Literature review of head injury biomechanics

Int. J. Impact Engng Vol. 15, No. 4, pp. 561-586, 1994

~ ) Pergamon

0734-743X(94)E0023-O

Elsevier Science Ltd Printed in Great Britain 0734--743X/94 $7.00+0.00

LITERATURE REVIEW OF HEAD INJURY BIOMECHANICS WARREN N. HARDY, TAWFIK B. KHALIL a n d ALBERT I. KING Bioengineering Center, Wayne State University, 818 W. Hancock, Detroit, MI 48202, U.S.A. (Received 2 November 1993; in revised form 14 March 1994)

Summary--The high incidence of head injuries resulting from transportation system crashes, sports, military activities, falls, assaults, etc. contributes to a preponderance of head injury biomechanics research. A wealth of publications result, addressing phenomenological and mechanistic issues associated with head response to mechanical impact. This literature siJrvey provides an assessment of hypothesized brain injury mechanisms, brain injury criteria, mathematical models of head injury and available techniques for measuring head kinematics and brain tissue deformations associated with exposure to dynamic loads.

NOTATION a g cg n t AIS ATD BCM BPT CI CSF DAI EDI ETS FE FMVSS GSI HIC ICP ISO JHTC JTI MCI MSC NDA NHTSA PTC RBKTA RBM SAP SDH TCI WSTC X

acceleration gravitational acceleration center of gravity exponent = 2.5 time in milliseconds abbreviated injury scale anthropomorphic test device brain compliance model blood pressure tolerance contusion index cerebral spinal fluid diffuse axonal injury effective displacement index experimental trauma severity finite element federal motor vehicle safety standards Gadd severity index head injury criterion intracranial pressure international standards organization Japan (JARI) head tolerance curve J tolerance index mean contusion index mean strain criterion neutral density aecelerometer national highway traffic safety administration prolonged traumatic coma rigid body kinematics transducer array revised brain model systemic arterial pressure subdural hematoma total contusion index Wayne State tolerance curve deformation

1. I N T R O D U C T I O N A p p r o x i m a t e l y 10 m i l l i o n h e a d i n j u r i e s h a v e b e e n r e p o r t e d in the U n i t e d States e a c h year, w i t h r o u g h l y 1 0 % o f t h e m b e i n g c o n s i d e r e d m o d e r a t e to s e v e r e a c c o r d i n g to L o n g a n d 561

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Novak [1]. In a 1983 study of head injury cases in Maryland, 19% of those discharged after hospitalization were originally admitted for injury to the head. The total cost of care for these persons was $29,165,466 over a 1 year period. The average cost per case over that year was $8,277. However, AIS 5 head injuries averaged $105,570 for 1 year, while AIS 4 head injuries averaged $56,858 as reported by Mackenzie et al. I-2]. This represents a tremendous monetary, as well as human cost to society. Munoz 1-3] described estimates for 1982, suggesting a $61.025 billion societal cost due to trauma, with approximately 8 million Americans having sustained some form of trauma. An analysis in Great Britain of 68 patients who suffered severe concussion showed that 31 had either persistent problems, or were unemployable. Johnson and Gleave [4] stated that the "number of individuals left with persistent disability is not exactly known". Viano et al. [5] suggested "... neural injury is a major source of injury disability.., and much more research is needed on its mechanism and tolerance to impact". Biomechanics of head injury attempts to elucidate the physical process associated with the consequences of a mechanical impact on the head; and relate it to pathophysiological changes of head tissues. Head injuries typically result from either a direct impact on the head or from an indirect sudden motion applied through the neck. In either case, one or more of the following injuries can occur: scalp laceration, blood vessel rupture, skull fracture, brain dysfunction, etc. For obvious reasons brain injuries have received the most attention, and yet they remain among the most perplexing to understand. In 1943, Anzelius [6"] introduced the first mathematical model of head impact in which the brain was simulated by a spherical liquid mass, subjected to a sudden change in velocity. The rarefaction wave contributed to the cavitation hypothesis of brain damage. It appears to have been the first attempt to develop a mechanics based model of head injury. In 1945, Holbourn 17] used a physical model to argue that brain damage was most likely related to excessive shear strain, produced by head rotation. Some 20 years later, Goldsmith [8] applied his vast expertise in impact mechanics to head injury. Realizing the complexity of the problem and the societal need for a solution, he suggested a long term research approach using a combination of physical and mathematical models based on the mechanics of deformable media to delineate the transient response of the head when exposed to a blow. Goldsmith proposed a head model consisting of an elastic spherical shell filled with a compressible fluid and subjected to a point load. His landmark paper spawned much research in head injury biomechanics in the U.S., particularly from his own laboratory at the University of California in Berkeley, and in Europe, with researchers attempting to provide a rational understanding of the mechanical process involved and the consequences of head impact. Indeed, with his foresight, vision and multidisciplinary approach to physical science, Professor Goldsmith [9-11] contributed significantly not only to the study of the biomechanics of head injury, but to the understanding and quantifying of all aspects of human trauma resulting from impact loads. Available head models include those of subhuman primates, human cadavers, inanimate replicas of the head and mathematical models. They contribute significantly to our understanding of head trauma mechanisms and formulation of head injury criteria. The goal has been, and still is, to correlate clinical dysfunction with a mechanical impact dose. In addition to improving basic understanding, the ultimate objective is to develop a predictive model to be used in head injury diagnosis and to aid in the design of protective devices to mitigate head injury. The research primarily concentrates on explaining the coup/contrecoup phenomenon observed in clinical brain injuries, coup being injury experienced at the impact site of the head, and contrecoup being injury at the collateral site. The research findings shed some light on commonly posed questions including: Why is there a difference between moving (falling) and resting (hit) head impacts? Why is the incidence of contrecoup so much greater in falls? Why is there a difference between fixed and free head impacts? Why are there essentially no contrecoup injuries when the head is fixed? Why in lateral impacts, are injuries roughly equally distributed between both sides? What roles do strain and strain rate of biological tissues play? Other questions are yet to be answered, such as: What

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causes subdural hematoma (SDH)? What causes diffuse axonal injury (DAI)? Why are most brain injuries found in the anterior middle fossae, regardless of whether the impact occurred frontally, or occipitaily? The relationship between kinetic input and resultant head injury cannot be described in simple cause and effect terms. Often causality is not readily determined in an exact fashion. Of the many theories that exist, none is thought to be a definitive part of the solution to the problems of head injury. Precise mechanisms and tolerance criteria are not known. Theories are modified as new information becomes available. The quest to determine the governing parameters and predominant mechanisms to explain clinical and experimental findings creates several schools of thought, with different proponents of each. Attempts are made to categorize and classify outcome as it pertains to input, within the framework of available knowledge and experience. Such an effort is proferred by Ommaya 1-12]. Head injury lesions are divided into four major categories: scalp, skull, extracerebral bleeding (focal or diffuse) and brain tissue damage (neural and/or vascular). Injuries of the scalp are classified as either bruises, abrasions, lacerations, or avulsions. Injuries of the skull are classified as either suture separation, indentation, linear fracture, depressed fracture, or crushed skull. Extracerebral bleeding classifications are either subarachnoid hemorrhage, epidurai hematoma, or subdurai hematoma. Skull fracture is said to accompany epidural hematoma in 9 0 0 of cases, and subdural hematoma (often caused by torn bridging veins) in 5 0 o of acute cases. Finally, brain tissue damage is classified as either concussion, contusion, intracerebral hematoma, or cerebral laceration. A paradigm for head injury is described by Ommaya [12], relating various mechanical inputs to corresponding biological responses. Dynamic inputs (impact and impulse) are given strongest consideration, specifically those that pertain to inertial loading and especially rotation. Rotation is credited with producing both focal and diffuse effects, while translation is limited to focal effects, as are contact phenomena. Depending upon the extent of static input, focal or diffuse effects could be produced. Ommaya [12J stated that DAI is more likely to occur under distributed loading conditions with longer duration (> 10 ms) soft impact with negligible contact phenomena. Rotation is seen as the predominant factor. In cases of focused load, short duration (< 10 ms) hard impacts where contact phenomena and translation are primary factors, DAI is less likely to occur. To provide criteria for the myriad of injuries described, it is recommended that two methods are used. For contact impacts and translational accelerations a strain criterion is suggested, and for rotational accelerations, rotational acceleration and velocity about the cg of the head are suggested. Thresholds for each criterion are given for the corresponding Abbreviated Injury Scale (AIS) expected. The authors explore the possibility of using more than one criterion to more adequately predict or describe head injury. It is not unlikely that multiple criteria may ultimately be required to accurately assess the complex nature of head injuries. It is unlikely, however, that a consensus will be easily reached to satisfy all concerned. This paper attempts to provide a literature review of research on the biomechanics of head injury. Several such papers exist, notably a work by Prasad et al. [! 3] simply entitled "Head". However, because hundreds of papers have been written on subjects concerning various aspects of head injury, this paper focuses on the mechanical nature of head injury. 2. THEORIES OF BRAIN INJURY MECHANISMS Current theories of head injuries include negative pressure, positive pressure, pressure gradients and rotation and shear effects. 2.1. Negative pressure

