Nonlinear viscoelastic characterization of the porcine spinal cord

Three-dimensional Spinal Canal Morphometric Analysis and Relevant Spinal Cord Occupational Ratios in Congenital Cervical Spinal Stenosis: A Classification Algorithm of the Stenosis Phenotypes and Data-driven Decompression Approach

OBJECTIVES

No standardized magnetic resonance imaging (MRI) parameters have defined the 3-dimensional morphoanatomy and relevant spinal cord occupation ratios (occupation of spinal cord dimensions/similar dimensions within the spinal canal) in congenital cervical stenosis (CCS).

METHODS

A retrospective, comparative analysis was conducted on 200 patients >18 years of age with myelopathy and CCS (mean age, 52.4 years) and 200 age-matched controls with no myelopathy or radiculopathy. The variables assessed from high resolution MRI included sagittal and axial spinal canal dimensions (MRI Torg-Pavlov ratios) from C3 to C7. Morphometric dimensions from the sagittal retrodiscal and retrovertebral regions as well as axial MRI dimensions were compared. Sagittal and axial spinal cord occupation ratios were defined and correlated with spinal canal dimensions.

RESULTS

Multivariate analyses indicated reduced sagittal and axial anteroposterior (AP) spinal canal dimensions and a large reduction in transverse spinal canal dimensions at all spinal levels. There was a small significant correlation between AP sagittal spinal canal dimensions and axial transverse spinal canal dimensions at C3-C5, but not at C5-C6. Small correlations were noted between AP sagittal spinal canal dimensions and AP axial spinal cord and axial cross-sectional area occupation ratios at C3-C6, but there was no correlation with axial mediolateral spinal cord occupation ratios.

CONCLUSIONS

The stenosis effect can involve any dimension, including the transverse spinal canal dimension, independent of other dimensions. Owing to the varied observed morphoanatomies, a classification algorithm that defines CCS specific phenotypes was formulated. Objectivizing the stenosis morphoanatomy may allow for data-driven patient-focused decompression approaches in the future.

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.

The alteration of the structure and macroscopic mechanical response of porcine patellar tendon by elastase digestion

Background: The treatment of patellar tendon injury has always been an unsolved problem, and mechanical characterization is very important for its repair and reconstruction. Elastin is a contributor to mechanics, but it is not clear how it affects the elasticity, viscoelastic properties, and structure of patellar tendon. Methods: The patellar tendons from six fresh adult experimental pigs were used in this study and they were made into 77 samples. The patellar tendon was specifically degraded by elastase, and the regional mechanical response and structural changes were investigated by: (1) Based on the previous study of elastase treatment conditions, the biochemical quantification of collagen, glycosaminoglycan and total protein was carried out; (2) The patellar tendon was divided into the proximal, central, and distal regions, and then the axial tensile test and stress relaxation test were performed before and after phosphate-buffered saline (PBS) or elastase treatment; (3) The dynamic constitutive model was established by the obtained mechanical data; (4) The structural relationship between elastin and collagen fibers was analyzed by two-photon microscopy and histology. Results: There was no statistical difference in mechanics between patellar tendon regions. Compared with those before elastase treatment, the low tensile modulus decreased by 75%-80%, the high tensile modulus decreased by 38%-47%, and the transition strain was prolonged after treatment. For viscoelastic behavior, the stress relaxation increased, the initial slope increased by 55%, the saturation slope increased by 44%, and the transition time increased by 25% after enzyme treatment. Elastin degradation made the collagen fibers of patellar tendon become disordered and looser, and the fiber wavelength increased significantly. Conclusion: The results of this study show that elastin plays an important role in the mechanical properties and fiber structure stability of patellar tendon, which supplements the structure-function relationship information of patellar tendon. The established constitutive model is of great significance to the prediction, repair and replacement of patellar tendon injury. In addition, human patellar tendon has a higher elastin content, so the results of this study can provide supporting information on the natural properties of tendon elastin degradation and guide the development of artificial patellar tendon biomaterials.

