WO2002004938A2 - Appareil et procedes de determination des proprietes viscoelastiques des materiaux - Google Patents

Appareil et procedes de determination des proprietes viscoelastiques des materiaux Download PDF

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Publication number
WO2002004938A2
WO2002004938A2 PCT/US2001/021659 US0121659W WO0204938A2 WO 2002004938 A2 WO2002004938 A2 WO 2002004938A2 US 0121659 W US0121659 W US 0121659W WO 0204938 A2 WO0204938 A2 WO 0204938A2
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Prior art keywords
sample
cantilever
viscoelastic
piezoelectric elements
properties
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PCT/US2001/021659
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English (en)
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WO2002004938A3 (fr
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Robin Coger
Jeffrey Parsons
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University Of North Carolina At Charlotte
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Priority to AU2001273302A priority Critical patent/AU2001273302A1/en
Publication of WO2002004938A2 publication Critical patent/WO2002004938A2/fr
Publication of WO2002004938A3 publication Critical patent/WO2002004938A3/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/02—Analysing fluids
    • G01N29/032—Analysing fluids by measuring attenuation of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/01—Indexing codes associated with the measuring variable
    • G01N2291/012—Phase angle
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/024—Mixtures
    • G01N2291/02466—Biological material, e.g. blood
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/04—Wave modes and trajectories
    • G01N2291/042—Wave modes
    • G01N2291/0427—Flexural waves, plate waves, e.g. Lamb waves, tuning fork, cantilever
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/10—Number of transducers
    • G01N2291/106—Number of transducers one or more transducer arrays

Definitions

  • the present invention relates to apparatus and methods for determining the viscoelastic (rheologic) properties of materials.
  • the apparatus and methods of the present invention are particularly advantageous for determining the viscoelastic properties of extracellular matrices (ECMs) that are becoming increasingly important for advancing our understanding of biological and bioengineered systems.
  • ECMs extracellular matrices
  • Viscoelastic is used to describe materials that display properties that range in between the rigid boundaries defining solids and liquids.
  • An early example of a viscoelastic. material is silk thread. When a longitudinal load is applied to the thread, an immediate extension is manifested followed by a further lengthening with time as the load is continuously applied.
  • the silk thread Upon removal of the load, the silk thread displays an immediate contraction coupled with a gradual further decrease in length until the original length is restored. From this description, the silk thread displays properties encompassing both solid (elastic) and liquid (viscous) behavior.
  • the illumination of materials with such properties lead to the rapid development of rheology as a necessary scientific field where the concepts of elasticity and viscosity coalesced. Modern rheology is concerned with detenriining the viscoelastic properties of materials.
  • ECM material properties in the presence of the hydrating fluid.
  • Conventional methods like cone and plate and parallel plate rheometry evaluate the bulk material properties of gel materials while displacing the liquid film that hydrates the test sample. Since the test sample is secured between two surfaces during testing, the very design of these conventional rheometry techniques limit the fraction of the sample's surface area available for contact with the hydrating liquid. Such systems are therefore non deal for testing materials such as ECMs, whose properties change with dehydration.
  • these rheological methods quantify only the bulk properties of the sample, they are incapable of addressing the localized viscoelastic properties experienced by cells at the ECM/liquid interface.
  • Sample size is an additional concern when conducting rheological experimentation.
  • Conventional rheometers are often unsuitable for accurately measuring the viscoelastic properties of materials when only small sample volumes are available. This is a major concern regarding the biological applications of rheology where sample volume is commonly small due to the high cost of biological reagents.
  • Standing and Langer (1999) used a Bohlin Rheometer (Bohlin Rheologi, Lund, Sweden) with parallel plates to measure cell-polymer cartilage constructs. Although it used conventional parallel plate rheometry, the system additionally employed a liquid chamber that surrounded the parallel plates during testing. Therefore, by filling the chamber with tissue culture media, the circumference of the sample remained hydrated throughout the testing period. However, since the sample surfaces that contacted the plates (i.e., the test surface) were not hydrated, this scenario did not mimic the environment experienced by cells in culture.
  • the shortcomings of current rheometric methods described above necessitates the development of a rheometer that accurately measures a materials shear storage and loss moduli while allowing the test sample to remain completely hydrated at a substantially constant temperature for the duration of the experiment.
