- Email: [email protected]
Criteria to determine likelihood of brain injury during explosive events
Safety Science 48 (2010) 1387–1392
Contents lists available at ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Criteria to determine likelihood of brain injury during explosive events Thomas J.M. Connolly, J. Keith Clutter * Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, TX 78249, United States
a r t i c l e
i n f o
Article history: Received 2 June 2009 Accepted 16 May 2010
Keywords: Brain injury Blast injury Computational simulation
a b s t r a c t The occurrence of blast-induced brain injury in individuals serving in Iraq and Afghanistan is dramatically higher than in past conflicts. This has been attributed in part to the prevalence of roadside improvised explosive devices, or IEDs. There is a call from the military medical community to reduce the reliance on victim self-reporting as the primary diagnosis technique to determine the likelihood of brain injury after a blast. This study demonstrates the ability to establish criteria which correlates easily measured parameters to the probability of cerebral contusion and, thus, brain injury. Computational fluid dynamics (CFD) is used to establish the environment from a full range of threats. This is combined with bond graph modeling of varying levels of fidelity to estimate the dynamics of the skull and brain. Results clearly show that a boundary exists in the threat parameter space that determines whether brain injury is probable. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Advances in battlefield medicine have dramatically reduced the number of deaths in current warfare when compared to earlier conflicts such as the Vietnam War and World War II (Shea, 2006). However, military physicians are addressing issues such as blast injuries, which have become an increasingly common problem due in part to the asymmetric warfare tactics, such as roadside improvised explosive devices (IEDs) (Nelson et al., 2006). In an IED event several injury mechanisms exist, the first being primary fragments from the casing in conventional ordnance items. The explosives found inside the ordnance item are designed primarily to propel the case fragments but also produce a blast that generates two other kill mechanisms. The first is secondary fragments or debris which come from buildings and such and cause injury in much the same manner as the primary fragments. The other injury mechanism is that of the blast itself, and its effects on personnel. Blast loadings can cause a range of injuries, from ear drum and lung damage to more gross-level injuries including amputation of body parts. Another common injury is brain contusion. This type of blast injury is different in that it is not necessarily immediately visible. Many times these injuries go undetected for long periods of time (Zoroya, 2006a). One reason for this is the fact that military medical members have to rely primarily on self reporting by the injured soldier to determine if they can continue to function (Zoroya, 2006b). * Correspondence to: J.K. Clutter, MMI Engineering, Westheimer Rd., Suite 150, Houston, TX 77077, United States. E-mail address: [email protected] (J.K. Clutter). 0925-7535/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2010.05.013
The reliability of the self-reporting for diagnosis is flawed because the reluctance of members assigned to combat units to leave their brethren in arms. Also, many times identifiable effects such as memory loss do not become evident for some time. To quote a military neurologist, ‘‘We need a field test to be able to practically assess the safety of sending people back to duty” (Zoroya, 2006a). That is the focus of the current work: to lay the foundation for objective processes to determine the probability of brain injury following a bombing event. Since the use of animal models and other studies, which use experimental processes, can take considerable time to initiate, the work presented here will leverage the latest in computational modeling. 1.1. Explosive threats Over 20% of the wounded in the current wars in Iraq and Afghanistan have suffered traumatic brain injuries (Zoroya, 2006a). This has been directly attributed to the prevalence of the use of IEDs. Table 1 provides a representative list of ordnance items commonly used in IEDs and the explosive weight contained in each item (Clutter, 2004). The injury mode due to the blast is a function of the pressure loading on the person which is directly correlated to the distance between the explosive and the person. The load also depends on the chemical properties of the explosive in the item but a common practice is to use a TNT equivalence. We will take this approach in the current study. Using the data for TNT a matrix of incident pressures for a range of IED threat sizes and distances is presented in Table 2 and will be used in the current study. Local environmental factors such the presence of buildings can also effect loading and will be addressed in future studies (Nelson et al., 2006).