Role of the microtubule network in the passive anisotropic viscoelasticity of right ventricle with pulmonary hypertension progression

Cardiomyocytes are viscoelastic and contribute significantly to right ventricle (RV) mechanics. Microtubule, a cytoskeletal protein, has been shown to regulate cardiomyocyte viscoelasticity. Additionally, hypertrophied cardiomyocytes from failing myocardium have increased microtubules and cell stiffness. How the microtubules contribute to the tissue-level viscoelastic behavior in RV failure remains unknown. Our aim was to investigate the role of the microtubules in the passive anisotropic viscoelasticity of the RV free wall (RVFW) during pulmonary hypertension (PH) progression. Equibiaxial stress relaxation tests were conducted in the RVFW from healthy and PH rats under early (6%) and end (15%) diastolic strains, and at sub- (1Hz) and physiological (5Hz) stretch-rates. The RVFW viscoelasticity was also measured before and after the depolymerization of microtubules at 5Hz. In intact tissues, PH increased RV viscosity and elasticity at both stretch rates and strain levels, and the increase was stronger in the circumferential than longitudinal direction. At 6% of strain, the removal of microtubules reduced elasticity, viscosity, and the ratio of viscosity to elasticity in both directions and for both healthy and diseased RVs. However, at 15% of strain, the effect of microtubules was different between groups - both viscosity and elasticity were reduced in healthy RVs, but in the diseased RVs only the circumferential viscosity and the ratio of viscosity to elasticity were reduced. These data suggest that, at a large strain with collagen recruitment, microtubules play more significant roles in healthy RV tissue elasticity and diseased RV tissue viscosity. Our findings suggest cardiomyocyte cytoskeletons are critical to RV passive viscoelasticity under pressure overload. STATEMENT OF SIGNIFICANCE: This study investigated the impact of microtubules on the passive anisotropic viscoelasticity of the right ventricular (RV) free wall at healthy and pressure-overloaded states. We originally found that the microtubules contribute significantly to healthy and diseased RV viscoelasticity in both (longitudinal and circumferential) directions at early diastolic strains. At end diastolic strains (with the engagement of collagen fibers), microtubules contribute more to the tissue elasticity of healthy RVs and tissue viscosity of diseased RVs. Our findings reveal the critical role of microtubules in the anisotropic viscoelasticity of the RV tissue, and the altered contribution from healthy to diseased state suggests that therapies targeting microtubules may have potentials for RV failure patients.

Evaluating the Effects of Pulsed Electrical Stimulation on the Mechanical Behavior and Microstructure of Medulla Oblongata Tissues

The development of remote surgery hinges on comprehending the mechanical properties of the tissue at the surgical site. Understanding the mechanical behavior of the medulla oblongata tissue is instrumental for precisely determining the remote surgery implementation site. Additionally, exploring this tissue's response under electric fields can inform the creation of electrical stimulation therapy regimens. This could potentially reduce the extent of medulla oblongata tissue damage from mechanical compression. Various types of pulsed electric fields were integrated into a custom-built indentation device for this study. Experimental findings suggested that applying pulsed electric fields amplified the shear modulus of the medulla oblongata tissue. In the electric field, the elasticity and viscosity of the tissue increased. The most significant influence was noted from the low-frequency pulsed electric field, while the burst pulsed electric field had a minimal impact. At the microstructural scale, the application of an electric field led to the concentration of myelin in areas distant from the surface layer in the medulla oblongata, and the orderly structure of proteoglycans became disordered. The alterations observed in the myelin and proteoglycans under an electric field were considered to be the fundamental causes of the changes in the mechanical behavior of the medulla oblongata tissue. Moreover, cell polarization and extracellular matrix cavitation were observed, with transmission electron microscopy results pointing to laminar separation within the myelin at the ultrastructure scale. This study thoroughly explored the impact of electric field application on the mechanical behavior and microstructure of the medulla oblongata tissue, delving into the underlying mechanisms. This investigation delved into the changes and mechanisms in the mechanical behavior and microstructure of medulla oblongata tissue under the influence of electric fields. Furthermore, this study could serve as a reference for the development of electrical stimulation regimens in the central nervous system. The acquired mechanical behavior data could provide valuable baseline information to aid in the evolution of remote surgery techniques involving the medulla oblongata tissue.