  • the rheometer should preferably be usable with small sample sizes and additionally possess the ability to measure the localized surface properties of the material. It would also be advantageous to be able differentiate surface properties of a material from its bulk properties by having apparatus and methods that are capable of measuring localized surface properties of a material.
  • the present invention provides apparatus and methods for determining the viscoelastic properties of materials that overcome the deficiencies of prior apparatus and methods noted above.
  • Embodiments of the present invention provide rheometers that may be advantageously utilized to measure properties of materials that have been difficult or impossible to correctly measure with present rheometers.
  • the present invention provides a piezoelectrically actuated linear rheometer (PALR) designed to remedy the problems currently associated with rheometric methods when measuring viscoelastic properties of hydrated materials.
  • PLR piezoelectrically actuated linear rheometer
  • the novel apparatus comprises a cantilever that applies an oscillating load to the viscoelastic material in order to sense the material's deflection.
  • the cantilever uses at least one layer as an actuator and another piezopolymer layer to measure the lateral movement of an attached probe.
  • the viscoelastic nature of the test material adds damping to the system, resulting in the attenuation and phase shift of the sensor's output voltage. From these parameters, physical properties of a material, such as shear storage and loss modulus, may be quantified.
  • a rheometer of the present invention displays several advantages over conventional cone and plate and parallel plate rheometers.
  • a notable advantage is that embodiments of the present invention allow a test sample to remain hydrated throughout the experimentation period.
  • the sample cannot be exposed to a hydrating layer of liquid during testing, since the plates will push out this layer when they come into contact with the test sample.
  • the sample may dry out during the experiment leading to erroneous physical measurements.
  • the allowance of the hydrating layer in the present invention ensures sample stability and accurate determination of pertinent physical variables. This is especially important in biological applications such as the determination of the viscoelastic properties of extracellular matrices (ECMs).
  • a rheometer of the present invention is the ability to measure localized surface properties of a material.
  • apparatus and methods of the present invention allow a user to differentiate between a material's surface viscoelastic properties and its bulk viscoelastic properties that may be measured by conventional methods.
  • Prior Cone and plate and parallel plate rheometers only possess the capability of determining the bulk properties of a material. Therefore, these rheological methods are ineffective in many applications where the investigation of surface deformation and flow is desired.
  • embodiments of the present invention allow for the investigation of both surface and subsurface viscoelastic properties.
  • the capacity to differentiate between surface and subsurface properties permits use of a rheometer of the present invention in a wide array of applications including biological applications. Understanding a biological cell's interaction with its extracellular matrices
  • ECMs is an important area of research. Embodiments of the present invention permit accurate investigation of ECM surface properties which may be critical in determining the nature of the cell/ECM interaction.
  • a further advantage the present invention is that embodiments of the present invention may be utilized to make local measurements on the test sample. There is no need for the assumption of sample homogeneity if local measurements are desired. Extrapolation of local measurements to the macroscale is possible if so desired. Embodiments of the present invention, however, allow multiple test sample regions to be measured in order to experimentally ensure homogeneity. Prior cone and plate and parallel plate techniques assume sample homogeneity and only allow for global sample measurements. As a result, in prior methods sample inhomogeneity may lead to erroneous determination of a heterogeneous material's viscoelastic properties by these methods.
  • embodiments of the present invention to make localized measurements permits the investigation of inhomogeneous materials otherwise not possible with a macroscale rheological method. For example, one region of the test material may exhibit a higher viscosity than another section due to inhomogeneity.
  • the structural relationships between the high viscous and low viscous regions of a material could be examined. This would not be possible with prior cone and plate or parallel plate rheometers since these instruments measure material properties over the whole sample by an averaging process.
  • embodiments of the present invention permit the temperature of the sample to be precisely controlled and may also permit small sample volumes to be effectively analyzed. Material properties often vary with temperature. Therefore, a method that allows the determination of material properties over a wide range of temperatures is highly desirable. Moreover, embodiments of the present invention are capable of examining the viscoelastic properties of a material when only a small sample volume is available. This is advantageous especially in biological experimentation where sample volume is commonly small due to the high cost of biological reagents .
  • Figure 1 illustrates an embodiment of an apparatus of the present invention.
