Rheological properties of skin components under compressive load

Characterization was made of the mechanical properties under compression of four major skin components (collagen, elastin, chondroitin sulfate, and hyaluronic acid) placed in a gel matrix. Using the previous theoretical work of Bert et al., thickness under compression was related to degree of hydration and the results expressed in terms of pressure vs. hydration. All measurements were conducted at 14 degrees C, 21 degrees C, and 25 degrees C. Application of the findings to a model based on the finite deformation strain-energy theory of Aubert indicate that collagen, elastin, and chondroitin sulfate show a viscoelastic response under compression. On the other hand, hyaluronic acid and gelatin exhibit rubber-like behavior.     

Numerical study of how creep and progressive stiffening affect the growth stress formation in trees

It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of, e.g. shape stability. It is, for example, difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material-related factors. To increase the knowledge of the stress formation, a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed, whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro-fibril angle and maturation strain.     

Viscoelastic behaviour aids extrusion from and reabsorption of the liquid phase into the digesta plug: creep rheometry of hindgut digesta in the common brushtail possum Trichosurus vulpecula

Temporal variation in the rheometric properties of the proximal and distal colonic digesta of an arboreal marsupial folivore, the common brushtail possum, was examined to assess flow behaviour during peristalsis, segmentation and other aspects of intestinal motility. The time-dependent rheometric characteristics on application of a constant shear stress within the physiological range showed an initial elastic and subsequent viscoelastic phase, which fitted Burger’s model of creep compliance. Similarly, the time-dependent rheometric characteristics on recovery from shear stress fitted with a generalised two-component Maxwell model of elastic and viscoelastic components for creep recovery. Differences in the relative magnitudes of the viscoelastic components during recovery from those during shear indicated that the physical properties of the digesta plug changed with sustained shear stress, a phenomenon, which is likely to result from extrusion of the liquid phase from the solid elements of the digesta plug. There was significant viscoelastic recovery during the initial 4 s following cessation of stress, which would allow for prompt concomitant reabsorption of the liquid phase into the digesta plug. This supports a hypothesis of alternate extrusion and reabsorption of the liquid phase of the digesta plug. This would promote both nutrient absorption across the intestinal wall (from liquid extrusion) and enzyme permeation and digestion (from liquid absorption into the plug). However, the presence of a slower component of viscoelastic recovery indicates that liquid phase reabsorption into the digesta plug is incomplete if the interval before a subsequent contraction is less than 150 s, in which case unreabsorbed liquid may be driven either orally or aborally. This would at least partly account for differences in retention times of liquid and solid phase digesta markers reported for the gastrointestinal tracts of numerous vertebrate species.     

Creep measurements on gelatin gels

The present work describes creep measurements on a series of concentrations of gelatin gels well above the critical gel concentration C0, using a high precision constant stress rheometer. Results for the concentration dependence of compliance are close to those expected both from theory and from dynamic oscillatory measurements of gel modulus. The concentration dependence of viscosity follows an approximate power law behaviour, with eta proportional C1.1. This exponent is consistent with relaxation in the sol fraction, and in regions of dangling chain attached to the gel. At concentrations closer to C0 we predict that a higher power law regime will prevail.     

A model for the creep behaviour of tendon

A theoretical model is proposed to explain the viscoelastic behaviour of tendon. The model is based on the hypothesis that the mechanism of tendon deformation is one of shear of the mucopolysaccharide gel between the collagen ribbons in the ‘toe’ region¹ of the stress strain curve followed by fibrillar extension in the ‘linear’ region^2.3. Conventional linear viscoelastic parameters of the constituents of the tendon were used to describe the behaviour of the composite. Certain structural constants of the tendon and an appropriate form for the retardation spectrum of the composite also appear in the model. It was found that the following parameters play an important part in the viscoelastic deformation process; the mean value of the crimp angle of the strained fibres, 0_O; the broadness of the distribution of crimp angles $\text{α}$; the magnitude of the compliance difference for the gel, ΔJ_G and for the fibres, ΔD_F. Excellent agreement between experiment and theory has been observed for a variety of experimental circumstances. Values of 0_O, $\text{α}$ ΔJ_G and ΔD_F were determined for a number of specimens by fitting the model equations to the experimental data. The theory illustrates the expected influence on the viscoelastic properties of tendon which would result from changes in these parameters, which may arise from disease or ageing, for instance. The model also provides a challenge for future experimental work in that an independent determination of the parameters, 0_O, $\text{α}$ ΔJ_G and ΔD_F would confirm or refute the quantitative predictions of the theory presented here.     

