Viscoelasticity of Biomaterials - American Chemical Society

Chapter 16

Magnetic Rheometry of Bronchial Mucus Downloaded by STANFORD UNIV GREEN LIBR on October 12, 2012 | http://pubs.acs.org Publication Date: May 8, 1992 | doi: 10.1021/bk-1992-0489.ch016

Peter A. Edwards and Donovan B. Yeates Departments of Medicine and Bioengineering, University of Illinois, Chicago, IL 60680 To ascertain the viscous, elastic and yield properties of mucus, a magnetic rheometer was developed. Ferromag netic particles, suspended in viscous fluids or canine tra cheal pouch mucus and initially aligned by a magnetic field, were subjected to pulsed magnetic fields. The re manent magnetism of the particles was recorded with a fluxgate gradiometer after each pulse. The time courses of the remanent magnetism from particles suspended in viscosity standards were used to derive indices of vis cosity and to estimate the yield stress. The decrease in remanent magnetism due to the recoverable shear strain (elastic recoil) of the mucus was recorded when the field was turned off. For fresh canine tracheal pouch mu cus, the viscosity decreased from 1798 to 4.6 poise (p) at strain rates increasing from 0.01 to 7.3 s . The re coverable shear strain increased from 0.21 to 0.92 with strains increasing from 0.23 to 1.0; but did not vary with the strain rate. The yield stress ranged from 5.6 to 13 dynes/cm . Application of N-acetylcysteine ( N A C ) , 0.034 M, resulted in a greater decrease in yield (74% of control) than in viscosity (39%) and recoverable strain (22%). Five human sputum samples exhibited lower vis cosity values 68 to 2.5 p at 0.5 to 12 s and yield stress values 0.5 to 2.6 dynes/cm . N A C , 0.034 and 0.68 M did not alter the rheology of the sputum samples. This magnetic system can utilize small opaque mucus samples (down to 200 μl) while applying minute strains that are unlikely to cause shear degradation of the mucus. The rheological behavior of canine mucus under the condi tions of magnetic rheometry does not support the use of a Maxwell model for mucus. We suggest that the prop-1

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0097-6156/92A)489-0249$06.00/0 © 1992 American Chemical Society

In Viscoelasticity of Biomaterials; Glasser, W., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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VISCOELASTICITY OF BIOMATERIALS

Downloaded by STANFORD UNIV GREEN LIBR on October 12, 2012 | http://pubs.acs.org Publication Date: May 8, 1992 | doi: 10.1021/bk-1992-0489.ch016

erties of mucus when the applied stress is less than the yield stress are important for cilia-mucus interactions. The yield stress may prevent retrograde mucus flow while the viscosity and recoverable shear strain are important to bulk mucus flow within the airways. Mucociliary transport in the bronchial airways is responsible for the removal of inhaled deposited particles and organisms as well as intrapulmonary cellular debris. The effectiveness of this transport system is dependent on the viscoelastic properties of the mucus and its interaction with the beating cilia (1). The maximum velocity of the mucociliary transport process appears to require mucus of an optimum viscosity and elasticity (2,3). The lack of retrograde mucus flow under non-pathological conditions suggests the presence of a yield stress. The rheological properties of mucus and their relation to mucus transport have been recently reviewed (22). Pulmonary mucus, the viscoelastic gel phase of the pulmonary airway secretions, is shear thinning (4) and the elasticity is linear only for small strains (5). Also, mucus is thixotropic (6) and has measurable spinnability (7). These non-Newtonian rheological properties are primarily caused by the presence and interaction of glycoproteins and proteoglycans in an aqueous medium (8). Viscous and elastic properties of mucus have been evaluated in vitro using a number of types of rheometers (9-12). None of these are adaptable to the measurement of mucus viscosity and elasticity in vivo. We demonstrate, in vitro, the feasibility of a magnetic rheometry system whose principle of operation is applicable to the measurement of mucus rheology in vivo. In this system, micron-sized ferromagnetic particles were suspended in the test medium and rotated under the influence of pulsed magnetic fields. The time courses of rotation were sensed remotely by fluxgate magnetometry. Viscosity, elasticity and yield were derived from these. This magnetic rheometer measured viscosity, elasticity and yield stress of microliter samples of mucus utilizing minute strains. We measured the viscosity, recoverable shear strain (elastic recoil) and yield stress of fresh canine tracheal pouch mucus samples as small as 200 / i l and on opaque mucus samples over a range of shear rates and strains. Magnetic Rheometer Magnetic rheometry relies on the ability of ferromagnetic particles, suspended in a fluid, to align their magnetic moments with external magnetic field lines; the resultant magnitude of the field generated by these moments represents the orientation of the particles with respect to the sensing probe. The magnetic rheometer is shown schematically in Figure 1. The specimen and the magnetizing and sensing elements of the magnetic rheometer were contained within two concentric mumetal cylinders. These shields reduced steady and alternating magnetic fields of environmental origin. A copper wire torus around these shields was used for their periodic degaussing. The test specimen, a 5 m l suspension of 100 mg of ferromagnetic



