WO2005024367A2 - A method and system for calibrating resonating pressure sensors and calibratable resonating pressure sensors - Google Patents

A method and system for calibrating resonating pressure sensors and calibratable resonating pressure sensors Download PDF

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Publication number
WO2005024367A2
WO2005024367A2 PCT/IL2004/000807 IL2004000807W WO2005024367A2 WO 2005024367 A2 WO2005024367 A2 WO 2005024367A2 IL 2004000807 W IL2004000807 W IL 2004000807W WO 2005024367 A2 WO2005024367 A2 WO 2005024367A2
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WO
WIPO (PCT)
Prior art keywords
sensor
pressure
resonance frequency
point
flipping
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PCT/IL2004/000807
Other languages
French (fr)
Other versions
WO2005024367A3 (en
Inventor
Alexander Melamud
Stanislav Lokchine
Doron Girmonski
Shay Kaplan
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Microsense Cardiovascular Systems 1996
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Application filed by Microsense Cardiovascular Systems 1996 filed Critical Microsense Cardiovascular Systems 1996
Publication of WO2005024367A2 publication Critical patent/WO2005024367A2/en
Publication of WO2005024367A3 publication Critical patent/WO2005024367A3/en

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Classifications

    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B8/00—Diagnosis using ultrasonic, sonic or infrasonic waves
    • A61B8/04—Measuring blood pressure
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/02—Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
    • A61B5/021—Measuring pressure in heart or blood vessels
    • A61B5/0215—Measuring pressure in heart or blood vessels by means inserted into the body
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L27/00—Testing or calibrating of apparatus for measuring fluid pressure
    • G01L27/002—Calibrating, i.e. establishing true relation between transducer output value and value to be measured, zeroing, linearising or span error determination
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L9/00—Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means
    • G01L9/0001—Transmitting or indicating the displacement of elastically deformable gauges by electric, electro-mechanical, magnetic or electro-magnetic means
    • G01L9/0008—Transmitting or indicating the displacement of elastically deformable gauges by electric, electro-mechanical, magnetic or electro-magnetic means using vibrations
    • G01L9/0016—Transmitting or indicating the displacement of elastically deformable gauges by electric, electro-mechanical, magnetic or electro-magnetic means using vibrations of a diaphragm
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B2560/00—Constructional details of operational features of apparatus; Accessories for medical measuring apparatus
    • A61B2560/02—Operational features
    • A61B2560/0223—Operational features of calibration, e.g. protocols for calibrating sensors
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B2562/00—Details of sensors; Constructional details of sensor housings or probes; Accessories for sensors
    • A61B2562/02—Details of sensors specially adapted for in-vivo measurements

Definitions

  • the present invention relates to resonating sensors in general and to a method for calibrating resonating pressure sensors in particular.
  • U.S. Patent 5,619,997 to Kaplan discloses a passive sensor system using ultrasonic energy.
  • An ultrasonic activation and detection system ultrasonically activates passive sensors having vibratable parts (such as vibratable beams or vibratable membranes) which sensor(s) may be implanted in a body or disposed in other environments, by directing a beam of ultrasound at the passive sensor or sensors.
  • the passive sensors thus absorb ultrasonic energy from the exciting ultrasonic beam mostly at the frequency of vibration (resonance frequency) of the sensor.
  • the frequency (or frequency range) at which the passive sensor absorbs energy may be detected by a suitable detector and used to determine the value of the physical parameter.
  • the physical parameters measurable with such passive ultrasonic sensors may include, but are not limited to, temperature, pressure, the concentration of a chemical species in the fluid in which the sensor is immersed, and the thickness of a layer of substance deposited on the vibratable part of the sensor (for example, the thickness of plaque material deposited on the surface of a sensor intraluminally implanted within an artery). If the exciting ultrasonic beam is pulsed, the ultrasonic sensor may continue to vibrate after a pulse terminates. The ultrasonic radiation emitted by the activated passive sensor after turning the exciting ultrasonic beam off may be detected and used to determine the value of the physical parameter of interest.
  • Patent 6,331,163 to Kaplan discloses implantable passive sensors having a protective coating. Such sensors may be used, inter alia, for measuring intraluminal blood pressure by intraluminal implantation of the sensor(s).
  • Methods for measuring the resonance frequency of passive ultrasonic sensor are known in the art.
  • a beam of exciting ultrasound may be directed toward the sensor, the resonance frequency of the sensor may be determined from the ultrasonic signal returning from the sensor (or, alternatively, by determining the amount of energy absorbed by the sensor from the exciting beam).
  • the interrogating ultrasonic beam may be continuous, pulsed or chirped. Such methods are disclosed, inter alia, in U.S.
  • Another method for determining the resonance frequency of passive ultrasonic sensors by using the Doppler effect is disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled “METHODS AND DEVICES FOR DETERMIMNG THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS” filed on April 21, 2004, incorporated herein by reference in its entirety for all purposes.
  • This method allows the determination of the resonance frequency of one or more resonating sensors by using an interrogating ultrasound beam directed at the sensor(s) and containing a carrier frequency and a plurality of selected lower excitation frequencies.
  • the vibratable part of the sensor(s) vibrates at the lower excitation frequencies and modulates the higher carrier frequency by Doppler shifting the carrier frequency.
  • Frequency domain analysis of the modulated carrier frequency enables the determination of the modulated signal amplitude at each one of the selected low excitation frequencies, wherein the highest amplitude of the modulated signal is at the excitation frequency closest to the resonance frequency of the sensor.
  • a common problem when resonating sensors such as, but not limited to, the sensors described above are implanted within a living body is the deposition of tissue or other materials of biological origin on the sensor or on parts thereof.
  • various substances or living cells may attach to the surface of the resonating sensor or to various parts thereof and adjacent tissues may cause the deposition of a layer or film of material and/or cells, and/or tissues on the sensor's surface.
  • the deposition of tissues or other biological materials on the vibratable part of the sensor such as (but not limited to) the vibratable membrane of a passive (or active) resonating sensor may cause changes in the vibratable membrane (or the other vibratable part) resonance characteristics such as, inter alia, the resonance frequency, sensitivity to stress, and vibration amplitude of the vibratable membrane.
  • Such changes may affect the sensor's performance by affecting, inter alia the dependence of the resonance frequency of the sensor's resonating part on the physical parameter being measured.
  • the deposition of extraneous materials or tissues on the vibratable part of the sensor may change the dependence of the resonance frequency on the external pressure.
  • a resonating sensor is disposed within a fluid or gas or other medium or measurement environment which contains various substances (such as, for example, within a chemical reaction mixture in a reactor or in a measurement environment containing sprays or aerosols or the like)
  • deposition of liquid or solid material or particles on the vibratable part of the resonating sensor may similarly affect the resonance characteristics of the vibratable part of the sensor with similar effects on the sensor's performance.
  • a resonating sensor may be calibrated before placement or implantation of the sensor in the measurement environment, the sensor's characteristics may continuously change after placement or implantation. Since in most measurement situations it is not usually possible to directly determine the amount of material or tissue deposited on the vibratable part of the resonating sensor, the accuracy of measurement may change over time, causing an unknown measurement error.
  • a calibratable pressure sensor group having a working pressure range.
  • the sensor group includes a first resonating pressure sensor having a single known resonance frequency extremum point within the working pressure range and at least a second resonating pressure sensor having a single known resonance frequency extremum point within the working pressure range.
  • the resonance frequency extremum point of the first sensor and the resonance frequency extremum point of the second sensor occur at different pressure values within the working pressure range.
  • the at least a second sensor of the calibratable pressure sensor group is disposed adjacent to the first sensor.
  • the at least second sensor of the calibratable pressure sensor group is disposed sufficiently close to the first sensor to ensure that the first sensor and the at least a second sensor are exposed to substantially the same pressure and temperature when disposed in a pressure measurement environment.
  • the first sensor and the at least a second sensor are passive resonating ultrasonic pressure sensors.
  • the first sensor and the at least a second sensor each include at least one sealed chamber having a pressure level therewithin and at least one vibratable member forming part of the sealed chamber, and the pressure level within the at least one sealed chamber of the first sensor is different than the pressure level within the at least one sealed chamber of the at least second sensor.
  • the first sensor and the at least second sensor are formed within a common substrate.
  • at least one sealed chamber of the first sensor and the at least one sealed chamber of the at least second sensor are formed within a common substrate.
  • the first sensor and the at least a second sensor are formed as parts of a sensor assembly.
  • the sensor assembly includes a sensor supporting member attached to the first sensor and to the at least second sensor.
  • the sensor supporting member is part of a sensor anchoring device.
  • the first sensor and the at least second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure and the calibration curve is approximated by a parabola equation within the pressure working range.
  • the first sensor and the at least second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure and the calibration curve is approximated by a polynomial equation having a single extremum point within the pressure working range.
  • at least one sensor of said group is a composite pressure sensor comprising a plurality of sealed chambers having one or more vibratable members forming part of the sealed chambers.
  • the sensor group includes a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range.
  • the group also includes at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value of said second pressure sensor within said working pressure range.
  • the flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor
  • the system includes: means for obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor, and means for computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor.
  • the system also includes user interface means for enabling communication between a user and the system.
  • a system for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein includes a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range and at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value within the working pressure range.
  • the flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor.
  • the system includes a measurement unit configured for determining the resonance frequency of at least the first sensor and the second sensor to obtain a data set including: the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor.
  • the system also includes at least one processing unit operatively connected to the measurement unit for computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor.
  • the system also includes one or more user interface units operatively connected to at least one of the measurement unit and the at least one processing unit.
  • a method for calibrating resonating pressure sensors includes the step of disposing within a measurement environment having a varying pressure therein a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range, the flipping point pressure value of the first sensor is different than the flipping point pressure value of said second sensor.
  • the method also includes the step of obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor.
  • the method also includes the step of computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor.
  • a method for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein includes a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range.
  • the flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor.
  • the method includes the step of obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor.
  • the method also includes the step of computing from the data set calibration curve parameters for at least one sensor of the first sensor and the at least second sensor.
  • the varying pressure is a periodically varying pressure.
  • the step of obtaining includes the steps of: obtaining for each sensor of the first sensor and the second sensor data representing the sensor's resonance frequency as a function of time, dete ⁇ nining from the data the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, and the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, and determining from the data the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of said first sensor.
  • / is the resonance frequency of said at least one sensor
  • aj are polynomial coefficients
  • p is the external pressure in the measurement environment
  • N is an integer number.
  • some of the polynomial coefficients & ⁇ are equal to zero.
  • the pressure within the measurement environment is a periodically varying pressure having pressure cycles.
  • the data includes data obtained from a plurality of the pressure cycles, and the extremum resonance frequency at the first flipping point pressure value of the first sensor, the extremum resonance frequency at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the first flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the second flipping point pressure value of said first sensor are mean values computed from one or more measurements performed over the plurality of pressure cycles.
  • Figs. 1A-1C are schematic cross-sectional views illustrating a prior art passive ultrasonic pressure sensor at three different external pressure values
  • Fig. 2 is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar to the sensor of Figs. 1 A-1C on the external pressure acting on the sensor
  • Fig. 1A-1C are schematic cross-sectional views illustrating a prior art passive ultrasonic pressure sensor at three different external pressure values
  • Fig. 2 is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar to the sensor of Figs. 1 A-1C on the external pressure acting on the sensor
  • Fig. 1A-1C are schematic cross-sectional views illustrating a prior art passive ultrasonic pressure sensor at three different external pressure values
  • Fig. 2 is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar to the
  • FIG. 3 is a graph schematically illustrating the dependence of the resonance frequency of a vibratable membrane of two exemplary resonating pressure sensors included in a calibratable sensor pair, in accordance with an embodiment of the present invention
  • Fig. 4 is a schematic graph illustrating an example of a periodically varying pressure that may need to be determined within a measurement environment
  • Fig. 5 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor, having a resonance frequency versus pressure curve described by the curve 60 of Fig. 3, to the pressure represented by the curve 80 of Fig. 4;
  • FIG. 6 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor, having a resonance frequency versus pressure curve described by the curve 70 of Fig. 3, to the pressure represented by the curve 80 of Fig. 4;-
  • Fig. 7 is a schematic flow chart illustrating steps of a method for performing the calibration of the sensors of a calibratable pair of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention;
  • Fig. 8 is a schematic cross-sectional view illustrating two resonating passive pressure sensors disposed in a measurement environment and usable together as a calibratable sensor pair, in accordance with an embodiment of the present invention; Fig.
  • FIG. 9 is a schematic cross-sectional view illustrating a calibratable sensor assembly including two resonating passive pressure sensors attached to a sensor anchoring member which may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention
  • Fig. 10 is a schematic cross-sectional view illustrating a calibratable sensor assembly including two or more resonating passive pressure sensors formed within the same substrate that may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention
  • Fig. 11 is a schematic flow chart illustrating steps of a general method for performing the calibration of the sensors of a calibratable group of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention
  • Fig. 12 is a schematic block diagram illustrating a system for performing the calibration of sensors of a group of sensors including calibratable resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention.
  • the present invention discloses methods for calibrating resonating pressure sensors disposed in a measurement environment, and/or implantable resonating pressure sensors disposed in any other measurement medium or measurement environment in a body having dynamically changing pressure levels.
  • the sensor calibration methods, calibrated sensors, and pressure measurement methods described herein may be useful, inter alia, in overcoming the problems associated with changes in the sensor's pressure response characteristics due to deposition or attachment of extraneous materials, or cells, or tissues, or the like on the sensor's resonating part or parts.
