Methods A small-scale MRI scanner and complementary imaging method to visualize and quantify xylem embolism formation

system was tested visualizing embolism formation in Fagus sylvatica during bench dehydration. High-quality images of water content and T 2 were readily obtained, which could be utilized to detect the cavitation of vessels smaller than could be spatially resolved. A multiplication of both map types yielded images in which ﬁlled xylem appeared with even greater contrast. (cid:1) T 2 imaging with small-scale MRI devices allows straightforward visualization of the spatial and temporal dynamics of embolism formation and the derivation of vulnerability curves.


Introduction
As a result of shifts in temperature and precipitation patterns, forests worldwide are expected to experience an increase in duration and frequency of drought and widespread forest dieback events (Dai, 2013;Park Williams et al., 2013;Trenberth et al., 2014). One of the main causes of drought-induced tree mortality is thought to be embolism formation, resulting in reduced xylem conductivity and, ultimately, hydraulic failure (McDowell et al., 2008;Choat et al., 2018). While there is a good basic understanding of, and a large body of literature on, xylem embolism formation, most of it is based on results obtained by means of invasive methods, applied to excised stem pieces. Only in recent decades have noninvasive imaging methods emerged that allow the spatially explicit visualization of the dynamics of xylem embolism formation and spread (Fukuda et al., 2015).
High-resolution computed tomography (HRCT) is currently the most used noninvasive method and is known for the excellent resolution that it affords (Choat et al., 2016). It has, for instance, been shown to be capable of fully resolving individual xylem vessels in three dimensions (3D; Brodersen et al., 2010Brodersen et al., , 2011Choat et al., 2016). However, an important drawback of HRCT is the use of ionizing radiation. It was found to damage living tissue (Savi et al., 2017) and cause growth inhibition (Dhondt et al., 2010) and disruption of cellular function (Petruzzellis et al., 2018). It is thus less suitable for long-term repeated observations or for investigations of recovery, even though current evidence suggests that xylem vulnerability per se, as it primarily depends on the integrity of the dead xylem structure rather than on its living cells and surroundings, is not easily affected by HRCT.
Magnetic resonance imaging (MRI, also known as nuclear magnetic resonance (NMR) imaging) is unusual in that it does not, in contrast to most other imaging or sensing methods, image the absorption of radiation in the visible or X-ray domain. Inside an magnetic resonance (MR) magnet, protons in water within a sample can be excited to emit a weak radio signal. The latter is achieved by means of radio frequency (RF) signals of an appropriate frequency and amplitude, neither damaging nor appreciably heating up the sample. MRI is thus well suited for continuous or long-term measurements. The technology has been used to image structure and anatomy (Robinson et al., 2000;Metzner et al., 2014;Hesse et al., 2018), plant water content (Schepper et al., 2012), and to measure phloem and xylem sap flow (K€ ockenberger et al., 1997;Scheenen et al., 2000;Windt et al., 2006). For detailed reviews and more examples see van As et al. (2009) and Borisjuk et al. (2012). In the scope of plant hydraulics, MRI has been used to study embolism formation Fukuda et al., 2015), refilling (Holbrook et al., 2001), hydraulic vulnerability segmentation (Hochberg et al., 2016) and the spread of disease in the xylem (Utsuzawa et al., 2005).
In the context of embolism formation, large high field stationary imagers based on superconducting or resistive magnets have been employed to study grapevine (Holbrook et al., 2001;Choat et al., 2010;Hochberg et al., 2017), woody lianas (Clearwater & Clark, 2003), maple (Zwieniecki et al., 2013) and various herbaceous species (such as the stem of cucumber by Scheenen et al. (2007), roots of maize by Ilja Kaufmann et al. (2009) and tomato pedicel by van de Wal et al. (2017)). However, despite their proven utility, large stationary MRI scanners that are suitable for imaging living plants are rare. The problem is not only the significant cost of such systems, but also the fact that most imagers have an unfavorable hardware configuration. The most limiting factors are: the inaccessibility of the magnet for intact plants (e.g. bore not wide enough, bore horizontal instead of vertical, isocenter not accessible for other reasons); the strength and accessibility of the imaging gradients (imaging gradients do not offer access or cannot be opened, maximum gradient strength too low for microimaging of small samples); or size and accessibility of the RF coil (coil too large relative to the sample to achieve a satisfactory signal-to-noise ratio, coil cannot be split to accept long samples such as stems). For these reasons, imaging plants has so far remained the domain of laboratories that have the technical knowhow to modify their equipment to match the geometry of the plant organ of interest and research question at hand.
