Anisotropic constitutive equations and experimental tensile behavior of brain tissue

The Transverse Isotropy of Spinal Cord White Matter Under Dynamic Load

The rostral-caudally aligned fiber-reinforced structure of spinal cord white matter (WM) gives rise to transverse isotropy in the material. Stress and strain patterns generated in the spinal cord parenchyma following spinal cord injury (SCI) are multidirectional and dependent on the mechanism of the injury. Our objective was to develop a WM constitutive model that captures the material transverse isotropy under dynamic loading. The WM mechanical behavior was extracted from the published tensile and compressive experiments. Combinations of isotropic and fiber-reinforcing models were examined in a conditional quasi-linear viscoelastic (QLV) formulation to capture the WM mechanical behavior. The effect of WM transverse isotropy on SCI model outcomes was evaluated by simulating a nonhuman primate (NHP) contusion injury experiment. A second-order reduced polynomial hyperelastic energy potential conditionally combined with a quadratic reinforcing function in a four-term Prony series QLV model best captured the WM mechanical behavior (0.89 < R2 < 0.99). WM isotropic and transversely isotropic material models combined with discrete modeling of the pia mater resulted in peak impact forces that matched the experimental outcomes. The transversely isotropic WM with discrete pia mater resulted in maximum principal strain (MPS) distributions which effectively captured the combination of ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and the rostral/caudal spread of damage observed in in vivo injuries. The results suggest that the WM transverse isotropy could have an important role in correlating tissue damage with mechanical measures and explaining the directional sensitivity of the spinal cord to injury.

Viscoelasticity of subcortical gray matter structures

Viscoelastic mechanical properties of the brain assessed with magnetic resonance elastography (MRE) are sensitive measures of microstructural tissue health in neurodegenerative conditions. Recent efforts have targeted measurements localized to specific neuroanatomical regions differentially affected in disease. In this work, we present a method for measuring the viscoelasticity in subcortical gray matter (SGM) structures, including the amygdala, hippocampus, caudate, putamen, pallidum, and thalamus. The method is based on incorporating high spatial resolution MRE imaging (1.6 mm isotropic voxels) with a mechanical inversion scheme designed to improve local measures in pre-defined regions (soft prior regularization [SPR]). We find that in 21 healthy, young volunteers SGM structures differ from each other in viscoelasticity, quantified as the shear stiffness and damping ratio, but also differ from the global viscoelasticity of the cerebrum. Through repeated examinations on a single volunteer, we estimate the uncertainty to be between 3 and 7% for each SGM measure. Furthermore, we demonstrate that the use of specific methodological considerations-higher spatial resolution and SPR-both decrease uncertainty and increase sensitivity of the SGM measures. The proposed method allows for reliable MRE measures of SGM viscoelasticity for future studies of neurodegenerative conditions. Hum Brain Mapp 37:4221-4233, 2016. © 2016 Wiley Periodicals, Inc.

Observation of direction-dependent mechanical properties in the human brain with multi-excitation MR elastography

Magnetic resonance elastography (MRE) has shown promise in noninvasively capturing changes in mechanical properties of the human brain caused by neurodegenerative conditions. MRE involves vibrating the brain to generate shear waves, imaging those waves with MRI, and solving an inverse problem to determine mechanical properties. Despite the known anisotropic nature of brain tissue, the inverse problem in brain MRE is based on an isotropic mechanical model. In this study, distinct wave patterns are generated in the brain through the use of multiple excitation directions in order to characterize the potential impact of anisotropic tissue mechanics on isotropic inversion methods. Isotropic inversions of two unique displacement fields result in mechanical property maps that vary locally in areas of highly aligned white matter. Investigation of the corpus callosum, corona radiata, and superior longitudinal fasciculus, three highly ordered white matter tracts, revealed differences in estimated properties between excitations of up to 33%. Using diffusion tensor imaging to identify dominant fiber orientation of bundles, relationships between estimated isotropic properties and shear asymmetry are revealed. This study has implications for future isotropic and anisotropic MRE studies of white matter tracts in the human brain.