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
Table 1 Representative ordnance items used in IEDs and corresponding explosive weight they hold. Ordnance item
Net explosive weight (NEW)
60 mm mortar 105 mm artillery shell 155 mm artillery shell Missile warhead
lb
kg
0.33 4.84 26.4 286
0.15 2.2 12 130
of a model that involves fluid and solid object interaction like here is whether the two systems must be represented in a closely coupled manner or if they can be represented separately. Given the short duration of blast forces and the inertial properties of the head, the head is typically loaded and unloaded by the blast prior
Table 2 Incident pressures for a range of explosive sizes (expressed in terms of net explosive weight) and distances. P (atm)
R (m)
NEW (kg)
1.52 3.05 6.10 15.24 22.86 30.48
0.15
2.2
12
130
2.286 1.357 1.129 1.039 1.021 1.017
10.929 3.071 1.5 1.121 1.071 1.051
32.143 8.5 2.571 1.286 1.143 1.107
106.143 38.214 10.357 2.214 1.571 1.357
Fig. 1. Location of virtual pressure probes that record pressure time histories. Probes 1–8 are along the center line, whereas probe 9 is located at the ear.
In keeping with the typical IED threats found in Iraq, the explosive is considered to be located at ground level (Clutter, 2004). The pressure waves output are initially hemispherical but at distances away from the explosion become planar to any objects, such as a standing individual. Although for some of the distances selected in the current study, the blast waves are still hemispherical in nature relative to a standing person, planar waves relative to the victim will be assumed for this initial study. 1.2. Injury mechanism When considering the blast driven injury mechanism the differential loading on a person can produce a resultant force that can cause the brain to impact the skull resulting in bruising and swelling. Studies of protective gear for de-mining operations have shown the dominant component of head acceleration is in the anterior-posterior direction (Markris et al., 2000). It has also been found the response of the head is decoupled from the body because there is not significant displacement of the head (Zou et al., 2007). However, the dynamics of the event are such that the motion of the brain is induced and the potential of contusion exists. Other studies of brain motion support the analysis of the head in an isolated fashion (Nelson, 2006). This study focuses on determining the impact of the brain with the skull and the subsequent compression of the brain. To accomplish this objective, the blast loading on the head will be determined for the range of threats shown in Table 1. These loadings will be used to calculate the displacement of both the skull and brain, which will aid in determining whether cerebral contusion is likely to occur. The final objective is to determine if the likelihood of contusion can be correlated to the bomb’s weight and distance from the victim. 2. Method and materials To accurately determine the occurrence of blast-induced brain injury, both the explosive system and the biological system must be represented. The explosive system modeling entails modeling the fluid dynamic processes that set the pressure distributions. The biological system comprises the skull and brain and the dynamics of their motion. The first decision in the construction
Fig. 2. Pressure time histories from three different incident pressure scenarios: 1.1 and 3.1 atm, respectively.
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
to motion being induced. Based on this scenario, a decoupled analysis can be performed. 2.1. Blast load modeling There are many ways to model a blast event and the resultant load on objects. One option is to use the well-known variation of pressure and impulse with distance for explosives (Smith and Rose, 2006). This simplified approach does not capture true loading phenomena and critical wave interaction. A better approach, which is applied in this work, is to employ a computational fluid dynamics (CFD) modeling, which solves the full set of governing equations for fluid dynamics on a mesh or grid that defines the environment and objects involved. The code used employs a 3-D Cartesian, adaptive meshing strategy to define objects. The algorithms in the code have been validated for various explosion scenarios (Clutter et al., 2007). Using the more sophisticated blast modeling resolves the role that wave interactions plays in setting the differential loading on objects. Earlier studies have shown the loading on the posterior side is dependent on how the blast waves wrap around the body (Mathis and Clutter, 2007). This phenomena needs to be resolved since any change to the differential loading changes the acceleration of the skull and brain. To capture the loading history from the blast on the head, a set of virtual pressure probes where used and there locations are shown in Fig. 1. All were situated along the center plane of the head except Probe 9, which was placed next to the ear to record the incident pressure allowing the results to be correlated to the threats depicted in Table 2. Due to who blast loadings scale with NEW and distance, a single simulation can represent multiple threat scenarios. The plots in Fig. 2 shows pressure time histories recorded on the anterior and posterior of the head along with the incident pressure. The data show variation in the loading as the threat changes. Changing the threat size affects the maximum pressure and the degree to which secondary pulses and over expansion waves are visible.