16.

EDWARDS & YEATES

Magnetic Rheometry of Bronchial Mucus

Figure 1. Schematic diagram of the magnetic rheometer. The magnetizing coil (outer diameter = 20.3 cm, inner diameter = 10.3 cm, and length = 38.5 cm) was powered by three separate D C power supplies: (1) Lambda L E S - F 02-OV (0-18 v) for magnetic fields from 0 to 20 G ; (2) Newark ElectronicsBrute II (5-55 v) for secondary fields of 10 to 200 G ; and (3) Displex, Inc. (50-110 v) for primary magnetization and strong secondary fields of 200 to 500 G . The output of the power supplies was controlled by the Apple He microcomputer A / D converter via the controller. The output of the fluxgate gradiometer and the Gaussmeter were interfaced with the Apple He microcomputer for data collection, storage, and hardcopy production. The temperature and humidity of the sample was maintained at 37° C and 100% humidity by a temperature controlled humidifier. The magnetic shielding is not shown.


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VISCOELASTICnY OF BIOMATERIALS


particles, was contained in a plastic microbeaker (Fisherbrand 5 m l disposable). This suspension was placed between two antiparallel fluxgate Brand gradiometer probes, 7 cm apart, that were aligned coaxially with the magnetizing coil. A s any resultant magnetic field generated by the particles decreases rapidly with distance, the placement of the specimen immediately adjacent to only one of the probes enabled the measurement of the field generated by the particles while subtracting out any remaining low frequency fields of environmental origin that were common to both probes. To measure viscosity and yield stress, the time course of the summation of the remanent fields from the suspended particles was recorded. Initially, the particles were randomly oriented and thus produced no resultant magnetic field. The particles' magnetic moments were aligned with the axes of the probes by applying a strong magnetic field, usually 200-400 G . This alignment process, termed "primary magnetization," utilized the magnetizing coil, a 5500-turn copper wire solenoid positioned such that its axis was coaxial with that of the shields. Since the magnetic moments of the particles were aligned parallel to the axes of the gradiometer probes, a maximum remanent field was measured. To ascertain the viscous and yield properties of the fluid, the time course of the reorientation of the particles, caused by a magnetic field of opposite direction, "secondary magnetization," was measured. A s the remanent magnetic field of the particles could not be measured by the gradiometer while the magnetizing coil was energized, the secondary magnetism was generated by applying, to the magnetizing coils, a sequence of square wave current pulses of constant magnitude. The pulses were typically 5-10 s long with 5—15 s pauses between them. The remanent fields due to the reorientation of the particles were measured and recorded between the pulses and after the last pulse of each sequence. The angular velocity with which the particles rotated was a function of both the strength of the applied magnetizing field and the resistance to rotation by the viscous fluid in which they were suspended. The strain and rate of strain for the magnetic rheometer were dependent upon the magnitude and duration of each pulse. The strength of the magnetic fields produced by the magnetizing coil were measured by an incremental Gaussmeter (Bell 640). The magnetic rheometer was automated by interfacing the data acquisition and experimental control functions with a microcomputer v i a an A / D converter. This automated rheometer was used to characterize the rheological behavior of mucus at a variety of strains and strain rates. A hard copy of the stored data was obtained using a digital plotter (Gould DS10). To measure elasticity, the relaxation of the remanent field immediately following each pulse of secondary magnetism was measured. This relaxation was a measure of the elastic recoil of the specimen. The recoverable shear strain was the normalized difference between the magnitude of the remanent field immediately following primary magnetization and the magnitude of the remanent field immediately after secondary magnetization. The normalized elastic recoil was the recoverable shear strain. The difference between the shear strain and recoverable shear strain is the non-recoverable shear strain (flow).



