Mechanical difference between white and gray matter in the rat cerebellum measured by scanning force microscopy

Non-ideal effects in indentation testing of soft tissues

Indentation has several advantages as a loading mode for determining constitutive behavior of soft, biological tissues. However, indentation induces a complex, spatially heterogeneous deformation field that creates analytical challenges for the calculation of constitutive parameters. As a result, investigators commonly assume small indentation depths and large sample thicknesses to simplify analysis and then restrict indentation depth and sample geometry to satisfy these assumptions. These restrictions limit experimental resolution in some fields, such as brain biomechanics. However, recent experimental evidence suggests that conventionally applied limits are in fact excessively conservative. We conducted a parametric study of indentation loading with various indenter geometries, surface interface conditions, sample compressibility, sample geometry and indentation depth to quantitatively describe the deviation from previous treatments that results from violation of the assumptions of small indentation depth and large sample thickness. We found that the classical solution was surprisingly robust to violation of the assumption of small strain but highly sensitive to violation of the assumption of large sample thickness, particularly if the indenter was cylindrical. The ramifications of these findings for design of indentation experiments are discussed and correction factors are presented to allow future investigators to account for these effects without recreating our finite element models.

Long-term in vivo imaging of viscoelastic properties of the mouse brain after controlled cortical impact

Traumatic brain injury (TBI) presents a variety of causes and symptoms, thus making the development of reliable diagnostic methods and therapeutic treatments challenging. Magnetic resonance elastography (MRE) is a technique that allows for a noninvasive assessment of the mechanical properties of soft biological tissue, such as tissue stiffness, storage modulus, and loss modulus. Importantly, by quantifying the changes in the stiffness of tissue that is often associated with disease, MRE is able to detect tissue pathologies at early stages. Recent improvements in instrumentation have allowed for the investigation of small samples with microscopic resolution (μMRE). We hypothesize that μMRE can sensitively detect variations in micromechanical properties in the brain caused by the compressive and shearing forces sustained during TBI. To test this hypothesis, we randomized 13 C57BL mice to receive a controlled cortical impact at a 0.5 mm or 0.75 mm depth, with both sham and naïve mice as controls. Our objective was to propagate mechanical shear waves throughout the brain for in vivo TBI μMRE imaging. The mechanical properties of the injured brain tissue were determined at days 0, 1, 7, and 28 post-injury. For both groups, we observed a significant drop in the stiffness of the impacted region immediately following the injury; the 0.75 mm animals experienced increased tissue softness that lasted longer than that for the 0.5 mm group. Although the shear stiffness, storage modulus, and loss modulus parameters all followed the same trend, the tissue stiffness yielded the most statistically significant results. Overall, this article introduces a transformative technique for mechanically mapping the brain and detecting brain diseases and injury.

Quantitative study of the elastic modulus of loosely attached cells in AFM indentation experiments

When measuring the elastic (Young's) modulus of cells using AFM, good attachment of cells to a substrate is paramount. However, many cells cannot be firmly attached to many substrates. A loosely attached cell is more compliant under indenting. It may result in artificially low elastic modulus when analyzed with the elasticity models assuming firm attachment. Here we suggest an AFM-based method/model that can be applied to extract the correct Young's modulus of cells loosely attached to a substrate. The method is verified by using primary breast epithelial cancer cells (MCF-7) at passage 4. At this passage, approximately one-half of cells develop enough adhesion with the substrate to be firmly attached to the substrate. These cells look well spread. The other one-half of cells do not develop sufficient adhesion, and are loosely attached to the substrate. These cells look spherical. When processing the AFM indentation data, a straightforward use of the Hertz model results in a substantial difference of the Young's modulus between these two types of cells. If we use the model presented here, we see no statistical difference between the values of the Young's modulus of both poorly attached (round) and firmly attached (close to flat) cells. In addition, the presented model allows obtaining parameters of the brush surrounding the cells. The cellular brush observed is also statistically identical for both types of cells. The method described here can be applied to study mechanics of many other types of cells loosely attached to substrates, e.g., blood cells, some stem cells, cancerous cells, etc.

