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.     

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.     

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.     

Determination of rigid body registration marker error from edge error

Registration markers affixed to rigid bodies (fixed to bone as opposed to skin) are commonly used when tracking 3D rigid body motion. The measured positions of registration markers are subject to unavoidable errors, both systematic and non-systematic. Prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes, while others have focused on the error associated with a specific position tracking system under restricted conditions. Theoretical and simulation-based error propagation requires knowledge of the variation due to individual registration markers; however, the variation in registration marker position measurement has previously been either assumed or determined from static cases. The objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers (edge lengths), which are invariant under rotation and translation. Simulations were used to validate and characterize the introduced technique, demonstrating that the predictions improve with greater edge length and additional markers, converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation, and that under ideal conditions the confidence interval about the predicted variation is within 7% of the maximum variation associated with that marker set. The introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non-static measurements of the same registration markers, where the non-static variation exceeded the static variation by an average factor of 12.7.     

Principal component analysis of dynamic relative displacement fields estimated from MR images

Non-destructive measurement of acceleration-induced displacement fields within a closed object is a fundamental challenge. Inferences of how the brain deforms following skull impact have thus relied largely on indirect estimates and course-resolution cadaver studies. We developed a magnetic resonance technique to quantitatively identify the modes of displacement of an accelerating soft object relative to an object enclosing it, and applied it to study acceleration-induced brain deformation in human volunteers. We show that, contrary to the prevailing hypotheses of the field, the dominant mode of interaction between the brain and skull in mild head acceleration is one of sliding arrested by meninges.     

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.     

How long does DNA keep the memory of its conformation? A time-dependent canonical correlation analysis of molecular dynamics simulation

The time dependence of the correlation between motions of different parts of DNA is analyzed from a 200 ps molecular dynamics simulation of the double-stranded self-complementary d(CTGATCAG) in the B form. Each nucleotide is decomposed into three subunits corresponding to the furanose ring (SU), the base (BA), and the backbone (SK). The motion of each subunit is considered as the superimposition of rigid body translation, rigid body rotation, and internal deformation. Canonical time-dependent correlation functions calculated with coordinates describing the different components of the subunits motion are defined and computed. This allows us to probe how long a particular type of motion of one subunit influences the other types of motions of other subunits (cross correlation functions) or how long a particular subunit keeps the memory of its own conformation or location (autocorrelation functions). From auto-correlation analysis it is found that deformation decorrelates within a few tenths of picoseconds, rotational correlation times are on the order of 8 ps, while translational motions are long-time correlated. The deformation of a subunit is not correlated to the deformation of another one (at the 200 ps time scale of our simulation), but influences slightly their translation and orientation as time increases. © 1996 John Wiley & Sons, Inc.     

Assessment of screw displacement axis accuracy and repeatability for joint kinematic description using an electromagnetic tracking device

Screw displacement axes (SDAs) have been employed to describe joint kinematics in biomechanical studies. Previous reports have investigated the accuracy of SDAs combining various motion analysis techniques and smoothing procedures. To our knowledge, no study has assessed SDA accuracy describing the relative movement between adjacent bodies with an electromagnetic tracking system. This is important, since in relative motion, neither body is fixed and consequently sensitivity to potential measurement errors from both bodies may be significant. Therefore, this study assessed the accuracy of SDAs for describing relative motion between two moving bodies. We analyzed numerical simulated data, and physical experimental data recorded using a precision jig and electromagnetic tracking device. The numerical simulations demonstrated SDA position accuracy (p=0.04) was superior for single compared to relative body motion, whereas orientation accuracy (p=0.2) was similar. Experimental data showed data-filtering (Butterworth filter) improved SDA position and orientation accuracies for rotation magnitudes smaller or equal to 5.0 degrees, with no effect at larger rotation magnitudes (p<0.05). This suggests that in absence of a filter, SDAs should only be calculated at rotations of greater than 5.0 degrees. For rotation magnitudes of 0.5 degrees (5.0 degrees ) about the SDA, SDA position and orientation error measurements determined from filtered experimental data were 3.75+/-0.30 mm (3.31+/-0.21 mm), and 1.10+/-0.04 degrees (1.04+/-0.03 degrees ), respectively. Experimental accuracy values describing the translation along and rotation about the SDA, were 0.06+/-0.00 mm and 0.09+/-0.01 degrees, respectively. These small errors establish the capability of SDAs to detect small translations, and rotations. In conclusion, application of SDAs should be a useful tool for describing relative motion in joint kinematic studies.     

