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.

     

Infant brain subjected to oscillatory loading: material differentiation,properties, and interface conditions

Past research into brain injury biomechanics has focussed on short duration impulsive events as opposed to the oscillatory loadings associated with Shaken Baby Syndrome (SBS). A series of 2D finite element models of an axial slice of the infant head were created to provide qualitative information on the behaviour of the brain during shaking. The test series explored variations in subarachnoid cerebrospinal fluid (CSF) representation, brain matter stiffness, dissipation, and nonlinearity, and differentiation of brain matter type. A new method of CSF modelling based on Reynolds lubrication theory was included to provide a more realistic brain–CSF interaction. The results indicate that solid CSF representation for this load regime misrepresents the phase lag of displacement, and that the volume of subarachnoid CSF, and inclusion of thickness variations due to gyri, are important to the resultant behavior. Stress concentrations in the deep brain are reduced by fluid redistribution and gyral contact, while inclusion of the pia mater significantly reduces cortex contact strains. These results provide direction for future modelling of SBS.     

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.     

The importance of nonlinear tissue modelling in finite element simulations of infant head impacts

Despite recent efforts on the development of finite element (FE) head models of infants, a model capable of capturing head responses under various impact scenarios has not been reported. This is hypothesized partially attributed to the use of simplified linear elastic models for soft tissues of suture, scalp and dura. Orthotropic elastic constants are yet to be determined to incorporate the direction-specific material properties of infant cranial bone due to grain fibres radiating from the ossification centres. We report here on our efforts in advancing the above-mentioned aspects in material modelling in infant head and further incorporate them into subject-specific FE head models of a newborn, 5- and 9-month-old infant. Each model is subjected to five impact tests (forehead, occiput, vertex, right and left parietal impacts) and two compression tests. The predicted global head impact responses of the acceleration–time impact curves and the force–deflection compression curves for different age groups agree well with the experimental data reported in the literature. In particular, the newly developed Ogden hyperelastic model for suture, together with the nonlinear modelling of scalp and dura mater, enables the models to achieve more realistic impact performance compared with linear elastic models. The proposed approach for obtaining age-dependent skull bone orthotropic material constants counts both an increase in stiffness and decrease in anisotropy in the skull bone—two essential biological growth parameters during early infancy. The profound deformation of infant head causes a large stretch at the interfaces between the skull bones and the suture, suggesting that infant skull fractures are likely to initiate from the interfaces; the impact angle has a profound influence on global head impact responses and the skull injury metrics for certain impact locations, especially true for a parietal impact.     

Infant skull and suture properties: measurements and implications for mechanisms of pediatric brain injury

The mechanical properties of the adult human skull are well documented, but little information is available for the infant skull. To determine the age-dependent changes in skull properties, we tested human and porcine infant cranial bone in three-point bending. The measurement of elastic modulus in the human and porcine infant cranial bone agrees with and extends previous published data [McPherson, G. K., and Kriewall, T. J. (1980), J. Biomech., 13, pp. 9-16] for human infant cranial bone. After confirming that the porcine and human cranial bone properties were comparable, additional tensile and three-point bending studies were conducted on porcine cranial bone and suture. Comparisons of the porcine infant data with previously published adult human data demonstrate that the elastic modulus, ultimate stress, and energy absorbed to failure increase, and the ultimate strain decreases with age for cranial bone. Likewise, we conclude that the elastic modulus, ultimate stress, and energy absorbed to failure increase with age for sutures. We constructed two finite element models of an idealized one-month old infant head, one with pediatric and the other adult skull properties, and subjected them to impact loading to investigate the contribution of the cranial bone properties on the intracranial tissue deformation pattern. The computational simulations demonstrate that the comparatively compliant skull and membranous suture properties of the infant brain case are associated with large cranial shape changes, and a more diffuse pattern of brain distortion than when the skull takes on adult properties. These studies are a fundamental initial step in predicting the unique mechanical response of the pediatric skull to traumatic loads associated with head injury and, thus, for defining head injury thresholds for children.     

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.     

