Quantification of hydraulic redistribution in maize roots using neutron radiography

Plants redistribute water from wet to dry soil layers through their roots, in the process called hydraulic redistribution. Although the relevance and occurrence of this process are well accepted, resolving the spatial distribution of hydraulic redistribution remains challenging. Here, we show how to use neutron radiography to quantify the rate of water efflux from the roots to the soil. Maize (Zea mays L.) plants were grown in a sandy substrate 40 cm deep. Deuterated water (D2O) was injected in the bottom wet compartment, and its transport through the roots to the top dry soil was imaged using neutron radiography. A diffusion–convection model was used to simulate the transport of D2O in soil and root and inversely estimate the convective fluxes. Overnight, D2O appeared in nodal and lateral roots in the top compartment. By inverse modeling, we estimated an efflux from lateral roots into the dry soil equal to jr = 2.35 × 10−7 cm−1. A significant fraction of the redistributed water flew toward the tips of nodal roots (3.85 × 10−8 cm3 s−1 per root) to sustain their growth. The efflux from nodal roots depended on the roots’ length and growth rate. In summary, neutron imaging was successfully used to quantify hydraulic redistribution. A numerical model was needed to differentiate the effects of diffusion and convection. The highly resolved images showed the spatial heterogeneity of hydraulic redistribution.


INTRODUCTION
Water is heterogeneously distributed in soils, and understanding how root water uptake and root growth respond to such heterogeneity is crucial to predict plant response to drought. Root water uptake from deep wet soil layers helps plants to tolerate drought periods (Sharp & Davies, 1985;Zegada-Lizarazu & Iijima, 2004). Besides sustaining the transpiration demand of plants, a fraction of the water extracted from 2008) and increases nutrient availability in drier soil (Caldwell, Dawson, & Richards, 1998;Snyder, James, Richards, & Donovan, 2008;Wang, Tang, Guppy, & Sale, 2009).
Although the occurrence, relevance, and amount of HR are well accepted and documented, resolving the spatial distribution of HR along the root system and into the soil remains challenging. Neutron radiography, thanks to its high sensitivity to water and thus to roots, is an imaging method with great potential to quantitatively estimate root distribution and water flow in soil and roots (Moradi et al., 2011;Oswald et al., 2008). Warren, Bilheux, Kang, et al. (2013) used neutron radiography and deuterated water (D 2 O) to trace HR in seedlings of Zea mays L. and Panicum virgatum L. The authors showed a high sensitivity of neutron radiography to small changes in D 2 O concentrations, which enables them to visualize the translocation of D 2 O through the roots of young plants.
Interpretation of time-series radiographs of D 2 O is challenging , and several possible artifacts should be considered. The neutron attenuation coefficient of D 2 O is much lower than that of H 2 O. When D 2 O replaces H 2 O in a given root or soil region, the attenuation coefficient of that region largely drops, making the redistribution of D 2 O visible over time. However, neutron attenuation does not depend only on the fraction of D 2 O and H 2 O, but also on the total content of liquid (the sum of D 2 O and H 2 O). This value changes in soils due to water uptake and HR and small increases (or decreases) in liquid content can cause significant underestimation (or overestimation) of the concentration of D 2 O . This problem is more critical for soils (whose moisture content easily varies from 0 to 0.4) than for roots. However, root shrinkage might similarly affect the interpretation of the neutron signal. An additional complexity is that the transport of D 2 O in soils and plants depends on both diffusion and convection. It means that an increase (or decrease) of D 2 O in roots and soil does not necessarily indicate a net flow into (or from) roots, but it might be caused by diffusion driven by gradients in D 2 O concentration. Zarebanadkouki, Kroener, Kaestner, and Carminati (2014) conducted a series of D 2 O tracing experiments during the day and nighttime and developed a numerical model simulating diffusion and convection of D 2 O in soil and roots. The authors proved that the diffusion of D 2 O from the root surface to its xylem is as significant as the convective fluxes, also during the daytime, and it should be properly modeled to quantify the local fluxes of water. The method was used for quantifying root water uptake in homogeneous soil moisture conditions (Ahmed, Zarebanadkouki, Kaestner, & Carminati, 2016;Ahmed et al., 2018), but it has not yet been tested to quantify the efflux of water from the roots during nighttime.
The objective of this technical note was to test whether the combination of neutron radiography, D 2 O injection, and a