An anisotropic hyperelastic constitutive model of brain white matter in biaxial tension and structural-mechanical relationships

Computational models of the brain require accurate and robust constitutive models to characterize the mechanical behavior of brain tissue. The anisotropy of white matter has been previously demonstrated; however, there is a lack of data describing the effects of multi-axial loading, even though brain tissue experiences multi-axial stress states. Therefore, a biaxial tensile experiment was designed to more fully characterize the anisotropic behavior of white matter in a quasi-static loading state, and the mechanical data were modeled with an anisotropic hyperelastic continuum model. A probabilistic analysis was used to quantify the uncertainty in model predictions because the mechanical data of brain tissue can show a high degree of variability, and computational studies can benefit from reporting the probability distribution of model responses. The axonal structure in white matter can be heterogeneous and regionally dependent, which can affect computational model predictions. Therefore, corona radiata and corpus callosum regions were tested, and histology and transmission electron microscopy were performed on tested specimens to relate the distribution of axon orientations and the axon volume fraction to the mechanical behavior. These measured properties were implemented into a structural constitutive model. Results demonstrated a significant, but relatively low anisotropic behavior, yet there were no conclusive mechanical differences between the two regions tested. The inclusion of both biaxial and uniaxial tests in model fits improved the accuracy of model predictions. The mechanical anisotropy of individual specimens positively correlated with the measured axon volume fraction, and, accordingly, the structural model exhibited slightly decreased uncertainty in model predictions compared to the model without structural properties.

On the accuracy and fitting of transversely isotropic material models

Fiber reinforced structures are central to the form and function of biological tissues. Hyperelastic, transversely isotropic material models are used widely in the modeling and simulation of such tissues. Many of the most widely used models involve strain energy functions that include one or both pseudo-invariants (I4 or I5) to incorporate energy stored in the fibers. In a previous study we showed that both of these invariants must be included in the strain energy function if the material model is to reduce correctly to the well-known framework of transversely isotropic linear elasticity in the limit of small deformations. Even with such a model, fitting of parameters is a challenge. Here, by evaluating the relative roles of I4 and I5 in the responses to simple loadings, we identify loading scenarios in which previous models accounting for only one of these invariants can be expected to provide accurate estimation of material response, and identify mechanical tests that have special utility for fitting of transversely isotropic constitutive models. Results provide guidance for fitting of transversely isotropic constitutive models and for interpretation of the predictions of these models.

Mechanical Characterization of Immature Porcine Brainstem in Tension at Dynamic Strain Rates

Background

Many brain injury cases involve pediatric road traffic accidents, and among these, brainstem injury causes disastrous outcomes. A thorough understanding of the tensile characterization of immature brainstem tissue is crucial in modeling traumatic brain injury sustained by children, but limited experimental data in tension is available for the immature brain tissue at dynamic strain rates.

Material/Methods

We harvested brainstem tissue from immature pigs (about 4 weeks old, and at a developmental stage similar to that of human toddlers) as a byproduct from a local slaughter house and very carefully prepared the samples. Tensile tests were performed on specimens at dynamic strain rates of 2/s, 20/s, and 100/s using a biological material instrument. The constitutive models, Fung, Ogden, Gent, and exponential function, for immature brainstem tissue material property were developed for the recorded experimental data using OriginPro^® 8.0 software. The t test was performed for infinitesimal shear modules.

Results

The curves of stress-versus-stretch ratio were convex in shape, and inflection points were found in all the test groups at the strain of about 2.5%. The average Lagrange stress of the immature brainstem specimen at the 30% strain at the strain rates of 2, 20, and 100/s was 273±114, 515±107, and 1121±197 Pa, respectively. The adjusted R-Square (R²) of Fung, Ogden, Gent, and exponential model was 0.820≤R²≤0.933, 0.774≤R²≤0.940, 0.650≤R²≤0.922, and 0.852≤R²≤0.981, respectively. The infinitesimal shear modulus of the strain energy functions showed a significant association with the strain rate (p<0.01).

