A mathematical model of biofilm growth and spread within plant xylem: Case study of Xylella fastidiosa in olive trees

Xylem-limited bacterial pathogens cause some of the most destructive plant diseases. Though imposed measures to control these pathogens are generally ineffective, even among susceptible taxa, some hosts can limit bacterial loads and symptom expression. Mechanisms by which this resistance is achieved are poorly understood. In particular, it is still unknown how differences in vascular structure may influence biofilm growth and spread within a host. To address this, we developed a novel theoretical framework to describe biofilm behaviour within xylem vessels, adopting a polymer-based modelling approach. We then parameterised the model to investigate the relevance of xylem vessel diameters on Xylella fastidiosa resistance among olive cultivars. The functionality of all vessels was severely reduced under infection, with hydraulic flow reductions of 2-3 orders of magnitude. However, results suggest wider vessels act as biofilm incubators; allowing biofilms to develop over a long time while still transporting them through the vasculature. By contrast, thinner vessels become blocked much earlier, limiting biofilm spread. Using experimental data on vessel diameter distributions, we were able to determine that a mechanism of resistance in the olive cultivar Leccino is a relatively low abundance of the widest vessels, limiting X. fastidiosa spread.

Droplet Microfluidic-Based In Situ Analyzer for Monitoring Free Nitrate in Soil

Monitoring nutrients in the soil can provide valuable information for understanding their spatiotemporal variability and informing precise soil management. Here, we describe an autonomous in situ analyzer for the real-time monitoring of nitrate in soil. The analyzer can sample soil nitrate using either microdialysis or ultrafiltration probes placed within the soil and quantify soil nitrate using droplet microfluidics and colorimetric measurement. Compared with traditional manual sampling and lab analysis, the analyzer features low reagent consumption (96 μL per measurement), low maintenance requirement (monthly), and high measurement frequency (2 or 4 measurements per day), providing nondrifting lab-quality data with errors of less than 10% using a microdialysis probe and 2-3% for ultrafiltration. The analyzer was deployed at both the campus garden and forest for different periods of time, being able to capture changes in free nitrate levels in response to manual perturbation by the addition of nitrate standard solutions and natural perturbation by rainfall events.

Statistical Effective Diffusivity Estimation in Porous Media Using an Integrated On-site Imaging Workflow for Synchrotron Users

Transport in porous media plays an essential role for many physical, engineering, biological and environmental processes. Novel synchrotron imaging techniques and image-based models have enabled more robust quantification of geometric structures that influence transport through the pore space. However, image-based modelling is computationally expensive, and end users often require, while conducting imaging campaign, fast and agile bulk-scale effective parameter estimates that account for the pore-scale details. In this manuscript we enhance a pre-existing image-based model solver known as OpenImpala to estimate bulk-scale effective transport parameters. In particular, the boundary conditions and equations in OpenImpala were modified in order to estimate the effective diffusivity in an imaged system/geometry via a formal multi-scale homogenisation expansion. Estimates of effective pore space diffusivity were generated for a range of elementary volume sizes to estimate when the effective diffusivity values begin to converge to a single value. Results from OpenImpala were validated against a commercial finite element method package COMSOL Multiphysics (abbreviated as COMSOL). Results showed that the effective diffusivity values determined with OpenImpala were similar to those estimated by COMSOL. Tests on larger domains comparing a full image-based model to a homogenised (geometrically uniform) domain that used the effective diffusivity parameters showed differences below 2 % error, thus verifying the accuracy of the effective diffusivity estimates. Finally, we compared OpenImpala's parallel computing speeds to COMSOL. OpenImpala consistently ran simulations within fractions of minutes, which was two orders of magnitude faster than COMSOL providing identical supercomputing specifications. In conclusion, we demonstrated OpenImpala's utility as part of an on-site tomography processing pipeline allowing for fast and agile assessment of porous media processes and to guide imaging campaigns while they are happening at synchrotron beamlines.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11242-023-01993-7.

A 3D image-based modelling approach for understanding spatiotemporal processes in phosphorus fertiliser dissolution, soil buffering and uptake by plant roots

Phosphorus (P) is a key yield-limiting nutrient for crops, but the main source of P fertiliser is finite. Therefore, efficient fertilisation is crucial. Optimal P application requires understanding of the dynamic processes affecting P availability to plants, including fertiliser dissolution rate and soil buffer power. However, standard soil testing methods sample at fixed time points, preventing a mechanistic understanding of P uptake variability. We used image-based modelling to investigate the effects of fertiliser dissolution rate and soil buffer power on P uptake by wheat roots imaged using X-ray CT. We modelled uptake based on 1-day, 1-week, and 14-week dissolution of a fixed quantity of total P for two common soil buffer powers. We found rapid fertiliser dissolution increased short-term root uptake, but total uptake from 1-week matched 1-day dissolution. We quantified the large effects root system architecture had on P uptake, finding that there were trade-offs between total P uptake and uptake per unit root length, representing a carbon investment/phosphorus uptake balance. These results provide a starting point for predictive modelling of uptake from different P fertilisers in different soils. With the addition of further X-ray CT image datasets and a wider range of conditions, our simulation approach could be developed further for rapid trialling of fertiliser-soil combinations to inform field-scale trials or management.

Projected Increases in Precipitation Are Expected To Reduce Nitrogen Use Efficiency and Alter Optimal Fertilization Timings in Agriculture in the South East of England

Nitrogen fertilization is vital for productive agriculture and efficient land use. However, globally, approximately 50% of the nitrogen applied is lost to the environment, causing inefficiencies, pollution, and greenhouse gas emissions. Rainfall and its effect on soil moisture are the major components controlling nitrogen losses in agriculture. Thus, changing rainfall patterns could accelerate nitrogen inefficiencies. We used a mechanistic modeling platform to determine how precipitation-optimal nitrogen fertilization timings and resulting crop nitrogen uptake have changed historically (1950-2020) and how they are predicted to change under the RCP8.5 climate scenario (2021-2069) in the South East of England. We found that historically, neither precipitation-optimal fertilization timings nor resulting plant uptake changed significantly. However, there were large year-to-year variations in both. In the 2030s, where it is projected to get wetter, precipitation-optimal fertilization timings are predicted to be later in the season and the resulting plant uptake noticeably lower. After 2040, the precipitation-optimal uptakes are projected to increase with earlier precipitation-optimal timings closer to historical values, corresponding to the projected mean daily rainfall rates decreasing to the historical values in these growing seasons. It seems that the interannual variation in precipitation-optimal uptake is projected to increase. Ultimately, projected changes in precipitation patterns will affect nitrogen uptake and precipitation-optimal fertilization timings. We argue that the use of bespoke fertilization timings in each year can help recuperate the reduced N uptake due to changing precipitation.

Impact of root hairs on microscale soil physical properties in the field

AIMS

Recent laboratory studies revealed that root hairs may alter soil physical behaviour, influencing soil porosity and water retention on the small scale. However, the results are not consistent, and it is not known if structural changes at the small-scale have impacts at larger scales. Therefore, we evaluated the potential effects of root hairs on soil hydro-mechanical properties in the field using rhizosphere-scale physical measurements.