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.

Ultrasound Shear Wave Elastography Quantitatively Assesses Tension Changes of Supraspinous/Interspinous Ligament Complex Under Varied Loads

BACKGROUND

Although interspinous and supraspinous ligaments of the lumbar spine are thought to contribute to spinal stability, little is known about their dynamic biomechanics. We demonstrate that shear wave elastography (SWE) offers a novel technique to noninvasively and quantitatively evaluate posterior spinous ligament complex functional loading and stiffness in different physiologic positions.

METHODS

We performed SWE and measured the length of the interspinous/supraspinous ligament complex in cadaveric torsos (N = 5), isolated ligaments (N = 10), and healthy volunteers (N = 9) to obtain length and shear wave velocity measurements. For cadavers and volunteers, SWE was utilized in 2 lumbar positions: lumbar spine flexion and extension. In addition, SWE was performed on isolated ligaments undergoing uniaxial tension to correlate shear wave velocities with experienced load.

RESULTS

Average shear wave velocity in cadaveric supraspinous/interspinous ligament complexes increased for lumbar levels (23%-43%) and most thoracic levels (0%-50%). This corresponded to an average increase in interspinous distance from extension to flexion for the lumbar spine (19%-63%) and thoracic spine (3%-8%). Volunteer spines also demonstrated an average increase in shear wave velocity from extension to flexion for both the lumbar spine (195% at L2-L3 to 200% at L4-L5) and thoracic spine (31% at T10-T11). There was an average increase in interspinous distance from extension to flexion for the lumbar spine (93% at L2-L3 to 127% at L4-L5) and thoracic spine (11% at T10-T11). In isolated ligaments, there was a positive correlation between applied tensile load and average shear wave velocity.

CONCLUSION

This study creates a foundation to apply SWE as a noninvasive tool for assessing the mechanical stiffness of posterior ligamentous structures and has potential applications in augmenting or evaluating these ligaments in patients with spine pathology.

CLINICAL RELEVANCE

The interspinous and supraspinous ligaments are critical soft tissue supports of the posterior lumbar spine. Disruption of these structures is thought to have a negative impact on spinal stability in trauma and spine deformities.

LEVEL OF EVIDENCE: 4

Alterations of biaxial viscoelastic properties of the right ventricle in pulmonary hypertension development in rest and acute stress conditions

Introduction: The right ventricle (RV) mechanical property is an important determinant of its function. However, compared to its elasticity, RV viscoelasticity is much less studied, and it remains unclear how pulmonary hypertension (PH) alters RV viscoelasticity. Our goal was to characterize the changes in RV free wall (RVFW) anisotropic viscoelastic properties with PH development and at varied heart rates. Methods: PH was induced in rats by monocrotaline treatment, and the RV function was quantified by echocardiography. After euthanasia, equibiaxial stress relaxation tests were performed on RVFWs from healthy and PH rats at various strain-rates and strain levels, which recapitulate physiological deformations at varied heart rates (at rest and under acute stress) and diastole phases (at early and late filling), respectively. Results and Discussion: We observed that PH increased RVFW viscoelasticity in both longitudinal (outflow tract) and circumferential directions. The tissue anisotropy was pronounced for the diseased RVs, not healthy RVs. We also examined the relative change of viscosity to elasticity by the damping capacity (ratio of dissipated energy to total energy), and we found that PH decreased RVFW damping capacity in both directions. The RV viscoelasticity was also differently altered from resting to acute stress conditions between the groups-the damping capacity was decreased only in the circumferential direction for healthy RVs, but it was reduced in both directions for diseased RVs. Lastly, we found some correlations between the damping capacity and RV function indices and there was no correlation between elasticity or viscosity and RV function. Thus, the RV damping capacity may be a better indicator of RV function than elasticity or viscosity alone. These novel findings on RV dynamic mechanical properties offer deeper insights into the role of RV biomechanics in the adaptation of RV to chronic pressure overload and acute stress.