  • the method may be applied for performing sensor calibration and for measuring blood pressure within any part of a heart, including but not limited to a cardiac atrium, a cardiac ventricle, the aorta or any other lumen or cavity of the heart or of any blood vessels associated with the heart, or in pulmonary blood vessels, or the like.
  • a cardiac atrium a cardiac ventricle
  • the aorta any other lumen or cavity of the heart or of any blood vessels associated with the heart, or in pulmonary blood vessels, or the like.
  • the methods described herein are not limited to the measurement of blood pressure in a blood vessel and may be applied to calibrating resonating pressure sensors disposed in any measurement environment known in the art having a suitable dynamically changing pressure therewithin as is disclosed in detail hereinafter.
  • Exemplary sensors that may be employed using the methods and devices of the present invention may include implantable resonating pressure sensors for medical, veterinary, and other applications, and non-implanted sensors for medical, veterinary, or various other industrial sensing applications.
  • Figs. 1A-1C are schematic cross-sectional views of a prior art passive ultrasonic pressure sensor at three different external pressure values.
  • the passive ultrasonic sensor 10 has a housing 12.
  • a thin vibratable membrane 12A is sealingly attached to, or may form an integral part of the housing 12.
  • the housing 12 and the vibratable membrane 12A form a sealed chamber 14.
  • the sealed chamber 14 has a gas or a mixture of gases therein.
  • the internal pressure inside the sealed chamber is Pi .
  • the internal pressure Pi may be set at a desired value at the time of manufacturing of the sensor 10 by sealing the housing 12 in the presence of a gas or a mixture of gasses having the desired pressure value.
  • the external pressure of the medium outside the sensor 10 is P E .
  • the vibratable membrane 12A may be made to vibrate by directing a beam of ultrasound (not shown) onto the sensor 10.
  • Such a beam of ultrasound may excite the vibratable membrane 12A and may cause the membrane 12A to vibrate.
  • the membrane 12A When the membrane 12A is vibrating it may radiate or emit an ultrasonic signal at its vibration frequency (or at its vibration frequencies if it vibrates at more than one vibration mode).
  • the vibratable membrane 12A may keep emitting a continuous ultrasonic signal as long as it is excited by the incident ultrasonic beam directed onto the sensor 10. If the exciting ultrasonic beam is shut off, the membrane 12A may keep vibrating for some time after the exciting beam is switched off and may emit an ultrasonic signal having an amplitude that decays in time.
  • Such continuous or decaying ultrasonic signals emitted by the passive sensor 10 may be detected and further processed to determine the external pressure P E .
  • the resonance frequency of membrane 12A may depend, inter alia, on the shape, mass, thickness and stress of the membrane 12 A.
  • the frequency of the exciting ultrasonic beam is at the resonance frequency of the membrane 12 A, the amplitude of the vibration of the membrane 12A is maximal and the amplitude of the ultrasonic signal emitted by the resonating membrane 12A is maximal.
  • the frequency of the exciting ultrasonic beam is different than the resonance frequency of the membrane 12A (by being either higher or lower than the resonance frequency of the membrane 12 A), the amplitude of the vibrations of the membrane 12A is reduced and the intensity of the ultrasonic signal emitted by the vibrating membrane 12A is reduced.
  • IB schematically illustrates the sensor 10 when the internal pressure within the chamber 14 is larger than the external pressure outside the sensor 10 (Pi > P E ). Under such conditions the membrane 12A is pushed outward and may assume a convex shape.
  • the double headed arrow labeled X(t) represents the displacement of the center of the membrane 12 A from a plane representing the position of the membrane 12 A under conditions in which Pi is equal to P E (see Fig. 1A).
  • the dashed line 13 schematically represents the position of the membrane 12A under the conditions in which Pi is equal to P E .
  • IC schematically illustrates the sensor 10 when the internal pressure within the chamber 14 is smaller than the external pressure outside the sensor 10 (Pi ⁇ PE ). Under such conditions the membrane 12A is pushed inward and may assume a concave shape.
  • the double headed arrow labeled X(t) represents the displacement of the center of the membrane 12A from a plane representing the position of the membrane 12A under conditions in which Pi is equal to P E (see Fig. 1A).
  • the dashed line 13 schematically represents the position of the membrane 12A under the conditions in which Pi is equal to P E ⁇ It is noted that in Fig.
  • X(t) assumes (arbitrarily) a negative value indicating that the displacement is in a direction opposite to the direction of the displacement of the membrane shown in Fig. IB.
  • the flipping point P f of the sensor is an extremum point of the curve.
  • the configuration and construction of resonating sensors is known in the art, is not the subject matter of the present invention, and is therefore nor described in detail hereinafter.
  • many different types of resonating sensors may be used in implementing the methods and systems of the present invention.
  • Patents 5,619,997, 5,989,190, 6,083,165, and 6,331,163, may be used to implement the methods and systems of the present invention, but other suitable types of resonating pressure sensors and having a flipping point known in the art may also be used.
  • resonating pressure sensors of the type schematically illustrated in Figs. 1A- 1C (and for other resonating sensors having a flipping point as disclosed hereinabove), the dependence of the resonance frequency on the external pressure P E is often a function that is approximately symmetrical with respect to the flipping point P f of the sensor.
  • FIG. 2 which is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar (though not necessarily identical) to the sensor of Figs. 1 A-1C on the external pressure acting on the sensor.
  • the curve 40 schematically illustrates the dependence of the resonance frequency of the vibratable membrane of a passive resonating ultrasonic sensor (not shown) on the external pressure acting on the sensor.
  • the horizontal axis represents the external pressure (in arbitrary units), and the vertical axis represents the resonance frequency of the vibratable membrane of the sensor (in KHz).
  • the curve 40 is a general typical schematic representation of the sensor's resonance frequency as a function the external pressure is given by way of example only and does not represent an actual experimental result.
  • the triangular symbol 42 represents the flipping point P f of the sensor (at which point the external pressure PE is equal to the internal pressure Pi).
  • the vibratable membrane of the sensor (such as, for example, the vibratable membrane 12A of Figs. 1A-1C) resonates at approximately 50 KHz.
  • the filled circular symbols 44 and 46 represent two points of the curve 40 at which the vibratable membrane 12A of the sensor has similar resonance frequencies (at about 55 KHz).
  • the external pressure value is P A and at the point 46 the external pressure is P ⁇ .
  • each resonance frequency of the curve 40 may be associated with two different pressure values (the sensor may have two different pressure values at which the vibratable membrane resonates at the same resonance frequency value).
  • the sensor may have a resonance frequency of approximately 61KHZ at the pressure values of Pc and P ⁇ .
  • the flipping point P f represents the pressure point at which the vibratable membrane of the sensor is flat and experiences minimal stress
  • the flipping point pressure value does not change when extraneous matter or tissue or cells become attached to or deposited on the vibratable membrane of the sensor. While such deposition or attachment of extraneous matter or tissue or cells may change the shape of the curve 40 and the value of the resonance frequency at the flipping point pressure of a resonating pressure sensor, the position of the flipping point P f on the pressure axis does not change upon such deposition or attachment because the pressure at which the vibratable membrane 12A is minimally stressed (as disclosed hereinabove with respect to Fig.
  • the coefficients a, b and c are the parameters that need to be determined. If the three parameters a, b and c are unknown, three equations are needed. The number of unknown parameters is equal to the number of needed equations, hi order to solve this problem, a sensor with three known points is needed, or few sensors with the sum of three known points. For example, if the variable f (the resonance frequency) is measured, and for three different measured values of f : fi, f 2 and fj we can determine three different values of p, such that:
  • the calibration curve coefficients a, b and c may be computed.
  • the flipping point 42 may be used as a known pressure point pi of the unknown parameter.
  • a pair of sensors is simultaneously used in the same measurement environment.
  • the flipping points of the two sensors of the sensor pair are at different pressure values and both flipping point pressure values are within the working pressure range for the measurement environment.
  • the two different flipping points may be obtained by using two sensors having different internal pressure values (such as, but not limited to, the sensor 10 of Figs. 1A-1C) and by setting the internal pressure value (Pi) of the first sensor of the sensor pair to be different than the internal pressure value of the second sensor of the sensor pair.
  • the parabola coefficients for the first sensor may be designated ai, bi, and Ci
  • the parabola coefficients for the second sensor may be designated a 2 , b 2 , and c 2 (see equation 1 above). Since the first and the second sensors of the sensor pair are simultaneously subjected to the same pressure within the same measurement environment, each sensor has two points for which the pressure is known and the resonance frequency may be measured.
  • the first point for a sensor is the flipping point of the sensor.
  • the pressure value for the flipping point is known for the first sensor at the time of manufacturing and, for a constant temperature, does not change by deposition of material (as explained in detail hereinabove), and the second point for the first sensor is the point at the pressure value of the flipping point of the second sensor of the sensor pair.
  • the resonance frequency of the first sensor at this second point may also be measured.
  • the third equation that may be used for computing the values of the parabola coefficients is the minimum equation of a parabola for one of the sensors.
  • Fig. 3 is a graph schematically illustrating the dependence of the resonance frequency of a vibratable membrane of two exemplary resonating pressure sensors included in a calibratable sensor pair, in accordance with an embodiment of the present invention.
  • the horizontal axis represents the external pressure (in Torriceli) acting on the two sensors of the calibratable pressure sensor pair and the vertical axis represents the resonance frequency values (in KHz) of the sensors.
  • the curve 60 represents the (unknown) calibration curve for the first sensor (not shown) of the sensor pair.
  • the curve 60 is modeled as a first parabola having its minimum point at the flipping point 62 of the first sensor.
  • the curve 70 represents the (unknown) calibration curve for the second sensor (not shown) of the sensor pair.
  • the curve 70 is modeled as a second parabola having its minimum point at the flipping point 72 of the second sensor.
  • parabolic curves 60 and 70 are schematic curves that do not represent experimental results of actual sensors, but are curves given for demonstrating the principle of the calibration method of the present invention.
  • the point 74 on the curve 70 represents the resonance frequency (85 KHz in the schematic non-limiting example of Fig. 3) of the second sensor at a pressure value equal to the flipping point pressure of the first sensor (at 820 Torriceli in the schematic non- limiting example of Fig. 3).
  • the point 64 on the curve 60 represents the resonance frequency (55 KHz in the schematic non-limiting example of Fig. 3) of the first sensor at a pressure value equal to the flipping point pressure of the second sensor (at 830 Torriceli in the schematic non-limiting example of Fig. 3).
  • the flipping point for any resonating sensor may be determined by measuring the resonance frequency of the sensor at different pressure values (for example, by using the Doppler measurement method described in detail in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al.
  • FIG. 4 is a schematic graph illustrating an example of a periodically varying pressure that may need to be determined within a measurement environment.
  • the horizontal axis of Fig. 4 represents time (in seconds) and the vertical axis of Fig. 4 represents the pressure in the measurement environment (in Torriceli).
  • the curve 80 of Fig. 4 represents the pressure to be measured as a function of time. It is noted that the sinusoidal pressure curve 80 illustrated in Fig. 4 is given by way of example only to demonstrate the methods of the present invention and that the pulsatile pressure in a biological measurement environment (such as, but not limited to, in the lumen of a blood vessel) may exhibit different characteristics.
  • Fig. 5 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor having a resonance frequency versus pressure curve described by the curve 60 of Fig. 3 to the pressure represented by the curve 80 of Fig. 4.
  • the horizontal axis of Fig. 5 represents time (in seconds) and the vertical axis of Fig. 5 represents the resonance frequency of the sensor (in KHz).
  • FIG. 6 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor having a resonance frequency versus pressure curve described by the curve 70 of Fig. 3 to the pressure represented by the curve 80 of Fig. 4.
  • the horizontal axis of Fig. 6 represents time (in seconds) and the vertical axis of Fig. 6 represents the resonance frequency of the sensor (in KHz).
  • a resonating sensor such as, but not limited to, the sensor 10 of Figs. 1A-1C
  • the pulsatile pressure represented by the curve 80 of Fig.
  • the resonance frequency of the sensor varies with time as illustrated by the curve 90 of Fig. 5.
  • the flipping point of the sensor is at a pressure value of 820 Torriceli. Therefore, the resonance frequency curve 90 has minimum points at the times when the pressure is 820 Torriceli (for example, the points 92 and 94 represent such minimum points).
  • the resonance frequency of the sensor is about 61.5 KHz (examples of such points are the points 96 and 98 on the curve 90).
  • the resonance frequency of the sensor is about 81.5 KHz (examples of such points are the points 100 and 102 on the curve 90).
  • a second resonating sensor such as, but not limited to, the sensor 10 of Figs. 1A-1C
  • the resonance frequency of the sensor is measured as a function of time
  • the resonance frequency of the sensor varies with time as illustrated by the curve 104 of Fig. 6.
  • the flipping point of the second sensor is at a pressure value of 830 Torriceli.
  • the resonance frequency curve 104 has minimum points at the times when the pressure is 830 Torriceli (for example, the points 106 and 108 represent such minimum points).
  • the resonance frequency of the second sensor is about 81.5 KHz (examples of such points are the points 110 and 112 on the curve 104).
  • the resonance frequency of the sensor is about 142 KHz (examples of such points are the points 114 and 116 on the curve 104).
  • a sensor pair including two resonating sensors having different flipping point pressure values of the calibratable is disposed or implanted at a region in the measurement environment (step 120).
  • the sensors may be any two resonating pressure sensors known in the art and/or described hereinabove provided that the mathematical function used for modeling the resonance frequency of the sensor as a function of the pressure (the calibration curve) of each of the sensors has a single extremum point within the working pressure range of the sensors.