METHODS

Changes in soil water retention properties as well as mechanical and hydraulic characteristics were monitored in both silt loam and sandy loam soils. Measurements were taken from plant establishment to harvesting in field trials, comparing three barley genotypes representing distinct phenotypic categories in relation to root hair length. Soil hardness and elasticity were measured using a 3-mm-diameter spherical indenter, while water sorptivity and repellency were measured using a miniaturized infiltrometer with a 0.4-mm tip radius.

RESULTS

Over the growing season, plants induced changes in the soil water retention properties, with the plant available water increasing by 21%. Both soil hardness (P = 0.031) and elasticity (P = 0.048) decreased significantly in the presence of root hairs in silt loam soil, by 50% and 36%, respectively. Root hairs also led to significantly smaller water repellency (P = 0.007) in sandy loam soil vegetated with the hairy genotype (-49%) compared to the hairless mutant.

CONCLUSIONS

Breeding of cash crops for improved soil conditions could be achieved by selecting root phenotypes that ameliorate soil physical properties and therefore contribute to increased soil health.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11104-022-05530-1.

Multimodal correlative imaging and modelling of phosphorus uptake from soil by hyphae of mycorrhizal fungi

Phosphorus (P) is essential for plant growth. Arbuscular mycorrhizal fungi (AMF) aid its uptake by acquiring P from sources distant from roots in return for carbon. Little is known about how AMF colonise soil pore-space, and models of AMF-enhanced P-uptake are poorly validated. We used synchrotron X-ray computed tomography to visualize mycorrhizas in soil and synchrotron X-ray fluorescence/X-ray absorption near edge structure (XRF/XANES) elemental mapping for P, sulphur (S) and aluminium (Al) in combination with modelling. We found that AMF inoculation had a suppressive effect on colonisation by other soil fungi and identified differences in structure and growth rate between hyphae of AMF and nonmycorrhizal fungi. Our results showed that AMF co-locate with areas of high P and low Al, and preferentially associate with organic-type P species over Al-rich inorganic P. We discovered that AMF avoid Al-rich areas as a source of P. Sulphur-rich regions were found to be correlated with higher hyphal density and an increased organic-associated P-pool, whilst oxidized S-species were found close to AMF hyphae. Increased S oxidation close to AMF suggested the observed changes were microbiome-related. Our experimentally-validated model led to an estimate of P-uptake by AMF hyphae that is an order of magnitude lower than rates previously estimated - a result with significant implications for the modelling of plant-soil-AMF interactions.

Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data

Vegetation enhances soil shearing resistance through water uptake and root reinforcement. Analytical models for soils reinforced with roots rely on input parameters that are difficult to measure, leading to widely varying predictions of behaviour. The opaque heterogeneous nature of rooted soils results in complex soil–root interaction mechanisms that cannot easily be quantified. The authors measured, for the first time, the shear resistance and deformations of fallow, willow-rooted and gorse-rooted soils during direct shear using X-ray computed tomography and digital volume correlation. Both species caused an increase in shear zone thickness, both initially and as shear progressed. Shear zone thickness peaked at up to 35 mm, often close to the thickest roots and towards the centre of the column. Root extension during shear was 10–30% less than the tri-linear root profile assumed in a Waldron-type model, owing to root curvature. Root analogues used to explore the root–soil interface behaviour suggested that root lateral branches play an important role in anchoring the roots. The Waldron-type model was modified to incorporate non-uniform shear zone thickness and growth, and accurately predicted the observed, up to sevenfold, increase in shear resistance of root-reinforced soil.

Significance of root hairs for plant performance under contrasting field conditions and water deficit

BACKGROUND AND AIMS

Previous laboratory studies have suggested selection for root hair traits in future crop breeding to improve resource use efficiency and stress tolerance. However, data on the interplay between root hairs and open-field systems, under contrasting soils and climate conditions, are limited. As such, this study aims to experimentally elucidate some of the impacts that root hairs have on plant performance on a field scale.

METHODS

A field experiment was set up in Scotland for two consecutive years, under contrasting climate conditions and different soil textures (i.e. clay loam vs. sandy loam). Five barley (Hordeum vulgare) genotypes exhibiting variation in root hair length and density were used in the study. Root hair length, density and rhizosheath weight were measured at several growth stages, as well as shoot biomass, plant water status, shoot phosphorus (P) accumulation and grain yield.

KEY RESULTS

Measurements of root hair density, length and its correlation with rhizosheath weight highlighted trait robustness in the field under variable environmental conditions, although significant variations were found between soil textures as the growing season progressed. Root hairs did not confer a notable advantage to barley under optimal conditions, but under soil water deficit root hairs enhanced plant water status and stress tolerance resulting in a less negative leaf water potential and lower leaf abscisic acid concentration, while promoting shoot P accumulation. Furthermore, the presence of root hairs did not decrease yield under optimal conditions, while root hairs enhanced yield stability under drought.

CONCLUSIONS

Selecting for beneficial root hair traits can enhance yield stability without diminishing yield potential, overcoming the breeder's dilemma of trying to simultaneously enhance both productivity and resilience. Therefore, the maintenance or enhancement of root hairs can represent a key trait for breeding the next generation of crops for improved drought tolerance in relation to climate change.

Precipitation-optimised targeting of nitrogen fertilisers in a model maize cropping system

Typically, half of the nitrogen (N) fertiliser applied to agricultural fields is lost to the wider environment. This inefficiency is driven by soil processes such as denitrification, volatilisation, surface run-off and leaching. Rainfall plays an important role in regulating these processes, ultimately governing when and where N fertiliser moves in soil and its susceptibility to gaseous loss. The interaction between rainfall, plant N uptake and N losses, however, remains poorly understood. In this study we use numerical modelling to predict the optimal N fertilisation strategy with respect to rainfall patterns and offer mechanistic explanations to the resultant differences in optimal times of fertiliser application. We developed a modelling framework that describes water and N transport in soil over a growing season and assesses nitrogen use efficiency (NUE) of split fertilisations within the context of different rainfall patterns. We used ninety rainfall patterns to determine their impact on optimal N fertilisation times. We considered the effects of root growth, root N uptake, microbial transformation of N and the effect of soil water saturation and flow on N movement in the soil profile. On average, we show that weather-optimised fertilisation strategies could improve crop N uptake by 20% compared to the mean uptake. In drier years, weather-optimising N applications improved the efficiency of crop N recovery by 35%. Further analysis shows that maximum plant N uptake is greatest under drier conditions due to reduced leaching, but it is harder to find the maximum due to low N mobility. The model could capture contrasting trends in NUE seen in previous arable cropping field trials. Furthermore, the model predicted that the variability in NUE seen in the field could be associated with precipitation-driven differences in N leaching and mobility. In conclusion, our results show that NUE in cropping systems could be significantly enhanced by synchronising fertiliser timings with both crop N demand and local weather patterns.