The primary component of negative pressure theory is cavitation, either coup or contrecoup. Contrecoup site negative pressures are said to form upon impact, and coup site negative pressures are said to form when the skull, having been deformed, rapidly returns to its original geometry. Of three possible methods of tissue damage, (1) rapid

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release of dissolved gases; (2) flash vaporization; and (3) cavitation collapse, cavitation collapse is held as the most plausible. It is thought that regional negative pressures could overcome the tensile strength of brain tissue, creating a vacuum cavity as the brain and/or meninges separate from the skull. The subsequent collapse of this cavity could be very destructive to neural tissue as it is typically accompanied by high tensile stress. Contrecoup injuries were explained as being due to the formation of a vacuum under membranes by Denny-Brown and Russell [,14]. This concept was discussed by Gross [15]. By impacting fluid filled flasks, negative collateral pressures and cavitation were obtained. In some instances the glass vials were destroyed when the cavities collapse. Gross suggested that it was this violent collapse, not negative pressure alone, that caused contrecoup injury. It was also suggested that the spring return of the skull during impact could cause coup injuries. Engin and Akkas [,16] used a spherical sandwich shell model based on negative pressures to determine tolerance criteria for primates. Lubock and Goldsmith [17] created a fluid filled head and neck model to examine cavitation. Their acrylic spherical shell experienced coup, contrecoup and resonating cavitation. The cavitation was found to coincide with negative pressure transients. They noted that it was expected that bubbles would form in cranial fluids, not tissues. Suh et al. [,18] investigated the response of a fluid-filled spherical shell to a localized load of varying ultrasonic pulse shapes. It was found that negative pressure regions were not generally located in the region opposite the impact, which did not support the notion of contrecoup lesion. Stalhammar 119,20] and Stalhammar and Oisson [,21] reported that the negative pressures developed in impacted rabbits did not seem to be important to the injury mechanism. Similarly, Nusholtz et al. [22], stated that the negative pressures developed during impact are non-injurious, although present. In a later study, impacting Macaques, Nusholtz et al. [-23] suggested that cavitation was not an injury mechanism, but head and neck positioning was of importance. 2.2. Positive pressure Those who subscribe to the theory of positive pressure contend that damage of the brain occurs in locations of positive pressure. Presumably this accounts for coup injuries when the head is impacted, and contrecoup injuries during fall. This concept was postulated by Lindenburg [-24], extending pathological findings to suggest a thinning of the cerebro-spinal fluid (CSF) layer between the brain and dura at the contralateral site during a fall. Edberg et al. [25], impacted milling yellow and gel filled cellulose acetate skull models. Positive impact site pressures and negative contralateral pressures were found during impact, but negative impact site pressures and positive contralateral site pressures were found prior to impact during a fall. In support of these findings, Dawson et al. [26] described the rotational tendency of the human body compared to the human head during a fall. They suggested body mass causes acceleration of the head to be greater than I g, while the brain sees only 1 g. It was said that this causes the brain to shift out of position (away from the impact surface), creating a pre-impact negative pressure at the impact site and a positive pressure at the collateral, soon to be, contrecoup site. The water filled head and neck model of Yanagida et al. [27] was in agreement with this idea. 2.3. Pressure gradients One of the most popular head injury theories centers around the development of pressure gradients upon impact. This concept is preliminary to the development of other injury mechanisms. These gradients create shear stresses which result in local deformations of brain tissue. Presumably, rough bony architecture would resist deformations, causing the most damage in these areas, especially in the proximity of the craniospinal junction. Gurdjian and Lissner [28] employed strain gauges and pressure plugs to investigate the dynamic skull stress in impacted dogs. They found compression and pressure increase at the impact site, and tension and pressure decrease at the opposite site. They concluded that dynamic stresses were produced by pressure gradients. Gurdjian et al. [29] further

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related intracranial pressure (ICP) to head injury by measuring acceleration and ICP and observing concussive effects in impacted dogs. This study suggested that injuries .might develop either from short duration, high acceleration and high pressure impacts, or long duration, low acceleration and low pressure impacts. A plastic sagittal section head model filled with milling yellow exhibited shear stresses and hence strains at the craniospinal junction when impacted, as reported by Gurdjian and Lissner 1-30]. Thomas et al. [31] investigated pressure gradients during impact with geil filled skulls. Brass stems, each containing five pressure transducers, were mounted orthogonally two at a time in the skulls. Accelerations and pressures were recorded. It was stated that as acceleration and pressure increased, the pressure gradients became steeper. It was concluded that pressure gradients did exist in the brain during impact and that both acceleration and compression were important. Gurdjian et al. [32] found that impact induced acceleration and skull deformation caused pressure gradients. The brain attempted to "flow" from areas of high pressure to low pressure, and regional brain deformation took place in response to shear stresses. Brain deformation was found to be elastic, as well. Kopecky and Ripperger [33] investigated pressure distribution in the struck skull by way of a fluid filled cylinder impact model. They found positive and negative pressures to be a function of acceleration, with the point of zero pressure being variable. Rhesus monkey heads sectioned at the median plane were subjected to occipital blows after being placed under a glass plate, by Gurdjian [34]. The plate served to seal the halved cranium and allowed observation of the brain during impact. Most noteworthy was the formation of a frontal space during an occipital blow, and movements of the brain stem. Pressure gradient theories became integral to other theories of brain and head injury. Kenner and Goldsmith [35] investigated the pressure gradients in aluminium and acrylic spherical shell models filled with distilled water. The models were subjected to short duration impact (50-500 ps), applied along the axis of symmetry. The experimental results, which were also confirmed with an analytical series solution from coupled shell-fluid theory, confirmed the presence of a compression wave near the impact site, and a tensile wave opposite from the impact location. Khalil et al. [36] extended the previous study to investigate how a protective device may influence the pressure magnitudes, when the structure was exposed to axisymmetric impact. Their model consisted of a spherical aluminium shell, filled with distilled water enveloped by a hemispherical layered shell constructed from aluminium and polystyrene~ The hemispherical shell served as a simple model of a helmet. The influence of the protective device was demonstrated by reducing the shell strains and the fluid pressures. Landkof et al. [37] extended the use of the models described by Kenner and Goldsmith [35] to investigate the effect of a neck constraint on fluid pressure. They also determined the subsequent head motion when the impact duration was extended beyond 0.5 ms. 2.4. R o t a t i o n The concept of rotational brain injury asserts that clinical findings may be duplicated by application of angular acceleration alone, and that linear translation has little to do with injury mechanisms. It is primarily the brain's inability to rotate freely in the frontal compartments of the skull that causes shear stresses and strains, and hence injury. This would presumably explain the predominance of anterior fossae injury regardless of frontal or occipital impacts. The rotational head injury concept was discussed at length in a series of papers by Holbourn [38,7] who assumed uniform density throughout the brain and CSF, and incompressibility of the cranial contents. This coupled with a low modulus of rigidity suggested that rotation was of far greater influence than translation to head injury. Holbourn stated that only shear stresses and strains were injurious. Because of the rough constraining geometry of the skull in the frontal and temporal regions and around the foramen magnum, shear stresses, and hence injury, should be highest in these areas. Holbourn also distinguished between high kinetic energy, and high momentum missiles to explain the difference between impacted and falling head injuries.