Small-scale imagers based on permanent magnets have the potential to make MRI of plants much more affordable and can be tailored for use on plant stems (van As & van Duynhoven, 2013). C-shaped magnets (Umebayashi et al., 2011;Lechthaler et al., 2016) or ring-shaped Halbach magnets that can be opened from the side (Windt & Bl€ umler, 2015) may be especially well suited to image plants. Indeed, a number of such imagers have already been applied to study xylem embolism formation and pine wilt disease (Umebayashi et al., 2011;Fukuda et al., 2015;Ogasa et al., 2016;Umebayashi et al., 2016).
The technology to make small-scale imagers more broadly available thus seems within reach. However, so far, most smallscale MRI scanners still appear to be based on design principles from medical imaging. They employ strong and highly homogeneous magnets, relatively weak imaging gradients, and run singlespin echo (SSE) imaging sequences (i.e. a sequence of commands to operate an MRI scanner; see Fig. 1) with very long echo times. These specifications are optimal for applications on animals or humans, but will have drawbacks for applications on plants.
Highly homogeneous magnets have desirable traits: they allow imaging with narrow spectral widths, thus reducing external RF noise; they permit the use of weak imaging gradients, as a result of which gradients can be large and wide, and gradient amplifiers need only modest power; and they allow 3D and multi-slice imaging over large fields of view. However, they will also be wider, heavier and more costly, or have a smaller air gap than is optimal to allow access to plants. Further, their wide but slow gradients may limit the types of imaging sequences that they can run. SSE has been used by all small-scale MRI studies of plants to date, but in that application it has many drawbacks. Advantageous properties of SSE are that it is robust, does not require fast gradient switching and allows for easy implementation of multislice imaging: it is one of the most efficient ways to image a 3D volume with optimal signal to noise. However, in plant stems where 3D imaging is not needed, SSE mainly has drawbacks. In single slice mode it inefficiently samples the available NMR signal (Fig. 1). Furthermore, especially if acquired with long echo times, the resulting images will not only be weighted by water content, but also by tissue-dependent differences in signal relaxation (T 2 ). SSE images thus do not quantitatively reflect either of these two quantities, and for that reason, may be difficult to interpret.
We propose here that a multi-spin echo sequence (MSE) would be much better suited when imaging plants with smallscale MR imagers, in which field strength inherently limits signal-to-noise performance. Using MSE, the exponentially decaying signal is sampled many times per excitation (Fig. 1). This makes for efficient signal acquisition and enables quantitative proton density imaging, even when long repetition times are required to avoid signal loss as a result of saturation. An additional benefit is that MSE (at short echo times) is relatively insensitive to magnet inhomogeneity (Donker et al., 1997). In  Fig. 1 Comparison of a single-spin echo (SSE) (a) and multi-spin echo (MSE) (b) imaging pulse sequences. In both cases (SSE and MSE) the sample is excited by means of a 90°pulse, after which the signal decays according to the relaxation time T 2 , reflecting physicochemical sample characteristics such as proton mobility. In an SSE sequence the signal is refocused by means of a single radio frequency pulse (180°pulse), and acquired after a certain echo time (TE). In the SSE sequence this happens only once and TE is usually chosen to be very long. In the MSE sequence used here, the signal is refocused and acquired many times per excitation and TE is chosen to be as short as possible. S 0 is the amplitude of the signal immediately after excitation.