Core Ideas
• Measuring the spatial distribution of HR along the root system remains challenging. • Neutron radiography was used to trace the transport of D 2 O from wet to dry soil layers. • Radial fluxes were estimated using diffusionconvection model of D 2 O transport in soil and root. • Water was redistributed from wet to dry soil layers through fine lateral roots. • A fraction of HR water was used to sustain the growth of young nodal roots. diffusion-convection model allows quantification of HR and hydraulic lift. To test the feasibility of the method, we grew maize (Z. mays) plants in a sandy substrate that was partitioned into two horizontal compartments hydraulically separated by a 1-cm layer of coarse sand acting as a capillary barrier. When plants were well established, we let the upper compartment dry while we kept the lower compartment wet. Then D 2 O was injected at the lower wet compartment, and its transport within the root system was monitored for a period of ∼15 h (a daytime cycle followed by a nighttime cycle) using a time series neutron radiography. We also made two additional tests: (a) we injected H 2 O instead of D 2 O to monitor possible root shrinkage and swelling; and (b) we injected D 2 O in a sample whose top and bottom compartments were both kept wet, to test the effect of diffusion on D 2 O dynamics in the top compartment.

Soil and plant preparation
Three maize plants were grown in aluminum containers (40 cm high, 40 cm wide, and 1 cm thick). The containers were filled with a mixture of silt and sand (1:1 ratio) with particle size <1 mm and a bulk density of 1.4 g cm −3 . A 1-cm layer of fine gravels (particle size of 2-2.5 mm) was placed at a depth of 20 cm to hydraulically disconnect the top and bottom soil compartments without hindering the root growth (similar to Ahmed et al. , 2016;Zarebanadkouki et al., 2012). Maize seeds were germinated for 48 h and then planted in the containers (one seed per container). The soil surface was covered with fine gravels (particle size of 2-2.5 mm) to minimize evaporation. Plants were grown in a climate room with a photoperiod of 14 h (from 7:00 a.m. to 9:00 p.m.), day/night temperature of 24/19˚C, relative humidity of 60%, and light intensity of 750 μmol m 2 s −1 . Plants were irrigated every third day during the first 3 wk, allowing roots to grow uniformly in both compartments. Afterwards, the soil water contents (SWCs) were adjusted in the top and bottom compartments to the following scenarios. First, in two plants, the top soil compartment was kept dry (SWC ≤0.06, corresponding to a matric potential <−1,000 hPa, as estimated according to the water retention measured in Hayat et al., 2020) and the bottom compartment was kept wet (SWC ≈ 0.22, corresponding to a water matric potential of approximately −80 hPa); we refer to this scenario as dry-wet. Second, in one plant, both compartments were kept wet (SWC ≈ 0.22); we refer to this scenario as wet-wet. Prior to neutron radiography experiments, a lightemitting diode (LED) lamp (GC 9, Greenception, with specifications of photon flux intensity at height of 30 cm above plant ≈ 1.800 μmol m 2 s −1 and maximum spectrum wavelength = 700 nm) was installed above the plants. The average transpiration at daytime of dry-wet and wet-wet samples was 4.66 ± 0.26 and 4.87 g h −1 , respectively. The neutron radiography measurements started when plants were 40 d old.

