Pressure Probe Technique Research Articles

Discrimination of water stress in pepper using thermography and leaf turgor pressure probe techniques

The use of technology is spreading rapidly in modern agriculture with remote sensing and sensor technologies becoming more important. The objective of this study is to investigate the possibilities of determining the water stress level and irrigation time in peppers using leaf pressure probes based on turgor pressure and thermography techniques. An experiment consisting of four different irrigation treatments (100%, 75%, 50% and 25%) was conducted in Canakkale province, Turkey in the 2017–2018 summer growing seasons. During this seasons, leaf turgor pressure (Pp) and soil moisture levels were recorded in real time by a remote monitoring system. Thermographic measurements were taken before each irrigation. Data were analyzed using the analysis of variance and regression tree methods. Results show that both Pp and thermal data significantly differed according to water stress. Pp values decreased partially after irrigation and increased until the next irrigation. However, it was observed that it is not enough to decide the irrigation time using results obtained from graphical readings only. Models including meteorological features strengthen the decision-making models. According to the classification and regression tree analysis, it was revealed that there is a potential to separate the treatments, especially in models including thermal indices. Leaf turgor pressure data and thermal indices, which are plant-based monitoring techniques, have the potential to be used in determining irrigation time and distinguishing water stress in the pepper plant. However, there is a need for more studies especially in laboratory conditions, to understand the mechanisms in plants and how environmental conditions affect the responses of Pp probes.

High hydrostatic pressure effects on membrane-related quality parameters of fresh radish tubers

The impacts of high hydrostatic pressure (HHP) treatments on metabolic functionality and quality of fruit and vegetables are still poorly understood. The effects of pressure intensity (100, 150 and 200 MPa) and holding time (5 and 10 min), and temperatures (20, 30 and 40 °C) during HHP treatment on fresh radish tubers has been studied. Colour, stiffness and turgor of the tubers were evaluated using colorimetry, texture analyses and direct turgor measurements with the cell pressure probe techniques. Comparison of turgor and stiffness losses, and colour changes, of skin and thin-walled parenchymatous inner radish tissue showed the effects of the various HHP treatment parameters on the permeability of biomembranes. HHP treatment resulted in a rapid reduction of cell turgor and, concomitantly of tuber stiffness, but also in a cellular redistribution of anthocyanins as indicated by colour changes. These responses were partially reversible up to 100 MPa applied pressure at 20-40 °C for 5–10 min, yielding a turgor threshold of 0.1 MPa. Beyond these limits, changes were irreversible, most probably due to the denaturation of membrane bound proteins such as ion channels and pumps. Overall, even short-term HHP treatments at room temperature are not suitable for sanitation by inactivating bacteria of perishable produce.

Hydraulic conductivity of soil-grown lupine and maize unbranched roots and maize root-shoot junctions

Improving or maintaining crop productivity under conditions of long term change of soil water availability and atmosphere demand for water is one the big challenges of this century. It requires a deep understanding of crop water acquisition properties, i.e. root system architecture and root hydraulic properties among other characteristics of the soil-plant-atmosphere continuum. A root pressure probe technique was used to measure the root hydraulic conductances of seven-week old maize and lupine plants grown in sandy soil. Unbranched root segments were excised in lateral, seminal, crown and brace roots of maize, and in lateral roots of lupine. Their total hydraulic conductance was quantified under steady-state hydrostatic gradient for progressively shorter segments. Furthermore, the axial conductance of proximal root regions removed at each step of root shortening was measured as well. Analytical solutions of the water flow equations in unbranched roots developed recently and relating root total conductance profiles to axial and radial conductivities were used to retrieve the root radial hydraulic conductivity profile along each root type, and quantify its uncertainty. Interestingly, the optimized root radial conductivities and measured axial conductances displayed significant differences across root types and species. However, the measured root total conductances did not differ significantly. As compared to measurements reported in the literature, our axial and radial conductivities concentrate in the lower range of herbaceous species hydraulic properties. In a final experiment, the hydraulic conductances of root junctions to maize stem were observed to highly depend on root type. Surprisingly maize brace root junctions were an order of magnitude more conductive than the other crown and seminal roots, suggesting potential regulation mechanism for root water uptake location and a potential role of the maize brace roots for water uptake more important than reported in the literature.

