Correlations between tissue-level stresses and strains and cellular damage within the guinea pig spinal cord white matter

Strain magnitude, strain rate, axon location, axon size, and the local tissue stress state have been proposed as the mechanisms governing primary cellular damage within the spinal cord parenchyma during slow compression injury. However, the mechanism of axon injury has yet to be fully elucidated. The objective of this study was to correlate cellular damage within the guinea pig spinal cord white matter, quantified by a horseradish peroxidase (HRP) exclusion test, with tissue-level stresses and strains using a combined experimental and computational approach. Force-deformation curves were acquired by transversely compressing strips of guinea pig spinal cord white matter at a quasi-static rate. Hyperelastic material parameters, derived from a Mooney-Rivlin constitutive law, were varied within a nonlinear, plane strain finite element model of the white matter strips until the computational force-deformation curve converged to the experimental results. In addition, white matter strips were subjected to nominal compression levels of 25%, 50%, 70%, and 90% to assess axonal damage by quantifying HRP uptake. HRP uptake density increased with tissue depth and with increased nominal compression. Using linear and nonlinear regression analyses, the strongest correlations with HRP uptake density were found for groups of tissue-level stresses and groups of log-transformed tissue-level strains.     

A transversely isotropic constitutive model of excised guinea pig spinal cord white matter

Narrowing of the spinal canal generates an amalgamation of stresses within the spinal cord parenchyma. The tissue’s stress state cannot be quantified experimentally; it must be described using computational methods, such as finite element analysis. The objective of this research was to propose a compressible, transversely isotropic constitutive model, an augmentation of the isotropic Mooney–Rivlin hyperelastic strain energy function, to describe the guinea pig spinal cord white matter. Model parameters were derived from a combination of inverse finite element analysis on transverse compression experiments and least squared error analysis applied to quasi-static longitudinal tensile tests. A comparison of the residual errors between the predicted response and the experimental measurements indicated that the transversely isotropic constitutive law that incorporates an offset stretch reduced the error by a factor of four when compared to other commonly used models.     

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.     

Effect of Spinal Cord Compression on Local Vascular Blood Flow and Perfusion Capacity

Spinal cord injury (SCI) can induce prolonged spinal cord compression that may result in a reduction of local tissue perfusion, progressive ischemia, and potentially irreversible tissue necrosis. Due to the combination of risk factors and the varied presentation of symptoms, the appropriate method and time course for clinical intervention following SCI are not always evident. In this study, a three-dimensional finite element fluid-structure interaction model of the cervical spinal cord was developed to examine how traditionally sub-clinical compressive mechanical loads impact spinal arterial blood flow. The spinal cord and surrounding dura mater were modeled as linear elastic, isotropic, and incompressible solids, while blood was modeled as a single-phased, incompressible Newtonian fluid. Simulation results indicate that anterior, posterior, and anteroposterior compressions of the cervical spinal cord have significantly different ischemic potentials, with prediction that the posterior component of loading elevates patient risk due to the concomitant reduction of blood flow in the arterial branches. Conversely, anterior loading compromises flow through the anterior spinal artery but minimally impacts branch flow rates. The findings of this study provide novel insight into how sub-clinical spinal cord compression could give rise to certain disease states, and suggest a need to monitor spinal artery perfusion following even mild compressive loading.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

The development of an improved physical surrogate model of the human spinal cord—Tension and transverse compression

To prevent spinal cord injury, optimize treatments for it, and better understand spinal cord pathologies such as spondylotic myelopathy, the interaction between the spinal column and the spinal cord during injury and pathology must be understood. The spinal cord is a complex and very soft tissue that changes properties rapidly after death and is difficult to model. Our objective was to develop a physical surrogate spinal cord with material properties closely corresponding to the in vivo human spinal cord that would be suitable for studying spinal cord injury under a variety of injurious conditions. Appropriate target material properties were identified from published studies and several candidate surrogate materials were screened, under uniaxial tension, in a materials testing machine. QM Skin 30, a silicone elastomer, was identified as the most appropriate material. Spinal cords manufactured from QM Skin 30 were tested under uniaxial tension and transverse compression. Rectangular specimens of QM Skin 30 were also tested under uniform compression. QM Skin 30 produced surrogate cords with a Young's modulus in tension and compression approximately matching values reported for in vivo animal spinal cords (0.25 and 0.20 MPa, respectively). The tensile and compressive Young's modulus and the behavior of the surrogate cord simulated the nonlinear behavior of the in vivo spinal cord.     

