Passive mechanical behavior of human neutrophils: power-law fluid.

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.     

Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration.

Continuous deformation and entry flow of single blood granulocytes into small caliber micropipets at various suction pressures have been studied to determine an apparent viscosity for the cell contents and to estimate the extent that dissipation in a cortical layer adjacent to the cell surface contributes to the total viscous flow resistance. Experiments were carried out with a wide range of pipet sizes (2.0-7.5 microns) and suction pressures (10(2)-10(4) dyn/cm2) to examine the details of the entry flow. The results show that the outer cortex of the cell maintains a small persistent tension of approximately 0.035 dyn/cm. The tension creates a threshold pressure below which the cell will not enter the pipet. The superficial plasma membrane of these cells appears to establish an upper limit to surface dilation which is reached after microscopic "ruffles" and "folds" have been pulled smooth. With aspiration of cells by small pipets (less than 2.7 microns), the limit to surface expansion was derived from the maximal extension of the cell into the pipet; final areas were measured to be 2.1 to 2.2 times the area of the initial spherical shape. For suctions in excess of a threshold, the response to constant pressure was continuous flow in proportion to excess pressure above the threshold with only a small nonlinearity over time until the cell completely entered the pipet (for pipet calibers greater than 2.7 microns). With a theoretical model introduced in a companion paper, (Yeung, A., and E. Evans., 1989, Biophys. J. 56:139-149) the entry flow response versus pipet size and suction pressure was analyzed to estimate the apparent viscosity of the cell interior and the ratio of cortical flow resistance to flow resistance from the cell interior. The apparent viscosity was found to depend strongly on temperature with values on the order of 2 x 10(3) poise at 23 degrees C, lower values of 1 x 10(3) poise at 37 degrees C, but extremely large values in excess of 10(4) poise below 10 degrees C. Because of scatter in cell response, it was not possible to accurately establish the characteristic ratio for flow resistance in the cortex to that inside the cell; however, the data showed that the cortex does not contribute significantly to the total flow resistance.     

The viscosity of neutrophils and their transit times through small pores

Passive neutrophils from five different individuals are rapidly aspirated at constant suction pressure and at room temperature into a pipet with a diameter of 4 microns. The excess suction pressures (i.e., the pressures in excess of the small threshold pressure required to produce continuous flow into the pipet) are 5000, 10,000 and 20,000 dyn/cm2 (0.5, 1 and 2 kPa) and are comparable to those encountered in the microcirculation. The rate of entry into the pipet is modeled with a linearized version of a theory by Yeung and Evans for the newtonian flow of a neutrophil into a pipet or pore. From this theory and measurements of the cell size and its rate of entry into the pipet, we can calculate a value for the cytoplasmic viscosity. A linear (newtonian) fit of the theory to the experimental data gives a value for the viscosity of 1050 poise. A non-linear fit predicts a decrease in the "apparent viscosity" from about 1500 poise at zero excess pressure to 1000 poise at an excess aspiration pressure of 20,000 dyn/cm2. Our experiments and analysis also allow us to calculate a value for the transit time through short pores over a wide range of excess aspiration pressures and pore diameters. For example, for a pore diameter of 3 microns and an aspiration pressure of 1250 dyn/cm2, we predict a transit time of about 70 s. At 6 microns and 20,000 dyn/cm2, the predicted transit time is only about 0.04 s.     

