Comparison of in vivo and ex vivo viscoelastic behavior of the spinal cord

Regional biomechanical characterization of the spinal cord tissue: dynamic mechanical response

Characterizing the dynamic mechanical properties of spinal cord tissue is deemed important for developing a comprehensive knowledge of the mechanisms underlying spinal cord injury. However, complex viscoelastic properties are vastly underexplored due to the spinal cord shows heterogeneous properties. To investigate regional differences in the biomechanical properties of spinal cord, we provide a mechanical characterization method (i.e., dynamic mechanical analysis) that facilitates robust measurement of spinal cord ex vivo, at small deformations, in the dynamic regimes. Load-unload cycles were applied to the tissue surface at sinusoidal frequencies of 0.05, 0.10, 0.50 and 1.00 Hz ex vivo within 2 h post mortem. We report the main response features (e.g., nonlinearities, rate dependencies, hysteresis and conditioning) of spinal cord tissue dependent on anatomical origin, and quantify the viscoelastic properties through the measurement of peak force, moduli, and hysteresis and energy loss. For all three anatomical areas (cervical, thoracic, and lumbar spinal cord tissues), the compound, storage, and loss moduli responded similarly to increasing strain rates. Notably, the complex modulus values of ex vivo spinal cord tissue rose nonlinearly with rising test frequency. Additionally, at every strain rate, it was shown that the tissue in the thoracic spinal cord was significantly more rigid than the tissue in the cervical or lumbar spinal cord, with compound modulus values roughly 1.5-times that of the lumbar region. At strain rates between 0.05 and 0.50 Hz, tan δ values for thoracic (that is, 0.26, 0.25, 0.06, respectively) and lumbar (that is, 0.27, 0.25, 0.07, respectively) spinal cord regions were similar, respectively, which were higher than cervical (that is, 0.21, 0.21, 0.04, respectively) region. The conditioning effects tend to be greater at relative higher deformation rates. Interestingly, no marked difference of conditioning ratios is observed among all three anatomical regions, regardless of loading rate. These findings lay a foundation for further comparison between healthy and diseased spinal cord to the future development of spinal cord scaffold and helps to advance our knowledge of neuroscience.

Identification of constitutive materials of bi-layer soft tissues from multimodal indentations

The personalisation of finite element models is an important problem in the biomechanical fields where subject-specific analyses are fundamental, particularly in studying soft tissue mechanics. The personalisation includes the choice of the constitutive law of the model's material, as well as the choice of the material parameters. In vivo identification of the material properties of soft tissues is challenging considering the complex behaviour of soft tissues that are, among other things, non-linear hyperelastic and heterogeneous. Hybrid experimental-numerical methods combining in vivo indentations and inverse finite element analyses are common to identify these material parameters. Yet, the uniqueness and the uncertainty of the multi-material hyperelastic model have not been evaluated. This study presents a sensitivity analysis performed on synthetic indentation data to investigate the identification uncertainties of the material parameters in a bi-material thigh phantom. Synthetic numerical data, used to replace experimental measurements, considered several measurement modalities: indenter force and displacement, stereo-camera 3D digital image correlation of the indented surface, and ultrasound B-mode images. A finite element model of the indentation was designed with either Ogden-Moerman or Mooney-Rivlin constitutive laws for both materials. The parameters' identifiability (i.e. the possibility of converging to a unique parameter set within an acceptable margin of error) was assessed with various cost functions formulated using the different synthetic data sets. The results underline the need for multiple experimental modalities to reduce the uncertainty of the identified parameters. Additionally, the experimental error can impede the identification of a unique parameter set, and the cost function depends on the constitutive law. This study highlights the need for sensitivity analyses before the design of the experimental protocol. Such studies can also be used to define the acceptable range of errors in the experimental measurement. Eventually, the impact of the evaluated uncertainty of the identified parameters should be further investigated according to the purpose of the finite element modelling.

