L-type Voltage-Gated calcium channels partly mediate Mechanotransduction in the intervertebral disc.

Background: Intervertebral disc (IVD) degeneration continues to be a major global health challenge, with strong links to lower back pain, while the pathogenesis of this disease is poorly understood. In cartilage, much more is known about mechanotransduction pathways involving the strain-generated potential (SGP) and function of voltage-gated ion channels (VGICs) in health and disease. This evidence implicates a similar important role for VGICs in IVD matrix turnover. However, the field of VGICs, and to a lesser extent the SGP, remains unexplored in the IVD. Methods: A two-step process was utilized to investigate the role of VGICs in the IVD. First, immunohistochemical staining was used to identify and localize several different VGICs in bovine and human IVDs. Second, a pilot study was conducted on the function of L-type voltage gated calcium channels (VGCCs) by inhibiting these channels with nifedipine (Nf) and measuring calcium influx in monolayer or gene expression from 3D cell-embedded alginate constructs subject to dynamic compression. Results: Several VGICs were identified at the protein level, one of which, Cav2.2, appears to be upregulated with the onset of human IVD degeneration. Inhibiting L-type VGCCs with Nf supplementation led to an altered cell calcium influx in response to osmotic loading as well as downregulation of col 1a, aggrecan and ADAMTS-4 during dynamic compression. Conclusions: This study demonstrates the presence of several VGICs in the IVD, with evidence supporting a role for L-type VGCCs in mechanotransduction. These findings highlight the importance of future detailed studies in this area to fully elucidate IVD mechanotransduction pathways and better inform treatment strategies for IVD degeneration.

The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity.

The strain-generated potential (SGP) is a well-established mechanism in cartilaginous tissues whereby mechanical forces generate electrical potentials. In articular cartilage (AC) and the intervertebral disc (IVD), studies on the SGP have focused on fluid- and ionic-driven effects, namely Donnan, diffusion and streaming potentials. However, recent evidence has indicated a direct coupling between strain and electrical potential. Piezoelectricity is one such mechanism whereby deformation of most biological structures, like collagen, can directly generate an electrical potential. In this review, the SGP in AC and the IVD will be revisited in light of piezoelectricity and mechanotransduction. While the evidence base for physiologically significant piezoelectric responses in tissue is lacking, difficulties in quantifying the physiological response and imperfect measurement techniques may have underestimated the property. Hindering our understanding of the SGP further, numerical models to-date have negated ferroelectric effects in the SGP and have utilised classic Donnan theory that, as evidence argues, may be oversimplified. Moreover, changes in the SGP with degeneration due to an altered extracellular matrix (ECM) indicate that the significance of ionic-driven mechanisms may diminish relative to the piezoelectric response. The SGP, and these mechanisms behind it, are finally discussed in relation to the cell response.

The Importance of the Mixing Energy in Ionized Superabsorbent Polymer Swelling Models.

The Flory-Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

Piezoelectricity in the Intervertebral disc.

Lower back pain is a major global health challenge that can often be caused by degeneration of the Intervertebral Disc (IVD). While IVD biomechanics are a key factor in the degenerative cycle, many mechanotransduction pathways remain unknown, in particular the electro-mechanical coupling in the loaded tissue. However, despite evidence for a role in the mechanically-induced remodelling of similar tissue, piezoelectricity has been overlooked in the IVD. In this study, we investigate the piezoelectric properties of the Annulus Fibrosus (AF) and the Nucleus Pulposus (NP) by measuring the direct piezoelectric effect of mechanically-induced electrical potential change. To verify these findings, we conducted Piezoresponse Force Microscopy (PFM) to measure the inverse effect of electrically-induced deformation. We demonstrate that, for the first time, piezoelectricity is generated throughout the IVD. Piezoelectric effects were greater in the AF than the NP, owing to the organised collagen networks present. However, the piezoresponse found in the NP indicates piezoelectric properties of non-collagenous proteins that have not yet been studied. The voltage generated by longitudinal piezoelectricity in-vivo has been calculated to be ~1 nV locally, indicating that piezoelectric effects may directly affect cell alignment in the AF and may work in conjunction with streaming potentials throughout the IVD. In summary, we have highlighted an intricate electro-mechanical coupling that appears to have distinct physiological roles in the AF and NP. Further study is required to elucidate the cell response and determine the potential role of piezoelectric effects in regeneration and preventative measures from degeneration.

