An accurate constitutive law for the annulus fibrosus (AF) is critical to modeling the complex loads and deformations of the intervertebral disc. In the healthy disc, the loads applied to the AF are primarily a combination of tension and torsion. Several researchers [1–5] have developed nonlinear strain energy functions to model the AF using the fiber-reinforced composite theory of Spencer [6]. However, a limitation to these previous studies is that they did not include shear data in calculating the model coefficients. Although many of these models have non-physical representations of the stress contribution of the collagen fibers [1, 2, 4], (i.e. collagen fibers only support tensile loads, but in the models they also support compressive axial loads), others have implemented a tension-only restriction for collagen fibers [3, 5]. The objective of this study was to model shear behavior of the AF in addition to previously modeled loading conditions [2]. The currently proposed model includes shear data in determining model coefficients. Additionally, we examined the effect of a tension-only representation of collagen fibers on the model’s fit to the experimental data.

The aortic root is the portion of the outflow tract of the left ventricle that includes the aortic leaflets, the aortic annulus, the sinuses of Valsalva and the sinotubular junction. The impairment of one or more of these structures can lead not only to dysfunctions of the root, but also to alterations of the adjacent anatomical sites, such as the ascending aorta. The raise and the progress of the alterations are often related to more concomitant factors, whose separated effect can be difficult to assess. At this purpose computational finite element (FE) models can be a useful tool, given their capability the recreate different scenarios by varying one or more parameters of the model in a controlled fashion.

Intervertebral disc (IVD) is the largest avascular structure in the human body and nutrition supply into IVD is mainly through diffusion from the peripheral blood vessels. Poor nutrition supply to the disc is believed to be one of the causes for disc degeneration. While many studies have aimed at studying and analyzing the effect of mechanical loading on water content, chemical composition, and nutritional levels in IVD [1–3], no study has been reported to investigate the effect of mechanical compression on oxygen diffusion in the IVD tissue. The objective of this study was to determine oxygen diffusivity in annulus fibrosus (AF) samples under different levels of compression.

Degeneration in the spinal structures can be a major source of pain that increases with aging in a roughly linear progression. Pain has been further correlated with the regions of high stress and strain concentrations. Due to difference in the regional anatomy and physiology of the cervical, thoracic, and lumbar levels, their biomechanical response to physiological loadings is different. The fluid egresses outside in the radial direction from nucleus pulposus (NP) to annulus fibrosus (AF) under compression, which generates a hydrostatic pressure against an external applied load. The increased NP pressure, in many clinical cases, results into various abnormal disc pathologies such as protrusions and herniations. Chiropractic care in the management of these spinal dysfunctions uses manual manipulation therapies such as distraction techniques to relieve the disc from high pressure and radial bulging. Despite manual distraction therapy is a three-dimensional force application; major proportion of the load is exerted in the axial upward direction. Although few biomechanical studies have compared the segmental biomechanics under axial traction loads, to the best of our knowledge, there is no study that distinguishes between the behavior of cervical, thoracic, and lumbar segments to these loads. The objective of the present study, therefore, was to investigate that how the biomechanical stresses, that were developed under upper body weight (BW), changes in the various spinal segments (cervical, thoracic, and lumbar) and in the different spinal structures (top vertebra, superior endplate, and disc) when the traction forces were applied as the therapeutic modalities in the chiropractic interventions.

The mitral valve annulus is an anatomical structure joining the leaflets and left ventricle wall. It is divided into the fibrous annulus in the anteromedial section and the myocardium annulus in the posterolateral section, according to annulus histology. Two trigones are in the fibrous annulus. Mitral annulus supports leaflets in the valve coaptation and controls inflow hemodynamics during a cardiac cycle. When the mitral valve is fully open during diastole, inflow drag force on the leaflets and chordae pulls the leaflets approximately apically. As mitral valve leaflets coaptate during systole, trans-mitral pressure acts on the leaflets and induces leaflet tension which is transferred to the annulus and chordae. The leaflet tension at the annulus per unit length is defined as annulus tension (AT). Annulus dilatation is a mitral valve pathology that is related to AT and its interaction with the myocardium. Little is known about the detailed mechanism of annulus dilatation. But from mechanics standpoint, there are two possible mechanisms that change annulus size. AT pulls annulus towards the center of mitral valve orifice and is balanced by myocardium force on the annulus that pulls the annulus outward. Annulus size depends upon which force is predominant in annulus mechanics. It is hypothesized that the AT is one of the important mechanism to control annulus size. This hypothesis suggests that annulus size can be controlled by the AT and its interaction with the myocardium. We aim to understand annulus dilatation by the AT. The objective of the current study was to understand the tension transferred to the mitral annulus by the leaflets during the valve coaptation.