Mechanics in neuronal development and repair

Biological cells are well known to respond to a multitude of chemical signals. In the nervous system, chemical signaling has been shown to be crucially involved in development, normal functioning, and disorders of neurons and glial cells. However, there are an increasing number of studies showing that these cells also respond to mechanical cues. Here, we summarize current knowledge about the mechanical properties of nervous tissue and its building blocks, review recent progress in methodology and understanding of cellular mechanosensitivity in the nervous system, and provide an outlook on the implications of neuromechanics for future developments in biomedical engineering to aid overcoming some of the most devastating and currently incurable CNS pathologies such as spinal cord injuries and multiple sclerosis.

Method for quantitative measurements of the elastic modulus of biological cells in AFM indentation experiments

Here we overview and further develop a quantitative method to measure mechanics of biological cells in indentation experiments, which is based on the use of atomic force microscopy (AFM). We demonstrate how the elastic modulus of the cell body should be measured when the cellular brush is taken into account. The brush is an essential inelastic part of the cell, which surrounds all eukaryotic (the brush is mostly microvilli and glycocalyx) and gram-negative prokaryotic cells (the brush is polysaccharides). The other main feature of the described method is the use of a relatively dull AFM probe to stay in the linear stress-strain regime. In particular, we show that the elastic modulus (aka the Young's modulus) of cells is independent of the indentation depth up to 10-20% deformation for the eukaryotic cells studied here. Besides the elastic modulus, the method presented allows obtaining the parameters of cellular brush, such as the effective length and grafting density of the brush. Although the method is demonstrated on eukaryotic cells, it is directly applicable for all types of cells, and even non-biological soft materials surrounded by either a brush or any field of long-range forces.

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.

Complex stiffness gradient substrates for studying mechanotactic cell migration

Polyacrylamide gels are cast upon a stiff support with controlled topography, resulting in a thin gel layer of variable height. The topographical profiles project a stiffness map onto the gel, resulting in controlled linear and non-linear 2D stiffness gradients. Fibroblasts, which migrate towards stiffer substrates, accumulate in areas with a gel thickness below 15 μm.

Mechanical environment modulates biological properties of oligodendrocyte progenitor cells

Myelination and its regenerative counterpart remyelination represent one of the most complex cell-cell interactions in the central nervous system (CNS). The biochemical regulation of axon myelination via the proliferation, migration, and differentiation of oligodendrocyte progenitor cells (OPCs) has been characterized extensively. However, most biochemical analysis has been conducted in vitro on OPCs adhered to substrata of stiffness that is orders of magnitude greater than that of the in vivo CNS environment. Little is known of how variation in mechanical properties over the physiological range affects OPC biology. Here, we show that OPCs are mechanosensitive. Cell survival, proliferation, migration, and differentiation capacity in vitro depend on the mechanical stiffness of polymer hydrogel substrata. Most of these properties are optimal at the intermediate values of CNS tissue stiffness. Moreover, many of these properties measured for cells on gels of optimal stiffness differed significantly from those measured on glass or polystyrene. The dependence of OPC differentiation on the mechanical properties of the extracellular environment provides motivation to revisit results obtained on nonphysiological, rigid surfaces. We also find that OPCs stiffen upon differentiation, but that they do not change their compliance in response to substratum stiffness, which is similar to embryonic stem cells, but different from adult stem cells. These results form the basis for further investigations into the mechanobiology of cell function in the CNS and may specifically shed new light on the failure of remyelination in chronic demyelinating diseases such as multiple sclerosis.

Finite element study of the mechanical response in spinal cord during the thoracolumbar burst fracture

Background

The mechanical response of the spinal cord during burst fracture was seldom quantitatively addressed and only few studies look into the internal strain of the white and grey matters within the spinal cord during thoracolumbar burst fracture (TLBF). The aim of the study is to investigate the mechanical response of the spinal cord during TLBF and correlate the percent canal compromise (PCC) with the strain in the spinal cord.

