Influence of Anatomical Spatial Architecture of Pinus devoniana on Pressure Gradients Inferred from Coupling Three-Dimensional CT Imaging and Numerical Flow Simulations

Abstract

Conifer forests in Michoacán are facing climate change. Pinus devoniana Lindley, with natural distribution in the state, has shown certain adaptability, and knowing the influence of anatomy in the flow system is essential to delimit how it contributes to safety margins and water efficiency. For this, the pressure gradients in the cell lumens and their ramifications were analyzed by numerical simulations of flow throughout the real microstructure. Xylem were evaluated in radial, tangential and longitudinal directions. With the skeletonization of lumens and their constrictions, a branching system of interconnection between tracheids, ray cells, intercellular chambers, extensions, and blind pits were identified. In the simulation, the branched system bypasses the longitudinal fluid passage through the pores in membranes of pairs of pits to redirect it through the direct path branching, contributing to safety margins and water efficiency. Thus, resilience at low pressures because of the lower pressure drop in the extensions. The interface between the branching system and the cell lumens are sites of higher pressure gradient, more conducive to water-vapor formation or air leakage in the face of the lowest pressure system. The flow lines move along easy paths, regardless of the simulated flow direction. Deposits in the cell extensions were shown to be attached to the S3 layer of the cell wall, leaving the center of the duct free to flow. It is concluded that the spatial architecture of the xylem anatomy of Pinus dvoniana is a factor in the resilience at low pressures due to high water stress of the species.

1. Introduction

Pinus devoniana Lindley (Pinus michoacana Martínez) is a widely distributed species in Michoacán, with a potential area for plantations of 1127.36 km², on slopes between 0% and 30% in this state [1]. It has the property of doubling the gain of stabilized carbon transfer from vegetation to soil after 20 years [2]. This characteristic suggests a reduced probability of hydraulic failure [3] in the face of climate change in the last four decades in the state of Michoacán, Mexico, supported by the data on environmental variables from the European Union’s Earth-monitoring program, ERA5-ECMWF [4]. Due to the high photosynthesis rates required, giving great interest to the species for a possible optimal flow system is advantageous.

Drought events can become a threat to the survival of forests [5,6,7], and reducing the vulnerability of populations to climate change by strengthening adaptation processes and increasing resilience is one of the priority objectives of the special climate change program (PECC) 2021–2024 in Mexico [8]. However, addressing these issues requires precise knowledge of the conditions that allow it, such as an efficient and safe flow in the xylem anatomy.

Studies on xylem ducts suggest hydraulic failure of the transport system, when the water column in the ducts is interrupted during a severe drought (embolism), due to cavitated ducts by the formation of gaseous bubbles from the liquid phase subjected to high water stress [3,9,10,11]. This inhibits growth and induces dieback in conifers [12,13,14], highlighting the importance of elucidating the role of xylem anatomy in mass flow behavior. The extent of xylem embolism or loss of hydraulic conductance has been shown to be a function of low applied pressures [15,16], resulting in water potentials (P₅₀) that cause losses greater than 50% of hydraulic conductance, unique to each species. The importance of the networking between the pits connectivity in the Pinus massoniana xylem was also analyzed by computed microtomography (CT), concluding that the spatial organization and connectivity of wood rays as an essential construction element for the xylem network [17]. The cambium of xylem in eucalyptus was also analyzed by CT, demonstrating that larger changes occur when the plant is irrigated, in comparison to those in drought seedlings [18].

The resilience of the species at low pressures due to high water stress could be determined by biological processes of restoration or that anticipate failure [19,20] by generating a sugar concentration in the apoplast [21], activation of aquaporin genes [22], and changes in gene expression levels [23]. On the other hand, by abiotic physical phenomena given by the influence of the anatomy to resist losses in hydraulic conductance or by its capacity for the dissolution of bubbles during flow in its cavities [24,25,26]. Studies on conifers show a probable inverse relationship between the water security of narrower tracheids and water efficiency with wider lumens [27,28,29,30,31]. Various hypotheses have suggested the intertracheal pit pairs to be sites of air (gas)-seeding propagation from already embolized ducts, into functional ducts with sap, through membrane porosities or during torus displacement out of the aperture due to extreme low pressures [16,32], but it is not sufficiently clear [33], partly because of the great difficulty in experimentally studying the phenomenon. Theoretically and according to continuous flow dynamics, water stress develops with pressure differences between two points in the flow system where they exceed the threshold, at which displacements have a linear relationship with increases in pressure differential, that is, when xylem water efficiency is inadequate to maintain constant water supply because of increases in transpiration or soil water insufficiency [15,34,35]; since mass flow depends on the pressures developed in the ducts [36], changes in internal pressures may be a good descriptor of flow behavior. Therefore, pressure gradients could indicate the influence of anatomic spatial architecture and potential sites for cavitation.