Conclusions

The immature brainstem is a rate-dependent material in dynamic tensile tests, and the tissue becomes stiffer with increased strain rate. The reported results may be useful in the study of brain injuries in children who sustain injuries in road traffic accidents. Further research in more detail should be performed in the future.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

The importance of structural anisotropy in computational models of traumatic brain injury

Understanding the mechanisms of injury might prove useful in assisting the development of methods for the management and mitigation of traumatic brain injury (TBI). Computational head models can provide valuable insight into the multi-length-scale complexity associated with the primary nature of diffuse axonal injury. It involves understanding how the trauma to the head (at the centimeter length scale) translates to the white-matter tissue (at the millimeter length scale), and even further down to the axonal-length scale, where physical injury to axons (e.g., axon separation) may occur. However, to accurately represent the development of TBI, the biofidelity of these computational models is of utmost importance. There has been a focused effort to improve the biofidelity of computational models by including more sophisticated material definitions and implementing physiologically relevant measures of injury. This paper summarizes recent computational studies that have incorporated structural anisotropy in both the material definition of the white matter and the injury criterion as a means to improve the predictive capabilities of computational models for TBI. We discuss the role of structural anisotropy on both the mechanical response of the brain tissue and on the development of injury. We also outline future directions in the computational modeling of TBI.

Anisotropic polyvinyl alcohol hydrogel phantom for shear wave elastography in fibrous biological soft tissue: a multimodality characterization

Shear wave elastography imaging techniques provide quantitative measurement of soft tissues elastic properties. Tendons, muscles and cerebral tissues are composed of fibers, which induce a strong anisotropic effect on the mechanical behavior. Currently, these tissues cannot be accurately represented by existing elastography phantoms. Recently, a novel approach for orthotropic hydrogel mimicking soft tissues has been developed (Millon et al 2006 J. Biomed. Mater. Res. B 305-11). The mechanical anisotropy is induced in a polyvinyl alcohol (PVA) cryogel by stretching the physical crosslinks of the polymeric chains while undergoing freeze/thaw cycles. In the present study we propose an original multimodality imaging characterization of this new transverse isotropic (TI) PVA hydrogel. Multiple properties were investigated using a large variety of techniques at different scales compared with an isotropic PVA hydrogel undergoing similar imaging and rheology protocols. The anisotropic mechanical (dynamic and static) properties were studied using supersonic shear wave imaging technique, full-field optical coherence tomography (FFOCT) strain imaging and classical linear rheometry using dynamic mechanical analysis. The anisotropic optical and ultrasonic spatial coherence properties were measured by FFOCT volumetric imaging and backscatter tensor imaging, respectively. Correlation of mechanical and optical properties demonstrates the complementarity of these techniques for the study of anisotropy on a multi-scale range as well as the potential of this TI phantom as fibrous tissue-mimicking phantom for shear wave elastographic applications.

An experimental study on the mechanical properties of rat brain tissue using different stress-strain definitions

There are different stress-strain definitions to measure the mechanical properties of the brain tissue. However, there is no agreement as to which stress-strain definition should be employed to measure the mechanical properties of the brain tissue at both the longitudinal and circumferential directions. It is worth knowing that an optimize stress-strain definition of the brain tissue at different loading directions may have implications for neuronavigation and surgery simulation through haptic devices. This study is aimed to conduct a comparative study on different results are given by the various definitions of stress-strain and to recommend a specific definition when testing brain tissues. Prepared cylindrical samples are excised from the parietal lobes of rats' brains and experimentally tested by applying load on both the longitudinal and circumferential directions. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) are used to determine the elastic modulus, maximum stress and strain. The highest non-linear stress-strain relation is observed for the Almansi-Hamel strain definition and it may overestimate the elastic modulus at different stress definitions at both the longitudinal and circumferential directions. The Green-St. Venant strain definition fails to address the non-linear stress-strain relation using different definitions of stress and triggers an underestimation of the elastic modulus. The results suggest the application of the true stress-true strain definition for characterization of the brain tissues mechanics since it gives more accurate measurements of the tissue's response using the instantaneous values.

