Mechanics of cranial sutures during simulated cyclic loading

Previous computational and experimental analyses revealed that cranial sutures, fibrous joints between the bones, can reduce the strain experienced by the surrounding skull bones during mastication. This damping effect reflects the importance of including sutures in finite element (FE) analyses of the skull. Using the FE method, the behaviour of three suture morphologies of increasing complexity (butt-ended, moderate interdigitated, and complex interdigitated) during static loading was recently investigated, and the sutures were assumed to have linear elastic properties. In the current study, viscoelastic properties, derived from published experimental results of the nasofrontal suture of young pigs (Sus scrofa), are applied to the three idealised bone-suture models. The effects of suture viscoelasticity on the stress, strain, and strain energy in the models were computed for three different frequencies (corresponding to periods of 1, 10, and 100s) and compared to the results of a static, linear elastic analysis. The range of applied frequencies broadly represents different physiological activities, with the highest frequency simulating mastication and the lowest frequency simulating growth and pressure of the surrounding tissues. Comparing across all three suture morphologies, strain energy and strain in the suture decreased with the increase in suture complexity. For each suture model, the magnitude of strain decreased with an increase in frequency, and the magnitudes were similar for both the elastic and 1s frequency analyses. In addition, a viscous response is less apparent in the higher frequency analyses, indicating that viscous properties are less important to the behaviour of the suture during those analyses. The FE results suggest that implementation of viscoelastic properties may not be necessary for computational studies of skull behaviour during masticatory loading but instead might be more relevant for studies examining lower frequency physiological activities.     

Role of the acetabular labrum in load support across the hip joint

The relatively high incidence of labral tears among patients presenting with hip pain suggests that the acetabular labrum is often subjected to injurious loading in vivo. However, it is unclear whether the labrum participates in load transfer across the joint during activities of daily living. This study examined the role of the acetabular labrum in load transfer for hips with normal acetabular geometry and acetabular dysplasia using subject-specific finite element analysis. Models were generated from volumetric CT data and analyzed with and without the labrum during activities of daily living. The labrum in the dysplastic model supported 4-11% of the total load transferred across the joint, while the labrum in the normal model supported only 1-2% of the total load. Despite the increased load transferred to the acetabular cartilage in simulations without the labrum, there were minimal differences in cartilage contact stresses. This was because the load supported by the cartilage correlated with the cartilage contact area. A higher percentage of load was transferred to the labrum in the dysplastic model because the femoral head achieved equilibrium near the lateral edge of the acetabulum. The results of this study suggest that the labrum plays a larger role in load transfer and joint stability in hips with acetabular dysplasia than in hips with normal acetabular geometry.     

Computational hip joint simulator for wear and heat generation

This paper presents a computational simulator for the hip to compute the wear and heat generation on artificial joints. The friction produced on artificial hip joints originates wear rates that can lead to failure of the implant. Furthermore, the frictional heating can increase the wear. The developed computational model calculates the wear in the joint and the temperature in the surrounding zone, allowing the use of different combinations of joint materials, daily activities and different individuals. The pressure distribution on the joint bearing surfaces is obtained with the solution of a contact model. The heat generation by friction and the volumetric wear is computed from the pressure distribution and the sliding distance. The temperature is obtained from the solution of a transient heat conduction problem that includes the time-dependent heat generated by friction. The contact and heat conduction problems are solved numerically with the Finite Element Method. The developed computational model performs a full simulation of the acetabular bearing surface behaviour, which is useful for acetabular cup design and material selection. The results obtained by the present model agree with experimental and clinical data, as well as other numerical studies.     

Bone ingrowth around porous-coated acetabular implant: a three-dimensional finite element study using mechanoregulatory algorithm

Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent on the mechanical environment of the implant–bone structure. The objective of the study is to gain an insight into the tissue differentiation around an acetabular component. A mapping framework has been developed to simulate appropriate mechanical environment in the three-dimensional microscale model, implement the mechanoregulatory tissue differentiation algorithm and subsequently assess spatial distribution of bone ingrowth around an acetabular component, quantitatively. The FE model of implanted pelvis subjected to eight static load cases during a normal walking cycle was first solved. Thereafter, a mapping algorithm has been employed to include the variations in implant–bone relative displacement and host bone material properties from the macroscale FE model of implanted pelvis to the microscale FE model of the beaded implant–bone interface. The evolutionary tissue differentiation was observed in each of the 13 microscale models corresponding to 13 acetabular regions. The total implant–bone relative displacements, averaged over each region of the acetabulum, were found to vary between 10 and 60 \(\upmu \hbox {m}\). Both the linear elastic and biphasic poroelastic models predicted similar mechanoregulatory peri-prosthetic tissue differentiation. Considerable variations in bone ingrowth (13–88 %), interdigitation depth (0.2–0.82 mm) and average tissue Young’s modulus (970–3430 MPa) were predicted around the acetabular cup. A progressive increase in the average Young’s modulus, interdigitation depth and decrease in average radial strains of newly formed tissue layer were also observed. This scheme can be extended to investigate tissue differentiation for different surface texture designs on the implants.     