The differential in arrival time on the anterior and posterior of the head also changes which affects differential loading and head acceleration. Fig. 3 shows and example blast loading and its interaction with the head. Visible is how the incident wave rebounds generating a temporary vacuum on the anterior side and how waves that travel over the top and around the side of the head coalesce increasing the effective loading on the back of the head. This load information is next used with a model of the skull and brain to simulate the dynamics of the head system.
Fig. 4. Schematic of the brain–skull model.
Table 3 Modeling parameters used in the brain/skull model. Symbol
Description
Value
Units
mb kb b
Mass of the brain Stiffness of the brain Effective viscous damping coefficient of cerebrospinal fluid Space between brain and skull Mass of the skull Effective surface area of the face
1.5 10,165 0.007
kg N/m N-s/ m m kg m2
d ms A
Fig. 3. Sequence of plots showing the blast wave interaction with the head.
0.088 1.0 0.039
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
2.2. Brain–skull interaction modeling The dynamics of the interaction between the brain and the skull can be modeled with a variety of techniques. Here a bond graph modeling approach is used to represent the brain–skull system as depicted in Fig. 4. The brain and skull are represented as rigid bodies with masses, mb and ms, respectively. The authors recognize that the viscoelastic behavior of brain material cause the skull– brain dynamics to be complex and this aspect will be included in
Fig. 5. Bond graph model of the brain and skull.
future studies. The cerebro-spinal fluid and meninges are modeled as resistive elements imparting a net viscous friction, denoted by the damping coefficient, b. Two springs, each with a stiffness kb, simulate compression of the brain with the distance between the brain and the springs, d, representing the space occupied by the cerebro-spinal fluid and meninges. The blast loading results were used to define externally applied forces, Ff(t) and Fr(t), to the skull. Published values were used for the masses of the skull and brain and the space between the them, d, was estimated by using human data. The stiffness of the springs, kb, was calculated using published values for the elastic modulus of brain tissue and the volume of an average adult human brain. The viscous damping coefficient, b, was calculated by assuming that the meninges and cerebro-spinal fluid constitute an incompressible medium layer between the surfaces of the skull and brain. A summary of the modeling parameters is given in Table 3. Bond graph models are based on the power flow between the lumped elements of a system. The bond graph model of this system is shown in Fig. 5 features a signal flow that captures the nonlinear effect (dead zone) introduced by the springs, which are not compressed until the brain sufficiently displaces to make contact with either of them. The Boolean variable n is used to activate elastic portion of the model (represented by a C element.) Analysis of the bond graph reveals that the system is third-order. Its dynamics are represented by a system of first-order differential equations and an auxiliary algebraic equation
Fig. 6. Dynamics of the skull and brain for the 1.2 atm case (brain–skull collision does not occur).
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
Fig. 7. Dynamics of the skull and brain for the 2.7 atm case (brain–skull collision occurs).
p p p_ b ¼ b b s þ F kb þ F r F r ðtÞ mb ms p p p_ b ¼ b b s þ F kb mb ms x_ bs ¼
pb p s mb ms
F kb ¼ fkb ðx bs dÞxbs > dkb ðxbs þ dÞxbs < dg where ps is the momentum of the skull, pb is momentum of the brain, xb is displacement of the brain, xs is displacement of the skull, and Fkb is the force imparted by either of the springs on the brain. Sample results from the dynamic simulations are shown in Figs. 6 and 7, which correspond to blast source pressures of 1.2 and 2.7 atm, respectively. The figures contain time histories for: (a) force inputs on the front and rear skull, (b) brain compression, (c) brain velocity, and (d) skull velocity. For some cases, the motion induced in the brain caused multiple impacts with the skull. In the plots above, only the initial impacts are shown since the objective is to determine a Boolean-type result, i.e., whether the brain impacts the skull or not. A summary of the blast forces for all cases is provided in Fig. 8. The brain was found to impact the skull for cases with an incident pressure of 1.5 atm and higher. Table 4 provides a summary of the simulation results for all blast source pressure cases.
Table 4 Summary of brain/skull dynamics for the various blast source pressure cases.
Fig. 8. Correlation between threat size (blast source pressure) and forces experienced on front and rear of the skull. The shaded region indicates that brain/skull collision occurs.
Case
Max anterior force (N)
Max posterior force (N)
Brain collision with skull?
