The mechanical behaviour of brain tissue: large strain response and constitutive modelling

The non-linear mechanical behaviour of porcine brain tissue in large shear deformations is determined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory shear experiments with a strain amplitude of 0.01 and frequencies ranging from 0.04 to 16 Hz are given. The immediate loss of structural integrity, due to large deformations, influencing the mechanical behaviour of brain tissue, at the time scale of loading, is investigated. No significant immediate mechanical damage is observed for these shear deformations up to strains of 0.45. Moreover, the material behaviour during complex loading histories (loading-unloading) is investigated. Stress relaxation experiments for strains up to 0.2 and constant strain rate experiments for shear rates from 0.01 to 1 s(-1) and strains up to 0.15 are presented. A new differential viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.     

Age-dependent material properties of the porcine cerebrum: effect on pediatric inertial head injury criteria

During growth and development, the immature central nervous system undergoes rapid alterations in constituents and structure. We hypothesize that these alterations are accompanied by changes in the mechanical properties of brain tissue which, in turn, influence the response of the brain to traumatic inertial loads. Samples of frontal cerebrum from neonatal (2–3 days) and adult pigs were harvested and tested within 3 h post-mortem. The complex shear modulus of the samples was measured in a custom-designed oscillatory shear testing device at engineering shear strain amplitudes of 2.5% or 5% from 20–200 Hz, at 25°C and 100% humidity. In this range, the elastic and viscous components of the complex shear modulus increased significantly with the development of the cerebral region of the brain. Using an idealized model of the developing head, the age-dependent material properties of brain tissue were shown to affect the mechanical response of the brain to inertial loading. This study is a first step toward developing head injury tolerance criteria specifically for the pediatric population.     

Mechanical response of periodontal ligament: Effects of specimen geometry, preconditioning cycles and time lapse

This study was conducted as part of research line addressing the mechanical response of periodontal ligament (PDL) to tensile–compressive sinusoidal loading. The aim of the present project was to determine the effect of three potential sources of variability: (1) specimen geometry, (2) tissue preconditioning and (3) tissue structural degradation over time. For the three conditions, selected mechanical parameters were evaluated and compared.(1) Standard flat specimens (obtained by sequentially slicing portions of bone, PDL and dentin using a precision band saw) and new cylindrical specimens (extracted with a diamond-coated trephine drill) were obtained from bovine mandibular first molars and subjected to a sinusoidal load profile. (2) Specimens were loaded with up to 2000 cycles. (3) Specimens were immersed in saline and tested after 0, 30 and 60 min.From the data generated, the following was concluded: (1) specimen geometry and preparation technique do not influence the mechanical response of the PDL; (2) the mechanical response stabilizes after approximately 1000 cycles; and (3) no major structural degradation occurs when PDL is immersed in saline for a time lapse up to 60 min.     

Post-mortem timing of skeletal muscle biochemical and mechanical degradation

Fresh cadaveric human tissue is a valuable resource that is used to address important clinical questions. However, it is unknown how post-mortem time impacts skeletal muscle mechanical and biochemical properties. We simulated morgue conditions in rabbits and tested the passive mechanical properties of muscle bundles, and the degradation of myosin heavy chain, collagen, and titin at specific intervals up to 7 days post-mortem. While a great deal of inter-specimen variability was observed, it was independent of post-mortem time. Passive mechanics, myosin heavy chain, and collagen content were all unaffected while the titin protein degraded up to 80% over 7 days post-mortem. These data indicate that fresh cadaveric tissue may be used for passive mechanical testing and that certain biochemical properties are unchanged up to 7 days after death.     

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. Current FE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model for brain tissue and implemented it in an explicit FE code. To obtain sufficient numerical accuracy for modeling the nearly incompressible brain tissue, deviatoric and volumetric stress contributions are separated. Deviatoric stress is modeled in a non-linear viscoelastic differential form. Volumetric behavior is assumed linearly elastic. Linear viscoelastic material parameters were derived from published data on oscillatory experiments, and from ultrasonic experiments. Additionally, non-linear parameters were derived from stress relaxation (SR) experiments at shear strains up to 20%. The model was tested by simulating the transient phase in the SR experiments not used in parameter determination (strains up to 20%, strain rates up to 8s(-1)). Both time- and strain-dependent behavior were predicted accurately (R2>0.96) for strain and strain rates applied. However, the stress was overestimated systematically by approximately 31% independent of strain(rate) applied. This is probably caused by limitations of the experimental data at hand.     