With the solution of the Navier–Stokes equations, these and other properties of the fluid are defined through a series of partial differential equations [37]. However, the analytical solution is unfeasible in a porous medium of complex geometry such as the xylem. The discretization of the equations allows approximations to the solution through computational fluid dynamics (CFDs) simulations, using the finite volume numerical method or Lattice Boltzmann method (LBM) in multiphase fluids [38,39]. The accuracy of these simulations can be increased due to the digitized replicas of the unmodified xylem used as model geometry for meshing. Recent analyses of flow in 3D reconstructions suggest that the degree of pits membrane constrictions plays an important role; the effect of membranes on embolic resistance is also widely discussed [40,41]. On a larger scale, the small loss in water potential in the upper part of the stem when segmenting 50% of the lower diameter of the stem [42] was explained by the redistribution of the simulated flow in the tangential direction to overcome the cut [43], showing the importance of the analysis at the basic cell level. Starting from simplifying hypotheses, such as the study of laminar, single-phase, capillary-stress-free flow in an un-deformable medium, it is possible to obtain the local pressure gradient at each point (x, y, z) at a specific time, which can spatially project the fluid dynamics for visualization and analysis at the basic xylem cell level. However, the interconnectivity of the cell lumens could drastically influence the flow passage [44] and analyzing the different branches of these constrictions can result in a difficult spatial visualization task due to the high similarity between the branches and the cell lumen during projection, differences between their resolution, and also because of the required accuracy of the segmentation process.

In this work, we counter with the extraction of the central voxel chain (skeletonization), in which the minimum distance map of all voxels to the voxels of the nearest contour is calculated. Subsequently, voxel thinning is performed, and the distance is used for the sequence of nodes and segments that form the spatial graph object (3D), obtained as the reconstruction of the complete system that could employ the mass flow in the xylem cell. Likewise, differentiation of the wood cell walls layers with the deposits adhering to the wall is necessary for the analysis of flow obstruction by deposits. Here, the level of brightness in the voxel gray scale was used for differentiation. Therefore, the objective of the present investigation was to analyze the influence of the intercellular spaces and anatomical capillaries of Pinus devoniana wood’s basic cells on flow pressure gradients by coupling 3D CT images and numerical flow simulations.

2. Materials and Methods

2.1. Sample Preparation

The sample used for this study was collected from a Pinus devoniana Lindley tree with a straight trunk, in a 5% slope located in the town of Rio Bello, municipality of Morelia, Michoacan, Mexico, latitude 19°38′51″ N and longitude 101°8′3″ W and an altitude of 2058 mnm, with a mean annual temperature of 15.7 °C and rainfall 98.7 days/year of 0.04 in. The tree has a height of 28 m and a diameter at breast height of 0.75 m. The material analyzed was extracted at 1.30 m above the base of the tree stem. The external and internal phloem were removed from the area, and then drilling began from the xylem, inside the sapwood zone (Figure 1a). For drilling at 1000 rpm, 5 and 2 cm internal diameter punches were used (Figure 1b,c). The extracted cylinders of 5 and 2 cm were dried until reaching the equilibrium humidity of 12% in a natural way inside the laboratory. Subsequently, the 5 cm cylinder was selected, as it had greater tissue integrity, and from this, cylindrical specimens of 1.6 and 4 mm in diameter were made on a wood lathe for tomography scanning in the section perpendicular to the axis of the tree, for a length of 5 and 8 mm, respectively, parallel to the axis of the tree. A specimen free of apparent defects was selected for each dimension above mentioned.

2.2. Three-Dimensional Images Acquisition

An acquisition of 3D images was performed with a Zeiss Versa 510 Xradia nanotomograph (Carl-Zeiss-Strasse, Oberkochen, Germany) with a high-energy X-ray source (30–160 kV, 10 W). To obtain the attenuation of the X-ray beam through the material, the sample was placed between the beam source and the CCD detector, and the voxel size was adjusted. A voltage of 50 kV was used and 1600 X-rays were taken at an angular displacement of 0.225° around the sample, with an exposure time of 2 s per shot. The voxel resolution of the 3D images was according to the sample’s diameter, 1.6 µm and 4 µm, respectively.

