JP2010042235A - Method and device for detecting parameter for characterization of kinetic sequence at human or animal body - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a bending sensor for detecting function parameters for the characterization of kinetic sequences at a human or animal body, comprising a fixing element 20 for fixing the bending sensor on the skin of the human or animal body, a bending-sensitive detector 10 for detecting bending parameters of the bending sensor, in particular a bending angle, a bending rate, and a bending acceleration, and a data memory 30 for storing the detected bending parameters in order to obtain reliable data similar to long-time EKG measurements. <P>SOLUTION: A fixing element is extensible and comprises an extensible cavity for accommodating a measuring sensor of a detector. The measuring sensor is fixed at a reference point of the fixing element in the cavity. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for detecting parameters for characterizing the movement characteristic course in a human or animal body and to a bending or bending sensor for carrying out this method.

  Back pain is more or less a major pain in a human back, and the causes are very different. The doctor talks about dorsalgia or lumbalgia when the lumbar-sacral region is applicable. The most common cause of back pain is joint dysfunction in the area of the spine. However, about 90% of all chronic (recurrent or continuous) back pain remains unspecified. In other words, it does not show a finding that can fully explain pain within the framework of medical research. For example, at present, the motor function for treating unspecified back pain is not objectively grasped. Although structural findings are usually made by imaging diagnostics, unspecified back pain is not captured by this diagnostic.

  The task of the present invention therefore makes it possible to detect functional parameters for characterizing the motor course characteristics in the human or animal body so that undetected or chronic pain can be associated with detected motion patterns Is to provide a device. Detection of bending or bending information should be performed primarily in the lumbar region. This is because here you can see most of the causes of any back pain.

  The measurement of dynamic functional parameters is a very important field that has not been developed in spinal medicine. The bending or bending sensor of the present invention offers the possibility to gain insight into daily exercise, function, activity, and exercise frequency. The detection of motion parameters using the bending sensor of the present invention can be regarded as corresponding to EKG for a long time for orthopedics and spinal medicine.

  This problem is solved by a bending sensor for detecting a functional parameter for characterizing a movement course characteristic in a human or animal body according to claim 1. The bending sensor has a fixing element, in particular a fixing band aid, for fixing the bending sensor to the skin of the human or animal body. Furthermore, a bending or bending sensitive detector is provided for detecting the bending or bending parameters of the bending sensor. Detected bending parameters such as bending angle, bending speed and / or bending acceleration are stored in a data memory. The fixing element is extensible and has an extensible hollow space for receiving the measuring detector of the detector. The measurement detector is fixed at the reference point of the fixed element in the hollow space.

  A sensor or measurement detector or measurement feeler is a technical component that can quantitatively detect a predetermined physical or chemical property as a measurement quantity. These quantities are subsequently converted into processable quantities (usually electrical signals).

  For example, the bending sensor of the present invention is adapted to detect back bending. The body deformation due to the bending is expressed as a load acting in a direction perpendicular to the body axis. In order to detect the dynamic characteristics of the motion course characteristics in the human body (eg the back in the region of the lumbar spine), one or more measuring detectors using fixation elements, in particular fixed band aids, are fixed on the skin in the corresponding positions. I want to be done. The skin stretches when the back is bent. Stretching is the relative dimensional change (extension or contraction) of the body under load. When body dimensions are expanded, positive stretching occurs, otherwise negative stretching or compression strain occurs. The stretching of the skin during flexion of the back is a length change of about 50% in the region of the lumbar spine during flexion movement. The securing means must therefore be extensible so that it cannot be dissociated on the basis of the aforementioned skin length change. The measurement detector is secured to human skin (preferably to the left and right of the spine to detect back movement) using extensible anchoring elements. In this case, the sensor tape is connected to the fixed element only via the reference point and slides freely in the hollow space formed by the fixed element. In other words, the hollow space forms a guide channel in which the measurement detector is held by the body and its movement is retrofitted, in which case it is not necessary to retrofit the skin length change It is like that. That is, the measurement detector is fixed to the body so as to retrofit the body flex without the need to retrofit the skin length change.