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.

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.

Decellularized peripheral nerve as an injectable delivery vehicle for neural applications

Damage to the nervous system can result in loss of sensory and motor function, paralysis, or even death. To facilitate neural regeneration and functional recovery, researchers have employed biomaterials strategies to address both peripheral and central nervous system injuries. Injectable hydrogels that recapitulate native nerve extracellular matrix are especially promising for neural tissue engineering because they offer more flexibility for minimally invasive applications and provide a growth-permissive substrate for neural cell types. Here, we explore the development of injectable hydrogels derived from decellularized rat peripheral nerves (referred to as "injectable peripheral nerve [iPN] hydrogels"), which are processed using a newly developed sodium deoxycholate and DNase (SDD) decellularization method. We assess the gelation kinetics, mechanical properties, cell bioactivity, and drug release kinetics of the iPN hydrogels. The iPN hydrogels thermally gel when exposed to 37°C in under 20 min and have mechanical properties similar to neural tissue. The hydrogels demonstrate in vitro biocompatibility through support of Schwann cell viability and metabolic activity. Additionally, iPN hydrogels promote greater astrocyte spreading compared to collagen I hydrogels. Finally, the iPN is a promising delivery vehicle of drug-loaded microparticles for a combinatorial approach to neural injury therapies.

A Hyper-Viscoelastic Continuum-Level Finite Element Model of the Spinal Cord Assessed for Transverse Indentation and Impact Loading

Finite Element (FE) modelling of spinal cord response to impact can provide unique insights into the neural tissue response and injury risk potential. Yet, contemporary human body models (HBMs) used to examine injury risk and prevention across a wide range of impact scenarios often lack detailed integration of the spinal cord and surrounding tissues. The integration of a spinal cord in contemporary HBMs has been limited by the need for a continuum-level model owing to the relatively large element size required to be compatible with HBM, and the requirement for model development based on published material properties and validation using relevant non-linear material data. The goals of this study were to develop and assess non-linear material model parameters for the spinal cord parenchyma and pia mater, and incorporate these models into a continuum-level model of the spinal cord with a mesh size conducive to integration in HBM. First, hyper-viscoelastic material properties based on tissue-level mechanical test data for the spinal cord and hyperelastic material properties for the pia mater were determined. Secondly, the constitutive models were integrated in a spinal cord segment FE model validated against independent experimental data representing transverse compression of the spinal cord-pia mater complex (SCP) under quasi-static indentation and dynamic impact loading. The constitutive model parameters were fit to a quasi-linear viscoelastic model with an Ogden hyperelastic function, and then verified using single element test cases corresponding to the experimental strain rates for the spinal cord (0.32–77.22 s⁻¹) and pia mater (0.05 s⁻¹). Validation of the spinal cord model was then performed by re-creating, in an explicit FE code, two independent ex-vivo experimental setups: 1) transverse indentation of a porcine spinal cord-pia mater complex and 2) dynamic transverse impact of a bovine SCP. The indentation model accurately matched the experimental results up to 60% compression of the SCP, while the impact model predicted the loading phase and the maximum deformation (within 7%) of the SCP experimental data. This study quantified the important biomechanical contribution of the pia mater tissue during spinal cord deformation. The validated material models established in this study can be implemented in computational HBM.