Simulation of the power transmission of bone-conducted sound in a finite-element model of the human head

Bone conduction (BC) sound is the perception of sound transmitted in the skull bones and surrounding tissues. To better understand BC sound perception and the interaction with surrounding tissues, the power transmission of BC sound is investigated in a three-dimensional finite-element model of a whole human head. BC sound transmission was simulated in the FE model and the power dissipation as well as the power flow following a mechanical vibration at the mastoid process behind the ear was analyzed. The results of the simulations show that the skull bone (comprises the cortical bone and diploë) has the highest BC power flow and thereby provide most power transmission for BC sound. The soft tissues was the second most important media for BC sound power transmission, while the least BC power transmission is through the brain and the surrounding cerebrospinal fluid (CSF) inside the cranial vault. The vibrations transmitted in the skull are mainly concentrated at the skull base when the stimulation is at the mastoid. Other vibration transmission pathways of importance are located at the occipital bone at the posterior side of the head while the transmission of sound power through the face, forehead and vertex is minor. The power flow between the skull bone and skull interior indicate that some BC power is transmitted to and from the skull interior but the transmission of sound power through the brain seem to be minimal and only local to the brain–bone interface.     

Probabilistic description of infant head kinematics in abusive head trauma

Abusive head trauma (AHT) is a potentially fatal result of child abuse, but the mechanisms by which injury occur are often unclear. To investigate the contention that shaking alone can elicit the injuries observed, effective computational models are necessary. The aim of this study was to develop a probabilistic model describing infant head kinematics in AHT. A deterministic model incorporating an infant’s mechanical properties, subjected to different shaking motions, was developed in OpenSim. A Monte Carlo analysis was used to simulate the range of infant kinematics produced as a result of varying both the mechanical properties and the type of shaking motions. By excluding physically unrealistic shaking motions, worst-case shaking scenarios were simulated and compared to existing injury criteria for a newborn, a 4.5 month-old, and a 12 month-old infant. In none of the three cases were head kinematics observed to exceed previously-estimated subdural haemorrhage injury thresholds. The results of this study provide no biomechanical evidence to demonstrate how shaking by a human alone can cause the injuries observed in AHT, suggesting either that additional factors, such as impact, are required, or that the current estimates of injury thresholds are incorrect.     

A modified human head model for the study of impact head injury

A recently published finite element (FE) head model is modified to consider the viscoelasticity of the meninges, the spongy and compact bone in the skull. The cerebrospinal fluid (CSF) is simulated explicitly as a hydrostatic fluid by using a surface-based fluid modelling method, which allows fluid and structure interaction. It is found that the modified model yields smoother pressure responses in a head impact simulation. The baseline model underestimated the peak von Mises stress in the brain by 15% and the peak principal stress in the skull by 33%. The increase in the maximum principal stress in the skull is mainly caused by the updation of the material's viscoelasticity, and the change in the maximum von Mises stress in the brain is mainly caused by the improvement of the CSF simulation. The study shows that the viscoelasticity of the head tissue should be considered, and that the CSF should be modelled as a fluid, when using FE analysis to study head injury due to impact.     

Modelling hollow organs for impact conditions: a simplified case study

This study compares the performances of three numerical approaches [Lagrangian (LAG), arbitrary Lagrangian–Eulerian (ALE) and control volume (CV)] for modelling the response of a short cylindrical pipe representing a portion of the intestines subjected to large and rapid compressions. While not being able to simulate sustained fluid flow, the LAG approach provided similar results as the ALE for moderate levels of compression. However, it was the stiffest approach for larger levels and had numerical issues for extreme compressions. While the ALE did not have these issues, its computing cost was very high, which would be problematic for large models. The CV approach had the lowest computing cost and seemed promising for larger compressions. However, its response was the softest and further investigations are needed to define its dependency to modelling parameters.     

Mechanical properties of bovine pia-arachnoid complex in shear

Traumatic brain injury (TBI) has become a major public health and socioeconomic problem that affects 1.5 million Americans annually. Finite element methods have been widely used to investigate TBI mechanisms. The pia-arachnoid complex (PAC) covering the brain plays an important role in the mechanical response of the brain during impact or inertial loading. Existing finite element brain models have tended to oversimplify the response of the PAC due to a lack of accurately defined material properties of this structure, possibly resulting in a loss of accuracy in the model predictions. The objectives of this study were to experimentally determine the material properties of the PAC under shear loading. Bovine PAC was selected in the current study in view of its availability and comparability with previous studies. Tangential shear tests were conducted at 0.8, 7.3, and 72 s(-1). The mean shear moduli were 11.73, 20.04, and 22.37 kPa at the three strain rates tested. The ultimate stress, at the three strain rates, was 9.21, 17.01, and 22.26 kPa, while the ultimate strain was 1.52, 1.58, and 1.81. Results from the current study provide essential information to properly model the PAC membrane, an important component in the skull/brain interface, in a computational model of the human/animal head. Such an improved representation of the in vivo skull/brain interface will enhance future studies investigating brain injury mechanisms under various loading conditions.     