  Advantageously, the anchoring element has an elastic underlayer with a biocompatible thermally activatable adhesive layer for application to the skin. In addition, an elastic upper layer portion is provided so that a hollow space is formed between the upper layer portion and the lower layer portion. The hollow space is therefore not a rigid body, and its shape and extent depend on the integrated measurement detector and the state of the elastic upper and lower layers. However, the upper and lower layers serve to be held on the body, for example the back, so that the measurement detector is not acted upon by a corresponding change in the length of the skin, but to bend the body, for example the back. Is.

  An advantageous embodiment of the bending sensor of the present invention includes a measurement detector having a light guide. The light guide has a transfer function that varies depending on the bending of the light guide. The light guide is a guide device for transmitting visible light as well as light in the ultraviolet or infrared region. Examples of light guides are optical waveguides, glass fibers, polymer optical fibers or other light guide members made of synthetic resin and fiber optic components. Each light guide has a transfer function. The transfer function of the light guide represents the ratio of the input signal to the output signal for different frequencies of input coupled light. As the light guide bends, the transfer function changes, i.e., the bent light guide couples less light than the unbent light guide relative to the input signal. Therefore, the degree of bending of the light guide can be obtained by determining the transfer function.

  The light output coupling can be performed at the end of a fiber-shaped light guide, for example. Based on the output coupled light, it is detected whether or not the light guide body is bent, and how much the light guide body is bent. However, it is not easy to detect the bending direction of the light guide. The light guide therefore advantageously has an additional lateral opening for light output coupling. The opening exists on the upper surface of the light guide. In particular, the opening can be provided with a pointed recess or notch. Since the side openings are scattering points that are opened or closed more when bent, the light output at the end of the fiber is either increased or decreased (linear signal for positive and negative bending directions). Further, the side opening determines where the measured bend occurs, that is, the bend can be detected in place. Advantageously, a plurality of parallel extending light guides with lateral openings provided in different segments are used so that bending at different locations can be detected. The

  According to an advantageous embodiment of the invention, the measurement detector has one or more strain gauges. The strain gauge (Dehnungsmessstreifen = DMS) is a measuring device for detecting a stretching deformation. When they are deformed even a little, their impedance changes and they are used as stretch sensors.

  The electrical impedance of the strain gauge changes as the strain gauge extends or contracts. By measuring the impedance, in particular the electrical resistance, the extent of the strain gauge length change can be determined. When the strain gauge is housed in a hollow space forming a guide channel in the test object, e.g. the back, as is the case with the present invention, the strain gauge will bend accordingly when the back is bent. The gauge changes its length.

  The bending sensor of the present invention advantageously includes a detector having a detection device. The detection device detects a change in the electrical impedance of the strain gauge or the transfer function of the light guide. Thereby, the bending sensor has a measure for the bending of the object to be inspected.

  The detector of the bending sensor according to the invention advantageously has a tension-resistant and elastically bendable substrate to which the measurement detector is fixed. The substrate is such that any tensile or compressive stresses that occur are not caused to change the length of the strain gauge. This is because if such a length change occurs, it would be inadvertently interpreted as a measure for the bending of the inspection object. A suitable substrate that allows bending but prevents strain gauge expansion or contraction is spring steel. Spring steel is a steel having a relatively high strength compared to other steels. A workpiece made of spring steel can bend to a stress (elastic limit) determined by the workpiece and then be restored elastically rather than remaining deformed. The material property that makes it possible is elasticity. The substrate need not be spring strip steel. It may be FR4. FR4 is a title for the fire resistance of printed circuit board materials, and FR4 is a common standard for consumer electronics.

  According to an advantageous embodiment of the invention, the detector comprises a plurality of measurement detectors, which are fixed on the opposite side of the substrate. The reliability of the detected data is the highest requirement for biomechanical applications. The two measurement detectors detect substantially the same bend of the test object, for example the substrate retrofitting the back bend. As a result, the bending is represented by two simultaneously measured values of the measurement detector. Therefore, the actual bend can be obtained with relatively high accuracy and reliability.