Static-Dynamic Profited Viscoelastic Hydrogels for Motor-Clutch-Regulated Neurogenesis

Viscoelasticity, a time-scale mechanical feature of the native extracellular matrix (ECM), is reported to play crucial roles in plentiful cellular behaviors, whereas its effects on neuronal behavior and the underlying molecular mechanism still remain obscure. Challenges are faced in the biocompatible synthesis of neural ECM-mimicked scaffolds solely controlled with viscoelasticity and due to the lack of suitable models for neurons-viscoelastic matrix interaction. Herein, we report difunctional hyaluronan-collagen hydrogels prepared by a static-dynamic strategy. The hydrogels show aldehyde concentration-dependent viscoelasticity and similar initial elastic modulus, fibrillar morphology, swelling as well as degradability. Utilizing the resulting hydrogels, for the first time, we demonstrate matrix viscoelasticity-dependent neuronal responses, including neurite elongation and expression of neurogenic proteins. Then, a motor-clutch model modified with a tension dissipation component is developed to account for the molecular mechanism for viscoelasticity-sensitive neuronal responses. Moreover, we prove enhanced recovery of rat spinal cord injury by implanting cell-free viscoelastic grafts. As a pioneer finding on neurons-viscoelastic matrix interaction both in vitro and in vivo, this work provides intriguing insights not only into nerve repair but also into neuroscience and tissue engineering.

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.

Correlating Tissue Mechanics and Spinal Cord Injury: Patient-Specific Finite Element Models of Unilateral Cervical Contusion Spinal Cord Injury in Non-Human Primates

Non-human primate (NHP) models are the closest approximation of human spinal cord injury (SCI) available for pre-clinical trials. The NHP models, however, include broader morphological variability that can confound experimental outcomes. We developed subject-specific finite element (FE) models to quantify the relationship between impact mechanics and SCI, including the correlations between FE outcomes and tissue damage. Subject-specific models of cervical unilateral contusion SCI were generated from pre-injury MRIs of six NHPs. Stress and strain outcomes were compared with lesion histology using logit analysis. A parallel generic model was constructed to compare the outcomes of subject-specific and generic models. The FE outcomes were correlated more strongly with gray matter damage (0.29 < R² < 0.76) than white matter (0.18 < R² < 0.58). Maximum/minimum principal strain, Von-Mises and Tresca stresses showed the strongest correlations (0.31 < R² < 0.76) with tissue damage in the gray matter while minimum principal strain, Von-Mises stress, and Tresca stress best predicted white matter damage (0.23 < R² < 0.58). Tissue damage thresholds varied for each subject. The generic FE model captured the impact biomechanics in two of the four models; however, the correlations between FE outcomes and tissue damage were weaker than the subject-specific models (gray matter [0.25 < R² < 0.69] and white matter [R² < 0.06] except for one subject [0.26 < R² < 0.48]). The FE mechanical outputs correlated with tissue damage in spinal cord white and gray matters, and the subject-specific models accurately mimicked the biomechanics of NHP cervical contusion impacts.

A comprehensive finite element model of surgical treatment for cervical myelopathy

BACKGROUND

Cervical myelopathy is a common and debilitating chronic spinal cord dysfunction. Treatment includes anterior and/or posterior surgical intervention to decompress the spinal cord and stabilize the spine, but no consensus has been made as to the preferable surgical intervention. The objective of this study was to develop an finite element model of the healthy and myelopathic C2-T1 cervical spine and common anterior and posterior decompression techniques to determine how spinal cord stress and strain is altered in healthy and diseased states.

METHODS

A finite element model of the C2-T1 cervical spine, spinal cord, pia, dura, cerebral spinal fluid, and neural ligaments was developed and validated against in vivo human displacement data. To model cervical myelopathy, disc herniation and osteophytes were created at the C4-C6 levels. Three common surgical interventions were then incorporated at these levels.

