By Mariusz Ziejewski, PhD, Inz, Ghodrat Karami, PhD, and Iskander Akhatov, PhD

This paper will introduce the importance of the biomechanics analysis of brain injury under blast loading. It will demonstrate the implementation procedures of a mechanized, and a multiscale model for head, brain tissues and brain cells in an effort to address the level of brain injury under blast loading. In such a modeling scheme, the objective will be to conduct the analysis and characterization procedures in a multi-step process so that the brain injury can be detected at different levels and under different blasts with various severities. The Finite Elements computational algorithms will be used for the analysis needed throughout. Also, cavitation, a microscale phenomenon, which happens as a result of the movements of the elements of brain under impact loading, will be dealt with using the small-scaled fluid dynamics phenomena.

Introduction

With an increasing use of improvised explosive devices (IEDs) in terrorist and insurgent activities, exposure to blasts is becoming more frequent. Research into diagnosing cases of Traumatic Brain Injury (TBI), caused by these kinds of blasts, is a critical component in treating the injuries and in preventing the onset of serious physical consequences and impairments that can result from them. Although tremendous new developments in neuroimaging have become available in diagnosing and assessing TBIs, two challenges remain: 1) identifying all distinguishable evidence; and 2) linking that evidence to the trauma. Blast injuries can be multiple and complex and can often not be assessed in the same manner that other brain injuries might be examined. A better approach to take in evaluating a brain injury caused by a blast may, therefore, be to conduct the evaluation based on the mechanism (cause) of the injury [1]. Mathematical modeling and computer simulation due to the speed, versatility and mechanized nature of such methods, facilitate closely-approximated solutions for biomechanical diagnosis of resulted injuries.

Primary blast injuries occur as a result of blast wave-induced changes in atmospheric pressure and affect organs (i.e., brain); secondary blast injuries occur from objects put in motion by the blast hitting people; tertiary blast injuries occur by people being forcefully put in motion by the blast; and quaternary blast injuries occur from burns, or inhalation of gases [2]. Secondary and tertiary blast injuries have been studied for many years by biomechanical researchers. The primary blast injury category, which results in traumatic brain injury (TBI), however, is the main subject of this article.

The researchers from the Impact Biomechanics laboratory at North Dakota State University have been involved in analysis of brain injury mechanisms employing biomechanical modeling under impact loading including impacts due to blasts and explosions. The group has devised the scientific analysis of TBI caused by a blast into several steps as shown in Figure 1.

FIGURE 1: Flow chart of blast injury analysis

Steps one and two involve blast simulation using LS Dyna Finite Elements Model (FEM) coupled with human dynamic model of Articulated Total Body (ATB) [3]. The outcome of steps one and two include a profile of pressure distribution and head acceleration. Step three involves FEM of brain tissue using brain images from MRIs, etc [4]. The outcome of step three is to analyze the stress/strain characteristics of the brain tissue. Step four is multiscale cellular analysis [5], with the outcome being the effect of blast originated impulse on cellular damage, which is the solid mechanics approach. Step five involves cavitation, cellular modeling of the solid/liquid and cell matrix interaction. The outcome of this step is the effect of blast originated impulse on micro damage due to cavitation inception in micro/nanoscale structure based on a fluid dynamics approach [6,7].

Physics of Blast

Blasts mostly happen with the presence of an explosive material such as TNT. The threat of explosive materials is defined by two equally important elements: 1) the explosive charge weight, which is normally measured using the equivalent amount of TNT; and 2) the standoff distance between the blast source and the target. With the detonation of a mass of TNT at, or near, the ground surface, the peak blast pressures resulting from this hemispherical explosion decay as a function of the distance from the origin (see Figure 2a).

FIGURE 2: (a) Variation of pressure with distance, (b) Blast wave pressure-time history [8]

The pressures can, however, be amplified by a reflection factor as the shock wave encounters an object, or structure, in its path. The reflected pressure is at least twice that of the incident shock wave. It is also proportional to the strength of the incident shock, which is proportional to the charge weight. The blast pressure decays exponentially and eventually becomes negative as shown in Figure 2b.

For mathematical modeling and simulation purposes, the human head should be subjected to the incoming wave from an explosion. The explosion can be assumed to happen in an open space, as well as within a contained space. The fluid/solid interaction (air and the object) will determine the impact on the confronting object. The energy of the blast will quickly change into other forms of destructive energy. In Figure 3, the results of the change of blast energy within a contained block are shown as a result of an explosion. As seen, the total energy can be transferred to kinetic, as well as internal energy, as time goes by after the explosion.