Chemically Responsive Hydrogel Deformation Mechanics: A Review.

A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.

Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels.

In numerous industrial applications, the microstructure of materials is critical for performance. However, finite element models tend to average out the microstructure. Hence, finite element simulations are often unsuitable for optimisation of the microstructure. The present paper presents a modelling technique that addresses this limitation for superabsorbent polymers with a partially cross-linked surface layer. These are widely used in the industry for a variety of functions. Different designs of the cross-linked layer have different material properties, influencing the performance of the hydrogel. In this work, the effects of intrinsic properties on the fracture nucleation and propagation in cross-linked hydrogels are studied. The numerical implementation for crack propagation and nucleation is based on the framework of the extended finite element method and the enhanced local pressure model to capture the pressure difference and fluid flow between the crack and the hydrogel, and coupled with the cohesive method to achieve crack propagation without re-meshing. Two groups of numerical examples are given: (1) effects on crack propagation, and (2) effects on crack nucleation. Within each example, we studied the effects of the stiffness (shear modulus) and ultimate strength of the material separately. Simulations demonstrate that the crack behaviour is influenced by the intrinsic properties of the hydrogel, which gives numerical support for the structural design of the cross-linked hydrogel.

On the Physics Underlying Longitudinal Capillary Recruitment.

Numerous researchers have found that capillary vessel haematocrit depends on the vasodilatory state of the arterioles. At rest, vessel haematocrit is down to 15 %, suggesting a red blood cell velocity three times higher than the plasma velocity. This finding is analysed in the context of present understanding of propulsion of red blood cells (RBCs) and plasma by means of the arteriovenous pressure gradient. Interfacial forces between the red blood cells and the plasma are proposed as a rational explanation of the observed red blood cell velocities. While the arteriovenous pressure gradient across the capillaries propels the red blood cell and the plasma jointly, interfacial forces along the red blood cell membrane can propel RBCs at the cost of the plasma. Different options are explored for the physical origin of these interfacial forces and oxygen gradients are found to be the most probable source.

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability.

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogels. The extremely large degree of swelling is one of the most distinctive characteristics of such hydrogels, as the volume increase can be about 30 times its original volume when exposed to physiological solution. The large deformation resulting from the swelling demands careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using the mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on the swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of the local mass conservation of MHFEM contributes to a more accurate calculation of the deformation as the permeability across the swelling gel in a transient state is highly non-uniform. We show that the proposed model is able to simulate the free swelling of a random-shaped gel and the squeezing of fluid out of a swollen gel. Finally, we make use of the proposed numerical model to study the onset of surface instability in transient swelling.

Convection associated with exclusion zone formation in colloidal suspensions.

The long-range repulsion of colloids from various interfaces has been observed in a wide range of studies from different research disciplines. This so-called exclusion zone (EZ) formation occurs near surfaces such as hydrogels, polymers, or biological tissues. It was recently shown that the underlying physical mechanism leading to this long-range repulsion is a combination of ion-exchange at the interface, diffusion of ions, and diffusiophoresis of colloids in the resulting ion concentration gradients. In this paper, we show that the same ion concentration gradients that lead to exclusion zone formation also imply that diffusioosmosis near the walls of the sample cell must occur. This should lead to convective flow patterns that are directly associated with exclusion zone formation. We use multi-particle tracking to study the dynamics of particles during exclusion zone formation in detail, confirming that indeed two pronounced vortex-like convection rolls occur near the cell walls. These dramatic flow patterns persist for more than 4 hours, with the typical velocity decreasing as a function of time. We find that the flow velocity depends strongly on the surface properties of the sample cell walls, consistent with diffusioosmosis being the main physical mechanism that governs these convective flows.