The mechanical properties of the spinal cord: a systematic review

BACKGROUND CONTENT

Spinal cord compression is a source of pathology routinely seen in clinical practice. However, there remain unanswered questions surrounding both the understanding of pathogenesis and the best method of treatment. This arises from limited real-life testing of the mechanical properties of the spinal cord, either through cadaveric human specimens or animal testing, both of which suffer from methodological, as well as ethical, issues.

PURPOSE

To conduct a review of the literature on the mechanical properties of the spinal cord.

STUDY DESIGN/SETTING

A systematic review of the literature on the mechanical properties of the spinal cord is undertaken.

PATIENT SAMPLE

All literature reporting the testing of the mechanical properties of the spinal cord.

OUTCOME MEASURES

Reported physiological mechanical properties of the spinal cord.

METHODS

The methodological quality of the studies has been assessed within the ARRIVE guidelines using the CAMARADES framework and SYRCLE's risk of bias tool. This paper details the methodologies and results of the reported testing.

RESULTS

We show that (1) the research quality of previous work does not follow published guidelines on animal treatment or risk of bias, (2) no standard protocol has been employed for sample preparation or mechanical testing, (3) this leads to a wide distribution of results for the tested mechanical properties, not applicable to the living human or animal, and (4) animal testing is not a good proxy for human application.

CONCLUSIONS

The findings summarize the sum of current knowledge inherent to the mechanical properties of the spinal cord and may contribute to the development of a physical model which is applicable to the living human for analysis and testing in a controlled and repeatable fashion. Such a model would be the basis for further clinical research to improve outcomes from spinal cord compression.

Diametric compression of rings to analyze Guadua bamboo creep on the transverse plane

Guadua angustifolia is a bamboo species that has been used in construction since it is an excellent sustainable material. However, it creeps under sustained loading, modifying the structural behavior of culms and joints. Thus, this study was aimed at describing the creep behavior of Guadua on the transverse plane. To this end, 60 Guadua rings were submitted to a diametric compression load by means of steel blocks, while the diametric displacement was measured over time. In tests conducted for up to 90 days, the displacements did not reach a stationary value. A high degree of deformation over time was measured, which was about 2-3 times that reported for bamboo creep under axial bending. The data were successfully fitted to a generalized Maxwell model and a Burgers model. Model parameters were not significantly different when being fitted at 30, 50, 60, and 90 days, suggesting that parameters of viscoelastic models to represent bamboo creep on the transverse plane can be captured with tests lasting 30 days. Eleven rings failed at a stress level of 3.64 MPa (Coefficient of variation CV = 0.22) and a strain level of 0.0373 (CV = 0.20) which are 39% lower and 78% higher than the failure stress and strain, respectively, obtained in static control tests. The substantial creep on the transverse plane indicates that the stiffness and capacity of some types of bamboo joints may be drastically reduced over time. Fitted parameters may be used in theoretical models to assess the performance of bamboo elements and joints under transverse loading over time.

An atlas of the heterogeneous viscoelastic brain with local power-law attenuation synthesised using Prony-series

This review addresses the acute need to acknowledge the mechanical heterogeneity of brain matter and to accurately calibrate its local viscoelastic material properties accordingly. Specifically, it is important to compile the existing and disparate literature on attenuation power-laws and dispersion to make progress in wave physics of brain matter, a field of research that has the potential to explain the mechanisms at play in diffuse axonal injury and mild traumatic brain injury in general. Currently, viscous effects in the brain are modelled using Prony-series, i.e., a sum of decaying exponentials at different relaxation times. Here we collect and synthesise the Prony-series coefficients appearing in the literature for twelve regions: brainstem, basal ganglia, cerebellum, corona radiata, corpus callosum, cortex, dentate gyrus, hippocampus, thalamus, grey matter, white matter, homogeneous brain, and for eight different mammals: pig, rat, human, mouse, cow, sheep, monkey and dog. Using this data, we compute the fractional-exponent attenuation power-laws for different tissues of the brain, the corresponding dispersion laws resulting from causality, and the averaged Prony-series coefficients. STATEMENT OF SIGNIFICANCE: Traumatic brain injuries are considered a silent epidemic and finite element methods (FEMs) are used in modelling brain deformation, requiring access to viscoelastic properties of brain. To the best of our knowledge, this work presents 1) the first multi-frequency viscoelastic atlas of the heterogeneous brain, 2) the first review focusing on viscoelastic modelling in both FEMs and experimental works, 3) the first attempt to conglomerate the disparate existing literature on the viscoelastic modelling of the brain and 4) the largest collection of viscoelastic parameters for the brain (212 different Prony-series spanning 12 different tissues and 8 different animal surrogates). Furthermore, this work presents the first brain atlas of attenuation power-laws essential for modelling shear waves in brain.

