A multi-body dynamics study on a weight-drop test of rat brain injury

Traumatic brain injury (TBI), induced by impact of an object with the head, is a major health problem worldwide. Rats are a well-established animal analogue for study of TBI and the weight-drop impact-acceleration (WDIA) method is a well-established model in rats for creating diffuse TBI, the most common form of TBI seen in humans. However, little is known of the biomechanics of the WDIA method and, to address this, we have developed a four-degrees-of-freedom multi-body mass-spring-damper model for the WDIA test in rats. An analytical expression of the maximum skull acceleration, one of the important head injury predictor, was derived and it shows that the maximum skull acceleration is proportional to the impact velocity but independent of the impactor mass. Furthermore, a dimensional analysis disclosed that the maximum force on the brain and maximum relative displacement between brain and skull are also linearly proportional to impact velocity. Additionally, the effects of the impactor mass were examined through a parametric study from the developed multi-body dynamics model. It was found that increasing impactor mass increased these two brain injury predictors.     

The brain uses extrasomatic information to estimate limb displacement

A fundamental problem faced by the brain is to estimate whether a touched object is rigidly attached to a ground reference or is movable. A simple solution to this problem would be for the brain to test whether pushing on the object with a limb is accompanied by limb displacement. The mere act of pushing excites large populations of mechanoreceptors, generating a sensory response that is only weakly sensitive to limb displacement if the movements are small, and thus can hardly be used to determine the mobility of the object. In the mechanical world, displacement or deformation of objects frequently co-occurs with microscopic fluctuations associated with the frictional sliding of surfaces in contact or with micro-failures inside an object. In this study, we provide compelling evidence that the brain relies on these microscopic mechanical events to estimate the displacement of the limb in contact with an object, and hence the mobility of the touched object. We show that when pressing with a finger on a stiff surface, fluctuations that resemble the mechanical response of granular solids provoke a sensation of limb displacement. Our findings suggest that when acting on an external object, prior knowledge about the sensory consequences of interacting with the object contributes to proprioception.     

Improved measurement of brain deformation during mild head acceleration using a novel tagged MRI sequence

In vivo measurements of human brain deformation during mild acceleration are needed to help validate computational models of traumatic brain injury and to understand the factors that govern the mechanical response of the brain. Tagged magnetic resonance imaging is a powerful, noninvasive technique to track tissue motion in vivo which has been used to quantify brain deformation in live human subjects. However, these prior studies required from 72 to 144 head rotations to generate deformation data for a single image slice, precluding its use to investigate the entire brain in a single subject. Here, a novel method is introduced that significantly reduces temporal variability in the acquisition and improves the accuracy of displacement estimates. Optimization of the acquisition parameters in a gelatin phantom and three human subjects leads to a reduction in the number of rotations from 72 to 144 to as few as 8 for a single image slice. The ability to estimate accurate, well-resolved, fields of displacement and strain in far fewer repetitions will enable comprehensive studies of acceleration-induced deformation throughout the human brain in vivo.     

Fluid–structure interaction simulation of the brain–skull interface for acute subdural haematoma prediction

Traumatic brain injury is a leading cause of disability and mortality. Finite element-based head models are promising tools for enhanced head injury prediction, mitigation and prevention. The reliability of such models depends heavily on adequate representation of the brain–skull interaction. Nevertheless, the brain–skull interface has been largely simplified in previous three-dimensional head models without accounting for the fluid behaviour of the cerebrospinal fluid (CSF) and its mechanical interaction with the brain and skull. In this study, the brain–skull interface in a previously developed head model is modified as a fluid–structure interaction (FSI) approach, in which the CSF is treated on a moving mesh using an arbitrary Lagrangian–Eulerian multi-material formulation and the brain on a deformable mesh using a Lagrangian formulation. The modified model is validated against brain–skull relative displacement and intracranial pressure responses and subsequently imposed to an experimentally determined loading known to cause acute subdural haematoma (ASDH). Compared to the original model, the modified model achieves an improved validation performance in terms of brain–skull relative motion and is able to predict the occurrence of ASDH more accurately, indicating the superiority of the FSI approach for brain–skull interface modelling. The introduction of the FSI approach to represent the fluid behaviour of the CSF and its interaction with the brain and skull is crucial for more accurate head injury predictions.