  A bending sensor according to an advantageous embodiment includes a detector, which has a plurality of measuring detectors for detecting bending parameters in different measuring zones. The measurement detectors may be arranged in cascade or overlapping connection. Thereby, it is possible to detect the bending information generated due to the movement of the body in terms of location and to detect the measurement technique. Each bending sensitive measurement zone detects the bending applied respectively in the measurement section in the positive or negative bending direction in at least one space plane. Measurement detectors arranged in different measurement zones are preferably time-shifted and drive-controlled, in particular with a clock frequency of 1 kHz or higher (pulse activation = current saving). The higher the frequency, the better. This significantly reduces the amount of data detected. The reason is that only data from a single measurement detector is read out at each time. At the same time, the readout frequency is large enough to detect the dynamic characteristics of the motion in a resolved manner. For example, if there is a drive control frequency of 1 kHz and there are, for example, 10 bending zones, a readout frequency of 100 Hz is possible to enable dynamic motion detection (bending speed, acceleration).

  Furthermore, the bending sensor of the present invention may have a spatial position sensor for detecting the position of the measurement detector relative to the earth's gravity field or geomagnetic field. The earth's gravity field is predetermined in a certain direction. The bending-resolved measurement of the bend makes it possible to detect a bend in a given plane relative to the direction of the gravity field. Thus, for example, it can be determined how the back is bent to lift the load.

  The spatial position sensor can also determine a starting point vector for detecting bending information. The spatial position sensor therefore detects the position of the sensor on the back before the start of the bending measurement. The bend detected after that represents a relative deviation with respect to the orientation of the starting point vector.

  The data detected by the detector is preferably output as a digitized electronic signal by a detection device and stored in an electronic data memory. As the data memory, for example, a flash memory such as an SD memory card or a micro SD card can be used. Flash memory offers the advantage that it is relatively small and light and stores stored data without having to connect the data memory to the energy supply. The flash memory can be fixed together with the fixing element to the inspection object. Certainly, the flash memory needs a current supply for reading or reading data. Alternatively, the data memory may be provided in a separate memory unit. In this case, data transmission is performed to an external data memory by wire or wireless. According to this embodiment, the electronic part of the bending sensor can be made extremely small.

  The bending sensor according to the invention can in particular have a readable identification code memory unit. The identification code memory unit includes an electronic identification code for identifying the fixed element. This allows the fixing element to be identified and prevented from being improperly replaced with another product. This feature is particularly useful for quality assurance. This is because it is guaranteed that only bending sensors with fixed elements that are set for measurement can be used.

  As an identification code memory unit for identifying a fixed element, for example, an RFID transponder for wirelessly reading out an electronic identification code may be provided. The English concept of Radio Frequency Identification (RFID) represents a system for identification using electromagnetic waves. The RFID system consists of a transponder present in and characterizing the object to be identified and a reading device for reading the identification code of the transponder. In that case, the detector of the present invention can be provided in the RFID transponder together with a reading device for reading the identification code. Reading is performed via an antenna, in which case the existing data lines for the measurement data transfer are used as antennas, in which case these lines are modulated, for example at 13.2 MHz, so that they can be used as antennas. As a result, there is room for change of other electrical lines with respect to the antenna. This measure ensures that neither the detector nor the fixed element can be replaced with another product. This enables a unique association with the manufacturer and the number of uses. This eliminates multiple use of fixed elements.

  The measuring detector or detectors are preferably in containers sealed against environmental influences by laminating, extruding, casting, welding (Einschweissen) or shrinking or shrink fitting or heating of shrinking hoses. Be trapped. This feature ensures that the measurement detector is protected against potential harmful environmental effects such as moisture or dirt. This type of protection is necessary, especially when the bending sensor of the present invention is used for long-term inspections over days or weeks.

  The detected bending parameters are advantageously used to locate a number of dynamic parameters. In particular, the bending angle as a function of time and / or place, the bending speed as a function of time and / or place, the bending acceleration as a function of time and / or place, the Fourier transform of the function of bending angle, the bending speed and / or Alternatively, the bending acceleration can be derived.

  The detected bending data is preferably entered in a histogram for a graphical display of the dynamic parameter frequency distribution. A histogram is a graphic representation of the frequency distribution of measured values. Starting from data organized according to size, the entire area of the specimen examination is distributed to the classes. For each class, a surface with an area proportional to the class-specific frequency is established. In particular, the bending angle, bending speed or bending acceleration is displayed in such a histogram. The frequency distribution of the spatial position of the bending sensor is likewise displayed as a histogram or as a gray value in the coordinate system. The detected bending parameters are compared with the average bending parameters to identify aberrations in the movement parameters. This kind of comparison is facilitated by a histogram display.