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Unterharnscheidt and Higgins [39] investigated Holbourn's theories by applying controlled angular accelerations to squirrel monkeys. The monkeys experienced nondeforming rotation only (no direct impact) and suffered subdurai hematoma, torn bridging veins, and lesions of the brain and spinal cord. Major proponents of rotation as the cause of the majority of head injuries are Gennareili et al. [40-42] and Adams et al. [43-48]. Their experimentation focused on nondeforming rotational acceleration of monkey heads. Gennarelli et al. [40] related levels of concussion to levels of angular acceleration, and developed an experimental trauma severity scale (ETS). Good agreement with clinical findings was reported. Adams et al. [45] reported that the neuropathological data from the primate experiments of Gennarelli et al. [40] are very close to clinical findings in humans. However, Adams et al. [45] found no diffuse white matter damage, but did find subdural hematoma. Gennarelli [49] then attempted to produce diffuse axonal injury by modifying the acceleration pulses delivered to the primates. Subdural hematoma was produced by short duration, high amplitude angular accelerations, and DAI was produced by longer, lower amplitude coronal accelerations, as found by Adams et al. [47]. Gennarelli [49] stated that "virtually all types of primary head injury can be produced by angular acceleration applied to the head in the apporpriate manner". Mass lesions, hypoxia and ischemia were considered as secondary, according to Gennarelli et al. [42]. However, aside from individual theories, combinations of theories have been formed. Gurdjian and Gurdjian [50] suggested a combination of elastic skull deformation, positive and negative pressures, and inertial brain lag could present a clearer picture of head injury. Ommaya et al. [51] and Ommaya and Hirsch 152] contended that rotation alone could not produce the levels of injury caused by direct impact, unless twice the predicted rotational velocity was applied. Ommaya suggested that rotation could account for approximately half of the injury picture, with skull deformation accounting for the other half. However, Ono et al. [53] found that the occurrence of concussion in monkeys did not correlate with rotational acceleration of the head, but did highly correlate with linear acceleration of the head. Resultant average head acceleration and the duration of the acceleration was therefore used to determine the threshold of concussion in the monkey. 2.5. Diffuse neuronal injury Animal head injury models were extended to sub-human primates with limited success. Included are a fluid-percussion model in the cat by Sullivan et al. [54], a fluid-percussion model in the rat by Dixon et al. [55], and a controlled cortical impact model in the ferret by Lighthall [56]. Chason et al. [57] investigated the morphological changes associated with pressure pulse induced concussion and reviewed three series of tests performed on mongrel dogs. The first series involved eight control and 19 experimental animals. A pressure pulse was applied to the right parietal area of the intact dura of the immobilized head. The pressure (air) pulse lasted 10 ms and resulted in intracranial pressure rises between 3 and 38 psi, Twelve areas of the brain were surveyed: four symmetrical section pairs from the cerebral hemispheres, and blocks from the midbrain, pons, medulla and cervical cord. Sections were stained with Luxol-fast blue silver nitrate stain for axos cylinders and myelin sheaths. Sections were also stained with Nissl stain, hematocylin and eosin stain. It was found that "the most significant change was central chromatolysis of the larget cells of the reticular substance in certain areas of the brain stem". Large num.bers of altered cells were found among the retro-olivary cells of the medulla. Fewer changes were found in the pons and even less in the midbrain. Swollen and fragmented axis cylinders and myelin sheaths were found only after exposure to the highest ranges (fatal) of pressure. The next series of tests applied 28 psi pressure pulses for 25 ms to various locations of the dura. Pressure was applied laterally to frontal, parietal, temporal and occipital regions, and midline frontal, parietal and occipital regions. The animals were sacrificed on the seventh day because previous experience suggested this interval to be optimal for the demonstration of cytologic changes. "In the animals of all three series the principal and regular site of the cytologic change was in the medulla just dorsal to the inferior olive, medially but especially laterally."

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However, the site of pontine involvement was not found to be uniform as affected cells were generally found singly. Strich 1-58] investigated diffuse injury to white matter in autopsied human brains. Each subject had survived between 2 days and 2 years after having suffered head injury. Prior to death, the patients exhibited no significant intracranial hemorrhage, no raised intracranial pressure, no raised blood pressure and normal respiration. The Marchi method for staining the products of acute myelin breakdown was modified to disclose long-standing degeneration. While widespread diffuse degeneration of the white matter was found, almost no injury was found in the gray matter. In the cases of long survival, this degeneration was characterized by the presence of many fat-granule cells in the corpus callosum and brain stem. In the cases of survival less than 6 weeks myelin and nerve fiber degeneration were seen. Severed nerve fibers exhibited retraction balls, evidence of axoplasm having flowed from the end of the fiber. Strich stated that diffuse axonal injury (DAI) followed closed and uncomplicated head injury, and may leave the patient incapacitated and demented. It was also stated that white matter lesions can result from secondary degeneration or stretched or torn nerves. It was suggested that these injuries are products of shear stresses or strains and can be found deep in the brain. It was concluded that the observed injuries were an immediate mechanical effect an anoxia would affect the gray matter, and edema would generate fibrous gliosis, each requiring time to develop. Oppenheimer 1-59] analysed diffuse microscopic lesions in 50 cases of head injury. Anoxic changes, diffuse capillary hemorrhages, tract degenerations and diffuse white matter lesions were discussed, yet the focus of the study was the presence or absence of foci of microglial reaction. Anoxic changes and capillary hemorrhage were observed with standard staining techniques while myelin, fat and Marchi product stains were needed for the observation of diffuse white matter lesions. However, a modified Weil and Davenport staining method was used for the disclosure of microglia. Microglial cells were observed in cases where death occurred as early as 15 h after injury, however the cells were small. Between 24 and 48 h the microglia cells increased in number and size, and formed clusters. After 48 h axonal retraction balls were found near the clusters. Microglial cells enlarged and formed pseudopodia during the first 2 weeks and reactive astrocytes were noted at 3 weeks. At 6 weeks, swollen-bodied astrocytes were found as was diffuse microglia. It was suggested that nerve fibers tear at points of intersection with blood vessels. Adams et al. 1-43] note that persons having little external evidence of head injury could have sustained severe and irreversible brain damage, while many with fracture could have little brain damage and recover with little consequence. It was suggested that diffuse brain damage could be the most common cause of a persistent vegetative state. Under the premise that all brain injury in head injured patients was directly attributable to impact, 151 autopsies of brains of persons having had various lengths of survival after injury were performed. The brains and spinal cords were fixed in 10% formol saline for 3 weeks. Staining techniques include Nissl and Woelke methods. Marchi techniques were used to disclose the breakdown products of myelin, and the Glees or Palmgren methods for axons. Microglia were disclosed by the Nauomenko and Feigin technique. Numerous retraction balls were found throughout the mid-brain and pons in cases of short survival. These lesions were often found near a blood vessel or near orthogonally lying tissues. Many hypertrophied microglia were found in cases of intermediate survival. This occurred in white matter in the brain-stem, cerebellum and cerebral hemispheres. Marchi preparations indicated white matter degeneration particularly in the ascending and descending tracts in the brain-stem. It was concluded that diffuse white matter injury occurred at the moment of impact, and it was probable that diffuse damage to white matter was the most important single factor governing the outcome in a patient who sustained a non-missile head injury. Adams et al. [44] developed the contusion index to categorize brain damage after head injury. Contusion was assessed microscopically from fixed coronal slices of cerebral hemispheres and from cerebellar slices. Staining methods included Nissl's technique and Heidenhain's modification of Woelke's technique. The contusion index (CI) was based on the depth and extent of injuries found. The total contusion index (TCI) corresponded to