Assessment of in vivo and post-mortem mechanical behavior of brain tissue using magnetic resonance elastography

The knowledge of in vivo brain tissue mechanical properties is essential in several biomedical engineering fields, such as injury biomechanics and neurosurgery simulation. Almost all existing available data have been obtained in vitro by invasive experimental protocols. However, the difference between in vivo and post-mortem mechanical properties remains poorly known, essentially due to the lack of a common method that could measure them both in vivo and ex vivo. In this study, we report the use of magnetic resonance elastography (MRE) for the non-invasive assessment of in vivo brain tissue viscoelastic properties and for the investigation of their evolution after the death. Experiments were performed on seven adult male rats. Shear storage and loss moduli were measured in vivo, just after death and at post-mortem time of approximately 24h. A significant increase in shear storage modulus G(') of approximately 100% was found to occur just after death (p=0.002), whereas no significant difference was found between in vivoG(') and G(') at 24h post-mortem time. No significant difference was found between shear loss modulus G(')in vivo and just after death, whereas a decrease of about 50% was found to occur after 24h (p=0.02). These results illustrate the ability of MRE to investigate some of the critical soft tissue biomechanics-related issues, as it can be used as a non-invasive tool for measuring soft tissue viscoelastic properties.     

Are in vivo and in situ brain tissues mechanically similar?

Brain tissue mechanical properties have been well-characterized in vitro, and were found to be inhomogeneous, nonlinear anisotropic and influenced by neurological development and postmortem time interval prior to testing. However, brain in vivo is a vascularized tissue, and there is a paucity of information regarding the effect of perfusion on brain mechanical properties. Furthermore, mechanical properties are often extracted from preconditioned tissue, and it remains unclear if these properties are representative of non-preconditioned tissue. We present non-preconditioned (NPC) and preconditioned (PC) relaxation responses of porcine brain (N = 10) obtained in vivo, in situ and in vitro, at anterior, mid and posterior regions of the cerebral cortex during 4mm indentations at either 3 or 1 mm/s. Material property characteristics showed no dependency on the site tested, thus revealing that cortical gray matter on the parietal and frontal lobes can be considered homogenous. In most cases, preconditioning decreased the shear moduli, with a more pronounced effect in the dead (in situ and in vitro) brain. For most conditions, it was found that only the long-term time constant of relaxation (tau > 20 s) significantly decreased from in vivo to in situ modes (p < 0.02), and perfusion had no effect on any other property. These findings support the concept that perfusion does not affect the stiffness of living cortical tissue.     

Temporal development of hippocampal cell death is dependent on tissue strain but not strain rate

Deformation of brain tissue in response to mechanical loading of the head is the root-cause of traumatic brain injury (TBI). Even below ultimate failure limits, deformation activates pathophysiological cascades resulting in delayed cell death. Injury response of soft tissues, such as the chest and spinal cord, is dependent on the product of deformation and velocity, a parameter termed the viscous criterion. We set out to test if hippocampal cell death could be predicted by a similar combination of strain and strain rate and if the viscous criterion was valid for hippocampus. Quantitative prediction of the brain's biological response to mechanical stimuli is difficult to achieve in animal models of TBI, so we utilized an in vitro model of TBI based on hippocampal slice cultures. We quantified the temporal development of cell death after precisely controlled deformations for 30 combinations of strain (0.05-0.50) and strain rate (0.1-50s(-1)) relevant to TBI. Loading conditions for a subset of cultures were verified by analysis of high-speed video. Cell death was found to be significantly dependent on time-post injury, on strain magnitude, and to a lesser extent, on anatomical region by a repeated-measures, three-way ANOVA. The responses of the CA1 and CA3 regions of the hippocampus were not statistically different in contrast to some in vivo TBI studies. Surprisingly, cell death was not dependent on strain rate leading us to conclude that the viscous criterion is not a valid predictor for hippocampal tissue injury. Given the large data set and extensive combinations of biomechanical parameters, predictive mathematical functions relating independent variables (strain, region, and time post-injury) to the resultant cell death were defined. These functions can be used as tolerance criteria to equip finite element models of TBI with the added capability to predict biological consequences.     