Research
New Phytologist the data analysis following MSE acquisition, a monoexponential fit of the decaying signal for every pixel in the image will yield quantitative parameter maps of proton density (i.e. water content) and the relaxation time of the signal (T 2 ). T 2 is highly correlated to water mobility and compartment size (van der Weerd et al., 2000) (also see Theory section). The T 2 relaxation time of water in wide lumina such as xylem vessels is much longer than that in the surrounding tissue, a property that can be measured even if the vessels themselves cannot be resolved Schepper et al., 2012;Robert et al., 2014). This may make T 2 a valuable parameter for monitoring the cavitation of vessels, even if they are smaller than the pixels.
In this study we demonstrate how a small-scale MRI scanner and complementary imaging method based on MSE can be used to visualize and quantify embolism formation. We constructed a magnet in which size, weight, robustness, pole gap width and accessibility for stems and branches was prioritized over sheer magnet homogeneity. The device was fitted with custom-built, plane parallel gradients that are open from the front, yet strong and fast enough to enable the use of MSE-type sequences, programmed on a small-scale spectrometer. Embolism formation was visualized and quantified using Fagus sylvatica (European beech) as a model species, a tree that is both drought-sensitive and of high economic relevance (Leuschner et al., 2006;Tomasella et al., 2019).

Theory: T 2 relaxation behavior in plants
Nuclear magnetic resonance relies on the fact that certain nuclei have a magnetic moment (spin). In plants the most abundant nucleus with spin is the proton (i.e. the nucleus of hydrogen 1 H). When placed in a strong homogeneous magnetic field, protons will orient themselves along with and opposite to the field direction. One of these two states will be slightly more populated, leading to a weak sample magnetization. After exciting the sample with an appropriate RF pulse, a signal can be detected as the protons induce a weak voltage in an RF coil placed around the sample (Schild, 1992;K€ ockenberger et al., 1997). Two types of signal relaxation can be distinguished: spin-lattice relaxation (T 1 ) and spin-spin relaxation (T 2 ) (Haacke et al., 1999). In the context of this study, only T 2 relaxation is of interest.
Spin-spin-relaxation describes the exponential decay of the amplitude of the signal (S) immediately after excitation (S 0 ), and is strongly correlated with proton mobility (Fig. 1). It reflects intra-and intermolecular proton-proton interactions that cause the signal (S) to decay exponentially as a function of time (t): Signal amplitude S 0 thus linearly and quantitatively correlates with proton density, and, after normalizing against a phantom of 100% water, can be used to quantify the amount of water (A) in a pixel in absolute or relative terms.
The T 2 relaxation time of watery solutions in confined compartments or pores is a function of their inherent T 2 relaxation time, and the probability that water molecules of the solution reach the compartment membrane or wall (Brownstein & Tarr, 1979). Protons that pass through membranes are likely to end up in narrow compartments with much smaller relaxation times (cytoplasm, cell wall, intracellular spaces) and thus more rapidly lose their magnetization, or may interact with the compartment wall directly and lose their magnetization in that manner (van As, 2007).
Imaging maize and pearl millet, van der Weerd et al. (2001) modeled and demonstrated this correlation in living plant tissue. They modeled T 2 relaxation (T 2,obs ) as a function of the T 2 of the bulk liquid (T 2,bulk ) and the surface to volume ratio S/V, the latter of which scales with the inverse of the compartment size: The rate of wall relaxation or sink strength density H has been found to vary as a function of membrane permeability (van der Weerd et al., 2000), but differences in compartment size typically dominate T 2 . In practice, cells with the largest vacuoles and conduits with the widest diameters give rise to the longest T 2 relaxation times, approximating the T 2 of the bulk liquid (up to 2 s for pure water), whereas narrow pores, conduits or small cells give rise to T 2 values that are much smaller (tens of milliseconds). Correlations between the wide xylem vessels and long T 2 values have been observed in poplar , cherry (Homan et al., 2007), oak (Schepper et al., 2012) and Avicennia marina (Robert et al., 2014).
In this study we test if the correlation between the relaxation time T 2 and compartment size can be utilized to detect waterfilled xylem conduits or, conversely, visualize their disappearance as a result of cavitation.

Plant material and experimental treatment
Two-to five-year-old European beech (Fagus sylvatica) saplings were purchased at a local nursery (Baumschule Veith, Merzenich, Germany) and grown in a glasshouse (16 h : 8 h, 20°C : 16°C, day : night), supplemental lighting provided by a set of metal halogen vapor lamps (SON-T Agro 250 W; Philips Lighting, Eindhoven, the Netherlands). They were watered every second day to capacity.
During the dehydration experiment the plants were continuously illuminated by a sodium vapor lamp (SON-T Agro 400W; Philips Lighting). Three polyethylene reference tubes (inner diameter 1 mm, Perfusor Line; Braun, Melsungen, Germany) were attached to every stem, filled with nickel nitrate-doped water (T 2 = 66, 165 and 296 ms). The MRI scanner was mounted around the stems of the intact trees at 110, 110 and 85 cm above the soil, for trees B1, B2 and B3, respectively. Stem diameters at the imaging slice were 10.2, 9.3 and 9.9 mm, respectively; the stem diameters at the base of the tree were 30.6, 22.3 and 34.6 mm. The stems were fixed with aluminum laboratory clamps above and below the position of the MRI magnet, and at the base of the stem. First, MR images of the intact, well-watered trees were acquired. Second, the stems were cut 10 cm above the soil to initiate desiccation. The distances between the cut end of the stem and the imaging slice were thus 100 cm (B1 and B2) and 75 cm (B3). The drying trees were imaged every 2 h. After the MRI measurements, the imaged stem section was excised and stored at À20°C for microscopy.