  Advantageously, simultaneously with the bending parameters, other parameters are detected, for example pain parameters, posture parameters, activity parameters, and a statistical correlation is taken between the bending parameters and the other parameters. However, statistical correlation cannot explain whether there is a causal relationship between various parameters. However, identification of this type of relationship by a scientist or doctor is facilitated when a corresponding statistical correlation can be displayed.

  The detection of the bending parameters of the bending sensor is advantageously performed over a time space of at least 24 hours in order to enable long-term analysis. As a result, the application is performed analogously to EKG for a long time, and measurements are possible in any time space up to 24 hours. The detection of the bending parameter is performed in conjunction with the therapy so that a positive or negative correlation between the therapy measure and the detected motion parameter is established.

  The invention will now be described in detail with reference to the illustrated embodiment.

  FIG. 1 shows the bending sensor of the present invention attached to a human back. A two-strip bend sensitive detector 10 is illustrated, the strips being mounted side by side on a human back. The strip-shaped flexible tape extends along the back parallel to the spine in FIG. These are fixed to the back using a fixing element 20. A data line 40 for transmitting the detected bending parameters to the electronic data memory 30 is provided.

  FIG. 2 schematically shows a part of the strip-shaped detector 10 of FIG. The detector 10 has a strip-shaped substrate 50. Strain gauges 60 and 70 are disposed on opposite sides of the strip-shaped substrate 50, respectively. Each of the strain gauges arranged on the opposite side defines the measuring zone of the detector. The strain gauges 60 and 70 are measuring devices for detecting extensional deformation. If they are deformed even slightly, their impedance is changed and they are used as extension sensors. When the person illustrated in FIG. 1 bends his back, the strain gauges 60 and 70 are each extended. This mechanical deformation changes the electrical resistance of the strain gauges 60 and 70.

  FIG. 3 shows the relationship between the mechanical deformation of the strain gauge and the change in electrical resistance in the Cartesian coordinate system. The bending angle Φ is shown on the horizontal axis. The bending angle Φ is a linear function of the strain gauge extension. Each individual bending sensitive measurement zone of the sensor tape is calibrated, with the calibration curve being stored in the electronics of the sensor tape. The vertical axis of the coordinate system represents a change ΔR in electrical resistance with respect to the resistance of the strain gauge that is not deformed. Reference numeral 85 represents a calibration curve. That is, it is a simple straight line passing through the origin of the coordinate system. This curved shape is only illustrated. However, the calibration curve 85 moves away from the curve shape as the bending angle Φ increases. Calibration is necessary to allow as accurate detection of the bending angle as possible. In addition to a strain gauge (Dehnungsmessstreifen = DMS), a light guide having a surface structure in the region of the bending sensitive measurement zone can also be used as the sensor element. In addition to ohmic resistance, changes in electrical capacitance or inductance can also be used as a measure for the bending angle. In general, the complex AC resistance Z or impedance for the bending angle to be detected can be recorded as a calibration curve.

  FIG. 4 illustrates another embodiment of the bending sensor of the present invention. The bend sensor includes a unit for the detector electronics 120 connected to the bend sensitive detector 10. The bend sensitive detector includes a strip-shaped substrate 50. A large number of strip-shaped strain gauges 110 are arranged along the strip-shaped substrate 50. The longitudinal axes of the strain gauges 110 are each oriented parallel to the longitudinal axis of the strip-shaped substrate 50. Since the adjacent strain gauges 110 are aligned and sequentially positioned on the strip-shaped substrate 50, the start point portion of the first strain gauge 110 exists next to the end point portion of the subsequent strain gauge. Reference numeral 130 represents a cross-section through the bend sensitive detector where the start and end portions of two adjacent strain gauges are arranged side by side.

  FIG. 5 shows a cross section of the bending sensitive detector 10 taken along the cross section 130 of FIG. The substrate 50 shown in FIG. 5 is preferably made from spring steel. This material has sufficient strength and flexibility to accommodate the strain gauge 110. In FIG. 5, the strain gauge 110 is fixed to the substrate 50 using an adhesive layer 140. For example, an epoxy resin can be used as the adhesive layer 140. This at the same time serves for effective electrical isolation of the strain gauge from the substrate. The substrate 50 and the strain gauge are confined by the protective cover 100. A shrink hose is preferably used as the protective cover.