Space and time-resolved monitoring of phosphorus release from a fertilizer pellet and its mobility in soil using microdialysis and X-ray computed tomography

Phosphorus is an essential nutrient for crops. Precise spatiotemporal application of P fertilizer can improve plant P acquisition and reduce run-off losses of P. Optimizing application would benefit from understanding the dynamics of P release from a fertilizer pellet into bulk soil, which requires space- and time-resolved measurements of P concentration in soil solutions. In this study, we combined microdialysis and X-ray computed tomography to investigate P transport in soil. Microdialysis probes enabled repeated solute sampling from one location with minimal physical disturbance, and their small dimensions permitted spatially resolved monitoring. We observed a rapid initial release of P from the source, producing high dissolved P concentrations within the first 24 h, followed by a decrease in dissolved P over time compatible with adsorption onto soil particles. Soils with greater bulk density (i.e., reduced soil porosity) impeded the P pulse movement, which resulted in a less homogeneous distribution of total P in the soil column at the end of the experiment. The model fit to the data showed that the observed phenomena can be explained by diffusion and adsorption. The results showed that compared with conventional measurement techniques (e.g., suction cups), microdialysis measurements present a less invasive alternative. The time-resolved measurements ultimately highlighted rapid P dynamics that require more attention for improving P use efficiency.

Developing a system for in vivo imaging of maize roots containing iodinated contrast media in soil using synchrotron XCT and XRF

AIMS

We sought to develop a novel experimental system which enabled application of iodinated contrast media to in vivo plant roots intact in soil and was compatible with time-resolved synchrotron X-ray computed tomography imaging. The system was developed to overcome issues of low contrast to noise within X-ray computed tomography images of plant roots and soil environments, the latter of which can complicate image processing and result in the loss of anatomical information.

METHODS

To demonstrate the efficacy of the system we employ the novel use of both synchrotron X-ray computed tomography and synchrotron X-ray fluorescence mapping to capture the translocation of the contrast media through root vasculature into the leaves.

RESULTS

With the application of contrast media we identify fluid flow in root vasculature and visualise anatomical features, which are otherwise often only observable in ex vivo microscopy, including: the xylem, metaxylem, pith, fibres in aerenchyma and leaf venation. We are also able to observe interactions between aerenchyma cross sectional area and solute transport in the root vasculature with depth.

CONCLUSIONS

Our novel system was capable of successfully delivering sufficient contrast media into root and leaf tissues such that anatomical features could be visualised and internal fluid transport observed. We propose that our system could be used in future to study internal plant transport mechanisms and parameterise models for fluid flow in plants.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11104-020-04784-x.

Image-based quantification of soil microbial dead zones induced by nitrogen fertilization

Microbial communities in agricultural soils underpin many ecosystem services including the maintenance of soil structure, food production, water purification and carbon storage. However, the impact of fertilization on the health of microbial communities is not well understood. This study investigates the spatial and temporal dynamics of nitrogen (N) transport away from a fertilizer granule with pore scale resolution. Specifically, we examined how soil structure and moisture content influence fertilizer derived N movement through the soil pore network and the subsequent impact of on soil microbial communities. We develop a mathematical model to describe N transport and reactions in soil at the pore-scale. Using X-ray Computed Tomography scans, we reconstructed a microscale description of a soil-pore geometry as a computational mesh. Solving two-phase water/air model produced pore-scale water distributions at 15, 30 and 70% water-filled pore volume. The N-speciation model considered ammonium (NH₄⁺), nitrate (NO₃^-) and dissolved organic N (DON), and included N immobilization, ammonification and nitrification processes, as well as diffusion in soil solution. We simulated the dissolution of a fertilizer pellet and a pore scale N cycle at three different water saturations. To aid interpretation of the model results, microbial activity at a range of N concentrations was measured. The model showed that the diffusion and concentration of N in water films is critically dependent upon soil moisture and N species. We predict that the maximum NH₄⁺ and NO₃^- concentrations in soil solution around the pellet under dry conditions are in the order of 1 × 10³ and 1 × 10⁴ mol m^-3 respectively, and under wet conditions 2 × 10² and 1 × 10³ mol m^-3, respectively. Supporting experimental evidence suggests that these concentrations would be sufficient to reduce microbial activity in the short-term in the zone immediately around the fertilizer pellet (ranging from 0.9 to 3.8 mm), causing a major loss of soil biological functioning. This model demonstrates the importance of pore-scale processes in regulating N movement and their interactions with the soil microbiome.

Linking root structure to functionality: the impact of root system architecture on citrate-enhanced phosphate uptake

Root citrate exudation is thought to be important for phosphate solubilization. Previous research has concluded that cluster-like roots benefit most from this exudation in terms of increased phosphate uptake, suggesting that root structure plays an important role in citrate-enhanced uptake (additional phosphate uptake due to citrate exudation). Time-resolved computed tomography images of wheat root systems were used as the geometry for 3D citrate-phosphate solubilization models. Citrate-enhanced uptake was correlated with morphological measures of the root systems to determine which had the most benefit. A large variation of citrate-enhanced uptake over 11 root structures was observed. Root surface area dominated absolute phosphate uptake, but did not explain citrate-enhanced uptake. Number of exuding root tips correlated well with citrate-enhanced uptake. Root tips in close proximity could collectively exude high amounts of citrate, resulting in a delayed spike in citrate-enhanced uptake. Root system architecture plays an important role in citrate-enhanced uptake. Singular morphological measurements of the root systems cannot entirely explain variations in citrate-enhanced uptake. Root systems with many tips would benefit greatly from citrate exudation. Quantifying citrate-enhanced uptake experimentally is difficult as variations in root surface area would overwhelm citrate benefits.

Mechanisms of root reinforcement in soils: an experimental methodology using four-dimensional X-ray computed tomography and digital volume correlation

Vegetation on railway or highway slopes can improve slope stability through the generation of soil pore water suctions by plant transpiration and mechanical soil reinforcement by the roots. To incorporate the enhanced shearing resistance and stiffness of root-reinforced soils in stability calculations, it is necessary to understand and quantify its effectiveness. This requires integrated and sophisticated experimental and multi-scale modelling approaches to develop an understanding of the processes at different length scales, from individual root-soil interaction through to full soil-profile or slope scale. One of the challenges with multi-scale models is ensuring that they sufficiently closely represent real behaviour. This requires calibration against detailed high-quality and data-rich experiments. This study presents a novel experimental methodology, which combines in situ direct shear loading of a willow root-reinforced soil with X-ray computed tomography to capture the three-dimensional chronology of soil and root deformation within the shear zone. Digital volume correlation (DVC) analysis was applied to the computed tomography dataset to obtain full-field three-dimensional displacement and strain information. This paper demonstrates the feasibility and discusses the challenges associated with DVC experiments on root-reinforced soils.

A four-compartment multiscale model of fluid and drug distribution in vascular tumours

The subtle relationship between vascular network structure and mass transport is vital to predict and improve the efficacy of anticancer treatments. Here, mathematical homogenisation is used to derive a new multiscale continuum model of blood and chemotherapy transport in the vasculature and interstitium of a vascular tumour. This framework enables information at a range of vascular hierarchies to be fed into an effective description on the length scale of the tumour. The model behaviour is explored through a demonstrative case study of a simplified representation of a dorsal skinfold chamber, to examine the role of vascular network architecture in influencing fluid and drug perfusion on the length scale of the chamber. A single parameter, P, is identified that relates tumour-scale fluid perfusion to the permeability and density of the capillary bed. By fixing the topological and physiological properties of the arteriole and venule networks, an optimal value for P is identified, which maximises tumour fluid transport and is thus hypothesised to benefit chemotherapy delivery. We calculate the values for P for eight explicit network structures; in each case, vascular intervention by either decreasing the permeability or increasing the density of the capillary network would increase fluid perfusion through the cancerous tissue. Chemotherapeutic strategies are compared and indicate that single injection is consistently more successful compared with constant perfusion, and the model predicts optimal timing of a second dose. These results highlight the potential of computational modelling to elucidate the link between vascular architecture and fluid, drug distribution in tumours.