MRI hardware and methods
A 0.25 T, 16 kg C-shaped permanent NdFeB magnet with a 35 mm air gap was custom-built and fitted with a three-axis plane parallel gradient set. The gradient set was etched on layers of two-sided 105 lm copper circuit boards (Octamex, London, UK) and mounted on an openable, aluminum frame that also served as a Faraday cage and a heat sink (Fig. 2a). To reduce magnetic field drift resulting from temperature changes, the poles of the magnet were equipped with resistive heating wire and coupled to an accurate temperature controller, regulating magnet temperature to a set point value of 29°C. The MR imager was connected to a standard Kea II spectrometer (Magritek, Wellington, New Zealand) with a built-in 100 W RF amplifier. The gradients were driven by a set of three BAFPA40 gradient amplifiers (Bruker, Rheinstetten, Germany), yielding a maximum gradient strength of 0.24 T m -1 over a spherical volume of 25 mm. Before placing the plant inside the magnet, an 11-turn, 15-mm-diameter solenoidal RF coil was hand-wound around the stem with the help of a split Teflon coil former. The magnet was mounted on an adjustable nonmagnetic stand constructed of aluminum and stainless steel (Fig. 2b). If built in series, it is conceivable that small-scale MR imagers with similar specifications could be produced for less than, for example, a set of high-end portable infrared gas analyzers.
For image acquisition, an MSE (modified Carr, Purcell, Meiboom, Gill sequence (Edzes et al., 1998), with an XY-8 phase cycling scheme) type imaging pulse sequence was used. Imaging was done using the following settings: matrix size 128 9 128, repetition time 1.5 s, 64 echoes, first echo time 3.95 ms, all subsequent echo times 2.01 ms for B1 and 2.1 for B2 and B3. The slice thicknesses were 4.5, 5.5 and 5.0 mm, the fields of view 18.0, 15.5 and 14.7 mm, and the number of averages 32, 32 and 24, for plants B1, B2 and B3, respectively.
All image acquisition and initial data processing were done in PROSPA (Magritek). First, all images were masked and phase corrected according to Ma et al. (2008). Quantitative water content (A) and T 2 maps were calculated on the basis of a monoexponential fit of the signal (S(t)) for every pixel according to Eqn 1. Water content maps were normalized by dividing them by the average water content value of all three reference tubes. A 9 T 2 product maps were obtained by performing a pixel-by-pixel multiplication of the amplitude and T 2 maps.

Obtaining vulnerability curves
Before each MR measurement, the plant leaf water potential was determined according to Scholander et al. (1964). For this purpose a random twig was bagged, cut off and quickly transferred to a pressure chamber (Model 1000; PMS Instrument Co., Albany, NY, USA). On the basis of calibration curves that were acquired by means of independently obtained dry-down measurements, we found the difference between stem and leaf water potential to be insignificant for beech saplings after stomatal closure occurred, at water potentials of À1.5 MPa and lower.

New Phytologist
To obtain vulnerability curves (VCs), xylem masks were created for all measurements. The xylem region was selected by hand, excluding the phloem, bark and reference tubes from further analysis. Slight changes in stem position over the course of the dry-down experiment were corrected by shifting the masks accordingly. VCs were calculated using four different methods. First, by determining the loss of conductivity on the basis of the number pixels lost within binarization masks of (method 1) the amplitude or (method 2) the A 9 T 2 product maps; and second, on the basis of the loss of the total proton density (i.e. the amount of water per pixel) that was lost during dry-down from within the previously mentioned binarized masks, made on the basis of water content (method 3) or A 9 T 2 product maps (method 4).
To obtain a relative value for the embolized xylem area (% emb ), the initial pixel count or amplitude sum (P initial ) and the final pixel count or amplitude sum (P min ) were calculated from the number of pixels above threshold (P abv ): The resulting curves of all four approaches mentioned were fitted with a sigmodial function (Pammenter & van der Willigen, 1998): where the slope and the position of the curve in x-direction are denoted by S and Ψ 50 , respectively, the latter indicating the water potential at which 50% of the xylem is embolized. All fits were performed with MATLAB (Mathworks, Natick, MA, USA) and fitting errors were calculated according to Press (2002).

Light microscopy
After the dry-down experiment, the imaged stem pieces were marked and excised. Transverse sections of 20 µm were prepared with a sliding microtome (GSL1; Schenkung Dapples, Z€ urich, Switzerland) and stained with a 1 : 1 (v/v) mixture of safranin and astrablue, following G€ artner & Schweingruber (2013). Images of the cross-section were obtained with a digital camera connected to a light microscope (Leica Microsystems GmbH, Wetzlar, Germany), at a magnification of 94 in combination with a digital camera (Kappa PS30; Kappa optronics GmbH, Gleichen, Germany). All images were merged with Adobe PHO-TOSHOP CS2 to obtain the picture of the whole cross-section.