  FIG. 6 illustrates another embodiment of the present invention. Reference numeral 120 in FIG. 6 represents the detector electronics unit of the illustrated bending sensor. That is, it is preferably connected via a data line to an external data memory not shown in FIG. Thereby, the size and weight of the bending sensor can be reduced as a whole. It is of course possible to transfer the detected bending parameters via a wireless connection, for example Bluetooth (IEEE802.5.1), WLAN (IEEE802.11) or UMTS. Evaluation and storage of the bending parameters thus detected can be transmitted to an external computer. In particular, it is possible to evaluate the detected data in real time to convey information to relieve or prevent back pain to the carrier of the bending sensor.

  The bending sensor shown in FIG. 6 further includes a substrate 50 on which a strain gauge 110 is arranged in cascade. Only the spatial arrangement of the strain gauges is represented here by the concept of cascade connection. The strain gauges 110 are not connected in series but are connected in parallel. Thus, each strain gauge can be driven and read individually. Each strain gauge 110 is provided to detect bending parameters at different positions or measurement zones, so that a position-resolved display of bending parameters can be obtained. The strain gauges 110 are sequentially arranged along the longitudinal axis of the substrate 50. FIG. 6 shows only one plane of the bending sensor. A strain gauge is also arranged on the back surface (not shown) of the bending sensor in the same manner as the front surface shown.

  In FIG. 7, a cross-section of the bending sensor of FIG. A strain gauge 110 is disposed on the opposite side of the substrate 50. The strain gauges 110 are each fixed to the substrate 50 using the adhesive layer 140. By combining two measuring detectors arranged in parallel (sandwich structure), oppositely or in the same direction, per bending-sensitive measuring zone, measuring accuracy, measuring area, fault tolerance, and consequently bending Signal reproducibility is enhanced. This is because thermal, mechanical and electromagnetic influences and measurement detector degradation are compensated.

Schematic showing a state where the bending sensor of the present invention is attached to a human back. Schematic diagram showing a first embodiment of the detector of the bending sensor of the present invention. The figure which shows the Cartesian coordinate system by which the dependence with respect to bending angle ((PHI)) of the electrical resistance change ((DELTA) R) of a detector is illustrated. Schematic diagram of a second embodiment for the bending sensor of the present invention. Schematic cross-sectional view of the bending sensor of the second embodiment cut along a cross-section 130 Schematic of a third embodiment for the bending sensor of the present invention. Schematic cross-sectional view of the bending sensor of the third embodiment cut along a cross-section 130

Explanation of symbols

  10 bending sensitive detectors, 20 fixed elements, 30 data memory, 40 data lines, 50 substrate, 60 upper strain gauge, 70 lower strain gauge, 80 measurement zone, 85 calibration curve, 90 power supply, 100 protective cover, 110 Strain gauge, 120 Detector electronic unit, 130 Cutting surface, 140 Adhesive for strain gauge

Claims (30)

