Mechanical Properties Of Brain Tissue Research Articles

Mechanical properties of brain tissue by indentation: Interregional variation

Although many studies on the mechanical properties of brain tissue exist, some controversy concerning the possible differences in mechanical properties of white and gray matter tissues remains. Indentation experiments are conducted on white and gray matter tissues of various regions of the cerebrum and on tissue from the thalamus and the midbrain to study interregional differences. An advantage of indentation, when compared to standard rheological tests as often used for the characterization of brain tissue, is that it is a local test, requiring only a small volume of tissue to be homogeneous. Indentation tests are performed at different speeds and the force relaxation after a step indent is measured as well. White matter tissue is found to be stiffer than gray matter and to show more variation in response between different samples which is consistent with structural differences between white matter and gray matter. In addition to differences between white matter and gray matter, also different regions of brain tissue are compared.

Changes to the viscoelastic properties of brain tissue after traumatic axonal injury

While it has been shown that repetitive mild brain injuries can cause cumulative damage to the brain, changes to the mechanical properties of brain tissue at large deformations were also noted in the literature. The goal of this study was to show that the viscoelastic properties of brain tissue significantly change after traumatic axonal injury (TAI). An impact acceleration model was used to create TAI in the rat brainstem which was quantified with an immunohistochemistry technique at the ponto-medullary junction (PmJ) and pyramidal decussation (PDx). The viscoelastic properties at these two points with and without preconditioning were characterized using an indentation technique combined with finite element analysis and a comparison was made between injured and uninjured specimens, which revealed statistically significant reduction in the instantaneous elastic force at PDx where the brain tissue sustained a significantly higher level of injury. The result of this study can be used to characterize a damage function for the brain tissue undergoing large deformation.

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 ≈ 24 h . 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 vivo G ′ and G ′ at 24 h 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 24 h ( 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.

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.

Characterisation of the mechanical behaviour of brain tissue in compression and shear

No validated, generally accepted data set on the mechanical properties of brain tissue exists, not even for small strains. Most of the experimental and methodological issues have previously been addressed for linear shear loading. The objective of this work was to obtain a consistent data set for the mechanical response of brain tissue to either compression or shear. Results for these two deformation modes were obtained from the same samples to reduce the effect of inter-sample variation. Since compression tests are not very common, the influence of several experimental conditions for the compression measurements was analysed in detail. Results with and without initial contact of the sample with the loading plate were compared. The influence of a fluid layer surrounding the sample and the effect of friction were examined and were found to play an important role during compression measurements.To validate the non-linear viscoelastic constitutive model of brain tissue that was developed in Hrapko et al. (Biorheology 43 (2006), 623-636) and has shown to provide a good prediction of the shear response, the model has been implemented in the explicit Finite Element code MADYMO. The model predictions were compared to compression relaxation results up to 15% strain of porcine brain tissue samples. Model simulations with boundary conditions varying within the physical ranges of friction, initial contact and compression rate are used to interpret the compression results.

Mechanical Characterization of Brain Tissue in High-Rate Extension

Mechanical properties of brain tissue characterized in high-rate loading regime are indispensable for the analysis of traumatic brain injury (TBI). However, data on such properties are very limited. In this study, we measured transient response of brain tissue subjected to high-rate extension. A series of uniaxial extension tests at strain rates ranging from 0.9 to 25 s-1 and stress relaxation tests following a step-like displacement to different strain levels (15-50%) were conducted in cylindrical specimens obtained from fresh porcine brains. A strong rate sensitivity was found in the brain tissue, i.e., initial elastic modulus was 4.2 ± 1.6, 7.7 ± 4.0, and 18.6 ± 3.6 kPa (mean ± SD) for a strain rate of 0.9, 4.3, and 25 s-1, respectively. In addition, the relaxation function was successfully approximated to be strain-time separable, i.e., material response can be expressed as a product of time-dependent and strain-dependent components as:K(t) = G(t)σe(e), where G(t) is a reduced relaxation function, G(t) = 0.416e-t/0.0096+0.327e-t/0.0138+0.256e-t/1.508, and σe(e) is the peak stress following a step input of e. Results of the present study will improve biofidelity of computational models of a human head and provide useful information for the analysis of TBI under injurious environments with strain rates greater than 10 s-1.

Mechanical Heterogeneity of the Rat Hippocampus Measured by Atomic Force Microscope Indentation

Knowledge of brain tissue mechanical properties may be critical for formulating hypotheses about traumatic brain injury (TBI) mechanisms and for accurate TBI simulations. To determine the local mechanical properties of anatomical subregions within the rat hippocampus, the atomic force microscope (AFM) was adapted for use on living brain tissue. The AFM provided advantages over alternative methods for measuring local mechanical properties of brain because of its high spatial resolution, high sensitivity, and ability to measure live samples under physiologic conditions. From AFM indentations, a mean pointwise or depth-dependent apparent elastic modulus, E, was determined for the following hippocampal subregions: CA1 pyramidal cell layer (CA1P) and stratum radiatum (CA1SR), CA3 pyramidal cell layer (CA3P) and stratum radiatum (CA3SR), and the dentate gyrus (DG). For all regions, E was indentation-depth-dependent, reflecting the nonlinearity of brain tissue. At an indentation depth of 3microm, E was 234 +/- 152 Pa for CA3P, 308 +/- 184 Pa for CA3SR, 137 +/- 97 Pa for CA1P, 169 +/- 52 Pa for CA1SR, and 201 +/- 133 Pa for DG (mean +/- SD). Our results demonstrate for the first time that the hippocampus is mechanically heterogeneous. Based on our findings, we discuss hypotheses accounting for experimentally observed patterns of hippocampal cell death, which can be tested with biofidelic finite element models of TBI.

Mechanical Characterization of Brain Tissue in High-Rate Compression

Mechanical properties of brain tissue in high strain region are indispensable for the analysis of brain damage during traffic accidents. However, accurate data on the mechanical behavior of brain tissue under impact loading condition are sparse. In this study, mechanical properties of porcine brain tissues were characterized in their cylindrical samples cored out from their surface. The samples were compressed in their axial direction at strain rates ranging from 1 to 50 s-1. Stress relaxation test was also conducted following rapid compression with a rise time of ∼30 ms to different strain levels (20-70%). Brain tissue exhibited stiffer responses under higher impact rates: initial elastic modulus was 5.7±1.6, 11.9±3.3, 23.8±10.5 kPa (mean±SD) for strain rate of 1, 10, 50 s-1, respectively. We found that stress relaxation K(t,e) could be analysed in time and strain domains separately. The relaxation response could be expressed as the product of two mutually independent functions of time and strain as: K(t,e)=G(t)σe(e), where σe(e) is an elastic response, i.e., the peak stress in response to a step input of strain e, and G(t) is a reduced relaxation function: G(t)=0.642e-t/0.0207+0.142e-t/0.482+0.216e-t/18.9, i.e., the time-dependent stress response normalized by the peak stress. The reduced relaxation function obtained here will serve as a useful tool to predict mechanical behavior of brain tissue in compression with strain rate greater than 10 s-1.

Determination of the elasticity parameters of brain tissue with combined simulation and registration

Reliable elasticity parameters describing the behavior of a given material are an important issue in the context of physically-based simulation. In this paper we introduce a method for the determination of the mechanical properties of brain tissue. Elasticity parameters Young's modulus E and Poisson's ratio nu are estimated in an iterative framework coupling a finite element simulation with image registration. Within this framework, the outcome of the simulation is parameterized with both elasticity moduli that are automatically varied until optimal image correspondence between the simulated and the intraoperative data is achieved. We calculated optimal mechanical properties of brain tissue in six cases. The statistical analysis of the obtained values showed a good correlation of the results, thus proving the value of the method. An approach combining simulation and registration for the determination of the mechanical brain tissue properties is presented. This contributes to performing reliable physically-based simulation of soft tissue movement.

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 4 mm 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 ( τ>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.

Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64×10 −2 s −1, are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress−strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress−strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyperelastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain ∈〈−0.3,0.2〉) for strain rates ranging over five orders of magnitude.

Mechanical properties of brain tissue in-vivo: experiment and computer simulation

Realistic computer simulation of neurosurgical procedures requires incorporation of the mechanical properties of brain tissue in the mathematical model. Possible applications of computer simulation of neurosurgery include non-rigid registration, virtual reality training and operation planning systems and robotic devices to perform minimally invasive brain surgery. A number of constitutive models of brain tissue, both single-phase and bi-phasic, have been proposed in recent years. The major deficiency of most of them, however, is the fact that they were identified using experimental data obtained in vitro and there is no certainty whether they can be applied in the realistic in vivo setting. In this paper we attempt to show that previously proposed by us hyper-viscoelastic constitutive model of brain tissue can be applied to simulating surgical procedures. An in vivo indentation experiment is described. The force–displacement curve for the loading speed typical for surgical procedures is concave upward containing no linear portion from which a meaningful elastic modulus might be determined. In order to properly analyse experimental data, a three-dimensional, non-linear finite element model of the brain was developed. Magnetic resonance imaging techniques were used to obtain geometric information needed for the model. The shape of the force–displacement curve obtained using the numerical solution was very similar to the experimental one. The predicted forces were about 31% lower than those recorded during the experiment. Having in mind that the coefficients in the model had been identified based on experimental data obtained in vitro, and large variability of mechanical properties of biological tissues, such agreement can be considered as very good. By appropriately increasing material parameters describing instantaneous stiffness of the tissue one is able, without changing the structure of the model, to reproduce experimental curve almost perfectly. Numerical studies showed also that the linear, viscoelastic model of brain tissue is not appropriate for the modelling brain tissue deformation even for moderate strains.

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.

Pathophysiological mechanisms of brain edema development: role of tissue factors.

In experiments carried out on adult rabbit "chest-head" preparations the volume changes of the exposed brain (BrV) were determined in repeated tests during a controlled increase of the systemic venous pressure (SVP) of about 13 mm Hg. The changes of both SVP and BrV were usually parallel at the onset of the experiments, but when the brains became preedematous hysteresis appeared in the plots of their relationships. The hysteresis increased gradually (sometimes with periods of partial decrease) thus indicating a delay in the draining of blood from the brain's venous system and in the removal of excess extracellular fluid from the cebral tissue. Evidence for water filtration through the capillary walls during increase of the SVP, and, thus, of brain intravascular pressure, was obtained by detecting the dynamics of [Na+] and [K+] in the extracellular fluid of the cerebral cortex by ion-selective electrodes. This process appeared reversible in normal brains while in the preedematous ones the excessive water filtration resulted in brain edema. The preedematous state of the brain is believed to be caused by changes of the mechanical properties of brain tissue and/or by changes in osmolarity.