METHOD FOR DETERMINING PHYSICAL PARAMETERS OF VASCULAR TISSUE OF A PLANT

Abstract

The invention provides a method for determining a physical vessel parameter of a vascular tissue in a vascular plant (10), wherein the method comprises: a detection stage comprising detecting acoustic emission radiation (121) from the vascular plant (10) and providing an emission-related signal; and an analysis stage comprising determining the physical vessel parameter based on the emission-related signal, wherein the physical vessel parameter comprises an elasticity or a vessel dimension, and wherein the analysis stage comprises fitting at least part of the emission-related signal to a model of flexural modes of a cylindrical beam, and determining the physical vessel parameter based on the model.

Claims

1. A method for determining a physical vessel parameter of a vascular tissue (20) in a vascular plant (10), wherein the method comprises: a detection stage comprising detecting acoustic emission radiation (121) from the vascular plant (10) and providing an emission-related signal; and an analysis stage comprising determining the physical vessel parameter based on the emission-related signal, wherein the physical vessel parameter comprises an elasticity or a vessel dimension, and wherein the analysis stage comprises fitting at least part of the emission-related signal to a model of flexural modes of a cylindrical beam, and determining the physical vessel parameter based on the model.

2. The method according to claim 1, wherein the method comprises: an excitation stage comprising providing acoustic excitation radiation (111) to the vascular plant (10), wherein the acoustic excitation radiation (111) comprises radiation having a frequency selected from the range of 1-250 kHz.

3. The method according to claim 2, wherein the acoustic excitation radiation (111) comprises broadband radiation having one or more frequencies in the range of 10-150 kHz.

4. The method according to claim 2, wherein the excitation stage comprises providing the acoustic excitation radiation (111) via a pulse, wherein the pulse has a pulse duration that is larger than a characteristic settling time due to damping of the vascular tissue (20).

5. The method according to claim 2, wherein the excitation stage comprises providing the acoustic excitation radiation (111) via a pulse, wherein the pulse has a pulse duration smaller than a time-of-flight of the acoustic excitation radiation through the vascular tissue (20).

6. The method according to claim 2, wherein one or more applies of: the excitation stage comprises an excitation frequency sweep from a first frequency to a second frequency; and the detection stage comprises an emission frequency sweep from the first frequency to the second frequency; wherein the first frequency and the second frequency are selected from the range of 1-250 kHz.

7. The method according to claim 1, wherein the vascular tissue (20) is a xylem tissue in a plant stem (11) or in a plant branch (12).

8. The method according to claim 1, wherein the vascular tissue (20) has a longitudinal axis (A), and wherein the detection stage comprises detecting: acoustic emission radiation (121) from the vascular plant (10) at a first location arranged axially with respect to the longitudinal axis (A); and/or acoustic emission radiation (121) from the vascular plant (10) at a second location arranged perpendicular with respect to the longitudinal axis (A).

9. The method according to claim 1, wherein the analysis stage comprises fitting an exponential decay curve to at least part of the emission-related signal and determining a decay parameter, wherein the physical vessel parameter is determined based on the decay parameter, wherein the physical vessel parameter comprises one or more of a xylem vessel radius, a sap viscosity, and a xylem viscoelasticity.

10. The method according to claim 1, wherein the analysis stage comprises determining one or more peaks in at least part of the emission-related signal in the frequency domain, wherein the physical vessel parameter is determined based on the one or more peaks, and wherein the physical vessel parameter comprises one or more of a xylem vessel element length, and a Young's modulus.

11. The method according to claim 1, wherein the method further comprises controlling a plant cultivation condition based on the physical vessel parameter, wherein the plant cultivation condition is selected from the group comprising a watering regime, a lighting regime, and a nutrient regime.

12. The method according to claim 1, wherein the method comprises determining the physical vessel parameter for a plurality of vascular plants (10), wherein the method comprises selecting one or more vascular plants (10) of the plurality of vascular plants (10) for breeding based on the physical vessel parameters.

13. A system (1000) for determining a physical vessel parameter of a vascular tissue (20) in a vascular plant (10), wherein the system (100) comprises an acoustic radiation device (100) and a control system (300), wherein the system (1000) has an operational mode, wherein the operational mode comprises: a detection stage comprising the acoustic radiation device (100) detecting acoustic emission radiation (121) from the vascular plant (10) and providing an emission-related signal to the control system (300); and an analysis stage comprising the control system (300) determining the physical vessel parameter based on the emission-related signal, wherein the physical vessel parameter comprises an elasticity or a vessel dimension, and the control system (300) fitting at least part of the emission-related signal to a model of flexural modes of a cylindrical beam, and determining the physical vessel parameter based on the model.