Hydrodynamic study of two phase flow of column flotation using electrical resistance tomography and pressure probe techniques

Gas dispersion characteristics are very important to design and selection of flotation process for the fine particle separation. Although the separation of flotation process heavily depends on hydrophobicity of given solid particles, but their rate of attachment and detachment depends on local gas dispersion characteristics. In this work, gas dispersion characteristics in a 100 mm laboratory column flotation have been investigated by exploring the flow behavior in terms of the local and mean gas hold-up, bubble rise velocity and bubble size distribution across the column. This experimental data has been used to demonstrate the validation of the two-fluid CFD model predictions in the column flotation. The column hydrodynamics are estimated by using high speed dual planar Electrical Resistance Tomography (ERT) system and pressure transducers. In all the experiments, water is used as the liquid phase and air (bubbles) as the disperse phase. Using the ERT system, measurement of two phase distributions are examined for a wide range of design and operating conditions of the column including different spargers and frother dosage, where the flow changes from homogenous to transition bubbly flow. It is confirmed by ERT that the gas-holdup increases with an increase in the sparger porosity, air superficial velocity, liquid height and liquid feed flow rate. To test the reliability of ERT measurements, simultaneously a set of pressure transducers is used to obtain the sectional average gas holdup and validated. It is observed that bubble density occupancy is more at center region of the column and gas holdup value increases with the increase of gas superficial velocity. Dynamic gas disengagement technique is utilized to measure bubble rise velocity and sauter mean bubble diameter. At end this ERT data has been used to validate two-fluid CFD model (modified with suitable drag and lift forces via user defined functions) predictions in the column and found a close agreement.

Characterization of high hydrostatic pressure effects on fresh produce cell turgor using pressure probe analyses

To improve the safety of fresh high quality convenience products, high hydrostatic pressure treatments (HHP) may provide a gentle, quality retainion alternative to traditional chemical preservation. However, information about the potential impact of HHP on metabolic functionality of fresh produce is rare; the few published studies indicate HHP has effects on physiological activity. These effects were highly product specific due to pronounced variations in both pressure sensitivity and stress responsivity. Biomembranes generally seem to be major physiological targets of HHP treatments. Cell turgor inevitably requires fully intact cell membranes. Turgor has an important impact on the fresh appearance of fresh produce, especially texture. Up to now, there is no investigation available that has directly evaluated the effects of HHP treatments on turgor of fresh vegetable tissue. In this study, the pressure probe technique was applied to comprehensively analyse the turgor of red cabbage tissue by directly measuring the hydrostatic pressure of individual cells. The effects of HHP on the cell turgor were tested at pressures ranging between 150MPa and 250MPa, applied for 5, 10, 15 and 20min. As pronounced changes in pressure could result in related temperature changes, the effects of temperature (35°C to 55°C) on turgor was characterised separately. At 35°C and 45°C, leaf turgor transiently declined after HHP treatment of 150MPa (for up to 10min) but recovered again within 24h; at 55°C, however, it irreversibly dropped to near zero. The same occurred when HHP of 175MPa or above was applied. In general, HHP treatment and temperature increases as well as the duration of treatments interactively affected cell turgor of red cabbage leaves. Critical process parameters derived for gentle application of HHP were 150MPa at 45°C for 10min treatment time.

Mucilage exudation facilitates root water uptake in dry soils.

As plant roots take up water and the soil dries, water depletion is expected to occur in the rhizosphere. However, recent experiments showed that the rhizosphere was wetter than the bulk soil during root water uptake. We hypothesise that the increased water content in the rhizosphere was caused by mucilage exuded by roots. It is probably that the higher water content in the rhizosphere results in higher hydraulic conductivity of the root-soil interface. In this case, mucilage exudation would favour the uptake of water in dry soils. To test this hypothesis, we covered a suction cup, referred to as an artificial root, with mucilage. We placed it in soil with a water content of 0.03cm3cm-3, and used the root pressure probe technique to measure the hydraulic conductivity of the root-soil continuum. The results were compared with measurements with roots not covered with mucilage. The root pressure relaxation curves were fitted with a model of root water uptake including rhizosphere dynamics. The results demonstrated that when mucilage is added to the root surface, it keeps the soil near the roots wet and hydraulically well conductive, facilitating the water flow from dry soils towards the root surface. Mucilage exudation seems to be an optimal plant trait that favours the capture of water when water is scarce.