The mechanical behavior of bovine spinal cord white matter under various strain rate conditions: tensile testing and visco-hyperelastic constitutive modeling

The mechanical behavior of the white matter is important for estimating the damage of the spinal cord during accidents. In this study, we conducted uniaxial tension testing in vitro of bovine spinal cord white matter under extremely high strain rate conditions (up to 100 s^-1). A visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the bovine spinal cord white matter was developed. A set of material constants was obtained using a Levenberg-Marquardt fitting algorithm to match the uniaxial tension experimental data with various strain rates. Our experimental data confirmed that the modulus and tensile strength increased when the strain rate is higher. For the extremely high strain rate condition (100 s^-1), we found that both the modulus and failure stress significantly increased compared with the low strain rate case. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the developed constitutive model will allow researchers to perform more realistic finite element modeling and simulation of spinal cord injury damage under various complicated conditions.

A Critical Comparison of Comparators Used to Demonstrate Credibility of Physics-Based Numerical Spine Models

The ability of new medical devices and technology to demonstrate safety and effectiveness, and consequently acquire regulatory approval, has been dependent on benchtop, in vitro, and in vivo evidence and experimentation. Regulatory agencies have recently begun accepting computational models and simulations as credible evidence for virtual clinical trials and medical device development. However, it is crucial that any computational model undergo rigorous verification and validation activities to attain credibility for its context of use before it can be accepted for regulatory submission. Several recently published numerical models of the human spine were considered for their implementation of various comparators as a means of model validation. The comparators used in each published model were examined and classified as either an engineering or natural comparator. Further, a method of scoring the comparators was developed based on guidelines from ASME V&V40 and the draft guidance from the US FDA, and used to evaluate the pertinence of each comparator in model validation. Thus, this review article aimed to score the various comparators used to validate numerical models of the spine in order to examine the comparator's ability to lend credibility towards computational models of the spine for specific contexts of use.

Strain-Dependent Stress Relaxation Behavior of Healthy Right Ventricular Free Wall

The increasing evidence of stress-strain hysteresis in large animal or human myocardium calls for extensive characterizations of the passive viscoelastic behavior of the myocardium. Several recent studies have investigated and modeled the viscoelasticity of the left ventricle while the right ventricle (RV) viscoelasticity remains poorly understood. Our goal was to characterize the biaxial viscoelastic behavior of RV free wall (RVFW) using two modeling approaches. We applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) theories to experimental stress relaxation data from healthy adult ovine. A three-term Prony series relaxation function combined with an Ogden strain energy density function were used in the QLV modeling, while a power-law formulation was adopted in the NLV approach. The ovine RVFW exhibited an anisotropic and strain-dependent viscoelastic behavior relative to anatomical coordinates, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. From the QLV fitting, the relaxation term associated with the largest time constant played the dominant role in the overall relaxation behavior at all strains from early to late diastole, whereas the term associated with the smallest time constant was pronounced only at low strains at early diastole. From the NLV fitting, the parameters showed a nonlinear dependence on the strain. Overall, our study characterized the anisotropic, nonlinear viscoelasticity to capture the elastic and viscous resistances of the RVFW during diastole. These findings deepen our understanding of RV myocardium dynamic mechanical properties. STATEMENT OF SIGNIFICANCE: Although significant progress has been made to understand the passive elastic behavior of the right ventricle free wall (RVFW), its viscoelastic behavior remains poorly understood. In this study, we originally applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) models to published experimental data from healthy ovine RVFW. Our results revealed an anisotropic and strain-dependent viscoelastic behavior of the RVFW. The parameters from the NLV fitting showed nonlinear relationships with the strain, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. These findings characterize the anisotropic, nonlinear viscoelasticity of RVFW to fully capture the total (elastic and viscous) resistance that is critical to diastolic function.