14. The system (1000) according to claim 13, wherein the operational mode further comprises: an excitation stage comprising the acoustic radiation device (100) providing acoustic excitation radiation (111) to the vascular plant (10), wherein the acoustic excitation radiation comprises radiation having a frequency selected from the range of 1-250 kHz.

15. The system (1000) according to claim 14, wherein the system (1000) comprises a stem mount (1100) configured for attaching the acoustic radiation device (100) to a plant stem (11) of the vascular plant (10), wherein the operational mode comprises providing acoustic excitation radiation to the plant stem (11) and detecting acoustic emission radiation from the plant stem (11).

16. The system (1000) according to claim 14, wherein the excitation stage comprises the acoustic radiation device (100) providing the acoustic excitation radiation (111) via a pulse, wherein one or more applies of: the pulse has a pulse duration that is larger than a characteristic settling time of the vascular tissue (20); and the pulse has a pulse duration smaller than a time-of-flight of the acoustic excitation radiation through the vascular tissue (20).

17. The system (1000) according to claim 14, wherein the acoustic excitation radiation comprises broadband radiation having one or more frequencies in the range of 10-150 kHz.

18. The system (1000) according to claim 14, wherein: the excitation stage comprises the acoustic radiation device (100) providing an excitation frequency sweep from a first frequency to a second frequency; and the detection stage comprises the acoustic radiation device (100) providing an emission frequency sweep from the first frequency to the second frequency; wherein the first frequency and the second frequency are selected from the range of 1-250 kHz.

19. The system (1000) according to claim 13, wherein the vascular tissue (20) has a longitudinal axis (A), and wherein the system (1000) further comprises a measurement site (1010) configured for hosting the vascular plant (10), wherein: the acoustic radiation device (100) comprises an axial radiation detection device radiation detection device (120a) arranged at a first location arranged axially along the longitudinal axis (A); and/or the acoustic radiation device (100) comprises a radial radiation detection device (120b) arranged at a second location arranged perpendicular to the longitudinal axis (A).

20. The system (1000) according to claim 13, wherein the analysis stage comprises one or more of: the control system (300) fitting an exponential decay curve to at least part of the emission-related signal and determining a decay parameter, wherein the physical vessel parameter is determined based on the decay parameter, wherein the physical vessel parameter comprises one or more of a xylem vessel radius, a sap viscosity, and a xylem viscoelasticity; and the control system (300) determining one or more peaks in at least part of the emission-related signal in the frequency domain, wherein the physical vessel parameter is determined based on the one or more peaks, and wherein the physical vessel parameter comprises one or more of a xylem vessel element length, and a Young's modulus.

21. The system (1000) according to claim 13, wherein the operational mode comprises an execution stage, wherein the execution stage comprises the control system controlling a plant cultivation condition based on the physical vessel parameter, wherein the plant cultivation condition is selected from the group comprising a watering regime, a lighting regime, and a nutrient regime.

22. A use of acoustic emission radiation (121) from a vascular plant (10) emitted by the vascular plant (10) for determining a physical vessel parameter of a vascular tissue (20) in the vascular plant (10), wherein the physical vessel parameter comprises an elasticity or a vessel dimension.

23. The use according to claim 22, wherein the acoustic emission radiation (121) has a frequency selected from the range of 1-250 kHz.

24. The use according to claim 22, wherein the acoustic emission radiation (121) is naturally emitted by the vascular plant (10).

25. The use according to claim 22, wherein the vascular plant (10) is in a stressed condition.

26. The use according to claim 22, wherein the vascular plant (10) is in a stressed conditions as a result of drought.

27. The use according to claim 22, wherein the use comprises detecting the acoustic emission radiation using a acoustic radiation device (100).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

[0116] FIG. 1 schematically depicts embodiments of the method and the system of the invention.

[0117] FIG. 2 schematically depicts an a vascular tissue and a resonating beam model representation thereof.

[0118] FIG. 3A-E schematically depict experimental data obtained using the method of the invention. The schematic drawings are not necessarily on scale.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0119] FIG. 1 schematically depicts the method and the system 1000 of the invention.

[0120] In particular, FIG. 1 schematically depicts the method for determining a physical vessel parameter of a vascular tissue 20 in a vascular plant 10. The method may comprise an excitation stage, a detection stage and/or an analysis stage.