  • the pressure in the measurement environment may vary periodically within the time period in which the calibration procedure is performed such that the resonance frequency of each of the sensors may be measured (at least once) at the flipping point pressures of both sensors.
  • the flipping point pressure values of the two resonating pressure sensors needs to be selected such that the two different flipping points pressure values of the two sensors fall within the pulsation pressure range within the blood vessel lumen at the time of performing the calibration procedure (the blood vessel's pulsation pressure range is the range between the maximal and the minimal blood pressure in the lumen within the time period of performing the measurements necessary for the calibration procedure).
  • the pressure need not obligatorily vary periodically as long as the pressure does vary over a pressure value range including the two flipping point pressure values of the two sensors during the measurement period used for obtaining data for calibration purposes.
  • the calibration procedure may be started (at a desired time after placement or implantation of the sensor pair) by obtaining for each sensor data representing the sensor's resonance frequency as a function of time (step 122).
  • the data sampling frequency may depend, inter alia, on the rate of variation of the pressure in the measurement environment.
  • the sampling rate for the sensor's resonance frequency data is, preferably, sufficiently high to enable the determination of the minimum point of each of the resonance frequency curves of both sensors (the sensors' flipping points) with acceptable accuracy.
  • the sampling rate for the sensor's resonance frequency data is, preferably, sufficiently high to enable the determination of the minimum point of each of the resonance frequency curves of both sensors (the sensors' flipping points) with acceptable accuracy.
  • the minimum points of the resonance frequency may be determined by taking the value of the data point with the minimal value (such as, for example, the point 92 of Fig. 5 for the first sensor and the point 106 of Fig. 6 for the second sensor).
  • the minimum points of the resonance frequency may be determined by taking the value of the data point with the minimal value (such as, for example, the point 92 of Fig. 5 for the first sensor and the point 106 of Fig. 6 for the second sensor).
  • the minimum points of the resonance frequency may be determined by taking the value of the data point with the minimal value (such as, for example, the point 92 of Fig. 5 for the first sensor and the point 106 of Fig. 6 for the second sensor).
  • the value of the resonance frequency at the flipping point pressure may be obtained by computing the mean of the resonance frequency values of the points 92 and 94 (or of all the minimum points within the curve 90) of Fig. 5 for the first sensor.
  • a similar averaging procedure may be used for computing the resonance frequency at the flipping point pressure for the second sensor.
  • the value of one or more of the minimum points of the resonance frequency may be computed by using various suitable curve fitting methods to obtain a computed curve fitting the acquired data points and finding the minimum point(s) of the fitted curve.
  • the flipping point pressure and the resonance frequency at the flipping point pressure are found for each sensor (stepl24).
  • the resonance frequency of the sensor at the flipping point pressure value of the other sensor may be obtained from the resonance frequency versus time data of the two sensors or from suitable curves fitted to that data (step 126).
  • the first two data points (f l5 p ⁇ ) and ( f 2 ,p 2 ) are known and the calibration curve parameters for one or more of the sensors of the sensor pair may be computed (step 128).
  • the coefficients of the parabola calibration curve may be computed as follows.
  • the third equation (minimum point equation for the first sensor) is:
  • the third equation (minimum point equation for the first sensor) is:
  • the estimation of the parabola may be done by least square (LS) method.
  • LS least square
  • a, b and c may be estimated as follows.
  • i - is an index representing the sensor's number.
  • Fi - is the frequency vector of the sensor i.
  • f m i n i — is the minimum frequency (which is the flipping point frequency) of sensor i.
  • fi - is the frequency of sensor i when sensor 3-i is at the flipping point pressure.
  • Hi - is the LS model matrix for sensor i.
  • Hi 7 — is the transpose of the LS model matrix H of sensor i. i - is the flipping point pressure of sensor i. a;, bi and Ci - are the LS model parameters which are the parabola's coefficients.
  • step 128 it is possible to compute both sets of parabola coefficients for both sensors of the sensor pair, or only one set of parabola coefficients (for the first sensor only, or for the second sensor only).
  • step 128 it is possible to perform pressure measurements in the measurement environment by measuring the resonance frequency of one or more of the sensors of the sensor pair for which the parabola coefficients are known.
  • the pressure in the measurement environment may be determined from the resonance frequency values of one of the sensors (either the first sensor or the second sensor) by computing the pressure values from the parabola equation, using the parabola calibration curve of the single sensor used for the frequency measurement.
  • the pressure in the measurement environment may be determined by measuring the resonance frequency of both of the sensors of the sensor pair and computing the pressure values from measured resonance frequencies of each of the two sensors using the parabola coefficients computed for each of the sensors.
  • the two pressure values computed from the resonance frequencies of the two sensors may then be averaged and the mean pressure may be taken as the pressure measurement result.
  • the calibration methods of the present invention are not limited to the use of the parabola model.
  • the calibration methods disclosed herein may be adapted for use with other types of calibration curve models.
  • the method may be used, for example, for calibration of calibratable sensors comprising multiple (more than two) pressure sensors by using polynomial calibration models of the general type shown in equation 8 below.
  • f ao+ aip + a 2 p 2 + a 3 p 3 + a 4 p 4 +.... (8) wherein, f - is the sensor's resonance frequency, ao, ai, a , a 3 , a ,....- are the polynomial coefficients (some of the polynomial coefficients may assume the value of zero), and p - is the external pressure in the measurement environment.
  • / is the sensor's resonance frequency
  • aj are the polynomial coefficients (some of the polynomial coefficients may assume the value of zero)
  • p - is the external pressure in the measurement environment
  • N is an integer number.
  • Such polynomial functions of any desired degree may be used for calibration as long as there is a single extremum point (either a minimum point or a maximum point) for each sensor's calibration curve within the working pressure range for which the calibration is performed, and provided a sufficient number of sensors having different definitive flipping points is used simultaneously in the same measurement environment for providing a sufficient number of known flipping pressure points (and the corresponding measured resonance frequencies of the sensors) to solve the equation systems required to compute the polynomial coefficients of the polynomial function used, as is known in the art.
  • the selection of the proper calibration curve model may depend, inter alia, on the resonating pressure sensor's type and construction.
  • Fig. 8 is a schematic cross-sectional view of two resonating passive pressure sensors disposed in a measurement environment and usable together as a calibratable sensor pair, in accordance with an embodiment of the present invention.
  • the calibratable sensor pair 131 includes two separate resonating sensors 130 and 132.
  • the sensor 130 includes a recessed substrate layer 136 having a recess 135 formed therein.
  • a second layer 142 is suitably sealingly attached or glued to the recessed substrate layer 136 to form a sealed cavity 134 containing a gas or mixture of gases at a pressure PI.
  • the part of the second layer 142 that overlies the sealed cavity 134 forms a vibratable membrane 142 A.
  • the sensor 132 includes a recessed substrate layer 140 having a recess 137 formed therein.
  • a second layer 144 is suitably sealingly attached or glued to the recessed substrate layer 140 to form a sealed cavity 138 containing a gas or mixture of gases at a pressure P2.
  • the pressures PI and P2 are different (Pl ⁇ P2).
  • the sensors 130 and 132 may be disposed within the measurement environment.
  • the pressure value in the measurement environment (P E ) acts on the vibratable membranes 142 A and 144A.
  • the details of construction and operation of the individual resonating pressure sensors 130 and 132 are known in the art and disclosed in U.S. Patents 5,989,190 and 6,083,165 to Kaplan and in Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al.
  • the pressure values PI and P2 of the sensors 130 and 132 are selected such that the flipping point pressure of both of the sensors 130 and 132 are different from each other as disclosed hereinabove, and are both within the working pressure range for P E .
  • the individual resonating sensors included in the calibratable pressure sensor assembly may be suitably attached to the same substrate or to an anchor device, as is known in the art and described hereinabove. Reference is now made to Fig.
  • FIG. 9 which is a schematic cross-sectional view of a calibratable sensor assembly including two resonating passive pressure sensors attached to a sensor anchoring member which may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention.
  • the calibratable sensor pair assembly 133 of Fig. 9 includes two separate resonating sensors 130 and 132 constructed and operative as explained for the sensors 130 and 132 of Fig. 8 hereinabove.
  • the resonating sensors 130 and 132 are suitably glued or attached to a sensor anchor member 148.
  • the pressures PI and P2 are different (Pl ⁇ P2).
  • the calibratable sensor pair assembly 133 may be disposed within the measurement environment.
  • the pressure value in the measurement environment (P E ) acts on the vibratable membranes 142A and 144A of the sensors 130 and 132.
  • the pressure values PI and P2 of the sensors 130 and 132, respectively, are selected such that the flipping point pressure of both of the sensors 130 and 132 are different from each other as disclosed hereinabove, and are both within the working pressure range for
  • the resonating sensors included in the calibratable pressure sensor may also be formed or constructed within a common substrate, in a way similar to the compensated sensors disclosed in U.S. Patents 5,989,190 and 6,083,165 to Kaplan, and in Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21 , 2004 cited hereinabove, or in any other way disclosed hereinabove or known in the art of resonating sensors.
  • the calibratable sensor assembly 150 of Fig. 10 includes a recessed substrate layer 152.
  • the recessed substrate layer 152 has two recesses 155 and 157 formed therein.
  • the calibratable sensor assembly 150 also includes a second layer 154 suitably sealingly glued or attached to the recessed substrate layer 152 to form two sealed cavities 160 and 162 therein.
  • the sealed cavities 160 and 162 are filled with a gas or a mixture of gases such that the pressure within the sealed cavity 160 is PI, and the pressure within the sealed cavity 162 is P2.
  • the calibratable sensor assembly 150 may be disposed within the measurement environment.
  • the pressure value in the measurement environment (P E ) acts on the vibratable membranes 154A and 154B.
  • the pressure values PI and P2 within the sealed cavities 160 and 162, respectively, are selected such that the flipping point pressure of both of the sensors vibratable membranes 154A and 154B are different from each other as disclosed hereinabove, and are both within the working pressure range for
  • the calibratable sensor assembly may include a plurality of sealed chambers with vibratable membranes such that a first group of sealed cavities has an internal pressure of PI and a second group of sealed cavities has an internal pressure of P2. It is noted that the calibratable sensor pairs and sensor pair assemblies, such as, for example, the calibratable sensor pairs 131 and 133 of Figs. 8 and 9, respectively, and the calibratable sensor assembly 150 of Fig. 10 are not limited to the use of sensors having a single vibratable member.
  • each of the sensors 130 and 132 of Figs. 8 and 9, or both of the sensors 130 and 132 may be substituted by a multi- membrane sensor having multiple vibratable members or multiple membranes or multiple resonating parts.
  • An example of such multi-membrane sensors is the sensor 20 illustrated in Figs. 2-3 of Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004.
  • other different sensors with multiple membranes or with multiple resonating parts or members may also be used in the calibratable sensor pairs or the calibratable sensor assemblies of the present invention.
  • Fig. 11 is a schematic flow chart illustrating steps of a general method for performing the calibration of the sensors of a calibratable group of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention.
  • Fig. 11 describes a calibration procedure that may be performed for calibrating one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein.
  • the group of sensors may include a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range.
  • the resonance frequency extremum point of the first sensor of the group of sensors and the resonance frequency extremum point of the second sensor occur at different pressure values within the working pressure range.
  • the flipping point pressure values for the different sensors are known before placement of the sensors in the measurement environment and may be determined by suitable measurements of sensor's resonance frequency as a function of external pressure performed in a controlled pressure chamber.
  • Suitable corrections for the change of the flipping point pressure value with change of temperature may be calculated from the gas laws equations, as is known in the art.
  • the method may include performing resonance frequency measurements on the group of sensors which may include a first sensor and at least a second sensor when the sensors are disposed in a measurement environment having a varying pressure therein (Step 200).
  • the method may also include obtaining (from the resonance frequency measurements) a data set comprising the extremum resonance frequency at the first flipping point pressure value of the first sensor, the extremum resonance frequency at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the first flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the second flipping point pressure value of the first sensor (step 202).
  • the method may also include computing from the data set calibration curve parameters for at least one sensor (step 204), as disclosed hereinabove in detail with respect to Figs 3-7.
  • the method may be used to compute calibration curve parameters for the first sensor, or for the second sensor, or for the first and the second sensor. It will be appreciated by those skilled in the art that, while the examples disclosed and illustrated in the drawings include pairs of resonating sensors, it may be possible to use more than two sensors to form calibratable sensor groups which may be calibrated in a way similar to that described hereinabove.
  • Fig. 12 is a schematic block diagram illustrating a system for performing the calibration of sensors of a group of sensors including calibratable resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention.
  • the system 210 may include a measuring unit 212 in communication with one or more processing units 214 and one or more (optional) user interface units 216.
  • the measuring unit 212 may be any type of suitable measuring unit configured for measuring the resonance frequency of resonating sensors (such as but not limited to resonating pressure sensors).
  • the measuring unit 212 may include or may be part of any of the ultrasonic systems for determining the resonance frequency of resonators disclosed in U.S. Patents 5,619,997, 5,989,190 and 6,083,165 to Kaplan or may be any of the various systems (or suitable parts of such systems) using the Doppler effect disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al.
  • the processing unit(s) 214 may be one or more processing devices capable of processing measurement results or data communicated from the measuring unit 212.
  • the processing unit(s) 214 may include but is not limited to, one or more computers, processors, digital data processors, analog data processors, hybrid digital/analog processors, personal computers, mini-computers, multi-processor based computers, workstations, desktop or mobile computing devices, microprocessors, computer based networks, or the like. It is noted that the processing unit(s) 214 may include one or more suitable data storage devices (not shown) and/or one or more memory devices (not shown), and/or suitable other internal or external components and interfaces required for performing data processing or computational tasks.
