The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

Viscoelasticity of Human Blood

Measurements made for oscillatory flow of blood in circular tubes show that blood possesses elastic properties which make consideration of its viscous properties alone inadequate. Results are for a frequency of 10 Hz while varying the amplitude of the velocity gradient for red blood cells in plasma at concentrations ranging from 0 to 100% apparent hematocrit. For velocity gradients less than 1-2 sec^-1 both the viscous and elastic components of the shearing stress are linearly related to the gradient. For hematocrits above 20% the elastic component of the complex coefficient of viscosity increases with hematocrit approximately to the third power while the viscous component increases exponentially. Oscillatory flow measurements at very low hematocrits, when extrapolated to zero cell concentration, give the intrinsic viscosity of the average individual isolated red cell. The viscous part of this is found to be 1.7 which is compared with theoretical values from the rigid ellipsoid model for which the minimum possible value is 2.5. This difference is attributed to cell deformability. With increasing velocity gradient nonlinear properties develop. The viscous component of the complex viscosity becomes of the order of the steady flow viscosity at high gradients while the elastic component tends to decrease in inverse proportion to the gradient. Thus, the elastic component of the oscillatory stress tends to saturate, this tendency appearing at the approximate level of the yield stress.     

Impedance spectroscopy flow cytometry: on-chip label-free cell differentiation.

BACKGROUND: The microfabricated impedance spectroscopy flow cytometer used in this study permits rapid dielectric characterization of a cell population with a simple microfluidic channel. Impedance measurements over a wide frequency range provide information on cell size, membrane capacitance, and cytoplasm conductivity as a function of frequency. The amplitude, opacity, and phase information can be used for discrimination between different cell populations without the use of cell markers. METHODS: Polystyrene beads, red blood cells (RBCs), ghosts, and RBCs fixed in glutaraldehyde were passed through a microfabricated flow cytometer and measured individually by using two simultaneously applied discrete frequencies. The cells were characterized at 1,000 per minute in the frequency range of 350 kHz to 20 MHz. RESULTS: Cell size was easily measured with submicron accuracy. Polystyrene beads and RBCs were differentiated using opacity. RBCs and ghosts were differentiated using phase information, whereas RBCs and fixed RBCs were differentiated using opacity. RBCs fixed using increasing concentrations of glutaraldehyde showed increasing opacity. This increased opacity was linked to decreased cytoplasm conductivity and decreased membrane capacitance, both resulting from protein cross-linking. CONCLUSIONS: This work presents label-free differentiation of cells in an on-chip flow cytometer based on impedance spectroscopy, which will be a powerful tool for cell characterization.     

Abnormal arterial flows by a distributed model of the fetal circulation

Modeling the propagation of blood pressure and flow along the fetoplacental arterial tree may improve interpretation of abnormal flow velocity waveforms in fetuses. The current models, however, either do not include a wide range of gestational ages or do not account for variation in anatomical, vascular, or rheological parameters. We developed a mathematical model of the pulsating fetoumbilical arterial circulation using Womersley's oscillatory flow theory and viscoelastic arterial wall properties. Arterial flow waves are calculated at different arterial locations from which the pulsatility index (PI) can be determined. We varied blood viscosity, placental and brain resistances, placental compliance, heart rate, stiffness of the arterial wall, and length of the umbilical arteries. The PI increases in the umbilical artery and decreases in the cerebral arteries, as a result of increasing placental resistance or decreasing brain resistance. Both changes in resistance decrease the flow through the placenta. An increased arterial stiffness increases the PIs in the entire fetoplacental circulation. Blood viscosity and peripheral bed compliance have limited influence on the flow profiles. Bradycardia and tachycardia increase and decrease the PI in all arteries, respectively. Umbilical arterial length has limited influence on the PI but affects the mean arterial pressure at the placental cord insertion. The model may improve the interpretation of arterial flow pulsations and thus may advance both the understanding of pathophysiological processes and clinical management.     