Time of collision (ms)
1.1 atm 1.2 atm 1.5 atm 2.7 atm 3.1 atm
725 1486 3963 14,921 19,525
125 387 1098 3711 4613
No No Yes Yes Yes
– – 11.30 2.39 1.93
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
fractional derivatives (Connolly, et al., 2009). Additionally, it will be benchmarked against available experimental and clinical data to better understand the injury mechanism. This work will support a parallel effort underway by the authors and others to develop devices to notify victims and medical personnel to the potential of blast-induced brain injury. References Fig. 9. Delineation in threat parameter space of the probability of cerebral contusion.
3. Conclusions The primary objective of this preliminary study was to determine if a correlation could be made between measureable parameters from the battlefield and if cerebral contusion occurs. A range of threats were selected, based on actual events that occur in the Iraqi Theater of Operations (Clutter, 2004). The results clearly show that such a correlation between relative location from the blast source to the victim, R(m), and its suspected net explosive weight, NEW, can be made. Fig. 9 shows a notional chart for such a process. In this work, the incidence of brain injury, i.e., whether or not an injury occurs, was the extent of assessment. As part of future work, which will include multiple metrics as part of a more sophisticated algorithm, the severity of a brain injury can also be indicated using a scale whose granularity can be determined by the level of detail incorporated into the algorithm. This study will be followed by further research into refining the computational model by incorporating material models that utilize
Clutter, J.K., 2004. Personal Experience while Serving in Operation Iraqi Freedom as an Explosive Ordnance Disposal Officer, 2004. Clutter, J.K., Mathis, J.T., Stahl, M.W., 2007. Modeling environmental effects in the simulation of explosion events. International Journal of Impact Engineering 34 (5), 973–989. Connolly, T.J., Contreras, J.A., 2009. Bond graph primitives for modeling systems with fractional differential equations. Journal of Fractional Calculus and Applied Analysis 12 (4), 391–408. Markris, A, Dionne, J.P., Bass, C.R., Chichester, C., 2000. Reduction of blast induced head acceleration in the field of anti-personnel mine clearance. In: IRCOBI Conference on the Biomechanics of Impact, Montpellier, France, September 2000. Mathis, J.T., Clutter, J.K., 2007. Evaluation of orientation and environmental factors on the blast hazards to bomb suit wearers. Applied Ergonomics 38 (5), 567–579. Nelson, T.J. et al., 2006. Predictors of mortality in close proximity blast injuries during operation Iraqi freedom. Journal of American College of Surgeons, 418– 422. Shea, N., 2006. The Heroes, the Healing. National Geographic, December 2006. Smith, P.D., Rose, T.A., 2006. Blast wave propagation in city streets – an overview. Progress in Structural Engineering Materials 8, 16–28. Zoroya, G., 2006. Troops Risk Undetected Brain Injury. USA Today, June 7, 2006. Zoroya, G., 2006. Even Mild Injuries to Brain Add Up. USA Today, June 7, 2006. Zou, H., Schmiedeler, J.P., Hardy, W.N., 2007. Separating brain motion into rigid body displacement and deformation under low-severity impacts. Journal of Biomechanics 40 (6), 1183–1191.