Systematic review and meta-analysis of the biomechanical properties of the human dura mater applicable in computational human head models

Accurate biomechanical properties of the human dura mater are required for computational models and to fabricate artificial substitutes for transplantation and surgical training purposes. Here, a systematic literature review was performed to summarize the biomechanical properties of the human dura mater that are reported in the literature. Furthermore, anthropometric data, information regarding the mechanically tested samples, and specifications with respect to the used mechanical testing setup were extracted. A meta-analysis was performed to obtain the pooled mean estimate for the elastic modulus, ultimate tensile strength, and strain at maximum force. A total of 17 studies were deemed eligible, which focused on human cranial and spinal dura mater in 13 and 4 cases, respectively. Pooled mean estimates for the elastic modulus (n?=?448), the ultimate tensile strength (n?=?448), and the strain at maximum force (n?=?431) of 68.1 MPa, 7.3 MPa and 14.4% were observed for native cranial dura mater. Gaps in the literature related to the extracted data were identified and future directions for mechanical characterizations of human dura mater were formulated. The main conclusion is that the most commonly used elastic modulus value of 31.5 MPa for the simulation of the human cranial dura mater in computational head models is likely an underestimation and an oversimplification given the morphological diversity of the tissue in different brain regions. Based on the here provided meta-analysis, a stiffer linear elastic modulus of 68 MPa was observed instead. However, further experimental data are essential to confirm its validity.

     

Effect of boundary conditions,impact loading and hydraulic stiffening on femoral fracture strength

Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading.     

Respiratory load compensation in infants.

We have studied the respiratory compensation for elastic loads in 15 term and preterm infants. Elastic loads, approximately equal to the infant's effective elastance, were applied to the airway for five breaths while tidal volume and mask pressure were monitored. Motion of the rib cage and abdomen were monitored simultaneously with magnetometers. The studies were done both in active or REM sleep and in quiet or non-REM sleep. During quiet sleep the load immediately reduced the tidal volume by about 50% but a progressive increase in tidal volume occurred over the next four loaded breaths. During active sleep load compensation was disorganized with respect to both tidal volume and frequency, and compensation was significantly less. Active sleep was also characterized by marked rib cage distortion. We suggest that during active sleep there is tonic inhibition of the intercostal muscles, allowing the diaphragm to distort the rib cage. This distortion impairs load compensation by a direct mechanical effect and indirectly by initiating an intercostal-phrenic reflex.     

An information-based machine learning approach to elasticity imaging

An information-based technique is described for applications in mechanical property imaging of soft biological media under quasi-static loads. We adapted the Autoprogressive method that was originally developed for civil engineering applications for this purpose. The Autoprogressive method is a computational technique that combines knowledge of object shape and a sparse distribution of force and displacement measurements with finite-element analyses and artificial neural networks to estimate a complete set of stress and strain vectors. Elasticity imaging parameters are then computed from estimated stresses and strains. We introduce the technique using ultrasonic pulse-echo measurements in simple gelatin imaging phantoms having linear-elastic properties so that conventional finite-element modeling can be used to validate results. The Autoprogressive algorithm does not require any assumptions about the material properties and can, in principle, be used to image media with arbitrary properties. We show that by selecting a few well-chosen force–displacement measurements that are appropriately applied during training and establish convergence, we can estimate all nontrivial stress and strain vectors throughout an object and accurately estimate an elastic modulus at high spatial resolution. This new method of modeling the mechanical properties of tissue-like materials introduces a unique method of solving the inverse problem and is the first technique for imaging stress without assuming the underlying constitutive model.     