Effects of transients on pulsatile flow in arteries

Analytical solutions to the model problem of unsteady Newtonian fluid flow in straight, elastic-walled vessels can provide: theoretical insights into the flow of blood in arteries; a theoretical basis for clinical measurements in diagnoses of arterial flow rates; and guidance for boundary conditions in numerical simulations of flow in finite computational domains. However, while Womersley's analyses of blood flow assume solution forms that treat the flow as periodic and continuously unsteady, many flow variables in the smaller arteries are not continuously unsteady at all. They are characterized more accurately as rapid transient motions followed by a period of recovery to a stationary state, repeated in successive cycles. These flows are not continually unsteady ones described by Womersley's solutions but unsteady flows restarted from rest in each cycle, characterized as initial-boundary value problems. In this paper, we compare the Womersley and initial-boundary value solutions for model transients that stop then restart, explain these previously unreported limitations of Womersley's solutions, and demonstrate how the initial-boundary value solutions provide excellent agreement with measurements of blood flow in the anterior tibial and popliteal arteries of patients. Some consequences of these findings for understanding and interpreting measurements of blood flow, and for prescribing boundary conditions in computer simulations of arterial blood flow are discussed.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Measurements of human forearm viscoelasticity

In human subjects, stiffness of the relaxed elbow was measured by three methods, using a forearm manipulandum coupled to a.d.c. torque motor. Elbow stiffness calculated from frequency response characteristics increased as the driving amplitude decreased. Step displacements of the forearm produced restoring torques linearly related to the displacement. The stiffness was very similar to that calculated from natural frequencies at amplitudes above 0.1 rad. Thirdly, elbow stiffness was estimated from brief test pulses, 120 ms in duration, by mathematically simulating the torque-displacement functions. Stiffness values in the limited linear range (under +/- 0.1 rad) were higher than in the linear range of the first two methods. A major component of elbow stiffness appears to decay within 1 s. The coefficients of viscosity determined from the simulation were, however, very similar to those calculated from the frequency response. Test pulse simulation was then used to determine joint impedance for different, actively maintained elbow angles. Joint stiffness and viscosity increased with progressive elbow flexion.     

Improved frequency response of pneumotachometers by digital compensation

To measure impedance one measures or estimates flow, which is commonly done by measuring the pressure drop across a pneumotachometer. The frequency response characteristics of standard pneumotachometer/pressure transducers (PPT) limit their use to relatively low frequencies. Also, the frequency response of PPTs has been reported to be "load" dependent. Thus, the frequency response characteristics measured under "no-load" conditions, which theoretically could be used to compensate subsequent measurements, may not be appropriate for measurements made under loaded conditions. Another method of measuring impedance exists which depends on a reference impedance element other than a pneumotachometer. In this method, an oscillatory flow signal with known amplitude is generated and used to force the system being tested. Unlike PPTs, this oscillatory flow generator (OFG) is a closed system that allows measurements to be made only during breath holding. Our objective was to determine whether the frequency response of a PPT could be compensated using measurements made under no-load conditions, such that it accurately measured an impedance load. The frequency response of the PPT under no-load conditions was measured by the OFG and used to compensate the output of the PPT in subsequent impedance measurements. The compensated PPT was used to measure the impedance of a mechanical structure and the impedances of four human subjects. The impedances of the mechanical structure and the subjects were also measured using the OFG.(ABSTRACT TRUNCATED AT 250 WORDS)     

Shear and extensional rheology of cellulose/ionic liquid solutions

In this study, we characterize the shear and extensional rheology of dilute to semidilute solutions of cellulose in the ionic liquid 1-ethyl-3-methylimidazolium acetate (EMIAc). In steady shear flow, the semidilute solutions exhibit shear thinning, and the high-frequency complex modulus measured in small amplitude oscillatory shear flow exhibits the characteristic scaling expected for solutions of semiflexible chains. Flow curves of the steady shear viscosity plotted against shear rate closely follow the frequency dependence of the complex viscosity acquired using oscillatory shear, thus satisfying the empirical Cox-Merz rule. We use capillary thinning rheometry (CaBER) to characterize the relaxation times and apparent extensional viscosities of the semidilute cellulose solutions in a uniaxial extensional flow that mimics the dynamics encountered in the spin-line during fiber spinning processes. The apparent extensional viscosity and characteristic relaxation times of the semidilute cellulose/EMIAc solutions increase dramatically as the solutions enter the entangled concentration regime at which fiber spinning becomes viable.     