Strain rate effects on the mechanical properties and fracture mode of skeletal muscle

The present study aimed to characterize the mechanical response of beagle sartorius muscle fibers under strain rates that increase logarithmically (0.1mm/min, 1mm/min and 10mm/min), and provide an analysis of the fracture patterns of these tissues via scanning electron microscopy (SEM). Muscle tissue from dogs' sartorius was excised and test specimens were sectioned with a lancet into sections with nominal length, width, and thickness of 7, 2.5 and 0.6mm, respectively. Trimming of the tissue was done so that the loading would be parallel to the direction of the muscle fiber. Samples were immediately tested following excision and failures were observed under the SEM. No statistically significant difference was observed in strength between the 0.1mm/min (2.560±0.37MPa) and the 1mm/min (2.702±0.55MPa) groups. However, the 10mm/min group (1.545±0.50MPa) had a statistically significant lower strength than both the 1mm/min group and the 0.1mm/min group with p<0.01 in both cases. At the 0.1mm/min rate the primary fracture mechanism was that of a shear mode failure of the endomysium with a significant relative motion between fibers. At 1mm/min this continues to be the predominant failure mode. At the 10mm/min strain rate there is a significant change in the fracture pattern relative to other strain rates, where little to no evidence of endomysial shear failure nor of significant motion between fibers was detected.

The mechanics of traumatic brain injury: a review of what we know and what we need to know for reducing its societal burden

Traumatic brain injury (TBI) is a significant public health problem, on pace to become the third leading cause of death worldwide by 2020. Moreover, emerging evidence linking repeated mild traumatic brain injury to long-term neurodegenerative disorders points out that TBI can be both an acute disorder and a chronic disease. We are at an important transition point in our understanding of TBI, as past work has generated significant advances in better protecting us against some forms of moderate and severe TBI. However, we still lack a clear understanding of how to study milder forms of injury, such as concussion, or new forms of TBI that can occur from primary blast loading. In this review, we highlight the major advances made in understanding the biomechanical basis of TBI. We point out opportunities to generate significant new advances in our understanding of TBI biomechanics, especially as it appears across the molecular, cellular, and whole organ scale.

A micromechanical procedure for viscoelastic characterization of the axons and ECM of the brainstem

In this study, the optimal viscoelastic material parameters of axon and extracellular matrix (ECM) in porcine brain white matter were identified using a genetic algorithm (GA) optimization procedure. The procedure was combined with micromechanical finite element analysis (FEA) of brain tissue and experimental stress relaxation tests on brainstem specimens to find the optimal material coefficients of axon and ECM. The stress relaxation tests were performed in tension on 10 brainstem specimens at 3% strain level. The axonal volume fraction in brainstem was measured from the Scanning Electron Microscopy images of the brain tissue. A square periodic volume element was selected to represent the microscale homogenized brainstem tissue. Periodic boundary conditions were applied on the square volume element to mimics the repetitive nature of the volume element. Linear viscoelastic material properties were assumed for the brain tissue constituents under small deformation. The constitutive behavior was expressed in terms of Prony series. The GA procedure searched for the optimal material parameters by fitting the time-dependent tissue stresses of brain tissue FEA to the stresses of relaxation tests under the same loading conditions. The optimization procedure converged after 60 iterations. The initial elastic modulus of axon was found to be 12.86kPa, three times larger than that of ECM. The long-term elastic modulus of axon was 3.7kPa, while for ECM this value was 1.03kPa. The concordance correlation coefficient between FEA estimated elastic modulus of brainstem tissue using the optimal material properties and the experimental elastic modulus of brainstem specimens was 0.952, showing a strong agreement. The optimal material properties of brain tissue constituents can find applications in micromechanical analysis of brain tissue to gain insight into diffuse axonal injures (DAIs).

Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue

Brain tissue modelling has been an active area of research for years. Brain matter does not follow the constitutive relations for common materials and loads applied to the brain turn into stresses and strains depending on tissue local morphology. In this work, a hyperviscoelastic fibre-reinforced anisotropic law is used for computational brain injury prediction. Thanks to a fibre-reinforcement dispersion parameter, this formulation accounts for anisotropic features and heterogeneities of the tissue owing to different axon alignment. The novelty of the work is the correlation of the material mechanical anisotropy with fractional anisotropy (FA) from diffusion tensor images. Finite-element (FE) models are used to investigate the influence of the fibre distribution for different loading conditions. In the case of tensile-compressive loads, the comparison between experiments and simulations highlights the validity of the proposed FA-k correlation. Axon alignment affects the deformation predicted by FE models and, when the strain in the axonal direction is large with respect to the maximum principal strain, decreased maximum deformations are detected. It is concluded that the introduction of fibre dispersion information into the constitutive law of brain tissue affects the biofidelity of the simulations.

A comprehensive experimental study on material properties of human brain tissue

A comprehensive study on the biomechanical response of human brain tissue is necessary to investigate traumatic brain injury mechanisms. Published brain material property studies have been mostly performed under a specific type of loading, which is insufficient to develop accurate brain tissue constitutive equations. In addition, inconsistent or contradictory data in the literature made it impossible for computational model developers to create a single brain material model that can fit most, if not all, experimental results. In the current study, a total of 240 brain tissue specimens were tested under tension (n=72), compression (n=72), and shear (n=96) loading modes at varying strain rates. Gray-white matter difference, regional difference, and directional difference within white matter were also investigated. Stress-strain relationships of human brain tissue were obtained up to 50% of engineering strain. Strain rate dependency was observed under all three loading modes. White matter was stiffer than gray matter in compression and shear. Corona radiata was found to be stiffer than cortex, thalamus, and corpus callosum in tension and compression. Directional dependency of white matter was observed under shear loading.

Local mechanical properties of white matter structures in the human brain

The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure.

Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter

White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve strain energy density functions that depend on the I4 and I5 pseudo-invariants of the Cauchy-Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I4 but not on I5. Here, we explore the small strain limits of these models in the context of experimental measurements that probe these dependencies. Models in which strain energy depends on I4 but not I5 can capture differences in Young's (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I4 and I5 strain pseudo-invariants; and (2) behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.

Reality based modeling and simulation of gallbladder shape deformation using variational methods

PURPOSE

Accurate soft tissue deformation modeling is important for realistic surgical simulation. The aim of this study is to develop a reality-based gallbladder model and to determine material constants that represent gallbladder wall mechanical properties.

METHODS

Mechanical experiments on porcine gallbladder were performed to investigate tissue deformation, and an exponential strain energy function was used to describe the nonlinear stress-strain behavior of the gallbladder wall. A new volumetric function based upon the exponential strain energy function was proposed to model the gallbladder organ. A genetic algorithm was used to identify the material parameters of the proposed biomechanical model from the experimental data.

RESULTS

The material constants of the exponential strain energy model were determined based on the experimental data. Deformation simulation and haptic rendering using the proposed gallbladder model were presented. Comparison between deformation predicted by the proposed model and that of the experimental data on gallbladder wall and gallbladder organ tissues demonstrates the applicability of this reality-based variational method for deformation simulation.

CONCLUSION

An accurate soft tissue deformation model was developed using material constants identified for gallbladder. The model is suitable for interactive haptic rendering and deformation simulation. This model has potential applications for simulation of other hollow organs.