Root-induced soil deformation influences Fe, S and P: rhizosphere chemistry investigated using synchrotron XRF and XANES

Rhizosphere soil has distinct physical and chemical properties from bulk soil. However, besides root-induced physical changes, chemical changes have not been extensively measured in situ on the pore scale. In this study, we couple structural information, previously obtained using synchrotron X-ray computed tomography (XCT), with synchrotron X-ray fluorescence microscopy (XRF) and X-ray absorption near-edge structure (XANES) to unravel chemical changes induced by plant roots. Our results suggest that iron (Fe) and sulfur (S) increase notably in the direct vicinity of the root via solubilization and microbial activity. XANES further shows that Fe is slightly reduced, S is increasingly transformed into sulfate (SO₄^2- ) and phosphorus (P) is increasingly adsorbed to humic substances in this enrichment zone. In addition, the ferrihydrite fraction decreases drastically, suggesting the preferential dissolution and the formation of more stable Fe oxides. Additionally, the increased transformation of organic S to sulfate indicates that the microbial activity in this zone is increased. These changes in soil chemistry correspond to the soil compaction zone as previously measured via XCT. The fact that these changes are colocated near the root and the compaction zone suggests that decreased permeability as a result of soil structural changes acts as a barrier creating a zone with increased rhizosphere chemical interactions via surface-mediated processes, microbial activity and acidification.

Significance of root hairs at the field scale - modelling root water and phosphorus uptake under different field conditions

ABSTRACT

BACKGROUND AND AIMS

Root hairs play a significant role in phosphorus (P) extraction at the pore scale. However, their importance at the field scale remains poorly understood.

METHODS

This study uses a continuum model to explore the impact of root hairs on the large-scale uptake of P, comparing root hair influence under different agricultural scenarios. High vs low and constant vs decaying P concentrations down the soil profile are considered, along with early vs late precipitation scenarios.

RESULTS

Simulation results suggest root hairs accounted for 50% of total P uptake by plants. Furthermore, a delayed initiation time of precipitation potentially limits the P uptake rate by over 50% depending on the growth period. Despite the large differences in the uptake rate, changes in the soil P concentration in the domain due to root solute uptake remains marginal when considering a single growth season. However, over the duration of 6 years, simulation results showed that noticeable differences arise over time.

CONCLUSION

Root hairs are critical to P capture, with uptake efficiency potentially enhanced by coordinating irrigation with P application during earlier growth stages of crops.

Quantifying citrate-enhanced phosphate root uptake using microdialysis

AIMS

Organic acid exudation by plant roots is thought to promote phosphate (P) solubilisation and bioavailability in soils with poorly available nutrients. Here we describe a new combined experimental (microdialysis) and modelling approach to quantify citrate-enhanced P desorption and its importance for root P uptake.

METHODS

To mimic the rhizosphere, microdialysis probes were placed in soil and perfused with citrate solutions (0.1, 1.0 and 10 mM) and the amount of P recovered from soil used to quantify rhizosphere P availability. Parameters in a mathematical model describing probe P uptake, citrate exudation, P movement and citrate-enhanced desorption were fit to the experimental data. These parameters were used in a model of a root which exuded citrate and absorbed P. The importance of soil citrate-P mobilisation for root P uptake was then quantified using this model.

RESULTS

A plant needs to exude citrate at a rate of 0.73 μmol cm^-1 of root h^-1 to see a significant increase in P absorption. Microdialysis probes with citrate in the perfusate were shown to absorb similar quantities of P to an exuding root.

CONCLUSION

A single root exuding citrate at a typical rate (4.3 × 10^-5 μmol m^-1 of root h^-1) did not contribute significantly to P uptake. Microdialysis probes show promise for measuring rhizosphere processes when calibration experiments and mathematical modelling are used to decouple microdialysis and rhizosphere mechanisms.

Soil carbon dioxide venting through rice roots

The growth of rice in submerged soils depends on its ability to form continuous gas channels-aerenchyma-through which oxygen (O2 ) diffuses from the shoots to aerate the roots. Less well understood is the extent to which aerenchyma permits venting of respiratory carbon dioxide (CO2 ) in the opposite direction. Large, potentially toxic concentrations of dissolved CO2 develop in submerged rice soils. We show using X-ray computed tomography and image-based mathematical modelling that CO2 venting through rice roots is far greater than thought hitherto. We found rates of venting equivalent to a third of the daily CO2 fixation in photosynthesis. Without this venting through the roots, the concentrations of CO2 and associated bicarbonate (HCO3- ) in root cells would have been well above levels known to be toxic to roots. Removal of CO2 and hence carbonic acid (H2 CO3 ) from the soil was sufficient to increase the pH in the rhizosphere close to the roots by 0.7 units, which is sufficient to solubilize or immobilize various nutrients and toxicants. A sensitivity analysis of the model showed that such changes are expected for a wide range of plant and soil conditions.

Stabilizing gold nanoparticles for use in X-ray computed tomography imaging of soil systems

This investigation establishes a system of gold nanoparticles that show good colloidal stability as an X-ray computed tomography (XCT) contrast agent under soil conditions. Gold nanoparticles offer numerous beneficial traits for experiments in biology including: comparatively minimal phytotoxicity, X-ray attenuation of the material and the capacity for functionalization. However, soil salinity, acidity and surface charges can induce aggregation and destabilize gold nanoparticles, hence in biomedical applications polymer coatings are commonly applied to gold nanoparticles to enhance stability in the in vivo environment. Here we first demonstrate non-coated nanoparticles aggregate in soil-water solutions. We then show coating with a polyethylene glycol (PEG) layer prevents this aggregation. To demonstrate this, PEG-coated nanoparticles were drawn through flow columns containing soil and were shown to be stable; this is in contrast with control experiments using silica and alumina-packed columns. We further determined that a suspension of coated gold nanoparticles which fully saturated soil maintained stability over at least 5 days. Finally, we used time resolved XCT imaging and image based models to approximate nanoparticle diffusion as similar to that of other typical plant nutrients diffusing in water. Together, these results establish the PEGylated gold nanoparticles as potential contrast agents for XCT imaging in soil.

Multiple Scale Homogenisation of Nutrient Movement and Crop Growth in Partially Saturated Soil

In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth of each tuber is dependent on the uptake of nutrients via a sink term within the soil representing root nutrient uptake. Special attention is paid to the reduction in void space, resulting change in local water content and the impact on nutrient diffusion within the soil as the tubers increase in size. To validate the multiple scale homogenisation procedure, we compare the system of homogenised equations to the original set of equations and find that the solutions between the two models differ by [Formula: see text]. However, we find that the computation time between the two sets of equations differs by several orders of magnitude. This is due to the combined effects of the complex three-dimensional geometry and the implementation of a moving boundary condition to capture tuber growth.