     

Influence of the lateral ventricles and irregular skull base on brain kinematics due to sagittal plane head rotation

Two-dimensional physical models of the human head were used to investigate how the lateral ventricles and irregular skull base influence kinematics in the medial brain during sagittal angular head dynamics. Silicone gel simulated the brain and was separatedfrom the surrounding skull vessel by paraffin that provided a slip interface between the gel and vessel. A humanlike skull base model (HSB) included a surrogate skull base mimicking the irregular geometry of the human. An HSBV model added an elliptical inclusion filled with liquid paraffin simulating the lateral ventricles to the HSB model. A simplified skull base model (SSBV) included ventricle substitute but approximated the anterior and middle cranial fossae by a flat and slightly angled surface. The models were exposed to 7600 rad/s2 peak angular acceleration with 6 ms pulse duration and 5 deg forced rotation. After 90 deg free rotation, the models were decelerated during 30 ms. Rigid body displacement, shear strain and principal strains were determined from high-speed video recorded trajectories of grid markers in the surrogate brains. Peak values of inferior brain surface displacement and strains were up to 10.9X (times) and 3.3X higher in SSBV than in HSBV. Peak strain was up to 2.7X higher in HSB than in HSBV. The results indicate that the irregular skull base protects nerves and vessels passing through the cranial floor by reducing brain displacement and that the intraventricular cerebrospinal fluid relieves strain in regions inferior and superior to the ventricles. The ventricles and irregular skull base are necessary in modeling head impact and understanding brain injury mechanisms.     

Modelling of intracranial behaviour on occiput impact in judo

Acute subdural hematoma (ASDH) sometimes occurred in judo because of the bridging veins’ failure by rotation of the brain in the skull. However, the relationship between intracranial behaviour and the motion of the body on occiput impact has not yet been clarified. In this study, we developed an intracranial mechanical model based on multibody dynamics and compared it with experimental results. The results show the importance of modelling bridging veins and cerebral spinal fluid to the relative displacement between brain and skull. The proposed model will contribute to accident analyses or the optimum design of supporting devices.     

Separating brain motion into rigid body displacement and deformation under low-severity impacts

The relative motion of the brain with respect to the skull has been widely studied to investigate brain injury mechanisms under impacts, but the motion patterns are not yet thoroughly understood. This work analyzes brain motion patterns using the most recent and advanced experimental relative brain/skull motion data collected under low-severity impacts. With a minimum total pseudo-strain energy, the closed-form solutions for rigid body translation and rotation were obtained by matching measured neutral density target (NDT) positions with initial NDT positions. The brain motion was thus separated into rigid body displacement and deformation. The results show that the brain has nearly pure rigid body displacement at low impact speed. As the impact becomes more severe, the increased brain motion primarily is due to deformation, while the rigid body displacement is limited in magnitude for both translation and rotation. Under low-severity impacts in the sagittal plane, the rigid body brain translation has a magnitude of 4-5 mm, and the whole brain rotation is on the order of +/-5 degrees.     

A mathematical model for the determination of viscoelastic behavior of brain in vivo. II. Relaxation response

In a recent experiment for determining the mechanical response of brain in vivo. a probe, inserted through scalp, skull and dura, is placed in contact with and normal to the brain, given a prescribed motion, and the time variation of corresponding force is measured. In the corresponding continuum mechanical model, brain is idealized as a linear isotropic viscoelastic solid constrained by a rigid skull. At the mating surface, the shear stress and normal displacement vanish everywhere except under the probe which exerts a local radial displacement. This model introduces effective viscoelastic moduli in shear, which is unknown, and in dilatation, which is considered known from other sources. Part II of this study is concerned with stress relaxation induced by a small step displacement of the probe. From the solution of the corresponding quasi-static boundary value problem, a nonlinear Volterra integral equation is established from which the shear stress relaxation function can be solved in terms of measured probe displacement and force. A numerical method of solution is developed.     

Global/local head models to analyse cerebral blood vessel rupture leading to ASDH and SAH