  • the measuring unit 212 may perform measurements for determining the required resonance frequency values of the sensor pairs or sensor group that are described in detail in the methods disclosed hereinabove.
  • the measurement results may then be communicated to the processing unit(s) 214 for processing.
  • the processing unit(s) 214 may perform the necessary data processing or computations to obtain the parameters of the calibration curves for one or more sensors as disclosed in detail hereinabove.
  • the processing unit(s) 214 may use the computed calibration curve parameters for computing the pressure values from the determined values of the sensor's (or sensors') resonance frequency and may also store the calibration (or recalibration) curve parameters for further use in other future measurements.
  • the system 210 may also include one or more user interface units 216 that may be suitably connected to the processing unit(s) 214 and to the measuring unit 212.
  • the user interface unit(s) may include but are not limited to suitable devices for providing input from a user to the system 210 for operating the system and may also include output devices for providing output to the user of the system 210.
  • the user interface unit(s) 216 may include one or more input or output devices or peripheral equipment including but not limited to, display devices, data storage devices, keyboards, pointing devices (such as, but not limited to, a mouse), light pens, touch sensitive display screens, graphic tablets, printers, or any other suitable input or output device(s) known in the art.
  • the calibration results for one or more of the sensors may be displayed on one or more user interface devices 216, such as but not limited to a suitable display device or computer screen or the like.
  • the displayed calibration results may include but are not limited to numerical calibration data and graphical data (calibration curves) or combinations of graphical and numerical data. It is noted that in accordance with an embodiment of the present invention, the processing unit(s) 214 may also communicate the computed values of the calibration curve parameters (for one or more of the sensors) to the measuring unit 212 (in cases in which the measuring unit 212 has processing capabilities), and the measurement unit 212 may store the calibration parameters and may use them for producing calibrated measurement results. Alternatively, the processing and computation of calibrated measurement results may be performed by the processing unit(s) 214. It will be appreciated that while the system 210 of Fig.
  • the configuration of the system of the present application is not limited to the specific configuration illustrated in Fig. 12.
  • the entire system 212 may be implemented within one of the systems disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al.
  • the system 212 may be implemented as the system 32 illustrated in Fig. 4 of U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. which includes, inter alia, a measurement unit a processing /controlling unit and a user interface.
  • the calibration curve(s) obtained in the calibration procedure may be used to compute the pressure values in the measurement environment for a certain period of time after calibration.
  • it accordance with another possible embodiment of the present invention it is possible to repeat the calibration procedure, each time a pressure measurement is needed.
  • This embodiment may be advantageous, inter alia, in situations in which the rate of deposition of extraneous material or tissues on the sensor is not known in advance, or behaves sporadically, or when the changes in the calibration curve parameters are by themselves of interest.
  • the flipping point pressure of the passive ultrasonic pressure sensors is temperature dependent, the calibration method described hereinabove is performed under isothermal conditions.
  • the sensors of the group should be at the same known temperature. If needed, temperature differences (between the temperature values measured in the measurement environment during and the temperature at which each sensor of the group was calibrated after manufacturing of the sensor) may be corrected or compensated by using the gas law equations as is known in the art by determining the temperature in the measurement environment using any suitable type of temperature measurement known in the art (such as, for example, by using a thermometer or temperature sensor to measure the temperature of a patient in which the calibratable sensor group is implanted or by determining the temperature in any measurement environment in which the calibratable sensor group is disposed by using any other type of temperature sensor or temperature measurement method, as is known in the art). It is noted that while for the simple exemplary sensor type illustrated in Figs. 1A-
  • the flipping point of the sensor 10 may occur when the internal pressure Pi is equal to the external pressure P E and the vibratable membrane 12A is flat (planar) this is not obligatory for practicing the present invention.
  • the sensor may be constructed to have a minimum resonance frequency while the membrane 12A is not planar. Therefore, for the purposes of the present application the term "flipping point pressure value" is used herein to define the pressure value (within the pressure working range of the sensor) at which the resonance frequency of the sensor has an extremum point (a minimum or a maximum point depending, inter alia, on the sensor's type and construction). While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made which are within the scope and spirit of the invention.

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Abstract

A calibratable pressure sensor group having a working pressure range. The sensor group may include a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at another different flipping point pressure value within the working pressure range. Methods for calibrating the sensor groups may include measuring the resonance frequency of the first sensor at the known flipping point pressure values of the first sensor and second sensor, measuring the resonance frequency of the second sensor at the flipping point pressure value of the first sensor, measuring the resonance frequency of the first sensor at the flipping point pressure value of the second sensor and computing calibration curve parameters for one or more of the sensors in the sensor group. For a periodically varying pressure the measurements may be repeated for multiple cycles and averaged values may be used in the computations. Methods and systems are provided for calibrating sensors of the group.

Description

A METHOD AND SYSTEM FOR CALIBRATING RESONATING PRESSURE SENSORS AND CALIBRATABLE RESONATING PRESSURE SENSORS
FIELD OF THE INVENTION The present invention relates to resonating sensors in general and to a method for calibrating resonating pressure sensors in particular.
BACKGROUND OF THE INVENTION Methods, devices and systems, using ultrasonically activated passive sensors usable for sensing and measuring the values of different physical parameters within a human body or in other environments and scientific and industrial applications, have been described. U.S. Patent 5,619,997 to Kaplan, incorporated herein by reference in its entirety for all purposes, discloses a passive sensor system using ultrasonic energy. An ultrasonic activation and detection system ultrasonically activates passive sensors having vibratable parts (such as vibratable beams or vibratable membranes) which sensor(s) may be implanted in a body or disposed in other environments, by directing a beam of ultrasound at the passive sensor or sensors. The activated passive sensor(s), or vibratable parts thereof, vibrate or resonate at a frequency that is a function of the value of the physical variable to be measured. The passive sensors thus absorb ultrasonic energy from the exciting ultrasonic beam mostly at the frequency of vibration (resonance frequency) of the sensor. The frequency (or frequency range) at which the passive sensor absorbs energy may be detected by a suitable detector and used to determine the value of the physical parameter. The physical parameters measurable with such passive ultrasonic sensors may include, but are not limited to, temperature, pressure, the concentration of a chemical species in the fluid in which the sensor is immersed, and the thickness of a layer of substance deposited on the vibratable part of the sensor (for example, the thickness of plaque material deposited on the surface of a sensor intraluminally implanted within an artery). If the exciting ultrasonic beam is pulsed, the ultrasonic sensor may continue to vibrate after a pulse terminates. The ultrasonic radiation emitted by the activated passive sensor after turning the exciting ultrasonic beam off may be detected and used to determine the value of the physical parameter of interest. Since more than one physical variable may influence the vibration frequency of passive sensors, a correction may be needed in order to compensate for the effects of other physical parameters unrelated to the physical parameter which needs to be determined on the measured sensor vibration frequency. For example, if pressure is the physical parameter to be determined, changes in temperature may affect the vibration frequency of the sensor. U.S. Patents 5,989,190 and 6,083,165 to Kaplan, both of which are incorporated herein by reference in their entirety for all purposes, disclose compensated sensor pairs and methods for their use for compensating for the effects of unrelated different physical variables on the determined value of another physical variable which is being determined. For example, such compensated sensor pairs, may be used for compensating for inaccuracies in pressure measurements due to temperature changes. U.S. Patent 6,331,163 to Kaplan, incorporated herein by reference in its entirety for all purposes, discloses implantable passive sensors having a protective coating. Such sensors may be used, inter alia, for measuring intraluminal blood pressure by intraluminal implantation of the sensor(s). Methods for measuring the resonance frequency of passive ultrasonic sensor are known in the art. A beam of exciting ultrasound may be directed toward the sensor, the resonance frequency of the sensor may be determined from the ultrasonic signal returning from the sensor (or, alternatively, by determining the amount of energy absorbed by the sensor from the exciting beam). The interrogating ultrasonic beam may be continuous, pulsed or chirped. Such methods are disclosed, inter alia, in U.S. Patents 5,619,997, 5,989,190 and 6,083,165 to Kaplan. Another method for determining the resonance frequency of passive ultrasonic sensors by using the Doppler effect is disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMIMNG THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004, incorporated herein by reference in its entirety for all purposes. This method allows the determination of the resonance frequency of one or more resonating sensors by using an interrogating ultrasound beam directed at the sensor(s) and containing a carrier frequency and a plurality of selected lower excitation frequencies. The vibratable part of the sensor(s) vibrates at the lower excitation frequencies and modulates the higher carrier frequency by Doppler shifting the carrier frequency. Frequency domain analysis of the modulated carrier frequency enables the determination of the modulated signal amplitude at each one of the selected low excitation frequencies, wherein the highest amplitude of the modulated signal is at the excitation frequency closest to the resonance frequency of the sensor. A common problem when resonating sensors such as, but not limited to, the sensors described above are implanted within a living body is the deposition of tissue or other materials of biological origin on the sensor or on parts thereof. For example, various substances or living cells may attach to the surface of the resonating sensor or to various parts thereof and adjacent tissues may cause the deposition of a layer or film of material and/or cells, and/or tissues on the sensor's surface. The deposition of tissues or other biological materials on the vibratable part of the sensor, such as (but not limited to) the vibratable membrane of a passive (or active) resonating sensor may cause changes in the vibratable membrane (or the other vibratable part) resonance characteristics such as, inter alia, the resonance frequency, sensitivity to stress, and vibration amplitude of the vibratable membrane. Such changes may affect the sensor's performance by affecting, inter alia the dependence of the resonance frequency of the sensor's resonating part on the physical parameter being measured. For example, in resonating pressure sensors, such as but not limited to the passive ultrasonic resonating sensor disclosed hereinabove, the deposition of extraneous materials or tissues on the vibratable part of the sensor may change the dependence of the resonance frequency on the external pressure. Similarly, when a resonating sensor is disposed within a fluid or gas or other medium or measurement environment which contains various substances (such as, for example, within a chemical reaction mixture in a reactor or in a measurement environment containing sprays or aerosols or the like), deposition of liquid or solid material or particles on the vibratable part of the resonating sensor may similarly affect the resonance characteristics of the vibratable part of the sensor with similar effects on the sensor's performance. While a resonating sensor may be calibrated before placement or implantation of the sensor in the measurement environment, the sensor's characteristics may continuously change after placement or implantation. Since in most measurement situations it is not usually possible to directly determine the amount of material or tissue deposited on the vibratable part of the resonating sensor, the accuracy of measurement may change over time, causing an unknown measurement error.
SUMMARY OF THE INVENTION There is therefore provided, in accordance with an embodiment of the present invention, a calibratable pressure sensor group having a working pressure range. The sensor group includes a first resonating pressure sensor having a single known resonance frequency extremum point within the working pressure range and at least a second resonating pressure sensor having a single known resonance frequency extremum point within the working pressure range. The resonance frequency extremum point of the first sensor and the resonance frequency extremum point of the second sensor occur at different pressure values within the working pressure range. Furthermore, in accordance with an embodiment of the present invention, the at least a second sensor of the calibratable pressure sensor group is disposed adjacent to the first sensor. Furthermore, in accordance with an embodiment of the present invention, the at least second sensor of the calibratable pressure sensor group is disposed sufficiently close to the first sensor to ensure that the first sensor and the at least a second sensor are exposed to substantially the same pressure and temperature when disposed in a pressure measurement environment. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least a second sensor are passive resonating ultrasonic pressure sensors. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least a second sensor each include at least one sealed chamber having a pressure level therewithin and at least one vibratable member forming part of the sealed chamber, and the pressure level within the at least one sealed chamber of the first sensor is different than the pressure level within the at least one sealed chamber of the at least second sensor. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least second sensor are formed within a common substrate. Furthermore, in accordance with an embodiment of the present invention, at least one sealed chamber of the first sensor and the at least one sealed chamber of the at least second sensor are formed within a common substrate. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least a second sensor are formed as parts of a sensor assembly. Furthermore, in accordance with an embodiment of the present invention, the sensor assembly includes a sensor supporting member attached to the first sensor and to the at least second sensor. Furthermore, in accordance with an embodiment of the present invention, the sensor supporting member is part of a sensor anchoring device. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure and the calibration curve is approximated by a parabola equation within the pressure working range. Furthermore, in accordance with an embodiment of the present invention, the first sensor and the at least second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure and the calibration curve is approximated by a polynomial equation having a single extremum point within the pressure working range. Furthermore, in accordance with an embodiment of the present invention, at least one sensor of said group is a composite pressure sensor comprising a plurality of sealed chambers having one or more vibratable members forming part of the sealed chambers. There is also provided, in accordance with an embodiment of the present invention, a system for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein. The sensor group includes a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range. The group also includes at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value of said second pressure sensor within said working pressure range. The flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor, The system includes: means for obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor, and means for computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor. Furthermore, in accordance with an embodiment of the present invention, the system also includes user interface means for enabling communication between a user and the system. There is also provided, in accordance with an embodiment of the present invention, a system for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein. The system includes a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range and at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value within the working pressure range. The flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor. The system includes a measurement unit configured for determining the resonance frequency of at least the first sensor and the second sensor to obtain a data set including: the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor. The system also includes at least one processing unit operatively connected to the measurement unit for computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor. Furthermore, in accordance with an embodiment of the present invention, the system also includes one or more user interface units operatively connected to at least one of the measurement unit and the at least one processing unit. There is further provided, in accordance with an embodiment of the present invention, a method for calibrating resonating pressure sensors. The method includes the step of disposing within a measurement environment having a varying pressure therein a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range, the flipping point pressure value of the first sensor is different than the flipping point pressure value of said second sensor. The method also includes the step of obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor. The method also includes the step of computing from the data set calibration curve parameters for at least one sensor of the first sensor and the second sensor. There is further provided, in accordance with an embodiment of the present invention, a method for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein, the group includes a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range. The flipping point pressure value of the first sensor is different than the flipping point pressure value of the second sensor. The method includes the step of obtaining a data set including the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of the first sensor. The method also includes the step of computing from the data set calibration curve parameters for at least one sensor of the first sensor and the at least second sensor. Furthermore, in accordance with an embodiment of the present invention, the varying pressure is a periodically varying pressure. Furthermore, in accordance with an embodiment of the present invention, the step of obtaining includes the steps of: obtaining for each sensor of the first sensor and the second sensor data representing the sensor's resonance frequency as a function of time, deteπnining from the data the extremum resonance frequency of the first sensor at the flipping point pressure value of the first sensor, and the extremum resonance frequency of the second sensor at the flipping point pressure value of the second sensor, and determining from the data the resonance frequency of the first sensor at the flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the flipping point pressure value of said first sensor. Furthermore, in accordance with an embodiment of the present invention, the step of computing includes computing the calibration curve parameters for at least one sensor of the first sensor and the second sensor by using parabola equations representing the calibration curves of the first sensor and the at least second sensor. Furthermore, in accordance with an embodiment of the present invention, the step of computing includes computing the calibration curve parameters for at least one sensor of the first sensor and the at least second sensor by using polynomial equations having a single extremum point within the working pressure range for representing the calibration curves of the first sensor and the at least second sensor. Furthermore, in accordance with an embodiment of the present invention, the polynomial equations include equations of the type: f =
Figure imgf000011_0001
Wherein,
/ is the resonance frequency of said at least one sensor , aj are polynomial coefficients, p is the external pressure in the measurement environment, and N is an integer number. Furthermore, in accordance with an embodiment of the present invention, some of the polynomial coefficients &\ are equal to zero. Finally, in accordance with an embodiment of the present invention, the pressure within the measurement environment is a periodically varying pressure having pressure cycles. The data includes data obtained from a plurality of the pressure cycles, and the extremum resonance frequency at the first flipping point pressure value of the first sensor, the extremum resonance frequency at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the first flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the second flipping point pressure value of said first sensor are mean values computed from one or more measurements performed over the plurality of pressure cycles.