FINDINGS

The finite element model accurately predicted healthy and myelopathic spinal cord displacement compared to motions observed in vivo. Spinal cord strain increased during extension in the cervical myelopathy finite element model. All surgical techniques affected spinal cord stress and strain. Specifically, adjacent levels had increased stress and strain, especially in the anterior cervical discectomy and fusion case.

INTERPRETATIONS

This model is the first biomechanically validated, finite element model of the healthy and myelopathic C2-T1 cervical spine and spinal cord which predicts spinal cord displacement, stress, and strain during physiologic motion. Our findings show surgical intervention can cause increased strain in the adjacent levels of the spinal cord which is particularly worse following anterior cervical discectomy and fusion.

The Influence of Neuron-Extrinsic Factors and Aging on Injury Progression and Axonal Repair in the Central Nervous System

In the aging western population, the average age of incidence for spinal cord injury (SCI) has increased, as has the length of survival of SCI patients. This places great importance on understanding SCI in middle-aged and aging patients. Axon regeneration after injury is an area of study that has received substantial attention and made important experimental progress, however, our understanding of how aging affects this process, and any therapeutic effort to modulate repair, is incomplete. The growth and regeneration of axons is mediated by both neuron intrinsic and extrinsic factors. In this review we explore some of the key extrinsic influences on axon regeneration in the literature, focusing on inflammation and astrogliosis, other cellular responses, components of the extracellular matrix, and myelin proteins. We will describe how each element supports the contention that axonal growth after injury in the central nervous system shows an age-dependent decline, and how this may affect outcomes after a SCI.

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.

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.

High-Speed Fluoroscopy to Measure Dynamic Spinal Cord Deformation in an In Vivo Rat Model

Although spinal cord deformation is thought to be a predictor of injury severity, few researchers have investigated dynamic cord deformation, in vivo, during impact. This is needed to establish correlations among impact parameters, internal cord deformation, and histological and functional outcomes. Relying on surface deformations alone may not sufficiently represent spinal cord deformation. The objective of this study was to develop a high-speed fluoroscopic method of tracking the surface and internal cord deformations of rat spinal cord during experimental cord injury. Two radio-opaque beads were injected into the cord at C5/6 in the dorsal and ventral white matter. Four additional beads were glued to the surface of the cord. Dynamic bead displacement was tracked during a dorsal impact (130 mm/sec, 1 mm depth) by high-speed radiographic imaging at 3000 FPS, laterally. The internal spinal cord beads displaced significantly more than the surface beads in the ventral direction (1.1-1.9 times) and more than most surface beads in the cranial direction (1.2-1.5 times). The dorsal beads (internal and surface) displaced more than the ventral beads during all impacts. The bead displacement pattern implies that the spinal cord undergoes complex internal and surface deformations during impact. Residual displacement of the internal beads was significantly greater than that of the surface beads in the cranial-caudal direction but not the dorsoventral direction. Finite element simulation confirmed that the additional bead mass likely had little effect on the internal cord deformations. These results support the merit of this technique for measuring in vivo spinal cord deformation.

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.

Compressive mechanical characterization of non-human primate spinal cord white matter

The goal of developing computational models of spinal cord injury (SCI) is to better understand the human injury condition. However, finite element models of human SCI have used rodent spinal cord tissue properties due to a lack of experimental data. Central nervous system tissues in non human primates (NHP) closely resemble that of humans and therefore, it is expected that material constitutive models obtained from NHPs will increase the fidelity and the accuracy of human SCI models. Human SCI most often results from compressive loading and spinal cord white matter properties affect FE predicted patterns of injury; therefore, the objectives of this study were to characterize the unconfined compressive response of NHP spinal cord white matter and present an experimentally derived, finite element tractable constitutive model for the tissue. Cervical spinal cords were harvested from nine male adult NHPs (Macaca mulatta). White matter biopsy samples (3 mm in diameter) were taken from both lateral columns of the spinal cord and were divided into four strain rate groups for unconfined dynamic compression and stress relaxation (post-mortem <1-hour). The NHP spinal cord white matter compressive response was sensitive to strain rate and showed substantial stress relaxation confirming the viscoelastic behavior of the material. An Ogden 1st order model best captured the non-linear behavior of NHP white matter in a quasi-linear viscoelastic material model with 4-term Prony series. This study is the first to characterize NHP spinal cord white matter at high (>10/sec) strain rates typical of traumatic injury. The finite element derived material constitutive model of this study will increase the fidelity of SCI computational models and provide important insights for transferring pre-clinical findings to clinical treatments.