Blunt and rotational head impacts due to vehicular collisions, falls and contact sports cause relative motion between the brain and skull. This increases the normal and shear stresses in the (skull/brain) interface region consisting of cerebrospinal fluid (CSF) and subarachnoid space (SAS) trabeculae. The relative motion between the brain and skull can explain many types of traumatic brain injuries (TBI) including acute subdural hematomas (ASDH) and subarachnoid hemorrhage (SAH) which is caused by the rupture of bridging veins that transverse from the deep brain tissue to the superficial meningeal coverings. The complicated geometry of the SAS trabeculae makes it impossible to model all the details of the region. Investigators have compromised this layer with solid elements, which may lead to inaccurate results. In this paper, the failure of the cerebral blood vessels due to the head impacts have been investigated. This is accomplished through a global/local modelling approach. Two global models, namely a global solid model (GSM) of the skull/brain and a global fluid model (GFM) of the SAS/CSF, were constructed and were validated. The global models were subjected to two sets of impact loads (head injury criterion, HIC = 740 and 1044). The relative displacements between the brain and skull were determined from GSM. The CSF equivalent fluid pressure due to the impact loads were determined by the GFM. To locally study the mechanism of the injury, the relative displacement between the brain and skull along with the equivalent fluid pressure were implemented into a new local solid model (LSM). The strains of the cerebral blood vessels were determined from LSM. These values were compared with their relevant experimental ultimate strain values. The results showed an agreement with the experimental values indicating that the second impact (HIC = 1044) was strong enough to lead to severe injury. The global/local approach provides a reliable tool to study the cerebral blood vessel ruptures leading to ASDH and/or SAH.     

Phenotypic integration of neurocranium and brain

Evolutionary history of Mammalia provides strong evidence that the morphology of skull and brain change jointly in evolution. Formation and development of brain and skull co-occur and are dependent upon a series of morphogenetic and patterning processes driven by genes and their regulatory programs. Our current concept of skull and brain as separate tissues results in distinct analyses of these tissues by most researchers. In this study, we use 3D computed tomography and magnetic resonance images of pediatric individuals diagnosed with premature closure of cranial sutures (craniosynostosis) to investigate phenotypic relationships between the brain and skull. It has been demonstrated previously that the skull and brain acquire characteristic dysmorphologies in isolated craniosynostosis, but relatively little is known of the developmental interactions that produce these anomalies. Our comparative analysis of phenotypic integration of brain and skull in premature closure of the sagittal and the right coronal sutures demonstrates that brain and skull are strongly integrated and that the significant differences in patterns of association do not occur local to the prematurely closed suture. We posit that the current focus on the suture as the basis for this condition may identify a proximate, but not the ultimate cause for these conditions. Given that premature suture closure reduces the number of cranial bones, and that a persistent loss of skull bones is demonstrated over the approximately 150 million years of synapsid evolution, craniosynostosis may serve as an informative model for evolution of the mammalian skull.     

Prediction of brain deformations and risk of traumatic brain injury due to closed-head impact: quantitative analysis of the effects of boundary conditions and brain tissue constitutive model

In this study, we investigate the effects of modelling choices for the brain–skull interface (layers of tissues between the brain and skull that determine boundary conditions for the brain) and the constitutive model of brain parenchyma on the brain responses under violent impact as predicted using computational biomechanics model. We used the head/brain model from Total HUman Model for Safety (THUMS)—extensively validated finite element model of the human body that has been applied in numerous injury biomechanics studies. The computations were conducted using a well-established nonlinear explicit dynamics finite element code LS-DYNA. We employed four approaches for modelling the brain–skull interface and four constitutive models for the brain tissue in the numerical simulations of the experiments on post-mortem human subjects exposed to violent impacts reported in the literature. The brain–skull interface models included direct representation of the brain meninges and cerebrospinal fluid, outer brain surface rigidly attached to the skull, frictionless sliding contact between the brain and skull, and a layer of spring-type cohesive elements between the brain and skull. We considered Ogden hyperviscoelastic, Mooney–Rivlin hyperviscoelastic, neo–Hookean hyperviscoelastic and linear viscoelastic constitutive models of the brain tissue. Our study indicates that the predicted deformations within the brain and related brain injury criteria are strongly affected by both the approach of modelling the brain–skull interface and the constitutive model of the brain parenchyma tissues. The results suggest that accurate prediction of deformations within the brain and risk of brain injury due to violent impact using computational biomechanics models may require representation of the meninges and subarachnoidal space with cerebrospinal fluid in the model and application of hyperviscoelastic (preferably Ogden-type) constitutive model for the brain tissue.     