The intervertebral disc (IVD) is the largest cartilaginous structure in human body that contributes to flexibility and load support in the spine. To accomplish these functions, the disc has a unique architecture consisting of a centrally-located nucleus pulposus (NP) surrounded superiorly and inferiorly by cartilage endplates (CEP) and peripherally by the annulus fibrosus (AF). Disc degeneration is strongly linked to low back pain. Poor nutrient supply has been suggested as a potential mechanism for disc degeneration. Previous theoretical studies have shown that the distributions of nutrients and metabolites (e.g., oxygen, glucose, and lactate) within the IVD depended on tissue diffusivities, nutrient supply, and cellular metabolic rates [1, 2]. Based on a multiphasic mechano-electrochemical finite element model of human IVD [3], our recent theoretical study suggested that the mechanical loading has little effect on small solute transport (e.g., glucose), but significantly affects large solute transport (e.g., growth factor). The objective of this study was to further develop the multiphasic finite element model of IVD by including the cartilage endplate and considering the nutrient consumption of disc cells. Using this model, the effects of endplate and mechanical loading on solute transport in IVD were examined.

The mitral valve annulus is a dynamic structure that changes in its shape during the cardiac cycle. It changes from a flat shape during diastole to a non-planar saddle shape during systole, which has been confirmed in animals and humans using various techniques. However a teleologic reason for nature’s selection of this shape and its role in mitral valve mechanics are poorly understood. Recent studies from our laboratory indicate that mitral annular saddle optimizes the force distribution on the valve components that could potentially affect valve function and mechanics. The objective of this study is to provide a quantitative and mechanistic insight into the synergy between the non-planar mitral annular shape and posterior leaflet mechanics. The posterior leaflet was specifically selected as most mitral valve surgeries require placement of suture lines in this region, which fail in more than 40% of the patients due to high strains in this region.

Structural alterations of the disc are accompanied by changes in disc tissue structure and composition during degeneration processes. Fissures and cracks appear in the disc some times extending from the outer annulus to the nucleus. Animal studies have shown that when a rim lesion was introduced in the annulus, progressive failure on the inner annulus was observed (1). From a macroscopic study on lumbar motion segments originating from regular autopsies it was shown (2) that nuclear clefts precede annular tears. Within the annular tears, rim lesions follow the radial and concentric tears. These age-related changes in disc tissue decrease the structural integrity of the disc contributing to the progression of degeneration. The effect of existing cracks and fissures in the lumbar discs on the biomechanics of the disc is an area where there is very little information currently in the literature.

The intervertebral disc is comprised of complex components that provide the disc with nonlinear, viscoelastic and anisotropic mechanical properties. The annulus fibrosus (AF) is a highly organized structure composed of concentric layers of collagen fibers embedded in a proteoglycan matrix. The AF has a high tensile stiffness and supports the large loads encountered by the disc. Mathematical models are needed to interpret and elucidate the meaning of experimental measurements made in mechanical tests. Based upon the classic work of Spencer [1], the AF has been modeled as a fiber-induced anisotropic hyperelastic material [e.g.,2–6], using the principle invariants of the Green deformation tensor and structural tensors representing the collagen fiber populations. Contributions of other AF components to mechanical behaviors are less understood than the fibers or matrix and may include connections between collagens and proteoglycans that can be incorporated into models through fiber-matrix interactions [2–4]. The previous models, however, have not been applied to experimental data from both nondegenerate and degenerate tissue. Constitutive modeling applied to nondegenerate and degenerate AF may elucidate microstructural changes with degeneration, will be useful for finite element models [5], and provide targets for disc treatments, such as tissue engineered constructs [7].

Physiological cyclic loading of the intervertebral disc generally occurs between 1 and 5 Hz [1]. However, most mechanical assessments of disc AF tissue have relied on uniaxial tensile tests under quasi-static conditions [2]. Furthermore, the few studies that have addressed AF viscoelasticity have reported only static viscoelastic properties such as creep or stress-relaxation [3]. As such, there exists almost no data characterizing the dynamic viscoelastic properties of AF tissue in tension. Such data would be critical for several applications: to elucidate the mechanical progression of intervertebral disc degeneration, to develop and validate structural finite element models, and to provide native tissue benchmarks for regenerative approaches that aim to restore mechanical function to diseased or degenerate tissue. Therefore, the objectives of this study are to: (1) quantify human AF tissue frequency-dependent and strain-dependent viscoelastic properties of human AF tissue in circumferential tension, and (2) determine the effects of disc degeneration on these properties.