Long-range repulsion of colloids driven by ion exchange and diffusiophoresis.

Interactions between surfaces and particles in aqueous suspension are usually limited to distances smaller than 1 µm. However, in a range of studies from different disciplines, repulsion of particles has been observed over distances of up to hundreds of micrometers, in the absence of any additional external fields. Although a range of hypotheses have been suggested to account for such behavior, the physical mechanisms responsible for the phenomenon still remain unclear. To identify and isolate these mechanisms, we perform detailed experiments on a well-defined experimental system, using a setup that minimizes the effects of gravity and convection. Our experiments clearly indicate that the observed long-range repulsion is driven by a combination of ion exchange, ion diffusion, and diffusiophoresis. We develop a simple model that accounts for our data; this description is expected to be directly applicable to a wide range of systems exhibiting similar long-range forces.

Ageing and degenerative changes of the intervertebral disc and their impact on spinal flexibility.

PURPOSE: Degeneration of the intervertebral disc is associated with various morphological changes of the disc itself and of the adjacent structures, such as reduction of the water content, collapse of the intervertebral space, disruption and tears, and osteophytes. These morphological changes of the disc are linked to alterations of the spine flexibility. This paper aims to review the literature about the ageing and degenerative changes of the intervertebral disc and their link with alterations in spinal biomechanics, with emphasis on flexibility. METHODS: Narrative literature review. RESULTS: Clinical instability of the motion segment, usually related to increased flexibility and hypothesized to be connected to early, mild disc degeneration and believed to be responsible for low back pain, was tested in numerous in vitro studies. Despite some disagreement in the findings, a trend toward spinal stiffening with the increasing degeneration was observed in most studies. Tests about tears and fissures showed inconsistent results, as well as for disc collapse and dehydration. Vertebral osteophytes were found to be effective in stabilizing the spine in bending motions. CONCLUSIONS: The literature suggests that the degenerative changes of the intervertebral disc and surrounding structures lead to subtle alteration of the mechanical properties of the functional spinal unit. A trend toward spinal stiffening with the increasing degeneration has been observed in most studies.

Confined compression and torsion experiments on a pHEMA gel in various bath concentrations.

The constitutive behaviour of cartilaginous tissue is the result of complex interaction between electrical, chemical and mechanical forces. Electrostatic interactions between fixed charges and mobile ions are usually accounted for by means of Donnan osmotic pressure. Recent experimental data show, however, that the shear modulus of articular cartilage depends on ionic concentration even if the strain is kept constant. Poisson-Boltzmann simulations suggest that this dependence is intrinsic to the double-layer around the proteoglycan chains. In order to verify this premise, this study measures whether--at a given strain--this ionic concentration-dependent shear modulus is present in a polymerized hydroxy-ethyl-methacrylate gel or not. A combined 1D confined compression and torque experiment is performed on a thin cylindrical hydrogel sample, which is brought in equilibrium with, respectively, 1, 0.1 and 0.03 M NaCl. The sample was placed in a chamber that consists of a stainless steel ring placed on a sintered glass filter, and on top a sintered glass piston. Stepwise ionic loading was cascaded by stepwise 1D compression, measuring the total stress after equilibration of the sample. In addition, a torque experiment was interweaved by applying a harmonic angular displacement and measuring the torque, revealing the relation between aggregate shear modulus and salt concentration at a given strain.

Biomechanical behavior of a biomimetic artificial intervertebral disc.