An examination of suitability of multi-hole pressure probe technique for skin friction measurement in turbulent flow

The problems of misalignment to flow direction and the need to drill a tapping hole on a measurement surface to obtain total and static pressures make the use of Preston probe in skin friction measurement in a turbulent flow a cumbersome task. The suitability of a multi-hole pressure probe in a non-nulling mode to overcome these problems was, therefore, investigated. The near-wall effect on multi-hole pressure probe readings was examined both experimentally and theoretically. The results indicate that the presence of the wall had negligible overall effect. Experiments were carried out in a pipe, on a flat plate and on a swept forward facing step to simulate one-, two-, and three-dimensional turbulent flows. The skin friction coefficient determined using the multi-hole pressure probe was found to have good agreement with published data. Since the technique is based on similarity principle with probe diameter as a characteristic parameter, it is expected that the method would be effective with probe geometries of different sizes provided that they are small enough to be submerged in the boundary layer and that their calibration coefficients are accurately determined.

Comparative monitoring of temporal and spatial changes in tree water status using the non-invasive leaf patch clamp pressure probe and the pressure bomb

Abstract Real-time monitoring of plant water status under field conditions remains difficult to quantify. Here we give evidence that the magnetic-based leaf patch clamp pressure (LPCP) probe is a non-invasive and online-measuring method that can elucidate short- and long-term temporal and spatial dynamics of leaf water status of trees with high precision in real time. Measurements were controlled remotely by telemetry and data transfer to the Internet. Concomitant measurements using the pressure chamber technique (frequently applied for leaf water status monitoring) showed that both techniques yield in principle the same results despite of the high sampling variability of the pressure chamber data. There was a very good correlation between the output pressure signals of the LPCP probe and the balancing pressure values (on average r 2 = 0.90 ± 0.05; n = 8), i.e. the external pressure at which water appears at the cut end of a leaf under pressure chamber conditions. Simultaneously performed direct measurements of leaf cell turgor pressure using the well-established cell turgor pressure probe technique evidenced that both techniques measure relative changes in leaf turgor pressure. The output pressure signals of the LPCP probe and the balancing pressure values were inversely correlated to turgor pressure. Consistent with this, the balancing pressure values and the cell turgor pressure values could be fitted quite well by the same firm theoretical backing derived recently for the LPCP probe ( Zimmermann et al., 2008 ). This finding suggests that use of the LPCP probe technique in agricultural water management can be built up on the knowledge accumulated on spot leaf or stem water potential measurements.

가스터빈 입구에서의 유동 및 스칼라 분포 특성

The goal of paper is to investigate the flow and scalar distribution through the HP Nozzle Guide Vane (NGV) passage. Flow and scalar distribution measurement are conducted by using 5-hole pressure probe and tracing technique, respectively. Three different experimental cases are considered depending on cooling flow condition. The result shows that the vortical secondary flow patterns are observed clearly and these flow characteristics maintain through the NGV passage regardless of cooling flow injection. Compared to center region, the high axial velocity flow is observed near wall region due to cooling flow injection. Without cooling flow, the (scalar) distribution becomes to be uniform quickly due to the strong flow mixing phenomenon. However, in cases of cooling flow, scalar distribution is significantly non-uniform.

Water permeability differs between growing and non-growing barley leaf tissues

A pressure probe technique and an osmotic swelling assay were used to compare water transport properties between growing and non-growing tissues of leaf three of barley. The epidermis was analysed in planta by pressure probe, whereas (predominantly) mesophyll protoplasts were analysed by osmotic swelling. Hydraulic conductivity (Lp) and, by implication, water permeability (Pf) of epidermal cells was 31% higher in the leaf elongation zone (Lp=0.5+/-0.2 microm s-1 MPa-1; Pf=65+/-25 microm s-1; means+/-SD of n=17 cells) than in the, non-growing, emerged leaf zone (Lp=0.4+/-0.1 microm s-1 MPa-1; Pf=50+/-15 microm s-1; n=24; P<0.05). Similarly, water permeability of mesophyll protoplasts was by 55% higher in the elongation compared with emerged leaf zone (Pf=13+/-1 microm s-1 compared with 8+/-1 microm s-1; n=57 and 36 protoplasts, respectively; P<0.01). Within the leaf elongation zone, a small population of larger-sized protoplasts could be distinguished. These protoplasts, which originated most likely from parenchymateous bundle sheath or midrib parenchyma cells, had a three-fold higher water permeability (P<0.001) as mesophyll protoplasts. The effect on Lp and Pf of known aquaporin inhibitors was tested with the pressure probe (Au+, Ag+, Hg2+, phloretin) and the osmotic swelling assay (phloretin). Only phloretin, when applied to protoplasts in the swelling assay caused an average decrease in Pf, but the effect varied between isolations. Technical approaches and cell-type and growth-specific differences in water transport properties are discussed.