One-dimensional computer analysis of oscillatory flow in rigid tubes.

The dynamic characteristics of catheter-transducer systems using rigid tubes with compliance lumped in the transducer and oscillatory flow of fluid in rigid tubes were analyzed. A digital computer model based on one dimensional laminar oscillatory flow was developed and verified by exact solution of the Navier-Stokes Equation. Experimental results indicated that the damping ratio and resistance is much higher at higher frequencies of oscillation than predicted by the one dimensional model. An empirical correction factor was developed and incorporated into the computer model to correct the model to the experimental data. Amplitude of oscillation was found to have no effect on damping ratio so it was concluded that the increased damping ratio and resistance at higher frequencies was not due to turbulence but to two dimensional flow effects. Graphs and equations were developed to calculate damping ratio and undamped natural frequency of a catheter-transducer system from system parameters. Graphs and equations were also developed to calculate resistance and inertance for oscillatory flow in rigid tubes from system parameters and frequency of oscillation.     

Human blood oscillating axially in a tube

Experiments were performed to study the rheological response of human blood at hematocrit ratios of 0 to 0.45 in axial oscillatory flow in a tube of uniform bore. Three principal regimes of flow were identified, depending on the amplitude of oscillation. At the highest amplitudes (and therefore the largest range of shear rates in the blood) there was turbulent motion and the friction coefficient increased in proportion to the square of the hematocrit. At small amplitudes the friction decreased with increase in amplitude, the rate of decrease increasing with hematocrit. At intermediate amplitudes the friction increased in proportion to the square of the hematocrit. Glutaraldehyde fixation of the red cells caused increase in the friction, and reduced the rate of decrease of friction with amplitude at small amplitudes. With a stenosis of very modest degree and span the friction in normal blood increased disproportionately, and a small blind hole in the lumen of the stenosis caused additional and disproportionate increase in friction.     

Impedance spectroscopy of solutions at physiological glucose concentrations

Impedance spectroscopy has been proposed as possible approach for non-invasive glycaemia monitoring. However, few quantitative data are reported about impedance variations related to glucose concentration variations, especially below the MHz band. Furthermore, it is not clear whether glucose directly affects the impedance parameters or only indirectly by inducing biochemical phenomena. We investigated the impedance variations in glucose-water, glucose-sodium chloride, and glucose-blood samples, for increasing glucose values (up to 300 mg/dl). In all the frequency range (0.1-10(7) Hz) glucose-water samples showed impedance modulus increases for increasing glucose values (up to 135%). In blood and sodium chloride samples the impedance modulus showed only slight variations (2% and 1.4%), but again in wide frequency ranges. Therefore: i) glucose directly affects the impedance parameters of solutions; ii) effects are more relevant at frequencies below the MHz band; iii) the influence on the impedance is decreased in high conductivity solutions, but still clearly present.     