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.     

Regional ventilation during spontaneous breathing and mechanical ventilation in dogs

We evaluated the effects of the different patterns of chest wall deformation that occur with different body positions and modes of breathing on regional lung deformation and ventilation. Using the parenchymal marker technique, we determined regional lung behavior during mechanical ventilation and spontaneous breathing in five anesthetized recumbent dogs. Regional lung behavior was related to the patterns of diaphragm motion estimated from X-ray projection images obtained at functional residual capacity (FRC) and end inspiration. Our results indicate that 1) in the prone and supine positions, FRC was larger during mechanical ventilation than during spontaneous breathing; 2) there were significant differences in the patterns of diaphragm motion and regional ventilation between mechanical ventilation and spontaneous breathing in both body positions; 3) in the supine position only, there was a vertical gradient in lung volume at FRC; 4) in both positions and for both modes of breathing, regional ventilation was nonlinearly related to changes in lobar and overall lung volumes; and 5) different patterns of diaphragm motion caused different sliding motions and differential rotations of upper and lower lobes. Our results are inconsistent with the classic model of regional ventilation, and we conclude that the distribution of ventilation is determined by a complex interaction of lung and chest wall shapes and by the motion of the lobes relative to each other, all of which help to minimize distortion of the lung parenchyma.     

Accuracy of an optical active-marker system to track the relative motion of rigid bodies

The measurement of relative motion between two moving bones is commonly accomplished for in vitro studies by attaching to each bone a series of either passive or active markers in a fixed orientation to create a rigid body (RB). This work determined the accuracy of motion between two RBs using an Optotrak optical motion capture system with active infrared LEDs. The stationary noise in the system was quantified by recording the apparent change in position with the RBs stationary and found to be 0.04 degrees and 0.03 mm. Incremental 10 degrees rotations and 10-mm translations were made using a more precise tool than the Optotrak. Increasing camera distance decreased the precision or increased the range of values observed for a set motion and increased the error in rotation or bias between the measured and actual rotation. The relative positions of the RBs with respect to the camera-viewing plane had a minimal effect on the kinematics and, therefore, for a given distance in the volume less than or close to the precalibrated camera distance, any motion was similarly reliable. For a typical operating set-up, a 10 degrees rotation showed a bias of 0.05 degrees and a 95% repeatability limit of 0.67 degrees. A 10-mm translation showed a bias of 0.03 mm and a 95% repeatability limit of 0.29 mm. To achieve a high level of accuracy it is important to keep the distance between the cameras and the markers near the distance the cameras are focused to during calibration.     

Numerical model (switchable/dual model) of the human head for rigid body and finite elements applications

In this paper, a methodology for the development and validation of a numerical model of the human head using generic procedures is presented. All steps required, starting with the model generation, model validation and applications will be discussed. The proposed model may be considered as a dual one due to its capabilities to switch from deformable to a rigid body according to the application's requirements. The first step is to generate the numerical model of the human head using geometry files or medical images. The required stiffness and damping for the elastic connection used for the rigid body model are identified by performing a natural frequency analysis. The presented applications for model validation are related to impact analysis. The first case is related to Nahum's (Nahum and Smith 1970) experiments pressure data being evaluated and a pressure map generated using the results from discrete elements. For the second case, the relative displacement between the brain and the skull is evaluated according to Hardy's (Hardy WH, Foster CD, Mason, MJ, Yang KH, King A, Tashman S. 2001.Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray. Stapp Car Crash J. 45:337–368, SAE Paper 2001-22-0016) experiments. The main objective is to validate the rigid model as a quick and versatile tool for acquiring the input data for specific brain analyses.     

The finite displacements vector's method: an application to the scoliotic spine

This paper presents a vectorial method to directly obtain the components of the screw displacement between two positions of a body in a three-dimensional space (position of the helical axis of motion, rotation around this axis and translation along it). This method can be applied either to the case of a bone, moving with respect to the reference frame, or to the case of the relative motion of a joint; it gives exact formulae even if the displacements are finite; it generalizes the results (already published) obtained for finite displacements in the plane. The involved computation is easy, and the use of this method deals with only a small magnification of experimental errors. The technique of a screw displacement is applied to the vertebral segments of a scoliolic spine. The necessary data is taken from a couple of in-vivo X-rays. The goals of this study are: first, to describe the shape of the spine at each step of its evolution and second, to quantify the evolution in time of any segment of the spine between two states.     