Mechanical strain increases gene transfer to skeletal muscle cells

Gene transfer techniques possess tremendous potential for treating diseases and for facilitating the study of basic physiological processes. However, further development of efficient and safe methods for gene transfer is needed. The purpose of this study was to test the hypothesis that mechanical strain increases the transfer of DNA to differentiated skeletal muscle cells. We tested this hypothesis by applying cyclic strain to cultured skeletal myotubes either prior to or immediately after the introduction of exogenous DNA complexed with lipids, with strains of varying magnitude (10%, 20% and 30%), number (1800, 3600 and 7200 strain cycles) and frequency (0.5, 1.0 and 1.5 Hz). Results demonstrated that DNA transfection was increased by exposing muscle cells to cyclic strain, and that strain magnitude, number and frequency each influenced DNA transfection. Optimal strain conditions (20% strain magnitude, 3600 cycles applied at 1 Hz) were utilized to examine the role of membrane transport systems in strain-induced increases in DNA transfection. Filipin III was used to inhibit caveolar transport and was found to inhibit strain-mediated increases in DNA transfection, whereas chlorpromazine, used to inhibit clathrin-coated vesicle transport, had no effect. These results indicate that mechanical strain may be an effective method for increasing DNA transfection in skeletal muscle through enhanced caveolar transport.     

Effects of tissue storage and freezing on brain glutamate uptake

Glutamate uptake appears to be stable when measured in rat striatal synaptosomes from tissue stored for up to four hours post-mortem at 25°C. Between four and eight hours storage at room temperature there is a sharp 70% decrease in uptake. Freezing of tissue on dry ice, storage at 4°C for up to 7 days and at ?80°C for 5 days results in 20–30% residual glutamate uptake. Quantitatively similar data can be obtained in eight extrastriatal brain areas. Kinetic analysis of glutamate uptake in stored and frozen tissue reveals the loss of the majority of both sodium-dependent high affinity and temperature-sensitive low affinity sites (v_max-values) while the respective K_m-values are not significantly changed. Pharmacological properties of the high affinity uptake versus a number of specific and metabolic uptake inhibitors remain unaltered by the storage and freezing procedure. The tissue treatment chosen for the present study roughly corresponds with the preparation of human post-mortem brain tissue for enzyme-, receptor-binding- or neuro-transmitter assays. It therefore seems conceivable that meaningful uptake studies can be performed on human autopsy material, thus adding an important parameter to the battery of neurochemical markers already accessible for post-mortem $\text{in}$$\text{vitro}$ examination.     

Mechanical properties of porcine brain tissue in vivo and ex vivo estimated by MR elastography

The mechanical properties of brain tissue in vivo determine the response of the brain to rapid skull acceleration. These properties are thus of great interest to the developers of mathematical models of traumatic brain injury (TBI) or neurosurgical simulations. Animal models provide valuable insight that can improve TBI modeling. In this study we compare estimates of mechanical properties of the Yucatan mini-pig brain in vivo and ex vivo using magnetic resonance elastography (MRE) at multiple frequencies. MRE allows estimations of properties in soft tissue, either in vivo or ex vivo, by imaging harmonic shear wave propagation. Most direct measurements of brain mechanical properties have been performed using samples of brain tissue ex vivo. It has been observed that direct estimates of brain mechanical properties depend on the frequency and amplitude of loading, as well as the time post-mortem and condition of the sample. Using MRE in the same animals at overlapping frequencies, we observe that porcine brain tissue in vivo appears stiffer than porcine brain tissue samples ex vivo at frequencies of 100 Hz and 125 Hz, but measurements show closer agreement at lower frequencies.     