Generation of optimum pseudorandom signals for respiratory impedance measurements

Spontaneous breathing may impair the reliability of forced oscillatory impedance estimates at low frequencies, especially when the oscillatory power is distributed among many frequency values. Since the amplitude of the external forcing is limited to avoid non-linearities, it is suggested that the total energy of a composite electrical signal driving the loudspeaker be maximized at a given amplitude by finding the optimum phase relationships of the signal components, and that the low-frequency components increase in energy at the expense of the less disturbed high-frequency region. In healthy children and adults and in obstructed patients, the coherences and the coefficients of variation of the respiratory system impedance (Z_rs) at 2 and 3 Hz were studied in the case of three test signals of 2–15 Hz bandwidth. Signals T1 and T2 had a flat power spectrum, whereas the components of T3 decreased sharply between 2 and 5 Hz; T1 was generated by simple random selection of phase angles, while optimization for maximum energy was done for T2 and T3. Optimization alone (T2) increased the reliability of the Z_rs estimates at all frequencies, whereas enhancement of the low-frequency power (T3) resulted in a radical improvement of the estimates at 2 and 3 Hz, without loss in reliability at higher frequencies.     

Postural muscle activity patterns during standing at rest and on an oscillating floor.

Postural muscle activity pattern was examined in the eyes-closed state after adequate adaptation to floor anteroposterior oscillation. Twenty-three subjects were grouped almost evenly according to dominance of anterior or posterior postural muscles in the trunk and thigh during quiet stance. In the posterior-dominant group, this dominance was maintained at every frequency in most subjects. In the anterior-dominant group, this dominance was maintained in most subjects at 0.1 and 0.5 Hz but changed to posterior dominance at 1.0 and 1.5 Hz in about half the subjects. Periodicity of muscle activity was evaluated by EMG amplitude spectrum at the floor oscillation frequency. Periodicity of posterior-dominant muscles in the trunk and thigh increased with increasing oscillatory frequency. In the trunk, the periodicity did not differ significantly between posterior-dominant and anterior-dominant groups. However, in the thigh, periodicity was significantly lower in the anterior-dominant muscles. This was considered to be caused by nonperiodic alternating action of the anterior and posterior muscles. In the lower leg, posterior dominance was observed in quiet stance and at all oscillation frequencies. Periodicity of soleus and gastrocnemius increased at higher frequencies and was higher in gastrocnemius than in soleus. The periodicity difference between both muscles decreased with increasing oscillation frequency.     

Impedance analysis of the organ of corti with magnetically actuated probes

An innovative method is presented to measure the mechanical driving point impedance of biological structures up to at least 40 kHz. The technique employs an atomic force cantilever with a ferromagnetic coating and an external magnetic field to apply a calibrated force to the cantilever. Measurement of the resulting cantilever velocity using a laser Doppler vibrometer yields the impedance. A key feature of the method is that it permits measurements for biological tissue in physiological solutions. The method was applied to measure the point impedance of the organ of Corti in situ, to elucidate the biophysical basis of cochlear amplification. The basilar membrane was mechanically clamped at its tympanic surface and the measurements conducted at different radial positions on the reticular lamina. The tectorial membrane was removed. The impedance was described by a generalized Voigt-Kelvin viscoelastic model, in which the stiffness was real-valued and independent of frequency, but the viscosity was complex-valued with positive real part, which was dependent on frequency and negative imaginary part, which was independent of frequency. There was no evidence for an inertial component. The magnitude of the impedance was greatest at the tunnel of Corti, and decreased monotonically in each of the radial directions. In the absence of inertia, the mechanical load on the outer hair cells causes their electromotile displacement responses to be reduced by only 10-fold over the entire range of auditory frequencies.     

Complex viscosity of bovine red blood cells in suspensions

The complex viscosity eta* has been measured of bovine red blood cells suspended in a medium of isotonic NaCl solutions including dextran and buffered with potassium phosphate at pH 7.0. A multiple lumped resonator apparatus was used at the frequencies of 144, 572, 1491, 3742, and 8026 Hz at 20.0 degrees C. Due to the high molecular weight of dextran the medium also exhibited some visco-elasticity eta s*. So we adopted the complex specific viscosity eta sp* = (eta*-eta s*)/[eta s*]. At 20.0 degrees C eta sp* decreased with the frequency where the hematocrit was 0.233 and eta s 0.34 poise. The measurements were made for the medium with different viscosity at 5.0 degrees C and 25.0 degrees C. The results are compared with the theory of elastic shells.     