Mechanical characteristics of synthetic polyelectrolyte gel as a physical model of the cytoskeleton

A physical model of the cytoskeleton based on synthetic polyelectrolyte hydrogel of polymethacrylic acid has been proposed. From the physicochemical point of view, the structures of polyelectrolyte gel and the cytoskeleton show a high degree of similarity. It has been shown that polyelectrolyte gel can shorten and produce mechanical stress in response to changes in the composition of the surrounding solution. The mechanical properties of the model gel have been evaluated: Young modulus (2–6 kPa), stress relaxation time (0.1–1 s), and apparent viscosity (0.3–3 kPa s). The viscoelastic properties of the gel depend on the degree of its swelling. It has been demonstrated that the mechanical properties of gels of polymethacrylic acid are close to those of biological objects.     

A gel network constituted by rigid schizophyllan chains and nonpermanent cross-links

This work reports a gel network formed by rigid schizophyllan (SPG) chains with Borax as a cross-linking agent. The formed cross-links are non-permanent and somewhat dynamic in nature because the cross-linking reaction is governed by a complexation equilibrium. Gelation processes are traced by dynamic viscoelastic measurements to examine the effects of Borax content, SPG concentration, temperature, salt concentration, salt type, and strain. The first-order kinetic model containing three parameters, t(0) (induction time), 1/tau(c) (gelation rate), and (saturated storage modulus), is successfully applied to describe the gelation of the SPG-Borax system. Gelation occurs faster at higher Borax content, higher SPG concentration, higher salt concentration, or lower temperature. Moreover the gelation is cation-type-specific. Storage modulus is a linear function of both Borax content and SPG concentration. The linear relationship between storage modulus and Borax content can be explained by a modified ideal rubber elasticity theory with a front factor alpha to take into account the presence of ineffective cross-links and the effect of SPG chain rigidity. On the other hand, the linear dependence of storage modulus on SPG concentration could be explained on the basis of chain-chain contacting behavior of extended SPG chains. Apparent activation energy and cross-linking enthalpy are calculated to be -74.5 and -32.4 kJ/mol for the present system. Strain sweep measurements manifest that the elasticity behavior of this gel starts to deviate from Gaussian-chain network at a small strain of 10%.     

Rheological properties of mixtures of protein-polysaccharide-dynamic viscoelasticity of blend gels of acylated gelatin, kappa-carrageenan, and agarose

Complex Young's modulus of blend gels of gelatin and kappa-carrageenan or agarose has been measured in order to clarify the protein-polysaccharide interaction in biological systems. The mixture of gelatin and kappa-carrageenan showed phase separation in the intermediate volume fraction of gelatin, and it formed a homogeneous gel when the volume fraction of gelatin is very large or very small. Since the dynamic Young's modulus for blend gels of kappa-carrageenan and gelatin was larger than the calculated one from a theory for dispersed systems, some structural reinforcing must occur. The mixture of agarose and gelatin showed the inverse tendency. It was concluded that the role of electrolytic groups was dominant in dilute gels, while molecular entanglement became more important in concentrated gels.     

A model of fracture testing of soft viscoelastic tissues

Fracture, or tear, toughness of soft tissues can be computed from the work of fracture divided by the area of new crack surface. For soft tissues without significant plastic deformation, total work, which can be measured experimentally, is composed of the sum of fracture and viscoelastic work. In order to deduce fracture work, a method is needed to estimate viscoelastic work.Two different methods (Ph.D. Dissertation, University of Minnesota, 2000; J. Mater. Sci.: Mater. Med. 12 (2001) 327) have been proposed to estimate viscoelastic work in a fracture test of a soft tissue. The relative merits of these methods are unknown because the true viscoelastic work in an experiment is unknown. In order to characterize the accuracy of these methods, a theoretical model of crack propagation of viscoelastic soft tissue in a tensile test is presented, from which the exact viscoelastic work is calculated. The material is assumed to obey the standard linear solid model.The "exact" solution for the viscoelastic work during the fracture is computed from the model and compared with the work estimated by the two methods. It was found that both methods tend to underestimate the viscoelastic work done, and thus overestimate the fracture work and fracture toughness, although the errors were greater with the Fedewa method. It was further found that low displacement rates can give rise to a "snap" effect, where rapid crack growth can cause a disproportionate amount of viscoelastic energy to be dissipated during unloading. This modeling approach may be useful in evaluating other experimental methods of soft tissue fracture.     