Streamlined,Inexpensive 3D Printing of the Brain and Skull

Neuroimaging technologies such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) collect three-dimensional data (3D) that is typically viewed on two-dimensional (2D) screens. Actual 3D models, however, allow interaction with real objects such as implantable electrode grids, potentially improving patient specific neurosurgical planning and personalized clinical education. Desktop 3D printers can now produce relatively inexpensive, good quality prints. We describe our process for reliably generating life-sized 3D brain prints from MRIs and 3D skull prints from CTs. We have integrated a standardized, primarily open-source process for 3D printing brains and skulls. We describe how to convert clinical neuroimaging Digital Imaging and Communications in Medicine (DICOM) images to stereolithography (STL) files, a common 3D object file format that can be sent to 3D printing services. We additionally share how to convert these STL files to machine instruction gcode files, for reliable in-house printing on desktop, open-source 3D printers. We have successfully printed over 19 patient brain hemispheres from 7 patients on two different open-source desktop 3D printers. Each brain hemisphere costs approximately $3–4 in consumable plastic filament as described, and the total process takes 14–17 hours, almost all of which is unsupervised (preprocessing = 4–6 hr; printing = 9–11 hr, post-processing = <30 min). Printing a matching portion of a skull costs $1–5 in consumable plastic filament and takes less than 14 hr, in total. We have developed a streamlined, cost-effective process for 3D printing brain and skull models. We surveyed healthcare providers and patients who confirmed that rapid-prototype patient specific 3D models may help interdisciplinary surgical planning and patient education. The methods we describe can be applied for other clinical, research, and educational purposes.     

Miniaturization and its effects on cranial morphology in plethodontid salamanders, genus Thorius (Amphibia, Plethodontidae): II. The fate of the brain and sense organs and their role in skull morphogenesis and evolution

Relative size and arrangement of the brain and paired sense organs are examined in three species of Thorius, a genus of minute, terrestrial salamanders that are among the smallest extant tailed tetrapods. Analogous measurements of representative species of three related genera of larger tropical (Pseudoeurycea, Chiropterotriton) and temperate (Plethodon) salamanders are used to identify changes in gross morphology of the brain and sense organs that have accompanied the evolution of decreased head size in Thorius and their relation to associated changes in skull morphology. In adult Thorius, relative size (area measured in frontal plane, and length) of the eyes, otic capsules, and brain each is greater than in adults of all of the larger genera; relative size of the nasal capsules is unchanged or slightly smaller. Interspecific scaling phenomena--negative allometry of otic capsule, eye and brain size, isometry or slight positive allometry of nasal capsule size, all with respect to skull length--also are characteristic of intraspecific (ontogenetic) comparisons in both T. narisovalis and Pseudoeurycea goebeli. Predominance of the brain and eyes in Thorius results in greater contact and overlap among these structures and the nasal capsules in the anterior portion of the head. This is associated with anterior displacement of both the eyes and nasal capsules, which now protrude anterior to the skull proper; a change in eye shape; and medial deformation of anterior braincase walls. Posteriorly, predominance of the otic capsules has effected a reorientation of the jaw suspensorium to a fully vertical position that is correlated with the novel presence of a posteriorly directed squamosal process and shift in origin of the quadropectoralis muscle. Many of these changes in cranial morphology may be explained simply as results of mechanical (physical) interactions among the skeletal, nervous, and sensory components during head development at reduced size. This provides further evidence of the role of nervous, sensory, and other "soft" tissues in cranial skeletal morphogenesis, and reinforces the need to consider these tissues in analyses of skull evolution.     

Technique and preliminary findings for in vivo quantification of brain motion during injurious head impacts

Computational models of the human brain are widely used in the evaluation and development of helmets and other protective equipment. These models are often attempted to be validated using cadaver tissue displacements despite studies showing neural tissue degrades quickly after death. Addressing this limitation, this study aimed to develop a technique for quantifying living brain motion in vivo using a closed head impact animal model of traumatic brain injury (TBI) called CHIMERA. We implanted radiopaque markers within the brain of three adult ferrets and resealed the skull while the animals were anesthetized. We affixed additional markers to the skull to track skull kinematics. The CHIMERA device delivered controlled, repeatable head impacts to the head of the animals while the impacts were fluoroscopically stereo-visualized. We observed that 1.5 mm stainless steel fiducials (∼8 times the density of the brain) migrated from their implanted positions while neutral density targets remained in their implanted position post-impact. Brain motion relative to the skull was quantified in neutral density target tests and showed increasing relative motion at higher head impact severities. We observed the motion of the brain lagged behind that of the skull, similar to previous studies. This technique can be used to obtain a comprehensive dataset of in vivo brain motion to validate computational models reflecting the mechanical properties of the living brain. The technique would also allow the mechanical response of in vivo brain tissue to be compared to cadaveric preparations for investigating the fidelity of current human computational brain models.     