Rapid flow of passive neutrophils into a 4 microns pipet and measurement of cytoplasmic viscosity

Neutrophils from five different individuals are isolated with a density separation technique. A total of 151 unactivated (passive) cells are rapidly aspirated at constant suction pressure and at room temperature into a pipet with a diameter of 4 microns. The suction pressures in excess of an initial yield threshold are 0.5, 1 and 2 kPa and are comparable to those encountered in the microcirculation. These pressures are well in excess of the small suction pressure of approximately 20 Pa that is required to form a static hemispherical bump on the cell. At a given aspiration pressure, the leading edge of an individual cell is "tracked" as it flows into the pipet. A theory based on the flow of a Newtonian liquid from either a hemisphere or a spherical segment into a cylinder is used to model the entry process. Both theory and experiment show that during most of the entry process the leading edge of the cell moves at a nearly constant velocity with a rapid acceleration at the end. For cells from five different individuals at the three different excess aspiration pressures, Newtonian theory gives a cytoplasmic viscosity of 135 +/- 54 Pa.s and overall entry times of 3.3s (0.5 kPa), 1.6s (1 kPa) and 0.82s (2 kPa). These results and those of Evans and Yeung at lower aspiration pressures indicate that the complex cytoplasm inside unactivated neutrophils behaves as a nearly Newtonian fluid with a viscosity on the order of 10(2) Pa.s over almost a two order of magnitude range in aspiration pressure and, thus, rate of deformation.     

Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets.

Many nonadherent cells exist as spheres in suspension and when sucked into pipets, deform continuously like liquids within the fixed surface area limitation of a plasma membrane envelope. After release, these cells eventually recover their spherical form. Consequently, pipet aspiration test provides a useful method to assay the apparent viscosity of such cells. For this purpose, we have analyzed the inertialess flow of a liquid-like model cell into a tube at constant suction pressure. The cell is modeled as a uniform liquid core encapsulated by a distinct cortical shell. The method of analysis employs a variational approach that minimizes errors in boundary conditions defined by the equations of motion for the cortical shell where the trial functions are exact solutions for the flow field inside the liquid core. For the particular case of an anisotropic liquid cortex with persistent tension, we have determined universal predictions for flow rate scaled by the ratio of excess pressure (above the threshold established by the cortical tension) and core viscosity which is the reciprocal of the dynamic resistance to entry. The results depend on pipet to cell size ratio and a parameter that characterizes the ratio of viscous flow resistance in the cortex to that inside the cytoplasmic core. The rate of entry increases markedly as the pipet size approaches the outer segment diameter of the cell. Viscous dissipation in the cortex strongly influences the entry flow resistance for small tube sizes but has little effect for large tubes. This indicates that with sufficient experimental resolution, measurement of cell entry flow with different-size pipets could establish both the cortex to cell dissipation ratio as well as the apparent viscosity of the cytoplasmic core.     

Investigations into the rheological characteristics of bovine amniotic fluid

The rheological characteristics of bovine amniotic fluid have been studied at different shear rates. The viscosity of bovine amniotic fluid at 20°C was found to increase with time at a constant low shear rate during the measurement. Additionally, the viscosity was observed to decrease with increasing shear rate, indicating that a shear thinning behaviour of the fluid was occurring. The log-log plot of shear stress versus shear rate yielded a straight line, consistent with non-Newtonian behaviour of the fluid and characteristic of pseudoplastic liquids. The data of shear stress versus shear rate could be represented by a power law model. The treatment of amniotic fluid with cetylpyridinium chloride (CPC) resulted in the precipitation of a mixture of components, including complex sulphated polysaccharides and extracellular proteoglycans, with the viscosity of the resulting liquid similar to that of water at 20°C. In addition, the viscosity of the CPC-pretreated fluid did not increase with time at constant shear rate and remained constant with the increase in shear rate. The apparent increase in viscosity with time and the shear thinning behaviour of the amniotic fluid can thus be attributed to pseudoplastic liquid behaviour associated with the presence of structurally complex polysaccharides and extracellular proteoglycans. The implications of this fluid viscosity behaviour are discussed in terms of their impact on the operation of packed or expanded (fluidized) chromatographic bed systems when amniotic fluid biofeed-stocks are used as a source of commercially important proteins.     