Effect of Velocity and Contact Stress Area on the Dynamic Behavior of the Spinal Cord Under Different Testing Conditions

Knowledge of the dynamic behavior of the spinal cord under different testing conditions is critical for our understanding of biomechanical mechanisms of spinal cord injury. Although velocity and contact stress area are known to affect external mechanical stress or energy upon sudden traumatic injury, quantitative investigation of the two clinically relevant biomechanical variables is limited. Here, freshly excised rat spinal-cord–pia-arachnoid constructs were tested through indentation using indenters of different sizes (radii: 0.25, 0.50, and 1.00 mm) at various loading rates ranging from 0.04 to 0.20 mm/s. This analysis found that the ex vivo specimen displayed significant nonlinear viscoelasticity at <10% of specimen thickness depth magnitudes. At higher velocity and larger contact stress area, the cord withstood a higher peak load and exhibited more sensitive mechanical relaxation responses (i.e., increasing amplitude and speed of the drop in peak load). Additionally, the cord became stiffer (i.e., increasing elastic modulus) and softer (i.e., decreasing elastic modulus) at a higher velocity and larger contact stress area, respectively. These findings will improve our understanding of the real-time complex biomechanics involved in traumatic spinal cord injury.

Comparison of numerical methods for cerebrospinal fluid representation and fluid-structure interaction during transverse impact of a finite element spinal cord model

Spinal cord impacts can have devastating consequences. Computational models can investigate such impacts but require biofidelic numerical representations of the neural tissues and fluid-structure interaction with cerebrospinal fluid. Achieving this biofidelity is challenging, particularly for efficient implementation of the cerebrospinal fluid in full computational human body models. The goal of this study was to assess the biofidelity and computational efficiency of fluid-structure interaction methods representing the cerebrospinal fluid interacting with the spinal cord, dura, and pia mater using experimental pellet impact test data from bovine spinal cords. Building on an existing finite element model of the spinal cord and pia mater, an orthotropic hyperelastic constitutive model was proposed for the dura mater and fit to literature data. The dura mater and cerebrospinal fluid were integrated with the existing finite element model to assess four fluid-structure interaction methods under transverse impact: Lagrange, pressurized volume, smoothed particle hydrodynamics, and arbitrary Lagrangian-Eulerian. The Lagrange method resulted in an overly stiff mechanical response, whereas the pressurized volume method over-predicted compression of the neural tissues. Both the smoothed particle hydrodynamics and arbitrary Lagrangian-Eulerian methods were able to effectively model the impact response of the pellet on the dura mater, outflow of the cerebrospinal fluid, and compression of the spinal cord; however, the arbitrary Lagrangian-Eulerian compute time was approximately five times higher than smoothed particle hydrodynamics. Crucial to implementation in human body models, the smoothed particle hydrodynamics method provided a computationally efficient and representative approach to model spinal cord fluid-structure interaction during transverse impact.

Tensile mechanical properties of the cervical, thoracic and lumbar porcine spinal meninges

BACKGROUND

The spinal meninges play a mechanical protective role for the spinal cord. Better knowledge of the mechanical behavior of these tissues wrapping the cord is required to accurately model the stress and strain fields of the spinal cord during physiological or traumatic motions. Then, the mechanical properties of meninges along the spinal canal are not well documented. The aim of this study was to quantify the elastic meningeal mechanical properties along the porcine spinal cord in both the longitudinal direction and in the circumferential directions for the dura-arachnoid maters complex (DAC) and solely in the longitudinal direction for the pia mater. This analysis was completed in providing a range of isotropic hyperelastic coefficients to take into account the toe region.

METHODS

Six complete spines (C0 - L5) were harvested from pigs (2-3 months) weighing 43±13 kg. The mechanical tests were performed within 12 h post mortem. A preload of 0.5 N was applied to the pia mater and of 2 N to the DAC samples, followed by 30 preconditioning cycles. Specimens were then loaded to failure at the same strain rate 0.2 mm/s (approximately 0.02/s, traction velocity/length of the sample) up to 12 mm of displacement.