Mastication effort study using photorefractive holographic interferometry technique

The purpose of this work was the force–displacement response analysis of the masticatory process in a dried human skull by Double-Exposure Photorefractive Holographic Interferometry Technique (2E-PRHI). The load concentration and dissipation of the forces from dried human skull were analysed at applied loading stands as a Simulation of Isolated Contraction (SIC) of some mastication muscles. The 2EHI and Fringe Analysis Method were used to obtain the quantitative results of this force–displacement response. These results document quantitatively the real biomechanical response from dried human skull under applied loading and it can be used for complementary study by finite element model and others analysis type.     

Measurement of the dynamic shear modulus of mouse brain tissue in vivo by magnetic resonance elastography

In this study, the magnetic resonance (MR) elastography technique was used to estimate the dynamic shear modulus of mouse brain tissue in vivo. The technique allows visualization and measurement of mechanical shear waves excited by lateral vibration of the skull. Quantitative measurements of displacement in three dimensions during vibration at 1200 Hz were obtained by applying oscillatory magnetic field gradients at the same frequency during a MR imaging sequence. Contrast in the resulting phase images of the mouse brain is proportional to displacement. To obtain estimates of shear modulus, measured displacement fields were fitted to the shear wave equation. Validation of the procedure was performed on gel characterized by independent rheometry tests and on data from finite element simulations. Brain tissue is, in reality, viscoelastic and nonlinear. The current estimates of dynamic shear modulus are strictly relevant only to small oscillations at a specific frequency, but these estimates may be obtained at high frequencies (and thus high deformation rates), noninvasively throughout the brain. These data complement measurements of nonlinear viscoelastic properties obtained by others at slower rates, either ex vivo or invasively.     

Relationship between body mass, brain mass and craniometric parameters in the miniature pig Mini-Lewe

The relations between skull measurements, brain mass, and body mass were investigated in 30 female miniature pigs, being 6 month old. The relatively low correlation coefficients between the variables indicate a high variability in skull shape. We found an allometric exponent of 0.236 for the relation between brain and body mass with a coefficient of determination of 0.29. Both measurements show a highest correlation with the arcus zygomaticus width, which shows close relations with the occipital height and condylobasal length.     

Strain relief from the cerebral ventricles during head impact: experimental studies on natural protection of the brain

Physical models of the parasagittal human skull/brain have been tested to investigate whether the cerebral ventricles provide natural protection of the brain by relieving strain during head rotation. A sophisticated model included anatomical structures, and a semicircular model consisted of a cylinder divided into two semicircles. Silicone gel simulated the brain and was detached from the vessel by a layer of liquid paraffin simulating the cerebrospinal fluid. Both models were run with and without an elliptical inclusion filled with liquid paraffin simulating a cerebral ventricle. The 2D models were exposed to angular acceleration by a pendulum impact causing 7600 rad/s2 peak rotational acceleration with 6 ms pulse duration. After rotating 100 degrees, the models were decelerated during 30 ms. The trajectory of grid markers was analyzed from high-speed video (1000 frames/s). Rigid-body displacement, shear strain and principal strain were determined from the displacement of three-point sets inferior and superior to the ventricle. For the subventricular (inferior) region in the sophisticated model, approximately 40% lower peak strain values were obtained in the model with ventricle than in the one without. Subcortical displacement was reduced by 12%. Corresponding strain reduction in the subcortical (superior) region was approximately 40% following the acceleration and 25% following the deceleration. Similar but less pronounced effects were found for the semicircular model. The lateral ventricles play an important role as strain relievers and provide natural protection against brain injury.     

A Study on the Finite Element Model for Head Injury in Facial Collision Accident

In order to predict and evaluate injury mechanism and biomechanical response of the facial impact on head injury in a crash accident. With the combined modern medical imaging technologies, namely computed tomography (CT) and magnetic resonance imaging (MRI), both geometric and finite element (FE) models for human head-neck with detailed cranio-facial structure were developed. The cadaveric head impact tests were conducted to validate the headneck finite element model. The intracranial pressure, skull dynamic response and skull-brain relative displacement of the whole head-neck model were compared with experimental data. Nine typical cases of facial traffic accidents were simulated, with the individual stress wave propagation paths to the intracranial contents through the facial and cranial skeleton being discussed thoroughly. Intracranial pressure, von Mises stress and shear stress distribution were achieved. It is proved that facial structure dissipates a large amount of impact energy to protect the brain in its most natural way. The propagation path and distribution of stress wave in the skull and brain determine the mechanism of brain impact injury, which provides a theoretic basis for the diagnosis, treatment and protection of craniocerebral injury caused by facial impact.