Listening to ultrasound from plants reveals xylem vessel anatomy


 Plants emit ultrasound pulses under drought stress, which originate in their water-carrying xylem vessels, and can be recorded externally. We demonstrate that these ultrasound pulses consist of superposed damped oscillations at plant-specific frequencies in the range of 10 – 150 kHz, that are correlated to xylem dimensions. We present a method to relate geometrical and viscoelastic properties of xylem vessels with the time- and frequency-domain characteristics of the observed oscillations. We apply the method to ultrasound pulses from drying shoots of three vascular dicot plant species. The extracted parameters are validated with destructive measurements of xylem vessel radii, wall thickness, length of xylem vessel elements, and the elastic modulus of the vascular bundle by optical and scanning cryo-electron microscopy and tensile loading. Our method demonstrates the potential for non-invasive and continuous monitoring of plant vascular anatomy. We foresee applications in high-throughput phenotyping and early detection of vascular wilt diseases.

amplitudes. We observed that the time-domain waveforms of these pulses resembled damped oscillations, both when 52 recorded along the axial and in the radial directions (Figs. 1c and 1d). The pulse amplitude in time-domain decayed 53 exponentially with a 1/e time constant τs: the settling time (Methods). For stem sample A, we extracted τs= 28.8 ± 6.4 μs 54 (mean ± s.d.), for the pulses recorded in the axial direction. The corresponding value of τs for the radially recorded pulses was 55 41.7 ± 12.4 μs, which was statistically similar. The τs for the many individually measured axial and radial sound pulses of all 56 the three stem samples A, B, and C are shown in Supplementary Figs. 1 -3, respectively. The determined settling times of 57 samples B and C agreed with those of sample A. All pulses died out within ~ 0.3 ms, in agreement with reported work 7 .

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Based on this observation, we hypothesize that the damped oscillations are generated by resonant vibrations within the xylem 59 vessels. In the following paragraphs, the settling times and characteristic frequencies of ultrasound pulse waveforms were 60 interpreted to estimate xylem vessel dimensions and elasticity (Fig. 1e).

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Xylem vessel radius. In order to explain the origin of the observed ultrasound waveforms and to use them to extract 62 information about the plant's microstructure, we develop a model relating the micromechanics of the xylem to the waveform 63 of the generated ultrasound. We hypothesize that the damped oscillations are identical to those of an organ pipe filled with 64 water 29 . The bubble formation excites axial standing waves in the sap (water), whose resonance frequencies depend on the 65 longitudinal speed of sound in the pipe veff, and the xylem vessel element length L (Methods). We modelled the xylem vessel 66 as a resonant cylindrical pipe containing a series network of vessel elements of length L, which are bounded by scalariform 67 perforation plates 3, 25 (Fig. 2a). The perforation plates serve as non-ideal (leaky) reflecting surfaces at the termination of a pulses, and also from optical micrographs of the stem samples (Figs. 2d, Supplementary Fig. 4 ). The mean (± s.d.) acoustic 76 R for sample A was 9.93±1.6 μm. Similar values were obtained for stem samples B and C (Supplementary Fig. 4) Using 77 optical micrographs of latex-paint stained transverse cross-sections of the stem sample A (Fig. 2b), we observed the vessel 78 radius R = 11.9 ± 2.6 μm ( Fig. 2d and Table 1). These values were confirmed with scanning electron cryo-microscopy ( Fig.   79   2c). Thus, the calculated R, using the ultrasound analysis, agrees with that observed by optical and scanning electron 80 microscopy.

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We further validated our method using other plant species, namely H. macrophylla and S. lycopersicum (Figs. 2e -2j). The

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Xylem vessel (element) length and Young's modulus. To estimate the length L of the xylem vessel element, we analysed 89 the frequencies in the ultrasound pulses. The resonance frequencies fL are integer multiples of the ratio veff / L (Methods). We 90 found that the Fourier spectra of representative ultrasound pulses (recorded axially) exhibited characteristic peak frequencies 91 (Fig. 3a). The peak frequency with the largest amplitude, fp(axial) for sample A was 34±5 kHz. In addition, peaks close to 92 integral multiples of fp(axial) were observed (Supplementary Table 1). Analysis of pulses from samples B and C showed 93 similar trends (Supplementary Fig. 5). Similar data were observed in the pulses recorded in the radial direction of the stem 94 samples (Fig. 3b, Supplementary Fig. 5, Supplementary Table 2).