Correlative 3D Imaging and Microfluidic Modelling of Human Pulmonary Lymphatics using Immunohistochemistry and High-resolution μCT

Lung lymphatics maintain fluid homoeostasis by providing a drainage system that returns fluid, cells and metabolites to the circulatory system. The 3D structure of the human pulmonary lymphatic network is essential to lung function, but it is poorly characterised. Image-based 3D mathematical modelling of pulmonary lymphatic microfluidics has been limited by the lack of accurate and representative image geometries. This is due to the microstructural similarity of the lymphatics to the blood vessel network, the lack of lymphatic-specific biomarkers, the technical limitations associated with image resolution in 3D, and sectioning artefacts present in 2D techniques. We present a method that combines lymphatic specific (D240 antibody) immunohistochemistry (IHC), optimised high-resolution X-ray microfocus computed tomography (μCT) and finite-element mathematical modelling to assess the function of human peripheral lung tissue. The initial results identify lymphatic heterogeneity within and between lung tissue. Lymphatic vessel volume fraction and fractal dimension significantly decreases away from the lung pleural surface (p < 0.001, n = 25 and p < 0.01, n = 20, respectively). Microfluidic modelling successfully shows that in lung tissue the fluid derived from the blood vessels drains through the interstitium into the lymphatic vessel network and this drainage is different in the subpleural space compared to the intralobular space. When comparing lung tissue from health and disease, human pulmonary lymphatics were significantly different across five morphometric measures used in this study (p ≤ 0.0001). This proof of principle study establishes a new engineering technology and workflow for further studies of pulmonary lymphatics and demonstrates for the first time the combination of correlative μCT and IHC to enable 3D mathematical modelling of human lung microfluidics at micrometre resolution.

Imaging microstructure of the barley rhizosphere: particle packing and root hair influences

Soil adjacent to roots has distinct structural and physical properties from bulk soil, affecting water and solute acquisition by plants. Detailed knowledge on how root activity and traits such as root hairs affect the three-dimensional pore structure at a fine scale is scarce and often contradictory. Roots of hairless barley (Hordeum vulgare L. cv Optic) mutant (NRH) and its wildtype (WT) parent were grown in tubes of sieved (<250 μm) sandy loam soil under two different water regimes. The tubes were scanned by synchrotron-based X-ray computed tomography to visualise pore structure at the soil-root interface. Pore volume fraction and pore size distribution were analysed vs distance within 1 mm of the root surface. Less dense packing of particles at the root surface was hypothesised to cause the observed increased pore volume fraction immediately next to the epidermis. The pore size distribution was narrower due to a decreased fraction of larger pores. There were no statistically significant differences in pore structure between genotypes or moisture conditions. A model is proposed that describes the variation in porosity near roots taking into account soil compaction and the surface effect at the root surface.

Surface tension, rheology and hydrophobicity of rhizodeposits and seed mucilage influence soil water retention and hysteresis

AIMS

Rhizodeposits collected from hydroponic solutions with roots of maize and barley, and seed mucilage washed from chia, were added to soil to measure their impact on water retention and hysteresis in a sandy loam soil at a range of concentrations. We test the hypothesis that the effect of plant exudates and mucilages on hydraulic properties of soils depends on their physicochemical characteristics and origin.

METHODS

Surface tension and viscosity of the exudate solutions were measured using the Du Noüy ring method and a cone-plate rheometer, respectively. The contact angle of water on exudate treated soil was measured with the sessile drop method. Water retention and hysteresis were measured by equilibrating soil samples, treated with exudates and mucilages at 0.46 and 4.6 mg g-1 concentration, on dialysis tubing filled with polyethylene glycol (PEG) solution of known osmotic potential.

RESULTS

Surface tension decreased and viscosity increased with increasing concentration of the exudates and mucilage in solutions. Change in surface tension and viscosity was greatest for chia seed exudate and least for barley root exudate. Contact angle increased with increasing maize root and chia seed exudate concentration in soil, but not barley root. Chia seed mucilage and maize root rhizodeposits enhanced soil water retention and increased hysteresis index, whereas barley root rhizodeposits decreased soil water retention and the hysteresis effect. The impact of exudates and mucilages on soil water retention almost ceased when approaching wilting point at -1500 kPa matric potential.

CONCLUSIONS

Barley rhizodeposits behaved as surfactants, drying the rhizosphere at smaller suctions. Chia seed mucilage and maize root rhizodeposits behaved as hydrogels that hold more water in the rhizosphere, but with slower rewetting and greater hysteresis.

Can VEGFC Form Turing Patterns in the Zebrafish Embryo?

This paper is concerned with a late stage of lymphangiogenesis in the trunk of the zebrafish embryo. At 48 hours post-fertilisation (HPF), a pool of parachordal lymphangioblasts (PLs) lies in the horizontal myoseptum. Between 48 and 168 HPF, the PLs spread from the horizontal myoseptum to form the thoracic duct, dorsal longitudinal lymphatic vessel, and parachordal lymphatic vessel. This paper deals with the potential of vascular endothelial growth factor C (VEGFC) to guide the differentiation of PLs into the mature lymphatic endothelial cells that form the vessels. We built a mathematical model to describe the biochemical interactions between VEGFC, collagen I, and matrix metalloproteinase 2 (MMP2). We also carried out a linear stability analysis of the model and computer simulations of VEGFC patterning. The results suggest that VEGFC can form Turing patterns due to its relations with MMP2 and collagen I, but the zebrafish embryo needs a separate control mechanism to create the right physiological conditions. Furthermore, this control mechanism must ensure that the VEGFC patterns are useful for lymphangiogenesis: stationary, steep gradients, and reasonably fast forming. Generally, the combination of a patterning species, a matrix protein, and a remodelling species is a new patterning mechanism.

The effect of root exudates on rhizosphere water dynamics

Most water and nutrients essential for plant growth travel across a thin zone of soil at the interface between roots and soil, termed the rhizosphere. Chemicals exuded by plant roots can alter the fluid properties, such as viscosity, of the water phase, potentially with impacts on plant productivity and stress tolerance. In this paper, we study the effects of plant exudates on the macroscale properties of water movement in soil. Our starting point is a microscale description of two fluid flow and exudate diffusion in a periodic geometry composed from a regular repetition of a unit cell. Using multiscale homogenization theory, we derive a coupled set of equations that describe the movement of air and water, and the diffusion of plant exudates on the macroscale. These equations are parametrized by a set of cell problems that capture the flow behaviour. The mathematical steps are validated by comparing the resulting homogenized equations to the original pore scale equations, and we show that the difference between the two models is ≲7% for eight cells. The resulting equations provide a computationally efficient method to study plant-soil interactions. This will increase our ability to predict how contrasting root exudation patterns may influence crop uptake of water and nutrients.

Using high resolution X-ray computed tomography to create an image based model of a lymph node

Lymph nodes are an important part of the immune system. They filter the lymphatic fluid as it is transported from the tissues before being returned to the blood stream. The fluid flow through the nodes influences the behaviour of the immune cells that gather within the nodes and the structure of the node itself. Measuring the fluid flow in lymph nodes experimentally is challenging due to their small size and fragility. In this paper, we present high resolution X-ray computed tomography images of a murine lymph node. The impact of the resulting visualized structures on fluid transport are investigated using an image based model. The high contrast between different structures within the lymph node provided by phase contrast X-ray computed tomography reconstruction results in images that, when related to the permeability of the lymph node tissue, suggest an increased fluid velocity through the interstitial channels in the lymph node tissue. Fluid taking a direct path from the afferent to the efferent lymphatic vessel, through the centre of the node, moved faster than the fluid that flowed around the periphery of the lymph node. This is a possible mechanism for particles being moved into the cortex.