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the sum of CI for all the contused areas within a given brain. The mean contusion index (MCI) corresponded to the average CI for a given specific anatomical location. The CI was offered as a method to quantitatively assess the importance of the magnitude of brain injury. Adams et al. [46] examined 45 cases of DAI compared to 132 cases of fatal head injury without the presence of DAI. DAI was associated with a lower incidence of a lucid interval, lower incidence of fracture, reduced cerebral contusion and fewer cases of intracranial hematoma. However, there was an accompanying increase in the incidence of raised intracranial pressure (ICP) and suggestion of a link to automotive accidents. It was also suggested that DAI occurred at the time of head injury and was not due to complicating factors such as hypoxia, brain swelling or raised ICP. Focal lesions of the corpus callosum, dorsolateral quadrant and the rostral brain-stem were found. It was stated that DAI occurred at the moment of injury and was the result of a mechanical mechanism. Gennarelli et al. [42] investigated the effects of sagittal, oblique and lateral angular acceleration on coma in primates. Injury was described as concussion (unconscious less than 15 min) or prolonged traumatic coma (PTC). PTC was divided into mild (coma lasting longer than 15 min but less than 2 h), moderate (coma lasting between 2 and 6 h), and severe (longer than 6 h) categories. Diffuse injury was characterized as axonal retraction balls or abnormal axonal morphology scattered throughout the white matter of the cerebral hemispheres. In severe cases, DAI was found in the cerebellum and upper brain-stem. It was stated that it was found in isolation and was not associated with infarction, contusion, ischemic cell changes or intracerebral hemorrhage. DAI was graded on a 1-3 scale. Grade 1 consisted of DAI in the parasagittal white matter of the cerebral hemispheres. Grade 2 added focal lesions in the corpus callosum to the criteria of grade 1. Grade 3 consisted of grade 2 accompanied by lesions in the superior cerebellar peduncle. G o o d correlation between DAI and injury severity was found, and coronal angular head acceleration was cited as a major cause of prolonged traumatic coma. Povlishock et al. [60] investigated low grade head injury in 35 cats by observation of anterograde axonai transport of horseradish peroxidase (HRP). It was suggested that "minor brain injury could ultimately disrupt axons without physically tearing or shearing them". Lobulated and non-lobulated swelling was found between 4 and 6 h after injury, while ball and club-like swelling was found between 12 and 24h. It was thought that proximal swelling indicated impeded anterograde transport, and that distal swelling indicated impeded retrograde transport. Jane et al. [61] investigated the disruption of axons in the brain-stems of primates having received minor head injuries. The brains were examined 7 days after injury by Fink-Heimer and Nauta staining techniques ("degenerating neural tissue has an increased affinity for silver"). It was stated that "the demonstration of axonal and synaptic damage induced by minor head injury was important.., from a sociological point of view it was obviously necessary to revolt our society's somewhat permissive attitude regarding these injuries". Adams et al. [48] described the principal forms of diffuse brain damage as diffuse axonal injury, diffuse brain swelling and diffuse hypoxic brain damage, with DAI being cited as the most important factor in severe head injury. It was found that short term survival was marked by retraction balls or coarsely beaded axons. Survival over several weeks was indicated by the presence of small clusters of microglia. Long term survival was marked by Wallerian type degeneration in long tracts. It should be noted that investigation of DAI in humans could only be investigated microscopically at autopsy, compounding an already difficult problem. 3. HEAD INJURY CRITERIA Experimental determination of head injury tolerance to mechanical impact and development of predictive indices are problems that have long demanded the attention of biomechanical researchers. Most criteria attempt to relate measured dynamic or kinematic input or output parameters to observed injury phenomena. Most methods are gross approximations of a complex living biological system being damaged by external impact.

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This is an approach that has been criticized by some head injury researchers. However, considerable difficulty is encountered when an attempt is made to replace the current head injury criterion due to the lack of information regarding the response of the brain to given mechanical inputs. Location of impact, magnitude and direction of impact, and duration and input all influence the response of the brain and skull. This response can be modified greatly by skull fracture. Gurdjian et al. 1-623 discussed a pressure-time tolerance curve derived from analysing the concussive effects in anesthetized dogs subjected to varying pressure pulses applied directly to the dural sac. An acceleration-time tolerance curve was developed by combining the pressure data with linear skull fracture data in human cadaveric heads. This became known as the Wayne State tolerance curve (WSTC). The basic finding was that high acceleration can be withstood for short durations, while lower accelerations can be tolerated for longer intervals. The relationship between acceleration and skull fracture for longer duration accelerations was furthered by Ono et al. [53] with the development of the Japan automobile research institute (JARI) human head impact tolerance curve, usually referred to as the Japan head tolerance curve (JHTC). The Gadd severity index (GSI) described by Gadd 1'-633 is an extension of the WSTC. The GSI is a weighted approach taking the form: SI = f1,a(t)]" dt

(1)

where a is the response function (i.e. acceleration), n is a weighting factor and t is time. The value of n = 2.5 was offered as an approximation of the slope of a log-log plot of the WSTC. The weighting factor suggested a disproportionate influence of different levels of acceleration, meaning that high response levels have a profound effect upon injury, and low levels have little effect. The integral attempts to accommodate varying pulse shapes, and eliminates the need to assess the importance of different portions of the pulse, as the entire pulse is used. A value of 1000 for this index was suggested as an injury threshold from analysis of data from Wayne State, the FAA and NASA. Extremely long duration pulses were not dealt with as it was assumed that most injury pulses were shorter than 50 ms. The index is not valid for long durations, as well. The index known as HIC (head injury criterion) was introduced by Versace 1,64] and was eventually adopted by NHTSA as the head injury criterion for FMVSS 208 i-65]. It was also described by Advani et al. 1-66].

HIC=(t2-tl)

a(t)dt

( t 2 - t l ) -1 _

.

(2)

J M a x

HIC is calculated by choosing the range for integration of the resultant acceleration of the cg of the head such that the function is maximized (the supremum). A tolerance limit of 1000 has been adopted by NHTSA. There is a dispute regarding the duration of integration between NHTSA and ISO. The NHTSA limit is 36ms while the ISO recommended limit is 15 ms. HIC is described by Eppinger 1-67] as "a measure of the rate of change of specific kinetic energy.., modulated by the square root of the average acceleration" over the integration interval. As with most injury criteria, HIC has had proponents and detractors. Controversies associated with the acceptance of HIC have shown that not only is the determination of head injury mechanisms a difficult problem, but the determination of the best predictive method or injury index is a struggle as well. Nahum and Smith [68] performed a series of blunt head impacts on unembalmed cadavers in an effort to correlate extent of brain injury with measured SI and HIC. Their work supported the ability of HIC to predict relative degrees of intracranial trauma. However, Newman [69] suggested that the assumption of a cause and effect relationship between linear acceleration measured at the

