A three-dimensional nonlinear finite element model of lumbar intervertebral joint in torsion

Torsion as a cause of failure in the lumbar intervertebral joint was studied using a three-dimensional nonlinear finite element model. The role of facets and ligaments as well as the stress distributions in the posterior elements, the disk, the ligaments, and the vertebral body were examined. For physiological range of torsion, the facets carried 10 to 40 percent of the torque. The fiber stresses in the disk were the highest at the lateral margin of the outer layer of the annulus. Therefore, torsion itself is unlikely to cause posterior or posterolateral disk prolapse.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine

To date, studies that have investigated the kinematics of spinal motion segments have largely focused on the contributions that the spinal ligaments play in the resultant motion patterns. However, the specific roles played by intervertebral disk components, in particular the annulus fibrosus, with respect to global motion is not well understood in spite of the relatively large literature base with respect to the local ex vivo mechanical properties of the tissue. The primary objective of this study was to implement the nonlinear and orthotropic mechanical behavior of the annulus fibrosus in a finite element model of an L4/L5 functional spinal unit in the form of a strain energy potential where the individual mechanical contributions of the ground substance and fibers were explicitly defined. The model was validated biomechanically under pure moment loading to ensure that the individual role of each soft tissue structure during load bearing was consistent throughout the physiologically relevant loading range. The fibrous network of the annulus was found to play critical roles in limiting the magnitude of the neutral zone and determining the stiffness of the elastic zone. Under flexion, lateral bending, and axial rotation, the collagen fibers were observed to bear the majority of the load applied to the annulus fibrosus, especially in radially peripheral regions where disk bulging occurred. For the first time, our data explicitly demonstrate that the exact fiber recruitment sequence is critically important for establishing the range of motion and neutral zone magnitudes of lumbar spinal motion segments.     

Tunable Collagen I Hydrogels for Engineered Physiological Tissue Micro-Environments

Collagen I hydrogels are commonly used to mimic the extracellular matrix (ECM) for tissue engineering applications. However, the ability to design collagen I hydrogels similar to the properties of physiological tissues has been elusive. This is primarily due to the lack of quantitative correlations between multiple fabrication parameters and resulting material properties. This study aims to enable informed design and fabrication of collagen hydrogels in order to reliably and reproducibly mimic a variety of soft tissues. We developed empirical predictive models relating fabrication parameters with material and transport properties. These models were obtained through extensive experimental characterization of these properties, which include compression modulus, pore and fiber diameter, and diffusivity. Fabrication parameters were varied within biologically relevant ranges and included collagen concentration, polymerization pH, and polymerization temperature. The data obtained from this study elucidates previously unknown fabrication-property relationships, while the resulting equations facilitate informed a priori design of collagen hydrogels with prescribed properties. By enabling hydrogel fabrication by design, this study has the potential to greatly enhance the utility and relevance of collagen hydrogels in order to develop physiological tissue microenvironments for a wide range of tissue engineering applications.     

Biocomposite hydrogels with carboxymethylated, nanofibrillated cellulose powder for replacement of the nucleus pulposus

Biocomposite hydrogels with carboxymethylated, nanofibrillated cellulose (c-NFC) powder were prepared by UV polymerization of N-vinyl-2-pyrrolidone with Tween 20 trimethacrylate as a cross-linking agent for replacement of the native, human nucleus pulposus (NP) in intervertebral disks. The swelling ratios and the moduli of elasticity in compression of neat and biocomposite hydrogels were evaluated in dependence of c-NFC concentration (ranging from 0 to 1.6% v/v) and degree of substitution (DS, ranging from 0 to 0.23). The viscoelastic properties in shear and the material relaxation behavior in compression were measured for neat and biocomposite hydrogels containing 0.4% v/v of fibrils (DS ranging from 0 to 0.23), and their morphologies were characterized by cryo-scanning electron microscopy (cryo-SEM). The obtained results show that the biocomposite hydrogels can successfully mimic the mechanical and swelling behavior of the NP. In addition, the presence of the c-NFC shows lower strain values after cyclic compression tests and consequently creates improved material relaxation properties compared with neat hydrogels. Among the tested samples, the biocomposite hydrogel containing 0.4% v/v of c-NFC with a DS of 0.17 shows the closest behavior to native NP. Further investigation should focus on evaluation and improvement of the long-term relaxation behavior.     

Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk

Analytical and finite element models (FEMs) were used to quantify poroelastic material properties for a human intervertebral disk. An axisymmetric FEM based on a poroelastic view of disk constituents was developed for a representative human spinal motion segment (SMS). Creep and steady-state response predicted by FEMs agreed with experimental observations, i.e., long-time creep occurs with flow in the SMS, whereas for rapid steady-state loading an "undrained," nearly incompressible response is evident. A relatively low value was determined for discal permeability. Transient and long-term creep FE analyses included the study of deformation, pore fluid flow, stress, and pore fluid pressure. Relative fluid motion associated with transient creep is related to nuclear nutrition and the overall mechanical response in the normal disk. Degeneration of the disk may be associated with an increase in permeability.     