Viscoelastic and Thermal Properties of Collagen–Xanthan Gum and Collagen–Maltodextrin Suspensions During Heating and Cooling

The purpose of this work was to investigate the viscoelastic properties of aqueous suspensions of crude collagen powder extracted from bovine hides and nonsubmitted to the hydrolysis reaction that leads to gelatin. The studied variables included the collagen concentration and the addition of xanthan gum or maltodextrin at varied concentrations during heating/cooling of the mixtures. Differential scanning calorimetry thermograms showed that the addition of polysaccharides decreased the endothermic peak areas observed at the denaturation temperature of collagen. The rheological properties of the pure collagen suspensions were highly dependent on concentration: 4% and 6% collagen suspensions presented a great increase in the storage modulus after heating/cooling, whereas for concentrations of 8% and 10% G′ decreased during heating and did not recover its original value after heating/cooling. The frequency sweeps showed that the thermal treatment was responsible by the strengthening of the interactions that formed the polymer network. Addition of 0.1% xanthan gum to collagen suspensions increased the gel strength, especially after heating/cooling of the system, whereas increasing gum concentration to 0.3% resulted in a weaker gel, which could indicate thermodynamic incompatibility between the biopolymers. Mixtures of collagen and maltodextrin resulted in more fluid structures than those obtained with pure collagen at the same collagen concentration and the range of temperatures in which these mixtures behaved as a gel decreased with increasing concentrations of both collagen and maltodextrin, suggesting incompatibilities between the biopolymers.     

Rheological properties of binary and ternary protein-polysaccharide co-hydrogels and comparative release kinetics of salbutamol sulphate from their matrices

Rheological properties of binary (AgarGelA and AgarGelB) and ternary (AgarGelAB and GelABAgar) co-hydrogels of agar (polysaccharide) with gelatin A and gelatin B (proteins) were studied to investigate their differential viscoelastic behavior. Two sets of rheological experiments, isochronal temperature and isothermal frequency sweep, were performed and the storage modulii, G' was measured which could be correlated to the gel strengths. Two separate peaks at 70°C and 35°C, corresponding to melting temperatures of agar and gelatin gels respectively, were obtained when derivative of G' with respect to temperature, dG'/dT was plotted against temperature which clearly showed the presence of two separate networks of gelatin and agar interconnected to each other. The results revealed that AgarGelAB was the strongest and AgarGelA was the weakest gel among all the gels studied. In order to see the effect of gel microstructure on drug encapsulation and release behavior, a model drug salbutamol was encapsulated in various gel matrices and the release of the same was seen in phosphate buffer pH 7.4, in simulated gastric fluid pH 1.2 (SGF) and in simulated intestinal fluid pH 6.8 (SIF) media. The drug release behavior universally followed sigmoidal kinetics invariant of gel composition. It is concluded that the hydrogel microstructure influenced the release behavior and best release, in all the three media, could be found with binary gel, AgarGelB, and ternary gel, AgarGelAB. Finally, microstructure of these gels is proposed.     

The viscoelastic properties of actin solutions

The viscoelastic properties in actin solutions were investigated by measuring their elastic modulus and viscous modulus using a rheometer. The polymerization/gelation process of actin solutions was accompanied by an increase of both parameters, indicating the formation of a protein network. High shear rotational motion destroyed this network which, however, would reanneal if left undisturbed. At 25 °C under low ionic strength conditions, the viscoelastic moduli of a Spudich-Watt globular (G) actin preparation increased with time, while G-actin, purified by gel filtration maintained low viscoelastic moduli. The rigidity of the filamentous (F) actin network in a solution of Spudich-Watt actin, measured by the elastic modulus, was somewhat lower than that of gel-filtration-purified actin at the same protein concentration. The crosslink density of these F-actin networks was estimated, using models from rubber elasticity theory. The calculated density was 1 crosslink/50 actin monomers for the purified actin and 1 crosslink/120 actin monomers for Spudich-Watt actin. The results are consistent with the idea that a small amount of regulatory factor(s), which could be removed by the gel filtration step, modulates the structure of an actin network.     