The national DBS brain tissue network pilot study: need for more tissue and more standardization

Over 70,000 DBS devices have been implanted worldwide; however, there remains a paucity of well-characterized post-mortem DBS brains available to researchers. We propose that the overall understanding of DBS can be improved through the establishment of a Deep Brain Stimulation-Brain Tissue Network (DBS-BTN), which will further our understanding of DBS and brain function. The objectives of the tissue bank are twofold: (a) to provide a complete (clinical, imaging and pathological) database for DBS brain tissue samples, and (b) to make available DBS tissue samples to researchers, which will help our understanding of disease and underlying brain circuitry. Standard operating procedures for processing DBS brains were developed as part of the pilot project. Complete data files were created for individual patients and included demographic information, clinical information, imaging data, pathology, and DBS lead locations/settings. 19 DBS brains were collected from 11 geographically dispersed centers from across the U.S. The average age at the time of death was 69.3 years (51?C92, with a standard deviation or SD of 10.13). The male:female ratio was almost 3:1. Average post-mortem interval from death to brain collection was 10.6 h (SD of 7.17). The DBS targets included: subthalamic nucleus, globus pallidus interna, and ventralis intermedius nucleus of the thalamus. In 16.7% of cases the clinical diagnosis failed to match the pathological diagnosis. We provide neuropathological findings from the cohort, and perilead responses to DBS. One of the most important observations made in this pilot study was the missing data, which was approximately 25% of all available data fields. Preliminary results demonstrated the feasibility and utility of creating a National DBS-BTN resource for the scientific community. We plan to improve our techniques to remedy omitted clinical/research data, and expand the Network to include a larger donor pool. We will enhance sample preparation to facilitate advanced molecular studies and progenitor cell retrieval.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

Rapid Preparation of Synaptosomes from Mammalian Brain Using Nontoxic Isoosmotic Gradient Material (Percoll)

A new procedure is described for the isolation of synaptosomes from various parts of mammalian brain. This method utilizes an isoosmotic Percoll/sucrose discontinuous gradient and has some advantages over the traditionally used synaptosomal isolation techniques: (1) it is possible to prepare suitable gradients while retaining isoosmolarity; (2) the time of the preparation is remarkably short (approximately 1 h); (3) if necessary, the gradient material can be easily removed from the samples. Intact synaptosomes were recovered from the 10%/16% (vol/vol) Percoll interphase. The fractions were identified and characterized by electron microscopy and by several biochemical markers for synaptosomes and other subcellular organelles. The homogeneity of the preparations is comparable to or better than that of synaptosomes prepared by the conventional methods. This procedure has been successfully used for the isolation of synaptosomes from very small tissue samples of various experimental animals and human brain.     

Assessment of post-mortem-induced changes to the mouse brain proteome

This study was designed to assess the influence of high-energy head-focused microwave irradiation and the post-mortem interval on measurements of the mouse brain proteome. Difference gel electrophoresis was used to compare mouse brain protein levels in animals killed by decapitation, where the tissue was held at 25°C for selected time intervals post-mortem, and by high-energy head-focused microwave irradiation followed by immediate resection. Microwave-mediated killing was used because it comprehensively snap-inactivates enzymes while largely retaining brain cytoarchitecture. Of the 912 protein spots common to at least eight of 10 gels analyzed, 35 (3.8%) showed significant differences in levels ( t -test; p  < 0.05) depending on whether animals were killed by microwave irradiation or decapitation. When animals were killed by decapitation, 43 protein spots (4.7%) showed changes in levels over the post-mortem interval ( anova ; p  < 0.05). The vast majority of the near 1000 proteins evident on a 2D gel were stable for up to 4 h. These data have important implications for studies of proteins in the brain, whether based on analysis of tissue derived from animal models or from humans.     