Mechanical characterization of brain tissue in tension at dynamic strain rates

Mechanical characterization of brain tissue at high loading velocities is crucial for modeling Traumatic Brain Injury (TBI). During severe impact conditions, brain tissue experiences compression, tension and shear. Limited experimental data is available for brain tissue in extension at dynamic strain rates. In this research, a High Rate Tension Device (HRTD) was developed to obtain dynamic properties of brain tissue in extension at strain rates of ≤90/s. In vitro tensile tests were performed to obtain properties of brain tissue at strain rates of 30, 60 and 90/s up to 30% strain. The brain tissue showed a stiffer response with increasing strain rates, showing that hyperelastic models are not adequate. Specifically, the tensile engineering stress at 30% strain was 3.1±0.49kPa, 4.3±0.86kPa, 6.5±0.76kPa (mean±SD) at strain rates of 30, 60 and 90/s, respectively. Force relaxation tests in tension were also conducted at different strain magnitudes (10-60% strain) with the average rise time of 24ms, which were used to derive time dependent parameters. One-term Ogden, Fung and Gent models were used to obtain material parameters from the experimental data. Numerical simulations were performed using a one-term Ogden model to analyze hyperelastic behavior of brain tissue up to 30% strain. The material parameters obtained in this study will help to develop biofidelic human brain finite element models, which can subsequently be used to predict brain injuries under impact conditions and as a reconstruction and simulation tool for forensic investigations.

Elastic characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

Determination of friction coefficient in unconfined compression of brain tissue

Unconfined compression tests are more convenient to perform on cylindrical samples of brain tissue than tensile tests in order to estimate mechanical properties of the brain tissue because they allow homogeneous deformations. The reliability of these tests depends significantly on the amount of friction generated at the specimen/platen interface. Thus, there is a crucial need to find an approximate value of the friction coefficient in order to predict a possible overestimation of stresses during unconfined compression tests. In this study, a combined experimental-computational approach was adopted to estimate the dynamic friction coefficient μ of porcine brain matter against metal platens in compressive tests. Cylindrical samples of porcine brain tissue were tested up to 30% strain at variable strain rates, both under bonded and lubricated conditions in the same controlled environment. It was established that μ was equal to 0.09±0.03, 0.18±0.04, 0.18±0.04 and 0.20±0.02 at strain rates of 1, 30, 60 and 90/s, respectively. Additional tests were also performed to analyze brain tissue under lubricated and bonded conditions, with and without initial contact of the top platen with the brain tissue, with different specimen aspect ratios and with different lubricants (Phosphate Buffer Saline (PBS), Polytetrafluoroethylene (PTFE) and Silicone). The test conditions (lubricant used, biological tissue, loading velocity) adopted in this study were similar to the studies conducted by other research groups. This study will help to understand the amount of friction generated during unconfined compression of brain tissue for strain rates of up to 90/s.

Temperature effects on brain tissue in compression

Extensive research has been carried out for at least 50 years to understand the mechanical properties of brain tissue in order to understand the mechanisms of traumatic brain injury (TBI). The observed large variability in experimental results may be due to the inhomogeneous nature of brain tissue and to the broad range of test conditions. However, test temperature is also considered as one of the factors influencing the properties of brain tissue. In this research, the mechanical properties of porcine brain have been investigated at 22°C (room temperature), and at 37°C (body temperature) while maintaining a constant preservation temperature of approximately 4-5°C. Unconfined compression tests were performed at dynamic strain rates of 30 and 50s(-1) using a custom made test apparatus. There was no significant difference (p=0.8559-0.9290) between the average engineering stresses of the brain tissue at the two different temperature conditions. The results of this study should help to understand the behavior of brain tissue at different temperature conditions, particularly in unconfined compression tests.