Neutron radiography
Neutron radiography is a noninvasive imaging technique that allows for imaging water and root distribution in the soil (Carminati et al., 2010;Tumlinson, Liu, Silk, & Hopmans, 2008;Zarebanadkouki, Kim, & Carminati, 2013). The transmitted neutrons beam carries the information of the sample composition and thickness. The Beer-Lambert law describes the attenuation of the neutron beam (Kasperl & Vontobel, 2005) through the sample by where I is the detected neutron intensity (cm −2 s −1 ), I 0 is the incident neutron intensity (cm −2 s −1 ), μ i is the neutron attenuation coefficient (cm −1 ), and d i is the thickness (cm) of the material i. The material composing our samples were aluminum, dry soil, root (here intended as dry mass), water (H 2 O), and deuterated water (D 2 O). The attenuation of dry soil and aluminum were derived from the radiograph of a container filled with dry soil. The attenuation coefficients of H 2 O and D 2 O were experimentally estimated from the radiograph of control samples with a known thickness of normal and deuterated water. The neutron radiography experiments were carried out at the NECTAR (neutron computed tomography and radiography) facility (Bücherl & Söllradl, 2015) at the Heinz Maier-Leibnitz center, Technical University Munich (TUM), using its new option of thermal neutron radiography (Mühlbauer et al., 2018).
The thermal neutron spectrum is provided at the measurement position through a flight tube of 4 m in length with an entrance aperture of 25 mm in diameter. This resulted in a calculated length/diameter ratio of 240 and a measured integral neutron intensity of 7.9 × 10 6 cm −2 s −1 at the sample position. The detector system consists of a 6 LiF/ZnS scintillator screen of 100-μm thickness, which converts the neutrons into light, which is mirrored on a Andor iKon-L-BV charge-coupled device (CCD) camera (Model DZ936N BV) with 2,048 × 2,048 px and a pixel size of 13.5 ×13.5 μm. The CCD camera was operated at a temperature of −97˚C, thus having a dark current of <0.0001 electrons px −1 s −1 .
The samples were placed as close as possible to the scintillator screen of the detector system (i.e., at a distance of ∼3 cm). This setup corresponds to a quasiparallel neutron beam geometry.
A complete set of data for one radiograph consisted of dark current images (i.e., images with the camera shutter and the neutron beam closed), flat field images (i.e., images without sample), and images with a sample. All images were recorded for 20 s each. From a series of dark images and flat field images, the mean dark image I DC (x, y) and the flat field image I FF (x, y) were calculated, respectively. As the sample sizes were larger than the beam area, succeeding measurements at two vertical and two horizontal positions each could be performed to scan the complete sample on a two-by-two grid with overlapping margins.
An identical LED lamp, used prior to neutron radiography, was installed above the plants during the day measurements.

D 2 O tracing experiment
Deuterated water (D 2 O) was used to trace the flow of water in soil and roots. Due to its lower neutron attenuation coefficient compared with H 2 O, D 2 O is easily distinguishable in neutron radiographs. We injected 30 ml of D 2 O (purity of 99.97%) at two selected locations in the bottom wet compartment (15 ml at each location) using fine syringes ( Figure 1). The spatiotemporal distribution of D 2 O in each compartment and its transport along the roots were monitored by time-series neutron radiography with a temporal resolution of one frame every 20 s. The D 2 O tracing measurements started during the daytime (between 4:30 and 6:00 p.m.) and continued till the next morning (around 8:00 a.m.). The light was turned off at 7:00 p.m. and turned on again at 7:00 a.m. The samples were not moved throughout the time series to avoid artifacts due to imprecise referencing. The reconstructed image of one entire sample before injection of D 2 O is shown in Figure 1. The image was obtained by overlapping four radiographs. The gray values show the water content in the sample (i.e., the darker the image, the higher the SWC

Control experiments
To ensure that the D 2 O measurements were correctly interpreted (see Section 4), in one of the samples of the drywet scenario, we first injected 30 ml of H 2 O in the bottom wet compartment and monitor water redistribution within the root system overnight. The D 2 O was injected 24 h later.

