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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.
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Fenómenos Químicos , Hidrogeles/química , Fenómenos Mecánicos , Algoritmos , Modelos QuímicosRESUMEN
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.
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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.
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Velocidad del Flujo Sanguíneo , Presión Sanguínea , Capilares/fisiología , Eritrocitos , Arteriolas , Fenómenos Biomecánicos , Membrana Celular , Hematócrito , Humanos , PlasmaRESUMEN
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.
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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.
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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.
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Envejecimiento , Degeneración del Disco Intervertebral/etiología , Disco Intervertebral/fisiopatología , Rango del Movimiento Articular , Humanos , Disco Intervertebral/anatomía & histología , Disco Intervertebral/metabolismo , Degeneración del Disco Intervertebral/fisiopatología , Osteofito/fisiopatologíaRESUMEN
Accurate modeling of blood dynamics in the coronary microcirculation is a crucial step toward the clinical application of in silico methods for the diagnosis of coronary artery disease. In this work, we present a new mathematical model of microcirculatory hemodynamics accounting for microvasculature compliance and cardiac contraction; we also present its application to a full simulation of hyperemic coronary blood flow and 3D myocardial perfusion in real clinical cases. Microvasculature hemodynamics is modeled with a compliant multi-compartment Darcy formulation, with the new compliance terms depending on the local intramyocardial pressure generated by cardiac contraction. Nonlinear analytical relationships for vessels distensibility are included based on experimental data, and all the parameters of the model are reformulated based on histologically relevant quantities, allowing a deeper model personalization. Phasic flow patterns of high arterial inflow in diastole and venous outflow in systole are obtained, with flow waveforms morphology and pressure distribution along the microcirculation reproduced in accordance with experimental and in vivo measures. Phasic diameter change for arterioles and capillaries is also obtained with relevant differences depending on the depth location. Coronary blood dynamics exhibits a disturbed flow at the systolic onset, while the obtained 3D perfusion maps reproduce the systolic impediment effect and show relevant regional and transmural heterogeneities in myocardial blood flow (MBF). The proposed model successfully reproduces microvasculature hemodynamics over the whole heartbeat and along the entire intramural vessels. Quantification of phasic flow patterns, diameter changes, regional and transmural heterogeneities in MBF represent key steps ahead in the direction of the predictive simulation of cardiac perfusion.
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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.
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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.
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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.
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Disco Intervertebral/química , Disco Intervertebral/fisiología , Salinidad , Resistencia a la Tracción/fisiología , Animales , Fenómenos Biomecánicos , Perros , Modelos BiológicosRESUMEN
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.
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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.
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Anillo Fibroso/fisiología , Fenómenos Electrofisiológicos , Animales , Anillo Fibroso/citología , Fenómenos Biomecánicos , Colágeno/metabolismo , Matriz Extracelular/metabolismo , Humanos , Mecanotransducción CelularRESUMEN
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.
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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.
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Agua Corporal/metabolismo , Colágenos Fibrilares/metabolismo , Transferencias de Fluidos Corporales/fisiología , Disco Intervertebral/fisiología , Modelos Biológicos , Presión Osmótica , Agua Corporal/química , Simulación por Computador , Colágenos Fibrilares/química , Humanos , Disco Intervertebral/química , Mecanotransducción Celular/fisiología , Concentración Osmolar , Estrés Mecánico , Soporte de Peso/fisiologíaRESUMEN
Throughout life, human bone is renewed continuously in a tightly controlled sequence of resorption and formation. This process of bone remodeling is remarkable because it involves cells from different lineages, collaborating in so-called basic multicellular units (BMUs) within small spatial and temporal boundaries. Moreover, the newly formed (secondary) osteons are aligned to the dominant load direction and have a density related to its magnitude, thus creating a globally optimized mechanical structure. Although the existence of BMUs is amply described, the cellular mechanisms driving bone remodeling-particularly the alignment process-are poorly understood. In this study we present a theory that explains bone remodelling as a self-organizing process of mechanical adaptation. Osteocytes thereby act as sensors of strain-induced fluid flow. Physiological loading produces stasis of extracellular fluid in front of the cutting cone of a tunneling osteon, which will lead to osteocytic disuse and (continued) attraction of osteoclasts. However, around the resting zone and the closing cone, enhanced extracellular fluid flow occurs, which will activate osteocytes to recruit osteoblasts. Thus, cellular activity at a bone remodeling site is well related to local fluid flow patterns, which may explain the coordinated progression of a BMU.
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Remodelación Ósea/fisiología , Huesos/fisiología , Modelos Biológicos , Huesos/citología , Humanos , Osteoblastos/fisiología , Osteoclastos/fisiología , Reología , Estrés MecánicoRESUMEN
Cortical bone has two systems of interconnected channels. The largest of these is the vascular porosity consisting of Haversian and Volkmann's canals, with a diameter of about 50 microm, which contains a.o. blood vessels and nerves. The smaller is the system consisting of the canaliculi and lacunae: the canaliculi are at the submicron level and house the protrusions of the osteocytes. When bone is differentially loaded, fluids within the solid matrix sustain a pressure gradient that drives a flow. It is generally assumed that the flow of extracellular fluid around osteocytes plays an important role not only in the nutrition of these cells, but also in the bone's mechanosensory system. The interaction between the deformation of the bone matrix and the flow of fluid can be modelled using Biot's theory of poroelasticity. However, due to the inhomogeneity of the bone matrix and the scale of the porosities, it is not possible to experimentally determine all the parameters that are needed for numerical implementation. The purpose of this paper is to derive these parameters using composite modelling and experimental data from literature. A full set of constants is estimated for a linear isotropic description of cortical bone as a two-level porous medium. Bone, however, has a wide variety of mechanical and structural properties; with the theoretical relationships described in this note, poroelastic parameters can be derived for other bone types using their specific experimental data sets.
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Huesos/fisiología , Simulación por Computador , Modelos Biológicos , Reología , Matriz Ósea/irrigación sanguínea , Matriz Ósea/fisiología , Huesos/irrigación sanguínea , Elasticidad , Espacio Extracelular/fisiología , Análisis de Elementos Finitos , Osteón/irrigación sanguínea , Osteón/fisiología , Hemodinámica , Porosidad , Presión , Estrés MecánicoRESUMEN
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.
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Fuerza Compresiva , Hidrogel de Polietilenoglicol-Dimetacrilato/química , Polihidroxietil Metacrilato/química , Cloruro de Sodio/química , Torsión Mecánica , Presión , Reproducibilidad de los Resultados , Estrés Mecánico , TorqueRESUMEN
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.