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The resonance frequency fL was calculated from fp(axial) (equation (6); Methods). Note that the two values differ due to the 96 high damping (small τs) in the sound pulse. To extract L from the resonance frequencies, we need the vessel wall thickness h 97 and the Young's modulus of elasticity E (equation (9); Methods). We found h to be ~ 1 μm via scanning electron cryo-98 microscopy ( Fig. 2c, Methods). We determined E of stem segments cut from the same plant, and from shoots similar in age 99 and size. For this, we measured the stress-strain curves via uniaxial tensile loading (Fig. 3c, Methods). The mean mass 100 density per stem segment was also estimated from the measured weights and dimensions. The linear slope of the stress-strain 101 curve (Fig. 3c) at small values of strain (≈ 10 -4 ) yields the value of E, which was extracted to be 0.2 ± 0.1 GPa for fresh 102 (hydrated) stem samples (Fig. 3d). For dry stem samples, E > 0.6 GPa were obtained. We observed an overall decline in E 103 with increasing mass density. This indicates that the water-content dominates the variations in E. This agrees with an earlier 104 empirical model 21 , where the dependence of E on the relative water content in the xylem is taken into account.

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We calculated L using h ≈ 1 μm and E = 0.2±0.1 GPa (equation (9); Methods). The histogram of L was extracted from the 106 axially recorded ultrasound pulses for stem samples. For sample A, L was 0.99±0.08 mm under a unimodal Gaussian fit 107 (Fig. 3e). Similar values were obtained for samples B and C (Supplementary Fig. 5). This highlights the reproducibility of 108 our method and the similarity of the recorded ultrasound pulses in the axial direction.

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We validated the assumption that L represents the actual length of xylem vessel element. First, we extracted the mean xylem 110 vessel length (a vessel contains several vessel elements) using latex paint staining 27 , by counting the number of stained 111 vessels on transverse cross-sections of the stem (Methods). These counts decrease exponentially with the distance 30 from the 112 lower end of the stem at which the paint was taken up (Supplementary Fig. 6). The mean xylem vessel lengths were found 113 to be in the range ~ 12 -17 mm for the three stem samples. The xylem vessel length is thus much larger than the L extracted 114 from the ultrasound pulses (~ 1 mm, Fig. 3e). This is because the Latex paint cannot penetrate the fused ends, but can pass 115 through the perforation plates between adjacent vessel elements 30 . Next, we observed individual vessel elements in 116 longitudinal sections of stem samples using scanning electron cryo-microscopy (Fig. 3f). The observed length ranged from 117 0.5 to 0.9 mm for individual xylem vessel elements (Fig. 3g, Table 1). Thus L, as obtained from our acoustic model, is a  the radial direction, and was subsequently detected by the broad-band microphone (Fig. 4a). Figures 4b and 4c show the  Our results have shown how ultrasound emissions from drought-stressed plant stems can be used to extract and monitor the 134 geometry and viscoelasticity of xylem vessels. In this section, we first interpret our results further and discuss the 135 applicability of our method to monitor the vascular physiology of plants. We end the section by commenting on its potential 136 in non-invasive plant health monitoring.

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Xylem radius (R). We have shown that by modelling the xylem vessel as cylindrical acoustic resonator, the radius R can be 138 extracted from the settling time of the ultrasound pulse, resulting in comparable values as those obtained from common 139 microscopy techniques. Using Hydrangea and Solanum as example plant species with relatively narrow and wide vessel radii 140 respectively, we validated the dependency of τs on R. Optically determined xylem vessel radii were slightly bigger (~ 2 μm) 141 than the acoustically determined radii (Figs. 2d, 2i, 2j, Supplementary Fig. 4). We attribute this to the assumption of a 142 constant dynamic viscosity of xylem sap ηl. In practice, ηl depends on ambient temperature, and concentration of dissolved 143 nutrients 31 . Moreover, water close to the sap-wall interface is held with adhesive forces, and thus has a slightly higher 144 dynamic viscosity 32 . As a corollary to our analysis, if the distribution of R is known directly from optical microscopy, one 145 can evaluate the effective kinematic viscosity (ηl /ρl) of the xylem sap. Note that the solid walls of the xylem vessels also 146 possess shear or extensional viscosity 33 . This means that elastic forces arise in them as a response to elongation, compression 147 or shear stresses. Shear viscosity is a property of solids to resist a change in deformation (shear rate). This additional 148 viscosity likely sets an upper bound on τs and R, beyond which the agreement between optical and acoustic radii likely