Contents lists available at ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Criteria to determine likelihood of brain injury during explosive events Thomas J.M. Connolly, J. Keith Clutter * Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, TX 78249, United States
a r t i c l e
i n f o
Article history: Received 2 June 2009 Accepted 16 May 2010
Keywords: Brain injury Blast injury Computational simulation
a b s t r a c t The occurrence of blast-induced brain injury in individuals serving in Iraq and Afghanistan is dramatically higher than in past conflicts. This has been attributed in part to the prevalence of roadside improvised explosive devices, or IEDs. There is a call from the military medical community to reduce the reliance on victim self-reporting as the primary diagnosis technique to determine the likelihood of brain injury after a blast. This study demonstrates the ability to establish criteria which correlates easily measured parameters to the probability of cerebral contusion and, thus, brain injury. Computational fluid dynamics (CFD) is used to establish the environment from a full range of threats. This is combined with bond graph modeling of varying levels of fidelity to estimate the dynamics of the skull and brain. Results clearly show that a boundary exists in the threat parameter space that determines whether brain injury is probable. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Advances in battlefield medicine have dramatically reduced the number of deaths in current warfare when compared to earlier conflicts such as the Vietnam War and World War II (Shea, 2006). However, military physicians are addressing issues such as blast injuries, which have become an increasingly common problem due in part to the asymmetric warfare tactics, such as roadside improvised explosive devices (IEDs) (Nelson et al., 2006). In an IED event several injury mechanisms exist, the first being primary fragments from the casing in conventional ordnance items. The explosives found inside the ordnance item are designed primarily to propel the case fragments but also produce a blast that generates two other kill mechanisms. The first is secondary fragments or debris which come from buildings and such and cause injury in much the same manner as the primary fragments. The other injury mechanism is that of the blast itself, and its effects on personnel. Blast loadings can cause a range of injuries, from ear drum and lung damage to more gross-level injuries including amputation of body parts. Another common injury is brain contusion. This type of blast injury is different in that it is not necessarily immediately visible. Many times these injuries go undetected for long periods of time (Zoroya, 2006a). One reason for this is the fact that military medical members have to rely primarily on self reporting by the injured soldier to determine if they can continue to function (Zoroya, 2006b). * Correspondence to: J.K. Clutter, MMI Engineering, Westheimer Rd., Suite 150, Houston, TX 77077, United States. E-mail address: [email protected] (J.K. Clutter). 0925-7535/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2010.05.013
The reliability of the self-reporting for diagnosis is flawed because the reluctance of members assigned to combat units to leave their brethren in arms. Also, many times identifiable effects such as memory loss do not become evident for some time. To quote a military neurologist, ‘‘We need a field test to be able to practically assess the safety of sending people back to duty” (Zoroya, 2006a). That is the focus of the current work: to lay the foundation for objective processes to determine the probability of brain injury following a bombing event. Since the use of animal models and other studies, which use experimental processes, can take considerable time to initiate, the work presented here will leverage the latest in computational modeling. 1.1. Explosive threats Over 20% of the wounded in the current wars in Iraq and Afghanistan have suffered traumatic brain injuries (Zoroya, 2006a). This has been directly attributed to the prevalence of the use of IEDs. Table 1 provides a representative list of ordnance items commonly used in IEDs and the explosive weight contained in each item (Clutter, 2004). The injury mode due to the blast is a function of the pressure loading on the person which is directly correlated to the distance between the explosive and the person. The load also depends on the chemical properties of the explosive in the item but a common practice is to use a TNT equivalence. We will take this approach in the current study. Using the data for TNT a matrix of incident pressures for a range of IED threat sizes and distances is presented in Table 2 and will be used in the current study. Local environmental factors such the presence of buildings can also effect loading and will be addressed in future studies (Nelson et al., 2006).
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
Table 1 Representative ordnance items used in IEDs and corresponding explosive weight they hold. Ordnance item
Net explosive weight (NEW)
60 mm mortar 105 mm artillery shell 155 mm artillery shell Missile warhead
lb
kg
0.33 4.84 26.4 286
0.15 2.2 12 130
of a model that involves fluid and solid object interaction like here is whether the two systems must be represented in a closely coupled manner or if they can be represented separately. Given the short duration of blast forces and the inertial properties of the head, the head is typically loaded and unloaded by the blast prior
Table 2 Incident pressures for a range of explosive sizes (expressed in terms of net explosive weight) and distances. P (atm)
R (m)
NEW (kg)
1.52 3.05 6.10 15.24 22.86 30.48
0.15
2.2
12
130
2.286 1.357 1.129 1.039 1.021 1.017
10.929 3.071 1.5 1.121 1.071 1.051
32.143 8.5 2.571 1.286 1.143 1.107
106.143 38.214 10.357 2.214 1.571 1.357
Fig. 1. Location of virtual pressure probes that record pressure time histories. Probes 1–8 are along the center line, whereas probe 9 is located at the ear.