A bending sensor for detecting a functional parameter for characterizing the course of movement in a human or animal body,
A fixing element (20) for fixing the bending sensor on the skin of the human or animal body, for example a fixing band aid;
A bending sensitive detector (10) for detecting bending parameters of the bending sensor, such as bending angle, bending speed and bending acceleration;
In the form of a data memory (30) for storing the detected bending parameters;
The fixed element is extendable and has an expandable hollow space for accommodating the measurement detector of the detector, the measurement detector being fixed to a reference point of the fixed element in the hollow space. Bending sensor characterized by that. The anchoring element (20) has an elastic lower layer and an elastic upper layer with a biocompatible thermally activatable adhesive layer for mounting on the skin, the hollow space comprising the hollow space The bending sensor according to claim 1, wherein the bending sensor is formed between a lower layer and the upper device. The bending sensor according to claim 1 or 2, wherein the measurement detector has a light guide, and the light guide has a transfer function that varies depending on the bending of the light guide. 4. The bending sensor according to claim 3, wherein the measurement detector has a strain gauge having an impedance, and the impedance is changed by extension or compression of the strain gauge. The detector comprises a detection device, wherein the detection device detects a change in electrical impedance of the strain gauge (60, 70) or a change in transfer function of the light guide. The bending sensor according to any one of 4 to 4. The detection device is configured to detect a change in electrical impedance of the strain gauge (60, 70) or a change in transfer function of the light guide with a predetermined sampling frequency of, for example, 100 Hz. 5. The bending sensor according to 5. The bending sensor according to claim 5 or 6, further comprising an electronic data memory for storing a digitized electronic signal output from the detection device. The bending sensor according to any one of claims 1 to 7, wherein the detector has a substrate that can be bent elastically and elastically, and the measurement detector is fixed on the substrate. The bending sensor according to claim 8, wherein the substrate is made of spring steel. The bending sensor according to claim 8 or 9, wherein the detector has a plurality of measurement detectors, and the measurement detectors are fixed to the opposite side of the substrate. 11. A bending sensor according to any one of the preceding claims, wherein the detector (10) comprises a plurality of measuring detectors for detecting bending parameters in different measuring zones (80). The bending sensor according to claim 11, wherein the measurement detectors are arranged in cascade or overlapping. The detector is configured to drive and control measurement detectors located in different measurement zones (80) with a time shift, for example with a sampling frequency of at least 1 kHz. The bending sensor according to any one of claims 1 to 12. 14. A bending sensor according to any one of the preceding claims, comprising a spatial position sensor for detecting the position of the measurement detector relative to the earth's gravitational field or geomagnetism. 15. A bending sensor according to any one of claims 6 to 14, wherein the fixing element (20) has a layer of spring steel for mechanical stabilization and electromagnetic shielding. The fixed element (20) has a callable identification memory unit, and an electronic identification for identifying the fixed element is stored in the identification memory unit. The bending sensor according to item 1. The bending sensor according to claim 16, wherein the identification memory unit has an RFID transponder for wirelessly identifying and reading the electronic identification. 18. The bending sensor according to claim 16, wherein the detector has a reading device for reading the identification. The bending sensor according to claim 1, wherein the RFID transponder uses a data line that already exists for the measurement data transfer as an antenna. Fix the bending sensor to the human or animal body,
Detects the bending parameters of the bending sensor, such as bending angle, bending speed and bending acceleration;
In a method for detecting a functional parameter for characterizing a motion course characteristic in a human or animal body, comprising determining body movement based on the detected bending parameter,
An extensible fixing element for fixing the bending sensor is provided, wherein the fixing element has an extensible hollow space for receiving a measurement detector of a detector, and the measurement detector Fixing to a reference point of the fixing element in the hollow space. 21. The method of claim 20, wherein the position of the bending sensor is detected using a spatial position sensor, wherein a position relative to the earth's gravitational field or geomagnetism is detected. 22. A method according to claim 20 or 21, wherein the bending parameters are detected in a location-resolved manner by using a plurality of bending sensitive measuring zones (80) of the bending sensor to detect the bending parameters. The method according to any one of claims 20 to 22, wherein the bending parameter is detected in a time-resolved manner by detecting the bending parameter at a predetermined sampling frequency, for example, a sampling frequency of 100 Hz. The detected bending parameters may be a number of dynamic parameters such as bending angle as a function of time and / or location, bending speed as a function of time and / or location, bending acceleration as a function of time and / or location, 24. A method according to any one of claims 20 to 23, used to determine a Fourier transform of a function of bending angle, bending speed and / or bending acceleration. 25. A method according to claim 24, wherein a histogram is used to graphically display a frequency distribution of dynamic parameters, such as bending angle, bending speed or bending acceleration. 26. A method according to claim 24 or 25, wherein the frequency distribution of the spatial position of the bending sensor is displayed as a histogram or as a gray value in a coordinate system. 27. A method according to any one of claims 20 to 26, wherein the detected bending parameter is compared with an average bending parameter so that anomalies in the movement parameters are known. Simultaneously with the bending parameters, other parameters, such as pain parameters, posture parameters, activity parameters, are detected and a statistical correlation is formed between the bending parameters and the other parameters. The method of any one of these. 29. A method according to any one of claims 20 to 28, wherein the detection of bending parameters of the bending sensor is performed for at least 24 hours in order to enable long-term analysis. 30. A method according to any one of claims 20 to 29, wherein the detection of bending parameters is performed together with the therapy in order to establish a positive or negative correlation between the therapy measures and the detected bending parameters.

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