FIGURE 3: The energy change after a blast

Modeling of Injury

Studying the biomechanics (application of engineering in the study of living organisms such as the human body) is a method of analyzing the mechanism of the injury. Biomechanics determines forces acting on the human body and the effect of those forces. Biomechanical engineering analysis is a tool that, if used properly, can incorporate common-sense experience in understanding the nature and severity of injury to the human brain as a result of trauma, and in this case, a blast. Factored into the biomechanical analysis is the study of the environmental and human body dynamics and the human tolerance limits. Nowadays, there are two main approaches to biomechanical analysis: 1) experimental evaluation which is the most valuable, but not always practical; 2) detailed computer simulations using mathematically and numerically-based biomechanical formulae.Only computer simulation approaches allow inclusion of all necessary parameters in evaluation of specific scenarios.

Brain injury can result from the sudden change in velocity due to trauma such as head impact, or inertia loading of the head. An important influence on engineering parameters is the acceleration, representing the change in the velocity as a function of time. In the biomechanics field, the head acceleration, therefore, has been used in characterization of the severity of an insult to the brain. For a more detailed discussion of the above concepts, see Ziejewski, 2004 [9]. The complete global representation of the head motion, in terms of acceleration, can only be achieved, if the complex input of linear and angular acceleration is known. This includes three components for linear acceleration and three for angular acceleration, see Figure 4.

FIGURE 4: Types of acceleration

The head acceleration data can be used directly to assess the probability of TBI by extracting the resultant maximum values and the rate of change of acceleration, or by calculation of head injury assessment functions such as the Head Injury Criteria (HIC) (NHTSA 49), Head Impact Power (HIP), Power Index (PI) and others [10].

Additional parameters that deal with local brain deformation have also been developed. They are an extension of the evaluation based on head acceleration. It has been suggested that brain surface contusions, Diffuse Axonal Injury (DAI), and acute sub dural hematoma can be predicted using, among other things, brain motion, [11,12,13, 14,15,16, 17], sudden change in the inter cranial pressure, which is largely due to the linear acceleration [18], sheer strain, stress/strain concentration [19,20], and the product of stress and strain rate [21].

In order to gain better understanding of the head injury mechanisms, both clinical as well as laboratory studies have been conducted for decades. Among the biomechanical simulations, sophisticated 3D finite element analysis and rigid body bio dynamics methods have been used to study impact injury events and the response of the human head. In general, TBI develops when the internal mechanical responses exceed tissue tolerance levels, a process referred to as load-injury scheme.

Simulation of Primary Blast Injury

The brain is clearly vulnerable to both secondary and tertiary blast injuries. The issue of whether, or not, primary blast forces directly injure the brain, however, is still unresolved. The vulnerability of the brain to a primary blast is supported by recent animal studies [22]. One of the outcomes has been identified as the formation of gas emboli, leading to infarction [2]. A more in-depth understanding of that outcome, including the location, size and geometry of the damage site, would be of assistance to physicians in properly interpreting neuro diagnostic results. In an approach to be demonstrated briefly, the macro/micro scale solid mechanics modeling of brain tissues, cells, and head will be used in conjunction with the micro/nano scale fluid mechanics modeling of cavitation created under sudden movement of the elements of brain constituents.

Macro and Micro Scale Solid Mechanics Modeling

The finite element modeling (FEM) will be conducted at macroscale for head and brain tissues and at microscale for brain cells. LSDyna as a powerful finite element software and tool for the analysis under impact loading has the capacity to determine the motion of the brain elements, due to blast. Part of the input data to the LSDyna program can be determined using Articulated Total Body (ATB) [3]. ATB is a rigid-body dynamic simulation program that is especially suited to measure head and neck motion parameters when the body is exposed to attacking waves of explosion. The program will be used to measure accelerations (linear or angular) at different points of the head. The output will be forwarded to FEM for detailed stress and deformation of the skull and brain tissue analysis.

The macroscale global FEM brain analysis takes into account the detailed structure of the human head anatomy, including the brain, falx and tentorium, CSF, dura mater, pia mater, skull bone and scalp. The brain, CSF and skull bone will be modeled as first-order brick elements with eight-node [4,23,24,25]. The falx, tentorium, dura, pia and scalp will be modeled as four-node membrane or shell elements with uniform thickness. Figure 5 shows the 3D finite element model of these components [4].

FIGURE 5: The right-half model of the brain, CSF and skull bone

In an effort to examine the injury in a multiscaled approach, i.e., from cellular to the global head, the multi-scale modeling of the brain and its components will be advanced. The verifications are done through MRIs which can create a link between the mechanism of brain injury at the cellular level and the mechanism of mechanical loading on the head at the macroscopic level. The work will focus on:

• blasts and creation of destructive wave;
• determination of TBI at various scales;
• accurate modeling of brain material;
• damage and tolerance at cellular level;
• correlation of damage at different levels;
• material characterization of the brain and its components; and
• data for a systematic design of injury protection devices

The cellular analysis is an important issue in injury analysis. The cell, as a basic unit of life, is a biologically complex system. The understanding of cells’ behavior requires a combination of various disciplines and approaches including biomechanics. Cells must use genetic information, perform synthesis, sort, store, and transport biomolecules; convert different forms of energy; transduce signals; maintain internal structures; and respond to external environments [5,26,27]. Many of these processes involve mechanisms that should be dealt with using the principles of mechanics.