2.3. Image Processing

For the post-processing of the voxel data, the reconstructed images were exported to the specialized software Fiji and AVIZO™ (version 2019.1). Since the image was acquired in 16 bits due to the capacity of the CCD camera with a dynamic range of 65,535 gray levels, it was converted to 8 bits with 256 levels, in order to reduce the data consumption for the processed file. The defects in the image due to signal readings from dark current noise, photonic noise, reading variation, or component wear, among others, were not perceptible (Figure 2a,b). Therefore, only the brightness and contrast between the different intensity levels of the image were intensified for visualization purposes, not for measurements or image transformations, as binarization (Figure 2c). With this technique, it is possible to recalculate the voxel value, stretching the maximum and minimum intensity values of the image to cover the maximum possible dynamic range (0–255) defined by the active (8 bit) image. The image histogram conveniently adopts a more homogeneous distribution by intensifying the contrasts and is spread over the entire range of values (Figure 2d–f).

The virtual slices were oriented in the tangential, radial, and longitudinal direction to the growth rings of the wood (Figure 2d–f); this orientation was made with angular rotation about the x, y, and z axes of the image. The regions of interest for the virtual slices were selected based on the type of cellular tissue, with the help of the orthogonal slices of the analyzed volume. The slices were performed with the extraction of the selected voxel sub-volume.

The virtual segmentation of the solid and porous phases in wood was performed by binarization of the filtered image (Figure 2c). Binarization assigns a value of zero to pixels with a value outside a selected threshold and a value of one to the thresholded pixels. Because the image presents well-defined edges in the objects, it was sufficient to threshold by the global method based on the histogram of brightness intensity, selecting only the values corresponding to the cell wall, to separate it from the background or porosity (Figure 2c). Histogram methods do not consider operations in the neighborhood of voxels, only the separation of intensities. The segmented phases of spaces in the tissue were used for the permeability simulations.

For the reconstruction of the continuity of the cell cavities and intercellular spaces, the binary image corresponding to these phases was used to extract the skeleton surface or the central voxel chain. This set of connected voxels equidistantly separates the edges of the objects from the central voxel is obtained by calculating a distance map of the image. For that, it is using as the skeleton the centers of the maximum spheres inscribed within the lumen contours or their cell ramifications, and as the radius of the sphere the calculated distance of the map. Subsequently, the central voxel chain becomes a spatial graphic object that preserves in each of its points the information of the distance map to the nearest boundary (lumen contours), which will be used in the reconstruction of the continuity of the spaces. To verify that the intrinsic sensitivity of the map had not altered the ramifications of the voxel chain, only a visual inspection was performed through the assembly between the reconstructed images of continuity and cell wall, thus omitting the process of comparison of the number of components.

The region of interest of wood with early and late tissue (Figure 2g), was made with the virtual slice oriented radially over the transition zone of the growth ring. To image the xylem anatomy, colors were assigned to the wood cell wall layers based on the gray scale brightness level of each voxel (Figure 2h). Anatomical characterization was performed using 3D imaging with a procedure described elsewhere [45].

2.4. Numerical Flow Simulations

For the numerical flow simulations, the binary three-dimensional images were used, where the cell wall determined the boundary conditions for the computational domain. CFD (Computational Fluid Dynamics) simulations were performed in the flow simulation module of AVIZO™ software (version 2019.1). In the simplifying hypotheses, a laminar, single-phase, incompressible flow regime, an un-deformable medium, free of capillary stresses, was established. In the experimental configuration, the same flow rate was maintained at the inlet and outlet, with a pressure differential of 50,000 Pa, fluid viscosity of 0.001 Pa.s, and a convergence criterion of 0.0001. The simulations were performed in radial, tangential, and longitudinal direction; for the inactive direction, the software module seals the faces with a layer of voxels to prevent flow in that direction. The flow lines were observed by comparing the velocities in the three directions, using the same range of comparative reference velocities.