Imager and imaging
The half-open C-shaped design of the small-scale MR imager allowed mounting of the setup on a plant in < 20 min. Although still 16 kg, the weight of the magnet was low enough to allow its position, height and angle to be adjusted easily and by hand. An MSE imaging sequence (Edzes et al., 1998) was implemented and run continuously, which can be thermally challenging for a gradient set without active cooling. Here, up to 64 echoes could be acquired, for all examples shown in this study, without overheating the gradient system. The prototype imager proved to be reliable, allowing continuous operation during several months of tests and dry-down experiments. Water content and T 2 maps of stems of well-watered beech saplings were acquired, in which seven different types of tissue could be clearly identified (from outside to inside): bark, phloem and cambium, early-and latewood of the annual xylem rings, the pith and (in B1) xylem parenchyma rays. Despite the fact that all trees were furnished by the same grower, were of the same genotype and of comparable heights and stem diameters, their anatomy revealed strongly varying life histories. B1 and B3 had five annual rings at the imaging position, whereas B2 had only two. The current-year annual ring in B1 exhibited evidence of much faster growth than the annual rings from earlier years, whereas both annual rings of B2 showed fast growth.
The most striking features of the parameter maps were the bright bands in the annual rings, which became visible in the amplitude maps as well as in the T 2 maps. The contrast of these bright rings was fairly low in the amplitude maps, but much higher in the T 2 maps and could be improved even more by multiplying the two parameter maps to yield A 9 T 2 product maps (Fig. 3). The latter procedure resulted in images with excellent contrast and low noise that did not require any image manipulation to remove spikes resulting from erroneous fitting in areas of low signal intensity.
The bright rings of high water content and long T 2 were clearly associated with a high density of wide vessels, except for the oldest annual ring. This was illustrated by matching the microscopic xylem structure accurately with the MR images, overlaying the microscopy image of B3 with its T 2 map (Fig. 4). The water content in those bright rings was c. 70% (Fig. 3, row I), while the darker latewood surrounding those regions showed values of c. 30%. The T 2 maps showed a similar pattern but with much greater contrast (row II). The bright rings had T 2 values of c. 90 ms, while the remaining tissue exhibited values of c. 20 ms. The bright xylem rings in the T 2 maps were slightly wider than those in the amplitude maps.

Imaging embolism formation
During the dry-down experiment three beech saplings were bench dehydrated, while an MR measurement and a water potential measurement were conducted every 2 h. Of the resulting time series of images and water potential measurements, only the five sets that show the most significant changes are displayed (Fig. 5). Videos incorporating all product images that were acquired during dry-down of each plant are provided in Supporting Information Videos S1-S3.
In all parameter maps (water content (A), T 2 and A 9 T 2 ) the bright rings in the xylem were found to progressively disappear at increasingly negative water potentials, supporting the idea that Ó 2020 The Authors New Phytologist Ó 2020 New Phytologist Trust New Phytologist (2020) 226: 1517-1529 www.newphytologist.com the declining water content and the change in T 2 corresponded with the loss of water from previously filled xylem vessels. The percentage change in water content was much smaller than the percentage change in T 2 . The average amplitude loss observed for pixels with filled xylem vessels over the course of the dry-down ranged from 37% to 48% (B1, 37.1%; B2, 48.4%; B3, 35.5%), concomitant with a decrease in water potential of c. À1 to < À5 MPa. The corresponding changes in T 2 , however, were about twice as large and ranged from 67% to 72% (B1, 72.3%; B2, 71.3%; B3, 67.9%). At the end of the dry-down experiment, at water potentials < À5 MPa, in all three trees the residual xylem water content was c. 30% with a T 2 value of around 20 ms. As shown in Fig. 5, the contrast provided by the water content and T 2 maps could be improved even further by multiplying the two parameters. The resulting A 9 T 2 product maps were found to show even greater percentage changes over the course of the drydown (B1, 81.7%; B2, 85.0%; B3, 78.9%).
In most beech stems, the oldest annual rings lost water and showed declining T 2 values before the younger ones did. The only exception was the second annual ring in B3, which lost water before the third one (rings counted from the outside). For all beech trees, a homogeneous radial spread of emboli within the annual rings was observed, resulting in a narrowing of the bright xylem sections. As the dry-down continued, the radial spread of emboli within the rings was accompanied by a tangential spread. For all trees, the latewood within the rings was affected first (signal decline < À2 MPa), the earlywood last. Before the dry-down, in B1 a domain of low water content and T 2 within the current annual ring was already showing, extending in tangential direction (arrow in Fig. 5a, row III). Below À3 MPa this domain of low water content and T 2 values grew larger and spread in tangential and radial directions.