Material constants for a finite element model of the intervertebral disk with a fiber composite annulus

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The model incorporated four substructures: one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when nonaxisymmetric loads were imposed on the model. The annulus material was represented as a layered fiber-reinforced composite. This paper describes the selection of material constants to represent the anisotropic layers of the annulus. It shows that a single set of material constants can be chosen so that model predictions of gross disk behavior under compression, torsion, shear, and moment loading are in reasonable agreement with the mean and range of experimentally measured disk behaviors. It also examines the effects of varying annular material properties.     

THE ULTRASTRUCTURE OF Z DISKS FROM WHITE, INTERMEDIATE, AND RED FIBERS OF MAMMALIAN STRIATED MUSCLES

The Z disk ultrastructure of white, intermediate, and red fibers from mammalian muscle is examined. Three models are proposed that explain the differences between the three types of Z disk. The three models are all based on the same concept, i.e., looping filaments from both sides of the Z disk. The differences between the models are in terms of the spatial relationships of adjacent loops within the Z disk. In the white fiber Z disk model all the loops from one side of the Z disk are on the same plane. In intermediate fibers there are two planes of loops from both sides of the Z disk, whereas in red fibers there are three planes of loops from both sides. The implications of these three structures are discussed in relation to known physiological differences between the fiber types.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion-extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion–extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

Biomechanical influence of disk properties on the load transfer of healthy and degenerated disks using a poroelastic finite element model

Spine degeneration is a pathology that will affect 80% of the population. Since the intervertebral disks play an important role in transmitting loads through the spine, the aim of this study was to evaluate the biomechanical impact of disk properties on the load carried by healthy (Thompson grade I) and degenerated (Thompson grades III and IV) disks. A three-dimensional parametric poroelastic finite element model of the L4/L5 motion segment was developed. Grade I, grade II, and grade IV disks were modeled by altering the biomechanical properties of both the annulus and nucleus. Models were validated using published creep experiments, in which a constant compressive axial stress of 0.35 MPa was applied for 4 h. Pore pressure (PP) and effective stress (S(E)) were analyzed as a function of time following loading application (1 min, 5 min, 45 min, 125 min, and 245 min) and discal region along the midsagittal profile for each disk grade. A design of experiments was further implemented to analyze the influence of six disk parameters (disk height (H), fiber proportion (%F), drained Young's modulus (E(a),E(n)), and initial permeability (k(a),k(n)) of both the annulus and nucleus) on load-sharing for disk grades I and IV. Simulations of grade I, grade III, and grade IV disks agreed well with the available published experimental data. Disk height (H) had a significant influence (p<0.05) on the PP and S(E) during the entire loading history for both healthy and degenerated disk models. Young's modulus of the annulus (E(a)) significantly affected not only S(E) in the annular region for both disk grades in the initial creep response but also S(E) in the nucleus zone for degenerated disks with further creep response. The nucleus and annulus permeabilities had a significant influence on the PP distribution for both disk grades, but this effect occurred at earlier stages of loading for degenerated than for healthy disk models. This is the first study that investigates the biomechanical influence of both geometrical and material disk properties on the load transfer of healthy and degenerated disks. Disk height is a significant parameter for both healthy and degenerated disks during the entire loading. Changes in the annulus stiffness, as well as in the annulus and nucleus permeability, control load-sharing in different ways for healthy and degenerated disks.     

Modelling-informed cell-seeded nerve repair construct designs for treating peripheral nerve injuries

Millions of people worldwide are affected by peripheral nerve injuries (PNI), involving billions of dollars in healthcare costs. Common outcomes for patients include paralysis and loss of sensation, often leading to lifelong pain and disability. Engineered Neural Tissue (EngNT) is being developed as an alternative to the current treatments for large-gap PNIs that show underwhelming functional recovery in many cases. EngNT repair constructs are composed of a stabilised hydrogel cylinder, surrounded by a sheath of material, to mimic the properties of nerve tissue. The technology also enables the spatial seeding of therapeutic cells in the hydrogel to promote nerve regeneration. The identification of mechanisms leading to maximal nerve regeneration and to functional recovery is a central challenge in the design of EngNT repair constructs. Using in vivo experiments in isolation is costly and time-consuming, offering a limited insight on the mechanisms underlying the performance of a given repair construct. To bridge this gap, we derive a cell-solute model and apply it to the case of EngNT repair constructs seeded with therapeutic cells which produce vascular endothelial growth factor (VEGF) under low oxygen conditions to promote vascularisation in the construct. The model comprises a set of coupled non-linear diffusion-reaction equations describing the evolving cell population along with its interactions with oxygen and VEGF fields during the first 24h after transplant into the nerve injury site. This model allows us to evaluate a wide range of repair construct designs (e.g. cell-seeding strategy, sheath material, culture conditions), the idea being that designs performing well over a short timescale could be shortlisted for in vivo trials. In particular, our results suggest that seeding cells beyond a certain density threshold is detrimental regardless of the situation considered, opening new avenues for future nerve tissue engineering.     