[0121] The excitation stage may comprise providing acoustic excitation radiation 111 to the vascular plant 10, especially wherein the acoustic excitation radiation 111 comprises radiation having a frequency matching a resonance frequency of the vascular tissue 20, especially of a xylem tissue. In embodiments, the acoustic excitation radiation 111 may comprise radiation having a frequency selected from the range of 1-250 kHz.

[0122] The detection stage may comprise (resonance) acoustic emission radiation 121 from the vascular plant 10, especially from the vascular tissue 20. The detection stage may further comprise providing an emission-related signal.

[0123] The analysis stage may comprise determining the physical vessel parameter based on the emission-related signal, especially wherein the physical vessel parameter comprises a viscosity, an elasticity or a vessel dimension (of the vascular tissue 20), especially an elasticity or a vessel dimension.

[0124] In embodiments, the vascular tissue 20 may be a xylem tissue in a plant stem 11, in a plant branch 12, or in a plant root 13.

[0125] The vascular tissue 20 may have a longitudinal axis A. In particular, the longitudinal axis A may be parallel to a longitudinal axis of the plant stem 11. In the depicted embodiment, the detection stage comprises: acoustic emission radiation 121 from the vascular plant 10 at a first location arranged axially with respect to the longitudinal axis A; and acoustic emission radiation 121 from the vascular plant at a second location arranged perpendicular with respect to the longitudinal axis A.

[0126] In further embodiments, one or more applies of: the excitation stage comprising an excitation frequency sweep from a first frequency to a second frequency; and the detection stage comprising an emission frequency sweep from the first frequency to the second frequency; Especially wherein the first frequency and the second frequency are selected from the range of 1-250 kHz.

[0127] In further embodiments, the method may comprise determining the physical vessel parameter for a plurality of vascular plants 10, wherein the method comprises selecting one or more vascular plants 10 of the plurality of vascular plants 10 for breeding based on the physical vessel parameters.

[0128] FIG. 1 further schematically depicts a system 1000 for determining a physical vessel parameter of a vascular tissue 20 in a vascular plant 10, wherein the system 100 comprises an acoustic radiation device 100 and a control system 300. The acoustic radiation device may especially comprise one or more of a radiation generation device 110 and a radiation detection device 120, especially an ultrasound generator and an ultrasound sensor. The system 1000, especially the control system 300, may have an operational mode. The operational mode may especially comprise one or more of an excitation stage, a detection stage and an analysis stage.

[0129] In the excitation stage, the radiation generation device 110 may be configured to provide acoustic excitation radiation 111 to the vascular plant 10, especially to the vascular tissue 20. Hence, the excitation stage may comprise the acoustic radiation device 100, especially the radiation generation device 110, providing acoustic excitation radiation 111 to the vascular plant 10, especially to the vascular tissue 20. The acoustic excitation radiation 111 may comprise radiation having a frequency matching a resonance frequency of the vascular tissue 20, especially of a xylem tissue. In particular, the acoustic excitation radiation 111 may comprise radiation having a frequency selected from the range of 1-250 kHz.

[0130] In the detection stage, the radiation detection device 120 may be configured to detect (resonance) acoustic emission radiation 121 from the vascular plant, especially from the vascular tissue 20, and to provide an emission-related signal to the control system 300. Hence, the detection stage may comprise the acoustic radiation device 100, especially the radiation detection device 120, detecting (resonance) acoustic emission radiation 121 from the vascular plant 10 and providing an emission-related signal to the control system 300.

[0131] In the analysis stage, the control system may be configured to determine the physical vessel parameter based on the emission-related signal, wherein the physical vessel parameter comprises an elasticity or a vessel dimension. Hence, the analysis stage may comprise the control system 300 determining the physical vessel parameter based on the emission-related signal, wherein the physical vessel parameter comprises an elasticity or a vessel dimension.

[0132] In the depicted embodiment, the acoustic radiation device 100 is physically coupled to the control system 300. In further embodiments, the acoustic radiation device 100 may comprise a transmitter, wherein the transmitter is configured to (wirelessly) provide the emission-related signal to the control system 300.

[0133] In embodiments, the system 1000 may comprise a stem mount 1100 configured for attaching the acoustic radiation device 100, especially the radiation generation device 110, or especially the radiation detection device 120, to a plant stem 11 of the vascular plant 10. In such embodiments, the operational mode may comprise providing acoustic excitation radiation 111 to the plant stem 11 and detecting acoustic emission radiation from the plant stem 11. In the depicted embodiment, the system 1000 comprises a stem mount 1100 configured for attaching the radiation generating device 110 to the plant stem 11.

[0134] The vascular tissue 20, especially the xylem tissue, may have a longitudinal axis A, which may, for example, be parallel to a longitudinal axis of the plant stem 11 (or the plant branch 12). In embodiments, the acoustic radiation device 100 may comprise an axial radiation detection device 120,120a and/or a radial radiation detection device 120,120b, especially an axial radiation detection device 120,120a, or especially a radial radiation detection device 120,120b. In such embodiments, in the operational mode: the axial radiation detection device 120,120a may be arranged at a first location arranged axially along the longitudinal axis A; and/or the radial radiation detection device 120,120b may be arranged at a second location arranged perpendicular to the longitudinal axis A.

[0135] In embodiments, the system 1000 may further comprise a measurement site 1010 configured for hosting the vascular plant 10, wherein: the acoustic radiation device 100 comprises an axial radiation detection device 120,120a arranged at a first location (in the measurement site 1010) arranged axially along the longitudinal axis A (of the hosted vascular plant 10); and/or the acoustic radiation device 100 comprises a radial radiation detection device 120,120b arranged at a second location arranged perpendicular to the longitudinal axis A (of the hosted vascular plant 10).

[0136] FIG. 2 schematically depicts a vascular tissue 20, especially a xylem tissue, and a resonating beam model representation 25 thereof. The vascular tissue 20 may comprise a plurality of vascular tissue elements 21, especially xylem vessel elements, separated by perforation plates 22. Hence, a xylem vessel element may be defined by (the presence of) perforation plates 22 at each end. The xylem vessel elements may define the resonating unit for the ultrasound. The vascular tissue 20, especially the vascular tissue element 21 may have a radius R. Further, the vascular tissue element 21, especially the xylem vessel element, may have a length L, especially a xylem vessel length L. The vascular tissue 20 may further comprise a vascular tissue wall 23, wherein the vascular tissue wall 23 may have a wall thickness h, especially a xylem wall thickness h.

[0137] In embodiments, the analysis stage may comprise fitting at least part of the emission-related signal to a model of flexural modes of a cylindrical beam, and determining the physical vessel parameter (at least partially) based on the model. The dashed lines in FIG. 2 schematically depict the instantaneous shape of a vibrating beam.

[0138] Experiments

[0139] Experiments were performed based on naturally emitted ultrasound radiation by plants. In particular, during water-shortage in the roots and/or heavy transpiration, a water column in the xylem may be subjected to a large tensile stress. Beyond a critical tension, water may exist in a metastable state for a short time, which may lead to local cavitation. The stress may be released via gas-bubble nucleation. Apart from cavitation, bubble formation inside the xylem can occur through “air-seeding”, due to a pressure difference across the air-water meniscus at pores on xylem cell walls. The process of bubble formation may result in a release of the elastic energy stored in the water column, a part of which may be converted to acoustic emission radiation. In particular, peak frequencies may be observed across a multitude of (ultra-)sound pulses in the range 1-250 kHz, especially in the range of 10-150 kHz, which may be much lower than the theoretical resonant bubble frequencies. Hence, experiments were performed to determine whether this acoustic emission radiation is indicative of physical vessel parameters, especially a physical vessel parameter of a xylem tissue. The physical vessel parameter was also determined using prior art methods as comparative examples.

[0140] Hence, a vascular plant 10 may (spontaneously) emit acoustic emission radiation 121, especially from the vascular tissue 20, which may be indicative of a physical vessel parameter. However, in embodiments, the method may especially comprise providing acoustic excitation radiation 111 to the vascular plant 10, which may then subsequently provide the acoustic emission radiation 121.

[0141] Methods

[0142] Sample collection. Three potted biological replicates of Hydrangea quercifolia L. were obtained from “Intratuin” garden center (outdoor) in Elst, the Netherlands (51.913o N, 5.87o E) on 19 Nov. 2019 at 0930 hrs, and moved to the indoor laboratory environment by 1030 hrs on the same day at the Wageningen University and Research. Three leafy shoot samples labelled A, B, and C, one from each potted plant, were cut keeping the leaves intact and immediately kept in tap water to prevent embolism in the xylem vessels at the cut-end. From each sample, a 60-70 mm long trimmed (without leaf-petioles) stem segment was cut inside water to reduce, especially prevent, air entry and blockage. The segments were approximately cylindrical with a cross-sectional diameter of ˜5-6 mm.

[0143] Recording ultrasound emission. The leafy shoot samples A, B and C were then taken out of water, the excess water wiped from the stem-surface using tissue paper, and left on the bench for air-drying. resulting in an accelerated drought stress. A M500-USB ultrasound microphone (with a reliable sensitivity window between 10 kHz and 150 kHz) from Pettersson was placed first in the axial (˜2 mm from the cut-face of stem normal to the cross-section) and then in the radial (on the cylindrical surface of the stem) directions to record acoustic emission radiation at a sampling rate of 500 kHz in continuous time windows of 120 seconds. The frequency spectra of the measured signals were obtained via a 250-point Discrete Fourier Transform, spanning a time frame of 1.5 ms.

[0144] Comparative example—latex-paint infusion technique as described in Chatelet et al., “Xylem Structure and Connectivity in Grapevine (Vitis vinifera) Shoots Provides a Passive Mechanism for the Spread of Bacteria in Grape Plants”, Annals of Botany, 2006, which is hereby herein incorporated by reference. The stem segments were mounted vertically over a glass container filled with degassed latex-paint solution, with one end immersed in the paint and the other end tightly inserted into a plastic tube connected to a suction pump that applies a pressure difference of 400 mbar. The stem-tube junction was taped and smeared with Vaseline to prevent air leakage. As the pump sucked the solution through the stem for a duration of 12 hours, the paint filled up and remained confined in one xylem vessel while the clear water was conducted through the entire stem (via the bordering pits between adjacent xylem vessels) and emerged out in the tube. Subsequently, the stem samples were sliced with a blade at intervals of 5 mm. The number of painted vessels were then counted on each face of the cut slices from images captured by a VHX digital microscope from Keyence.

[0145] Comparative example—Scanning electron cryo-microscopy (cryo-SEM) of xylem wall and vessel elements. Transverse and longitudinal cross-sections of randomly chosen hydrangea stem segments were made using a razorblade. The cross-sections were left on filter paper for 1-2 minutes to remove most of the adhering water. After that the sections were fixed to a sample holder using Tissue-Tek. The samples were frozen by plunging the sample holder into liquid nitrogen. Subsequently the samples were transferred to a cryo-preparation chamber (Leica) under vacuum where it was kept at −90° C. for 3 minutes to remove ice from the surface (freeze etching to remove water vapor contamination). Still under vacuum the samples were coated with 12 nm of tungsten and transferred using a VCT100 shuttle (Leica) to a field emission scanning electron microscope (Magellan 400 from FEI). The samples were analyzed at 2 kV, 13 pA at −120° C. The physical thickness of the xylem cell walls was observed to be ˜1 The length of individual xylem vessel elements were observed to be between 0.6 mm and 1 mm.

[0146] Comparative example—uniaxial tensile loading for elastic modulus determination. Multiple stem segments of lengths in the range of 4-7 cm were cut and mounted vertically between two clamps of a Zwick/Roell Z005 tensile testing machine. The initial pre-strained length is equal to the vertical separation between the clamps and was kept as 20 mm. The uniaxial stress is calculated as the tensile force applied by the equipment divided by the average cross-section area of the stem segment, and the longitudinal strain is calculated as the change in stem length per unit initial length. The Young's modulus E is then extracted as the slope of the linear part of the stress-strain curve at small values of strain (about 10.sup.−4). The average mass density of each sample was also calculated from measured weight and volume just before the tensile loading procedure. The weights were measured with a Scaltec SBC 33 precision balance, while the dimensions were measured with a Vernier Caliper with a resolution of 0.1 mm.

[0147] Measurements

[0148] Ultrasound measurements. Freshly cut and hydrated stem samples were placed on a bench to induce accelerated drought stress at room temperature during daytime. Ultrasound pulses were measured with a broadband ultrasound microphone placed at a first location arranged axially with respect to a longitudinal axis A of the plant stem 11, and at a second location arranged perpendicular with respect to the longitudinal axis A of the plant stem 11. FIG. 3A depicts ultrasound emissions recorded at the first location and starting after 5 minutes into the drying process in amplitude A (in a.u.) versus time T (in seconds).

[0149] FIG. 3B and FIG. 3D schematically depict representative time-domain waveforms of single pulses for sample C in pulse amplitude A (in a.u.) over time T (in seconds) at the first location (FIG. 3B) and at the second location (FIG. 3D). FIGS. 3C and 3E schematically depict corresponding frequency domain spectra in pulse amplitude A (in dB) versus frequency f (in kHz) (obtained via a Fourier transformation of the pulse in time domain), wherein the 0 dB line refers to an amplitude of 1 in the time domain.

[0150] FIG. 3B depicts observations obtained at the first location. Specifically, FIG. 3B depicts line L.sub.1 representing a pulse starting at T=33.7263 s, and a corresponding fit envelope F.sub.1. The envelope of the pulse amplitude in time-domain decays exponentially with a 1/e time constant τ.sub.s, wherein τ.sub.s specifically refers to an acoustic emission radiation settling time. The (acoustic emission radiation) settling time τ.sub.s of the pulse can be obtained by fitting an exponential function to the fit envelope according to the formula

A(t)=A.sub.0*e.sup.−T/τ.sup.s

[0151] wherein A.sub.0 is the amplitude at the peak of the pulse (here at about T=0.3 s).

[0152] FIG. 3C schematically depicts frequency spectra corresponding to exemplary pulses measured at the first location. Specifically, line L.sub.2 corresponds to a pulse starting at T=19.5648 s and line L.sub.3 corresponds to a pulse starting at T=33.7263 s. The arrows indicate (broad) peaks that were used to determine physical vessel parameters (see below).

[0153] FIG. 3D depicts observations obtained at the second location. Specifically, FIG. 3D depicts line L.sub.4 representing a pulse starting at T=72.5614 s, and a corresponding fit envelope F.sub.2.

[0154] FIG. 3E schematically depicts frequency spectra corresponding to exemplary pulses measured at the second location. Specifically, line L.sub.5 corresponds to a pulse starting at T=48.4442 s and line L.sub.6 corresponds to a pulse starting at T=99.1434 s. The arrows indicate (broad) peaks that were used to determine physical vessel parameters (see below).

[0155] Based on the experimental measurements, the most probable τ.sub.s=19.1 μs, 20.9 μs, and 20 μs, for samples A, B, and C, respectively, for the pulses in the axial direction (measured at the first location). The corresponding values τ.sub.s for the radial direction (measured at the second location) were 33.8 μs, 14.1 μs, and 21 μs.

[0156] The most probable peak frequency f.sub.p (axial) with the largest amplitude in the sound pulses recorded axially from sample A, B, and C were found to be 36.5±4 kHz, 32.7±5 kHz, and 42.3±8.5 kHz respectively. In addition, peaks close to integral multiples of f.sub.p (axial) are observed as shown in FIG. 3C. The observed and calculated frequencies for the first location are summarized in table 1 below:

TABLE-US-00001 Sample A Sample B Sample C Mode Observed Calculated Observed Calculated Observed Calculated m [kHz] [kHz] [kHz] [kHz] [kHz] [kHz] 1 30-40 35 32-38 36 40-50 46 2 60-70 70 68-72 72 90-110 92 3 100-120 105 96-115 108 140-150 138 4 135-140 140 128-145 144 Below — noise floor

[0157] In table 1, the observed values refer to experimental measurements, whereas the calculated values are obtained by assuming that the observed frequency in the 30-50 kHz range corresponds to m=1, i.e., assuming that the smallest observed frequencies correspond to a mode order of 1.

[0158] Hence, as the observed values lie close to the calculated values, the resonance frequencies may be accurately determined from the acoustic emission radiation measured at the first location.

[0159] A similar behavior was observed in the frequency spectra of the radially recorded ultrasound pulses (see FIG. 3E), with the lowest characteristic peak frequency in the range 15-20 kHz present in all the three samples. In addition, characteristic frequencies corresponding to higher order resonances were observed mostly in the following intervals: 30-40 kHz, 55-70 kHz, 84-92 kHz, and 110-140 kHz. The observed and calculated frequencies for the second location are summarized in table 2 below:

TABLE-US-00002 Sample A Sample B Sample C Mode Observed Calculated Observed Calculated Observed Calculated n k.sub.T [kHz] [kHz] [kHz] [kHz] [kHz] [kHz] 1 4.73 — 5.4-7.25 — 8 — 5.4-6.5 2 7.8532 15-20 15-20 18-24 22 15-18 15-18 3 10.996 30-40 29.4-39.2 32-46 43.1 30-35 29.4-35.2 4 14.137 55-70 48.6-64.8 63-75 71.24 48-52 48.7-58.3 5 17.137 84-92 72.6-96.8 90-110 106.4 90-100 72.8-87.2 6 20.42 110-120 101.4-135.2 126-142 148.63 110-135 101.6-121.8

[0160] In table 2, the observed values refer to experimental measurements, whereas the calculated values are obtained by assuming that the observed frequency in the 15-24 kHz range corresponds to n=2, i.e., assuming that the smallest observed frequencies correspond to a mode order of 2.

[0161] Hence, similarly as for the measurements at the first location, the resonance frequencies may also be accurately determined from the acoustic emission radiation measured at the second location.

[0162] The acoustic emission radiation observed at the first location was interpreted by modelling the xylem vessel as a cylindrical pipe of effective length L sustaining longitudinal standing waves in the water whose resonance frequencies depend on the mode order m, and the longitudinal speed of sound in the pipe v.sub.eff. These sound waves (expected to be dominant in the axially recorded ultrasound) will undergo damping primarily due to the dynamic viscosity η.sub.l in the xylem. The damped oscillations can be described by a 2.sup.nd order linear resonator where the damping ratio ζ is a function of the acoustic inductance, resistance and capacitance of the system. From the observed f.sub.p(axial) and τ.sub.s, ζ is obtained as

[00006] $ζ = \frac{1}{\sqrt{1 + {(f_{p (axial)} . τ_{s})}^{2}}}$

[0163] and the effective acoustic xylem radius R is obtained as:

[00007] $R = \sqrt{\frac{4. η_{l} . τ_{s}}{ρ_{l}}}$

[0164] where ρl is the mass density of sap (water). Note that in this model, R can calculated independently of the length L, from the settling time of the measured time-domain acoustic signal.

[0165] The resonance frequency f.sub.L can be calculated from f.sub.p (axial) and ζ using:

f.sub.p=f.sub.L√{square root over (1−ζ.sup.2)}

[0166] The effective xylem length L, especially the length L of a xylem vessel element 21 can be expressed as:

[00008] $\frac{1}{L^{2}} = \frac{4 f_{L}^{2}}{m^{2} v_{eff}^{2}} = \frac{4 f_{L}^{2}}{m^{2}} [\frac{1}{v_{l}^{2}} + \frac{2 ρ_{l} R}{h} . (\frac{1}{E})]$

[0167] Where vi is the speed of sound in bulk water (≈1485 m/s at 20° C.), E is the elastic modulus of the xylem wall and h is the effective wall thickness (a fit parameter).

[0168] Hence, in embodiments, the method, especially the analysis stage, may comprise fitting an exponential decay curve to at least part of the emission-related signal (in the time domain) and determining a decay parameter, wherein the physical vessel parameter is determined based on the decay parameter, especially wherein the physical vessel parameter comprises one or more of a xylem vessel radius R, a sap viscosity, and a xylem viscoelasticity.

[0169] In further embodiments, the method, especially the analysis stage, may comprise determining one or more peaks in at least part of the emission-related signal in the frequency domain, wherein the physical vessel parameter is determined based on the one or more peaks, and wherein the physical vessel parameter comprises one or more of a xylem vessel element length L, and a Young's modulus E.

[0170] In embodiments, the method, especially the analysis stage, may comprise fitting at least part of the emission-related signal to a model of flexural modes of a cylindrical beam, and determining the physical vessel parameter based on the model. In particular, the acoustic emission radiation observed at the second location was analyzed with a model of flexural modes of a cylindrical beam surrounded by a viscoelastic material. A good match for the set of frequencies was obtained if the 2nd order mode is assigned to the frequency range 15-20 kHz for all the samples. Essentially, the xylem vessels are modelled as a viscoelastic cylindrical beam: a cell wall—water composite with an effective mass density ρ.sub.xylem. Freshly cut stem segments, collected from the same plant 10 and similar to the ones used for sound recording and paint infusion, were used to measure a mean mass density of ≈1300±300 kg.Math.m.sup.−3 which in turn provides a close estimate of ρ.sub.xylem. Using the beam model, this may result in:

[00009] $\frac{1}{L^{2}} = \frac{(4 π f_{T} \sqrt{ρ_{xylem}})}{k_{T}^{2} R} . (\frac{1}{\sqrt{E}})$

[0171] Where f.sub.T is the resonance frequency of transverse vibrations and k.sub.T is the mode constant. In combination with the equations above, this provides:

[00010] $E = {[\frac{4 ρ_{l} R^{2} k_{T}^{2} f_{L}^{2} v_{l}}{(m^{2} π {hf}_{T} ρ_{sylem}^{\frac{1}{2}} v_{l}) + \sqrt{m^{4} π^{2} h^{2} f_{T}^{2} ρ_{xylem} v_{l}^{2} - 8 h ρ_{l} R^{3} k_{T}^{4} f_{L}^{4}}}]}^{2}$

[0172] The time-domain damping in the radially recorded ultrasound may be dominated by the viscosity (η.sub.solid) in the solid matter comprising the cell wall, xylem fibres, cambium and other vascular tissues. Such a system may be modeled as a linear Maxwell material and η.sub.solid may be obtained from the 1/e settling time τ.sub.s of the pulse amplitude as:

[00011] $τ_{s} = \frac{η_{solid}}{E}$

[0173] Various physical vessel parameters were determined using the method of the invention—using above-mentioned equations—as well as using comparative (destructive) methods. The determined values are summarized in table 3 below:

TABLE-US-00003 Based on acoustic Parameter emission radiation Comparative method R [μm] 9.89 ± 1.6 9-18 Optical microscopy; scanning electron microscopy Xylem vessel 1.08 ± 0.18 6.38-8.45 Scanning electron element length L microscopy [μm] E [GPa] 0.4 ± 0.1 0.6-1.0 Uniaxial tensile loading η.sub.solid [kPa .Math. s] 10.8 ± 2.3 — — h [μm] 0.8 1.0 Scanning electron microscopy

[0174] Hence, the parameters may be accurately determined using non-destructive observations of acoustic emission radiation.

[0175] In particular, the experiments may demonstrate the use of acoustic emission radiation from a vascular plant emitted by the vascular plant for determining a physical vessel parameter of a vascular tissue in the vascular plant.

[0176] The term “plurality” refers to two or more. Furthermore, the terms “a plurality of” and “a number of” may be used interchangeably.

[0177] The terms “substantially” or “essentially” herein, and similar terms, will be understood by the person skilled in the art. The terms “substantially” or “essentially” may also include embodiments with “entirely”, “completely”, “all”, etc. Hence, in embodiments the adjective substantially or essentially may also be removed. Where applicable, the term “substantially” or the term “essentially” may also relate to 90% or higher, such as 95% or higher, especially 99% or higher, even more especially 99.5% or higher, including 100%. Moreover, the terms “about” and “approximately” may also relate to 90% or higher, such as 95% or higher, especially 99% or higher, even more especially 99.5% or higher, including 100%. For numerical values it is to be understood that the terms “substantially”, “essentially”, “about”, and “approximately” may also relate to the range of 90%-110%, such as 95%-105%, especially 99%-101% of the values(s) it refers to.

[0178] The term “comprise” includes also embodiments wherein the term “comprises” means “consists of”.

[0179] The term “and/or” especially relates to one or more of the items mentioned before and after “and/or”. For instance, a phrase “item 1 and/or item 2” and similar phrases may relate to one or more of item 1 and item 2. The term “comprising” may in an embodiment refer to “consisting of” but may in another embodiment also refer to “containing at least the defined species and optionally one or more other species”.

[0180] Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

[0181] The devices, apparatus, or systems may herein amongst others be described during operation. As will be clear to the person skilled in the art, the invention is not limited to methods of operation, or devices, apparatus, or systems in operation.

[0182] The term “further embodiment” and similar terms may refer to an embodiment comprising the features of the previously discussed embodiment, but may also refer to an alternative embodiment.

[0183] It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims.

[0184] In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim.

[0185] Use of the verb “to comprise” and its conjugations does not exclude the presence of elements or steps other than those stated in a claim. Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, “include”, “including”, “contain”, “containing” and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.

[0186] The article “a” or “an” preceding an element does not exclude the presence of a plurality of such elements.

[0187] The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In a device claim, or an apparatus claim, or a system claim, enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0188] The invention also provides a control system that may control the device, apparatus, or system, or that may execute the herein described method or process. Yet further, the invention also provides a computer program product, when running on a computer which is functionally coupled to or comprised by the device, apparatus, or system, controls one or more controllable elements of such device, apparatus, or system.

[0189] The invention further applies to a device, apparatus, or system comprising one or more of the characterizing features described in the description and/or shown in the attached drawings. The invention further pertains to a method or process comprising one or more of the characterizing features described in the description and/or shown in the attached drawings. Moreover, if a method or an embodiment of the method is described being executed in a device, apparatus, or system, it will be understood that the device, apparatus, or system is suitable for or configured for (executing) the method or the embodiment of the method respectively.

[0190] The various aspects discussed in this patent can be combined in order to provide additional advantages. Further, the person skilled in the art will understand that embodiments can be combined, and that also more than two embodiments can be combined. Furthermore, some of the features can form the basis for one or more divisional applications.

METHOD FOR DETERMINING PHYSICAL PARAMETERS OF VASCULAR TISSUE OF A PLANT

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Cpc classification

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G01N29/14

PHYSICS

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A01G7/00

HUMAN NECESSITIES

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G01N33/0098

PHYSICS

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A01G9/247

HUMAN NECESSITIES

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A01G9/249

HUMAN NECESSITIES

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A01G9/26

HUMAN NECESSITIES

International classification

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A01G9/26

HUMAN NECESSITIES

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G01N33/00

PHYSICS

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G01N29/14

PHYSICS

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A01G9/24

HUMAN NECESSITIES

Abstract

Claims

Description