  • Figure 2 illustrates a possible design of a cantilever comprising piezoelectric layers in an apparatus of the present invention utilized in the Examples described herein.
  • Figure 3 graphically presents the results of measuring the viscosity of the purely viscous fluid glycerol utilizing an apparatus of the present invention as described in the Examples herein.
  • Figure 4 graphically presents the results of measuring the viscoelastic properties of samples utilizing an apparatus of the present invention as described in the Examples herein.
  • Figure 5 graphically presents the results of measuring the viscsoelastic properties of samples utilizing an apparatus of the present invention as described in the Examples herein. Detailed Description of the Invention
  • An apparatus of the present invention for determining a mechanical property of a material comprises: a plurality of piezoelectric elements; a signal generator; an electrical connection between the signal generator and the piezoelectric elements; and data acquisition means for acquiring an output signal from at least one of the piezoelectric elements.
  • the apparatus may further comprise positioning means for positioning the piezoelectric elements in communication with a sample of the material.
  • the apparatus may further comprise a sample platform.
  • the sample platform may be adjustable.
  • the apparatus may still further comprise an incubation cabinet that surrounds at least the sample and the piezoelectric elements, and the sample platform if utilized.
  • the incubation cabinet preferably maintains the environment of the sample at a controlled and or substantially constant temperature, and may further maintain other environmental features, for example humidity, pressure, light in a controlled manner.
  • the sample platform, piezoelectric elements and/or positioning means may be mounted in a framework so that they are positioned with respect to each other in a manner that allows a sample to be tested.
  • the piezoelectric elements may be disposed above the sample platform.
  • the positioning means may operate to raise and lower the platform, to raise and lower the piezoelectric elements and/or both.
  • the piezoelectric elements comprise a portion of a cantilever.
  • the present invention also provides methods for determining a mechanical property of a test sample comprising: positioning a sample in proximity to a plurality of piezoelectric elements; contacting a surface of the sample with at least a pair of piezoelectric elements; supplying a sinusoidal electrical signal to the piezoelectric elements an as input signal; obtaining an output signal from the piezoelectric elements; using the output signal to determine a mechanical property of interest.
  • the method may further comprise placing the sample to be measured on a sample platform and positioning the sample platform to place the sample in proximity to the piezoelectric elements.
  • the method may still further comprise maintaining the sample in a controlled environment wherein at least one of the following environmental conditions is controlled: temperature, humidity, light, and/or pressure.
  • the controlling may comprise maintaining the environmental condition in a substantially constant state.
  • a method of the present invention is particularly advantageous for determining viscoelastic properties of a sample, including, but not limited to shear storage modulus (G'); shear loss modulus (G”); and dynamic viscosity ( ⁇ ).
  • the present invention is particularly useful in determining the viscoelastic properties of ECM samples at the boundary layer between an liquid layer and a solid cellular level.
  • a method of the present invention may comprise additional steps to precisely locate the piezoelectric elements at the boundary layers.
  • These additional steps may comprise: contacting a solid portion of the sample with the piezoelectric elements supplying a sinusoidal electrical signal to the piezoelectric elements as a first input signal; obtaining a first output signal from the piezoelectric elements; repositioning the piezoelectric elements in the liquid portion of the sample; supplying a sinusoidal electrical signal to the piezoelectric elements as a second input signal; obtaining a second output signal from the piezoelectric elements; utilizing the first and second output signals to position the piezoelectric elements at the boundary of the liquid and solid layers.
  • An embodiment of the present invention comprises a piezoelectrically actuated linear rheometer (PALR) that induces a linear shear strain in the test material, as opposed to the torsional shear strain induced by parallel plate rheometers.
  • the load inducing agent in the PALR is a cantilever composed of a plurality of piezoelectric layers whose inputs and outputs are connected to a data acquisition board. Once the tip of the cantilever is placed in contact with the test material, the data acquisition board directs a sinusoidal voltage to the cantilever's piezoelectric actuator, which causes the cantilever tip to apply and oscillatory shear stress to the test material.
  • a piezoelectric sensor attached to the cantilever then records the resulting tip displacement and shear strain of the sample. From the tip displacement, and the phase shift between the input and output voltages, the viscoelastic properties of the test material are then calculated.