Unconfined compression of white matter

The porous properties of brain tissue are important for understanding normal and abnormal cerebrospinal fluid flow in the brain. In this study, a poroviscoelastic model was fitted to the stress relaxation response of white matter in unconfined compression performed under a range of low strain rates. A set of experiments was also performed on the tissue samples using a no-slip boundary condition. Results from these experiments demonstrated that the rheological response of the white matter is primarily governed by the intrinsic viscoelastic properties of the solid phase. The permeability of white matter was found to be of the order of 10(-12) m4/Ns.     

An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment

This contribution presents a novel constitutive model in order to simulate an orthotropic rate-dependent behaviour of the passive myocardium at finite strains. The motivation for the consideration of orthotropic viscous effects in a constitutive level lies in the disagreement between theoretical predictions and experimentally observed results. In view of experimental observations, the material is deemed as nearly incompressible, hyperelastic, orthotropic and viscous. The viscoelastic response is formulated by means of a rheological model consisting of a spring coupled with a Maxwell element in parallel. In this context, the isochoric free energy function is decomposed into elastic equilibrium and viscous non-equilibrium parts. The baseline elastic response is modelled by the orthotropic model of Holzapfel and Ogden [Holzapfel GA, Ogden RW. 2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans Roy Soc A Math Phys Eng Sci. 367:3445–3475]. The essential aspect of the proposed model is the account of distinct relaxation mechanisms for each orientation direction. To this end, the non-equilibrium response of the free energy function is constructed in the logarithmic strain space and additively decomposed into three anisotropic parts, denoting fibre, sheet and normal directions each accompanied by a distinct dissipation potential governing the evolution of viscous strains associated with each orientation direction. The evolution equations governing the viscous flow have an energy-activated nonlinear form. The energy storage in the Maxwell branches has a quadratic form leading to a linear stress–strain response in the logarithmic strain space. On the numerical side, the algorithmic aspects suitable for the implicit finite element method are discussed in a Lagrangian setting. The model shows excellent agreement compared to experimental data obtained from the literature. Furthermore, the finite element simulations of a heart cycle carried out with the proposed model show significant deviations in the strain field relative to the elastic solution.     

Studies on expression of FSH and its anti-apoptotic effects on ischemia injury in rat spinal cord

Studies indicated that many tissues could express FSH. New functions of FSH have been recognized beyond reproduction regulation. However, no report has been made about the expression and function of FSH in rat spinal cord. Double-labeled immunofluorescence stain and in situ hybridization were used to study the co-localization of FSH with its receptor and co-localization of FSH with GnRH receptor in rat spinal cord. Spinal cord ischemia injury models were built, TUNEL stain and Fas immunostaining were made to observe the anti-apoptotic effects of FSH to neurons induced by spinal cord ischemia injury. The results found that some neurons and glias of rat spinal cord showed both FSH immunoreactivity and FSH mRNA positive signals; not only FSH and its receptor but also FSH and GnRH receptor co-located in cells of both gray matter and white matter; treatment with certain concentration of FSH before ischemia–reperfusion injury, less TUNEL positive cells and Fas positive cells were found in motor neurons of ventral gray matter in FSH experiment group than that in control group. These suggested that rat spinal cord could express FSH, it is also a target organ of FSH; FSH might exert functions through its receptor by paracrine or autocrine effects; GnRH in spinal cord might regulate FSH positive neurons through GnRH receptor; FSH might inhibit ischemia induced neuron apoptosis by down-regulating Fas expression in spinal cord.     

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 x 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 hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.     