Dynamics of aquaporins and water relations during hypocotyl elongation in Ricinus communis L. seedlings

The rate of water flow across biological membranes can be modulated by aquaporins which are expressed in many cells and tissues. The biological functions of these water channels in cellular processes have often been anticipated from the expression pattern, although the participation in the underlying process is not known in many cases. Ten putative aquaporin transcripts were identified in castor bean (Ricinus communis L.) seedlings and the water channel activity of three selected genes was analysed by heterologous expression in Xenopus oocytes, as well as the spatial and temporal expression by in situ hybridization/immunolocalization along the hypocotyl's axis. Water relations parameters were studied in elongating and non-elongating tissues using the cell pressure probe technique. These results indicate that (i) the amount of the RcPIP2-1 aquaporin correlated best with the elongation activity of the etiolated hypocotyl and (ii) the hydraulic conductivity of cortex cells is significantly higher in the elongating region of the hypocotyl compared with the non-elongating, mature region.

Turgor regulation in hyphal organisms

Turgor regulation in two saprophytic hyphal organisms was examined directly with the pressure probe technique. The ascomycete Neurospora crassa, a terrestrial fungi, regulates turgor after hyperosmotic treatments when growing in a minimal medium containing K +, Mg 2+, Ca 2+, Cl −, and sucrose. Turgor recovery by N. crassa after hyperosmotic treatment is concurrent with changes in ion transport: hyperpolarization of the plasma membrane potential and a decline in transmembrane ion conductance. In contrast the oomycete Achlya bisexualis, a freshwater hyphal organism, does not regulate turgor after hyperosmotic treatment, although small transient increases in turgor were occasionally observed. We also monitored turgor in both organisms during hypoosmotic treatment and did not observe a turgor increase, possibly due to turgor regulation. Both hyphal organisms grow with similar morphologies, cellular expansion rates and turgor (0.4–0.7 MPa), yet respond differently to osmotic stress. The results do not support the assumption of a universal mechanism of tip growth driven by cell turgor.

Use of the pressure probe in studies of stomatal function.

Over the past few decades the pressure probe has been used extensively in studies of the hydromechanical and osmotic properties of plant cells. However, although pressure probe techniques have been employed successfully in the study of stomatal function, there is no detailed account of this special application of the pressure probe technique. This paper describes the construction and use of the pressure probe in studies relating to stomatal function, and reviews the current state of knowledge of stomatal function in relation to guard cell and leaf hydromechanical properties.

On-line measurements of K+ activity in the tensile water of the xylem conduit of higher plants.

In higher plants the xylem is the main pathway for anti-gravitational, long-distance transport of nutrients and water from the root through the shoot to the upper leaves. In the xylem conduit water is in a metastable state if tension larger than 0.1 MPa (i.e. negative pressure) is developed. While diurnal changes in negative pressure of individual xylem vessels can quite accurately be recorded by the minimal-invasive xylem pressure probe technique and water flow by non-invasive NMR techniques, the problem of continuous monitoring of solute flow remains a hitherto unresolved challenge. As shown here, integration of a K+ selective and a potential measuring microelectrode into the xylem pressure probe allowed on-line measurements of the K+ activity in individual xylem vessels of maize roots together with pressure and trans-root potential, the potential difference between the xylem and the external medium (i.e. the overall driving force of ions through the root tissue). When light irradiation was increased from 10 micro mol m(-2) s(-1) to 300 micro mol m(-2) s(-1) and negative pressure developed in the vessel, xylem K+ activity dropped from 3.6 +/- 2.6 mm to 0.9 +/- 0.7 mm (n = 16), whereas the trans-root potential depolarized from -2 +/- 11 mV to + 12 +/- 11 mV (n = 11), i.e. by + 14 +/- 7 mV. The effect of light on all three parameters was reversible. Exposure of the root to various K+ activities in the bath ranging from 0.1 to 43 mm revealed that the K+ activity of the xylem sap was shielded against short-term fluctuations in K+ supply to a large extent. In contrast, control experiments in which the root was cut 1 cm below the probe insertion point, allowing direct entry of external K+ into the xylem vessels, demonstrated that the xylem equilibrated rapidly with external K+. This was taken simultaneously as a proof for the correct reading of the probe.