Determination of the number of cross-links in a protein gel from its mechanical and swelling properties

The relation between the chemical structure of a protein and the physical properties of a heat-set gel of that protein has been investigated. The physical properties of the gel are determined by means of mechanical experiments in which the viscoelastic properties of the gel are determined in terms of the storage shear modulus, the loss modulus and the stress-strain curve. The storage shear modulus defined the solid (elastic) character of the gel. The chemical structure of the protein and the nature of the solvent determine the nature and number of cross-links in the gel. The cross-links in gels formed by heating concentrated solutions of ovalbumin in 6M urea solutions were found to be disulfide bridges and the mechanical properties of these ovalbumin/urea gels approximated those of an ideal rubber. The latter finding enables one to calculate the number of cross-links per ovalbumin molecule from the value of the storage modulus, using the classical theory of rubber elasticity. This theory, together with the Flory-Huggins lattice model, can also be used to calculate the number of cros-links per ovalbumin molecule from the swelling behavior of ovalbumin/urea gels. The number of cross-links per ovalbumin molecule calculated from these two types of experiments are in mutual agreement and correspond with the number of thiol groups in ovalbumin. We conclude, thereforee, that theories of polymer physics can be used to relate the chemical structure of a protein to the physical properties of its gel.     

Proteolytic degradation of cold-water fish gelatin solutions and gels

The stability of cold-water fish gelatin (FG), both in solution and in the gel phase, has been studied as function of both temperature and exposure towards novel proteases of marine origin. A 1% (w/v) FG solution was readily degraded by such proteases above 20 degrees C, which was expected since FG at this temperature is a random coil molecule lacking the protective triple helical structure found in collagen. The dynamic storage modulus for a 10% (w/v) FG gel increased monotonically at 4 degrees C. Ramping the temperature to 6, 8 or 10 degrees C led to a drastic reduction in G', but an apparent partial recovery of the network (increasing G') was observed with time at all temperatures. In the presence of proteases, a lower storage modulus was observed. At constant 4 degrees C, an apparent maximum value was reached after curing for 2h followed by a decrease in G' indicating protease activity. Ramping of temperature in the presence of proteases led to an even more drastic reduction in G' and no recovery of structure was observed with time. In this case, the overall rheological behaviour is a complex function of both thermal influence as well as proteolytic activity. In an endeavour to quantify the effect of the presence of proteolytic enzymes on the gelatin network, rheological investigation were undertaken where the dynamic storage moduli were recorded on different 10% (w/v) FG samples that had been acid hydrolysed to yield different average molecular weights. A significant reduction in storage modulus for average molecular weights below 50 kDa was found. This critical molecular weight most probably reflects the on-set of a regime where shorter chain lengths prevent percolation due to an increase in the loose end and sol fraction as well as a reduction in the average length of the pyrrolidine-rich regions reducing the number of possible junction zones.     

Effects of velocity jumps on blood flow in large arteries

When a human being experiences a sudden velocity change, the blood flow is disturbed. A theoretical analysis to predict the effects of sudden velocity changes on blood flow in large arteries is presented. The situations is modelled as a one-dimensional flow problem in a viscoelastic tube where the fluid viscosity convective term in the equation of motion and nonlinearity in the elastic modulus of the tube wall are neglected. The governing equations of the model are solved by Laplace transformation. The computed results show that relatively high blood pressures, capable of harming circulation, are produced even by relatively moderate velocity jumps.     

Texture of SS Cross-linked Gelatin Gels

Relations among sensory properties, physical characteristics and the kinds of force supporting gel structure were studied by using thiolated gelatin.

Breaking stress of the gelatin gel was greatly influenced by contents of disulfide bonds in the gel. Young’s modulus of the gel was affected by its temperature. As to sensory properties of the gelatin gel, “hardness” highly correlated with Young’s modulus and “brittleness” correlated with breaking stress.

Therefore, it could be concluded that in the case of the gelatin gel, “hardness” was mainly attributed to hydrogen bonds and “brittleness” was to chemical bonds like disulfide linkages.     