Off-axis loads cause failure of the distal radius at lower magnitudes than axial loads: a finite element analysis

Distal radius (Colles') fractures are a common fall-related injury in older adults and frequently result in long-term pain and reduced ability to perform activities of daily living. Because the occurrence of a fracture during a fall depends on both the strength of the bone and upon the kinematics and kinetics of the impact itself, we sought to understand how changes in bone mineral density (BMD) and loading direction affect the fracture strength and fracture initiation location in the distal radius. A three-dimensional finite element model of the radius, scaphoid, and lunate was used to examine changes of +/-2% and +/-4% BMD, and both axial and physiologically relevant off-axis loads on the radius. Changes in BMD resulted in similar percent changes in fracture strength. However, modifying the applied load to include dorsal and lateral components (assuming a dorsal view of the wrist, rather than an anatomic view) resulted in a 47% decrease in fracture strength (axial failure load: 2752N, off-axis: 1448N). Loading direction also influenced the fracture initiation site. Axially loaded radii failed on the medial surface immediately proximal to the styloid process. In contrast, off-axis loads, containing dorsal and lateral components, caused failure on the dorsal-lateral surface. Because the radius appears to be very sensitive to loading direction, the results suggest that much of the variability in fracture strength seen in cadaver studies may be attributed to varying boundary conditions. The results further suggest that interventions focused on reducing the incidence of Colles' fractures when falls onto the upper extremities are unavoidable may benefit from increasing the extent to which the radius is loaded along its axis.     

Acute effect of static stretching on power output during concentric dynamic constant external resistance leg extension

The purpose of the present study was to clarify the effect of static stretching on muscular performance during concentric isotonic (dynamic constant external resistance [DCER]) muscle actions under various loads. Concentric DCER leg extension power outputs were assessed in 12 healthy male subjects after 2 types of pretreatment. The pretreatments included (a) static stretching treatment performing 6 types of static stretching on leg extensors (4 sets of 30 seconds each with 20-second rest periods; total duration 20 minutes) and (b) nonstretching treatment by resting for 20 minutes in a sitting position. Loads during assessment of the power output were set to 5, 30, and 60% of the maximum voluntary contractile (MVC) torque with isometric leg extension in each subject. The peak power output following the static stretching treatment was significantly (p < 0.05) lower than that following the nonstretching treatment under each load (5% MVC, 418.0 +/- 82.2 W vs. 466.2 +/- 89.5 W; 30% MVC, 506.4 +/- 82.8 W vs. 536.4 +/- 97.0 W; 60% MVC, 478.6 +/- 77.5 W vs. 523.8 +/- 97.8 W). The present study demonstrated that relatively extensive static stretching significantly reduces power output with concentric DCER muscle actions under various loads. Common power activities are carried out by DCER muscle actions under various loads. Therefore, the result of the present study suggests that relatively extensive static stretching decreases power performance.     

Drought tolerance of selected Eragrostis species correlates with leaf tensile properties

BACKGROUND AND AIMS: Previous studies on grass leaf tensile properties (behaviour during mechanical stress) have focused on agricultural applications such as resistance to trampling and palatability; no investigations have directly addressed mechanical properties during water stress, and hence these are the subject of this study. METHODS: Critical (lethal) relative water contents were determined for three species of grass in the genus Eragrostis varying in their tolerance to drought. Measurements were taken for leaf tensile strength, elastic modulus, toughness and failure load under different conditions of hydration, and light microscopy and histochemical analyses were undertaken. KEY RESULTS: Leaf tensile strength of fully hydrated leaves for the drought-intolerant E. capensis, the moderately drought-tolerant E. tef and the drought-tolerant E. curvula correlated well with drought tolerance (critical relative water content). Eragrostis curvula had higher tensile strength values than E. tef, which in turn had higher values than E. capensis. Measurements on the drought-tolerant grass E. curvula when fully hydrated and when dried to below its turgor loss point showed that tensile strength, toughness and the elastic modulus all increased under conditions of turgor loss, while the failure load remained unchanged. Additional tests of 100 mm segments along the lamina of E. curvula showed that tensile strength, toughness and the elastic modulus all decreased with distance from the base of the lamina, while again the failure load was unaffected. This decrease in mechanical parameters correlated with a reduction in the size of the vascular bundles and the amount of lignification, as viewed in lamina cross-sections. CONCLUSIONS: The results confirm that leaf mechanical properties are affected by both water status and position along the lamina, and suggest a positive correlation between leaf internal architecture, tensile strength, cell wall chemistry and tolerance to dehydration for grasses.     