The behavior of human neutrophils during flow through capillary pores

The passage times of individual human neutrophils through single capillary-sized pores in polycarbonate membranes were measured with the resistive pulse technique, and results were compared to those obtained from the micropipette aspiration of entire cells. Pore transit measurement serves as a useful means to screen populations of cells, and allows for protocols that measure time dependent changes to the population. Neutrophils exhibited a highly linear pressure/flow rate relationship at aspiration pressures from 200 Pa to 1,500 Pa in both the pore and pipette systems. Cellular viscosity, as determined by the method of Hochmuth and Needham, was 89.0 Pa.s for the pore systems and 134.9 Pa.s for the pipette systems. These results are in general agreement with recent values of neutrophil viscosity published in the literature. Extrapolation of the observed linear flow response revealed an apparent minimum pressure for whole cell aspiration significantly above the threshold pressure predicted by Evans' liquid drop model. However, whole cell aspiration was achieved in both the pore and pipette systems at pressures below this extrapolated minimum, although the calculated cellular viscosity was greatly increased. The implications of these two regimes of cell deformation is unclear. This behavior could be explained by shear thinning of the material in the cell body. However the origin of this phenomenon may be in the cortical region of the cell, which exhibits an elastic tension that may be deformation rate dependent.     

Passive mechanical behavior of human neutrophils: effect of cytochalasin B.

Actin is a ubiquitous protein in eukaryotic cells. It plays a major role in cell motility and in the maintenance and control of cell shape. In this article, we intend to address the contribution of actin to the passive mechanical properties of human neutrophils. As a framework for assessing this contribution, the neutrophil is modeled as a simple viscous fluid drop with a constant cortical ("surface") tension. The reagent cytochalasin B (CTB) was used to disrupt the F-actin structure, and the neutrophil cortical tension and cytoplasmic viscosity were evaluated by single-cell micropipette aspiration. The cortical tension was calculated by simple force balance, and the viscosity was calculated according to a numerical analysis of the cell entry into the micropipette. CTB reduced the cell cortical tension in a dose-dependent fashion: by 19% at a concentration of 3 microM and by 49% at 30 microM. CTB also reduced the cytoplasmic viscosity by approximately -25% at a concentration of 3 microM and by approximately 65% at a concentration of 30 microM when compared at the same aspiration pressures. All three groups of neutrophils, normal cells, and cells treated with either 3 or 30 microM CTB, exhibited non-Newtonian behavior, in that the apparent viscosity decreased with increasing shear rate. The dependence of the cytoplasmic viscosity on deformation rate can be described empirically by mu = mu c(gamma m/gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material coefficient.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mechanically stimulated cytoskeleton rearrangement and cortical contraction in human neutrophils.

A mechanical test with micropipets is used to characterize cytoskeleton rearrangement and contraction induced by mechanical stresses in human neutrophils. The yield shear resultant of the cell cortex is on the order of 0.06 to 0.09 mN.m-1. The measured yield shear resultant suggests that the neutrophil cortex is a weakly cross-linked structure. When a tether is pulled out from the cell surface, a polymer structure starts to fill it and spreads out from the cell body. The rate of advancement of the polymerization front is almost constant and, therefore, is not diffusion limited. The measured rate is much smaller than the one of spontaneous actin polymerization, suggesting that the limiting process is either the dissociation of actin monomers from their dimers with the capping proteins or the rate of formation of new nucleation sites or both. Polymerization is also observed after applying sufficient mechanical stresses on a small portion of the cell surface. The polymerization is followed by mass transfer from the cell into the prestressed region and later on by contraction of the main cell body. The pressure generating the flow is located in the prestressed region and most probably is a result of its "swelling" and contraction. The contraction of the main cell body is very similar (in its time dependence and magnitude) to the contraction during phagocytosis. The measured maximum cortical tension is on the order of 0.5 mN.m-1, which for a 3.5-microns diameter pipet corresponds to a maximum contraction force of 11 nN.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Effects of fluid shear on immobilized enzyme kinetics.