RESULTS

The following mean values were proposed for the elastic moduli of the spinal meninges. Longitudinal DAC elastic moduli: 22.4 MPa in cervical, 38.1 MPa in thoracic and 36.6 MPa in lumbar spinal levels; circumferential DAC elastic moduli: 20.6 MPa in cervical, 21.2 MPa in thoracic and 12.2 MPa in lumbar spinal levels; and longitudinal pia mater elastic moduli: 18.4 MPa in cervical, 17.2 MPa in thoracic and 19.6 MPa in lumbar spinal levels.

DISCUSSION

The variety of mechanical properties of the spinal meninges suggests that it cannot be regarded as a homogenous structure along the whole length of the spinal cord.

The posterior eye with age-related macular degeneration has isotropic and nonlinear viscoelastic properties

Here we characterize and compare the anisotropic and nonlinear viscoelastic properties of the posterior eye of advanced dry age-related macular degeneration (AMD) patients and age-matched normal subjects. Ten normal horizontal, ten normal vertical, ten AMD horizontal, and ten AMD vertical strips of the macular retina and the underlying choroid and sclera were preloaded, preconditioned, and subjected to incremental stress-relaxation tests in body-temperature saline. The stress-relaxation response was characterized by a fully nonlinear viscoelastic formulation in which the relaxation modulus was approximated by a Prony series and a second-order polynomial using the comprehensive viscoelastic characterization method. Normal retina, choroid, and sclera were found to be anisotropic, whereas AMD tissues were isotropic. AMD retina and choroid showed greater stress-relaxation response than normal tissues (p < 0.05), whereas AMD sclera had smaller stress-relaxation response than normal tissue (p < 0.05). The nonlinear viscoelastic stress-strain relationship of the posterior eye is hence describable for the first time.

Stiffness-matched biomaterial implants for cell delivery: clinical, intraoperative ultrasound elastography provides a 'target' stiffness for hydrogel synthesis in spinal cord injury

Safe hydrogel delivery requires stiffness-matching with host tissues to avoid iatrogenic damage and reduce inflammatory reactions. Hydrogel-encapsulated cell delivery is a promising combinatorial approach to spinal cord injury therapy, but a lack of in vivo clinical spinal cord injury stiffness measurements is a barrier to their use in clinics. We demonstrate that ultrasound elastography – a non-invasive, clinically established tool – can be used to measure spinal cord stiffness intraoperatively in canines with spontaneous spinal cord injury. In line with recent experimental reports, our data show that injured spinal cord has lower stiffness than uninjured cord. We show that the stiffness of hydrogels encapsulating a clinically relevant transplant population (olfactory ensheathing cells) can also be measured by ultrasound elastography, enabling synthesis of hydrogels with comparable stiffness to canine spinal cord injury. We therefore demonstrate proof-of-principle of a novel approach to stiffness-matching hydrogel-olfactory ensheathing cell implants to ‘real-life’ spinal cord injury values; an approach applicable to multiple biomaterial implants for regenerative therapies.

Current Understanding of the Biomechanics of Ventricular Tissues in Heart Failure

Heart failure is the leading cause of death worldwide, and the most common cause of heart failure is ventricular dysfunction. It is well known that the ventricles are anisotropic and viscoelastic tissues and their mechanical properties change in diseased states. The tissue mechanical behavior is an important determinant of the function of ventricles. The aim of this paper is to review the current understanding of the biomechanics of ventricular tissues as well as the clinical significance. We present the common methods of the mechanical measurement of ventricles, the known ventricular mechanical properties including the viscoelasticity of the tissue, the existing computational models, and the clinical relevance of the ventricular mechanical properties. Lastly, we suggest some future research directions to elucidate the roles of the ventricular biomechanics in the ventricular dysfunction to inspire new therapies for heart failure patients.