Methodology/Principal Findings

A three-dimensional (3D) finite element (FE) model of human T12-L1 spinal cord with visco-elastic property was generated based on the transverse sections images of spinal cord, and the model was validated against published literatures under static uniaxial tension and compression. With the validated model, a TLBF simulation was performed to compute the mechanical strain in the spinal cord with the PCC. Linear regressions between PCC and strain in the spinal cord show that at the initial stage, with the PCC at 20%, and 45%, the corresponding mechanical strains in ventral grey, dorsal grey, ventral white, dorsal white matters were 0.06, 0.04, 0.12, 0.06, and increased to 0.14, 0.12, 0.23, and 0.13, respectively. At the recoiled stage, when the PCC was decreased from 45% to 20%, the corresponding strains were reduced to 0.03, 0.02, 0.04 and 0.03. The strain was correlated well with PCC.

Conclusions/Significance

The simulation shows that the strain in the spinal cord correlated well with the PCC, and the mechanical strains in the ventral regions are higher than those in the dorsal regions of spinal cord tissue during burst fracture, suggesting that the ventral regions of the spinal cord may susceptible to injury than the dorsal regions.

Multifrequency inversion in magnetic resonance elastography

Time-harmonic shear wave elastography is capable of measuring viscoelastic parameters in living tissue. However, finite tissue boundaries and waveguide effects give rise to wave interferences which are not accounted for by standard elasticity reconstruction methods. Furthermore, the viscoelasticity of tissue causes dispersion of the complex shear modulus, rendering the recovered moduli frequency dependent. Therefore, we here propose the use of multifrequency wave data from magnetic resonance elastography (MRE) for solving the inverse problem of viscoelasticity reconstruction by an algebraic least-squares solution based on the springpot model. Advantages of the method are twofold: (i) amplitude nulls appearing in single-frequency standing wave patterns are mitigated and (ii) the dispersion of storage and loss modulus with drive frequency is taken into account by the inversion procedure, thereby avoiding subsequent model fitting. As a result, multifrequency inversion produces fewer artifacts in the viscoelastic parameter map than standard single-frequency parameter recovery and may thus support image-based viscoelasticity measurement. The feasibility of the method is demonstrated by simulated wave data and MRE experiments on a phantom and in vivo human brain. Implemented as a clinical method, multifrequency inversion may improve the diagnostic value of time-harmonic MRE in a large variety of applications.

Strength in the periphery: growth cone biomechanics and substrate rigidity response in peripheral and central nervous system neurons

There is now considerable evidence of the importance of mechanical cues in neuronal development and regeneration. Motivated by the difference in the mechanical properties of the tissue environment between the peripheral (PNS) and central (CNS) nervous systems, we compare substrate-stiffness-dependent outgrowth and traction forces from PNS (dorsal root ganglion (DRG)) and CNS (hippocampal) neurons. We show that neurites from DRG neurons display maximal outgrowth on substrates with a Young's modulus of ∼1000 Pa, whereas hippocampal neurite outgrowth is independent of substrate stiffness. Using traction force microscopy, we also find a substantial difference in growth cone traction force generation, with DRG growth cones exerting severalfold larger forces compared with hippocampal growth cones. The traction forces generated by DRG and hippocampal growth cones both increase with increasing stiffness, and DRG growth cones growing on substrates with a Young's modulus of 1000 Pa strengthen considerably after 18-30 h. Finally, we find that retrograde actin flow is almost three times faster in hippocampal growth cones than in DRG. Moreover, the density of paxillin puncta is significantly lower in hippocampal growth cones, suggesting that stronger substrate coupling of the DRG cytoskeleton is responsible for the remarkable difference in traction force generation. These findings reveal a differential adaptation of cytoskeletal dynamics to substrate stiffness in growth cones of different neuronal types, and highlight the potential importance of the mechanical properties of the cellular environment for neuronal navigation during embryonic development and nerve regeneration.

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.

Viscoelastic properties of the rat brain in the sagittal plane: effects of anatomical structure and age

Rat is the most commonly used animal model for the study of traumatic brain injury. Recent advances in imaging and computational modeling technology offer the promise of biomechanical models capable of resolving individual brain structures and offering greater insight into the causes and consequences of brain injury. However, there is insufficient data on the mechanical properties of brain structures available to populate these models. In this study, we used microindentation to determine viscoelastic properties of different anatomical structures in sagittal slices of juvenile and adult rat brain. We find that the rat brain is spatially heterogeneous in this anatomical plane supporting previous results in the coronal plane. In addition, the brain becomes stiffer and more heterogeneous as the animal matures. This dynamic, region-specific data will support the development of more biofidelic computational models of brain injury biomechanics and the testing of hypotheses about the manner in which different anatomical structures are injured in a head impact.