There have been a number of reports concerning the damaging effects of shear on globular proteins in solution. Some recent work has indicated, however, that globular proteins in solution are relatively stable, but may be inactivated at air-liquid interfaces during shearing. This study investigated the effects of fluid shear on immobilized enzyme activity. Immobilized enzyme reactors were built to operate with the enzyme immobilized at the boundary of a fluid flow field. Two different enzymes, penicillinase and lactate dehydrogenase, were covalently bound to the interior surface of nylon tubes. Fluid shear rate was changed by varying the flow rate of substrate (reactant) solution through the tube, and fluid shear stresses were increased by increasing the viscosity of the recirculating solution. There were no observed effects of fluid shear on immobilized penicillinase or lactate dehydrogenase activity at shear rates of up to 10,350 s-1 or at shear stresses of up to 73 Pa.     

Viscosity of passive human neutrophils undergoing small deformations.

At issue is the type of constitutive equation that can be used to describe all possible types of deformation of the neutrophil. Here a neutrophil undergoing small deformations is studied by aspirating it into a glass pipet with a diameter that is only slightly smaller than the diameter of the spherically shaped cell. After being held in the pipet for at least seven seconds, the cell is rapidly expelled and allowed to recover its undeformed, spherical shape. The recovery takes approximately 15 s. An analysis of the recovery process that treats the cell as a simple Newtonian liquid drop with a constant cortical (surface) tension gives a value of 3.3 x 10(-5) cm/s for the ratio of the cortical tension to cytoplasmic viscosity. This value is about twice as large as a previously published value obtained with the same model from studies of large deformations of neutrophils. This discrepancy indicates that the cytoplasmic viscosity decreases as the amount of deformation decreases. An extrapolated value for the cytoplasmic viscosity at zero deformation is approximately 600 poise when a value for the cortical tension of 0.024 dyn/cm is assumed. Clearly the neutrophil does not behave like a simple Newtonian liquid drop in that small deformations are inherently different from large deformations. More complex models consisting either of two or more fluids or multiple shells must be developed. The complex structure inside the neutrophil is shown in scanning electron micrographs of osmotically burst cells and cells whose membrane has been dissolved away.     

Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests.

Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm.     

Acto-myosin cytoskeleton dependent viscosity and shear-thinning behavior of the amoeba cytoplasm

The mechanical behavior of the human parasite Entamoeba histolytica plays a major role in the invasive process of host tissues and vessels. In this study, we set up an intracellular rheological technique derived from magnetic tweezers to measure the viscoelastic properties within living amoebae. The experimental setup combines two magnetic fields at 90° from each other and is adapted to an inverted microscope, which allows monitoring of the rotation of pairs of magnetic phagosomes. We observe either the response of the phagosome pair to an instantaneous 45° rotation of the magnetic field or the response to a permanent uniform rotation of the field at a given frequency. By the first method, we concluded that the phagosome pairs experience a soft viscoelastic medium, represented by the same mechanical model previously described for the cytoplasm of Dictyostelium discoideum [Feneberg et al. in Eur Biophys J 30(4):284–294 2001]. By the second method, the permanent rotation of a pair allowed us to apply a constant shear rate and to calculate the apparent viscosity of the cytoplasm. As found for entangled polymers, the viscosity decreases with the shear rate applied (shear-thinning behavior) and exhibits a power-law-type thinning, with a corresponding exponent of 0.65. Treatment of amoeba with drugs that affect the actin polymer content demonstrated that the shear-thinning behavior of the cytoplasm depends on the presence of an intact actin cytoskeleton. These data present a physiologic relevance for Entamoeba histolytica virulence. The shear-thinning behavior could facilitate cytoplasm streamings during cell movement and cell deformation, under important shear experienced by the amoeba during the invasion of human tissues. In this study, we also investigated the role of the actin-based motor myosin II and concluded that myosin II stiffens the F-actin gel in living parasites likely by its cross-linking activity.     

A sensitive measure of surface stress in the resting neutrophil.