3. Results

It can clearly be observed the spatial reconstruction of the skeletonization of what appear to be intercellular spaces (blue color) connected to the tracheid cavities through the pits chambers (Figure 3). The spaces in blue are actually extensions of the tracheid lumen or spoke cells. The extensions form a branched system (BS) of a continuous channel in a longitudinal (axial) orientation, from which individualized channels of the same diameter are branched and connected to the larger diameter chambers of the blind pits analogous to parallel connections (Figure 3a). Rarely, there are longitudinally oriented stretches of larger-diameter (brown) extensions (Figure 3b). In the rays, the simple pits correspond to the larger-diameter brown ducts; however, there is also a connection (semi-areolated) between the tracheids and parenchyma cells or radial tracheids through segments of intercellular extensions (Figure 3c). In the blind pits near the extremities of the tracheids, the duct continues through the extensions to the attached upper tracheid; when attached tracheid clusters are formed, the extensions at their ends continue to join into a single chamber. From here, it distributes to the blind pits of the next attached upper tracheid (Figure 3d). Also, in the junction channel between only two tracheids, it forms a chamber in the center of the junction. This may be evidence of the effect of high pressures concentrated at these points (perpendicular pressure on tracheid surface) when the fluid moves during ascent by transpiration between adjacent tracheids, due to the conservation of continuity in fluid dynamics. In the reconstruction of the continuity of the cell cavities and their extensions, no non-existent branches were generated, a product of the sensitivity of the distance map (Figure 3e). The ramifications are congruent with the cell structure. In the lumen, there are small remnants of deposits which are detected as boundary conditions by the distance map, which is why at these points, the reconstruction of the lumen shows deformations (Figure 3f). However, it is not an obstacle to reading the continuity of the cavities and their extensions. The results show that the extensions or sharp points of tracheids form a network interconnected with the blind pits along the tracheids. Therefore, this network is interconnected with the cellular cavities of the tracheids (TC) and the cavities of the radial parenchyma (PC), forming a branched system (BS), as shown in Figure 3c.

The tomography image of Pinus devoniana wood was obtained with sufficient definition to perform numerical simulations of the mass flow in its cell cavities and extensions (Figure 4a). In Figure 4a, the spaces observed between the corners of the tracheid vortices are the end of the tracheid ends (extensions) with sharp tips or extensions between aligned radios. In a parallel cut along one of these extensions (E), it can be observed that it is surrounded by deposits, identified in intense pink color (Figure 4a,b), which on very few occasions obstruct the space transversely (Figure 4a), since an important fact observed is that the substances adhere to the internal surface of the extension on the S3 layer, leaving the center free to the passage of fluids. It was possible to differentiate the substance adhered to the extension from the rest of the cell wall layers shown in Figure 4b, due to the virtual separation of components used in the present investigation, based on the voxel brightness level. In this image (Figure 4b), the LM middle lamella (ML) is observed in white color joining the cell walls, in gray colors the S2 layer, the S3 layer in light pink color, and the substance adhered to S3 in intense pink color. The primary and S1 layer, which is not very visible, corresponds to the faint gray color joined to white (Figure 4b). The roughness of the cell wall surface is also observed to be present for the effect of the simulations in Figure 4c and the interconnected extensions (Figure 4c,d).

3.1. Longitudinal Flow

The pressures in the longitudinal flow (Video S1) present an approximately similar gradient in the different diameters of the lumens, where the maximum pressure is observed (red color). In general, the gradient is similar at larger diameters in this spatial plot of pressures. In the first approach of the virtual section (Video S1), the pressure in an un-sectioned (complete) tracheid lumen is observed at different heights, which presents a different gradient, more premature and abrupt than the rest (Figure 5a), due to the pressure drop when the fluid enters from one tracheid to another. This pressure behavior was presented as typical and common behavior in all tracheids with the same anatomy with constrictions in the extensions. This strong pressure reduction is observed as a change to the blue scale (Video S1). The fast pressure drop at the end is increased or stabilized when pressure continues to be applied from outside the system. This is finally observed in the central part of the volume (Figure 5b), with average spatial values (Video S1). It is noted that the pits, as well as the ray, share the same pressure gradients as the tracheid lumen, in each specific case, in this longitudinal direction (Video S1), since the continuous system in the extensions presented a different differential affecting the trajectory, as shown in the text below.