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cg of the head of an anthropomorphic test device (ATD) and its time dependence, and injury was unfounded. The limit of 1000 was called into question, and the limitations of HIC in longer duration impacts discussed. Concerns were raised as to the validity of the original adult human cadaver data, and as to the assumption of viewing the head as a rigid body. The arguments were supported by a collection of data taken from various sources used in an attempt to correlate actual head injury, given as AIS, as a function of HIC. No correlation was found. Strengths and weaknesses of HIC were discussed in detail during a 1981 consensus workshop on head and neck injury criteria, held by NHTSA and edited by Ommaya [70]. Here it was suggested that given the wide variety of sources used to produce Newman's work it was likely that no correlation between AIS and HIC would be found. However, some again suggested that HIC of 1000 was too low, and 1500 might be a better threshold. In support of HIC, Locket [71] analysed acceleration based indices and maintained that they were biomechanically valid. Goldsmith [72] expressed concern that a single criterion, based upon a single parameter, be extended to describe tolerance to all types of head injury for all segments of the population. It was suggested that a simple rigid body analysis may not adequately describe or delineate the complex phenomena of injury to deformable components. The need to differentiate between mechanical and physiological damage to the central nervous system was emphasized, as well as the need to determine limiting stress values, as opposed to limiting acceleration values. The lack of treatment of rotational influences within HIC was disturbing as well. Information concerning age, sex and other population factors was felt to be crucial, as was information concerning the material properties of human head components. In an attempt to address what was deemed the proper use of HIC, Prasad and Mertz [73] produced risk curves of HIC versus life-threatening injury. Operating under the assumption that HIC is an appropriate indicator of injury, the authors produced a linear curve relating values of HIC between 0 and 3000 to percentage of persons that would be at risk of sustaining a life-threatening injury, from 1% to 99%. HIC of 1000 corresponded to 16%. The authors concluded that HIC of 1500 could not be recommended, as the corresponding risk was greater than 50%. It was also cautioned that HIC was not a " G o / N o - G o " criterion, and "compliance goals should be based on the degree of practicable protection" and the segment of the population to be protected in the environment under question. In belt restraint applications where there is no head contact, it was suggested that neck loads be viewed as the predominant concern, not HIC. The time duration limitation of HIC was also addressed, and it was suggested that head resultant acceleration HIC calculations be limited to 15 ms. Slattenschek et al. [74] described the use of a single degree of freedom second-order mechanical system (spring, mass, damper) to model relative displacements between the brain and skull during impact. This became known as the J tolerance index (JTI) and was developed at the Vienna Institute of Technology. In this index, injury was defined by a tolerance value J: j

X~a, Xtolr'

(3)

The injury threshold is then J = 1, with Xmax being the maximum relative displacement of the brain with respect to the skull and Xto~r the tolerable limit of this displacement. The response of this model was tuned and compared to the WSTC. Brinn and Staffeld [75] modified the Vienna model to include variable damping. This was termed the Effective Displacement Index, or EDI. The JTI was also the inspiration for the Revised Brain Model, or RBM, described by Fan [76]. Gurdjian et al. [77] studied the impedance characteristics of cadaver skulls and human subjects. Stalnaker and McElhaney [78] fitted parameters of a mechanical impedance model of the head to empirical longitudinal and lateral monkey and human cadaver head impact data. Normalized model deflection outputs could be taken as mean strains, with

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the maximum strain value being of greatest importance. This model was used to propose the maximum strain criterion. It was very sensitive to pulse shape. Stalnaker et al. [79] later revised the criterion and it became known as the mean strain criterion (MSC). With the addition of a second damper Stalnaker et al. [80] applied the New MSC. Viano [81] added viscous damping and a bilinear spring to produce the brain compliance model (BCM). Ward et al. [82] used finite element modelling to predict intracranial pressures throughout the brain and created the blood pressure tolerance (BPT). Experimental injury results were compared to computed pressures and it was determined that pressures above 34 psi could cause brain contusions. Head acceleration time histories which generate 34psi were proposed as a tolerance limit. Models were also used to predict, or were compared to, physiologic responses. Mucciardi et al. [83] used a complex algorithm to process kinematic head impact parameters to calculate AIS numbers. These numbers were compared to observed AIS in 26 impacted monkeys. Gennarelli et al. [41] developed their own method of quantifying physiological responses elicited from non-contact, angular acceleration of the head. It was a seven grade scale (0-6) based upon systemic arterial pressure (SAP), heart rate, respiration, level of consciousness, corneal reflex and behavioural alterations. It became the experimental trauma severity scale (ETS). Each method of injury prediction has its associated champions and critics. However, a few things appear to be certain: first, little is understood about brain injury and associated brain deformation or deformation gradients. Second, because little is understood, injury prediction and modeling are imprecise estimation procedures. Lastly, the definitive models of brain injury and methods of injury prediction do not yet exist. 4. BRAIN DEFORMATIONS Of particular interest are the methods researchers have used to observe or simulate relative motions between the brain and skull. Often there is an attempt to correlate rotations or displacements with focal and diffuse brain injury observed in animal models. Efforts also center on either validating or disproving brain injury mechanisms and predicting or determining strains. 4.1. Radiographic techniques

Hodgson et al. [84] conducted flash x-ray head impact studies on seven anesthetized dogs. Intravascular contrast media and lead tags were used to track the motion of the brain. The lead tags consisted of fine solder slugs, 0.1 inch long. The tags were inserted into the brain tissue with a hypodermic needle. The implanted tags form three separate linear patterns. Pre-impact x-rays were taken to obtain a baseline reference for the position of the tags. During impact, the x-ray system, which was a single film tray unit, captured one image approximately at the time of maximum compression of the head. The resulting curved shape of the lines of lead tags indicate the presence of shear. Post impact x-rays indicated that the tags returned to the original position, suggesting that the brain underwent an elastic deformation and that the inertial effect of the tags was less than the elastic capacity of the brain tissue. Gurdjian et al. [85,32], using similar techniques when impacting dogs and monkeys with linear and rotary hammers concluded that, "there is little doubt that movements of the brain occur during impact". Shatsky [86] described a high speed flash x-ray cinematography system to be used in subsequent testing. The system was capable of resolving diameters of 0.3 mm and an image rate of 1000 frames per second. The image from the device was ultimately captured on 16 mm film. Its intended use was the planar analysis of graded impacts to the monkey head, but the possibility of a bi-planar approach wad proposed. Shatsky et al. [87] used this system to investigate in vivo blunt head injury trauma in the sagittal plane. High speed angiography and ventricularography showed that the brain underwent significant displacements. Their findings included transitory high frequency skull displacements, early high frequency movement of cerebral blood vessels (anterior cerebral artery, 2-3 mm) and

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low frequency movement of cerebral blood vessels (approximately 2mm). Early high frequency oscillations and low frequency movements of the ventricular system were also found. Focal lesions and hemorrhage were observed, and strain was examined in terms of the changes in distance from the skull to the midline anterior cerebral artery. Shatsky et al. [88], using similar techniques, suggested that alternating areas of high and low radiographic density indicated the possible presence of "waves of force". Transient clearing of the vessels adjacent to the impact site were thought to indicate the presence of negative pressures. Stalnaker et al. [89] conducted 15 head impacts on human cadavers. When the impact load was found to not be a simple product of mass and acceleration, it was suspected that the head was not undergoing rigid body motion, and a decoupling of the brain and skull was postulated. High speed cineradiography was used to investigate the phenomenon. Lead markers in the skull indeed indicated a decoupling, and it was found that pressurization (vascular, CSF) improved the coupling appreciably. In a subsequent study, Nusholtz et al. [22] investigated head impact in anesthetized monkeys, deceased monkeys and repressurized cadavers using high speed x-ray (400 and 1000 frames/s). Four curved lines of neutral density radio-opaque gel were injected into the brains of the subjects. Radio-opaque targets on or near anatomical bony landmarks were also used. Local movement of the skull relative to the brain and differential rotational motion of the brain with respect to the skull were found. Also, internal movement of the brain was shown by the targets. 4.2. Cranial windows Shelden et al. [90] described the design of a Lucite calvarium, a translucent implant that replaced a portion of the skull, facilitating direct observation of the brain. The process included removal of the dura and attaching the calvarium to the skull with screws. Subsequently, Pudenz and Shelden [91] illustrated rotational motion through a Lucite calvarium affixed to craniectomized Macaques. High speed cinematography (2000-3000 frames/s) was used to record the impact events. Film analysis was performed using a Movieola. Motion of the sulci was observed to be maximal in the parieto-occipital region, and minimal in the frontal region, regardless of the site of impact. This was thought to be due to the restraint offered to the brain by the anterior fossa, thus limiting the development of shear strains. Rotary motion of the brain was observed to lag that of the skull in the sagittal plane, but not the coronal plane. It was thought that the falx cerebri limited coronal rotation. Subconcussive motion was described as rotary gliding, accompanied by post impact oscillations. In the tests where the heads were fixed, minimum contrecoup injury was obtained, but when the head was unrestrained, there were pronounced contrecoup lesions. Through tests with and without the cerebral spinal fluid, it was determined that CSF contributed heavily to damping effects in the brain. Ommaya et al. [92] developed a vacuum thermoforming technique for the fabrication of a Lexan calvarium and Gosch et al. [93] employed a Lexan calvarium when impacting Rhesus monkeys. Considerable brain movement relative to the cranium, cerebral contusions and contrecoup injuries were observed and EEG was monitored. It was found that minimal deformation was associated with concussion, but large relative movement between the brain and skull was associated with contusions. It was suggested that damage occurred as a consequence of interference of structures moving at different rates. Gosch et al. [94] employed a Lexan calvarium in 12 impacts to the heads of Rhesus monkeys. Maximum movement of the brain was found to be in the occipital region during frontal impacts. It was also found that CSF, blood and cerebral tissue moved out of the cranial space through the foramen magnum. The calvarium was also used for chronic observation of the brain. Motti et al. [95] used a Lexan calvarium for microscopic observation of circulation in 25 cats and dogs over a course of 2 years. 4.3. Strain models and methods Gurdjian and Lissner [30] used a l-inch thick plastic sagittal section model of the head to examine the presence of shear. A solution of 1.5% by weight milling yellow simulated