BRIEF DESCRIPTION OF THE DRAWINGS The invention is herein described, by way of example only, with reference to the accompanying drawings, in which like components are designated by like reference numerals, wherein: Figs. 1A-1C are schematic cross-sectional views illustrating a prior art passive ultrasonic pressure sensor at three different external pressure values; Fig. 2 is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar to the sensor of Figs. 1 A-1C on the external pressure acting on the sensor; Fig. 3 is a graph schematically illustrating the dependence of the resonance frequency of a vibratable membrane of two exemplary resonating pressure sensors included in a calibratable sensor pair, in accordance with an embodiment of the present invention; Fig. 4 is a schematic graph illustrating an example of a periodically varying pressure that may need to be determined within a measurement environment; Fig. 5 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor, having a resonance frequency versus pressure curve described by the curve 60 of Fig. 3, to the pressure represented by the curve 80 of Fig. 4; Fig. 6 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor, having a resonance frequency versus pressure curve described by the curve 70 of Fig. 3, to the pressure represented by the curve 80 of Fig. 4;- Fig. 7 is a schematic flow chart illustrating steps of a method for performing the calibration of the sensors of a calibratable pair of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention; Fig. 8 is a schematic cross-sectional view illustrating two resonating passive pressure sensors disposed in a measurement environment and usable together as a calibratable sensor pair, in accordance with an embodiment of the present invention; Fig. 9 is a schematic cross-sectional view illustrating a calibratable sensor assembly including two resonating passive pressure sensors attached to a sensor anchoring member which may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention; Fig. 10 is a schematic cross-sectional view illustrating a calibratable sensor assembly including two or more resonating passive pressure sensors formed within the same substrate that may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention; Fig. 11 is a schematic flow chart illustrating steps of a general method for performing the calibration of the sensors of a calibratable group of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention; and Fig. 12 is a schematic block diagram illustrating a system for performing the calibration of sensors of a group of sensors including calibratable resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
Notation Used Throughout The following notation is used throughout this document.
Term Definition μm micrometer Hz Hertz KHz Kilohertz MHz Megahertz US Ultrasound torr Torriceli (pressure unit) LS Least square
The present invention discloses methods for calibrating resonating pressure sensors disposed in a measurement environment, and/or implantable resonating pressure sensors disposed in any other measurement medium or measurement environment in a body having dynamically changing pressure levels. The sensor calibration methods, calibrated sensors, and pressure measurement methods described herein may be useful, inter alia, in overcoming the problems associated with changes in the sensor's pressure response characteristics due to deposition or attachment of extraneous materials, or cells, or tissues, or the like on the sensor's resonating part or parts. It is noted that while the systems, devices and methods disclosed herein describe using passive ultrasonic sensor(s) having flipping points for measuring pressure within a blood vessel, similar systems methods and devices may also be used for measuring dynamically or periodically changing pressure levels (such as, but not limited to, pulsatile or periodic or reciprocating pressure levels) within other body fluids and/or body cavities or other organs, or within any other measurement system having a dynamically changing pressure (such as, but not limited to, pulsatile or periodic or reciprocating pressure). For example, the method may be applied for performing sensor calibration and for measuring blood pressure within any part of a heart, including but not limited to a cardiac atrium, a cardiac ventricle, the aorta or any other lumen or cavity of the heart or of any blood vessels associated with the heart, or in pulmonary blood vessels, or the like. Thus, it will be appreciated by the person skilled in the art that the methods described herein are not limited to the measurement of blood pressure in a blood vessel and may be applied to calibrating resonating pressure sensors disposed in any measurement environment known in the art having a suitable dynamically changing pressure therewithin as is disclosed in detail hereinafter. Exemplary sensors that may be employed using the methods and devices of the present invention may include implantable resonating pressure sensors for medical, veterinary, and other applications, and non-implanted sensors for medical, veterinary, or various other industrial sensing applications. Reference is now made to Figs. 1A-1C which are schematic cross-sectional views of a prior art passive ultrasonic pressure sensor at three different external pressure values. The passive ultrasonic sensor 10 has a housing 12. A thin vibratable membrane 12A is sealingly attached to, or may form an integral part of the housing 12. The housing 12 and the vibratable membrane 12A form a sealed chamber 14. The sealed chamber 14 has a gas or a mixture of gases therein. The internal pressure inside the sealed chamber is Pi . The internal pressure Pi may be set at a desired value at the time of manufacturing of the sensor 10 by sealing the housing 12 in the presence of a gas or a mixture of gasses having the desired pressure value. The external pressure of the medium outside the sensor 10 is PE . Fig. 1A schematically illustrates a condition in which the pressure within the sealed chamber 14 and the external pressure in the medium outside of the sensor 10 are equal (Pi = PE ) and the vibratable membrane 12A is at minimum stress (it is noted that at minimum stress the membrane 12A may be planar as shown in Fig. 1 A but may also be non-planar). The vibratable membrane 12A may be made to vibrate by directing a beam of ultrasound (not shown) onto the sensor 10. Such a beam of ultrasound may excite the vibratable membrane 12A and may cause the membrane 12A to vibrate. When the membrane 12A is vibrating it may radiate or emit an ultrasonic signal at its vibration frequency (or at its vibration frequencies if it vibrates at more than one vibration mode). The vibratable membrane 12A may keep emitting a continuous ultrasonic signal as long as it is excited by the incident ultrasonic beam directed onto the sensor 10. If the exciting ultrasonic beam is shut off, the membrane 12A may keep vibrating for some time after the exciting beam is switched off and may emit an ultrasonic signal having an amplitude that decays in time. Such continuous or decaying ultrasonic signals emitted by the passive sensor 10 may be detected and further processed to determine the external pressure PE . Typically, the resonance frequency of membrane 12A may depend, inter alia, on the shape, mass, thickness and stress of the membrane 12 A. When the frequency of the exciting ultrasonic beam is at the resonance frequency of the membrane 12 A, the amplitude of the vibration of the membrane 12A is maximal and the amplitude of the ultrasonic signal emitted by the resonating membrane 12A is maximal. If the frequency of the exciting ultrasonic beam is different than the resonance frequency of the membrane 12A (by being either higher or lower than the resonance frequency of the membrane 12 A), the amplitude of the vibrations of the membrane 12A is reduced and the intensity of the ultrasonic signal emitted by the vibrating membrane 12A is reduced. Fig. IB schematically illustrates the sensor 10 when the internal pressure within the chamber 14 is larger than the external pressure outside the sensor 10 (Pi > PE). Under such conditions the membrane 12A is pushed outward and may assume a convex shape. The double headed arrow labeled X(t) represents the displacement of the center of the membrane 12 A from a plane representing the position of the membrane 12 A under conditions in which Pi is equal to PE (see Fig. 1A). The dashed line 13 schematically represents the position of the membrane 12A under the conditions in which Pi is equal to PE . When Pi > PE , the membrane 12A is stressed, and the resonance frequency of the membrane 12A is shifted to a higher frequency than its resonance frequency under non-stressed conditions. Fig. IC schematically illustrates the sensor 10 when the internal pressure within the chamber 14 is smaller than the external pressure outside the sensor 10 (Pi < PE ). Under such conditions the membrane 12A is pushed inward and may assume a concave shape. The double headed arrow labeled X(t) represents the displacement of the center of the membrane 12A from a plane representing the position of the membrane 12A under conditions in which Pi is equal to PE (see Fig. 1A). The dashed line 13 schematically represents the position of the membrane 12A under the conditions in which Pi is equal to PE ■ It is noted that in Fig. IC, X(t) assumes (arbitrarily) a negative value indicating that the displacement is in a direction opposite to the direction of the displacement of the membrane shown in Fig. IB. When Pi < PE , the membrane 12A is stressed, and the resonance frequency of the membrane 12A is shifted to a higher frequency than its resonance frequency under non- stressed conditions. Within a certain pressure range, the resonance frequency of the membrane 12A may be a function of the pressure difference ΔP (where ΔP = Pi - PE ). Since the resonance frequency of the membrane 12A is lowest at the non-stressed state, the pressure point at which Pi = PE is called the "flipping point" (Pf) of the sensor. In a curve representing the dependence of the resonance frequency of the membrane 12A on the external pressure PE, the flipping point Pf of the sensor is an extremum point of the curve. It is noted that the configuration and construction of resonating sensors, is known in the art, is not the subject matter of the present invention, and is therefore nor described in detail hereinafter. Generally, many different types of resonating sensors may be used in implementing the methods and systems of the present invention. For example, some of the passive ultrasonic pressure sensors disclosed in U.S. Patents 5,619,997, 5,989,190, 6,083,165, and 6,331,163, may be used to implement the methods and systems of the present invention, but other suitable types of resonating pressure sensors and having a flipping point known in the art may also be used. For resonating pressure sensors of the type schematically illustrated in Figs. 1A- 1C (and for other resonating sensors having a flipping point as disclosed hereinabove), the dependence of the resonance frequency on the external pressure PE is often a function that is approximately symmetrical with respect to the flipping point Pf of the sensor. Reference is now made to Fig. 2 which is a schematic graph illustrating the dependence of the resonance frequency of a vibratable membrane of an exemplary passive ultrasonic pressure sensor similar (though not necessarily identical) to the sensor of Figs. 1 A-1C on the external pressure acting on the sensor. In the graph of Fig. 2, the curve 40 schematically illustrates the dependence of the resonance frequency of the vibratable membrane of a passive resonating ultrasonic sensor (not shown) on the external pressure acting on the sensor. The horizontal axis represents the external pressure (in arbitrary units), and the vertical axis represents the resonance frequency of the vibratable membrane of the sensor (in KHz). It is noted that the curve 40 is a general typical schematic representation of the sensor's resonance frequency as a function the external pressure is given by way of example only and does not represent an actual experimental result. The triangular symbol 42 represents the flipping point Pf of the sensor (at which point the external pressure PE is equal to the internal pressure Pi). At this point, the vibratable membrane of the sensor (such as, for example, the vibratable membrane 12A of Figs. 1A-1C) resonates at approximately 50 KHz. The filled circular symbols 44 and 46 represent two points of the curve 40 at which the vibratable membrane 12A of the sensor has similar resonance frequencies (at about 55 KHz). At the point 44 the external pressure value is PA and at the point 46 the external pressure is Pβ. Similarly, the filled circular symbols 48 and 50 represent two points of the curve 40 at which the vibratable membrane of the sensor has similar resonance frequencies (at about 61 KHz). At the point 48 the external pressure value is Pc and at the point 50 the external pressure is Pp. Thus, each resonance frequency of the curve 40 may be associated with two different pressure values (the sensor may have two different pressure values at which the vibratable membrane resonates at the same resonance frequency value). For example, for a sensor having a resonance frequency curve described by the exemplary curve 40 of Fig. 2, the sensor may have a resonance frequency of approximately 61KHZ at the pressure values of Pc and Pβ. It is noted that since the flipping point Pf represents the pressure point at which the vibratable membrane of the sensor is flat and experiences minimal stress, the flipping point pressure value does not change when extraneous matter or tissue or cells become attached to or deposited on the vibratable membrane of the sensor. While such deposition or attachment of extraneous matter or tissue or cells may change the shape of the curve 40 and the value of the resonance frequency at the flipping point pressure of a resonating pressure sensor, the position of the flipping point Pf on the pressure axis does not change upon such deposition or attachment because the pressure at which the vibratable membrane 12A is minimally stressed (as disclosed hereinabove with respect to Fig. 1A) does not change by the deposition or attachment of such extraneous material or tissue or cells to the vibratable membrane 12 A. When using the pressure sensor in a measurement, a mathematical model describing the relation between the resonance frequency (the measured parameter) and the pressure (the unknown parameter) is needed. It was experimentally found that for many resonating pressure sensors of the general type illustrated in Figs. 1A-1C (pressure sensors having a sealed chamber and a vibratable membrane forming part of the wall of the sealed chamber) the curve describing the dependence of the resonance frequency on the external pressure may be reasonably well modeled by a parabola. It is noted that while a parabolic model was experimentally found to be practically sufficiently accurate for use with passive ultrasonic resonating sensors of the type schematically illustrated in Figs. 1A-1C and with other sensors having multiple resonating membranes overlying multiple sealed cavities, other types of different calibration curve models may also be used with such sensors or with other types of resonating pressure sensors having a flipping point, as is discussed in more detail hereinafter. If the known variable is f (which is the resonance frequency of the sensor), and the unknown variable is p (pressure), a model using the parabola equation is: f = ap2 +bp + c (1)