Dynamic mechanical response of brain tissue in indentation in vivo, in situ and in vitro

Characterizing the dynamic mechanical properties of brain tissue is deemed important for developing a comprehensive knowledge of the mechanisms underlying brain injury. The results gathered to date on the tissue properties have been mostly obtained in vitro. Learning how these results might differ quantitatively from those encountered in vivo is a critical step towards the development of biofidelic brain models. The present study provides novel and unique experimental results on, and insights into, brain biorheology in vivo, in situ and in vitro, at large deformations, in the quasi-static and dynamic regimes. The nonlinear dynamic response of the cerebral cortex was measured in indentation on the exposed frontal and parietal lobes of anesthetized porcine subjects. Load-unload cycles were applied to the tissue surface at sinusoidal frequencies of 10, 1, 0.1 and 0.01 Hz. Ramp-relaxation tests were also conducted to assess the tissue viscoelastic behavior at longer times. After euthanasia, the indentation test sequences were repeated in situ on the exposed cortex maintained in its native configuration within the cranium. Mixed gray and white matter samples were subsequently excised from the superior cortex to be subjected to identical indentation test segments in vitro within 6-7 h post mortem. The main response features (e.g. nonlinearities, rate dependencies, hysteresis and conditioning) were measured and contrasted in vivo, in situ and in vitro. The indentation response was found to be significantly stiffer in situ than in vivo. The consistent, quantitative set of mechanical measurements thereby collected provides a preliminary experimental database, which may be used to support the development of constitutive models for the study of mechanically mediated pathways leading to traumatic brain injury.

Indentation versus tensile measurements of Young's modulus for soft biological tissues

In this review, we compare the reported values of Young's modulus (YM) obtained from indentation and tensile deformations of soft biological tissues. When the method of deformation is ignored, YM values for any given tissue typically span several orders of magnitude. If the method of deformation is considered, then a consistent and less ambiguous result emerges. On average, YM values for soft tissues are consistently lower when obtained by indentation deformations. We discuss the implications and potential impact of this finding.

Experimental verification of brain tissue incompressibility using digital image correlation

For decades, incompressibility has been a major assumption in the mechanical study of brain tissue. This assumption is based on the hydrated nature of the biological tissues and the incompressibility of fluids. In this paper, an experimental validation of this assumption using digital image correlation is presented. Unconfined compression tests, relaxation tests and cyclic tests were performed on cylindrical samples of swine brains at loading rates suitable for neurosurgical applications. Digital image correlation was used to evaluate the evolution of the volume ratio throughout the tests. The preparation of the samples is described and it is demonstrated that it causes no statistically significant change of their mechanical properties. The results indicate that the brain tissue incompressibility assumption is verified.

Biomechanics of brain tissue

The dynamic behavior of porcine brain tissue, obtained from a series of in vitro observations and experiments, is analyzed and described here with the aid of a large strain, nonlinear, viscoelastic constitutive model. Mixed gray and white matter samples excised from the superior cortex were tested in unconfined uniaxial compression within 15h post mortem. The test sequence consisted of three successive load-unload segments at strain rates of 1, 0.1 and 0.01 s⁻¹, followed by stress relaxation (n=25). The volumetric compliance of the tissue was assessed for a subset of specimens (n=7) using video extensometry techniques. The tissue response exhibited moderate compressibility, substantial nonlinearity, hysteresis, conditioning and rate dependence. A large strain kinematics nonlinear viscoelastic model was developed to account for the essential features of the tissue response over the entire deformation history. The corresponding material parameters were obtained by fitting the model to the measured conditioned response (axial and volumetric) via a numerical optimization scheme. The model successfully captures the observed complexities of the material response in loading, unloading and relaxation over the entire range of strain rates. The accuracy of the model was further verified by comparing model predictions with the tissue response in unconfined compression at higher strain rate (10 s⁻¹) and with literature data in uniaxial tension. The proposed constitutive framework was also found to be adequate to model the loading response of brain tissue in uniaxial compression over a wider range of strain rates (0.01-3000 s⁻¹), thereby providing a valuable tool for simulations of dynamic transients (impact, blast/shock wave propagation) leading to traumatic brain injury.