Turgor regulation in osmotically stressed Arabidopsis epidermal root cells. Direct support for the role of inorganic ion uptake as revealed by concurrent flux and cell turgor measurements.

Hyperosmotic stress is known to significantly enhance net uptake of inorganic ions into plant cells. Direct evidence for cell turgor recovery via such a mechanism, however, is still lacking. In the present study, we performed concurrent measurements of net ion fluxes (with the noninvasive microelectrode ion flux estimation technique) and cell turgor changes (with the pressure-probe technique) to provide direct evidence that inorganic ion uptake regulates turgor in osmotically stressed Arabidopsis epidermal root cells. Immediately after onset of hyperosmotic stress (100/100 mM mannitol/sorbitol treatment), the cell turgor dropped from 0.65 to about 0.25 MPa. Turgor recovery started within 2 to 10 min after the treatment and was accompanied by a significant (30-80 nmol m-2 s-1) increase in uptake of K+, Cl-, and Na+ by root cells. In most cells, almost complete (>90% of initial values) recovery of the cell turgor was observed within 40 to 50 min after stress onset. In another set of experiments, we combined the voltage-clamp and the microelectrode ion flux estimation techniques to show that this process is, in part, mediated by voltage-gated K+ transporters at the cell plasma membrane. The possible physiological significance of these findings is discussed.

What are the driving forces for water lifting in the xylem conduit?

After Renner had shown convincingly in 1925 that the transpirational water loss generates tensions larger than 0.1 MPa (i.e. negative pressures) in the xylem of cut leafy twigs the Cohesion Theory proposed by Böhm, Askenasy, Dixon and Joly at the end of the 19th century was immediately accepted by plant physiologists. Introduction of the pressure chamber technique by Scholander et al. in 1965 enforced the general belief that tension is the only driving force for water lifting although substantial criticism regarding the technique and/or the Cohesion Theory was published by several authors. As typical for scientific disciplines, the advent of minimal- and non-invasive techniques in the last decade as well as the development of a new, reliable method for xylem sap sampling have challenged this view. Today, xylem pressure gradients, potentials, ion concentrations and volume flows as well as cell turgor pressure gradients can be monitored online in intact transpiring higher plants, and within a given physiological context by using the pressure probe technique and high-resolution NMR imaging techniques, respectively. Application of the pressure probe technique to transpiring plants has shown that negative absolute pressures (down to - 0.6 MPa) and pressure gradients can exist temporarily in the xylem conduit, but that the magnitude and (occasionally) direction of gradients contrasts frequently the belief that tension is the only driving force. This seems to be particularly the case for plants faced with problems of height, drought, freezing and salinity as well as with cavitation of the tensile water. Reviewing the current data base shows that other forces come into operation when exclusively tension fails to lift water against gravity due to environmental conditions. Possible candidates are longitudinal cellular and xylem osmotic pressure gradients, axial potential gradients in the vessels as well as gel- and gas bubble-supported interfacial gradients. The multiforce theory overcomes the problem of the Cohesion Theory that life on earth depends on water being in a highly metastable state.

Cell Turgor and Elasticity of Chicory Grown in Different Temperature Conditions

Chicory heads (Chichorium intybus L., var. Focus) grown at different nutrient temperatures of 14 °C (group T1) and 18 °C (group T2) for 21 days were used to find a difference in cell characteristics. Air temperature at the growing room was set to 16 °C for both groups. Cell pressure probe technique was employed to determine cell turgor pressure, cell elasticity and half time for water of intact leaf at ambient conditions of about 21 °C and 46% RH. Average volume of 80 epidermal cells of base part of chicory was 62.6µm3 for the group T1 and 92.6µm3 for the group T2. Cell turgor of group T1 showed 0.37 to 0.41 MPa and that of group T2 was 0.35 to 0.43 MPa. The decrease in turgor pressure caused by wilting was observed by continuous measurement for more than 1h. Cell elastic modulus of group T1 ranged 1.41 to 3.54 MPa though that of T2 ranged 3.94 to 14.7 MPa. Similar value of cell turgor was observed for both chicory heads of group T1 and T2 independent of their volume. However, cell elastic modulus was different for two groups and it showed the volume dependency. The smaller value of elastic modulus observed for the chicory heads of group T1 implied the potential of cell expansion if the growing period was set longer than 21 days.