Image analysis
The obtained neutron radiographs were normalized for the flat field (radiograph without sample) and dark current (signals recorded by the camera in the absence of a beam) as where x and y refer to the spatial coordinates of pixels in the x and y direction, t refers to the time after D 2 O injection, I norm (x, y, t) is the normalized image, I(x, y, t) is the recorded image at time t, I DC (x, y) is the dark current image, I FF (x, y) is the flat field image, and D 0 and D(t) are scalar values proportional to the neutron attenuation at time zero and any given time t in a blank area of radiographs, respectively. By combining the Beer-Lambert law for these samples, where I dry (x, y) is the radiography of the dry sample, μ H2O (cm −1 ) and d H2O (cm) are the attenuation coefficient and thickness of normal water (H 2 O), and μ D2O (cm −1 ) and d D2O (cm) are the attenuation coefficient and thickness of heavy water (D 2 O). The measured attenuation coefficients for normal water (μ H2O ) and deuterated water (μ D2O ) were 1.04 and 0.335 cm −1 , respectively. The sharp difference in water contents between roots and the surrounding soil allowed us to segment roots. We segmented roots using Matlab 2019b (Math-Works). The length and diameter of segmented roots were calculated using the Euclidean distance mapping functions in Matlab 2019b. The concentration of D 2 O within the roots was calculated according to the protocol presented in Zarebanadkouki et al. (2012). We define μ root (t) (cm cm −1 ) as the neutron attenuation in the pixel containing roots as where d root is the root thickness (cm). We assumed that the volumetric liquid content of the root tissue did not change after immersion in D 2 O. It follows that H2O root ( = 0) = D2O root ( ) + H2O root ( ) Then, the pixel-wise concentration of D 2 O in the pixel containing root can be calculated as The total liquid thickness in the root ( liq root ) was calculated as H 2 O thickness in the first radiograph before D 2 O was injected [i.e., liq root = H2O root ( = 0)]. Here, we assumed that the change in pixel-wise water content of the soil in the upper compartment is negligible. The concentration of D 2 O in the root was averaged along the root segment. F I G U R E 2 Illustration of the deuterated water (D 2 O) transport model into the root. Here, red and blue arrows show diffusive and convective fluxes, respectively. Radial water fluxes j r can be directed toward the root surface (water uptake) or toward the soil (hydraulic lift). Axial fluxes could be toward the root tip (to sustain growth and hydraulic lift) or toward the basal part (to sustain transpiration) We calculated the growth rate of roots assuming that water constitutes the major fraction of the root tissue: (8) where the right-hand side of Equation 8 refers to the summation of neutron attenuation in both x and y coordinates of pixels containing root tissue, μ root (t) refers to the average neutron attenuation across the thickness of root tissue in the radiographs, and Res is the pixel size.
We calculated the concentration of D 2 O in three different root types in the top soil compartment as illustrated in Figure 1. The first were seminal and primary root segments that reached the bottom compartment where D 2 O was injected. These roots took up D 2 O from the soil and transported it axially upwards towards the shoot via transpiration stream; we refer to these roots as seminal roots. The second were lateral roots that were located in the top compartment and were not immersed in D 2 O but received D 2 O from the seminal roots; we refer to these roots as lateral roots. The third were nodal and crown roots located in the top compartment and that had not yet crossed the capillary barriers and reached the D 2 O injected compartment; we refer to these roots as nodal roots. The second and third types of roots could only receive D 2 O from the root-shoot conjunction.

Model of D 2 O transport into roots
To derive the fluxes of water from the temporal dynamics of D 2 O concentration, we used a diffusion-convection model (Ahmed et al., 2016Zarebanadkouki et al., 2014). The transport of D 2 O in roots and soil depends on (a) diffusion due to gradients in the concentration of D 2 O in soil and root and (b) convection due to water fluxes driven by transpiration and HR.
We simulated the D 2 O transport in a single root, in which water flows axially along the xylem and radially across the cortex (Figure 2). The change in D 2 O concentration in the root is described by where θ(r, x) is the water content (cm 3 cm −3 ), C(r, x, t) is the D 2 O concentration in the root (cm 3 cm −3 ), t is the time (s), r is the radial coordinate (cm), x is the longitudinal coordinate (cm), j r (r) is the radial flux of water (cm s −1 ), j x (r, x) is the axial flux of water (cm s −1 ), and D is an effective diffusion coefficient of D 2 O (cm 2 s −1 ). The axial flux of water within the root xylem is estimated by mass conservation equation, assuming that the axial transport of D 2 O occurs only in the root xylem, as where the j x changes along x and j r is assumed to be uniform along x. The water flux into the roots at the basal part is referred to as j x,basal and at the root tip is called j x,tip (Figure 2). The axial fluxes can be positive or negative and indicate HR and water uptake, respectively (x increases toward the root tip). A positive j r indicates the efflux of water from the root to the soil and negative j r indicates root water uptake.