Micro and Nano Scale Fluid Mechanics Modeling (Cavitation)

An additional effect of primary blast injuries is based on the pressure differences that cause micro/nanoscale cavitation making a component of overall injury evaluation. The effect of such an impact on the brain has been investigated theoretically and experimentally with certain idealizations [28,29,30,31,32,33,34,35,36,37,38,39]. In these studies, an experimental and numerical analysis of a simple model of the human brain under impact was used. Namely, a water-filled cylinder was struck by a free-flying mass. Rigid-body acceleration time histories and the pressure at the fluid-cylinder interface were monitored during impact. Comparisons between the experimental results and the results of a computational model were made.

As a conclusion of this work, the following view of head impact was developed: when the head receives a blow and a positive pressure develops under the point of impact, a small cavity, opposite the impact, can form between the skull and the dura. This cavity is created due to negative pressure (tension) developed between the dura and the skull. Its subsequent collapse could be a mechanism of injury. The study also indicated that under complex loading conditions, cavitation could occur in the brain material, not just at the boundary. It was found that if the head underwent pre-impact acceleration, immediately before the head strike, internal cavitation was likely. Internal cavitation implies potential cellular tissue damage. It was admitted, therefore, that if the impact is severe enough, it may produce cavitation in the brain, and the associated violent cavity collapse could be a supplementary mechanism of brain injury.

The complexity of the problem is mainly due to the fact that liquid in the brain is confined between membranes and cells at very different scales from 1cm to 0.1 μm. When a blast occurs, it creates pressure waves. There are several different phases of the waves beginning with a positive phase, moving into a negative phase, moving into a smaller positive phase, and then moving into a smaller negative phase, etc., until it passes. It is the negative phases that result in cavitation. Our research shows that 1) in macro scale confinement (ventricles and subarachnoid space) a brain injury may be caused by cavitation bubble collapse; 2) in micro and nano scale confinement (neurons) cavitation inception may be a possible cause for a brain injury (see Figure 6).

FIGURE 6: Computational fluid dynamics modeling in nanoscopic environments

As can be seen in Figure 6, pressure induced by cavitation inception may cause significant positive pressure on the brain tissue in micro and/or nano scale channel, filled by bio-fluid. These types of channels can be found deep in the structure of the central nervous system. Fluid dynamics and cavitation inception in tight confinements will have a great impact on the integrity of neurons in general, and on axonal transport, or axoplasmic flow, in particular.

Developing theoretical approaches and experimental methods that allow an adequate prediction of liquid micro and nano film dynamics and cavitation in the brain are crucial for improving early diagnoses and interpretations of TBI. Physical concepts and mathematical tools for the dynamics of liquid micro and/or nano films confined between two solid or elastic surfaces, or membranes, need to be developed.

Conclusion

Recent world events related to terrorism and the increased use of IEDs, has led to a need for better understanding of the mechanism of blast injuries and early diagnoses and interpretations of TBI caused by blasts. The identification of all distinguishable evidence of blast injuries, however, continues to be a challenge for medical professionals working with the injured military personnel. The application of biomechanics for studying blast injuries provides a valuable tool to view the injury and its mechanism. Increased knowledge of cellular level damage, including cavitation, has the potential to be a field of research that could have tremendous impact on how those injured by blasts are diagnosed, treated and rehabilitated.

About the Authors

Mariusz Ziejewski, PhD, Inz, is an Associate Professor in the Department of Mechanical Engineering and Applied Mechanics at North Dakota State University, where he serves as Director of the Impact Biomechanics Laboratory and the Automotive Systems Laboratory. Dr. Ziejewski is also an adjunct Associate Professor in the Department of Neurosciences at the University of North Dakota School of Medicine. His research interests include short duration impact phenomena in the area of biomechanics, and the effect of such events on the human body, especially the head and neck.

Ghodrat Karami, PhD, is an Associate Professor in the Department of Mechanical Engineering and Applied Mechanics at North Dakota State University. Previously he was a visiting professor at the University of Wyoming and at Washington State University. He is currently researching multiscale modeling for noncomposite materials and has authored over 100 papers in the field of engineering.

Iskander Akhatov, PhD, is an Associate Professor in the Department of Mechanical Engineering and Applied Mechanics at North Dakota State University. He previously was a visiting researcher at Rensselear Polytechnic Institute, Boston University and the University of Gottingen. Dr. Akhatov also served as the Director of the Institute of Mechanics at the Ufa Branch of the Russian Academy of Sciences.

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