Vulnerability curves
Four methods to approximate the percentage loss of conductivity (PLC) were tested: (1) calculation of PLC on the basis of the loss of number of pixels containing water-filled vessels, determined on the basis of binarized amplitude maps; (2) as method 1 but calculated on the basis of binarized A 9 T 2 Fig. 3 Comparison of amplitude (A), relaxation time (T 2 ) and A 9 T 2 product maps of the stems of three well-watered beech (Fagus sylvatica) trees (B1, B2, B3), measured before commencing the dry-down experiment, and optical microscopy of the same positions in the stems after harvesting (bottom row). The first row shows the signal amplitude maps in au, normalized to relate linearly and quantitatively to water content (0-80%); the second row illustrates T 2 relaxation maps in ms; the third shows the product maps of amplitude and relaxation time. Bars indicate the values corresponding with black (minimum) and white (maximum) values. Next to the plants three reference tubes are visible. The fourth row shows microscopy images of each plant at the same position. In this window the grid indicates the magnetic resonance imaging pixel size (120 9 120 µm). (2020)  (3) as method 1 but based on the decrease in the cumulative proton density in the pixels identified by means of binarized amplitude maps; and (4) as method 3 but based on the cumulative proton density in the pixels identified by means of binarized A 9 T 2 product maps. Masks resulting from the binarization of water content and A 9 T 2 product maps are shown for five water potential values of B3 in Fig. 6(c,d). Using Eqn 3 and fitting the result with a sigmodial function (Eqn 4), VCs were calculated either on the basis of the number of pixels in the binarization masks, or by summing up amplitude values of those pixels (Fig. 6a,e,f). The exact values and error values of r 2 , slope and Ψ 50 for each plant are provided in Table S1. All four approaches resulted in VCs that matched the data points well, with values of r 2 close to 1. The vulnerabilities of samples B1 and B3 were found to be very similar (a difference of c. 0.1 MPa), whereas the Ψ 50 of B2 was found to be c. 0.6 MPa lower. An additional comparison of the four methods with all plants grouped together, done by means of the FITPLC package  Table S1. For a supplemental analysis of the data with the FITPLC package see Fig. S1.
The masks based on the product maps much more clearly reflected the filled xylem than those based on the amplitude maps (Fig. 6c,d). This corresponds to the fact that the contrast between filled and cavitated xylem pixels was much greater in the product maps than in the amplitude maps, as was the signal-to-noise ratio of the respective images.
Compared with VCs obtained from binarized product images (Fig. 6b,f), VCs obtained from binarized amplitude images (a and e) resulted in lower values of r 2 , steeper slopes and more negative values for Ψ 50 .

Imaging xylem embolism formation
Despite the low field strength and the relatively low resolution afforded by the small-scale MR imager, our method was remarkably successful at visualizing the appearance and spread of embolism in the xylem. The use of an MSE imaging sequence allowed for efficient signal acquisition, enabling the computation of quantitative water content and T 2 maps. Embolism formation became visible in all three parameter maps that were acquired, water content, T 2 and A 9 T 2 . The multiplication of amplitude and T 2 maps to yield A 9 T 2 product maps was especially helpful, as it provided even more contrast between filled and empty xylem than did either amplitude or T 2 maps, while also yielding cleaner and less noisy images without any further image processing.
The time resolution of the measurements (2 h) was sufficient to visualize the spread of emboli. Embolism spread happened first radially, from latewood to earlywood (i.e. from outside to inside), and subsequently in a tangential direction. This was indicated by bright (i.e. water-filled) rings becoming narrower from the outer to the inner xylem. We did not observe a spread of emboli between annual rings. This agrees with observations by Fukuda et al. (2015), who saw a similar narrowing of rings from outside to inside in Katsura and Japanese birch. Brodersen et al. (2013a, b) observed in grapevine a radial spread of emboli as well, but in the other direction, that is, from the pith towards the cambium via direct connections and xylem vessel relays between vessels.
Xylem conduits in the older annual rings of all samples cavitated at less negative water potentials than those in the youngest annual rings. This is in agreement with findings of previous noninvasive studies on angiosperms (Fukuda et al., 2015) and gymnosperms (Umebayashi et al., 2016). The phenomenon has been suggested to be caused by cavitation fatigue, attributed to repeated cycles of drought causing pit membrane degradation (Hacke et al., 2001;Melcher et al., 2003;Hillabrand et al., 2016).
A water content of c. 30% remained in the wood after water potentials dropped below À5 MPa, at which point most of the bright rings had already disappeared (Fig. 5). The T 2 value of this remaining water was c. 20 ms, which is significantly lower than the T 2 value of regions with filled vessels. The T 2 of the remaining water is depressed, because it resides in narrow lumina such as fiber tracheids (Schweingruber, 1990). While Fukuda et al. (2015), by means of scanning electron microscopy, also found remaining water in fiber tracheids surrounding cavitated vessels in the xylem of Katsura, this water was hardly visible in their MRI images. This may be attributed to the fact they used an SSE imaging sequence with an echo time of 13 ms. After that time, most signal from water in fiber tracheids can be assumed to be lost as a result of T 2 signal relaxation.