Stretching and Relaxation of Malaria-Infected Red Blood Cells

The invasion of red blood cells (RBCs) by malaria parasites is a complex dynamic process, in which the infected RBCs gradually lose their deformability and their ability to recover their original shape is greatly reduced with the maturation of the parasites. In this work, we developed two types of cell model, one with an included parasite, and the other without an included parasite. The former is a representation of real malaria-infected RBCs, in which the parasite is treated as a rigid body. In the latter, where the parasite is absent, the membrane modulus and viscosity are elevated so as to produce the same features present in the parasite model. In both cases, the cell membrane is modeled as a viscoelastic triangular network connected by wormlike chains. We studied the transient behaviors of stretching deformation and shape relaxation of malaria-infected RBCs based on these two models and found that both models can generate results in agreement with those of previously published studies. With the parasite maturation, the shape deformation becomes smaller and smaller due to increasing cell rigidity, whereas the shape relaxation time becomes longer and longer due to the cell’s reduced ability to recover its original shape.     

Stretching and Relaxation of Malaria-Infected Red Blood Cells

The invasion of red blood cells (RBCs) by malaria parasites is a complex dynamic process, in which the infected RBCs gradually lose their deformability and their ability to recover their original shape is greatly reduced with the maturation of the parasites. In this work, we developed two types of cell model, one with an included parasite, and the other without an included parasite. The former is a representation of real malaria-infected RBCs, in which the parasite is treated as a rigid body. In the latter, where the parasite is absent, the membrane modulus and viscosity are elevated so as to produce the same features present in the parasite model. In both cases, the cell membrane is modeled as a viscoelastic triangular network connected by wormlike chains. We studied the transient behaviors of stretching deformation and shape relaxation of malaria-infected RBCs based on these two models and found that both models can generate results in agreement with those of previously published studies. With the parasite maturation, the shape deformation becomes smaller and smaller due to increasing cell rigidity, whereas the shape relaxation time becomes longer and longer due to the cell’s reduced ability to recover its original shape.     

Assembly of Collagen Matrices as a Phase Transition Revealed by Structural and Rheologic Studies

We have studied the structural and viscoelastic properties of assembling networks of the extracellular matrix protein type-I collagen by means of phase contrast microscopy and rotating disk rheometry. The initial stage of the assembly is a nucleation process of collagen monomers associating to randomly distributed branched clusters with extensions of several microns. Eventually a sol-gel transition takes place, which is due to the interconnection of these clusters. We analyzed this transition in terms of percolation theory. The viscoelastic parameters (storage modulus G′ and loss modulus G″) were measured as a function of time for five different frequencies ranging from ω = 0.2 rad/s to 6.9 rad/s. We found that at the gel point both G′ and G″ obey a scaling law , with the critical exponent Δ = 0.7 and a critical loss angle being independent of frequency as predicted by percolation theory. Gelation of collagen thus represents a second order phase transition.     

The role of mucus gel viscosity, spinnability, and adhesive properties in clearance by simulated cough

We investigated the role of the viscoelastic and adhesive properties of mucus gel simulants on the clearance of mucus by simulated cough. Mucus-like gels with widely varying viscoelastic properties were prepared from polysaccharides crosslinked with sodium borate. Cough was simulated by opening a solenoid valve connecting a model trachea to a pressurized tank. The clearance of gels lining the model trachea was quantified by observing marker particle transport. Viscosity elastic modulus, relaxation time and yield stress were measured with a steady-shear viscoelastometer. Spinnability (thread formation) was determined with a filancemeter. Adhesivity (surface tension) was measured by the platinum ring technique. The viscoelastic and adhesive properties of the mucus gel simulants spanned the ranges observed for bronchial secretions from patients with COPD. The relationship between simulated cough clearance and the viscoelastic and adhesive properties of the gels was analyzed by stepwise linear regression of the non-zero data matrix. The major independent variable relating to clearance was viscosity. Secondary, but highly significant dependences, were also found for spinnability and adhesivity. Elastic modulus, relaxation time and yield stress had no independent effect on cough clearance over the investigated range. The results indicate that, in the absence of airway surface liquid, cough-type clearance relates primarily with mucus gel viscosity. For a given viscosity, clearance is also impaired by spinnability, i.e. the capacity of the mucus to form threads. At constant viscosity and spinnability, clearance is further impaired by an increase in the adhesivity of the mucus. The negative dependence of each of these physical factors can be rationalized in terms of their inhibitory effect on wave formation in the mucus lining layer during high velocity airflow interaction.