3D non-linear analysis of the acetabular construct following impaction grafting

The study investigates the short-term behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff–Ling impaction grafting technique; using 3D finite element analyses. An elasto-plastic material model is used to describe the constitutive behaviour of morsellised cortico-cancellous bone (MCB) graft, since it has been shown that MCB undergoes significant plastic deformation under normal physiological loads. Based on previous experimental studies carried out by the authors and others, MCB is modelled using non-linear elasticity and Drucker Prager Cap (DPC) plasticity. Loading associated with walking, sitting down, and standing up is applied to the acetabular cup through a femoral head using smooth sliding surfaces. The analyses yield distinctive patterns of migration and rotation due to different activities. These are found to be similar to those observed in the clinical setting.     

3D non-linear analysis of the acetabular construct following impaction grafting

The study investigates the short-term behaviour of the acetabular construct following revision hip arthroplasty, carried out using the Slooff-Ling impaction grafting technique; using 3D finite element analyses. An elasto-plastic material model is used to describe the constitutive behaviour of morsellised cortico-cancellous bone (MCB) graft, since it has been shown that MCB undergoes significant plastic deformation under normal physiological loads. Based on previous experimental studies carried out by the authors and others, MCB is modelled using non-linear elasticity and Drucker Prager Cap (DPC) plasticity. Loading associated with walking, sitting down, and standing up is applied to the acetabular cup through a femoral head using smooth sliding surfaces. The analyses yield distinctive patterns of migration and rotation due to different activities. These are found to be similar to those observed in the clinical setting.     

Rapid identification of elastic modulus of the interface tissue on dental implants surfaces using reduced-basis method and a neural network

This paper proposes a rapid inverse analysis approach based on the reduced-basis method (RBM) and neural network (NN) to identify the “unknown” elastic modulus (Young's modulus) of the interfacial tissue between a dental implant and the surrounding bones. In the present RBM–NN approach, a RBM model is first built to compute displacement responses of dental implant-bone structures subjected to a harmonic loading for a set of “assumed” Young's moduli. The RBM model is then used to train a NN model that is used for actual inverse analysis in real-time. Actual experimental measurements of displacement responses are fed into the trained NN model to inversely determine the “true” elastic modulus of the interfacial tissue. As an example, a physical model of dental implant-bone structure is built and inverse analysis is conducted to verify the present RBM–NN approach. Based on numerical simulation and actual experiments, it is confirmed that the identified results are very accurate, reliable, and the computational saving is very significant. The present RBM–NN approach is found robust and efficient for inverse material characterizations in noninvasive and/or nondestructive evaluations.     

3 种不同弹性模量钛合金股骨假体在羊股骨置换模型中应力分布的三维 有限元分析

目的:通过三维有限元分析方法来观察并比较3种不同弹性模量钛合金股骨假体在羊股骨置换模型中von-Mises应力分布的情况。方法:采用64排螺旋CT对一健康成年羊的下肢股骨进行全长的CT扫描,扫描层厚为0.5 mm,扫描所得的数据存储为DICOM文件。将得到的DICOM文件导入到CT图像分析软件Mimics 10.0,然后利用Mimics 10.0软件来生成股骨的骨质点云数据,再将生成的骨质点云数据导入到Simpleware分析软件,通过机械加工反求中的复杂曲面造型技术建立起精确的三维实体模型。对三维实体模型进行网格划分,确定了髓腔的形状,并根据羊下肢股骨髓腔的形状设计了作者实验用的羊股骨假体模型,然后在ANSYS 12.1软件中进行网格划分。给予加载缓慢行走载荷以及扭转载荷,分析并比较羊股骨以及3种不同弹性模量钛合金股骨假体在股骨置换模型中von-Mises应力分布的情况。结果:在缓慢行走载荷以及扭转载荷条件下,3种不同弹性模量钛合金股骨假体von-Mises应力分布变化趋势一致,假体的柄颈结合部以及假体柄上1/3为应力集中区域。3种不同弹性模量的最大应力集中点均位于柄颈结合部,60 GPa弹性模量的股骨假体植入后假体的最大应力最小(37.8 MPa、29.1 MPa),股骨的最大应力最大(12.6 MPa、24.5 MPa);80 GPa的次之,假体的最大应力(38.4 MPa、33.4 MPa),股骨的最大应力(12.5 MPa、24.5 MPa);110 GPa的股骨假体植入后假体的最大应力最大(38.9 MPa、38.1 MPa),股骨的最大应力最小(12.3 MPa、24.5 MPa)。60 GPa弹性模量的股骨假体植入后的假体最大位移和相对位移均最小(缓慢行走载荷下假体最大位移为0.551 mm、相对位移为0.008 mm,扭转载荷下假体最大位移为0.730 mm、相对位移为0.011 mm)。结论:较低弹性模量的钛合金股骨假体(60 GPa)由于其弹性模量更接近于骨组织的弹性模量,股骨假体与股骨间的"应力遮挡"效应较小,更有利于应力在股骨假体及股骨间的传递,增加了股骨假体的早期稳定性,延长了其临床寿命。     