The simplest parameterized model of the "passive" or "resting receptive" neutrophil views the cell as being composed of an outer cortex surrounding an essentially liquid-like highly viscous cytoplasm. This cortex has been measured to maintain a small persistent tension of approximately 0.035 dyn/cm (Evans and Yeung. 1989. Biophys. J. 56:151-160) and is responsible for recovering the spherical shape of the cell after large deformation. The origin of the cortical tension is at present unknown, but speculations are that it may be an active process related to the sensitivity of a given cell to external stimulation and the "passive-active" transition. In order to characterize further this feature of the neutrophil we have used a new micropipet manipulation method to give a sensitive measure of the surface stress as a function of the surface area dilation of the highly ruffled cellular membrane. In the experiment, a single cell is driven down a tapered pipet in a series equilibrium deformation positions. Each equilibrium position represents a balance between the stress in the membrane and the pressure drop across the cell. For most cells that seemed to be "passive," as judged by their spherical appearance and lack of pseudopod activity, area dilations of approximately 30% were accompanied by only a small increase in the membrane tension, indicative of a very small apparent elastic area expansion modulus (approximately 0.04 dyn/cm). Extrapolations back to zero area dilation gave a value for the tension in the resting membrane of 0.024 +/- 0.003 dyn/cm, in close agreement with earlier measures.(ABSTRACT TRUNCATED AT 250 WORDS)     

Role of the membrane cortex in neutrophil deformation in small pipets.

The simplest model for a neutrophil in its "passive" state views the cell as consisting of a liquid-like cytoplasmic region surrounded by a membrane. The cell surface is in a state of isotropic contraction, which causes the cell to assume a spherical shape. This contraction is characterized by the cortical tension. The cortical tension shows a weak area dilation dependence, and it determines the elastic properties of the cell for small curvature deformations. At high curvature deformations in small pipets (with internal radii less than 1 micron), the measured critical suction pressure for cell flow into the pipet is larger than its estimate from the law of Laplace. A model is proposed where the region consisting of the cytoplasm membrane and the underlying cortex (having a finite thickness) is introduced at the cell surface. The mechanical properties of this region are characterized by the apparent cortical tension (defined as a free contraction energy per unit area) and the apparent bending modulus (introduced as a bending free energy per unit area) of its middle plane. The model predicts that for small curvature deformations (in pipets having radii larger than 1.2 microns) the role of the cortical thickness and the resistance for bending of the membrane-cortex complex is negligible. For high curvature deformations, they lead to elevated suction pressures above the values predicted from the law of Laplace. The existence of elevated suction pressures for pipets with radii from 1 micron down to 0.24 micron is found experimentally. The measured excess suction pressures cannot be explained only by the modified law of Laplace (for a cortex with finite thickness and negligible bending resistance), because it predicts unacceptable high cortical thicknesses (from 0.3 to 0.7 micron). It is concluded that the membrane-cortex complex has an apparent bending modulus from 1 x 10(-18) to 2 x 10(-18) J for a cortex with a thickness from 0.1 micron down to values much smaller than the radius of the smallest pipet (0.24 micron) used in this study.     

Rheological characteristics of microbial suspensions of Pseudomonas aeruginosa and Bacillus cereus

The rheological properties of the bacteria Pseudomonas aeruginosa and Bacillus cereus have been investigated. The apparent viscosity of the bacterial suspensions has been measured at different conditions. The results showed that the bacterial suspensions' apparent viscosity increased with increasing biomass concentration of each of these strains. The P. aeruginosa suspension followed shear thinning behavior while B. cereus suspension followed shear thickening behavior. The shear stress versus shear rate experimental data were best represented by the Herschel-Bulkley model. The apparent viscosity of the P. aeruginosa and B. cereus suspensions decreased with increasing temperature. The relationship between the apparent viscosity and the shearing time highlighted the rheopectic behavior of the suspensions used in this work.     