The mitral valve apparatus is a complex structure with multiple components that require seamless, integrated operation for normal valve function. One of these components is the annulus, a fibrous ring of tissue that defines the boundary between the mitral valve leaflets and the surrounding superstructure of the heart. During the cardiac cycle the annulus undergoes large deformations and dramatic shape changes. Moreover, the annulus motion represents a key boundary condition for mitral valve leaflet deformation. Yet, to date our knowledge of the subtle deformations this structure undergoes during the cardiac cycle remains very limited. In the present study, an array of 1 mm diameter piezoelectric sonocrystals was implanted in 5 sheep to quantify annular deformation over the complete cardiac cycle. These crystals act as fiducial markers for the mitral annulus with a temporal resolution of ∼1ms and a special resolution of .01mm in a calibrated three dimensional space. A quintic order generalized 3D spline was developed to reconstruct the annular geometry.

The architecture of load-bearing fibrous tissues is optimized to enable a specific set of mechanical functions. This organization arises from a complex process of cell patterning, matrix deposition, and functional maturation [1]. In their mature state, these tissues span multiple length scales, encompassing nanoscale interactions of cells with extracellular matrix to the centimeter length scales of the anatomic tissue volume and shape. Two structures that typify dense fibrous tissues are the meniscus of the knee and the annulus fibrosus (AF) of the intervertebral disc (IVD). The mechanical function of the wedge-shaped knee meniscus is based on its stiff prevailing circumferential collagen architecture that resists tensile deformation [2,3]. Adding to its complexity, radial tie fibers and sheets are interwoven amongst these fibers, increasing stiffness in the transverse direction and binding the tissue together [4]. In the annulus fibrosus, multiple anisotropic lamellae are stacked in concentric rings with their prevailing fiber directions alternating above and below the horizontal axis in adjacent layers [5]. The high circumferential tensile properties of this laminate structure allow it to resist bulging of the nucleus pulposus with compressive loading of the spine. Given their structural properties, unique form, and demanding mechanical environments, the knee meniscus and the AF region of the IVD represent two of the most challenging tissues to consider for functional tissue engineering.

In vivo studies on the intervertebral disc (IVD) indicate that the magnitude, frequency, and duration of applied compression loading results in alterations in mRNA expression, composition, and annulus fibrosus structure [1]. In vivo models typically use small animal models or small sample sizes that make it difficult to evaluate multiple dependent variables on the same tissue. In this study, it was considered a priority to utilize a large animal model to investigate the effects of magnitude of compression loading on interacting dependent variable measurements of disc cell viability, biosynthesis, composition, structure, and biomechanics. A bovine IVD organ culture system was used because it provides control over mechanical and chemical boundary conditions while maintaining viable cells and normal cell-matrix interactions. To date, there are no studies investigating the response of the IVD in organ culture to dynamic mechanical loading.

The intervertebral disc (IVD) is a unique orthopaedic tissue consisting of at least two cell types: fibroblast-like annulus fibrosus (AF) cells and chondrocyte-like nucleus pulposus (NP) cells. Culture of cells in 3D gel matrices (such as alginate or agarose), maintains the normal morphology and ECM molecule production of chondrocytes for extended periods of time and also allows the application of various forms of mechanical stimulation, such as hydrostatic or compressive loading. In vivo studies have shown IVD cells to be responsive to frequency, duration, and amplitude of mechanical load [1]. IVD literature on mechanobiology uses varying methodologies to apply dynamic loads (compression, hydrostatic forces), with different times of mechanical stimulation, differences in model systems (in vivo, tissue culture, cell culture), species, and ages, and an optimal loading protocol to stimulate extracellular matrix protein accumulation is unknown. The overall goal of this work is to evaluate the potential, and perhaps even feasibility, of mechanical stimulation for extracellular matrix (ECM) regeneration using intervertebral disc cells. Also of interest is whether cells from mature tissue are capable of serving as a potential cell source for future IVD regeneration [2,3].

The intervertebral disc (IVD) is the largest cartilaginous structure in human body that contributes to flexibility and load support in the spine. To accomplish these functions, the disc has a unique architecture consisting of a centrally-located nucleus pulposus (NP) surrounded superiorly and inferiorly by cartilage endplates and peripherally by the annulus fibrosus (AF). Because the disc is avascular and experiences mechanical loads, the cells in IVD tissues live in a complex physical environment. Knowledge of mechanical, chemical and electrical signals within the tissue is important for understanding mechanobiology of IVD [1]. The objective of this study was to develop a three-dimensional (3D), inhomogeneous finite element model (FEM) for human IVD for analyzing the physical environment and solute transport within the tissue under different mechanical loading conditions. A case of IVD under axial compression was simulated and reported.