  • Embodiments of the present invention may further comprise an adjustable mounting platform that ensures precise cantilever placement within the sample leading to high experimental accuracy and reproducibility.
  • embodiments of the present invention may be designed to fit within a modified incubator that allows constant temperature control during experimental testing.
  • An embodiment of an apparatus of the present invention is shown schematically in Figure 1.
  • an apparatus of the present invention, 2 may comprise a frame 4.
  • the frame may include mounts, 6, for mounting the frame to a laboratory bench or other piece of equipment.
  • the mounts 6, may comprise a damping material, such as sorbothene or the like, for minimizing the effect of ambient vibrations on the apparatus 2.
  • Apparatus 2 further includes sample platform 8, for holding a sample 12.
  • An apparatus of the present invention is capable of being utilized with a wide variety of samples.
  • the dimension of the sample tray may be scaled depending on the intended use of the apparatus.
  • sample platform 8 may be designed to hold a standard size petri dish containing a sample.
  • Fastening means 14, which may comprise clamps or the like, may be utilized to precisely position the sample in the apparatus.
  • the frame 4 of the apparatus may include a plurality of positioning means, 10, (shown as holes) to receive pins or bolts from the sample platform and allow the sample platform to be positioned at different heights.
  • Apparatus 2 further comprises cantilever 16 that includes a plurality of piezoelectric elements as described in detail below. Cantilever 16 may be connected through frame 4 to a threaded positioning means 18 that enable the cantilever to be raised and lowered.
  • the piezoelectric elements are electrically connected through wires 20 to an electrical coupling 22 that can be connected to a data acquisition device
  • the entire frame may be constructed with clear side panels 24 to provide a temperature and/or humidity controlled environment for the sample measurement.
  • a piezoelectric cantilever may be constructed by binding two piezoelectric strips to a central thin metal foil sheet as demonstrated in Figure 2 which is described below with reference to the examples. Fabrication with only two piezoelectric layers facilitates the use of simple mathematical relations describing the cooperative nature of the piezoelectric layers when in operation. However, this does not indicate that a maximum of two piezoelectric strips is the only configuration for cantilever construction. More than two piezoelectric strips working together is possible.
  • the piezoelectric comprising the cantilever should exhibit high g-constants and have a low density, for example, a density below 5000 kg/m 3 , preferably below 2000 kg/m 3 .
  • PVDF Polyvinylidenefiuori.de
  • Other possible piezoelectrics include plastics, ceramics and other piezoelectrics having similar properties .
  • width of the piezoelectric strips ranges in the tens of millimeters (mm) and the thickness in the tens of microns ( ⁇ m).
  • the width a piezoelectric strip may comprise 10 to 50 mm, preferably 15 to 30 mm, more preferably 15 to 25 mm.
  • Suitable thickness for the piezoelectric strips (including silver electrodes) include thicknesses from 20 to 100 ⁇ m, preferably 25 to 60 ⁇ m, more preferably 30 to 50 ⁇ m.
  • a thin foil sheet located between the piezoelectric layers comprises a thickness ranging in the tens of microns ( ⁇ m) as well, generally 30 to 100 . ⁇ m, preferably30 to 75 ⁇ m, more preferably 35 to 60 ⁇ m.
  • the foil used in the cantilever comprises an electrically conductive foil, for example a metal foil. Suitable foils comprise copper, aluminum, silver, tin, gold, and/or alloys thereof. Contact between the cantilever and a test sample may be achieved utilizing a suitable probe connected to the end of the cantilever.
  • the probe will have at least one or more of the following characteristics high stiffness, low density or corrosion resistance.
  • Suitable probes includes those comprising glass, titanium, ceramics or similar materials.
  • the connection between the end of the cantilever and the probe may be achieved utilizing an adhesive, such as an epoxy.
  • the volume of the probe does not exceed 100 cubic millimeters, more preferable the volume of the glass probe does not exceed 10 mm 3 .
  • a piezoelectric element may be utilized to contact a sample.
  • the sides of the probe may be constructed from and or coated with a hydrophobic material to minimize adherence between an liquid medium above a sample and the probe.
  • a hydrophobic material to minimize adherence between an liquid medium above a sample and the probe.
  • one of the piezoelectric elements of the cantilever serves as an actuator, while the other serves as a position sensor.