Simulating embolism detection by means of T 2 relaxation
Embolism formation in vessels became visible more readily in the T 2 parameter maps than in the water content maps, confirming that T 2 provides a useful parameter with which the presence, and subsequent disappearance, of water in filled vessels with long T 2 relaxation times can be detected amongst the signal of water within the wood around the vessel lumina. The latter pool of water has much shorter relaxation times and is found in narrow structures such as fibers, intracellular spaces, or cell wall matrices. T 2 thus becomes a means to gain subpixel information: if in a pixel sufficient water is present in conduits with a T 2 that is much Fig. 7 Modeled relationship of the percentage change in amplitude (A) and relaxation time (T 2 ) that is expected if n vessels are present in a pixel, and all cavitate. In the model, pixels had a size of 120 9 120 µm and all conduits had a diameter of 25 µm. The simulation is run for 0-16 conduits with a volumetric water content of 100% with T 2 values of 100, 200 and 400 ms (see key). The wood around the conduits is assumed to have a volumetric water content of 30% with a T 2 of 20 ms. The resulting curves indicate a larger effect on the T 2 value of a pixel than on its amplitude value, in case only a few (one to six) vessels inside of it cavitate. The actual average changes in amplitude and T 2 that were measured in the different beech individuals were added to the graph (filled triangles) and match well with the modeled results.
Ó 2020 The Authors New Phytologist Ó 2020 New Phytologist Trust New Phytologist (2020) 226: 1517-1529 www.newphytologist.com longer than that of water in the surrounding wood, the T 2 relaxation time of the pixel as a whole will be elevated sufficiently to stand out clearly. The data acquisition and monoexponential fitting were simulated to compare how the two fit parameters are affected by the presence and subsequent cavitation of varying numbers of vessels inside of a pixel. The NMR signal before cavitation was assumed to be the sum of two pools of water in a pixel: water in conduits (S con ), comprising both tracheids and vessels with longer T 2 values (T 2,con ); and water in all other, much narrower spaces in the wood such as fibers and intracellular lumina (S other ), with a correspondingly short T 2 (T 2,other ). After cavitation of all conduits in a pixel, the only remaining NMR signal was assumed to originate from water in the wood surrounding the conduit lumina.
The signals of both pools of water were calculated assuming that all space not occupied by conduits was filled by wood, that all conduits had a diameter of 25 µm, and that the water content of the wood before and after cavitation remained at 30%. The conduit diameter was chosen on the basis of the observed conduit diameter distributions (see Fig. S2); the water content of the wood was estimated based on the water content next to the bright rings observed in the water content images. The NMR signal of a pixel was subsequently modeled on the basis of Eqn 1: ; Eqn 5 and S other ¼ 0:3 Â 1 À n con Â A con A pix exp À t T 2;other ; Eqn 6 where n con represents the number of conduits in a pixel, A con their cumulative cross-sectional area, and t the time after excitation. The simulated NMR signal was sampled according to the settings used for the actual image acquisition. The resulting data points were fitted monoexponentially, providing estimates for amplitude and T 2 , calculated first for the scenario in which all conduits were filled, second for the scenario in which all were cavitated. To estimate the response of both parameters to cavitation events, the percentage difference between the T 2 values of both scenarios was plotted against their difference in amplitude. The simulation was run for pixels with between 0 and 16 conduits (see pixel sketches in Fig. 7), in which the water in the conduits was modeled to have T 2,con values of 100, 200 and 400 ms. The results of the simulation corresponded well with the percentage change observed in the images (Fig. 7). The curves showed slopes of well over one for between one and five vessels, indicating that the presence and subsequent cavitation of only a few filled vessels already had a large influence on the observed T 2 value of a pixel. Please note that in the model, all vessels within a pixel are assumed to cavitate. For example, the cavitation of a single vessel which covers 3.4% of the pixel area will cause an amplitude change of 11%, but will cause an even larger increase in the T 2 relaxation time of 25-40%, depending on the value chosen for T 2,con . This difference decreased for larger numbers of vessels.
To facilitate a direct comparison between the parameter maps and the model, the average percentage changes of water content and T 2 within the bright xylem regions were plotted in Fig. 7. In the simulation, between three and seven vessels per pixel (n con ) explained the changes that were observed in amplitude and T 2 , for a value for T 2,con of between 100 and 400 ms. Those values accurately matched the numbers of vessels that have been found per MRI pixel (Fig. 4c).
During dry-down, the bright rings in the T 2 maps that indicate the presence of filled vessels were always equal in width or wider than the bright rings in the amplitude maps. This suggests that, even when in a pixel a few but not all conduits were cavitated, the T 2 value for such a pixel would remain higher. This response would correctly indicate the presence of filled conduits, but be binary in nature, contrary to the amplitude maps, in which the gradual cavitation of conduits in a pixel results in a gradual reduction of intensity. By combining the two parameters by a multiplication into the A 9 T 2 parameter maps, the strengths of both are combined, boosting contrast and alleviating the problem of the low SNR that is inherent to the use of a low-field MR imager. The near-binary response of T 2 to the presence of filled vessels is also expressed in the width of the bright rings in the xylem. During the course of the dry-down experiment, bright rings were wider in the T 2 maps than in the water content maps. Further, in the final dry-down images (< À5 MPa) the amplitude maps no longer showed evidence of the presence of remaining filled vessels, whereas in the T 2 and A 9 T 2 maps some pixels with filled conduits still remained (Fig. 5).
The sensitivity of the T 2 relaxation time to the presence of filled vessels is based on the large difference in the T 2 relaxation time of the NMR signal originating from water in wood and conduits. As T 2 increases with conduit diameter, the method is likely to be applicable for all species in which conduit diameters are similar to, or wider than, those of beech. However, to what degree mapping T 2 would yield comparable results in xylem architectures with smaller or fewer vessels than beech remains to be tested. If T 2 in narrow conduits approaches that of water in wood, the T 2 contrast advantage would be lost.