For this model the coefficients a, b and c, are the parameters that need to be determined. If the three parameters a, b and c are unknown, three equations are needed. The number of unknown parameters is equal to the number of needed equations, hi order to solve this problem, a sensor with three known points is needed, or few sensors with the sum of three known points. For example, if the variable f (the resonance frequency) is measured, and for three different measured values of f : fi, f2 and fj we can determine three different values of p, such that:
Figure imgf000019_0001
then, the calibration curve coefficients a, b and c may be computed. The inventors of the present invention have noticed that for sensors having a resonance frequency versus pressure curve having a flipping point (which is an extremum point) as described in detail hereinabove and illustrated by the exemplary curve 40 of Fig. 2, the flipping point 42 may be used as a known pressure point pi of the unknown parameter. Thus, in accordance with one embodiment of the present invention, a pair of sensors is simultaneously used in the same measurement environment. The flipping points of the two sensors of the sensor pair are at different pressure values and both flipping point pressure values are within the working pressure range for the measurement environment. The two different flipping points may be obtained by using two sensors having different internal pressure values (such as, but not limited to, the sensor 10 of Figs. 1A-1C) and by setting the internal pressure value (Pi) of the first sensor of the sensor pair to be different than the internal pressure value of the second sensor of the sensor pair. For a pair of sensors with different flipping points, the parabola coefficients for the first sensor may be designated ai, bi, and Ci , and the parabola coefficients for the second sensor may be designated a2, b2, and c2 (see equation 1 above). Since the first and the second sensors of the sensor pair are simultaneously subjected to the same pressure within the same measurement environment, each sensor has two points for which the pressure is known and the resonance frequency may be measured. The first point for a sensor is the flipping point of the sensor. The pressure value for the flipping point is known for the first sensor at the time of manufacturing and, for a constant temperature, does not change by deposition of material (as explained in detail hereinabove), and the second point for the first sensor is the point at the pressure value of the flipping point of the second sensor of the sensor pair. The resonance frequency of the first sensor at this second point may also be measured. Thus, for each sensor one may use two equations for the two points of each sensor for which the pressure is known and the resonance frequency is measured. The third equation that may be used for computing the values of the parabola coefficients is the minimum equation of a parabola for one of the sensors. At the minimum point of a parabola the first derivative of equation 1 above is equal to zero. Therefore, for the first sensor the third equation is 2aι ι + bi = 0, and for the second sensor the third equation is 2a2p2 + b2 = 0, wherein i is the known flipping point pressure value of the first sensor, and p2 is the known flipping point pressure value of the second sensor. Reference is now made to Fig. 3 which is a graph schematically illustrating the dependence of the resonance frequency of a vibratable membrane of two exemplary resonating pressure sensors included in a calibratable sensor pair, in accordance with an embodiment of the present invention. In Fig. 3, the horizontal axis represents the external pressure (in Torriceli) acting on the two sensors of the calibratable pressure sensor pair and the vertical axis represents the resonance frequency values (in KHz) of the sensors. The curve 60 represents the (unknown) calibration curve for the first sensor (not shown) of the sensor pair. The curve 60 is modeled as a first parabola having its minimum point at the flipping point 62 of the first sensor. The curve 70 represents the (unknown) calibration curve for the second sensor (not shown) of the sensor pair. The curve 70 is modeled as a second parabola having its minimum point at the flipping point 72 of the second sensor. It is noted that the parabolic curves 60 and 70 are schematic curves that do not represent experimental results of actual sensors, but are curves given for demonstrating the principle of the calibration method of the present invention. The point 74 on the curve 70 represents the resonance frequency (85 KHz in the schematic non-limiting example of Fig. 3) of the second sensor at a pressure value equal to the flipping point pressure of the first sensor (at 820 Torriceli in the schematic non- limiting example of Fig. 3). The point 64 on the curve 60 represents the resonance frequency (55 KHz in the schematic non-limiting example of Fig. 3) of the first sensor at a pressure value equal to the flipping point pressure of the second sensor (at 830 Torriceli in the schematic non-limiting example of Fig. 3). Thus, generally, if pi is the (known) pressure value at the flipping point of a first sensor, and the variable f can be measured at this pressure value, this provides the first point (pi, ft). The flipping point for any resonating sensor may be determined by measuring the resonance frequency of the sensor at different pressure values (for example, by using the Doppler measurement method described in detail in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERML TNG THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004 or by any other suitable method for determining the resonance frequency of a resonating pressure sensor known in the art and discussed hereinabove), and identifying the flipping point pressure as the pressure value at which the resonance frequency shows a minimum value. The flipping point of the first sensor may be used for another equation because it is the minimum point of the parabola. The third equation may then be obtained from a second sensor (implanted or disposed in the same measurement region as the same sensor) having a flipping point pressure that is different than the flipping point pressure of the first sensor. Reference is now made to Figs. 4-6. Fig. 4 is a schematic graph illustrating an example of a periodically varying pressure that may need to be determined within a measurement environment. The horizontal axis of Fig. 4 represents time (in seconds) and the vertical axis of Fig. 4 represents the pressure in the measurement environment (in Torriceli). The curve 80 of Fig. 4 represents the pressure to be measured as a function of time. It is noted that the sinusoidal pressure curve 80 illustrated in Fig. 4 is given by way of example only to demonstrate the methods of the present invention and that the pulsatile pressure in a biological measurement environment (such as, but not limited to, in the lumen of a blood vessel) may exhibit different characteristics. However, the methods described herein may also be similarly applied to many other types and shapes of pulsatile or cyclical or other non-sinusoidal pressure curves. Fig. 5 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor having a resonance frequency versus pressure curve described by the curve 60 of Fig. 3 to the pressure represented by the curve 80 of Fig. 4. The horizontal axis of Fig. 5 represents time (in seconds) and the vertical axis of Fig. 5 represents the resonance frequency of the sensor (in KHz). Fig. 6 is a schematic graph illustrating an example of the resonance frequency as a function of time that may be obtained by subjecting a resonating sensor having a resonance frequency versus pressure curve described by the curve 70 of Fig. 3 to the pressure represented by the curve 80 of Fig. 4. The horizontal axis of Fig. 6 represents time (in seconds) and the vertical axis of Fig. 6 represents the resonance frequency of the sensor (in KHz). Turning to Fig. 5, when a resonating sensor (such as, but not limited to, the sensor 10 of Figs. 1A-1C) having a resonance frequency versus pressure curve described by the curve 60 of Fig. 3 is subjected to the pulsatile pressure represented by the curve 80 of Fig. 4 and the resonance frequency of the sensor is measured as a function of time, the resonance frequency of the sensor varies with time as illustrated by the curve 90 of Fig. 5. As shown in the curve 60 of Fig. 3, the flipping point of the sensor is at a pressure value of 820 Torriceli. Therefore, the resonance frequency curve 90 has minimum points at the times when the pressure is 820 Torriceli (for example, the points 92 and 94 represent such minimum points).. At the points at which the pressure to be measured is maximal (835 Torriceli for the maximum pressure points of the curve 80), the resonance frequency of the sensor is about 61.5 KHz (examples of such points are the points 96 and 98 on the curve 90). At the points at which the pressure to be measured is minimal (795 Torriceli for the minimum pressure points of the curve 80), the resonance frequency of the sensor is about 81.5 KHz (examples of such points are the points 100 and 102 on the curve 90). Turning to Fig. 6, when a second resonating sensor (such as, but not limited to, the sensor 10 of Figs. 1A-1C) having a resonance frequency versus pressure curve described by the curve 70 of Fig. 3 is subjected to the pulsatile pressure represented by the curve 80 of Fig. 4 and the resonance frequency of the sensor is measured as a function of time, the resonance frequency of the sensor varies with time as illustrated by the curve 104 of Fig. 6. The flipping point of the second sensor is at a pressure value of 830 Torriceli.
Therefore, the resonance frequency curve 104 has minimum points at the times when the pressure is 830 Torriceli (for example, the points 106 and 108 represent such minimum points). At the points at which the pressure to be measured is maximal (835 Torriceli for the maximum pressure points of the curve 80), the resonance frequency of the second sensor is about 81.5 KHz (examples of such points are the points 110 and 112 on the curve 104). At the points at which the pressure to be measured is minimal (795 Torriceli for the minimum pressure points of the curve 80), the resonance frequency of the sensor is about 142 KHz (examples of such points are the points 114 and 116 on the curve 104). Reference is now made to Fig. 7 which is a schematic flow chart illustrating steps of a method for performing the calibration of the sensors of a calibratable pair of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention. A sensor pair including two resonating sensors having different flipping point pressure values of the calibratable is disposed or implanted at a region in the measurement environment (step 120). The sensors may be any two resonating pressure sensors known in the art and/or described hereinabove provided that the mathematical function used for modeling the resonance frequency of the sensor as a function of the pressure (the calibration curve) of each of the sensors has a single extremum point within the working pressure range of the sensors. The pressure in the measurement environment may vary periodically within the time period in which the calibration procedure is performed such that the resonance frequency of each of the sensors may be measured (at least once) at the flipping point pressures of both sensors. For example, in the non-limiting example of measuring the pulsatile blood pressure in the lumen of a blood vessel, the flipping point pressure values of the two resonating pressure sensors needs to be selected such that the two different flipping points pressure values of the two sensors fall within the pulsation pressure range within the blood vessel lumen at the time of performing the calibration procedure (the blood vessel's pulsation pressure range is the range between the maximal and the minimal blood pressure in the lumen within the time period of performing the measurements necessary for the calibration procedure). However, the pressure need not obligatorily vary periodically as long as the pressure does vary over a pressure value range including the two flipping point pressure values of the two sensors during the measurement period used for obtaining data for calibration purposes. After the sensor pair is positioned or disposed in the measurement environment (such as, for example, by implanting the sensor pair in the lumen of a blood vessel), the calibration procedure may be started (at a desired time after placement or implantation of the sensor pair) by obtaining for each sensor data representing the sensor's resonance frequency as a function of time (step 122). The data sampling frequency may depend, inter alia, on the rate of variation of the pressure in the measurement environment. Generally, the sampling rate for the sensor's resonance frequency data is, preferably, sufficiently high to enable the determination of the minimum point of each of the resonance frequency curves of both sensors (the sensors' flipping points) with acceptable accuracy. For example, when calibrating a pair of passive ultrasonic pressure sensors implanted in a blood vessel using the Doppler method Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004 for measuring the sensor's resonance frequency, using a sampling rate of 100Hz for the resonance frequency may be adequate. It is noted, however, that other different sampling rates may also be used, depending, inter alia, on the desired measurement and calibration accuracy, and on the parameters of the pressure variation within the blood vessel. If the rate at which the resonance frequency data is sampled is sufficiently high, the minimum points of the resonance frequency may be determined by taking the value of the data point with the minimal value (such as, for example, the point 92 of Fig. 5 for the first sensor and the point 106 of Fig. 6 for the second sensor). Alternatively, if a few periods of the periodically varying resonance frequency versus pressure curve are acquired for each sensor, it may be possible to average a number of such minimum points from several minima within the calibration measurement time interval. In a non- limiting example of the method, the value of the resonance frequency at the flipping point pressure may be obtained by computing the mean of the resonance frequency values of the points 92 and 94 (or of all the minimum points within the curve 90) of Fig. 5 for the first sensor. A similar averaging procedure may be used for computing the resonance frequency at the flipping point pressure for the second sensor. hi accordance with another embodiment of the method, the value of one or more of the minimum points of the resonance frequency may be computed by using various suitable curve fitting methods to obtain a computed curve fitting the acquired data points and finding the minimum point(s) of the fitted curve. By using any of the methods disclosed hereinabove for finding the resonance frequency minimum point(s) (or any other suitable method known in the art for determining minimum points), the flipping point pressure and the resonance frequency at the flipping point pressure are found for each sensor (stepl24). For each sensor, the resonance frequency of the sensor at the flipping point pressure value of the other sensor may be obtained from the resonance frequency versus time data of the two sensors or from suitable curves fitted to that data (step 126). At this stage the first two data points (fl5pι) and ( f2,p2) are known and the calibration curve parameters for one or more of the sensors of the sensor pair may be computed (step 128). For example, by using the parabola model curve for the non-limiting exemplary type of sensor 10 (of Figs. 1A-1C), the coefficients of the parabola calibration curve may be computed as follows.