CNS Cell Distribution and Axon Orientation Determine Local Spinal Cord Mechanical Properties

Mechanical signaling plays an important role in cell physiology and pathology. Many cell types, including neurons and glial cells, respond to the mechanical properties of their environment. Yet, for spinal cord tissue, data on tissue stiffness are sparse. To investigate the regional and direction-dependent mechanical properties of spinal cord tissue at a spatial resolution relevant to individual cells, we conducted atomic force microscopy (AFM) indentation and tensile measurements on acutely isolated mouse spinal cord tissue sectioned along the three major anatomical planes, and correlated local mechanical properties with the underlying cellular structures. Stiffness maps revealed that gray matter is significantly stiffer than white matter irrespective of directionality (transverse, coronal, and sagittal planes) and force direction (compression or tension) (K_g= ∼130 Pa vs. K_w= ∼70 Pa); both matters stiffened with increasing strain. When all data were pooled for each plane, gray matter behaved like an isotropic material under compression; however, subregions of the gray matter were rather heterogeneous and anisotropic. For example, in sagittal sections the dorsal horn was significantly stiffer than the ventral horn. In contrast, white matter behaved transversely isotropic, with the elastic stiffness along the craniocaudal (i.e., longitudinal) axis being lower than perpendicular to it. The stiffness distributions we found under compression strongly correlated with the orientation of axons, the areas of cell nuclei, and cellular in plane proximity. Based on these morphological parameters, we developed a phenomenological model to estimate local mechanical properties of central nervous system (CNS) tissue. Our study may thus ultimately help predicting local tissue stiffness, and hence cell behavior in response to mechanical signaling under physiological and pathological conditions, purely based on histological data.     

Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis

A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.     

Volar/dorsal compressive mechanical behavior of the transverse carpal ligament

Mechanical insult to the median nerve caused by contact with the digital flexor tendons and/or carpal tunnel boundaries may contribute to the development of carpal tunnel syndrome. Since the transverse carpal ligament (TCL) comprises the volar boundary of the carpal tunnel, its mechanics in part govern the potential insult to the median nerve. Using unconfined compression testing in combination with a finite element-based optimization process, nominal stiffness measurements and first-order Ogden hyperelastic material coefficients (μ and α ) were determined to describe the volar/dorsal compressive behavior of the TCL. Five different locations on the TCL were tested, three of which were deep to the origins of the thenar and hypothenar muscles. The average (± standard deviation) low-strain and high-strain TCL stiffness values in compression sites outside the muscle attachment region were 3.6 N/mm (±2.7) and 28.0 N/mm (±20.2), respectively. The average stiffness values at compression sites with muscle attachments were notably lower, with low-strain and high-strain stiffness values of 1.2 N/mm (±0.5) and 9.7 N/mm (±4.8), respectively. The average Ogden coefficients for the muscle attachment region were 51.6 kPa (±16.5) for μ and 16.5 (±2.0) for α, while coefficients for the non-muscle attachment region were 117.8 kPa (±86.8) for μ and 17.2 (±1.6) for α. These TCL compressive mechanical properties can help inprove computational models, which can be used to provide insight into the mechanisms of median nerve injury leading to the onset of carpal tunnel syndrome symptoms.     

Application of the u-p finite element method to the study of articular cartilage.

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the 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.     

An axonal strain injury criterion for traumatic brain injury

Computational models are often used as tools to study traumatic brain injury. The fidelity of such models depends on the incorporation of an appropriate level of structural detail, the accurate representation of the material behavior, and the use of an appropriate measure of injury. In this study, an axonal strain injury criterion is used to estimate the probability of diffuse axonal injury (DAI), which accounts for a large percentage of deaths due to brain trauma and is characterized by damage to neural axons in the deep white matter regions of the brain. We present an analytical and computational model that treats the white matter as an anisotropic, hyperelastic material. Diffusion tensor imaging is used to incorporate the structural orientation of the neural axons into the model. It is shown that the degree of injury that is predicted in a computational model of DAI is highly dependent on the incorporation of the axonal orientation information and the inclusion of anisotropy into the constitutive model for white matter.     