Artificial annelid robot driven by soft actuators

The annelid provides a biological solution of effective locomotion adaptable to a large variety of unstructured environmental conditions. The undulated locomotion of the segmented body in the annelid is characterized by the combination of individual motion of the muscles distributed along the body, which has been of keen interest in biomimetic investigation. In this paper, we present an annelid-like robot driven by soft actuators based on dielectric elastomer. To mimic the unique motion of the annelid, a novel actuation method employing dielectric elastomer is developed. By using the actuator, a three-degree-of-freedom actuator module is presented, which can provide up-down translational motion, and two rotational degree-of-freedom motion. The proposed actuation method provides advantageous features of reduction in size, fast response and ruggedness in operation. By serially connecting the actuator modules, a micro-robot mimicking the motion of the annelid is developed and its effectiveness is experimentally demonstrated.     

Finite element simulation of an artificial intervertebral disk using fiber reinforced laminated composite model

Degeneration of intervertebral disk (IVD) has been increased in recent years. The lumbar herniation can be cured using conservative and surgical procedures. Surgery is considered after failure of conservative treatment. Partial discectomy, fusion, and total disk replacement (TDR) are also common surgical treatments for degenerative disk disease. However, due to limitations and disadvantages of the current treatments, many studies have been carried out to approach the best design of mimicking natural disk. Recently, a new method of TDRs has been introduced using nature deformation of IVD by reinforced fibers of annulus fibrosis. Nonetheless, owing to limitations of experimental works on the human body, numerical studies of IVD may help to understand load transfer and biomechanical properties within the disks with reinforced fibers. In this study, a three-dimensional (3D) finite element model of the L2-L3 disk vertebrae unit with 12 vertical fibers embedded into annulus fibrosis was constructed. The IVD was subjected to compressive force, bending moment, and axial torsion. The most important parameters of disk failures were compared to that of experimental data. The results showed that the addition of reinforced fibers into the disk invokes a significant decrease of stress in the nucleus and annulus. The findings of this study may have implications not only for developing IVDs with reinforced fibers but also for the application of fiber reinforced IVD in orthopedics surgeries as a suitable implant.     

Design considerations and challenges for mechanical stretch bioreactors in tissue engineering

With the increase in average life expectancy and growing aging population, lack of functional grafts for replacement surgeries has become a severe problem. Engineered tissues are a promising alternative to this problem because they can mimic the physiological function of the native tissues and be cultured on demand. Cyclic stretch is important for developing many engineered tissues such as hearts, heart valves, muscles, and bones. Thus a variety of stretch bioreactors and corresponding scaffolds have been designed and tested to study the underlying mechanism of tissue formation and to optimize the mechanical conditions applied to the engineered tissues. In this review, we look at various designs of stretch bioreactors and common scaffolds and offer insights for future improvements in tissue engineering applications. First, we summarize the requirements and common configuration of stretch bioreactors. Next, we present the features of different actuating and motion transforming systems and their applications. Since most bioreactors must measure detailed distributions of loads and deformations on engineered tissues, techniques with high accuracy, precision, and frequency have been developed. We also cover the key points in designing culture chambers, nutrition exchanging systems, and regimens used for specific tissues. Since scaffolds are essential for providing biophysical microenvironments for residing cells, we discuss materials and technologies used in fabricating scaffolds to mimic anisotropic native tissues, including decellularized tissues, hydrogels, biocompatible polymers, electrospinning, and 3D bioprinting techniques. Finally, we present the potential future directions for improving stretch bioreactors and scaffolds. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:543–553, 2016     

The role of the nucleus pulposus in neutral zone human lumbar intervertebral disc mechanics

To study the effect of denucleation on the mechanical behavior of the human lumbar intervertebral disc through a 2mm incision, two groups of six human cadaver lumbar spinal units were tested in axial compression, axial rotation, lateral bending and flexion/extension after incremental steps of "partial" denucleation. Neutral zone, range of motion, stiffness, intradiscal pressure and energy dissipation were measured; the results showed that the contribution of the nucleus pulposus to the mechanical behavior of the intervertebral disc was more dominant through the neutral zone than at the farther limits of applied loads and moments.     

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R ²?>?0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.     

Effect of joint laxity on polyethylene wear in total knee replacement

Experimental simulator studies are frequently performed to evaluate wear behavior in total knee replacement. It is vital that the simulation conditions match the physiological situation as closely as possible. To date, few experimental wear studies have examined the effects of joint laxity on wear and joint kinematics and the absence of the anterior cruciate ligament has not been sufficiently taken into account in simulator wear studies.The aim of this study was to investigate different ligament and soft tissue models with respect to wear and kinematics.A virtual soft tissue control system was used to simulate different motion restraints in a force-controlled knee wear simulator.The application of more realistic and sophisticated ligament models that considered the absence of anterior cruciate ligament lead to a significant increase in polyethylene wear (p=0.02) and joint kinematics (p<0.01). We recommend the use of more complex ligament models to appropriately simulate the function of the human knee joint and to evaluate the wear behavior of total knee replacements. A feasible simulation model is presented.     

Stochastic differential equation model for cerebellar granule cell excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches.