Viscoelastic properties of the ovine posterior spinal ligaments are strain dependent

The Impact of Spine Pathology on Posterior Ligamentous Complex Structure and Function

PURPOSE OF REVIEW

Spinal ligament is an important component of the spinal column in mitigating biomechanical stress. Particularly the posterior ligamentous complex, which is composed of the ligamentum flavum, interspinous, and supraspinous ligaments. However, research characterizing the biomechanics and role of ligament health in spinal pathology and clinical context are scarce. This article provides a comprehensive review of the implications of spinal pathology on the structure, function, and biomechanical properties of the posterior ligamentous complex.

RECENT FINDINGS

Current research characterizing biomechanical properties of the posterior ligamentous complex is primarily composed of cadaveric studies and finite element modeling, and more recently incorporating patient-specific anatomy into finite element models. The ultimate goal of current research is to understand the relative contributions of these ligamentous structures in healthy and pathological spine, and whether preserving ligaments may play an important role in spinal surgical techniques. At baseline, posterior ligamentous complex structures account for 30-40% of spinal stability, which is highly dependent on the intrinsic biomechanical properties of each ligament. Biomechanics vary widely with pathology and following rigid surgical fixation techniques and are generally maladaptive. Often secondary to morphological changes in the setting of spinal pathology, but morphological changes in ligament may also serve as a primary pathology. Biomechanical maladaptations of the spinal ligament adversely influence overall spinal column integrity and ultimately predispose to increased risk for surgical failure and poor clinical outcomes. Future research is needed, particularly in living subjects, to better characterize adaptations in ligaments that can provide targets for improved treatment of spinal pathology.

Different Passive Viscoelastic Properties Between the Left and Right Ventricles in Healthy Adult Ovine

Ventricle dysfunction is the most common cause of heart failure, which leads to high mortality and morbidity. The mechanical behavior of the ventricle is critical to its physiological function. It is known that the ventricle is anisotropic and viscoelastic. However, the understanding of ventricular viscoelasticity is much less than that of its elasticity. Moreover, the left and right ventricles (LV&RV) are different in embryologic origin, anatomy, and function, but whether they distinguish in viscoelastic properties is unclear. We hypothesized that passive viscoelasticity is different between healthy LVs and RVs. Ex vivo cyclic biaxial tensile mechanical tests (1, 0.1, 0.01 Hz) and stress relaxation (strain of 3, 6, 9, 12, 15%) were performed for ventricles from healthy adult sheep. Outflow track direction was defined as the longitudinal direction. Hysteresis stress-strain loops and stress relaxation curves were obtained to quantify the viscoelastic properties. We found that the RV had more pronounced frequency-dependent viscoelastic changes than the LV. Under the physiological frequency (1 Hz), the LV was more anisotropic in the elasticity and stiffer than the RV in both directions, whereas the RV was more anisotropic in the viscosity and more viscous than the LV in the longitudinal direction. The LV was quasi-linear viscoelastic in the longitudinal but not circumferential direction, and the RV was nonlinear viscoelastic in both directions. This study is the first to investigate passive viscoelastic differences in healthy LVs and RVs, and the findings will deepen the understanding of biomechanical mechanisms of ventricular function.

Passive lumbar tissue loading during trunk bending at three speeds: An in vivo study

BACKGROUND

Low back disorders are closely related with the magnitude of mechanical loading on human spine. However, spinal loading contributed by the lumbar passive tissues is still not well understood. In this study, the effect of motion speed on lumbar passive moment output was investigated. In addition, the increase of lumbar passive moment during trunk bending was modeled.

METHODS

Twelve volunteers performed trunk-bending motions at three different speeds. Trunk kinematics and muscle activities were collected and used to estimate instantaneous spinal loading and the corresponding lumbar passive moment. The lumbar passive moments at different ranges of trunk motion were compared at different speed levels and the relationship between lumbar passive moment lumbar flexion was modeled.

FINDINGS

A non-linear, two-stage pattern of increase in lumbar passive moment was evident during trunk flexion. However, the effect of motion speed was not significant on lumbar passive moments or any of the model parameters.

INTERPRETATION

As reported previously, distinct lumbar ligaments may begin to generate tension at differing extents of trunk flexion, and this could be the cause of the observed two-stage increasing pattern of lumbar passive moment. The current results also suggest that changes in tissue strain rate may not have a significant impact on the total passive moment output at the relatively slow trunk motions examined here.

Load-relaxation properties of the human trunk in response to prolonged flexion: measuring and modeling the effect of flexion angle

Experimental studies suggest that prolonged trunk flexion reduces passive support of the spine. To understand alterations of the synergy between active and passive tissues following such loadings, several studies have assessed the time-dependent behavior of passive tissues including those within spinal motion segments and muscles. Yet, there remain limitations regarding load-relaxation of the lumbar spine in response to flexion exposures and the influence of different flexion angles. Ten healthy participants were exposed for 16 min to each of five magnitudes of lumbar flexion specified relative to individual flexion-relaxation angles (i.e., 30, 40, 60, 80, and 100%), during which lumbar flexion angle and trunk moment were recorded. Outcome measures were initial trunk moment, moment drop, parameters of four viscoelastic models (i.e., Standard Linear Solid model, the Prony Series, Schapery's Theory, and the Modified Superposition Method), and changes in neutral zone and viscoelastic state following exposure. There were significant effects of flexion angle on initial moment, moment drop, changes in normalized neutral zone, and some parameters of the Standard Linear Solid model. Initial moment, moment drop, and changes in normalized neutral zone increased exponentially with flexion angle. Kelvin-solid models produced better predictions of temporal behaviors. Observed responses to trunk flexion suggest nonlinearity in viscoelastic properties, and which likely reflected viscoelastic behaviors of spinal (lumbar) motion segments. Flexion-induced changes in viscous properties and neutral zone imply an increase in internal loads and perhaps increased risk of low back disorders. Kelvin-solid models, especially the Prony Series model appeared to be more effective at modeling load-relaxation of the trunk.