  • a sinusoidal voltage is applied to the actuator, such that the subsequent expansion and contraction produces a bending motion in the cantilever.
  • the piezoelectric element on the opposite side of the cantilever undergoes tension and compression as the cantilever oscillates. This generates an alternating current (AC) signal that is used to determine the displacement of the cantilever.
  • AC alternating current
  • Actuation of the cantilever may be accomplished utilizing a signal generating device.
  • actuation of the cantilever is accomplished using a 10V sinusoidal signal generated by Lab View 4.1 (National Instruments, Austin, TX), where the frequency of the input signal can be varied from 0.1 Hz to 10 Hz.
  • Other suitable signal generators include those commercially available from Omron and Hewlett Packard.
  • the signal generating device may be controlled by a data acquisition board that may also be advantageously utilized to control other aspects of the apparatus.
  • a data acquisition board (also referred to herein as a "DAQ") comprises a processor, for 11
  • Contact between the cantilever and a test sample may be achieved utilizing a suitable probe connected to the end of the cantilever.
  • the probe will have at least one or more of the following characteristics high stiffness, low density or corrosion resistance.
  • Suitable probes includes those comprising glass, titanium, ceramics or similar materials.
  • the connection between the end of the cantilever and the probe may be achieved utilizmg an adhesive, such as an epoxy.
  • the volume of the probe does not exceed 100 cubic millimeters, more preferable the volume of the glass probe does not exceed 10 mm 3 .
  • a piezoelectric element may be utilized to contact a sample.
  • the sides of the probe may be constructed from and/or coated with a hydrophobic material to minimize adherence between an liquid medium above a sample and the probe.
  • a hydrophobic material to minimize adherence between an liquid medium above a sample and the probe.
  • one of the piezoelectric elements of the cantilever serves as an actuator, while the other serves as a position sensor.
  • a sinusoidal voltage is applied to the actuator, such that the subsequent expansion and contraction produces a bending motion in the cantilever.
  • the piezoelectric element on the opposite side of the cantilever undergoes tension and compression as the cantilever oscillates. This generates an alternating current (AC) signal that is used to determine the displacement of the cantilever.
  • AC alternating current
  • Actuation of the cantilever may be accomplished utilizing a signal generating device.
  • actuation of the cantilever is accomplished using a 10V sinusoidal signal generated by Lab View 4.1 (National Instruments, Austin, TX), where the frequency of the input signal can be varied from 0.1 Hz to 10 Hz.
  • Other suitable signal generators include those commercially available from Omron and Hewlett Packard.
  • the signal generating device may be controlled by a data acquisition board that may also be advantageously utilized to control other aspects of the apparatus.
  • a data acquisition board (also referred to herein as a "DAQ”) comprises a processor, for 12 controlling at least one of a signal generator, cantilever adjuster means, and/or other aspects of the apparatus; user input means; such as a keyboard, mouse, switches, dials or the like; user ouput means, such as a display, dial, and/or a cable, IR or similar connection for uploading data into a computer; electrical connections, including wires or similar apparatus, in electrical communication with the piezoelectric elements; and software for controlling the DAQ and the connected devices.
  • the DAQ may further comprise memory, in the form of read only memory (ROM) or random access memory (RAM).
  • the software may be burned into ROM in communication with the processor or may reside in RAM while the DAQ is operating.
  • Suitable processors, user input and output means, electrical connections and other hardware for use in the data acquisition board includes components commercially available in the computer hardware field, such as microprocessors, ROM's , EPROM's, displays, keyboards, mice and the like.
  • the output signal generated by the cantilever's sensor may be elecrically filtered and amplified prior to its reception by the data acquisition board.
  • the output signal generated by the cantilever's sensor may be fed through a 20 Hz low-pass filter and a lOOOx amplification/buffer circuit before it is measured and recorded by the DAQ.
  • the longitudinal change in length, Al, due to an applied voltage in the thickness direction can be expressed as (Ikeda, 1990):
  • the piezoelectric 's finite time constant and the PALR's filtration circuitry establishes a base phase shift between the input and output signals. Hence when additional damping is added to the cantilever via its contact with the test sample, a total voltage phase shift ( ⁇ ) is observed. In operating the PALR it is this output voltage, V oub and the phase shift, ⁇ , of the output signal, that is measured and used to determine the storage (G') and loss moduli (G”) of the test sample.