STUDY DESIGN: The biomechanical behavior of a biomimetic artificial intervertebral disc (AID) was characterized in vitro in axial compression and compared with natural disc behavior. OBJECTIVE: To evaluate the strength and durability of a novel biomimetic AID and to demonstrate whether its axial deformation behavior is similar to that of a natural disc. SUMMARY OF BACKGROUND DATA: Current clinically used AIDs have reasonable success rates. However, because of their nonphysiological design, spinal mechanics are altered. To avoid long-term complications, a novel biomimetic AID, with a nucleus-annulus structure and osmotic swelling properties has been developed. METHODS: Eighteen AIDs in total were tested in axial compression. Six were loaded monotonically to determine strength. Six were tested in fatigue (600-6000 N). Another 6 were used to characterize the axial creep and dynamic behavior (0.01-10 Hz). Creep and dynamic response were also determined for 4 AIDs after fatigue loading. RESULTS: The AIDs remained intact up to 15 kN and 10 million cycles. The creep and dynamic behavior were similar to the natural disc behavior, except for hysteresis, which was 20% to 30% higher. After fatigue, creep decreased from 4% to 1%, stiffness increased 2-fold, and hysteresis was reduced to that for a normal disc. CONCLUSION: A strong and durable AID design was introduced. Compared with current clinical articulating AIDs, this biomimetic AID introduces the natural disc annulus-nucleus structure, resulting in axial behavior closer to that of the natural disc.

Design of next generation total disk replacements.

To improve the treatments for low back pain, new designs of total disk replacement have been proposed. The question is how well these designs can act as a functional replacement of the intervertebral disk. Four finite element models were made, for four different design concepts, to determine how well they can mimic the physiological intervertebral disk mechanical function. The four designs were a homogenous elastomer, a multi-stiffness elastomer, an elastomer with fiber jacket, and a hydrogel with fiber jacket. The best material properties of the four models were determined by optimizing the model behavior to match the behavior of the intervertebral disk in flexion-extension, axial rotation, and lateral bending. It was shown that neither a homogeneous elastomer nor a multi-stiffness elastomer could mimic the non-linear behavior within the physiological range of motion. Including a fiber jacket around an elastomer allowed for physiological motion in all degrees of freedom. Replacing the elastomer by a hydrogel yielded similar good behavior. Mimicking the non-linear behavior of the intervertebral disk, in the physiological range of motion is essential in maintaining and restoring spinal motion and in protecting surrounding tissues like the facet joints or adjacent segments. This was accomplished with designs mimicking the function of the annulus fibrosus.

Biaxial testing of canine annulus fibrosus tissue under changing salt concentrations.

The in vivo mechanics of the annulus fibrosus of the intervertebral disc is one of biaxial rather than uniaxial loading. The material properties of the annulus are intimately linked to the osmolarity in the tissue. This paper presents biaxial relaxation experiments of canine annulus fibrosus tissue under stepwise changes of external salt concentration. The force tracings show that stresses are strongly dependent on time, salt concentration and orientation. The force tracing signature of a response to a change in strain, is one of a jump in stress that relaxes partly as the new strain is maintained. The force tracing signature of a stepwise change in salt concentration is a progressive monotonous change in stress towards a new equilibrium value. Although the number of samples does not allow any definitive quantitative conclusions, the trends may shed light on the complex interaction among the directionality of forces, strains and fiber orientation on one hand, and on the other hand, the osmolarity of the tissue. The dual response to a change in strain is understood as an immediate response before fluid flows in or out of the tissue, followed by a progressive readjustment of the fluid content in time because of the gradient in fluid chemical potential between the tissue and the surrounding solution.

Biaxial testing of canine annulus fibrosus tissue under changing salt concentrations

The in vivo mechanics of the annulus fibrosus of the intervertebral disc is one of biaxial rather than uniaxial loading. The material properties of the annulus are intimately linked to the osmolarity in the tissue. This paper presents biaxial relaxation experiments of canine annulus fibrosus tissue under stepwise changes of external salt concentration. The force tracings show that stresses are strongly dependent on time, salt concentration and orientation. The force tracing signature of are sponse to a change instrain, is one of a jumpin stress that relaxes partly as the new strain is maintained. The force tracing signature of a stepwise change in salt concentration is a progressive monotonous change in stress towards a new equilibrium value. Although the number of samples does not allow any definitive quantitative conclusions, the trends may shed light on the complex interaction among the directionality of forces, strains and fiber orientation on one hand, and on the other hand, the osmolarity of the tissue. The dual response to a change in strain is understood as an immediate response before fluid flows in or out of the tissue, followed by a progressive readjustment of the fluid content in time because of the gradient in fluid chemical potential between the tissue and the surrounding solution.