Model implementation
We modeled the transport of D 2 O into roots in the top soil that had no direct access to D 2 O from the soil (lateral and nodal roots, Figure 1). The D 2 O transport was simulated in single roots (no branching) from their basal parts to the root tips. As roots grew during the measurements (16 h), root growth was included as convective flux toward the root tip (see below). The diffusion-convection equation (Equation 9) was numerically solved in radially symmetric coordinates using a finite difference method. The flow domain from soil towards the root xylem and from the tip roots towards the basal parts were represented in a two-dimensional computational grid with 40 equally spaced grid elements along the root radius and 110 grid elements along the root length. The diffusionconvection equation was solved assuming the following initial and boundary conditions: where r = 0 is the root center, r out is the outer radius of soil (radius of the root, r root , plus the thickness of soil used in our simulation), C 0 is the quantified D 2 O concentration at the root surface in the soil during the measurements, j root is the radial flux of water at the root surface, x = x tip refers to the position of the root tip, j x,tip is the axial flux of water at the root tip, x basal refers to the position of the root at its basal part, at which the root segment was connected to the seminal roots (for the case of lateral roots) and the root--shoot conjunction (for the case of crown roots), and j x,basal is the axial flux that the basal parts of each root segment. The diffusion coefficient of D 2 O in the soil was taken from the value of diffusion coefficient D 2 O in free water and scaled for the porosity and SWC, according to Millington and Quirk (1959). The F I G U R E 5 Summary of estimated fluxes along the measured root maize system. The fluxes of water from the root to the soil are shown in blue. The fluxes of water toward the root tip to sustain root growth are shown in green. j r is the radial flux of water and J x is the axial flow of water values of diffusion coefficient across the root tissues were taken from Ahmed et al. (2016). The inverse problem was solved in Matlab (2019b) using the patternsearch solver from its optimization toolbox.

RESULTS
Some selected neutron radiographs at different times after D 2 O injection in one of the two dry-wet samples are presented in Figure 3 (same plant as shown in Figure 1). The radiographs show the difference between the actual radiograph and that before D 2 O injection. The brighter is the color the higher is the D 2 O concentration. Shortly after being injected, D 2 O was taken up by seminal roots and was axially transported upwards towards the shoot following the transpiration stream ( Figure 3a). During nighttime (from 7:00 p.m. to 7:00 a.m.), the lateral roots that were not in direct contact with D 2 O in the injected compartment gradually turned bright. Similarly, the nodal roots that were not in direct contact with D 2 O in the injected compartment also turned gradually bright.
With time, the tip of nodal roots grew and appeared dark in the radiographs (Figure 3e). These observations (lateral roots turning bright over time) were consistent in the second sample (Supplemental Figure S1). In the sample in which both top and bottom compartments were kept wet (Supplemental Figure S2), no increase of D 2 O in lateral and nodal roots was detectable overnight. When only H 2 O was injected, lateral roots did not change their attenuation coefficient, indicating that neither shrinking nor swelling were detectable. The latter experiment was done to exclude that the increasing root transparency (observed in the case of the dry-wet scenario) was caused by root shrinkage.
The average D 2 O concentrations in roots located in the top compartment are shown in Figure 4. In seminal roots, the concentration of D 2 O increased shortly after D 2 O injection during daytime, and then it decreased and reached rather constant values during nighttime. The concentration increased again as transpiration restarted in the next morning. In the drywet scenario, D 2 O concentration in lateral roots progressively increased during the nighttime. On the contrary, lateral roots in the wet-wet scenario showed a slight increase in the concentration of D 2 O only in the first hour when the plant was still transpiring, whereas there was no increase overnight. Finally, we also plot the D 2 O concentration in the nodal roots, which was similar to those of the laterals.
We used the diffusion-convection model (Equation 9) to simulate the measured D 2 O concentration in laterals and nodal roots in the dry-wet scenarios. By inversely fitting the measured concentrations, we quantified the radial fluxes (j r ) of water during the night. The best fits are shown as solid lines in Figures 4b and 4c. The radial flux of water into or out of the root (j r ) was the only unknown parameter which was inversely adjusted. The best fits for the laterals in the two dry-wet samples were j r = 2.4 × 10 −7 and j r = 2.3 × 10 −7 cm s −1 , respectively. For the nodal roots, which grew overnight, the axial flux at the root tips was set to be equal to the root growth. The radial fluxes varied between the two nodal roots. In the longer nodal root, it was negligible (j r = 1 × 10 −11 cm s −1 ) as compared with the laterals, indicating that water was mainly redistributed to the dry soil through the laterals. Note that such a low flux is probably below the detection limit. However, this nodal root tip received a significant flux of water to sustain its growth (j x = 1.94 × 10 −4 cm s −1 ). For the shorter nodal (denoted by the dark yellow color in Figure 4c), the estimated radial flux was j r = 5 × 10 −7 cm s −1 , which is close to the value measured for laterals.