Vulnerability curves
Surprisingly, despite the noisy appearance of the masks resulting from the binarization of amplitude maps (Fig. 6c,d), all four approaches to obtain a measure for the relative loss of conductivity from binarized MR images successfully yielded VCs. The difference in the VCs based on amplitude maps (Fig. 6a,e) is that more water from nonconducting tissues is included. In binarizing the amplitude images much care was taken not to set the threshold too low, which, owing to the high noise floor, could have led to the exclusion of pixels with filled conduits. The application of a conservative threshold, conversely, will have resulted in the inclusion of pixels that contain wood and water, but no filled conduits. The masks based on A 9 T 2 product maps, thanks to the high contrast and low noise figure of the latter, most effectively singled out pixels with filled conduits.

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Vulnerability curves obtained from A 9 T 2 product masks resulted in curves with a higher r 2 , a more shallow slope and a less negative Ψ 50 , compared with the VCs obtained from the binarized amplitude images. In both cases, the difference between VCs calculated on the basis of the loss of water within the binarized masks (Fig. 7e,f), and those based on the mere number of pixels left in the mask (Fig. 7a,b), was negligible. The most convenient method to derive VCs from the imaging data thus proved the most useful: binarization on the basis of A 9 T 2 product images, combined with an estimation of the PLC on the basis of the decrease in the numbers of pixels within the binarization masks.
The differences in the estimates of Ψ 50 for the two methods were relatively minor, ranging from À3.2 and À3.3 (A 9 T 2 product masks) to À3.7 and À3.8 MPa (amplitude masks). These values are in good agreement with those reported in other studies on beech saplings (Caquet et al. (2009) and Aranda et al. (2015) reported values of À3.0 to À4.0, and À3.0 to À3.7 MPa, respectively), while there are also studies that found less negative values (Cochard et al. (1999) and Barigah et al. 2013) reported values of À2.5 to 3 and À2.5 MPa, respectively). Studies on mature beech trees also resulted in similar values (Lemoine et al., 2002, À2. Tomasella et al., 2018, À2.5 MPa). In the framework of the current study we have not been able to cross-correlate our results with established benchmark methods. In future experiments it would be most interesting to follow up on this study by making such a comparison.

Conclusions
In this study we have demonstrated that MRI scanners based on small-scale, low-field permanent magnets are capable of imaging embolism formation in diffuse-porous angiosperms such as beech. By combining such an imager with an MSE imaging sequence, quantitative parameter maps of water content and T 2 signal relaxation could be obtained. While both types of images could be used to detect xylem cavitation, T 2 parameter maps were found to be especially sensitive to it. By multiplying the parameter maps of water content and T 2 relaxation time, A 9 T 2 product maps could be obtained in which regions with filled vessels could be identified even more clearly. The improved contrast afforded by the A 9 T 2 product maps also provided a convenient way to obtain VCs by means of straightforward image binarization.
The MSE imaging sequence, as a means to quantitatively map T 2 relaxation times to visualize and detect filled conduits that are too small to be resolved spatially, could also be helpful when used on conventional imagers with much higher field strengths. In such imagers, signal to noise will not be limiting, but T 2 contrast may still be expected to facilitate the detection of filled conduits, if the latter cannot be identified, because of the limited spatial resolution, on the basis of imaging alone.

Supporting Information
Additional Supporting Information may be found online in the Supporting Information section at the end of the article.

Fig. S1
The data points of all three beech trees (Fagus sylvatica) were grouped together for analysis, to compare the four methods shown in Fig. 6 by means of FITPLC package (sigmodial model and 1000 resamples).
Table S1 r 2 , slopes and Ψ 50 of vulnerability curves of three beech (Fagus sylvatica) trees shown in Fig. 6.
Videos S1-S3 Videos of embolism formation in beech (Fagus sylvatica); shown are time series of magnetic resonance product (A 9 T 2 ) images of the stem of three beech trees, acquired during progressive dry-down.
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