A modified human head model for the study of impact head injury

A recently published finite element (FE) head model is modified to consider the viscoelasticity of the meninges, the spongy and compact bone in the skull. The cerebrospinal fluid (CSF) is simulated explicitly as a hydrostatic fluid by using a surface-based fluid modelling method, which allows fluid and structure interaction. It is found that the modified model yields smoother pressure responses in a head impact simulation. The baseline model underestimated the peak von Mises stress in the brain by 15% and the peak principal stress in the skull by 33%. The increase in the maximum principal stress in the skull is mainly caused by the updation of the material's viscoelasticity, and the change in the maximum von Mises stress in the brain is mainly caused by the improvement of the CSF simulation. The study shows that the viscoelasticity of the head tissue should be considered, and that the CSF should be modelled as a fluid, when using FE analysis to study head injury due to impact.     

Fetal head moulding: finite element analysis of a fetal skull subjected to uterine pressures during the first stage of labour

Fetal head moulding is a phenomenon which may contribute to satisfactory progress during delivery as it allows the fetal head to accommodate to the geometry of the passage. In contrast, excessive head moulding may result in cranial birth injuries and thus affect the infant shortly or even long after birth. One group of researchers in the past investigated the biomechanics of fetal head moulding from an engineering point of view and limited themselves to a static, linear model of the parietal bones. In this paper, we present a non-linear model of the deformation of a complete fetal skull, when subjected to pressures exerted by the cervix, during the first stage of labour. The design of the model involves four main steps: shape recovery of the fetal skull, the generation of a valid and compatible mesh for finite element analysis (FEA), the specification of a physical model and the analysis of deformation. Results of the analysis show good agreement with those obtained from clinical experiments on the quantitative assessment of fetal head moulding. The model also displays shapes after moulding which have been reported in previous studies and which are generally known in the obstetric and paediatric communities.     

Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches

Blast waves generated by improvised explosive devices can cause mild, moderate to severe traumatic brain injury in soldiers and civilians. To understand the interactions of blast waves on the head and brain and to identify the mechanisms of injury, compression-driven air shock tubes are extensively used in laboratory settings to simulate the field conditions. The overall goal of this effort is to understand the mechanics of blast wave–head interactions as the blast wave traverses the head/brain continuum. Toward this goal, surrogate head model is subjected to well-controlled blast wave profile in the shock tube environment, and the results are analyzed using combined experimental and numerical approaches. The validated numerical models are then used to investigate the spatiotemporal distribution of stresses and pressure in the human skull and brain. By detailing the results from a series of careful experiments and numerical simulations, this paper demonstrates that: (1) Geometry of the head governs the flow dynamics around the head which in turn determines the net mechanical load on the head. (2) Biomechanical loading of the brain is governed by direct wave transmission, structural deformations, and wave reflections from tissue–material interfaces. (3) Deformation and stress analysis of the skull and brain show that skull flexure and tissue cavitation are possible mechanisms of blast-induced traumatic brain injury.     

A critical comparison of different residence time measures in aneurysms

Flow stagnation and residence time (RT) are important features of diseased arterial flows that influence biochemical transport processes and thrombosis. RT calculation methods are classified into Eulerian and Lagrangian approaches where several measures have been proposed to quantify RT. Each of these methods has a different definition of RT, and it is not clear how they are related. In this study, image-based computational models of blood flow in an abdominal aortic aneurysm and a cerebral aneurysm were considered and RT was calculated using different methods. In the Lagrangian methods, discrete particle tracking of massless tracers was used to calculate particle residence time and mean exposure time. In the Eulerian methods, continuum transport models were used to quantify RT using Eulerian RT and virtual ink approaches. Point-wise RT and Eulerian indicator RT were also computed based on measures derived from velocity. A comparison of these methods is presented and the implications of each method are discussed. Our results highlight that most RT methods have a conceptually distinct definition of RT and therefore should be utilized depending on the specific application of interest.     