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EDWARDS & YEATES


To measure the yield stress of the test specimen, the maximum shear stress that would not produce non-recoverable shear strain was estimated. First, the minimum secondary field strength that would result in nonrecoverable shear strain was determined by repeated measurements using successively greater secondary field strengths (beginning with a secondary field of zero strength). The secondary field strengths that were less than the minimum resulted in only recoverable shear strain. Second, the vis cosity of the specimen was determined using successively weaker secondary fields, beginning with secondary field strengths greater than the minimum for non-recoverable shear strain and approaching the minimum secondary field for non-recoverable shear strain. T h i r d , comparison of the viscosity and shear rate during each of the viscosity measurements mentioned above allowed the calculation of the average shear stress during each measure ment. Finally, from a plot of the calculated shear stresses, the shear stress at the minimum secondary field strength was extrapolated. The extrapo lated shear stress was the estimate of the yield stress. Theory The theory of operation of the magnetic rheometer was derived by modeling the suspended particles as a collection of fluid-mechanically independent spheres, which (after prealignment of their magnetic moments) rotate in unison. The differential equation governing the rotation of a suspended sphere during magnetic rheometry was coupled to the differential equation for the fluid motion by the boundary condition at the surface of the particle. The equations of motion for the sphere were developed by performing a force balance. The law of conservation of angular momentum dictates that the rate of change of angular momentum must equal the sum of any applied torques. The two torques for this case were the magnetic torque (TM) due to the applied magnetic field and the viscous torque (Ty) due to the shear stress at the surface of the particle: I{dW/dt) = T

M

+ Tv

(1)

where J = moment of inertia and W = angular velocity A uniform magnetic field exerts a force on a ferromagnetic particle immersed in a medium that is equal to the cross product of the magnitude of the applied field (H) and the magnetic moment of the particle ( M ) multiplied by the permeability of the medium (μΜ)' Τ =μ (ΜχΗ) Μ

Μ

(2)

In this analysis the magnetic properties of the particles were assumed to be isotropic. For simplicity of notation, consider a spherical coordinate system ( r , 0 , F ) . For the case where the applied field was uniform, in the ζ d i rection (where F is the angle a vector makes with the ζ axis), and the


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magnetic vector is in the same plane as the field vector (the plane defined by r and Φ). The resulting torque causes rotation (no translation) of the particle in that same plane (provided that the two vectors are not parallel) and is a function of only r. The magnitude of magnetic torque was TM = μΜΜ Ηζ 0

sin Φ

(3)


The magnetic torque was opposed by a viscous torque resulting from drag at the surface of the particle. Insertion of Equation 3 into Equation 1 gave: T

V

= μ Μ Ηζ Μ

0

sin Φ - (2ma /5)[ά Φ/Λ ] 2

2

(4)