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the intracranial contents, the milling yellow being doubly refracting in the presence of shear. Impacting the model produced alternating bands corresponding to shear contours at the craniospinal junction. This result was recorded photographically at framing rates of up to 500 frames/s. Hodgson et al. [96] devised a two-dimensional head model from a mold of a 2.75 inch sagittal section of cadaver skull. The model was a polyester resin shell with its outer surface coated with several layers of fiber glass. The lateral surfaces were 0.125 inch thick Plexiglas plates. The spinal canal was simulated by a 2.75 inch long Plexiglas tube having an inner diameter of 0.675 inch and a wall thickness of 0.125 inch. This tube was fitted with a piston which was backed by a spring having a static rate of 10 lbs/inch. The brain was represented by silastic. With one of the lateral plates removed, half of the silastic was poured into the model. A 0.25 inch grid was then painted on the silastic surface, and the second half of the silastic was poured and the lateral plate was replaced. When curing the silastic, small bubbles formed in the model. During impact, these bubbles enlarged temporarily at the contrecoup site, presumably indicating regions of negative pressure. Deformation of the grid was observed by films taken at 7000 frames/s. The grid displayed S-shaped patterns, and it was decided that these patterns indicate the existence ofshear waves in the impacted brain. Shuck and Advani 1-97] characterized the in vitro dynamic properties of human brain in pure shear. They developed a four-parameter linear viscoelastic model usable up to 350Hz. They found a failure limit of 3500 microstrains for less than 10Hz and 1300 microstrains above 60 Hz. The relationship between strain rate and tissue failure was not described. Lowenhielm [98] devised a mathematical simulation of gliding contusions as a result of exposure to angular acceleration using the dynamic properties of the superior cerebral veins. It was stated that the site of maximum shear depended on the duration of the acceleration pulse, but that maximum shear basically occurred at a constant distance from the surface of the brain (8 mm). It was also noted that the deep brain could be injured while the surface was not injured, and that the region of maximum shear became deeper as the pulse length increased. Limiting strains and strain rates were calculated for the radius of rotation producing the largest shear. The limit for angular acceleration was given as 4500 rad/s 2 and with a change in angular velocity of less than 70 rad/s. Margulies et al. [99] compared regions of strain found in a physical model of an animal head to regions of DAI in a living animal head model and extended the findings to a physical model of the human head. Coronal cuts were made through baboon and human skulls 1.5 cm posterior to the plane passing through the pons, third ventricle, thalamus and corpus callosum. This plane was said to be most frequently associated with diffuse neural tissue damage. The anterior segment was used to fabricate the model. The foramen magnum was covered and the falx cerebri was simulated by a thin polyurethane sheet. The skulls were potted in aluminium tubes fitted to a " H Y G E ' device designed to deliver biphasic angular acceleration through a 65 ° arc at a 73 mm radius from the center of rotation to the center of mass of the model. The angular acceleration was not delivered via direct impact. The models were filled to the plane of interest with a simicon gel system, and black grids were painted on the gel surface in 1.5-3 mm spacings. The models were then completely filled with gel, topped with water and covered with a transparent plate which sealed the models. The falx was fixed to the plate to simulate tentorial and occipital attachments. The concept was to measure the deformation patterns in the models when they were subjected to angular accelerations, using 6600 frames/s film analysis. The resulting load levels and brain anesthetized baboons used the same mechanical drive mechanism. It was suggested that in this way a critical value of shear strain associated with DAI could be found, as well as the rotational tolerance for DAI. It was also suggested that this information could be extended to humans through comparison of the two physical models. The model response was shown to mimic the pathology found in the animals. The regions of highest strain corresponded to the regions of most DAI. It was decided that shear strain could be used as an index for angular acceleration induced tissue injury. Normalized maximum shear strains for different regions of the brain were plotted vs peak angular accelerations. It was found that maximum shear increased for increased angular acceleration

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in the regions of DAI. It was also decided that the larger mass human head model indicated a magnification of the strain field without changing the spatial distribution of strain. It was then proposed that the angular acceleration limit for DAI in the human (1067-gm) brain was 16,000rad/s 2. It was noted that the corresponding shear limits were local thresholds. It was also suggested that this approach could be applied to finite element modeling. McElhaney et al. [100] examined the mechanical properties of human and monkey bone in terms of density, tension and compression, simple shear, torsion and hardness. Samples were cut from a 10 mm grid pattern. A single material porous block model was used to describe the results. Galford and McElhaney [101] performed a viscoelastic study of scalp, brain and dura from human and monkey specimens. Creep and relaxation results were used to fit a four-parameter Maxwell-Kelvin model. This type of analysis was again used by McElhaney et al. [102] to determine the dynamic characteristics of the tissues of the head. Although investigators have examined the material and mechanical properties of the skull and its contents, and some have examined the injury responses of composite structures to mechanical input, one effort has related level of dysfunction to elongation for a single axon. Galbraith et al. 1-103] investigated the response of the squid giant axon to strain. Ability to conduct action potentials was monitored with respect to stretch injury. It was found that 12% elongation performed within 14 ms suppressed nerve activity for 3 min. As the loading rate increased, the injury response became more pronounced and longer lasting. After 20% elongation, 90% of the nerve resting potential was eventually regained, but after more than 20% elongation the axon would never fully recover. Elongation of 25% resulted in structural failure. Stimulus of stretch sensitive channels and deformation of ion channels were discussed as possible but not completely satisfactory mechanisms to explain the observed responses, which were described by a quasi-linear-viscoelastic model. 5. MATHEMATICAL MODELS OF HEAD INJURY Several impact models of the human head have been proposed and analysed. In a review paper by King and Chou [104], it was pointed out that 25 models of head impact were developed from 1966 to 1975, most of which modeled the head-brain complex as a fluid-filled spherical or oval shell, as suggested by Goldsmith in 1966 I-8]. All models attempted to approximate the cranial vault by an elastic shell and its contents by an inviscid or viscous fluid. Since that time, more geometrically complex models were developed using the finite element (FE) technique. Ward and Thompson's model [105] was one of the first FE models which approximated the three-dimensional anatomy of the brain. However, the skull was assumed to be rigid. Subsequent models by Nahum et al. 1,106] and by Ward et al. 1-82] predicted the pattern of pressure variation in the brain and showed that the dura, falx cerebri and tentorium to be important structures that affected the brain response. Khalil and Hubbard [107] used the FE method to model the head by axisymmetric spherical and oval fluid-filled shells. The model simulated the scalp, skull and brain, including the multi-layered skull. They found a linear pressure gradient in the fluid, with compression near the point of impact (coup) and tension on the opposite side (contrecoup). Shugar and Katona [108] proposed a two-dimensional plane strain model of the mid-sagittal section of the human head, represented by a shell and fluid. They predicted a quadratic pressure gradient with the contrecoup pressure about twice as large as the coup pressure. Shugar 1,109] developed a three-dimensional model which closely approximated the geometry of the human skull and brain. His model results included shell strain near the impact site and around the foramen magnum at the base of the skull. A nearly linear pressure gradient in the fluid was predicted. The model proposed by Hosey and Liu [110] was three-dimensional and simulated a layered skull, dura, cerebral spinal fluid, brain, spinal cord, cervical column and cerebral membranes. However, because of the geometric complexity of the model, it was not feasible to perform a detailed parametric study at the time it was developed. Recently, Ruan et al. [111] proposed a two-dimensional, plane strain FE model to study