In the displacement through the longitudinal pressure gradient (Video S2), it is observed that this changes approximately equally in axial or radial tracheids, epithelial cells and parenchyma cells, the latter with little difference (Figure 5c,d). This equality in a short segment shows that the different cells share the pressure gradient in the longitudinal flow (Video S2). On the contrary, in BS (Figure 5c,d), it is maintained at an approximately constant difference from the rest (Video S2), as a result of lower pressure loss and early response in these spaces and demonstrating flow efficiency or suction capability. Here, the flow presents lower pressure differential with respect to the outlet pressure of the system. With the pressure between adjacent lumens being similar, it flows preferentially through BS and not through the pairs of pits (Video S3). Video S3 initially shows a low-pressure condition (purple pits, lumens and extensions) that is estimated to be analogous to water recharge or water stress. Increasing pressures and progressive displacement within the tracheid cells are observed (Video S3). However, it is possible to note that when the pressure reaches the end of the tracheid, just in the area where the last blind pits interconnected with the space of the tracheid extensions are located, the fluid pressure is observed through the interior of BS (Figure 6a) before entering the lumen and the next pit upper attached tracheid (Video S3). The consequence of this flow phenomenon is, as shown in Video S3, the instantaneous appearance of pressure in the extensions of the next group of attached upper tracheids. This is due to the higher velocity presented in these spaces, but mainly because BS functioned as an open conduction system (bulk liquid flow), contrary to the transverse passage through punctuations. The pressure displacement towards the interior of the next tracheids in the upper position starts with the redistribution of the bulk flow through the extensions, blind pits, and chambers that interconnect the extensions of different tracheids, shown above in Figure 3. As the pressure progresses and increases, it is also possible to observe that, in a low pressure system (purple), the pressure in the extensions is higher than in the lumens, after the pressure has entered the lumen (Video S3). Subsequently, a high-pressure condition is reached (pits, lumens, and extensions in red), which is analogous to an active-recharged xylem, where solar radiation initiates the process of transpiration and water stress. Here, we observe the reverse effect, i.e., as the pressure decreases and the negative pressure is transmitted in the lumens, a state of high pressure remains in the space of the extensions, this happens before passing to the attached lower tracheids and due to the large difference between the diameter of the extension and the lumens, since the negative pressure was applied directly inside the sectioned lumens (Video S3). However, when the low pressure passes from the anterior to the posterior tracheids through BS (Figure 6b), the above-mentioned flow phenomenon occurs again (Video S3). It is in the extension that the low pressure first occurs (Video S3). This confirms that it is through the extension that the fluid initiates the displacement in a pressure drop system, like the ascent of water in the stem. That is, in a high-pressure system, the extension functions as a low-pressure system, which sucks fluid from the lumens, amplifying the pressure gradient (water stress) at the interface between the lumen and BS, and not between the lumen and pit (Video S3). Finally, the displacement through the volume shows that this phenomenon is similar in all the analyzed tissue (Video S3). The pressure behavior, when the fluid crosses from a lower to an upper tracheid through the chambers and extensions connected to the blind pits of the tracheids, is the typical one presented when the tracheids are complete.

3.2. Radial Flow

The pressure development in a radial direction clearly shows the pressure gradient as the flow moves in longitudinal direction in order to pass through the pits in a radial direction in any cell type (Video S4). A close-up clearly shows the steepest gradient as it moves from the lumen into the pit chamber and out of the pit with a large pressure drop in the next lumen (Figure 7a) in any cell type, including ray (Video S4). Subsequently, in the volume displacement, the extensions are observed to maintain approximately an average pressure with respect to the applied pressure differential, as was maintained in the longitudinal direction (Video S4). The gradient in axial and transverse cells is very similar, sharing practically the same pressure, with pronounced gradients when moving from one radial parenchyma cell to the next (Video S4). Even the influence of the 2 epithelial cells and the resiniferous channel on the radial gradient in axial cells (Figure 7b) is such that a diagonal in the gradient of the tracheids is observed, being more pronounced as it moves away from the radial resiniferous channel (Video S4). Finally, in the low- and high-pressure conditions, the behavior of the pressure gradient in BS is similar to its behavior in the longitudinal flow (Video S4).

3.3. Tangential Flow

In the tangential direction, the pressure gradient developed is less pronounced than in other directions, as a result of the greater number of pits on the tangential faces of the tracheids, and because the flow is basically through the semi-areolated pits in the crossing fields (Figure 8a). It is intuited that it conserves a little freer energy of the fluid in this direction (Video S5). Subsequently, in the displacement in the volume (Figure 8b), the extensions are observed to maintain an average pressure with respect to the applied differential, as in the radial and longitudinal direction (Video S5). However, in the low- and high-pressure condition, the pressure phenomenon is not observed in the extensions presented in the radial and longitudinal direction (Video S5).

3.4. Extensions and Blind Pits

The extensions observed in this species correspond to tracheid tips or pit spaces ray show the cavities of blind pits in two opposing tracheid lumens connected at the bottom with the extension space of a third tracheid (Video S6). Subsequently, the second approach (Video S6) follows an extension of a tracheid, showing that it has continuity and direct connection with the next tracheid (unsealed end), visible in black color at the end of the tracheid. The second stage of the video shows the extension joining the extremities (upper–lower) of more than 2 rays (Video S6). In the displacement through the rays in radial direction, this type of connection is observed periodically, each time the ray intersects the extension of an axial tracheid (Figure 9b), because the extensions of the tracheids are connected with the rays, i.e., they are aligned and interconnected longitudinally, forming a single system (Video S6).