2

This differential equation could not be solved in closed form, even for a simple viscous fluid, unless the inertial term was neglected. However, neglecting inertia resulted in a solution that could not satisfy the initial conditions of a particle at rest. Consequently, we utilized a semi-empirical method. The magnetic torque was calculated from the appropriate physical constants and was subtracted from the rate of change of angular momen tum which was calculated from the experimental data. The result of this subtraction was the viscous torque on the particle which was used to cal culate the stress on the surface of the particle while the strain and rate of strain at the particle surface were determined from the data (i.e., the time course of the rotation). The resultant of the magnetic fields of all suspended particles was used to determine the time course of movement of the particles. The data interpretation was simplified by assuming that the signal measured could be taken as the sum of the signals from the individual particles. Thus, the remanent particle field B (t) was related to the rotation angle, Φ, by the following relation (13): r

Β (0 Γ

= Β οοβ[Φ -Φ(0] Γβ

(5)

0

where Φ = the initial angle ~ 0 and B = B when Φ = Φ . The viscous torque on the sphere was the cross product of the force and the moment arm. For the case of a magnetic sphere under the influence of an external magnetic field the moment arm was simply the radius (a) and the unit area was the surface area (4Πα ). Thus the stress, r , was defined as follows: τ = Τ /4Πα (6) ro

0

r

0

2

ν

3

A value for the strain at the surface of the particle was also obtained from the gradiometer signal (B (t)). The 90° rotation was used as a charac teristic strain since it approximates the angle swept out by cilia in mucus during the "power stroke" phase of ciliary motion. Thus, all measures of deformation angle were divided by 90 for nondimensionalization. r

j(t)

= the strain = Φ(*)/90 = cos" [B (t)/B ]l^ l

r

ro


(7)


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Magnetic Rheometry of Bronchial Mucus 255

(Note: The deformation of the fluid at the surface of the particle is actually equal to the rotation angle multiplied by the radius of the particle; however, the radius i n the numerator and denominator cancel, leaving the result the same.) The average rate of strain over any given time period was equal to the strain divided by the elapsed time. The apparent viscosity was equal to the quotient of the stress and the rate of strain. Thus, equations 6 and 7 were used to calculate the viscosity of a test fluid provided the particles were spherical and the appropriate physical constants were known. A more practical approach was to empirically calibrate the instrument using viscos ity standards. The latter approach was used for the experiments described in subsequent sections. Nickel spheres, however, were used to validate the theoretical equations. The nickel spheres were suspended i n a viscoelastic polymer solution Polyox W S R - 3 0 1 (1%). The manufacturer's low shear rate viscosity data gave a value of 250-270 poise for this solution. The average value calculated from the theoretical equations for magnetic rheometry and experimental data was 217 p. Using empirical calibration (see below) the values ob tained were 250 and 248 p. Magnetic rheometry shows the good agreement between theory and experiment for nickel spheres, as well as agreement with the manufacturer's data. Unfortunately, the magnetic characteristics of the nickel spheres made them unsuitable for use with the secondary field strengths necessary to rotate them i n materials as viscous as mucus. Thus, the magnetite particles were used and necessitated the empirical calibration method. Calibration and Methods The magnetic rheometer was empirically calibrated using viscosity stan dards (Brookfield) of 9.80, 48.80, 130, 307.2, 620.0, and 960 poise. M a g netite particles (Pfizer), which ranged from 0.2 to 3.0 μτη in diameter, were suspended i n 5 m l samples of each viscosity standard. The suspensions also contained a small number of aggregates, which ranged from 5.0 to 30.0 μτη in diameter. For calibration purposes, 100 mg of the magnetic particles were suspended i n each sample. The time course of remanent magnetism of particles i n the 620.0 ρ viscosity standard after primary magnetization and during secondary magnetization is shown i n Figure 2a. The remanent magnetism changed sequentially from its maximum "positive" value. A s the particles rotated, the remanent field measured by the gradiometer de creased, reaching zero when the net magnetic moment of the particles was perpendicular to the axes of the probes and approaching a maximum nega tive value as their magnetic moments approached alignment i n the opposite direction. In the case presented i n Figure 2b, the average value correspond ing to each of the first six plateaus of remanent field, expressed as a percent of the maximum initial field, was plotted against the time for which the secondary field was applied. The time required for the remanent field to decrease to zero " 7 W was used as an index of viscosity. Measurements of TBQ were independent of the concentration of the suspended particles over