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the effects of membranes on intracranial pressure response when the head is subjected to side impact. This analysis showed that the membranes affect the frequency response of the brain and the spatial pressure distribution within the cranium. Dimasi et al. [112] have developed a three-dimensional model which predicted cortical strain of the brain during head impact with an automotive A-pillar. In 1992 Ruan et al. [113] developed a detailed three-dimensional model which investigated the coup~zontrecoup pressure distribution in the brain and compared the model response with experimental data from human cadavers reported by N a h u m et al. 1-106]. Occipital impacts cause more severe contrecoup injury than frontal impacts, and this model attempted to confirm this clinical observation. Ruan et al. [1 14,115-] also investigate the influence of brain viscoelasticity and impact location on the head. Figure 1 shows the FE model of the head used by Ruan et al., which consists of several components representing the scalp, skull, dura, falx and brain. The spatial pressure distributions resulting from frontal, occipital, lateral and crown impact are shown in Figs 2-5. The companion shear stress, and pressure distributions are shown in Figs 6-9. The model response agrees qualitatively with experimental head injury data as far as localization of stresses at areas susceptible to brain injury from head impact. 6. M E T H O D S O F M E A S U R I N G H E A D M O T I O N 6.1. Rigid body kinematics

Measurements of head translation and rotation subsequent to impact have been important in assessing head impact severity. Historically, however, generalized threedimensional angular acceleration and velocity measurements presented a variety of difficulties. This problem has generated a great deal of attention among biomechanical researchers and has recently gained attention from those involved in robotics, such as

Dura mater

Falx cerebri

dl outer table -

ull - dipole :ull - inner table

- right hemisphere

xy

;pinal fluid

Y FIG. 1. Three-dimensional finite element model of an average size human head. From Ruan et al. I-114].(Reprinted with permissionfrom SAE 933114. (~5)1993Societyof AutomotiveEngineers, Inc.)

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er al.

Contour Values

FIG. 2. Lines of isopressure contours within the cranium contents. calculated at peak impact force occurring at 5 ms, due to a ballistic impactor with an initial velocity = 6.33 m/s, diameter = 42 mm and mass = 5.23 kg, applied at the forehead. From Ruan ef al. [I 143. (Reprinted with permission from SAE 933114. 0 1993 Society of Automotive Engineers, Inc.)

Contour Values A = 185.0 B = 148.5 c = 113.1 D = 77.5 E = 41.8 F = -6.25 G = -35.3 H = -74.0 OW FIG. 3. Lines of isopressure contours within the cranium contents, calculated at peak impact force occurring at 5 ms, due to a ballistic impactor with an initial velocity = 6.33 m/s, diameter = 42 mm and mass = 5.23 kg, applied at the occipital region of the head. From Ruan et al. [I 141. (Reprinted with permission from SAE 933 114. 0 1993 Society of Automotive Engineers, Inc.)

Contour Values A = 220.0 B = 185.0 C = 150.0 D = 115.0 E = 80.0 F = 40,O G = -25.0 H = -60.0 WW

FIG. 4. Lines of isopressure contours within the cranium contents, calculated at peak impact force occurring at 5 ms, due to a ballistic impactor with an initial velocity = 6.33 m/s, diameter = 42 mm and mass = 5.23 kg, applied at the side of the head. From Ruan et a/. [114]. (Reprinted with permission from SAE 933114. 0 1993 Society of Automotive Engineers, Inc.)

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Contour Values A = 185.0 B = 160.0 c = 135.0 D = 105.0 E = 75.0 F = 40.0 G = 25.0 H = 10.0 b-W FIG. 5. Lines of isopressure contours within the cranium contents, calculated at peak impact force occurring at 5 ms, due to a ballistic impactor with an initial velocity = 6.33 m/s, diameter = 42 mm and mass = 5.23 kg, applied at the head crown.

Contour Values A = 75.0 B = 65.5 c = 55.0 D = 46.5 E = 37.5 F = 18.75 G = 9.375 H = 0.50 WW

FIG. 6. Midsagittal plane shear stress contours within the cranium from frontal impact. From et al. [114]. (Reprinted with permission from SAE933114.0 Society ofAutomotive Engineers,

Contour Values A = 38.5 B = 33.75. C = 28.1 D = 22.5 E = 16.8 F = 11.25 G = 5.625 &Pa)

FIG. 7. Midsagittal

plane

shear

stress

contours

within

the cranium

from

occipital

impact.

Ruan Inc.)

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Contour Values A = 45.0 B = 38.0 C = 28.O D = 22.0 E = 15.0 F = 10.0 G = 5.0 (kPa) FIG. 8. Midsagittal plane shear stress contours within the cranium from side impact.

Contour Values A = 32.5 B = 25.5 C = 20.5 D = 15.5 E = 10.75 F = 6.75 (kPa)

FIG. 9. Midsagittal plane shear stress contours within the cranium from crown impact.

Angeles [116], who also are attempting to solve kinematic problems. Planar application of linear accelerometry to the determination of angular acceleration was shown by Mertz [117]. This concept, coupled with the use of rate gyroscopes, was furthered by Ewing et al. [118] and Ewing and Thomas [119]. It is generally accepted that the first stable solution to the problem was presented by Padgaonkar et al. [120]. This solution is the Wayne State University Nine Accelerometer Mount, or the 3-2-2-2 method. A unique geometric array of linear accelerometers allows the calculation of angular acceleration, which can be integrated to find angular velocity. This concept was extended by Chou and Sinha [121] to determine kinematic quantities, i.e. linear components of acceleration, at a point on the rigid body, namely the cg of an impacted head, to facilitate calculation of HIC. Mital and King [122] addressed the problem of non-commutativity of finite rotations and developed a method based on an orientation vector approach to determine three-dimensional angular dislSlacements. Since the inception of the 3-2-2-2 method, researchers have struggled to develop an improved concept. Common sources of error have been identified as cross-axis sensitivity of transducers, machining errors in the mount, mismatched transducer pairs, signal noise, mounting fixture vibrations, zero shift and errors associated with numerical and recursive techniques. An in-line 15 accelerometer iterative approach was outlined by Viano et al. [ 123]. Spherical geometry was applied to a non-linear accelerometer array using centripetal accelerations (normal) to calculate angular velocity directly by Nusholtz et al. [124]. Bendjellal et al. [125] employed the MS-I mount for cadaver testing and the 18 channel

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FIG. 10. The WSU RBKTA fixture(wire frame drawing).