Dependence of alignment direction on magnitude of strain in esophageal smooth muscle cells

The response of cells in vitro to mechanical forces has been the subject of much research using devices to exert controlled mechanical stimulation on cultured cells or isolated tissue. In this study, esophageal smooth muscle cells were seeded on flexible polyurethane membranes to form a confluent cell layer. The cells were then subjected to uniform cyclic stretch of varying magnitudes at a frequency of approximately five cycles per minute in a custom made mechatronic bioreactor, providing similar strains experienced in the in vivo mechanical environment of the esophagus. The results show that the orientation response is dependent on the magnitude of cyclic stretch applied. Smooth muscle cells showed parallel alignment to the force direction at low cyclic strains (2%) compared to the hill‐valley morphology of static controls. At higher strains (5% and 10% magnitude), the cells exhibited a consistent alignment perpendicular to the strain. To our knowledge, this is the first time that the alignment direction's dependence on strain magnitude has been demonstrated. MTS analysis indicated that cell metabolism was reduced when mechanical strain was applied, and proliferation was inhibited by mechanical strain. Protein expression indicates a decrease in smooth muscle α‐actin, indicative of changes in cell phenotype, an increase in vimentin, which is associated with increased cell motility, and an increase in desmin, indicating differentiation in stimulated cells. Biotechnol. Bioeng. 2009;102: 1703–1711. © 2008 Wiley Periodicals, Inc.     

Comparison of porcine brain mechanical properties to potential tissue simulant materials in quasi-static and sinusoidal compression

In both finite element and physical surrogate models of head blast injury, accurate material properties of the brain and/or tissue simulants are necessary to ensure biofidelity in predicted response. Thus, there is a need for experimental comparisons between tissue and simulant materials under the same experimental conditions. This study compares the response of porcine brain tissue and a variety of brain tissue simulants in quasi-static and sinusoidal compression tests. Fresh porcine brain tissue was obtained from a local abattoir and tested within 4 h post mortem. Additionally, the effect of post mortem time was investigated by comparing samples stored at room temperature and stored frozen (−18 °C), at various time intervals. The brain tissue simulants tested were bovine gelatin (3%, 5%, and 10% concentration), agarose gelatin (e0.4%, 0.6%, 0.8% concentration), and Sylgard 527. The experiments were performed using a DMA apparatus (TA Instruments Q800). The quasi-static compression data were fit to Ogden hyperelastic functions so that parameters could be compared. It was found that bovine gelatin at 3% and 5% concentration demonstrated the closest response to brain tissue in quasi-static compression. Conversely, in sinusoidal compression, the agarose gel and Sylgard 527 were found to be in closer agreement with the tissue, than bovine gel. In terms of post mortem time and storage, there was no statistically significant difference detected in the response of tissue samples after 48 h, regardless of storage method. However, samples stored at room temperature after 48 h appeared to demonstrate a reduction in stiffness.     

Dynamic, regional mechanical properties of the porcine brain: indentation in the coronal plane

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ～10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.     

The standardisation of gauge length: Its influence on the relative extensibility of natural and chemically modified pericardium

Cyclic uniaxial load tests were performed on natural and chemically modified bovine pericardium which is used in the construction of heart valve substitutes. A template was employed to select specimens from the same sites in different pericardial sacs. When the pericardium was chemically modified by glutaraldehyde fixation as an entire sac the tissue showed increased extensibility after modification compared with the natural tissue. The undeformed stress-free length (gauge length) in both the natural and modified tissue was determined by a highly reproducible experimental method giving a coefficient of variation of less than 0.5%. Specimens excised from a natural pericardial sac demonstrated a significant increase (p < 0.03) in length, 4.97 ± 3.49%, after a single load cycle, compared with controls placed in isotonic saline but not mechanically tested. The test pieces had returned to their orginal length by 8.5 h after the mechanical test. After fixation the same specimens decreased significantly in length (p < 0.001) by 11.18 ± 4.28%. This shrinkage was not significantly different to that of the control specimens (11.09 ± 2.47%) which had not been tested. Uniaxial loading of these chemically modified strips demonstrated a similar increase in tissue extensibility compared to the natural tissue if the undeformed length of the test specimen after shrinkage was used as the gauge length. After mechanical conditioning the chemically modified tissue also demonstrated a significant increase (p < 0.001) in stress-free length (5.35 ± 0.59% after 36 cycles, 8.92 ± 1.50% after 2085 cycles). These deformations were not permanent. The tissue had returned to its original length after 38 h in its normal buffered glutaraldehyde storage medium.

On the basis of these observations, recommendations for the clarification and standardisation of gauge length definitions were made in natural, chemically modified and mechanically conditioned tissue.     

Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability

Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle—coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55–70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm³ volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.