Static and fatigue strength of a fixation device transducer for measuring anterior cruciate ligament graft tension

To determine which exercises do not overload the graft-fixation complex during intensive rehabilitation from reconstructive surgery of the anterior cruciate ligament (ACL), it would be useful to measure ACL graft loads during rehabilitative activities in vivo in humans. A previous paper by Ventura et al. (1998) reported on the design of an implantable transducer integrated into a femoral fixation device and demonstrated that the transducer could be calibrated to measure graft loads to better than 10 percent full-scale error in cadaveric knees. By measuring both the static and fatigue strengths of the transducer, the purpose of the present study was to determine whether the transducer could be safely implanted in humans without risk of structural failure. Eight devices were loaded to failure statically. Additionally, seven devices were tested using the up-and-down method to estimate the median fatigue strength at a life of 225,000 cycles. The average ultimate strength was 1856 +/- 74 N and the median fatigue strength was 441 N at a life of 225,000 cycles. The maximum graft load during normal daily activities is estimated to be 500 N and the 225,000 cycle life corresponds to that of the average healthy individual during a 12-week period. Considering that patients who have had an ACL reconstruction are less ambulatory than normal immediately following surgery and that biologic incorporation of the graft should be well developed by 12 weeks thus decreasing the load transmitted to the fixation device, the FDT can be safely implanted in humans without undue risk of structural failure.     

If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.     

If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.     

Parenchymal tethering, airway wall stiffness, and the dynamics of bronchoconstriction.

We do not yet have a good quantitative understanding of how the force-velocity properties of airway smooth muscle interact with the opposing loads of parenchymal tethering and airway wall stiffness to produce the dynamics of bronchoconstriction. We therefore developed a two-dimensional computational model of a dynamically narrowing airway embedded in uniformly elastic lung parenchyma and compared the predictions of the model to published measurements of airway resistance made in rats and rabbits during the development of bronchoconstriction following a bolus injection of methacholine. The model accurately reproduced the experimental time-courses of airway resistance as a function of both lung inflation pressure and tidal volume. The model also showed that the stiffness of the airway wall is similar in rats and rabbits, and significantly greater than that of the lung parenchyma. Our results indicate that the main features of the dynamical nature of bronchoconstriction in vivo can be understood in terms of the classic Hill force-velocity relationship operating against elastic loads provided by the surrounding lung parenchyma and an airway wall that is stiffer than the parenchyma.     

The viscoelastic standard nonlinear solid model: predicting the response of the lumbar intervertebral disk to low-frequency vibrations

Due to the mathematical complexity of current musculoskeletal spine models, there is a need for computationally efficient models of the intervertebral disk (IVD). The aim of this study is to develop a mathematical model that will adequately describe the motion of the IVD under axial cyclic loading as well as maintain computational efficiency for use in future musculoskeletal spine models. Several studies have successfully modeled the creep characteristics of the IVD using the three-parameter viscoelastic standard linear solid (SLS) model. However, when the SLS model is subjected to cyclic loading, it underestimates the load relaxation, the cyclic modulus, and the hysteresis of the human lumbar IVD. A viscoelastic standard nonlinear solid (SNS) model was used to predict the response of the human lumbar IVD subjected to low-frequency vibration. Nonlinear behavior of the SNS model was simulated by a strain-dependent elastic modulus on the SLS model. Parameters of the SNS model were estimated from experimental load deformation and stress-relaxation curves obtained from the literature. The SNS model was able to predict the cyclic modulus of the IVD at frequencies of 0.01 Hz, 0.1 Hz, and 1 Hz. Furthermore, the SNS model was able to quantitatively predict the load relaxation at a frequency of 0.01 Hz. However, model performance was unsatisfactory when predicting load relaxation and hysteresis at higher frequencies (0.1 Hz and 1 Hz). The SLS model of the lumbar IVD may require strain-dependent elastic and viscous behavior to represent the dynamic response to compressive strain.