STATEMENT OF SIGNIFICANCE

Spinal cord injury (SCI) finite element (FE) models provide an important tool to bridge the gap between animal studies and human injury, assess injury prevention technologies (e.g. helmets, seatbelts), and provide insight into the mechanisms of injury. Although, FE model outcomes depend on the assumed material constitutive model, there is limited experimental data for fresh spinal cords and all was obtained from rodent, porcine or bovine tissues. Central nervous system tissues in non human primates (NHP) more closely resemble humans. This study characterizes fresh NHP spinal cord material properties at high strains rates and large deformations typical of SCI for the first time. A constitutive model was defined that can be readily implemented in finite strain FE analysis of SCI.

Radiography used to measure internal spinal cord deformation in an in vivo rat model

Little is known about the internal mechanics of the in vivo spinal cord during injury. The objective of this study was to develop a method of tracking internal and surface deformation of in vivo rat spinal cord during compression using radiography. Since neural tissue is radio-translucent, radio-opaque markers were injected into the spinal cord. Two tantalum beads (260 µm) were injected into the cord (dorsal and ventral) at C5 of nine anesthetized rats. Four beads were glued to the lateral surface of the cord, caudal and cranial to the injection site. A compression plate was displaced 0.5 mm, 2 mm, and 3 mm into the spinal cord and lateral X-ray images were taken before, during, and after each compression for measuring bead displacements. Potential bead migration was monitored for by comparing displacements of the internal and glued surface beads. Dorsal beads moved significantly more than ventral beads with a range in averages of 0.57-0.71 mm and 0.31-0.35 mm respectively. Bead displacements during 0.5 mm compressions were significantly lower than 2 mm and 3 mm compressions. There was no statistically significant migration of the internal beads. The results indicate the merit of this technique for measuring in vivo spinal cord deformation. The pattern of bead displacements illustrates the complex internal and surface deformations of the spinal cord during transverse compression. This information is needed for validating physical and finite element spinal cord surrogates and to define relationships between loading parameters, internal cord deformation, and biological and functional outcomes.

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

Despite efforts to simulate the in vivo environment, post-mortem degradation and lack of blood perfusion complicate the use of ex vivo derived material models in computational studies of spinal cord injury. In order to quantify the mechanical changes that manifest ex vivo, the viscoelastic behavior of in vivo and ex vivo porcine spinal cord samples were compared. Stress-relaxation data from each condition were fit to a non-linear viscoelastic model using a novel characterization technique called the direct fit method. To validate the presented material models, the parameters obtained for each condition were used to predict the respective dynamic cyclic response. Both ex vivo and in vivo samples displayed non-linear viscoelastic behavior with a significant increase in relaxation with applied strain. However, at all three strain magnitudes compared, ex vivo samples experienced a higher stress and greater relaxation than in vivo samples. Significant differences between model parameters also showed distinct relaxation behaviors, especially in non-linear relaxation modulus components associated with the short-term response (0.1-1 s). The results of this study underscore the necessity of utilizing material models developed from in vivo experimental data for studies of spinal cord injury, where the time-dependent properties are critical. The ability of each material model to accurately predict the dynamic cyclic response validates the presented methodology and supports the use of the in vivo model in future high-resolution finite element modeling efforts.