  • the cantilever's position relative to the test sample be accurately and repeatably controlled from sample to sample.
  • this result may be achieved through the use of an adjustable mounting platform (AMP) for positioning of a sample.
  • AMP adjustable mounting platform
  • a sample platform comprises a planar surface that a sample may rest on.
  • Embodiments of the present invention may use adjustable kinematic mounts to keep the sample level during testing.
  • the dimensions of the platform may vary depending on the size of the samples being tested to suit individual experimental needs.
  • the platform may be constructed of a strong, relatively lightweight material, such as aluminum, titanium, magnesium, and/or alloys thereof; plastic and/or combinations thereof
  • the cantilever may be attached to the platform or may be isolated by a frame above the platform.
  • the cantilever is electrically isolated from the frame to which it is attached.
  • the cantilever is attahed to an adjustable mounting platform and electrically isolated using clamps comprising an electrically isolating material. The clamp is closed and held in place by suitable fasteners, such as screws, bolts, rivets or the like.
  • the sample platform comprises an adjustable mounting platform.
  • An adjustable mounting platform advantageously allows the vertical position of the cantilever relative to the sample t> be accurately controlled and adjusted.
  • the accuracy allowed by the AMP is advantageous, since the height, d, of the test sample, is related to the amount of damping added to the system.
  • Rao (1995) offers an effective model of this relationship. For sjstems in which the flat face of the system is in contact with the surface of the test sample, the viscous damping,
  • the cantilever is preferably positioned with an accuracy of 0.05 mm.
  • the adjustable nature of the sample platform may be achieved through the use of a threaded elongate member on which the sample platform is mounted. Rotating the member adjusts the relative position of the platform with respect to the cantilever.
  • a non-rotating micrometer may be utilized to provide an adjustment range of 0-25mm and accuracy to within 0.001mm.
  • the cantilever is preferably calibrated under the same thermal environment as the testing conditions (Tzou and Ye, 1996; Barnes et al., 1989). For biological materials, a temperature of 37 C ensures physiological semblance.
  • the cantilever and sample platform may be enclosed in an incubator.
  • the incubator may include heat transfer means to control the sample's temperature.
  • the incubator may also provide the important function of electrostatic shielding. Electrostatic shielding is advantageous because in embodiments of the apparatus the cantilever's electrodes may be unshielded, and its output signal may comprise small amplitudes that are extremely sensitive to electrical noise.
  • the inside of the incubator may be lined with grounding film, such as an aluminum film, and connected to the negative terminals of the cantilever. In this way, an electrostatic shield is established around the instrument, to reduce interference from outside sources (Young, 1992).
  • An apparatus of the present invention may be utilized to determine the complex shear moduli of a test sample by applying an oscillatory linear shear stress to the material and recording the induced shear strain.
  • a linear viscoelastic material is one that exhibits the characteristics of a Hookean elastic solid and a 15
  • the shear stress, ⁇ ( ⁇ t), in a viscoelastic material subject to an oscillatory shear force is then related to the shear strain according to:
  • ⁇ 0 is the amplitude of a sinusoidally varying strain
  • G*( ⁇ ) is the complex shear modulus of Eq. (4) (Barnes et al., 1989).
  • the shear moduli, G' and G" can then be related to traditional material parameters (i.e., the rigidity modulus, G and the dynamic viscosity, ⁇ , according to: 16
  • An apparatus of the present invention uses a vibrating cantilever to apply shear stresses to linear viscoelastic biomaterials. This technique may be utilized to quantify the rigidity modulus, G, and the dynamic viscosity, ⁇ , of a material. The relationship between these two material properties and the input force, cantilever tip displacement, x( ⁇ t), and the phase shift ⁇ sys , may be established using a mechanical vibration rheometer model.
  • the mechanical responses of an apparatus of the present invention x( ⁇ t) and ⁇ are related to the mechanical properties, G' and G", of the test sample by modelling the new rheometer as a discrete one-degree-of-freedom vibrating system.