The set of equations for the first Sensor
Using the flipping point [pi, fmjnι ] of the first sensor:
Figure imgf000026_0001
Using the flipping point pressure from the second sensor and the resonance frequency of the first sensor as measured at the flipping point pressure of the second sensor [p , fi]:
Figure imgf000026_0002
The third equation (minimum point equation for the first sensor) is:
0 = 2alp1 + δj (4)
the set of equations for the second sensor
Using the flipping point [p ) fmin2] of the second sensor:
f«ύn2 = a2P22 + b2P2 + C2 (5)
Using the flipping point pressure from the first sensor and the resonance frequency of the second sensor as measured at the flipping point pressure of the first sensor [pi, f2]: f2 = 2p1 2 +b2pl +c2 (6)
The third equation (minimum point equation for the first sensor) is:
0 = 2a2p2 +b2 (7)
In accordance with an embodiment of the present invention, the estimation of the parabola may be done by least square (LS) method.
For each sensor the three parameters: a, b and c may be estimated as follows.
F = J m * = 1,2 /,
Figure imgf000027_0001
wherein, i - is an index representing the sensor's number.
Fi - is the frequency vector of the sensor i. fmini — is the minimum frequency (which is the flipping point frequency) of sensor i. fi - is the frequency of sensor i when sensor 3-i is at the flipping point pressure.
Hi - is the LS model matrix for sensor i. Hi7 — is the transpose of the LS model matrix H of sensor i. i - is the flipping point pressure of sensor i. a;, bi and Ci - are the LS model parameters which are the parabola's coefficients.
It is noted that in step 128 (of Fig. 7) it is possible to compute both sets of parabola coefficients for both sensors of the sensor pair, or only one set of parabola coefficients (for the first sensor only, or for the second sensor only). Once a single set or both sets of parabola coefficients are known at the end of the calibration procedure, it is possible to perform pressure measurements in the measurement environment by measuring the resonance frequency of one or more of the sensors of the sensor pair for which the parabola coefficients are known. For example, in accordance with one possible embodiment of the present invention, after calibration of the sensor pair the pressure in the measurement environment may be determined from the resonance frequency values of one of the sensors (either the first sensor or the second sensor) by computing the pressure values from the parabola equation, using the parabola calibration curve of the single sensor used for the frequency measurement. In accordance with another possible embodiment of the present invention, after calibration of the sensor pair (comprising the computation of the parabola coefficients for both of the sensors of the sensor pair as disclosed hereinabove), the pressure in the measurement environment may be determined by measuring the resonance frequency of both of the sensors of the sensor pair and computing the pressure values from measured resonance frequencies of each of the two sensors using the parabola coefficients computed for each of the sensors. The two pressure values computed from the resonance frequencies of the two sensors may then be averaged and the mean pressure may be taken as the pressure measurement result. It is noted that while the parabola calibration curve model provides satisfactory results when applied in the calibration of resonating sensors having vibratable membranes as disclosed hereinabove, the calibration methods of the present invention are not limited to the use of the parabola model. hi principle, the calibration methods disclosed herein may be adapted for use with other types of calibration curve models. The method may be used, for example, for calibration of calibratable sensors comprising multiple (more than two) pressure sensors by using polynomial calibration models of the general type shown in equation 8 below.
f = ao+ aip + a2p2 + a3p3+ a4p4+.... (8) wherein, f - is the sensor's resonance frequency, ao, ai, a , a3, a ,....- are the polynomial coefficients (some of the polynomial coefficients may assume the value of zero), and p - is the external pressure in the measurement environment.
A more condensed form of the polynomial calibration is given below
ι=0
Wherein, / is the sensor's resonance frequency, aj are the polynomial coefficients (some of the polynomial coefficients may assume the value of zero), p - is the external pressure in the measurement environment, and
N is an integer number. Such polynomial functions of any desired degree may be used for calibration as long as there is a single extremum point (either a minimum point or a maximum point) for each sensor's calibration curve within the working pressure range for which the calibration is performed, and provided a sufficient number of sensors having different definitive flipping points is used simultaneously in the same measurement environment for providing a sufficient number of known flipping pressure points (and the corresponding measured resonance frequencies of the sensors) to solve the equation systems required to compute the polynomial coefficients of the polynomial function used, as is known in the art. The selection of the proper calibration curve model may depend, inter alia, on the resonating pressure sensor's type and construction. It is noted that while, in accordance with an embodiment of the present invention the methods of calibration disclosed hereinabove may be applied to two or more discrete resonating sensors each individually disposed in the same region of the measurement environment, the distance between such sensors should preferably be minimized to avoid pressure gradients within the measurement environment. Such pressure gradients may (if such gradients exist) result in the two (or more) sensors not experiencing the same pressure value simultaneously, which may result in undesirable errors in the computed calibration curve parameters. Reference is now briefly made to Fig. 8 which is a schematic cross-sectional view of two resonating passive pressure sensors disposed in a measurement environment and usable together as a calibratable sensor pair, in accordance with an embodiment of the present invention. The calibratable sensor pair 131 includes two separate resonating sensors 130 and 132. The sensor 130 includes a recessed substrate layer 136 having a recess 135 formed therein. A second layer 142 is suitably sealingly attached or glued to the recessed substrate layer 136 to form a sealed cavity 134 containing a gas or mixture of gases at a pressure PI. The part of the second layer 142 that overlies the sealed cavity 134 forms a vibratable membrane 142 A. The sensor 132 includes a recessed substrate layer 140 having a recess 137 formed therein. A second layer 144 is suitably sealingly attached or glued to the recessed substrate layer 140 to form a sealed cavity 138 containing a gas or mixture of gases at a pressure P2. The part of the second layer 144 overlying the sealed cavity 138, forms a vibratable membrane 144A. The pressures PI and P2 are different (Pl≠ P2). The sensors 130 and 132 may be disposed within the measurement environment. The pressure value in the measurement environment (PE) acts on the vibratable membranes 142 A and 144A. The details of construction and operation of the individual resonating pressure sensors 130 and 132 are known in the art and disclosed in U.S. Patents 5,989,190 and 6,083,165 to Kaplan and in Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004, cited above and are therefore not disclosed in detail hereinafter. The pressure values PI and P2 of the sensors 130 and 132, respectively, are selected such that the flipping point pressure of both of the sensors 130 and 132 are different from each other as disclosed hereinabove, and are both within the working pressure range for PE. hi accordance with another embodiment of the present invention, the individual resonating sensors included in the calibratable pressure sensor assembly may be suitably attached to the same substrate or to an anchor device, as is known in the art and described hereinabove. Reference is now made to Fig. 9 which is a schematic cross-sectional view of a calibratable sensor assembly including two resonating passive pressure sensors attached to a sensor anchoring member which may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention. The calibratable sensor pair assembly 133 of Fig. 9 includes two separate resonating sensors 130 and 132 constructed and operative as explained for the sensors 130 and 132 of Fig. 8 hereinabove. The resonating sensors 130 and 132 are suitably glued or attached to a sensor anchor member 148. The pressures PI and P2 are different (Pl≠ P2). The calibratable sensor pair assembly 133 may be disposed within the measurement environment. The pressure value in the measurement environment (PE) acts on the vibratable membranes 142A and 144A of the sensors 130 and 132. The pressure values PI and P2 of the sensors 130 and 132, respectively, are selected such that the flipping point pressure of both of the sensors 130 and 132 are different from each other as disclosed hereinabove, and are both within the working pressure range for
PE- The resonating sensors included in the calibratable pressure sensor may also be formed or constructed within a common substrate, in a way similar to the compensated sensors disclosed in U.S. Patents 5,989,190 and 6,083,165 to Kaplan, and in Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21 , 2004 cited hereinabove, or in any other way disclosed hereinabove or known in the art of resonating sensors. Reference is now made to Fig. 10 which is a schematic cross-sectional view of a calibratable sensor assembly including two or more resonating passive pressure sensors formed within the same substrate which may be disposed in a measurement environment and calibrated, in accordance with an embodiment of the present invention. The calibratable sensor assembly 150 of Fig. 10 includes a recessed substrate layer 152. The recessed substrate layer 152 has two recesses 155 and 157 formed therein. The calibratable sensor assembly 150 also includes a second layer 154 suitably sealingly glued or attached to the recessed substrate layer 152 to form two sealed cavities 160 and 162 therein. The sealed cavities 160 and 162 are filled with a gas or a mixture of gases such that the pressure within the sealed cavity 160 is PI, and the pressure within the sealed cavity 162 is P2. The parts of the second layer 154 overlying the recesses 155 and 157 for vibratable membranes 154A and 154B, respectively. The calibratable sensor assembly 150 may be disposed within the measurement environment. The pressure value in the measurement environment (PE) acts on the vibratable membranes 154A and 154B. The pressure values PI and P2 within the sealed cavities 160 and 162, respectively, are selected such that the flipping point pressure of both of the sensors vibratable membranes 154A and 154B are different from each other as disclosed hereinabove, and are both within the working pressure range for
PE- In all the embodiments of the calibratable pressure sensor or calibratable sensor assembly disclosed hereinabove and illustrated in Figs. 8-10, it is also desired to practically minimize the distance between the different sensors or the different resonating structures (having different flipping points) of the calibratable pressure sensor or sensor assembly, to avoid sensor calibration errors due to pressure gradients for the same reasons described hereinabove. It is noted that while the calibratable sensors and sensor assemblies of Figs. 8-10 are shown as including two sensors or two vibratable members, it is also possible to use multi-membrane sensors having a plurality of vibratable membranes, either within one or more of the individual sensors (such as, for example the sensors 130 and 132 of Fig. 8) included in a sensor pair, or within a single calibratable sensor assembly (such as, for example, the calibratable sensor assembly 150 of Fig. 10). For example, in accordance with other embodiments of the present invention, the calibratable sensor assembly may include a plurality of sealed chambers with vibratable membranes such that a first group of sealed cavities has an internal pressure of PI and a second group of sealed cavities has an internal pressure of P2. It is noted that the calibratable sensor pairs and sensor pair assemblies, such as, for example, the calibratable sensor pairs 131 and 133 of Figs. 8 and 9, respectively, and the calibratable sensor assembly 150 of Fig. 10 are not limited to the use of sensors having a single vibratable member. For example, each of the sensors 130 and 132 of Figs. 8 and 9, or both of the sensors 130 and 132 may be substituted by a multi- membrane sensor having multiple vibratable members or multiple membranes or multiple resonating parts. An example of such multi-membrane sensors is the sensor 20 illustrated in Figs. 2-3 of Co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004. However, other different sensors with multiple membranes or with multiple resonating parts or members may also be used in the calibratable sensor pairs or the calibratable sensor assemblies of the present invention. Reference is now made to Fig. 11 which is a schematic flow chart illustrating steps of a general method for performing the calibration of the sensors of a calibratable group of resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention; In the method described in Fig. 11 describes a calibration procedure that may be performed for calibrating one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein. The group of sensors may include a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within the working pressure range. The resonance frequency extremum point of the first sensor of the group of sensors and the resonance frequency extremum point of the second sensor occur at different pressure values within the working pressure range. The flipping point pressure values for the different sensors are known before placement of the sensors in the measurement environment and may be determined by suitable measurements of sensor's resonance frequency as a function of external pressure performed in a controlled pressure chamber. Suitable corrections for the change of the flipping point pressure value with change of temperature may be calculated from the gas laws equations, as is known in the art. The method may include performing resonance frequency measurements on the group of sensors which may include a first sensor and at least a second sensor when the sensors are disposed in a measurement environment having a varying pressure therein (Step 200). The method may also include obtaining (from the resonance frequency measurements) a data set comprising the extremum resonance frequency at the first flipping point pressure value of the first sensor, the extremum resonance frequency at the flipping point pressure value of the second sensor, the resonance frequency of the first sensor at the first flipping point pressure value of the second sensor, and the resonance frequency of the second sensor at the second flipping point pressure value of the first sensor (step 202). The method may also include computing from the data set calibration curve parameters for at least one sensor (step 204), as disclosed hereinabove in detail with respect to Figs 3-7. For example, the method may be used to compute calibration curve parameters for the first sensor, or for the second sensor, or for the first and the second sensor. It will be appreciated by those skilled in the art that, while the examples disclosed and illustrated in the drawings include pairs of resonating sensors, it may be possible to use more than two sensors to form calibratable sensor groups which may be calibrated in a way similar to that described hereinabove. If the group of sensors includes more than two sensors, the method may be used to similarly compute the calibration curve parameters for a some or for all the sensors in the group by using suitable computations for various suitable sensor pair combinations having suitable partially overlapping resonance frequency vs. pressure curves such that it is possible for selected sensor pairs to obtain the four data points as indicated for the pair of the first and second sensors in step 202 above. Reference is now made to Fig. 12 which is a schematic block diagram illustrating a system for performing the calibration of sensors of a group of sensors including calibratable resonating pressure sensors deployed in a measurement environment, in accordance with an embodiment of the present invention. The system 210 may include a measuring unit 212 in communication with one or more processing units 214 and one or more (optional) user interface units 216. The measuring unit 212 may be any type of suitable measuring unit configured for measuring the resonance frequency of resonating sensors (such as but not limited to resonating pressure sensors). For example, the measuring unit 212 may include or may be part of any of the ultrasonic systems for determining the resonance frequency of resonators disclosed in U.S. Patents 5,619,997, 5,989,190 and 6,083,165 to Kaplan or may be any of the various systems (or suitable parts of such systems) using the Doppler effect disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. entitled "METHODS AND DEVICES FOR DETERMINING THE RESONANCE FREQUENCY OF PASSIVE MECHANICAL RESONATORS" filed on April 21, 2004, but may also be any other type of measurement system or measurement unit known in the art for measuring the resonance frequency of resonating sensors disposed in a measurement environment. The processing unit(s) 214 may be one or more processing devices capable of processing measurement results or data communicated from the measuring unit 212. For example, the processing unit(s) 214 may include but is not limited to, one or more computers, processors, digital data processors, analog data processors, hybrid digital/analog processors, personal computers, mini-computers, multi-processor based computers, workstations, desktop or mobile computing devices, microprocessors, computer based networks, or the like. It is noted that the processing unit(s) 214 may include one or more suitable data storage devices (not shown) and/or