Conclusions 208
We showed for the first time that the radius, length, and viscoelasticity of xylem vessel elements can be co-determined non-209 destructively and rapidly. This was achieved using a lumped mechanical model of the water-carrying xylem vessel. We

Methods 223
Plant material. Three potted plants of Hydrangea quercifolia were obtained from a commercial garden center and moved to the laboratory 224 within 1 hour. One shoot sample per plant was cut, keeping the leaves intact, and immediately placed in tap water (Supplementary Fig. 7) to 225 prevent embolism in the xylem vessels at the cut-end. From each shoot sample, a 60-70 mm long and trimmed (i.e., without leaves and 226 petioles) stem segment was cut under water to prevent air entry and blockage. The segments were roughly cylindrical, with a cross-section 227 diameter of ~ 5-6 mm, and were used for vessel staining and optical microscopy. The rest of the sample was left intact to measure ultrasound 228 emissions. Additionally, one plant each of Hydrangea macrophylla and Solanum lycopersicum, was also obtained for optical microscopy and 229 ultrasound recording.

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Recording ultrasound pulses and signal processing. The shoot samples were taken out of water, dried using tissue paper, and left on the 231 bench for air-drying, resulting in accelerated drought stress. A M500-USB ultrasound microphone, with a reliable detection window between 232 10 kHz and 150 kHz, from Pettersson Elektronik AB (Uppsala, Sweden) was placed first in the axial (~2 mm from the cut-face of stem 233 normal to the cross-section) and then in the radial (on the cylindrical surface of the stem) directions (Fig. 1a) to record the ultrasound bursts

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The lumped model is valid as long as the dimensions L and R are smaller than the acoustic wavelength (~ 1-10 cm in water).

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Noting that f d is the same as the observed f p(axial) in the ultrasound pulses, ζ is obtained by combining equations (5) and (6) as :

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Combining equations (1) and (2), the effective xylem length L was obtained as: Scanning electron (cryo-) microscopy. Transverse sections from hydrangea stems were made using a razorblade. The cross-section was left 275 on filter paper for 1-2 minutes to remove most of the adhering water. Thereafter, the section was fixed to a sample holder using Tissue-Tek.

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The sample was frozen by plunging the sample holder into liquid nitrogen. Subsequently the sample was transferred to a cryo-preparation

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An exponential relationship was observed 55 for the number of continuous xylem vessels at varying lengths of a stem segment. Typically, it is 303 observed that longer vessels are also wider 56 . The complex relationship between xylem radius and length in a plant is largely affected by a 304 trade-off between hydraulic conductance (increases with increasing R and decreasing L), and vulnerability to cavitation 57 (increases with 305 increasing R and L). Sperry et al. 55,58 reported that the xylem vessel length has the following probability distribution function: Where the most probable vessel length is given by λ -1 xylem , while the mean and standard deviation are respectively given by 2 λ -1 xylem , and

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Massachusetts, USA). For radial transmission, the same stem segment was mounted between the transducer and the microphone such that the 320 longitudinal axis of the stem was perpendicular to the line of flight of the sound pulse (Fig. 4a). The transducer was excited with a voltage 321 step of 5 V and an on-time of 500 ms. The Fourier transform of the detected ultrasound pulse was performed over a time span of the first 100 322 μs (Fig. 4d), to observe the frequency components present in the pulse that propagated only through the stem.

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Where Q is the volumetric flow rate and η l is the dynamic viscosity of the fluid (water).

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So, to prevent mechanical failure, p < p crit . Substituting the above expressions and re-arranging the terms, we obtain:

Data availability 336
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Ultrasound method
Destructive measurement      (Figs. 2e, 2f, 3a, and 3b). The resonant frequency is obtained from peak frequency and settling time (Methods, equation (6)). Using these, xylem radius and xylem vessel element length are extracted (Table 1). Parameters of sap viscosity, vessel wall-thickness and young's modulus are taken as input.

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