  • the cantilever comprises a spring with some damping due to internal friction and the viscoelastic nature of its components. When the probe tip is placed 17 in contact with the surface of the test sample, the adherence will increase the total stiffness and damping of the system. This is analagous to adding an additional parallel spring and parallel damper to the system.
  • k and C c represent the spring constant and damping constant of the cantilever, respectively; k and C represent the spring and damping constants added by the test sample; and m eff is the effective mass of the system.
  • the effective mass is calculated from (Rao, 1995):
  • the natural frequency, f of the system corresponds to the frequency at which the system's oscillatory response is maximum.
  • ⁇ is the phase shift between the force, F ⁇ t), and the displacement, x( ⁇ t); and C tot and tot are given by (Rao, 1995):
  • Eqs. 17 and 18 can be used to calculate k and C for a given test sample.
  • the vibration model has established a method for determining k and C from the cantilever's mechanical response.
  • G' and G" for viscoelastic materials, their relationship to k and C must still be resolved. This result may be acheived by separately analyzing the elastic and viscous properties of the viscoelastic test sample, then using the principle of superposition to find the total response of the viscoelastic material.
  • the relationships are given in Eqs. (19) and (20) below:
  • An apparatus of the present invention was constructed and utilized to test the viscoelastic properties of samples as described below.
  • the samples to be tested were placed in a 35 mm petri dish secured within the inset of the bottom plate of the adjustable mounting platform (AMP).
  • AMP adjustable mounting platform
  • the cantilever With a free length of 54 mm and total thickness of approximately 200 nm, the cantilever comprised two piezoelectric polyvinylidenefluoride (PVDF) elements bonded to a 33 ⁇ m thick copper foil sheet.
  • PVDF piezoelectric polyvinylidenefluoride
  • the g-constants relate an applied stress to the resulting voltage, and are 20 to 40 times higher for PVDF than for most piezoceramics (Halvorsen, 1994). Consequently, PVDF generates a much higher voltage for the same stress input.
  • PVDF's piezoelectric constants are also highly temperature dependent, tight control of the cantilever's temperature is essential during calibration and testing (Sessler, 1981).
  • Each PVDF element is 16 mm wide and is made from 28 ⁇ m thick PVDF. Silver ink electrodes are screen-printed on each side, along with a thin insulating coating to bring the total thickness per element to 40 ⁇ m.
  • the PVDF elements are bonded to the copper backbone using Opticon 224 Fracture Sealer.
  • Adherence of the PALR's cantilever to the test sample is achieved using a 4 mm x 2 mm x 1 mm glass probe epoxied to the end of with a contact area, A . of 2 mm 2 .
  • he AMP is made of 6061 20 aluminum, is 9 inches wide by 6 inches deep and uses adjustable kinematic mounts to keep the sample level during testing.
  • the incubator containing the rheometer was set to 37 ⁇ and allowed to equilibrate for a minimum of 12 hours. It is important to note, however, that the air temperature in the vicinity of the test sample was also influenced by the room conditions. Measurements revealed that the room temperature ranged from 25°C to 28°C.
  • Each PALR test consisted of a frequency sweep from 0.1 to 10 Hz using a 10V input voltage.
  • Determination of the sample height for each test was executed in the following manner. An empty 35 mm tissue culture dish was first placed in the PALR, and the cantilever tip was then lowered until it just touched the dish. The corresponding micrometer position was then recorded, the cantilever was raised, and the petti dish was removed. Next the test sample was placed in the petti dish, allowed to gel (if applicable), and the petti dish was then placed back in the PALR. The cantilever was then lowered to the sample surface. The corresponding micrometer reading was then recorded and the difference between this reading and the previous reading is the height of sample, d.
  • Example 1 Three independent samples of glycerol were tested and the results averaged.
  • Each 0.75 ml sample of glycerol was added to a 35 mm tissue culture dish at room temperature, then placed in the rheometer's incubator for 10 minutes to equilibrate.
  • the PALR results match the order of magnitude of the comparative results, yet its measured G' values are consistently lower than those measured by Snyder, while its G" values are higher (10).
  • the influence of hydration on the material properties of biological materials has been established in the literature (11), and dehydration is one method used to stiffen ECMs.
  • the parallel plate configuration used by Snyder permitted the circumference of the ECM test sample to be hydrated with liquid media.