Measurement of micro-scale soil deformation around roots using four-dimensional synchrotron tomography and image correlation

This study applied time lapse (four-dimensional) synchrotron X-ray computed tomography to observe micro-scale interactions between plant roots and soil. Functionally contrasting maize root tips were repeatedly imaged during ingress into soil columns of varying water content and compaction. This yielded sequences of three-dimensional densiometric data, representing time-resolved geometric soil and root configurations at the micronmetre scale. These data were used as inputs for two full-field kinematic quantification methods, which enabled the analysis of three-dimensional soil deformation around elongating roots. Discrete object tracking was used to track rigid mineral grains, while continuum digital volume correlation was used to track grey-level patterns within local sub-volumes. These techniques both allowed full-field soil displacements to be quantified at an intra-rhizosphere spatial sampling scale of less than 300 µm. Significant differences in deformation mechanisms were identified around different phenotypes under different soil conditions. A uniquely strong contrast was observed between intact and de-capped roots grown in dry, compacted soil. This provides evidence that functional traits of the root cap significantly reduce the amount of soil disturbance per unit of root elongation, with this effect being particularly significant in drier soil.

Determination of macro-scale soil properties from pore scale structures: image-based modelling of poroelastic structures

We show how a combination of X-ray computed tomography (X-CT) and image-based modelling can be used to calculate the effect of moisture content and compaction on the macroscopic structural properties of soil. Our method is based on the equations derived in Daly & Roose (2018 Proc. R. Soc. A474, 20170141. (doi:10.1098/rspa.2017.0141)), which we have extended so they can be directly applied to the segmented images obtained from X-CT. We assume that the soils are composed of air-filled pore space, solid mineral grains and a mixed phase composed of both clay particles and water. We considered three different initial soil treatments, composed of two different compaction levels and two different moisture contents. We found that the effective properties of the soils were unaffected by compaction over the range tested in this paper. However, changing the moisture content significantly altered the hydraulic and mechanical properties of the soils. A key strength of this method is that it enables the optimization or even design of soils composed from different constituents, with specific mechanical and hydraulic properties.

Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

A Model of Uranium Uptake by Plant Roots Allowing for Root-Induced Changes in the soil

We develop a model with which to study the poorly understood mechanisms of uranium (U) uptake by plants. The model is based on equations for transport and reaction of U and acids and bases in the rhizosphere around cylindrical plant roots. It allows for the speciation of U with hydroxyl, carbonate, and organic ligands in the soil solution; the nature and kinetics of sorption reactions with the soil solid; and the effects of root-induced changes in rhizosphere pH. A sensitivity analysis showed the importance of soil sorption and speciation parameters as influenced by pH and CO₂ pressure; and of root geometry and root-induced acid-base changes linked to the form of nitrogen taken up by the root. The root absorbing coefficient for U, relating influx to the concentration of U species in solution at the root surface, was also important. Simplified empirical models of U uptake by different plant species and soil types need to account for these effects.

Determination of macro-scale soil properties from pore-scale structures: model derivation

In this paper, we use homogenization to derive a set of macro-scale poro-elastic equations for soils composed of rigid solid particles, air-filled pore space and a poro-elastic mixed phase. We consider the derivation in the limit of large deformation and show that by solving representative problems on the micro-scale we can parametrize the macro-scale equations. To validate the homogenization procedure, we compare the predictions of the homogenized equations with those of the full equations for a range of different geometries and material properties. We show that the results differ by [Formula: see text] for all cases considered. The success of the homogenization scheme means that it can be used to determine the macro-scale poro-elastic properties of soils from the underlying structure. Hence, it will prove a valuable tool in both characterization and optimization.

Quantification of root water uptake in soil using X-ray computed tomography and image-based modelling

Spatially averaged models of root-soil interactions are often used to calculate plant water uptake. Using a combination of X-ray computed tomography (CT) and image-based modelling, we tested the accuracy of this spatial averaging by directly calculating plant water uptake for young wheat plants in two soil types. The root system was imaged using X-ray CT at 2, 4, 6, 8 and 12 d after transplanting. The roots were segmented using semi-automated root tracking for speed and reproducibility. The segmented geometries were converted to a mesh suitable for the numerical solution of Richards' equation. Richards' equation was parameterized using existing pore scale studies of soil hydraulic properties in the rhizosphere of wheat plants. Image-based modelling allows the spatial distribution of water around the root to be visualized and the fluxes into the root to be calculated. By comparing the results obtained through image-based modelling to spatially averaged models, the impact of root architecture and geometry in water uptake was quantified. We observed that the spatially averaged models performed well in comparison to the image-based models with <2% difference in uptake. However, the spatial averaging loses important information regarding the spatial distribution of water near the root system.

Fluid flow in porous media using image-based modelling to parametrize Richards' equation

The parameters in Richards' equation are usually calculated from experimentally measured values of the soil-water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn-Hilliard-Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil-water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.

Plant exudates may stabilize or weaken soil depending on species, origin and time

We hypothesized that plant exudates could either gel or disperse soil depending on their chemical characteristics. Barley (Hordeum vulgare L. cv. Optic) and maize (Zea mays L. cv. Freya) root exudates were collected using an aerated hydroponic method and compared with chia (Salvia hispanica L.) seed exudate, a commonly used root exudate analogue. Sandy loam soil was passed through a 500-μm mesh and treated with each exudate at a concentration of 4.6 mg exudate g-1 dry soil. Two sets of soil samples were prepared. One set of treated soil samples was maintained at 4°C to suppress microbial processes. To characterize the effect of decomposition, the second set of samples was incubated at 16°C for 2 weeks at -30 kPa matric potential. Gas chromatography-mass spectrometry (GC-MS) analysis of the exudates showed that barley had the largest organic acid content and chia the largest content of sugars (polysaccharide-derived or free), and maize was in between barley and chia. Yield stress of amended soil samples was measured by an oscillatory strain sweep test with a cone plate rheometer. When microbial decomposition was suppressed at 4°C, yield stress increased 20-fold for chia seed exudate and twofold for maize root exudate compared with the control, whereas for barley root exudate decreased to half. The yield stress after 2 weeks of incubation compared with soil with suppressed microbial decomposition increased by 85% for barley root exudate, but for chia and maize it decreased by 87 and 54%, respectively. Barley root exudation might therefore disperse soil and this could facilitate nutrient release. The maize root and chia seed exudates gelled soil, which could create a more stable soil structure around roots or seeds.