APR 89-III for dummy testing. This mount was capable ogf 3-2-2-2, 3-3-3, or in-line measurement techniques. Recently, commercial transducers have been introduced to directly measure angular velocity (magnetohydrodynamic sensors) and acceleration (angular accelerometers). In cadaver or live subject testing, the instrumentation must not modify the physical parameters of the specimen (mass, moment of inertia etc.) to any great degree. These devices did not meet this objective, and there has been some discussion as to the performance limitations of each. A new development discussed by Hardy and King [126-1 suggests that a least squares approach using radial and tangential linear acceleration can provide a better solution for angular acceleration and velocity. It is this thinking that produced the rigid body kinematics transducer array (RBKTA). A conceptual drawing of a 24-accelerometer version of the device is shown in Fig. 10. The RBKTA uses a least square and centripetal acceleration approach to measure all angular acceleration and angular velocity components for cadaver testing. The mount is made of magnesium. It consists of 24 integrated accelerometer dice, IC Sensors 8063-200. Figure 11 shows the location and orientation of the 24 accelerometers which are located in the slots shown in Fig. 10. The holes serve as wiring passages and serve to reduce its weight. Investigation of the mathematical basis for the computation of angular velocity and acceleration ledto this new RBKTA- The RBKTA is smaller, lighter and more versatile than the 3-2-2-2 mount. It is also more rigid and vibration resistant than the 3-2-2-2 mount. In theory it also has the potential for being more accurate than the 3-2-2-2 method. Instead of using large Endevco 7264 accelerometers, the RBKTA uses IC Sensors integrated dice. These accelerometers are much less sensitive to cross-axis excitation than the 7264s, and their small size allows accurate alignment of the sensitive axes. Machining errors are minimized because the mounting locations consist only of slots to be milled. Radially oriented transducers allow the direct calculation of angular velocities. In-line arrays of tangential accelerometers give redundant measurements so that there are a number of possible methods of solution. A 24-accelerometer scheme will provide a least square approach with respect to radii differences. These multiple measurements also assure that

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FIG. 11. WSU RBKTA accelerometer (24) locations and orientations.

the loss of one channel will not render the entire test a failure, and that signal accuracy can be improved by averaging or regression techniques. It is not necessary to use every channel. Wiring is reduced by using a common excitation to all of the transducers. 6.2. Neutral density technology A biaxiai neutral density accelerometer (NDA) and a triaxial NDA have been developed at the Bioengineering Center of Wayne State University. The bi-axial NDA was implanted in the parietal lobe of unembalmed cadavers which underwent facial impacts via a cannon fired pendulum impactor. The biaxial NDA is described by Hardy and King 1-127] and consists of integrated accelerometer dice mounted orthogonally within a polyurethane foam injected polyester resin shell. It has circumferential flanges in three planes to resist rotation within the brain tissue. The density is 1.033 gm/ml and the volume is 2.264 ml. The design objectives for the NDA are to fabricate the smallest possible triaxial transducer with the density of brain tissue. The unit must be rigid and anti-resonant. It must be able to withstand the harsh environment of biological fluids. It also must maintain its position with respect to surrounding brain tissue during impact. The triaxial NDA is a considerable improvement over its predecessors. Accompanying the addition of a third channel, there is a 92% decrease in size. The biaxial NDA has a volume of 2.264 ml, but the tfiaxial NDA has a volume of only 0.187 ml and its largest dimension is 5.7 mm. Its density is 1.065 gm/ml. A biaxial unit is shown in Fig. 12(a) and a triaxial NDA (prior to final assembly) and a prototype are shown in Fig. 12(b). The triaxial NDA is fabricated using techniques similar to those used when constructing the biaxial unit. That is, the NDA consists of piezoresistive integrated accelerometer dice positioned orthogonally to each other within a polyurethane foam injected polyester resin shell. In the case of the biaxial NDA, the shell consists of two molded halves. The triaxial NDA shell is a five sided "box" with a separate "top". To mold the shell, an aluminium

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FIG. 12(a). A biaxial neutral density accelerometer (NDA).

5~

•

o

~o

,

x

FIG. 12(b). A triaxial neutral density accelerometer, prior to final assembly, and a prototype triaxial NDA.

exterior "positive" and interior "negative" are needed• Latex is used to form an exterior negative from the exterior positive• This form is then vulcanized• Locator holes are used to position the latex form over the interior negative when molding the N D A shell• Once the shell is formed the accelerometer dice are installed with cyanoacrylate and the

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polyurethane is injected. Excess foam is trimmed and the NDA is sealed with a layer of polyester. The entire unit is then coated with an acrylic spray. The latex and aluminium molds are reusable. 7. C O N C L U D I N G REMARKS There has been much progress toward understanding head injury biomechanics since Goldsmith [8-1 produced its landmark paper. Several physical models of the head and the head-neck complex have been constructed, instrumented and tested undergoing direct impact and gross kinematic motion. Mathematical models, created initially using closed form solutions such as that of Engin 1-128-1, and later by FE techniques, have also been developed and analysed to accompany the physical models. This combination of models, together with experimental data from animal models, human cadavers and human volunteers has significantly improved our comprehension of the consequences of a mechanical impact to the head. Newly developed FE models of the head and advances in computational technology and supercomputers combine to provide dramatic improvement over their recent counterparts. Responses of these models compare favorably with experimental data from human cadaver tests. They also provide enough detailed information concerning deformations and pressure and shear strain distributions within the cranium to allow formulation of new injury criteria based on pointwise material tolerance. It is anticipated that in the future these models may be used as an effective tool in clinical head injury diagnosis and in the assessment of impact severity and design of protective devices. There are still, however, certain aspects of head injury that require attention from the biomechanics community in collaboration with the human sciences researchers. These include: (1) development of relationships between physiological, pathophysiological and/or biochemical tissue damage and mechanical parameters produced in an impact event; (2) more accurate and representative constitutive models for head tissues, particularly the brain, at deformation levels and strain rates typical of real life impact conditions; and (3) development of injury criteria, based on macro or microscopic tissue damage to replace or complement current criteria based on gross head motion. REFERENCES 1. C. J. Long and T. A. Novack, Postconcussion symptoms after head trauma: interpretation and treatment. South Med. J. 79, 728-732 (1986). 2. E. J. MacKenzie, S. Shapiro and J. H. Siegel, The economic impact of traumatic injuries: One-year treatment-related expenditures. J. Am. Med. Ass. 260, 3290-3296 (1988). 3. E. Munoz, Economic costs of trauma, United States, 1982. J. Trauma 24, 237-244 (1984). 4. R. Johnson and J. Gleave, Counting the people disabled by head injury. Injury 18, 7-9 (1987). 5. D. C. Viano, A. I. King, J. W. Melvin and K. Weber, Injury biomechanics research: an essential element in the prevention of trauma. J. Biomech. 22, 405--417 (1989). 6. A. Anzelius, The effect of an impact on a spherical liquid mass. Acta Pathol. Microbiol. Scand. Suppl. 48, 153-159 (1943). 7. A. H. S. Holbourn, The mechanics of brain injuries. Br. Med. Bull. 3, 147-149 (1945). 8. W. Goldsmith, The physical process producing head injuries. In Head Injury Conference Proceedings (edited by W. F. Caveness and A. E. Walker), pp. 350-382. Lippincott, Philadelphia (1966). 9. W. Goldsmith, Biomechanics of head injury. In Biomechanics: Its Foundation and Objectives (edited by Y. C. Fung, N. Perrone and M. Anliker), pp. 585-643. Prentice Hall, Englewood Cliffs (1968). 10. W. Goldsmith, J. L. Sackman, G. Ouligan and M. Kabo, Response of a realistic human head-neck model. J. Biomech. Engng 100, 25-33 (1978). 1 I. W. Goldsmith, Some aspects of head and neck injury and protection. In Biomechanics, Proceedings of a NA TO Advanced Study Symposium on Biomechanics (edited by N. Akkas), pp. 337-377. Sijthoff and Noordhoff, Alpen aan den Rijin, Holland (1979). 12. A. K. Ommaya, Biomechanics of head injury: experimental aspects. In The Biomechanics of Trauma (edited by A. M. Nahum and J. W. Melvin), pp. 245-279. Appleton-Century-Crofts, Norwalk (1985). 13. P. Prasad, J. W. Melvin, D. F. Huelke, A. I. King and G. W. Nyquist, Head. In Review of Biomechanical Impact Response and Injury in the Automotive Environment, Task B Final Report (edited by J. W. Melvin and K. Weber), DOT Report No. HS-807-042. National Technical Information Service, Springfield (1985).

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