Rheological characterization of nephila spidroin solution

We report the results of an investigation into the rheology of solutions of natural spider silk dope (spinning solution). We demonstrate that dilute dope solutions showed only shear thinning as the shear rate increased while more concentrated solutions showed an initial shear thinning followed by a shear thickening and a subsequent decline in viscosity. The critical shear rate for shear thickening depended on dope concentration and was very low in concentrated solutions. This helps to explain how spiders are able to spin silk at very low draw rates and why they use a very concentrated dope solution. We also show that the optimum shear rate for shear thickening in moderately concentrated solutions occurred at pH 6.3 close to the observed pH at the distal end of the spider's spinning duct. Finally, we report that the addition of K(+) ions to dilute dope solutions produced a spontaneous formation of nanofibrils that subsequently aggregated and precipitated. This change was not seen after the addition of other common cations. Taken together, these observations support the hypothesis that the secretion of H(+) and K(+) by the spider's duct together with moderate strain rates produced during spinning induce a phase separation in the silk dope in which the silk protein (spidroin) molecules are converted into insoluble nanofibrils.     

Non-Newtonian flow-induced deformation from pressurized cavities in absorbing porous tissues

We investigate the behavior of a spherical cavity in a soft biological tissue modeled as a deformable porous material during an injection of non-Newtonian fluid that follows a power law model. Fluid flows into the neighboring tissue due to high cavity pressure where it is absorbed by capillaries and lymphatics at a rate proportional to the local pressure. Power law fluid pressure and displacement of a solid in the tissue are computed as function of radial distance and time. Numerical solutions indicate that shear thickening fluids exhibit less fluid pressure and induce small solid deformation as compared to shear thinning fluids. Absorption in the biological tissue increases as a consequence of flow-induced deformation for power law fluids. In most cases non-Newtonian results are compared with the viscous fluid case to magnify the differences.     

Changes in the mechanical properties of fibroblasts during spreading: a micromanipulation study

Cell morphology is controlled in part by physical forces. If the main mechanical properties of cells have been identified and quantitated, the question remains of how the cell structure specifically contributes to these properties. In this context, we addressed the issue of whether cell rheology was altered during cell spreading, taken as a fundamental morphological change. On the experimental side, we used a novel dual micromanipulation system. Individual chick fibroblasts were allowed to spread for varying amounts of time on glass microplates, then their free extremity was aspirated into a micropipet at given pressure levels. Control experiments were also done on suspended cells. On the theoretical side, the cell was modeled as a fluid drop of viscosity μ, bounded by a contractile cortex whose tension above a resting value was taken to be linearly dependent on surface area expansion. The pipet negative pressure was first adjusted to an equilibrium value, corresponding to formation of a static hemispherical cap into the pipet. This allowed computation, through Laplace's law, of the resting tension (τ ₀), on the order of 3×10^–4 N/m. No difference in τ ₀ was found between the different groups of cells studied (suspended, adherent for 5 min, spread for 0.5 h, and spread for 3 h). However, τ ₀ was significantly decreased upon treatment of fibroblasts with inhibitors of actin polymerization or myosin function. Then, the pressure was set at 30 mmH₂O above the equilibrium pressure. All cells showed a biphasic behavior: (1) a rapid initial entrance corresponding to an increase in surface area, which was used to extract an area expansion elastic modulus (K), in the range of 10^–2 N/m; this coefficient was found to increase up to 40% with cell spreading; (2) a more progressive penetration into the pipet, linear with time; this phase, attributed to viscous behavior of the cytoplasm, was used to compute the apparent viscosity (μ, in the range of 2–5×10⁴ Pa s) which was found to increase by as much as twofold with cell spreading. In some experiments the basal force at the cell-microplate interface was quantitated with flexible microplates and found to be around 1 nN, in agreement with values calculated from the model. Taken together, our results indicate a stiffening of fibroblasts upon spreading, possibly correlated with structural organization of the cytoskeleton during this process. This study may help understand better the morphology of fibroblasts and their mechanical role in connective tissue integrity. Received: 22 June 1998 / Revised version: 14 October 1998 / Accepted: 15 October 1998