Modeling new conceptual interpretations of development

In April 2011, researchers from diverse background met at the Gulbenkian Institute (Oeiras, Portugal) to discuss the emerging input of biophysics into the field of developmental biology. The scope of the workshop was to bring together scientists working in different model systems and to discuss some of the most recent advances towards understanding how physical forces affect embryonic development. Discussions and talks highlighted two main trends: that many aspects of embryogenesis can be accurately quantified and translated into a limited number of physical forces and biochemical parameters; and that simulations and modeling provide new conceptual interpretations of classical developmental questions.

Atomic force microscopy and its contribution to understanding the development of the nervous system

While our understanding of the influence of biochemical signaling on cell functioning is increasing rapidly, the consequences of mechanical signaling are currently poorly understood. However, cells of the nervous system respond to their mechanical environment; their mechanosensitivity has important implications for development and disease. Atomic force microscopy provides a powerful technique to investigate the mechanical interaction of cells with their environment with high resolution. This method can be used to obtain high-resolution surface topographies, stiffness maps, and apply well-defined forces to samples at different length scales. This review summarizes recent advances of atomic force microscopy, provides an overview about state-of-the-art measurements, and suggests directions for future applications to investigate the involvement of mechanics in the development of the nervous system.

Elucidating the mechanobiology of malignant brain tumors using a brain matrix-mimetic hyaluronic acid hydrogel platform

Glioblastoma multiforme (GBM) is a malignant brain tumor characterized by diffuse infiltration of single cells into the brain parenchyma, which is a process that relies in part on aberrant biochemical and biophysical interactions between tumor cells and the brain extracellular matrix (ECM). A major obstacle to understanding ECM regulation of GBM invasion is the absence of model matrix systems that recapitulate the distinct composition and physical structure of brain ECM while allowing independent control of adhesive ligand density, mechanics, and microstructure. To address this need, we synthesized brain-mimetic ECMs based on hyaluronic acid (HA) with a range of stiffnesses that encompasses normal and tumorigenic brain tissue and functionalized these materials with short Arg-Gly-Asp (RGD) peptides to facilitate cell adhesion. Scanning electron micrographs of the hydrogels revealed a dense, sheet-like microstructure with apparent nanoscale porosity similar to brain extracellular space. On flat hydrogel substrates, glioma cell spreading area and actin stress fiber assembly increased strongly with increasing density of RGD peptide. Increasing HA stiffness under constant RGD density produced similar trends and increased the speed of random motility. In a three-dimensional (3D) spheroid paradigm, glioma cells invaded HA hydrogels with morphological patterns distinct from those observed on flat surfaces or in 3D collagen-based ECMs but highly reminiscent of those seen in brain slices. This material system represents a brain-mimetic model ECM with tunable ligand density and stiffness amenable to investigations of the mechanobiological regulation of brain tumor progression.

Growth cones as soft and weak force generators

Many biochemical processes in the growth cone finally target its biomechanical properties, such as stiffness and force generation, and thus permit and control growth cone movement. Despite the immense progress in our understanding of biochemical processes regulating neuronal growth, growth cone biomechanics remains poorly understood. Here, we combine different experimental approaches to measure the structural and mechanical properties of a growth cone and to simultaneously determine its actin dynamics and traction force generation. Using fundamental physical relations, we exploited these measurements to determine the internal forces generated by the actin cytoskeleton in the lamellipodium. We found that, at timescales longer than the viscoelastic relaxation time of τ = 8.5 ± 0.5 sec, growth cones show liquid-like characteristics, whereas at shorter time scales they behaved elastically with a surprisingly low elastic modulus of E = 106 ± 21 Pa. Considering the growth cone's mechanical properties and retrograde actin flow, we determined the internal stress to be on the order of 30 pN per μm(2). Traction force measurements confirmed these values. Hence, our results indicate that growth cones are particularly soft and weak structures that may be very sensitive to the mechanical properties of their environment.