STATEMENT OF SIGNIFICANCE

Neural tissues (such as the brain and spinal cord) display time-dependent, or viscoelastic, mechanical behavior making it difficult to model how they respond to various loading conditions, including injury. Methods that aim to characterize the behavior of the spinal cord almost exclusively use ex vivo cadaveric or animal samples, despite evidence that time after death affects the behavior compared to that in a living animal (in vivo response). Therefore, this study directly compared the mechanical response of ex vivo and in vivo samples to quantify these differences for the first time. This will allow researchers to draw more accurate conclusions about spinal cord injuries based on ex vivo data (which are easier to obtain) and emphasizes the importance of future in vivo experimental animal work.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues.

The Transverse Isotropy of Spinal Cord White Matter Under Dynamic Load

The rostral-caudally aligned fiber-reinforced structure of spinal cord white matter (WM) gives rise to transverse isotropy in the material. Stress and strain patterns generated in the spinal cord parenchyma following spinal cord injury (SCI) are multidirectional and dependent on the mechanism of the injury. Our objective was to develop a WM constitutive model that captures the material transverse isotropy under dynamic loading. The WM mechanical behavior was extracted from the published tensile and compressive experiments. Combinations of isotropic and fiber-reinforcing models were examined in a conditional quasi-linear viscoelastic (QLV) formulation to capture the WM mechanical behavior. The effect of WM transverse isotropy on SCI model outcomes was evaluated by simulating a nonhuman primate (NHP) contusion injury experiment. A second-order reduced polynomial hyperelastic energy potential conditionally combined with a quadratic reinforcing function in a four-term Prony series QLV model best captured the WM mechanical behavior (0.89 < R2 < 0.99). WM isotropic and transversely isotropic material models combined with discrete modeling of the pia mater resulted in peak impact forces that matched the experimental outcomes. The transversely isotropic WM with discrete pia mater resulted in maximum principal strain (MPS) distributions which effectively captured the combination of ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and the rostral/caudal spread of damage observed in in vivo injuries. The results suggest that the WM transverse isotropy could have an important role in correlating tissue damage with mechanical measures and explaining the directional sensitivity of the spinal cord to injury.

A Unilateral Cervical Spinal Cord Contusion Injury Model in Non-Human Primates (Macaca mulatta)

The development of a non-human primate (NHP) model of spinal cord injury (SCI) based on mechanical and computational modeling is described. We scaled up from a rodent model to a larger primate model using a highly controllable, friction-free, electronically-driven actuator to generate unilateral C6-C7 spinal cord injuries. Graded contusion lesions with varying degrees of functional recovery, depending upon pre-set impact parameters, were produced in nine NHPs. Protocols and pre-operative magnetic resonance imaging (MRI) were used to optimize the predictability of outcomes by matching impact protocols to the size of each animal's spinal canal, cord, and cerebrospinal fluid space. Post-operative MRI confirmed lesion placement and provided information on lesion volume and spread for comparison with histological measures. We evaluated the relationships between impact parameters, lesion measures, and behavioral outcomes, and confirmed that these relationships were consistent with our previous studies in the rat. In addition to providing multiple univariate outcome measures, we also developed an integrated outcome metric describing the multivariate cervical SCI syndrome. Impacts at the higher ranges of peak force produced highly lateralized and enduring deficits in multiple measures of forelimb and hand function, while lower energy impacts produced early weakness followed by substantial recovery but enduring deficits in fine digital control (e.g., pincer grasp). This model provides a clinically relevant system in which to evaluate the safety and, potentially, the efficacy of candidate translational therapies.

Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression

Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p < 0.05), but changes in equilibrium stress disappeared (p > 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.

Skeletal muscle tensile strain dependence: Hyperviscoelastic nonlinearity

INTRODUCTION

Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain.

MATERIALS AND METHODS

Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components.

RESULTS

Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately.

CONCLUSIONS

Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model.