A mecânica in vivo do anel fibroso do disco intervertebral é baseada em carregamento biaxial ao invés de uniaxial. As propriedades materiais do anel estão intimamente ligadas à osmolaridade no tecido. O artigo apresenta experimentos de relaxação biaxiais do anel fibroso de um tecido canino sob mudanças abruptas na concentração externa de sal. A assinatura da força devido à mudança brusca de salinidade resulta em uma progressiva e monótona mudança na tensão em direção a um novo valor de equilíbrio. Embora o número de amostras não permita nenhuma conclusão quantitativa, as tendências podem abrir uma luz no entendimento das interações complexas na direção das forças, deformações e orientação das fibras por um lado e a osmolaridade do tecido por outro lado. A resposta dual devido à uma mudança na deformação é compreendida como uma resposta imediata antes do fluido escoar para dentro ou para fora do tecido, seguido de uma progressiva readaptação da quantidade de fluido notempo devido ao gradiente do potencial químico entre o tecido e a solução externa.

Mechanisms that play a role in the maintenance of the calcium gradient in the epidermis.

BACKGROUND/PURPOSE: Calcium regulates the proliferation and differentiation of keratinocytes and plays a role in restoration of the epidermal barrier function. The factors that maintain the calcium gradient in vivo are still unknown. A numerical model may give more insight into transport processes that maintain the epidermal calcium gradient. METHODS: In this study, transport of free calcium in the epidermis is described with diffusion, convection and electrophoresis. Binding and release of calcium results in equilibrium between free and bound calcium. The physiological epidermal calcium gradient as well as the calcium concentration in a damaged epidermis are modeled. RESULTS: The typical shape of the calcium gradient in the epidermis, as found in experimental studies, was maintained when separate formulations were used for free and bound calcium. Application of damage results in a decrease of the calcium concentration, especially in the upper living epidermis. Using this model, an estimate could be made about the fraction bound calcium in the epidermis. CONCLUSION: The typical shape of the gradient is predominantly determined by the bound calcium concentration. For both a normal and a damaged epidermis, the concentration of free calcium is mainly determined by electrophoresis in the living epidermis, whereas in the largest part of the stratum corneum diffusion is the most important factor. The convection that was determined by the transepidermal water loss did not have an effect on the calcium concentration.

Are disc pressure, stress, and osmolarity affected by intra- and extrafibrillar fluid exchange?

Because extrafibrillar water content dictates extrafibrillar osmolarity, we aimed to determine the influence of intra- and extrafibrillar fluid exchange on intradiscal pressures and stresses. As experimental results showed that extrafibrillar osmolarity affects intervertebral disc cell gene expression and crack propagation, quantification of the effects of changes in intra- and extrafibrillar fluid exchange is physiologically relevant. Therefore, our 3D osmoviscoelastic finite element (FE) model of the intervertebral disc was extended to include the intra- and extrafibrillar water differentiation. Two simulations were performed, one without intrafibrillar fluid and one with intrafibrillar fluid fraction as a function of the extrafibrillar osmotic pressure. The intrafibrillar fluid fraction as a function of the extrafibrillar osmotic pressure was exponentially fitted to human data and implemented into the model. Because of the low collagen content in the nucleus, no noticeable differences in intradiscal pressure estimation were observed. However, values of extrafibrillar osmolarity, hydrostatic pressure, and the total tissue stress calculated for the annulus were clearly different. Stresses, hydrostatic pressure, and osmolarity were underestimated when the intrafibrillar water value was neglected. As the loading increased, the discrepancies increased. In conclusion, the distribution of pressure and osmolarity in the disc is affected by intra- and extrafibrillar water exchange.