HIGHLIGHTS

Rheological measurements quantified physical behaviour of plant exudates and effect on soil stabilization.Barley root exudates dispersed soil, which could release nutrients and carbon.Maize root and chia seed exudates had a stabilizing effect on soil.Physical engineering of soil in contact with plant roots depends on the nature and origin of exudates.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

An Explicit Structural Model of Root Hair and Soil Interactions Parameterised by Synchrotron X-ray Computed Tomography

The rhizosphere is a zone of fundamental importance for understanding the dynamics of nutrient acquisition by plant roots. The canonical difficulty of experimentally investigating the rhizosphere led long ago to the adoption of mathematical models, the most sophisticated of which now incorporate explicit representations of root hairs and rhizosphere soil. Mathematical upscaling regimes, such as homogenisation, offer the possibility of incorporating into larger-scale models the important mechanistic processes occurring at the rhizosphere scale. However, we lack concrete descriptions of all the features required to fully parameterise models at the rhizosphere scale. By combining synchrotron X-ray computed tomography (SRXCT) and a novel root growth assay, we derive a three-dimensional description of rhizosphere soil structure suitable for use in multi-scale modelling frameworks. We describe an approach to mitigate sub-optimal root hair detection via structural root hair growth modelling. The growth model is explicitly parameterised with SRXCT data and simulates three-dimensional root hair ideotypes in silico, which are suitable for both ideotypic analysis and parameterisation of 3D geometry in mathematical models. The study considers different hypothetical conditions governing root hair interactions with soil matrices, with their respective effects on hair morphology being compared between idealised and image-derived soil/root geometries. The studies in idealised geometries suggest that packing arrangement of soil affects hair tortuosity more than the particle diameter. Results in field-derived soil suggest that hair access to poorly mobile nutrients is particularly sensitive to the physical interaction between the growing hairs and the phase of the soil in which soil water is present (i.e. the hydrated textural phase). The general trends in fluid-coincident hair length with distance from the root, and their dependence on hair/soil interaction mechanisms, are conserved across Cartesian and cylindrical geometries.

High-resolution synchrotron imaging shows that root hairs influence rhizosphere soil structure formation

In this paper, we provide direct evidence of the importance of root hairs on pore structure development at the root-soil interface during the early stage of crop establishment. This was achieved by use of high-resolution (c. 5 μm) synchrotron radiation computed tomography (SRCT) to visualise both the structure of root hairs and the soil pore structure in plant-soil microcosms. Two contrasting genotypes of barley (Hordeum vulgare), with and without root hairs, were grown for 8 d in microcosms packed with sandy loam soil at 1.2 g cm-3 dry bulk density. Root hairs were visualised within air-filled pore spaces, but not in the fine-textured soil regions. We found that the genotype with root hairs significantly altered the porosity and connectivity of the detectable pore space (> 5 μm) in the rhizosphere, as compared with the no-hair mutants. Both genotypes showed decreasing pore space between 0.8 and 0.1 mm from the root surface. Interestingly the root-hair-bearing genotype had a significantly greater soil pore volume-fraction at the root-soil interface. Effects of pore structure on diffusion and permeability were estimated to be functionally insignificant under saturated conditions when simulated using image-based modelling.

The Application of Contrast Media for In Vivo Feature Enhancement in X-Ray Computed Tomography of Soil-Grown Plant Roots

The use of in vivo X-ray microcomputed tomography (μCT) to study plant root systems has become routine, but is often hampered by poor contrast between roots, soil, soil water, and soil organic matter. In clinical radiology, imaging of poorly contrasting regions is frequently aided by the use of radio-opaque contrast media. In this study, we present evidence for the utility of iodinated contrast media (ICM) in the study of plant root systems using μCT. Different dilutions of an ionic and nonionic ICM (Gastrografin 370 and Niopam 300) were perfused into the aerial vasculature of juvenile pea plants via a leaf flap (Pisum sativum). The root systems were imaged via μCT, and a variety of image-processing approaches used to quantify and compare the magnitude of the contrast enhancement between different regions. Though the treatment did not appear to significantly aid extraction of full root system architectures from the surrounding soil, it did allow the xylem and phloem units of seminal roots and the vascular morphology within rhizobial nodules to be clearly visualized. The nonionic, low-osmolality contrast agent Niopam appeared to be well tolerated by the plant, whereas Gastrografin showed evidence of toxicity. In summary, the use of iodine-based contrast media allows usually poorly contrasting root structures to be visualized nondestructively using X-ray μCT. In particular, the vascular structures of roots and rhizobial nodules can be clearly visualized in situ.

A Mathematical Model of Lymphangiogenesis in a Zebrafish Embryo

The lymphatic system of a vertebrate is important in health and diseases. We propose a novel mathematical model to elucidate the lymphangiogenic processes in zebrafish embryos. Specifically, we are interested in the period when lymphatic endothelial cells (LECs) exit the posterior cardinal vein and migrate to the horizontal myoseptum of a zebrafish embryo. We wonder whether vascular endothelial growth factor C (VEGFC) is a morphogen and a chemotactic factor for these LECs. The model considers the interstitial flow driving convection, the reactive transport of VEGFC, and the changing dynamics of the extracellular matrix in the embryo. Simulations of the model illustrate that VEGFC behaves very differently in diffusion and convection-dominant scenarios. In the former case, it must bind to the matrix to establish a functional morphogen gradient. In the latter case, the opposite is true and the pressure field is the key determinant of what VEGFC may do to the LECs. Degradation of collagen I, a matrix component, by matrix metallopeptidase 2 controls the spatiotemporal dynamics of VEGFC. It controls whether diffusion or convection is dominant in the embryo; it can create channels of abundant VEGFC and scarce collagen I to facilitate lymphangiogenesis; when collagen I is insufficient, VEGFC cannot influence the LECs at all. We predict that VEGFC is a morphogen for the migrating LECs, but it is not a chemotactic factor for them.

Phase contrast synchrotron radiation computed tomography of muscle spindles in the mouse soleus muscle

Muscle spindles are skeletal muscle sensory organs involved in the sensation of position and movement of the body. We have explored the capability of phase contrast computed tomography to visualise muscle spindles in murine skeletal muscle. In particular, we have validated the visualisation of nerve fibres through phase contrast computed tomography using light microscopy on stained histological sections. We further present the first three-dimensional visualisation of muscle spindles in mouse soleus skeletal muscle in conjunction with the neurovascular bundle associated with it.

Measurement of strains experienced by viscerofugal nerve cell bodies during mechanosensitive firing using digital image correlation

Mechanosensory neurons detect physical events in the local environments of the tissues that they innervate. Studies of mechanosensitivity of neurons or nerve endings in the gut have related their firing to strain, wall tension, or pressure. Digital image correlation (DIC) is a technique from materials engineering that can be adapted to measure the local physical environments of afferent neurons at high resolution. Flat-sheet preparations of guinea pig distal colon were set up with arrays of tissue markers in vitro. Firing of single viscerofugal neurons was identified in extracellular colonic nerve recordings. The locations of viscerofugal nerve cell bodies were inferred by mapping firing responses to focal application of the nicotinic receptor agonist 1,1-dimethyl-4-phenylpiperazinium iodide. Mechanosensory firing was recorded during load-evoked uniaxial or biaxial distensions. Distension caused movement of surface markers which was captured by video imaging. DIC tracked the markers, interpolating the mechanical state of the gut at the location of the viscerofugal nerve cell body. This technique revealed heterogeneous load-evoked strain within preparations. Local strains at viscerofugal nerve cell bodies were usually smaller than global strain measurements and correlated more closely with mechanosensitive firing. Both circumferential and longitudinal strain activated viscerofugal neurons. Simultaneous loading in circumferential and longitudinal axes caused the highest levels of viscerofugal neuron firing. Multiaxial strains, reflecting tissue shearing and changing area, linearly correlated with mechanosensory firing of viscerofugal neurons. Viscerofugal neurons were mechanically sensitive to both local circumferential and local longitudinal gut strain, and appear to lack directionality in their stretch sensitivity.