Intervertebral disc tissue consists of a fluid-filled extra-cellular matrix, in which living cells are sparsely dispersed. The mechanical function is highly dependent on the composition of the extra-cellular matrix, which primary consists of collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans (PG’s), the cation concentration inside the tissue is higher than physiological. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue [1]. Because the intervertebral disc is gripped between two vertebrae, the swelling is constrained in vivo , resulting in a intradiscal pressure of 0.1 to 0.2 MPa in supine position. It has been shown that the osmotic pressure inside cartilaginous tissues is much higher than would be expected based on its FCD [2]. This is because part of the water in the tissue is absorbed by the collagen fibers. The proteoglycan molecules, because of their large size, are excluded from this intra-fibrillar space. This means that their effective concentrations are much higher in the extra-fibrillar space than if they were distributed uniformly throughout the entire matrix. Hence, the effective fixed charge density is higher than if computed from total tissue water content. A recent study demonstrates that intrafibrillar water increases osmolarity within the annulus fibrosus substantially [3]. On the other hand, Wognum et al. [4] showed by means of a physical and a numerical model of the disc that high osmolarity within the disc has a protective effect against crack propagation within the disc. Hence, the decrease in osmolarity associated with degeneration may be an explanation of (1) the growing number of cracks observed in the degenerating disc as well as (2) the poor correlation between external loading and crack propagation [5]. The purpose of the present study is to test the hypothesis of Wognum et al. [4] through direct observation of the deformation of annulus fibrosus tissue around discontinuities within its collagen network.

Current surgical treatments for intervertebral disc (IVD) degeneration result in decreased mobility of the spine [1]. A tissue engineering approach may provide an alternative that restores both IVD structure and function. The IVD is comprised of three distinct regions: the outer annulus fibrosus (OA), inner annulus fibrosus (IA), and the nucleus pulposus (NP). Each of the cell populations within these regions possess unique phenotypic properties that are greatly influenced by environmental factors, such as the surrounding 3-D extracellular matrix (ECM) and mechanical loading (i.e., hydrostatic pressurization) [2]. As such, both the 3-D scaffold and in vitro culture conditions may have marked effects on the development of tissue-engineered IVD constructs. Although the influence of mechanical loading on IVD cells and explants has been investigated, no prior studies have examined the impact of hydrostatic pressurization on OA and IA cells in 3-D culture. Therefore, the objective of this study was to determine the effects of dynamic hydrostatic pressurization on OA and IA cells seeded on 3-D fibrous poly(glycolic acid)-poly(L-lactic acid) (PGA-PLLA) scaffolds. We hypothesized that the application of hydrostatic pressure would promote increased production of type II collagen and chondroitin sulfate proteoglycan in both OA- and IA-seeded constructs.

Anterior surgical approach is commonly used for Total Disc Replacement (TDR) surgeries in the cervical spine. The general procedure includes removal of the nucleus and anterior annulus of the intervertebral disc. Resection of Anterior Longitudinal Ligaments (ALL) is often performed to enter the disc space. The cervical spine also contains a unique anatomical feature called Luschka’s joints. These “joints” are actually fissures in the disc which run approximately parallel to the uncinate processes. These joints are thought to provide biomechanical stability to the cervical spine. However, sometimes surgeons have to sacrifice the uncinate processes at the involved level as well. We hypothesized that the cervical spine loses stability if the uncinate processes are removed along with disc replacement. We used a Finite Element (FE) model of cervical spine to prove the hypothesis (Fig1).

Annulus dilation is one of the main causes of functional mitral regurgitation. Although the annulus dilation is usually accompanied by left ventricle dilation and dysfunction, the mechanical relation between them is not fully elucidated yet. In this paper, the assumption is made that the ventricular dysfunction increases the cyclic loading conditions on the mitral valve apparatus. This effect may cause fatigue and weaken the tissue. This hypothesis is investigated in vitro by applying increased cyclic loadings to the tissue and evaluating the tissue stiffness during the cycles. The results of this study show that the tissue loses its strength after cyclic fatigue loadings.

Collagen gel tissue-equivalents (TEs), which are simple model tissues with tunable properties, have been used to explore many properties of soft tissues, such as how structural and compositional properties affect mechanical function [1–4]. One aspect not captured in previous TE formulations is residual stress due to interactions among components, which has an important functional role in many tissues (e.g., blood vessels [5], ligaments [6], annulus fibrosus [7]). Since the in vivo stress state of native tissues is not easily replicated in TE fabrication, a different method for “pre-stressing” collagen networks of TEs was necessary. To this end, co-gel TEs were fabricated by adding hyaluronic acid (HA) to reconstituted Type-I collagen (Col) gels. When placed in solutions of varying osmolarity, HA-Col TEs swell as the HA binds water, which in turn will stretch (and stress) the collagen network. In this way, TEs with residual stress (i.e., pre-stressed collagen fibers) can be fabricated and evaluated in order to elucidate relationships between residual stress and functional properties. Therefore, the goals of the present study were to fabricate HA-Col TEs, make initial measurements of their swelling properties, and quantify the mechanical response and changes in microstructural organization under applied tensile load.