Baptiste Pierrat

Mechanical characterization of the P56 mouse brain under large-deformation dynamic indentation

The brain is a complex organ made up of many different functional and structural regions consisting of different types of cells such as neurons and glia, as well as complex anatomical geometries. It is hypothesized that the different regions of the brain exhibit significantly different mechanical properties, which may be attributed to the diversity of cells and anisotropy of neuronal fibers within individual brain regions. The regional dynamic mechanical properties of P56 mouse brain tissue in vitro and in situ at velocities of 0.71–4.28 mm/s, up to a deformation of 70 μm are presented and discussed in the context of traumatic brain injury. The experimental data obtained from micro-indentation measurements were fit to three hyperelastic material models using the inverse Finite Element method. The cerebral cortex elicited a stiffer response than the cerebellum, thalamus, and medulla oblongata regions for all velocities. The thalamus was found to be the least sensitive to changes in velocity, and the medulla oblongata was most compliant. The results show that different regions of the mouse brain possess significantly different mechanical properties, and a significant difference also exists between the in vitro and in situ brain.

Dynamic mechanical properties of murine brain tissue using micro-indentation

In the past 50 years significant advances have been made in determining the macro-scale properties of brain tissue in compression, tension, shear and indentation. There has also been significant work done at the nanoscale using the AFM method to characterise the properties of individual neurons. However, there has been little published work on the micro-scale properties of brain tissue using an appropriate indentation methodology to characterise the regional differences at dynamic strain rates. This paper presents the development and use of a novel micro-indentation device to measure the dynamic mechanical properties of brain tissue. The device is capable of applying up to 30/s strain rates with a maximum indentation area of 2500 μm(2). Indentation tests were carried out to determine the shear modulus of the cerebellum (2.11 ± 1.26 kPa, 3.15 ± 1.66 kPa, 3.71 ± 1.23 kPa) and cortex (4.06 ± 1.69 kPa, 6.14 ± 3.03 kPa, 7.05 ± 3.92 kPa) of murine brain tissue at 5, 15, and 30/s up to 14% strain. Numerical simulations were carried out to verify the experimentally measured force-displacement results.

A viscoelastic analysis of the P56 mouse brain under large-deformation dynamic indentation

The brain is a complex organ made up of many different functional and structural regions consisting of different types of cells such as neurons and glia, as well as complex anatomical geometries. It is hypothesized that the different regions of the brain exhibit significantly different mechanical properties which may be attributed to the diversity of cells within individual brain regions. The regional viscoelastic properties of P56 mouse brain tissue, up to 70μm displacement, are presented and discussed in the context of traumatic brain injury, particularly how the different regions of the brain respond to mechanical loads. Force-relaxation data obtained from micro-indentation measurements were fit to both linear and quasi-linear viscoelastic models to determine the time and frequency domain viscoelastic response of the pons, cortex, medulla oblongata, cerebellum, and thalamus. The damping ratio of each region was also determined. Each region was found to have a unique mechanical response to the applied displacement, with the pons and thalamus exhibiting the largest and smallest force-response, respectively. All brain regions appear to have an optimal frequency for the dissipation of energies which lies between 1 and 10Hz. STATEMENT OF SIGNIFICANCE We present the first mechanical characterization of the viscoelastic response for different regions of mouse brain. Force-relaxation tests are performed under large strain dynamic micro-indentation, and viscoelastic models are used subsequently, providing time-dependent mechanical properties of brain tissue under loading conditions comparable to what is experienced in TBI. The unique mechanical properties of different brain regions are highlighted, with substantial variations in the viscoelastic properties and damping ratio of each region. Cortex and pons were the stiffest regions, while the thalamus and medulla were most compliant. The cerebellum and thalamus had highest damping ratio values and those of the medulla were lowest. The reported material parameters can be implemented into finite element computer models of the mouse to investigate the effects of trauma on individual brain regions.

Finite element implementation of a new model of slight compressibility for transversely isotropic materials

Modelling transversely isotropic materials in finite strain problems is a complex task in biomechanics, and is usually addressed by using finite element (FE) simulations. The standard method developed to account for the quasi-incompressible nature of soft tissues is to decompose the strain energy function (SEF) into volumetric and deviatoric parts. However, this decomposition is only valid for fully incompressible materials, and its use for slightly compressible materials yields an unphysical response during the simulation of hydrostatic tension/compression of a transversely isotropic material. This paper presents the FE implementation as subroutines of a new volumetric model solving this deficiency in two FE codes: Abaqus and FEBio. This model also has the specificity of restoring the compatibility with small strain theory. The stress and elasticity tensors are first derived for a general SEF. This is followed by a successful convergence check using a particular SEF and a suite of single-element tests showing that this new model does not only correct the hydrostatic deficiency but may also affect stresses during shear tests (Poynting effect) and lateral stretches during uniaxial tests (Poissons effect). These FE subroutines have numerous applications including the modelling of tendons, ligaments, heart tissue, etc. The biomechanics community should be aware of specificities of the standard model, and the new model should be used when accurate FE results are desired in the case of compressible materials.

Indentation of heterogeneous soft tissue: Local constitutive parameter mapping using an inverse method and an automated rig

In the domain of soft tissue biomechanics, the development of numerical simulations has raised the experimental challenge of identifying local internal mechanical constitutive data of heterogeneous organs (e.g. brain tissue). In this context, this paper presents an ex-vivo alternative characterization method to full-field imaging techniques. It is based on automated, multiple indentations of an organ section using a custom-built rig, effectively allowing to map the viscoelastic and hyperelastic constitutive parameters of the tissue at the millimetre scale, under dynamic conditions. In this paper, this technique is described and used to map the constitutive data of three sections from porcine liver, kidney and brain tissues. The results of this mapping present strong evidence of correlation between the organ constituents (e.g. white/grey matter distribution) and the identified constitutive parameters. It was also found that brain and kidney tissues are highly heterogeneous in terms of identified properties, suggesting that such a technique is essential for fully characterizing their mechanical behaviour. This method opens the way to 3D mapping of constitutive parameters to feed finite element models of the organs with region-specific properties.

Protection of cortex by overlying meninges tissue during dynamic indentation of the adolescent brain

Traumatic brain injury (TBI) has become a recent focus of biomedical research with a growing international effort targeting material characterization of brain tissue and simulations of trauma using computer models of the head and brain to try to elucidate the mechanisms and pathogenesis of TBI. The meninges, a collagenous protective tri-layer, which encloses the entire brain and spinal cord has been largely overlooked in these material characterization studies. This has resulted in a lack of accurate constitutive data for the cranial meninges, particularly under dynamic conditions such as those experienced during head impacts. The work presented here addresses this lack of data by providing for the first time, in situ large deformation material properties of the porcine dura-arachnoid mater composite under dynamic indentation. It is demonstrated that this tissue is substantially stiffer (shear modulus, μ=19.10±8.55kPa) and relaxes at a slower rate (τ1=0.034±0.008s, τ2=0.336±0.077s) than the underlying brain tissue (μ=6.97±2.26kPa, τ1=0.021±0.007s, τ2=0.199±0.036s), reducing the magnitudes of stress by 250% and 65% for strains that arise during indentation-type deformations in adolescent brains. STATEMENT OF SIGNIFICANCE We present the first mechanical analysis of the protective capacity of the cranial meninges using in situ micro-indentation techniques. Force-relaxation tests are performed on in situ meninges and cortex tissue, under large strain dynamic micro-indentation. A quasi-linear viscoelastic model is used subsequently, providing time-dependent mechanical properties of these neural tissues under loading conditions comparable to what is experienced in TBI. The reported data highlights the large differences in mechanical properties between these two tissues. Finite element simulations of the indentation experiments are also performed to investigate the protective capacity of the meninges. These simulations show that the meninges protect the underlying brain tissue by reducing the overall magnitude of stress by 250% and up to 65% for strains.

Region and species dependent mechanical properties of adolescent and young adult brain tissue

Traumatic brain injuries, the leading cause of death and disability in children and young adults, are the result of a rapid acceleration or impact of the head. In recent years, a global effort to better understand the biomechanics of TBI has been undertaken, with many laboratories creating detailed computational models of the head and brain. For these models to produce realistic results they require accurate regional constitutive data for brain tissue. However, there are large differences in the mechanical properties reported in the literature. These differences are likely due to experimental parameters such as specimen age, brain region, species, test protocols, and fiber direction which are often not reported. Furthermore, there is a dearth of reported viscoelastic properties for brain tissue at large-strain and high rates. Mouse, rat, and pig brains are impacted at 10/s to a strain of ~36% using a custom-built micro-indenter with a 125 μm radius. It is shown that the resultant mechanical properties are dependent on specimen-age, species, and region, under identical experimental parameters.

Author Correction: Region and species dependent mechanical properties of adolescent and young adult brain tissue

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

A new formulation of slight compressibility for arterial tissue and its Finite Element implementation

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating the mechanical response of arterial tissue. The current standard method of accounting for slight compressibility of hyperelastic soft tissue assumes an additive decomposition of the strain-energy function into a volumetric and a deviatoric part. This has been shown, however, to be inconsistent with the linear theory and results in cubes retaining their cuboid shape under hydrostatic tension and compression, which seems at variance with the reinforcement of arterial tissue with two families of collagen fibres. A remedy for these defects is proposed here, a solution which generalises the current standard model of slight compressibility to include two additional terms, one of which is quadratic in the invariants and the other quadratic in . Experimental data are used to motivate typical values for the associated material constants of these additional terms. Some simulations are performed to allow contrasts and comparisons to be made between the current standard model of slight compressibility and its generalisation proposed here.