A Surgery Protocol for Adult Zebrafish Spinal Cord Injury

Adult zebrafish has a remarkable capability to recover from spinal cord injury,providing an excellent model for studying neuro-regeneration. Here we list equipment and reagents,and give a detailed protocol for complete transection of the adult zebrafish spinal cord. In this protocol,potential problems and their solutions are described so that the zebrafish spinal cord injury model can be more easily and reproducibly performed.In addition,two assessments are introduced to monitor the success of the surgery and functional recovery:one test to assess free swimming capability and the other test to assess extent of neuroregeneration by in vivo anterograde axonal tracing.In the swimming behavior test,successful complete spinal cord transection is monitored by the inability of zebrafish to swim freely for 1 week after spinal cord injury,followed by the gradual reacquisition of full locomotor ability within 6 weeks after injury.As a morphometric correlate,anterograde axonal tracing allows the investigator to monitor the ability of regenerated axons to cross the lesion site and increasingly extend into the gray and white matter with time after injury,confirming functional recovery.This zebrafish model provides a paradigm for recovery from spinal cord injury,enabling the identification of pathways and components of neuroregeneration.     

Protein deiminases: new players in the developmentally regulated loss of neural regenerative ability

Spinal cord regenerative ability is lost with development, but the mechanisms underlying this loss are still poorly understood. In chick embryos, effective regeneration does not occur after E13, when spinal cord injury induces extensive apoptotic response and tissue damage. As initial experiments showed that treatment with a calcium chelator after spinal cord injury reduced apoptosis and cavitation, we hypothesized that developmentally regulated mediators of calcium-dependent processes in secondary injury response may contribute to loss of regenerative ability. To this purpose we screened for such changes in chick spinal cords at stages of development permissive (E11) and non-permissive (E15) for regeneration. Among the developmentally regulated calcium-dependent proteins identified was PAD3, a member of the peptidylarginine deiminase (PAD) enzyme family that converts protein arginine residues to citrulline, a process known as deimination or citrullination. This post-translational modification has not been previously associated with response to injury. Following injury, PAD3 up-regulation was greater in spinal cords injured at E15 than at E11. Consistent with these differences in gene expression, deimination was more extensive at the non-regenerating stage, E15, both in the gray and white matter. As deimination paralleled the extent of apoptosis, we investigated the effect of blocking PAD activity on cell death and deiminated-histone 3, one of the PAD targets we identified by mass-spectrometry analysis of spinal cord deiminated proteins. Treatment with the PAD inhibitor, Cl-amidine, reduced the abundance of deiminated-histone 3, consistent with inhibition of PAD activity, and significantly reduced apoptosis and tissue loss following injury at E15. Altogether, our findings identify PADs and deimination as developmentally regulated modulators of secondary injury response, and suggest that PADs might be valuable therapeutic targets for spinal cord injury.     

Measurement of the hyperelastic properties of ex vivo brain tissue slices

The elastic and hyperelastic properties of brain tissue are of interest to the medical research community as there are several applications where accurate characterization of these properties is crucial for an accurate outcome. The linear response is applicable to brain elastography, while the non-linear response is of interest for surgical simulation programs. Because of the biological differences between gray and white matter, it is reasonable to expect a difference in their mechanical properties. The goal of this work is to characterize the elastic and hyperelastic properties of the brain gray and white matter. In this method, force-displacement data of these tissues were acquired from 25 different brain samples using an indentation apparatus. These data were processed with an inverse problem algorithm using finite element method as the forward problem solver. Young's modulus and the hyperelastic parameters corresponding to the commonly used Polynomial, Yeoh, Arruda-Boyce, and Ogden models were obtained. The parameters characterizing the linear and non-linear mechanical behavior of gray and white matters were found to be significantly different. Young's modulus was 1787±186 and 1195±157Pa for white matter and gray matter, respectively. Among hyperelastic models, due to its accuracy, fewer parameters and shorter computational time requirements, Yeoh model was found to be the most suitable. Due to the significant differences between the linear and non-linear tissue response, we conclude that incorporating these differences into brain biomechanical models is necessary to increase accuracy.