Mechanical hemolysis in blood flow: user-independent predictions with the solution of a partial differential equation

This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.     

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.     

Utilizing multiple scale models to improve predictions of extra-axial hemorrhage in the immature piglet

Traumatic brain injury (TBI) is a leading cause of death and disability in the USA. To help understand and better predict TBI, researchers have developed complex finite element (FE) models of the head which incorporate many biological structures such as scalp, skull, meninges, brain (with gray/white matter differentiation), and vasculature. However, most models drastically simplify the membranes and substructures between the pia and arachnoid membranes. We hypothesize that substructures in the pia–arachnoid complex (PAC) contribute substantially to brain deformation following head rotation, and that when included in FE models accuracy of extra-axial hemorrhage prediction improves. To test these hypotheses, microscale FE models of the PAC were developed to span the variability of PAC substructure anatomy and regional density. The constitutive response of these models were then integrated into an existing macroscale FE model of the immature piglet brain to identify changes in cortical stress distribution and predictions of extra-axial hemorrhage (EAH). Incorporating regional variability of PAC substructures substantially altered the distribution of principal stress on the cortical surface of the brain compared to a uniform representation of the PAC. Simulations of 24 non-impact rapid head rotations in an immature piglet animal model resulted in improved accuracy of EAH prediction (to 94 % sensitivity, 100 % specificity), as well as a high accuracy in regional hemorrhage prediction (to 82–100 % sensitivity, 100 % specificity). We conclude that including a biofidelic PAC substructure variability in FE models of the head is essential for improved predictions of hemorrhage at the brain/skull interface.     

Development of a high resolution voxelised head phantom for medical physics applications

Computational anthropomorphic phantoms have become an important investigation tool for medical imaging and dosimetry for radiotherapy and radiation protection. The development of computational phantoms with realistic anatomical features contribute significantly to the development of novel methods in medical physics. For many applications, it is desirable that such computational phantoms have a real-world physical counterpart in order to verify the obtained results.In this work, we report the development of a voxelised phantom, the HIGH_RES_HEAD, modelling a paediatric head based on the commercial phantom 715-HN (CIRS). HIGH_RES_HEAD is unique for its anatomical details and high spatial resolution (0.18 × 0.18 mm² pixel size). The development of such a phantom was required to investigate the performance of a new proton computed tomography (pCT) system, in terms of detector technology and image reconstruction algorithms.The HIGH_RES_HEAD was used in an ad-hoc Geant4 simulation modelling the pCT system. The simulation application was previously validated with respect to experimental results. When compared to a standard spatial resolution voxelised phantom of the same paediatric head, it was shown that in pCT reconstruction studies, the use of the HIGH_RES_HEAD translates into a reduction from 2% to 0.7% of the average relative stopping power difference between experimental and simulated results thus improving the overall quality of the head phantom simulation.The HIGH_RES_HEAD can also be used for other medical physics applications such as treatment planning studies.A second version of the voxelised phantom was created that contains a prototypic base of skull tumour and surrounding organs at risk.     

Deformation of the human brain induced by mild angular head acceleration

Deformation of the human brain was measured in tagged magnetic resonance images (MRI) obtained dynamically during angular acceleration of the head. This study was undertaken to provide quantitative experimental data to illuminate the mechanics of traumatic brain injury (TBI). Mild angular acceleration was imparted to the skull of a human volunteer inside an MR scanner, using a custom MR-compatible device to constrain motion. A grid of MR "tag" lines was applied to the MR images via spatial modulation of magnetization (SPAMM) in a fast gradient echo imaging sequence. Images of the moving brain were obtained dynamically by synchronizing the imaging process with the motion of the head. Deformation of the brain was characterized quantitatively via Lagrangian strain. Consistent patterns of radial-circumferential shear strain occur in the brain, similar to those observed in models of a viscoelastic gel cylinder subjected to angular acceleration. Strain fields in the brain, however, are clearly mediated by the effects of heterogeneity, divisions between regions of the brain (such as the central fissure and central sulcus) and the brain's tethering and suspension system, including the dura mater, falx cerebri, and tentorium membranes.