DISCUSSION AND CONCLUSIONS
We successfully showed that neutron radiography allows visualization of HR. Using a diffusion-convection model, the water fluxes in different root types were estimated. We performed two measurements with heterogeneous SWCs (top soil compartment dry and bottom soil compartment wet; i.e., dry-wet) and one with homogeneous SWC (both soil compartments wet; i.e., wet-wet). Additionally, in one of the two dry-wet samples, we injected H 2 O the day before injecting D 2 O. The experiments with H 2 O and the wet-wet scenario were needed to test whether the decreasing neutron attenuation in the roots in the top compartment overnight was caused by root shrinkage or diffusion of D 2 O along the xylem (note that diffusion does not require a mass flow). The two tests showed no detectable decrease in neutron attenuation in the upper roots, which confirms our interpretation that HR (a convective flux of water from the bottom to the top soil layer through the roots) was responsible for the detected signal in the dry-wet scenarios.
In the dry-wet scenario, lateral roots slowly turned more transparent during nighttime. This observation can be explained by two processes: (a) the roots located in the upper dry compartment shrunk and therefore appeared brighter in the radiographs; and (b) these roots received D 2 O from the main root axes (root transporting D 2 O upwards during the day), either via diffusion or HR (convection). The root shrinkage was not the case as we did not detect any change of root shrinking-swelling overnight (Supplemental Figure S3). Therefore, we conclude that increasing transparency of the laterals of the sample shown in Figure 1 was caused by an increase of D 2 O concentration. As laterals showed no growth and no detectable swelling, as observed in control experiments, a convective flow of water toward the lateral root tips means that water predominantly moved into the soil. On the contrary, nodal roots did grow. The convective fluxes toward the tip of nodal roots delivered water to the growing root tip. The efflux of water from the two nodal roots varied between the two roots. For the shorter one, the flux of water into the soil was similar to that from the lateral roots. For the longer roots, the flux of water into the soil was negligible. The differences in j r between the two nodal roots might be explained by their different length and growth rate. The faster growth rate of the longer nodal root (3.4 cm per 15.5 h, compared with 1.2 cm per 15.5 h for the shorter nodal) is likely to have caused a stronger suction at the root tip (to drive water toward the tip) and consequently along all the root, decreasing the gradient in water potential between the root and the soil needed to drive the water efflux into the soil. Additionally, the root radial hydraulic conductivity typically decreases with increasing distance from the root tip , which might have further reduced the water efflux from the long nodal root. These results show that HR varies between root types, and that the fraction of water that sustains root growth (dominant for nodal roots) and the one that flows into the soil (dominant for laterals) vary even more. The estimated fluxes are summarized in Figure 5.
The convective fluxes were estimated using inverse modeling. The model was needed to separate the effect of diffusion from that of convection. Therefore, the estimations are affected by the model assumptions. Relevant assumptions are constant diffusion coefficient during day and night, and uniform diffusion coefficient within the root tissue. These assumptions were instrumental to keep our model as sim-ple as possible and to reduce the number of unknowns in the inverse problem. The assumption of uniform diffusion coefficient within the root tissue was tested by Zarebanadkouki et al. (2014), who showed that the model results were not sensitive to the different pathways across the root. An additional assumption was that roots did not swell and shrink during the experiments. Root swelling (shrinking) would cause an underestimation (overestimation) of D 2 O concentration and, thus, of the HR. However, the test with H 2 O showed no detectable changes in root volume and water content in our experiment.
It has to be noted that the reported measurements are specific of the tested setup, in which the small container size (40-cm depth), the use of sandy substrate, and the low number of replicates might limit the generalization of the estimated fluxes.
Despite these limits, we have shown how to quantify HR by combining neutron radiography, injection of D 2 O, and a diffusion-convection model. For young maize, HR was highly variable along the root system and was root type specific. In conclusion, this method can be used for quantitative estimation of the spatial distribution of hydraulic lift in detailed laboratory experiments.

C O N F L I C T O F I N T E R E S T
The authors declare no conflict of interest.