Experimental Characterization and Finite Element Implementation of Soft Tissue Nonlinear Viscoelasticity

Finite element (FE) models of articular joint structures do not typically implement the fully nonlinear viscoelastic behavior of the soft connective tissue components. Instead, contemporary whole joint FE models usually represent the transient soft tissue behavior with significantly simplified formulations that are computationally tractable. The resultant fidelity of these models is greatly compromised with respect to predictions under temporally varying static and dynamic loading regimes. In addition, models based upon experimentally derived nonlinear viscoelastic coefficients that do not account for the transient behavior during the loading event(s) may further reduce the model’s predictive accuracy. The current study provides the derivation and validation of a novel, phenomenological nonlinear viscoelastic formulation (based on the single integral nonlinear superposition formulation) that can be directly inputted into FE algorithms. This formulation and an accompanying experimental characterization technique, which incorporates relaxation manifested during the loading period of stress relaxation experiments, is compared to a previously published characterization method and validated against an independent analytical model. The results demonstrated that the static and dynamic FE approximations are in good agreement with the analytical solution. Additionally, the predictive accuracy of these approximations was observed to be highly dependent upon the experimental characterization technique. It is expected that implementation of the novel, computationally tractable nonlinear viscoelastic formulation and associated experimental characterization technique presented in the current study will greatly improve the predictive accuracy of the individual connective tissue components for whole joint FE simulations subjected to static and dynamic loading regimes.

Describing the active region boundary of EMG-assisted biomechanical models of the low back

BACKGROUND

Electromyography-assisted (EMG-assisted) biomechanical models are used to characterize the muscle and joint reaction forces in the lumbar region. However, during a full-range trunk flexion, there is a transition of extension moment from the trunk extensor muscles to the passive tissues of the low back, indicating that the empirical EMG data used to drive these EMG-assisted models becomes less correlated with the extensor moment. The objectives of this study were to establish the trunk flexion angles at which the passive tissues generate substantial trunk extension moment and to document how these angles change with asymmetry.

METHODS

Participants performed controlled trunk flexion-extension motions in three asymmetric postures. The trunk kinematics data and the electromyographic activity from L3- and L4-level paraspinals and rectus abdominis were captured. The time-dependent net internal active moment (from an EMG-assisted model) and the net external moment were calculated. The trunk and lumbar angles at which the net internal active moment was less than 70% of the external moment were found.

FINDINGS

The trunk flexion angle at which the net internal moment reaches the stated criteria varied as a function of asymmetry of trunk flexion motion with the sagittally symmetric case providing the deepest flexion angle of 38° (asymmetry 15°: 33°; asymmetry 30°: 26°).

INTERPRETATION

These results indicate that EMG-assisted biomechanical models need to consider the role of passive tissues at trunk flexion angles significantly less than previously thought and these flexion angles vary as a function of the asymmetry and direction of motion.

Viscoelastic effects during loading play an integral role in soft tissue mechanics

Viscoelastic relaxation during tensioning is an intrinsic protective mechanism of biological soft tissues. However, current viscoelastic characterization methodologies for these tissues either negate this important behavior or provide correction methods that are severely restricted to a specific viscoelastic formulation and/or assume an a priori (linear) strain ramp history. In order to address these shortcomings, we present a novel finite ramp time correction method for stress relaxation experiments (to incorporate relaxation manifested during loading) that is independent of a specific viscoelastic formulation and can accommodate an arbitrary strain ramp history. We demonstrate transferability of our correction method between viscoelastic formulations by applying it to quasi-linear viscoelastic (QLV) and fully nonlinear viscoelastic constitutive equations. The errors associated with currently accepted methodologies for QLV and fully nonlinear viscoelastic formulations are elucidated. Our correction method is validated by demonstrating the ability of its fitted parameters to predict an independent cyclic experiment across multiple strain amplitudes and frequencies. The results presented herein: (i) indicate that our correction method significantly reduces the errors associated with previous methodologies; and (ii) demonstrate the necessity for the use of a fully nonlinear viscoelastic formulation, which incorporates relaxation manifested during loading, to model the viscoelastic behavior of biological soft tissues.

Human cervical spine ligaments exhibit fully nonlinear viscoelastic behavior

Spinal ligaments provide stability and contribute to spinal motion patterns. These hydrated tissues exhibit time-dependent behavior during both static and dynamic loading regimes. Therefore, accurate viscoelastic characterization of these ligaments is requisite for development of computational analogues that model and predict time-dependent spine behavior. The development of accurate viscoelastic models must be preceded by rigorous, empirical evidence of linear viscoelastic, quasi-linear viscoelastic (QLV) or fully nonlinear viscoelastic behavior. This study utilized multiple physiological loading rates (frequencies) and strain amplitudes via cyclic loading and stress relaxation experiments in order to determine the viscoelastic behavior of the human lower cervical spine anterior longitudinal ligament, the posterior longitudinal ligament and the ligamentum flavum. The results indicated that the cyclic material properties of these ligaments were dependent on both strain amplitude and frequency. This strain amplitude-dependent behavior cannot be described using a linear viscoelastic formulation. Stress relaxation experiments at multiple strain magnitudes indicated that the shape of the relaxation curve was strongly dependent on strain magnitude, suggesting that a QLV formulation cannot adequately describe the comprehensive viscoelastic response of these ligaments. Therefore, a fully nonlinear viscoelastic formulation is requisite to model these lower cervical spine ligaments during activities of daily living.