However, when the tracheid has a sealed end, it retains a connection to small chambers (shown above) at the ends (Video S7), which may be sealed or connected to tracheids or pits (Video S7). This can be corroborated by the development of the pressure (Video S8), in the close-up of the spatial graph of the pressure of a pit connected to a small chamber and, in turn, to a small extension (Figure 10a), which interconnects the lateral ends of two adjacent lower- and upper-tracheid lumens (Video S8). Following up on this same upper lumen (Figure 10b), we observe at the end of the tracheid, that the flow lines enter these spaces at the ends, without deflecting anteriorly out of the lumen at the pairs of areolated pits it encounters on its trajectory prior to the end (Video S9). As the pressure plots (Video S9) show, this is because the pressure between neighboring tracheids is similar, preventing lateral flow, reinforcing the fact that there is a pressure differential between the pairs of pits and BS. This differential allows axial flow to continue through the extensions and not through the pairs of pits, as would be expected.

3.5. Longitudinal Flow Lines

In the larger scale simulation of the tissue containing a large number of complete tracheids inside, in early wood and late wood (Figure 11a), the flow lines are observed with a characteristic behavior of velocity loss at a higher longitudinal displacement, due to the interaction with the tissue (Video S10). The range of velocities obtained in the simulation was originally shown in slow purple flow lines throughout the tissue. For this reason, we resorted to decreasing the velocity range in order to sensitize and graphically display the velocity differences between tissues (Video S10). In general, the flow path is observed through tissue with fewer obstacles (cells open to the outside), which is reflected as little flow through pits and little flow at sites with complete tracheids, as in late wood (Video S10). In the first zoom (Video S10), the flow lines are shown reaching a cluster of lumens with deposits. Then, in the second close-up, a pair of complete tracheids that start as a small lumen and end in the same way are followed (Video S10). Focusing on the flow lines from the top of the deposits and complete tracheids, the lack of flow lines at these sites is observed (Figure 11b); this is because the flow chooses the easy path of the sectioned open tracheids (Video S10). However, in the xylem with complete tracheids, the flow is restricted to pass between cells and the BS, so the behavior is actually the one shown inside the tracheids in the graph of Video S9. Later in this same Video S10, the pressure gradient is shown in retrospect, starting at the exit of the system (the end) and moving towards the entrance. Taking as a reference point the largest diameter of the axial resin channel, it is possible to observe, at the entrance of the system, that the pressure gradient (loss) is presented as the diameter of the ducts’ increases (Video S10). This occurs because the fluid in the smaller diameters has less mass; therefore, the greater mass in larger diameters gives them greater pressure potential at the beginning. Nevertheless, it is observed that the pressure loss is inverse, the smaller the diameter of the duct, the lower the pressure loss. In the pressure graph, this is clearly observed in the displacement towards the exit of the system, the smaller diameter tracheids in late wood, the smaller tracheids in early wood at the visible end of the growth ring, and the spaces at the ends are those that conserve greater pressure at greater distances (Figure 11c), confirming that the spaces in connection extensions (BS) are those that conserve the pressure potential at greater distances (Video S10). The effect on the larger-diameter axial resiniferous channel is a delayed pressure loss at the entrance of the system and a much more pronounced pressure loss with displacement than the rest of the xylem elements, due to the higher pressure potential consumption required by the larger diameter for fluid displacement (Video S10). The behavior in this graph (Video S10) is similar to that presented in the higher resolution graphs (Video S2) in a smaller volume.

3.6. Radial Flow Lines

The flow in the radial direction shows less difficulty of displacement across the radial cells (Figure 12). However, a high dependence of longitudinal displacements is also observed (Figure 12), which cross with greater difficulty through the pairs of tracheid pits on the radial and tangential faces.

3.7. Tangential Flow Lines

In the tangential direction, the flow is presented by pairs of pits (Figure 13a,b) and continues longitudinally through the lumen of the tracheids. When it encounters a crossing field, it then continues tangentially with little difficulty to the crossing with the ray cells (Figure 13a,b). Here, the pits function as preferential escape routes for the flow, which generates a high dependence of the flow to cross through the pairs of pits, thereby slowing down the flow and complicating its trajectory (Figure 13a,b), as in the central blue part of the image. In the tissue, the flow is also observed in the space of an extension in the ray. It enters through a ray, and at the upper tip of the ray aligned with an extension, it continues its trajectory through a radial tracheid pit that joins or leads into the space of an extension (Figure 13a). That is, this is evidence that the extensions can function as suction capillaries for the fluid. The periodicity of connected and aligned extensions on the radius (in radial tracheids and radial parenchyma) described above in Video S6 can be seen in this image (Figure 13b); the white arrows point to longitudinal flow lines, which detach from the flow on the radius periodically at junctions with tracheid extensions.