  • the hydrating layer was added after a) the top plate was lowered onto the sample and b) the ECM solution had completely gelled- such that hydration of the bulk of the sample was diffusion limited.
  • PALR performs local measurements on a well hydrated test surface, while Snyder' s values are inherently averaged over a large volume that is inhomogenously hydrated.
  • Type I Collagen Results To further verify the PALR's ability to measure the properties of hydrated ECMs, tests were also performed on 2.3 mg/ml type I collagen gels. For each sample, the average of three tests was used to calculate G' and G" at each frequency. Figure 5 shows the measurement results, as compared to results obtained by Knapp and associates (12) for collagen type I at 2.0 mg/ml concenttation.
  • Figs. 4 and 5 demonstrate the viscoelastic properties of two ECMs in the presence of a liquid hydrating layer at the test surface, and illustrate that the magnitude of the local elastic 24 shear moduli (determined via PALR) are appreciably lower than the elastic shear moduli values averaged over the bulk volume.

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  • Acoustics & Sound (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
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  • Apparatus Associated With Microorganisms And Enzymes (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

La présente invention concerne un appareil et des procédés permettant de déterminer les propriétés viscoélastiques (rhéologiques) des matériaux. Cet appareil et ces procédés sont particulièrement avantageux dans la détermination des propriétés viscoélastiques des matrices extracellulaires (ECM) qui sont de plus en plus importantes dans la modélisation prédictive des systèmes biologiques. Dans un premier aspect de l'invention, un rhéomètre linéaire à commande piézo-électrique (PALR) est conçu pour résoudre les problèmes actuels des méthodes rhéométriques qui surviennent pendant la mesure des propriétés viscoélastiques de la surface et du volume de matériaux hydratés. Ce nouvel appareil comprend une console qui applique une charge oscillante sur le matériau viscoélastique pour détecter sa déflexion. Cette console utilise une couche parmi la pluralité de couches qu'elle comprend comme actionneur et une autre couche comme piézopolymère pour mesurer le mouvement latéral d'une sonde fixe. La nature viscoélastique du matériau testé ajoute de l'amortissement au système, ce qui a pour effet d'atténuer et de déphaser la tension de sortie du capteur. A partir de ces paramètres, on peut quantifier les propriétés physiques d'un matériau, notamment le module de conservation de cisaillement et le module de perte.
PCT/US2001/021659 2000-07-10 2001-07-10 Appareil et procedes de determination des proprietes viscoelastiques des materiaux WO2002004938A2 (fr)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2568963C1 (ru) * 2014-06-30 2015-11-20 Виктор Андреевич Ломовской Измерительный преобразователь

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2336679A1 (fr) * 1975-12-22 1977-07-22 Forestier Francois Procede et dispositif pour l'examen de changements de phase dans un echantillon d'une suspension colloidale ou d'un gel
EP0578539A1 (fr) * 1992-07-03 1994-01-12 Bongrain S.A. Dispositif et procédé de caractérisation ou de mesure par ultrasons de texture de produits
US5659129A (en) * 1992-07-22 1997-08-19 Vserossiisky Nauchno-Issledovatelsky Institut Prirodnykh Gazoy I Gazovykh Device for excitation of oscillations and determination of properties of various fluid media
WO1997037217A2 (fr) * 1996-03-29 1997-10-09 Abbott Laboratories Procede et appareil d'analyse de produits fluides

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2336679A1 (fr) * 1975-12-22 1977-07-22 Forestier Francois Procede et dispositif pour l'examen de changements de phase dans un echantillon d'une suspension colloidale ou d'un gel
EP0578539A1 (fr) * 1992-07-03 1994-01-12 Bongrain S.A. Dispositif et procédé de caractérisation ou de mesure par ultrasons de texture de produits
US5659129A (en) * 1992-07-22 1997-08-19 Vserossiisky Nauchno-Issledovatelsky Institut Prirodnykh Gazoy I Gazovykh Device for excitation of oscillations and determination of properties of various fluid media
WO1997037217A2 (fr) * 1996-03-29 1997-10-09 Abbott Laboratories Procede et appareil d'analyse de produits fluides

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2568963C1 (ru) * 2014-06-30 2015-11-20 Виктор Андреевич Ломовской Измерительный преобразователь

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