, the powerful

(stress, strain and pressure) were derived from accidents reconstruction [36-37].

A global strain energy of the skull reaching 2.2 J is an indicator for skull fractures.

hematoma.

hematoma and subarachnoidal bleeding.

Methodology used in this paper is discussed below.

**3. Computational model validation** 

used, from Nahum [42] and [34].

**3.1. Methodology** 

*3.1.1. Software* 

**Figure 10.** Tolerance curves for DAI and cerebral concussion [4, 29]

Tolerance of the head to skull fracture is much easier to determine than tolerance to intracranial injury. This is because of the definite relationship between force applied to the skull, and failure of cranial bone. Applied maximum force can be calculated from the equations discussed in the background section of head injury. Also from the Wayne State Tolerance Curve [23-24], tolerance of the head to skull fracture can be determined [4].

Tolerance limits to specific types of head injury were from reconstructing accidents and comparing the injuries sustained with parameters calculated from the reconstructions. For example, Auer [33] reconstructed 25 fatal pedestrian accidents using various methods, including computer simulations. Head acceleration and impact duration were calculated, and from these, the upper tolerance limit (lowest level of loading above which the specific injury is always observed) and the lower tolerance limit (highest value below which the injury never occurs) for various kinds of brain injury were determined, shown in Figure 11 [4].

**Figure 11.** Upper and lower tolerance curves for ASDH, subarachnoid haematoma, and contusion [4]

The types of lesions examined were subdural haematoma, subarachnoid haematoma and brain contusions. While the authors did not elaborate on the relationship between the mechanical parameters and the lesions observed, they concluded that reconstructing pedestrian accidents could be a useful means of estimating tolerance limits for discrete brain injuries. However, due to lack of certainty about input variables, these are still very approximate estimations [4].

Since all head injury criteria are generally explained in terms of the resultant head accelerations, the resultant head acceleration are determined by placing an accelerometer to the desired points. The impact mechanisms are related with stresses, strain and pressure induced by the impact in the head which produce injury. Besides all these parameters affecting TBI with the resultant head accelerations, the following human head injury mechanisms and tolerance limits (stress, strain and pressure) were derived from accidents reconstruction [36-37].

A brain pressure reaching 200 kPa is an indicator for brain contusions, oedema and hematoma.

A brain Von Mises stress reaching 18 kPa is an indicator for moderate neurological injuries.

A brain Von Mises stress reaching 38 kPa is an indicator for severe neurological injuries.

A global strain energy of the brain skull interface reaching 5.4 J is an indicator for subdural hematoma and subarachnoidal bleeding.

A global strain energy of the skull reaching 2.2 J is an indicator for skull fractures.