The tangential flow also has difficulty filtering within the resiniferous canal, and the epithelial cells are observed avoiding these areas (Figure 13a). This is due to the resin covering the channel surface and lack of connectivity. The reduction in section at the junction of the pits generates the acceleration observed in red color at the flow lines or critical points of pressure loss. However, if the fluid pressure is similar in the lumen of 2 attached tracheids, the flow cancels out at the pairs of pits and is directed towards the blind pits connected to the extensions

3.8. Anatomical Characteristics

Quantitative data of the anatomical characteristics of the wood are listed below in

Table 1. Anatomical characteristics of the analyzed Pinus devoniana Lindley wood.

	Early Wood	Late Wood	Early Wood Distribution	Late Wood Distribution
Vf of cavities/without resin channels	0.75	0.42	--	--
Vf of cavities/with resin channels	0.82	0.78	--	--
Vf of radial face pits	0.0072	----	--	--
Lumen Diameter µm Surface µm2	mean 37.3 1658.2	mean 21.3 478.9
Extensions Diameter µm Surface µm2	mean 5.8 51.5	mean 4.4 24.1
Pit chamber Diameter µm Surface µm2	mean 13.5 192.5	mean 7.0 74.0
Aperture of pits Diameter µm Surface µm2	mean 2.8 14.0	mean 4.0 16.4
Resin channel (mean): Diameter µm Surface µm2	mean 139.4 19,740.4	mean 135.7 18,317.6
Wall thickness µm	3.3	7.0
Pits	Areolate, mostly uniseriate of 30 and 1, few opposite and alternate of 2. Blind pits of greater diameter at ends of tracheids. In crossing fields, fenestriform of 3 and 2 with rim.
Rays	Heterogeneous uniseriate 10, 7, 2 high and fusiform. Tangentially 6 per mm.
Tracheid	Polygonal with longitudinal extensions. Radial with serrated edges.

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4. Discussion

4.1. Tissue Hydraulics

The spatial architecture of the analyzed anatomy of Pinus devoniana and its function in the continuous fluid flow allow for estimating that the branched system (BS) of interconnection between the extensions of the tracheids or ray cells, intercellular chambers, and blind pits identified in this research and facilitates the flow and increases the safety, since it avoids the passage of the massive fluid through the membranes of the pits, to make its way preferentially through the open system of the extensions and blind pits. Generating with this is a greater hydraulic functionality in contrast to the flow described by [41] through the chamber or margo. Kučera [46] suggests that connections between blind pits and intercellular spaces may facilitate flow in the ray.

The reduced diameter and longer length of the segments of the BS (Table 1) determine an anticipated response, with a higher or lower pressure gradient, depending on whether the system is low- or high-pressure, as shown above in the results. In contrast to the ducts of the inter-tracheal pits, which are short length and prone to seal [44], this condition should provide greater resilience at low pressures, as in a cavitated lumen relief (water recovery), which would enter freely through the BS, and its inter-tracheal pits adjacent to another non-cavitated lumen would be expected to remain aspirated with the torus retracted into the non-cavitated tracheid for protection; but, due to the BS in the cavitated lumen, there will be a pressure gradient counteracting the flow of gas bubbles through the membrane pores into the non-cavitated lumen. This is regardless of the possible negative pressure within the lumens generated by the solutes, which would counteract even more. On the other hand, the pressure gradient obtained in BS is different from the gradient in pairs of pits and, with respect to the gradient at the outlet of the system, indicates that the interface between the lumen (tracheids or ray) and the BS is the site with the highest pressure gradient with potential for air filtration or water vapor formation, in a scenario of water insufficiency. This is congruent with Cochard et al. [47], where cavitation could be caused by capillary failure of an air–water meniscus, but contrasts with the site indicated in the pit. However, it is consistent with the trend reported by Hacke and Sperry [48] where the larger the lumen diameter, the greater the susceptibility to cavitation due to water stress. As shown in the results, the larger the lumen diameter, the greater the pressure drop and the greater the gradient between lumen and BS, so that the BS could leak air into the interior when the lumen exhausts its liquid.