Development of a Multimodal Apparatus to Generate Biomechanically Reproducible Spinal Cord Injuries in Large Animals

Rodents are widespread animal models in spinal cord injury (SCI) research. They have contributed to obtaining important information. However, some treatments only tested in rodents did not prove efficient in clinical trials. This is probably a result of significant differences in the physiology, anatomy, and complexity between humans and rodents. To bridge this gap in a better way, a few research groups use pig models for SCI. Here we report the development of an apparatus to perform biomechanically reproducible SCI in large animals, including pigs. We present the iterative process of engineering, starting with a weight-drop system to ultimately produce a spring-load impactor. This device allows a graded combination of a contusion and a compression injury. We further engineered a device to entrap the spinal cord and prevent it from escaping at the moment of the impact. In addition, it provides identical resistance around the cord, thereby, optimizing the inter-animal reproducibility. We also present other tools to straighten the vertebral column and to ease the surgery. Sensors mounted on the impactor provide information to assess the inter-animal reproducibility of the impacts. Further evaluation of the injury strength using neurophysiological recordings, MRI scans, and histology shows consistency between impacts. We conclude that this apparatus provides biomechanically reproducible spinal cord injuries in pigs.

Comparing Predictive Accuracy and Computational Costs for Viscoelastic Modeling of Spinal Cord Tissues

The constitutive equation used to characterize and model spinal tissues can significantly influence the conclusions from experimental and computational studies. Therefore, researchers must make critical judgements regarding the balance of computational efficiency and predictive accuracy necessary for their purposes. The objective of this study is to quantitatively compare the fitting and prediction accuracy of linear viscoelastic (LV), quasi-linear viscoelastic (QLV), and (fully) non-linear viscoelastic (NLV) modeling of spinal-cord-pia-arachnoid-construct (SCPC), isolated cord parenchyma, and isolated pia-arachnoid-complex (PAC) mechanics in order to better inform these judgements. Experimental data collected during dynamic cyclic testing of each tissue condition were used to fit each viscoelastic formulation. These fitted models were then used to predict independent experimental data from stress-relaxation testing. Relative fitting accuracy was found not to directly reflect relative predictive accuracy, emphasizing the need for material model validation through predictions of independent data. For the SCPC and isolated cord, the NLV formulation best predicted the mechanical response to arbitrary loading conditions, but required significantly greater computational run time. The mechanical response of the PAC under arbitrary loading conditions was best predicted by the QLV formulation.

Viscoelasticity of spinal cord and meningeal tissues

Compared to the outer dura mater, the mechanical behavior of spinal pia and arachnoid meningeal layers has received very little attention in the literature. This is despite experimental evidence of their importance with respect to the overall spinal cord stiffness and recovery following compression. Accordingly, inclusion of the mechanical contribution of the pia and arachnoid maters would improve the predictive accuracy of finite element models of the spine, especially in the distribution of stresses and strain through the cord's cross-section. However, to-date, only linearly elastic moduli for what has been previously identified as spinal pia mater is available in the literature. This study is the first to quantitatively compare the viscoelastic behavior of isolated spinal pia-arachnoid-complex, neural tissue of the spinal cord parenchyma, and intact construct of the two. The results show that while it only makes up 5.5% of the overall cross-sectional area, the thin membranes of the innermost meninges significantly affect both the elastic and viscous response of the intact construct. Without the contribution of the pia and arachnoid maters, the spinal cord has very little inherent stiffness and experiences significant relaxation when strained. The ability of the fitted non-linear viscoelastic material models of each condition to predict independent data within experimental variability supports their implementation into future finite element computational studies of the spine.

STATEMENT OF SIGNIFICANCE

The neural tissue of the spinal cord is surrounded by three fibrous layers called meninges which are important in the behavior of the overall spinal-cord-meningeal construct. While the mechanical properties of the outermost layer have been reported, the pia mater and arachnoid mater have received considerably less attention. This study is the first to directly compare the behavior of the isolated neural tissue of the cord, the isolated pia-arachnoid complex, and the construct of these individual components. The results show that, despite being very thin, the inner meninges significantly affect the elastic and time-dependent response of the spinal cord, which may have important implications for studies of spinal cord injury.