In keeping with the typical IED threats found in Iraq, the explosive is considered to be located at ground level (Clutter, 2004). The pressure waves output are initially hemispherical but at distances away from the explosion become planar to any objects, such as a standing individual. Although for some of the distances selected in the current study, the blast waves are still hemispherical in nature relative to a standing person, planar waves relative to the victim will be assumed for this initial study. 1.2. Injury mechanism When considering the blast driven injury mechanism the differential loading on a person can produce a resultant force that can cause the brain to impact the skull resulting in bruising and swelling. Studies of protective gear for de-mining operations have shown the dominant component of head acceleration is in the anterior-posterior direction (Markris et al., 2000). It has also been found the response of the head is decoupled from the body because there is not significant displacement of the head (Zou et al., 2007). However, the dynamics of the event are such that the motion of the brain is induced and the potential of contusion exists. Other studies of brain motion support the analysis of the head in an isolated fashion (Nelson, 2006). This study focuses on determining the impact of the brain with the skull and the subsequent compression of the brain. To accomplish this objective, the blast loading on the head will be determined for the range of threats shown in Table 1. These loadings will be used to calculate the displacement of both the skull and brain, which will aid in determining whether cerebral contusion is likely to occur. The final objective is to determine if the likelihood of contusion can be correlated to the bomb’s weight and distance from the victim. 2. Method and materials To accurately determine the occurrence of blast-induced brain injury, both the explosive system and the biological system must be represented. The explosive system modeling entails modeling the fluid dynamic processes that set the pressure distributions. The biological system comprises the skull and brain and the dynamics of their motion. The first decision in the construction
Fig. 2. Pressure time histories from three different incident pressure scenarios: 1.1 and 3.1 atm, respectively.
1389
T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
to motion being induced. Based on this scenario, a decoupled analysis can be performed. 2.1. Blast load modeling There are many ways to model a blast event and the resultant load on objects. One option is to use the well-known variation of pressure and impulse with distance for explosives (Smith and Rose, 2006). This simplified approach does not capture true loading phenomena and critical wave interaction. A better approach, which is applied in this work, is to employ a computational fluid dynamics (CFD) modeling, which solves the full set of governing equations for fluid dynamics on a mesh or grid that defines the environment and objects involved. The code used employs a 3-D Cartesian, adaptive meshing strategy to define objects. The algorithms in the code have been validated for various explosion scenarios (Clutter et al., 2007). Using the more sophisticated blast modeling resolves the role that wave interactions plays in setting the differential loading on objects. Earlier studies have shown the loading on the posterior side is dependent on how the blast waves wrap around the body (Mathis and Clutter, 2007). This phenomena needs to be resolved since any change to the differential loading changes the acceleration of the skull and brain. To capture the loading history from the blast on the head, a set of virtual pressure probes where used and there locations are shown in Fig. 1. All were situated along the center plane of the head except Probe 9, which was placed next to the ear to record the incident pressure allowing the results to be correlated to the threats depicted in Table 2. Due to who blast loadings scale with NEW and distance, a single simulation can represent multiple threat scenarios. The plots in Fig. 2 shows pressure time histories recorded on the anterior and posterior of the head along with the incident pressure. The data show variation in the loading as the threat changes. Changing the threat size affects the maximum pressure and the degree to which secondary pulses and over expansion waves are visible.
The differential in arrival time on the anterior and posterior of the head also changes which affects differential loading and head acceleration. Fig. 3 shows and example blast loading and its interaction with the head. Visible is how the incident wave rebounds generating a temporary vacuum on the anterior side and how waves that travel over the top and around the side of the head coalesce increasing the effective loading on the back of the head. This load information is next used with a model of the skull and brain to simulate the dynamics of the head system.
Fig. 4. Schematic of the brain–skull model.
Table 3 Modeling parameters used in the brain/skull model. Symbol
Description
Value
Units
mb kb b
Mass of the brain Stiffness of the brain Effective viscous damping coefficient of cerebrospinal fluid Space between brain and skull Mass of the skull Effective surface area of the face
1.5 10,165 0.007
kg N/m N-s/ m m kg m2
d ms A
Fig. 3. Sequence of plots showing the blast wave interaction with the head.
0.088 1.0 0.039
1390
T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
2.2. Brain–skull interaction modeling The dynamics of the interaction between the brain and the skull can be modeled with a variety of techniques. Here a bond graph modeling approach is used to represent the brain–skull system as depicted in Fig. 4. The brain and skull are represented as rigid bodies with masses, mb and ms, respectively. The authors recognize that the viscoelastic behavior of brain material cause the skull– brain dynamics to be complex and this aspect will be included in
Fig. 5. Bond graph model of the brain and skull.