Mechanical response of infant brain to manually inflicted shaking

Shaken baby syndrome (SBS) is a contentious issue on both biomechanical and medical fronts, primarily due to a lack of understanding of the loading-injury relationship of infant shaking and the parameters that are deterministic to its nature. In order to address this lack, a finite element (FE) representation of a three month infant head was developed to apply kinematics derived from physical testing with an anthropomorphic infant surrogate. The FE mesh was derived from a three-dimensional geometric basis, allowing for mesh size grading in regions of high importance, and future patient-specific adaptation. Cerebrospinal fluid (CSF) was represented through static pressure equilibration in combination with a locally based squeezing resistance. The results of the simulation indicate that anteroposterior shaking will lead to specific patterns of brain matter motion, increased likelihood of focal axonal injury at contact locations and deep brain structures, and a capacity for the development of subdural hematomas (SDH) due to rupture of central bridging veins.

Computational biology - modeling of primary blast effects on the central nervous system

OBJECTIVES

Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury (TBI). The reason for the prominence of TBI in these particular conflicts as opposed to others is unclear but may result from the increased survivability of blast due to improvements in body armor. In the military context blunt, ballistic and blast effects may all contribute to CNS injury, however blast in particular, has been suggested as a primary cause of military TBI. While blast effects on some biological tissues, such as the lung, are documented in terms of injury thresholds, this is not the case for the CNS. We hypothesized that using bio-fidelic models, allowing for fluid-solid interaction and basic material properties available in the literature, a blast wave would interact with CNS tissue and cause a possible concussive effect.

METHODS

The modeling approach employed for this investigation consisted of a computational framework suitable for simulating coupled fluid-solid dynamic interactions. The model included a complex finite element mesh of the head and intra-cranial contents. The effects of threshold and 50% lethal blast lung injury were compared with concussive impact injury using the full head model allowing upper and lower bounds of tissue injury to be applied using pulmonary injury as the reference tissue.

RESULTS

The effects of a 50% lethal dose blast lung injury (LD(50)) were comparable with concussive impact injury using the DVBIC-MIT full head model.

INTERPRETATION

CNS blast concussive effects were found to be similar between impact mild TBI and the blast field associated with LD(50) lung blast injury sustained without personal protective equipment. With the ubiquitous use of personal protective equipment this suggests that blast concussive effects may more readily ascertained in personnel due to enhanced survivability in the current conflicts.

The influence of test conditions on characterization of the mechanical properties of brain tissue

To understand brain injuries better, the mechanical properties of brain tissue have been studied for 50 years; however, no universally accepted data set exists. The variation in material properties reported may be caused by differences in testing methods and protocols used. An overview of studies on the mechanical properties of brain tissue is given, focusing on testing methods. Moreover, the influence of important test conditions, such as temperature, anisotropy, and precompression was experimentally determined for shear deformation. The results measured at room temperature show a stiffer response than those measured at body temperature. By applying the time-temperature superposition, a horizontal shift factor a(T)=8.5-11 was found, which is in agreement with the values found in literature. Anisotropy of samples from the corona radiata was investigated by measuring the shear resistance for different directions in the sagittal, the coronal, and the transverse plane. The results measured in the coronal and the transverse plane were 1.3 and 1.25 times stiffer than the results obtained from the sagittal plane. The variation caused by anisotropy within the same plane of individual samples was found to range from 25% to 54%. The effect of precompression on shear results was investigated and was found to stiffen the sample response. Combinations of these and other factors (postmortem time, donor age, donor type, etc.) lead to large differences among different studies, depending on the different test conditions.

Rheological properties of the tissues of the central nervous system: a review

Knowledge of the biomechanical properties of central nervous system (CNS) tissues is important for understanding mechanisms and thresholds for injury, and aiding development of computer or surrogate models of these tissues. Many investigations have been conducted to estimate the properties of CNS tissues including under shear, compressive and tensile loading, however there is much variability in this body of literature, making it difficult to separate the material properties from effects that result from a given experimental protocol. This review summarises previous studies of brain and spinal cord properties; discussing their main findings and points of difference, and displays the reported data on comparable scales. Additionally, based on the observed effects of methodological choices on reported tissue properties, recommendations for future studies of brain and spinal cord properties are made.

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.