Hydraulic conductivity of rice roots.

A pressure chamber and a root pressure probe technique have been used to measure hydraulic conductivities of rice roots (root Lp(r) per m(2) of root surface area). Young plants of two rice (Oryza sativa L.) varieties (an upland variety, cv. Azucena and a lowland variety, cv. IR64) were grown for 31-40 d in 12 h days with 500 micromol m(-2) s(-1) PAR and day/night temperatures of 27 degrees C and 22 degrees C. Root Lp(r) was measured under conditions of steady-state and transient water flow. Different growth conditions (hydroponic and aeroponic culture) did not cause visible differences in root anatomy in either variety. Values of root Lp(r) obtained from hydraulic (hydrostatic) and osmotic water flow were of the order of 10(-8) m s(-1) MPa(-1) and were similar when using the different techniques. In comparison with other herbaceous species, rice roots tended to have a higher hydraulic resistance of the roots per unit root surface area. The data suggest that the low overall hydraulic conductivity of rice roots is caused by the existence of apoplastic barriers in the outer root parts (exodermis and sclerenchymatous (fibre) tissue) and by a strongly developed endodermis rather than by the existence of aerenchyma. According to the composite transport model of the root, the ability to adapt to higher transpirational demands from the shoot should be limited for rice because there were minimal changes in root Lp(r) depending on whether hydrostatic or osmotic forces were acting. It is concluded that this may be one of the reasons why rice suffers from water shortage in the shoot even in flooded fields.

The essentials of direct xylem pressure measurement

ABSTRACTThis paper discusses the essentials of the oil‐filled pressure probe technique in the measurement of negative xylem pressures, focusing in particular on the technique and physics underlying our recent, successful experiment which has rekindled the debate on the validity of the Cohesion–Tension theory. We illustrate a number of general problems associated with the cell pressure probe and xylem pressure probe techniques, and propose appropriate criteria for micropipette construction. We enumerate factors dealing with the cavitation problem and suggest methods for eliminating air seeds in the system. We introduce reliable criteria for the successful measurement of xylem pressure, and emphasize the importance of the probe pressure relaxation test. Several problems regarding the controversy over the Cohesion–Tension theory are also discussed. We discuss the correlation between xylem pressure and the transpiration rate, the existence of absolute negative xylem pressure in intact plants, the most negative values of xylem pressure measured by the pressure probe, the agreement between the pressure probe and pressure bomb techniques, and the vulnerability to cavitation (tensile strength) of pressure probes.

Xylem Flow and its Driving Forces in a Tropical Liana: Concomitant Flow‐Sensitive NMR Imaging and Pressure Probe Measurements

Abstract: Flow‐sensitive NMR imaging and pressure probe techniques were used for measuring xylem water flow and its driving forces (i.e., xylem pressure as well as cell turgor and osmotic pressure gradients) in a tropical liana, Epipremnum aureum. Selection of tall specimens allowed continuous and simultaneous measurements of all parameters at various distances from the root under diurnally changing environmental conditions. Well hydrated plants exhibited exactly linearly correlated dynamic changes in xylem tension and flow velocity. Concomitant multiple‐probe insertions along the plant shoot revealed xylem and turgor pressure gradients with changing magnitudes due to environmental changes and plant orientation (upright, apex‐down, or horizontal). The data suggest that in upright and ‐ to a lesser extent ‐ in horizontal plants the transpirational water loss by the cells towards the apex during the day is not fully compensated by water uptake through the night. Thus, longitudinal cellular osmotic pressure gradients exist. Due to the tight hydraulic coupling of the xylem and the tissue cells these gradients represent (besides the transpiration‐induced tension in the xylem) an additional tension component for anti‐gravitational water movement from the roots through the vessels to the apex.