256


TIME (seconds)

TIME (seconds) Figure 2. Measurement of T for F e 0 4 particles i n a viscous fluid, (a) After primary magnetization (320 G ) , the remanent magnetic field of fer romagnetic particles suspended i n the 620 ρ viscosity standard decreases i n response to the 1.5 s pulses of secondary magnetization (200 G ) which were delivered at a pulse rate of 0.25 Hz. During each secondary pulse the gradiometer output was approximately zero, resulting i n a series of plateaus along the zero line. The spikes of remanent magnetism after each pulse were due to a transient response of the gradiometer probes to the strong magnetic field of the magnetizing coil, (b) The normalized value of each plateau i n Figure 2 a is shown as a function of time that the secondary field was applied (i.e., the time periods for recording the remanent plateaus were eliminated). B0

3



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EDWARDS & YEATES


the range of 0.1-20 m g / m l as demonstrated by the coincidence of the TBO (Figure 3) for the three suspensions. The TBO was derived for each viscosity standard using secondary field strengths of 60-340 G (40 G increments). The magnitude of T B O increased with increasing viscosity and decreased with increasing field strength. The viscosity is plotted against the T B O for most of the secondary field strengths and is shown i n Figure 4. The family of such curves forms a series of cali bration curves from which the viscosity of a test sample may be determined from its T B O at the appropriate secondary field strength. To evaluate the rheological properties of mucus obtained from a sub cutaneous tracheal pouch of an adult male beagle dog (14), the magnetite particles were blown onto the surface of the mucus sample using a Wright dust feeder. To avoid shear degradation due to mechanical mixing, the particles were drawn below the surface by a permanent magnet. Results The time course of remanent magnetism from particles suspended i n mucus during the magnetic rheometry process is shown i n Figure 5a. In contrast to the viscous oils, the remanent plateaus were actually relaxation curves. These relaxation curves were due to the elastic nature of mucus. The average values of the relaxed remanent fields after each pulse of secondary magnetism as a percent of the initial remanent field are shown as a function of the time the secondary field was applied i n Figure 5b. A n example of the complete relaxation of the remanent field from par ticles suspended in mucus is shown i n Figure 6. The elasticity of the mucus sample was measured by applying one 4.5 s pulse of secondary magnetiza tion (200 G ) and recording the complete relaxation of the remanent field. The magnitude of the relaxation was the elastic response. A n example of complete relaxation of the remanent field from particles suspended i n mucus is shown i n Figure 6. The difference between the initial plateau magnitude and the magnitude after complete relaxation was the viscous response. The recoil time constant for mucus, i.e., the time required for the relaxation to reach 63.2% of its final value, was 2.1 s. A n example of the remanent magnetic fields recorded during a deter mination of yield stress is shown i n Figure 7. Figure 7a shows the determi nation of the minimum secondary field strength for non-recoverable shear strain ( H ) , while Figure 7b shows the results of the successive viscosity measurements that lead to an estimation of the yield stress for a mucus sample. Ten canine tracheal pouch mucus samples exhibited viscosity values ranging from 1798 to 4.6 ρ at 0.1 to 7.3 sec" rates of strain, respectively. The normalized strain increased from 0.23 to 1.0 (see Figure 8), while the recoverable shear strain at fixed strain did not increase with the rate of strain (see Figure 9). The yield stress for these same samples ranged from 5.6 to 13.5 dynes/cm . Five human sputum samples exhibited lower viscosities (68 to 2.5 ρ at 0.5 to 12 sec" ) and yield stress values of 0.5 to 2.6 dynes/cm . The elastic m

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CONCENTRATION χ — 0 . 1 mg/ml

100H 80|

Q — 1 0 mg/ml


+....

§

60|

Viscoelasticity of Biomaterials - American Chemical Society

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