future studies. The cerebro-spinal fluid and meninges are modeled as resistive elements imparting a net viscous friction, denoted by the damping coefficient, b. Two springs, each with a stiffness kb, simulate compression of the brain with the distance between the brain and the springs, d, representing the space occupied by the cerebro-spinal fluid and meninges. The blast loading results were used to define externally applied forces, Ff(t) and Fr(t), to the skull. Published values were used for the masses of the skull and brain and the space between the them, d, was estimated by using human data. The stiffness of the springs, kb, was calculated using published values for the elastic modulus of brain tissue and the volume of an average adult human brain. The viscous damping coefficient, b, was calculated by assuming that the meninges and cerebro-spinal fluid constitute an incompressible medium layer between the surfaces of the skull and brain. A summary of the modeling parameters is given in Table 3. Bond graph models are based on the power flow between the lumped elements of a system. The bond graph model of this system is shown in Fig. 5 features a signal flow that captures the nonlinear effect (dead zone) introduced by the springs, which are not compressed until the brain sufficiently displaces to make contact with either of them. The Boolean variable n is used to activate elastic portion of the model (represented by a C element.) Analysis of the bond graph reveals that the system is third-order. Its dynamics are represented by a system of first-order differential equations and an auxiliary algebraic equation
Fig. 6. Dynamics of the skull and brain for the 1.2 atm case (brain–skull collision does not occur).
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T.J.M. Connolly, J.K. Clutter / Safety Science 48 (2010) 1387–1392
Fig. 7. Dynamics of the skull and brain for the 2.7 atm case (brain–skull collision occurs).
p p p_ b ¼ b b s þ F kb þ F r F r ðtÞ mb ms p p p_ b ¼ b b s þ F kb mb ms x_ bs ¼
pb p s mb ms
F kb ¼ fkb ðx bs dÞxbs > dkb ðxbs þ dÞxbs < dg where ps is the momentum of the skull, pb is momentum of the brain, xb is displacement of the brain, xs is displacement of the skull, and Fkb is the force imparted by either of the springs on the brain. Sample results from the dynamic simulations are shown in Figs. 6 and 7, which correspond to blast source pressures of 1.2 and 2.7 atm, respectively. The figures contain time histories for: (a) force inputs on the front and rear skull, (b) brain compression, (c) brain velocity, and (d) skull velocity. For some cases, the motion induced in the brain caused multiple impacts with the skull. In the plots above, only the initial impacts are shown since the objective is to determine a Boolean-type result, i.e., whether the brain impacts the skull or not. A summary of the blast forces for all cases is provided in Fig. 8. The brain was found to impact the skull for cases with an incident pressure of 1.5 atm and higher. Table 4 provides a summary of the simulation results for all blast source pressure cases.
Table 4 Summary of brain/skull dynamics for the various blast source pressure cases.
Fig. 8. Correlation between threat size (blast source pressure) and forces experienced on front and rear of the skull. The shaded region indicates that brain/skull collision occurs.
Case
Max anterior force (N)
Max posterior force (N)
Brain collision with skull?
Time of collision (ms)
1.1 atm 1.2 atm 1.5 atm 2.7 atm 3.1 atm
725 1486 3963 14,921 19,525
125 387 1098 3711 4613
No No Yes Yes Yes
– – 11.30 2.39 1.93
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fractional derivatives (Connolly, et al., 2009). Additionally, it will be benchmarked against available experimental and clinical data to better understand the injury mechanism. This work will support a parallel effort underway by the authors and others to develop devices to notify victims and medical personnel to the potential of blast-induced brain injury. References Fig. 9. Delineation in threat parameter space of the probability of cerebral contusion.
3. Conclusions The primary objective of this preliminary study was to determine if a correlation could be made between measureable parameters from the battlefield and if cerebral contusion occurs. A range of threats were selected, based on actual events that occur in the Iraqi Theater of Operations (Clutter, 2004). The results clearly show that such a correlation between relative location from the blast source to the victim, R(m), and its suspected net explosive weight, NEW, can be made. Fig. 9 shows a notional chart for such a process. In this work, the incidence of brain injury, i.e., whether or not an injury occurs, was the extent of assessment. As part of future work, which will include multiple metrics as part of a more sophisticated algorithm, the severity of a brain injury can also be indicated using a scale whose granularity can be determined by the level of detail incorporated into the algorithm. This study will be followed by further research into refining the computational model by incorporating material models that utilize
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