Differential neural control of intrarenal blood flow

To test whether renal sympathetic nerve activity (RSNA) can differentially regulate blood flow in the renal medulla (MBF) and cortex (CBF) of pentobarbital sodium-anesthetized rabbits, we electrically stimulated the renal nerves while recording total renal blood flow (RBF), CBF, and MBF. Three stimulation sequences were applied 1) varying amplitude (0.5-8 V), 2) varying frequency (0.5-8 Hz), and 3) a modulated sinusoidal pattern of varying frequency (0. 04-0.72 Hz). Increasing amplitude or frequency of stimulation progressively decreased all flow variables. RBF and CBF responded similarly, but MBF responded less. For example, 0.5-V stimulation decreased CBF by 20 +/- 9%, but MBF fell by only 4 +/- 6%. The amplitude of oscillations in all flow variables was progressively reduced as the frequency of sinusoidal stimulation was increased. An increased amplitude of oscillation was observed at 0.12 and 0.32 Hz in MBF and to a lesser extent RBF, but not CBF. MBF therefore appears to be less sensitive than CBF to the magnitude of RSNA, but it is more able to respond to these higher frequencies of neural stimulation.     

Dynamic viscoelastic properties of solutions of shear-degraded deoxyribonucleic acid

Calf thymus and salmon sperm deoxyribouncleie acid were degraded by high-shear stirring to molecular weights M in the range of 1.3–3.2 × 10⁶ and purified by chromatography on methylated bovine serum albumin. Dynamic viscoelastic properties of the fragmented products, in aqueous glycerol solutions in the concentration range of c = 0.003–0.01 g./ml., were investigated with the apparatus of Birnboim and Ferry. At values of the product cM higher than 4 × 10³, the frequency dependence of the components of the complex shear modulus, G′ and G″, displayed a plateau region in which G′ > G″ – ων₁η_S, similar to that observed in concentrated solutions of coiling polymers where it is attributed to an entanglement network (ω is radian frequency, ν₁ volume fraction of solvent, and η₈, solvent viscosity). The width of this plateau region on the logarithmic frequency scale is given by Δ = 3.8 (log cM – 3.56). At lower values of cM, the frequency dependence is intermediate between those predicted by the theory of Zimm for flexible coiled macromolecules and by the theory of Kirkwood and Auer for rods. Fitting to the Zimm theory gives highly discrepant values for molecular weights, while fitting the low-frequency end of the dispersion to the Kirkwood-Auer theory gives reasonable agreement for both molecular weight and rotary diffusion coefficient. It is concluded that the helical fragments appear as nearly rigid rods in their behavior at very low frequencies, but at higher frequencies reveal substantial bending flexibility.     

Effects of chain conformation and entanglement on the electrospinning of pure alginate

As a natural biopolymer, sodium alginate (SA) has been widely used in the biomedical field in the form of powder, liquid, gel, and compact solid, but not in the form of nanofiber. Electrospinning is an effective method to fabricate nanofibers. However, electrospinning of SA from its aqueous solution is still a challenge. In this study, an effort has been made to solve this problem and find the key reasons that hinder the electrospinning of alginate aqueous solution. Through this research, it was found that pure SA nanofibers could be fabricated successfully by introducing a strong polar cosolvent, glycerol, into the SA aqueous solutions. The study on the properties of the modified SA solution showed that increasing glycerol content increased the viscosity of the SA solution greatly and, meanwhile, decreased the surface tension and the conductivity of the SA solution. The rheological results indicated that the increase in glycerol content could result in the enhanced entanglements of SA chains. Two schematic molecular models were proposed to depict the change of SA chain conformation in aqueous solution with and without glycerol. The main contribution of glycerol to the electrospinning process is to improve the flexibility and entanglement of SA chains by disrupting the strong inter- and intramolecular hydrogen bondings among SA chains, then forming new hydrogen bondings with SA chains.