Image-based modelling of nutrient movement in and around the rhizosphere

In this study, we developed a spatially explicit model for nutrient uptake by root hairs based on X-ray computed tomography images of the rhizosphere soil structure. This work extends our previous work to larger domains and hence is valid for longer times. Unlike the model used previously, which considered only a small region of soil about the root, we considered an effectively infinite volume of bulk soil about the rhizosphere. We asked the question: At what distance away from root surfaces do the specific structural features of root-hair and soil aggregate morphology not matter because average properties start dominating the nutrient transport? The resulting model was used to capture bulk and rhizosphere soil properties by considering representative volumes of soil far from the root and adjacent to the root, respectively. By increasing the size of the volumes that we considered, the diffusive impedance of the bulk soil and root uptake were seen to converge. We did this for two different values of water content. We found that the size of region for which the nutrient uptake properties converged to a fixed value was dependent on the water saturation. In the fully saturated case, the region of soil we needed to consider was only of radius 1.1mm for poorly soil-mobile species such as phosphate. However, in the case of a partially saturated medium (relative saturation 0.3), we found that a radius of 1.4mm was necessary. This suggests that, in addition to the geometrical properties of the rhizosphere, there is an additional effect of soil moisture properties, which extends further from the root and may relate to other chemical changes in the rhizosphere. The latter were not explicitly included in our model.

Struvite: a slow-release fertiliser for sustainable phosphorus management?

BACKGROUND AND AIM

Recycled sources of phosphorus (P), such as struvite extracted from wastewater, have potential to substitute for more soluble manufactured fertilisers and help reduce the long-term threat to food security from dwindling finite reserves of phosphate rock (PR). This study aimed to determine whether struvite could be a component of a sustainable P fertiliser management strategy for arable crops.

METHODS

A combination of laboratory experiments, pot trials and mathematical modelling of the root system examined the P release properties of commercial fertiliser-grade struvite and patterns of P uptake from a low-P sandy soil by two different crop types, in comparison to more soluble inorganic P fertilisers (di-ammonium phosphate (DAP) and triple super phosphate (TSP)).

RESULTS

Struvite had greatly enhanced solubility in the presence of organic acid anions; buckwheat, which exudes a high level of organic acids, was more effective at mobilising struvite P than the low level exuder, spring wheat. Struvite granules placed with the seed did not provide the same rate of P supply as placed DAP granules for early growth of spring wheat, but gave equivalent rates of P uptake, yield and apparent fertiliser recovery at harvest, even though only 26 % of struvite granules completely dissolved. Fertiliser mixes containing struvite and DAP applied to spring wheat have potential to provide both optimal early and late season P uptake and improve overall P use efficiency.

CONCLUSIONS

We conclude that the potential resource savings and potential efficiency benefits of utilising a recycled slow release fertiliser like struvite offers a more sustainable alternative to only using conventional, high solubility, PR-based fertilisers.

Homogenization of two fluid flow in porous media

The macroscopic behaviour of air and water in porous media is often approximated using Richards' equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e. constant gas pressure, this model is shown to reduce to the simpler form of Richards' equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media with the underlying geometrical and material properties.

Assessing the influence of the rhizosphere on soil hydraulic properties using X-ray computed tomography and numerical modelling

Understanding the dynamics of water distribution in soil is crucial for enhancing our knowledge of managing soil and water resources. The application of X-ray computed tomography (CT) to the plant and soil sciences is now well established. However, few studies have utilized the technique for visualizing water in soil pore spaces. Here this method is utilized to visualize the water in soil in situ and in three-dimensions at successive reductive matric potentials in bulk and rhizosphere soil. The measurements are combined with numerical modelling to determine the unsaturated hydraulic conductivity, providing a complete picture of the hydraulic properties of the soil. The technique was performed on soil cores that were sampled adjacent to established roots (rhizosphere soil) and from soil that had not been influenced by roots (bulk soil). A water release curve was obtained for the different soil types using measurements of their pore geometries derived from CT imaging and verified using conventional methods, such as pressure plates. The water, soil, and air phases from the images were segmented and quantified using image analysis. The water release characteristics obtained for the contrasting soils showed clear differences in hydraulic properties between rhizosphere and bulk soil, especially in clay soil. The data suggest that soils influenced by roots (rhizosphere soil) are less porous due to increased aggregation when compared with bulk soil. The information and insights obtained on the hydraulic properties of rhizosphere and bulk soil will enhance our understanding of rhizosphere biophysics and improve current water uptake models.

How changing root system architecture can help tackle a reduction in soil phosphate (P) levels for better plant P acquisition

The readily available global rock phosphate (P) reserves may run out within the next 50-130 years, causing soils to have a reduced P concentration which will affect plant P uptake. Using a combination of mathematical modelling and experimental data, we investigated potential plant-based options for optimizing crop P uptake in reduced soil P environments. By varying the P concentration within a well-mixed agricultural soil, for high and low P (35.5-12.5 mg L(-1) respectively using Olsen's P index), we investigated branching distributions within a wheat root system that maximize P uptake. Changing the root branching distribution from linear (evenly spaced branches) to strongly exponential (a greater number of branches at the top of the soil) improves P uptake by 142% for low-P soils when root mass is kept constant between simulations. This causes the roots to emerge earlier and mimics topsoil foraging. Manipulating root branching patterns, to maximize P uptake, is not enough on its own to overcome the drop in soil P from high to low P. Further mechanisms have to be considered to fully understand the impact of P reduction on plant development.

Multiscale modelling of hydraulic conductivity in vuggy porous media

Flow in both saturated and non-saturated vuggy porous media, i.e. soil, is inherently multiscale. The complex microporous structure of the soil aggregates and the wider vugs provides a multitude of flow pathways and has received significant attention from the X-ray computed tomography (CT) community with a constant drive to image at higher resolution. Using multiscale homogenization, we derive averaged equations to study the effects of the microscale structure on the macroscopic flow. The averaged model captures the underlying geometry through a series of cell problems and is verified through direct comparison to numerical simulations of the full structure. These methods offer significant reductions in computation time and allow us to perform three-dimensional calculations with complex geometries on a desktop PC. The results show that the surface roughness of the aggregate has a significantly greater effect on the flow than the microstructure within the aggregate. Hence, this is the region in which the resolution of X-ray CT for image-based modelling has the greatest impact.

High resolution synchrotron imaging of wheat root hairs growing in soil and image based modelling of phosphate uptake

· Root hairs are known to be highly important for uptake of sparingly soluble nutrients, particularly in nutrient deficient soils. Development of increasingly sophisticated mathematical models has allowed uptake characteristics to be quantified. However, modelling has been constrained by a lack of methods for imaging live root hairs growing in real soils. · We developed a plant growth protocol and used Synchrotron Radiation X-ray Tomographic Microscopy (SRXTM) to uncover the three-dimensional (3D) interactions of root hairs in real soil. We developed a model of phosphate uptake by root hairs based directly on the geometry of hairs and associated soil pores as revealed by imaging. · Previous modelling studies found that root hairs dominate phosphate uptake. By contrast, our study suggests that hairs and roots contribute equally. We show that uptake by hairs is more localized than by roots and strongly dependent on root hair and aggregate orientation. · The ability to image hair-soil interactions enables a step change in modelling approaches, allowing a more realistic treatment of processes at the scale of individual root hairs in soil pores.