one or more memory devices (not shown), and/or suitable other internal or external components and interfaces required for performing data processing or computational tasks. The measuring unit 212 may perform measurements for determining the required resonance frequency values of the sensor pairs or sensor group that are described in detail in the methods disclosed hereinabove. The measurement results may then be communicated to the processing unit(s) 214 for processing. The processing unit(s) 214 may perform the necessary data processing or computations to obtain the parameters of the calibration curves for one or more sensors as disclosed in detail hereinabove. The processing unit(s) 214 may use the computed calibration curve parameters for computing the pressure values from the determined values of the sensor's (or sensors') resonance frequency and may also store the calibration (or recalibration) curve parameters for further use in other future measurements. The system 210 may also include one or more user interface units 216 that may be suitably connected to the processing unit(s) 214 and to the measuring unit 212. The user interface unit(s) may include but are not limited to suitable devices for providing input from a user to the system 210 for operating the system and may also include output devices for providing output to the user of the system 210. For example, the user interface unit(s) 216 may include one or more input or output devices or peripheral equipment including but not limited to, display devices, data storage devices, keyboards, pointing devices (such as, but not limited to, a mouse), light pens, touch sensitive display screens, graphic tablets, printers, or any other suitable input or output device(s) known in the art. The calibration results for one or more of the sensors may be displayed on one or more user interface devices 216, such as but not limited to a suitable display device or computer screen or the like. The displayed calibration results may include but are not limited to numerical calibration data and graphical data (calibration curves) or combinations of graphical and numerical data. It is noted that in accordance with an embodiment of the present invention, the processing unit(s) 214 may also communicate the computed values of the calibration curve parameters (for one or more of the sensors) to the measuring unit 212 (in cases in which the measuring unit 212 has processing capabilities), and the measurement unit 212 may store the calibration parameters and may use them for producing calibrated measurement results. Alternatively, the processing and computation of calibrated measurement results may be performed by the processing unit(s) 214. It will be appreciated that while the system 210 of Fig. 12 illustrates a general form of a system for performing the sensor calibrations, the configuration of the system of the present application is not limited to the specific configuration illustrated in Fig. 12. fn accordance with one possible embodiment example, the entire system 212 may be implemented within one of the systems disclosed in co-pending U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. In a non-limiting example, the system 212 may be implemented as the system 32 illustrated in Fig. 4 of U.S. Patent Application Serial no. 10/828,212 to Girmonski et al. which includes, inter alia, a measurement unit a processing /controlling unit and a user interface. It will be appreciated by those skilled in the art that many specific hardware implementations of the system 212 are possible which are considered to be within the scope and spirit of the present invention. It is noted that many permutations and combinations of multi-membrane and single membrane sensors are therefore possible within the scope of embodiments of the calibratable sensors of the present invention, and that such permutations and combinations may be calibrated using the calibration methods disclosed herein. It is further noted that the timing of performing the calibration procedure disclosed hereinabove may vary according to, inter alia, the type of environment within which the calibratable sensor or sensor assembly is disposed or implanted, the rate of deposition of extraneous material or tissues on the sensors resonating parts, and other considerations. Thus, in accordance with one embodiment of the present invention after calibration of the sensor(s), it may be possible to use the calibration curve(s) obtained in the calibration procedure to compute the pressure values in the measurement environment for a certain period of time after calibration. Alternatively, it accordance with another possible embodiment of the present invention, it is possible to repeat the calibration procedure, each time a pressure measurement is needed. This embodiment may be advantageous, inter alia, in situations in which the rate of deposition of extraneous material or tissues on the sensor is not known in advance, or behaves sporadically, or when the changes in the calibration curve parameters are by themselves of interest. It is further noted that as the flipping point pressure of the passive ultrasonic pressure sensors is temperature dependent, the calibration method described hereinabove is performed under isothermal conditions. The sensors of the group should be at the same known temperature. If needed, temperature differences (between the temperature values measured in the measurement environment during and the temperature at which each sensor of the group was calibrated after manufacturing of the sensor) may be corrected or compensated by using the gas law equations as is known in the art by determining the temperature in the measurement environment using any suitable type of temperature measurement known in the art (such as, for example, by using a thermometer or temperature sensor to measure the temperature of a patient in which the calibratable sensor group is implanted or by determining the temperature in any measurement environment in which the calibratable sensor group is disposed by using any other type of temperature sensor or temperature measurement method, as is known in the art). It is noted that while for the simple exemplary sensor type illustrated in Figs. 1A-
1C, the flipping point of the sensor 10 may occur when the internal pressure Pi is equal to the external pressure PE and the vibratable membrane 12A is flat (planar) this is not obligatory for practicing the present invention. For example, the sensor may be constructed to have a minimum resonance frequency while the membrane 12A is not planar. Therefore, for the purposes of the present application the term "flipping point pressure value" is used herein to define the pressure value (within the pressure working range of the sensor) at which the resonance frequency of the sensor has an extremum point (a minimum or a maximum point depending, inter alia, on the sensor's type and construction). While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made which are within the scope and spirit of the invention.

Claims

1. A calibratable pressure sensor group having a working pressure range, the sensor group comprising: a first resonating pressure sensor having a single known resonance frequency extremum point within said working pressure range; and at least a second resonating pressure sensor having a single known resonance frequency extremum point within said working pressure range, wherein the resonance frequency extremum point of said first sensor and the resonance frequency extremum point of said at least second sensor occur at different pressure values within said working pressure range.
2. The calibratable pressure sensor group according to claim 1 wherein said at least a second sensor is disposed adjacent to said first sensor.
3. The calibratable pressure sensor group according to claim 1 wherein said at least a second sensor is disposed sufficiently close to said first sensor to ensure that said first sensor and said at least a second sensor are exposed to substantially the same pressure and temperature when disposed in a pressure measurement environment.
4. The calibratable pressure sensor group according to claim 1 wherein said first sensor and said at least a second sensor are passive resonating ultrasonic pressure sensors.
5. The calibratable pressure sensor group according to claim 1 wherein said first sensor and said at least a second sensor each comprise at least one sealed chamber having a pressure level therewithin and at least one vibratable member forming part of said sealed chamber, and wherein the pressure level within said at least one sealed chamber of said first sensor is different than the pressure level within said at least one sealed chamber of said at least a second sensor.
6. The calibratable pressure sensor group according to claim 5 wherein said first sensor and said at least a second sensor are formed within a common substrate.
7. The calibratable pressure sensor group according to claim 6 wherein said at least one sealed chamber of said first sensor and said at least one sealed chamber of said at least a second sensor are formed within a common substrate.
8. The calibratable pressure sensor group according to claim 1 wherein said first sensor and said at least a second sensor are formed as parts of a sensor assembly.
9. The calibratable pressure sensor group according to claim 8 wherein said sensor assembly comprises a sensor supporting member attached to said first sensor and to said at least a second sensor.
10. The calibratable pressure sensor group according to claim 9 wherein said sensor supporting member comprises part of a sensor-anchoring device.
11. The calibratable pressure sensor group according to claim 1 wherein said first sensor and said at least a second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure, said calibration curve is approximated by a parabola equation within said pressure working range.
12. The calibratable pressure sensor group according to claim 1 wherein said first sensor and said at least a second sensor are configured to have a calibration curve correlating the sensor's resonance frequency with the external pressure, said calibration curve is approximated by a polynomial equation having a single extremum point within said pressure working range.
13. The calibratable pressure sensor group according to claim 1 wherein at least one sensor of said group is a composite pressure sensor comprising a plurality of sealed chambers having one or more vibratable members forming part of the sealed chambers.
14. A system for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein, said group comprises a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value of said second pressure sensor within said working pressure range, the flipping point pressure value of said first sensor is different than the flipping point pressure value of said second sensor, the system comprising: means for obtaining a data set comprising the extremum resonance frequency of said first sensor at the flipping point pressure value of said first sensor, the extremum resonance frequency of said second sensor at the flipping point pressure value of said second sensor, the resonance frequency of said first sensor at the flipping point pressure value of said second sensor, and the resonance frequency of said second sensor at the flipping point pressure value of said first sensor; and means for computing from said data set calibration curve parameters for at least one sensor of said first sensor and said second sensor.
15. The system according to claim 14 further including user interface means for enabling communication between a user and said system.
16. A system for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein, said group comprises a first resonating pressure sensor having a single resonance frequency extremum point at a known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at another known flipping point pressure value within said working pressure range, the flipping point pressure value of said first sensor is different than the flipping point pressure value of said second sensor, the system comprising: a measurement unit configured for determining the resonance frequency of at least said first sensor and said second sensor to obtain a data set comprising the extremum resonance frequency of said first sensor at the flipping point pressure value of said first sensor, the extremum resonance frequency of said second sensor at the flipping point pressure value of said second sensor, the resonance frequency of said first sensor at the flipping point pressure value of said second sensor, and the resonance frequency of said second sensor at the flipping point pressure value of said first sensor; and at least one processing unit operatively connected to said measurement unit for computing from said data set calibration curve parameters for at least one sensor of said first sensor and said second sensor.
17. The system according to claim 16 further including one or more user interface units operatively connected to at least one of said measurement unit and said at least one processing unit.
18. A method for calibrating resonating pressure sensors, the method comprising the steps of: disposing within a measurement environment having a varying pressure therein a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within said working pressure range, the flipping point pressure value of said first sensor is different than the flipping point pressure value of said second sensor; obtaining a data set comprising the extremum resonance frequency of said first sensor at the flipping point pressure value of said first sensor, the extremum resonance frequency of said second sensor at the flipping point pressure value of said second sensor, the resonance frequency of said first sensor at the flipping point pressure value of said second sensor, and the resonance frequency of said second sensor at the flipping point pressure value of said first sensor; and computing from said data set calibration curve parameters for at least one sensor of said first sensor and said second sensor.
19. A method for performing calibration of one or more pressure sensors in a group of resonating pressure sensors disposed in a measurement environment having a varying pressure therein, said group comprises a first resonating pressure sensor having a single resonance frequency extremum point at a first known flipping point pressure value within a working pressure range, and at least a second resonating pressure sensor having a single resonance frequency extremum point at a second known flipping point pressure value within said working pressure range, the flipping point pressure value of said first sensor is different than the flipping point pressure value of said second sensor, the method comprising the steps of: obtaining a data set comprising the extremum resonance frequency of said first sensor at the flipping point pressure value of said first sensor, the extremum resonance frequency of said second sensor at the flipping point pressure value of said second sensor, the resonance frequency of said first sensor at the flipping point pressure value of said second sensor, and the resonance frequency of said second sensor at the flipping point pressure value of said first sensor; and computing from said data set calibration curve parameters for at least one sensor of said first sensor and said at least second sensor.
20. The method according to claim 19 wherein said varying pressure is a periodically varying pressure.
21. The method according to claim 19, wherein said step of obtaining comprises the steps of: obtaining for each of said first sensor and said second sensor data representing the sensor's resonance frequency as a function of time; determining from said data the extremum resonance frequency of said first sensor at the flipping point pressure value of said first sensor, and the extremum resonance frequency of said second sensor at the flipping point pressure value of said second sensor; and determining from said data the resonance frequency of said first sensor at the flipping point pressure value of said second sensor, and the resonance frequency of said second sensor at the flipping point pressure value of said first sensor.
22. The method according to claim 19 wherein said step of computing comprises computing the calibration curve parameters for at least one sensor of said first sensor and said second sensor by using parabola equations representing the calibration curves of said first sensor and said at least second sensor.
23. The method according to claim 19 wherein said step of computing comprises computing the calibration curve parameters for at least one sensor of said first sensor and said at least second sensor by using polynomial equations having a single extremum point within said working pressure range for representing the calibration curves of said first sensor and said at least second sensor.
24. The method according to claim 23 wherein said polynomial equations comprise equations of the type
f = ∑«,P'
Wherein, is the resonance frequency of said at least one sensor , a; are polynomial coefficients, p is the external pressure in the measurement environment, and
N is an integer number.
25. The method according to claim 24 wherein some of said polynomial coefficients are equal to zero.
26. The method according to claim 19 wherein the pressure within said measurement environment is a periodically varying pressure having pressure cycles, said data comprises data obtained from a plurality of said pressure cycles, and wherein said extremum resonance frequency at the first flipping point pressure value of said first sensor, said extremum resonance frequency at the flipping point pressure value of said second sensor, said resonance frequency of said first sensor at the first flipping point pressure value of said second sensor, and said resonance frequency of said second sensor at the second flipping point pressure value of said first sensor are mean values computed from one or more measurements performed over said plurality of pressure cycles.
PCT/IL2004/000807 2003-09-08 2004-09-07 A method and system for calibrating resonating pressure sensors and calibratable resonating pressure sensors WO2005024367A2 (en)

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