Rationalization of kinematic descriptors for three-dimensional hand and finger motion

Modelling joint motion in three dimensions is often based on techniques taken from classical dynamics, each analysis resulting in a set of six parameters describing the relative motion betwen two body segments. The literature on joint kinematics has been difficult to compare due to use of different anatomical landmarks, axis nomenclature, and analytical methods. It is here shown that with care in sequence definition, the three alignment-based systems (Euler, Cardan, floating axis) give identical results for angular parameters. While the equivalent screw displacement axis system can be related simply to the other methods only if the functional axis of motion is aligned with a coordinate axis, the basic matrix for relating rigid body positions before and after a motion can always be reconstructed. Therefore the changes in alignment angles may be obtained from screw displacement parameters, permitting the results of different analyses to be compared. Translation parameters are most difficult to interpret in any system. Examples of the way in which simple planar motions are characterized by the various analytical methods are given.     

In vivo pons motion within the skull

Finite element (FE) models are used to identify head injury mechanisms and design new and improved injury prevention schemes. Although brain-skull boundary conditions strongly influence the model mechanical responses, limited experimental data are available to develop an informed representation. We hypothesize that the spinal cord tension and gravity contribute to the pons displacement in vivo. Static high-resolution T1-weighted sagittal MR images of the inferior portion of the head in neutral and flexion positions were acquired in 15 human volunteers in both supine and prone postures. Boundaries of the pons and clivus were extracted with a gradient-based algorithm, and the pontes were fitted into ellipses. Assuming rigid body motion of the skull, image pairs in different postures were co-registered with an autocorrelation technique. By comparing images before and after the motion, we found that while the rotation of the pons is negligible relative to the skull, the pons displaces significantly at the foramen magnum, on the order of approximately 2 mm. When the spinal cord tension and gravity act in concert, the pons moves caudally; when opposed, superiorly, such that the influence of gravity on the pons is six times that of the spinal cord tension. Based on these findings, we recommend that the brainstem-skull interface be treated as a sliding (with or without friction) boundary condition in FE models of the human head.     

A method for the intravital measurement of interspinous kinematics.

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of +/- 4 degrees rotation and +/- 4 mm translation determined the absolute maximum errors to be 0.2 degree and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1 degrees and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.     

Lateral Fluid Percussion: Model of Traumatic Brain Injury in Mice

Traumatic brain injury (TBI) research has attained renewed momentum due to the increasing awareness of head injuries, which result in morbidity and mortality. Based on the nature of primary injury following TBI, complex and heterogeneous secondary consequences result, which are followed by regenerative processes ^1,2. Primary injury can be induced by a direct contusion to the brain from skull fracture or from shearing and stretching of tissue causing displacement of brain due to movement ^3,4. The resulting hematomas and lacerations cause a vascular response ^3,5, and the morphological and functional damage of the white matter leads to diffuse axonal injury ^6-8. Additional secondary changes commonly seen in the brain are edema and increased intracranial pressure ⁹. Following TBI there are microscopic alterations in biochemical and physiological pathways involving the release of excitotoxic neurotransmitters, immune mediators and oxygen radicals ^10-12, which ultimately result in long-term neurological disabilities ^13,14. Thus choosing appropriate animal models of TBI that present similar cellular and molecular events in human and rodent TBI is critical for studying the mechanisms underlying injury and repair.Various experimental models of TBI have been developed to reproduce aspects of TBI observed in humans, among them three specific models are widely adapted for rodents: fluid percussion, cortical impact and weight drop/impact acceleration ¹. The fluid percussion device produces an injury through a craniectomy by applying a brief fluid pressure pulse on to the intact dura. The pulse is created by a pendulum striking the piston of a reservoir of fluid. The percussion produces brief displacement and deformation of neural tissue ^1,15. Conversely, cortical impact injury delivers mechanical energy to the intact dura via a rigid impactor under pneumatic pressure ^16,17. The weight drop/impact model is characterized by the fall of a rod with a specific mass on the closed skull ¹⁸. Among the TBI models, LFP is the most established and commonly used model to evaluate mixed focal and diffuse brain injury ¹⁹. It is reproducible and is standardized to allow for the manipulation of injury parameters. LFP recapitulates injuries observed in humans, thus rendering it clinically relevant, and allows for exploration of novel therapeutics for clinical translation ²⁰.We describe the detailed protocol to perform LFP procedure in mice. The injury inflicted is mild to moderate, with brain regions such as cortex, hippocampus and corpus callosum being most vulnerable. Hippocampal and motor learning tasks are explored following LFP.     

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.