4.2. Hypothesis

If the lumen contains liquid under stress, due to the cohesive forces of water, an eventual tension in the liquid would occur and could fail at sites where the cohesive force is lower, between the liquid–cell wall interface or BS liquid–liquid lumen interface, for the formation of an initial air microbubble. There is evidence indicating stronger liquid–wall interface [49]; in fern cells, it is estimated that a water tensile strength of up to 30 MPa could be reached in 10 nm interfibrillar pores [50,51], an absolute value higher than that required for cavitation in 40 species (−2.9 to 11.3 MPa) in conifers water potentials (P₅₀), which cause losses greater than 50% of hydraulic conductance [16]. From this, we derive a possible constant of the ratio of the diameter of the span diameters to the diameter of the lumens, useful for estimating the water safety margins (cavitation) in relation to a minimum moisture content. It follows that in the case where these extensions spaces are obstructed by deposits during transpiration, the maximum stress should occur in the pairs of pits due to the gradient. Then, the derived constant could be from the ratio of the diameter of the membrane openings in the pits [41] to the diameter of the basic cell lumen. To this effect, the simulations showed strong pressure drops in the pairs of pits, but in general longitudinal flow bypasses, the pairs of pits maintained a similar pressure in adjacent lumens and pairs of pits, downplaying the noted porosity properties of pit membranes and forcing flow to continue through the blind pits and extensions with less pressure loss than in the pairs of pits, in contrast to that indicated by Hacke and Sperry [48] and Domec et al. [52].

4.3. Flow in the Branched System

In a flow with constant water sufficiency, the simulations showed that the BS loses less pressure (about 40% of the pressure applied to the system) than the rest of the tissues, having more constant free energy along the flow in these spaces. In addition, here, the capillary potential would have less effect on fluid retention due to the reduced diameter, adding more free energy [35].

The BS flow phenomenon also indicates that the extensions exert suction on the flow in the lumen. Establishing a gradient decreasing from an upper to a lower tracheid, since, on a rise, the water in the lumens will reach the top of the tree in the lower pressure state. Therefore, the pressure gradient decreases from the top to the bottom of the tree. This is congruent with the higher radial contraction in the canopy recorded by Zweifel and Häsler [53] and Schäfer et al. [54]. Because this flow is from the reservoirs, it would exert a fluid displacement effect most likely by transmitting stress through the cohesive forces of water [55] to deform the cell wall, limited only by the low elastic modulus of the wall under saturated moisture conditions. In Pinaceae and Cupressaceae species, Pittermann et al. [31] suggest that tracheid walls were reinforced to resist collapse under negative pressures. Studies on 48 species reveal cell wall stresses during water stress [49]; even in foliar tracheids, collapse is reported at water potentials below −1.5 Mpa [56]. This would explain why, when there is a maximum point of water availability in the soil, maximum peaks of radial contraction are generated in the tree during transpiration [57]. Thus, if air or vapor bubbles are present in the lumen during dry periods, the transmission of stresses to the wall will decrease according to the percentage of volume occupied in the lumen by these bubbles (increased xylem resistance). This would result in lower flows and less radial contraction in the trunk during dry periods. In other words, the hydraulic resistance of the xylem may tend to infinity [58].

This behavior demonstrates that flow toward the top of the tree in the lumen of tracheids will require greater pressure potential than in the spaces of extensions. Consequently, cavitation will not necessarily occur in flows within the extensions with higher pressure potential.

5. Conclusions

Three-dimensional skeletonization of cell lumens with their branching constrictions revealed an auxiliary system of tracheid–tracheid and ray–tracheid interconnections through blind pits and extensions at tracheid ends, in the form of multiple connecting chambers or reduced-diameter ducts. The extensions are periodically aligned over the rays at the junction with tracheid corners, simulating intercellular spaces. The branched system has properties that prevent flow through the pores of the pits in the membranes, aiding water efficiency and security. These characteristics contribute to the greater resilience of the xylem anatomy to low-pressure systems such as drought stress. The spatial projection of fluid dynamics showed distinct pressure gradients in the branching system with respect to the lumen and inter-tracheal pits, determining the BS interface as points of higher gradient. In the lumens, the pressure drop was greater, as the lumen diameter is larger, which increased the pressure differential with respect to the BS.

It was demonstrated that 3D images can be coupled to numerical simulations, which can be useful to predict the flow throughout the wood. This will help to understand the behavior of wood growth at different climatic and location conditions. Further analysis is continuing to precisely describe the xylem anatomy and the interconnection in 3D and the effect that could generate the different phenomena that are occurring currently.