During vertebrate development, arteries exert a morphological control over the venous pattern through physical factors

The adult vasculature is comprised of three distinct compartments: the arteries, which carry blood away from the heart and display a divergent flow pattern; the capillaries, where oxygen and nutrient delivery from blood to tissues, as well as metabolic waste removal, occurs; and the veins, which carry blood back to the heart and are characterized by a convergent flow pattern. These compartments are organized in series as regard to flow, which proceeds from the upstream arteries to the downstream veins through the capillaries. However, the spatial organization is more complex, as veins may often be found paralleling the arteries. The factors that control the morphogenesis of this hierarchically branched vascular network are not well characterized. Here, we explain how arteries exert a morphological control on the venous pattern. Indeed, during vertebrate development, the following transition may be observed in the spatial organization of the vascular system: veins first develop in series with the arteries, the arterial and venous territories being clearly distinct in space (cis-cis configuration). But after some time, new veins grow parallel to the existing arteries, and the arterial and venous territories become overlapped, with extensive and complex intercalation and interdigitation. Using physical arguments, backed up by experimental evidence (biological data from the literature and in situ optical and mechanical measurements of the chick embryo yolk-sac and midbrain developing vasculatures), we explain how such a transition is possible and why it may be expected with generality, as organisms grow. The origin of this transition lies in the remodeling of the capillary tissue in the vicinity of the growing arteries. This remodeling lays down a prepattern for further venous growth, parallel to the existing arterial pattern. Accounting for the influence of tissue growth, we show that this prepatterned path becomes favored as the body extends. As a consequence, a second flow route with veins paralleling the arteries (cis-trans configuration) emerges when the tissue extends. Between the cis-cis and cis-trans configurations, all configurations are in principle possible, and self-organization of the vessels contributes to determining their exact pattern. However, the global aspect depends on the size at which the growth stops and on the growth rate.

Figure 1

Yolk-sac vessels at day 4, observed by reflection illumination: Example of veins $\left(\mathrm{V}\right)$ contiguous to arteries $\left(\mathrm{A}\right)$. Veins may appear on either side of the artery under study. Note that the main artery and vein both branch to form parallel secondary arteries and venules, which themselves branch to form even smaller parallel arteries and veins.

Figure 2

(Color online) Scheme of the shadowgraph setup used to map the surface topography of the growing yolk-sac. A parallel beam of light is shone on the surface of the yolk-sac, and the reflection is observed in the direction of specular reflection. Since the embryo is not flat, there is only one direction of observation, which may be difficult to find. Once this direction of specular reflection has been found, details of the surface appear as brighter or darker, depending on the surface curvature. A small concave feature, if approximated by a paraboloid, displays a bright spot in the center of a dark halo. Inversion of colors, as done in Fig. 9, right, allows recovering the natural impression of colors (bumps appear bright whereas fissures appear dark). By this mean, the details of the surface topography are evidenced. When the subject is not observed under a strict specular reflection, interesting shadowing effects may be obtained, which reveal the surface corrugations. Note that this technique is often used by physicists to explore refraction index gradients. For example, shining a parallel light through a warmed gas reveals temperature gradients and flows.

Figure 3

Air-puff tonometry: principle [Fig. 3a] and calibration using water and ethanol [Fig. 3b]. (a): Scheme of the air-puff tonometer used to map the local deformability of the growing yolk-sac. An air puff (approximately 10 cc/min) is blown through a 20- or $50\text{−}\mu \text{m}$ micropipette made using a pipette puller (Sega) and impacts the yolk-sac surface at a $45°$ angle. The pipette is mounted on a motorized rotating stage (Newport) to provide for tilt angle correction. The size of the area deformed by the air puff, which increases when the local deformability increases, is measured optically. For that purpose, the pipette has been modified to become the lighting element of the optical setup. Its end was first metallized by copper physical vapor deposition and additionally painted in order to guide the light and to ensure glass opacity. Then, the cleaved and bared end of a multimode optical fiber “working fiber” (HCP MO200T from SEDI) was introduced inside the pipette and inserted as deep as possible without obstructing the air flow path. The other end of the optical fiber was coupled to an “injection fiber” using a splice device (Siemon ULTRAsplice U.S.-250). At last, a laser beam produced by a diode (12 mW Melles Griot) was injected in the “injection fiber” using an optic positioner FP-1A and a bare fiber chuck holder FPH-J (Newport). The light spot thus emitted by the micropipette falls inside the deformation trough. Depending on the absolute angle of the pipette tip with respect to the surface, either the spot size or the spot position changes when the turning the air on, generally both. This can be adjusted by having the pipette shoot more or less ahead of the air jet. The spot is observed at right angle with an analog video camera (Watek 512) which continuously films the surface and records on line its size and displacement (with a frame grabber from SCION corporation interfaced with NIH-Image). The light spot appears in dark due color coding inversion. (b) APT calibration with respect to reference surfaces (water and ethanol). The figure shows the comparison between the spot deflections (in pixel units, corresponding to approximately $4\mu \text{m}/\text{pixels}$) obtained on ethanol and water surfaces, in otherwise exactly the same conditions, as a function of time. At the moment when the air is turned on, the spot is strongly deflected and it returns to its original position when the air is turned off. The data are offset for clarity. As expected, the ethanol surface is significantly more deformable than the water surface, the spot deflection for ethanol being about twice the deflection for water. Indeed, in this regime, where gravity effects are negligible compared to surface tension effects (i.e., negligible Bond number), the maximal penetration depth of the air jet into the liquid surface should be inversely proportional to the surface tension of the liquid [39]. Here, the water/ethanol surface tension ratio is of order 3.

Figure 4

Schematic description of the different steps leading to the formation of a vascular system: blood islands (aggregates of hematopoietic cells, the precursors of red blood cells, surrounded by endothelial cells, the constitutive cells of the capillary wall) form during the early phases of embryonic development. Following their formation, endothelial cells surrounding these blood islands soon anastomose to form a capillary meshwork, called the primary capillary plexus, which serves as a scaffold for the beginnings of circulation. The capillary plexus is subsequently remodeled into a complex hierarchical branching structure, including arteries and veins. Note that in this remodeling process, all large vessels, be it arteries or veins, were once capillaries of the smallest size. For more details, see [10].

Figure 5

(Color online) Yolk-sac (a) and brain (b) vessels in the cis-cis configuration (primary circulation stage). (a) A typical cis-cis vascular pattern in the yolk-sac at an early developmental stage (2.5-day embryo). For clarity, the heart and head are indicated. The vitelline artery is at the right, the cranial vein in the middle and elongating toward the top-left. The flow loops from the vitelline artery up to the cranial vein and back. The process of arterial disconnection (see text, Secs. 4A, 4B) starts already to be faintly visible, in the whiter and quite thin area that starts to surround the vitelline artery. (b) In vivo observation of a 3-day embryo midbrain showing the capillary plexus and the early cis-cis flow route. Note that the arterial inflow is situated deeper inside the brain shell, while veins are more superficial and appear with a better contrast. The structure of the initial flow pattern is three dimensional, whereas the yolk-sac is two dimensional. However, the topology is similar: a central arterial input flowing toward a distal venous collecting vessel located on top of the head and along the boundary between the mid-brain and forebrain.

Figure 6

Yolk-sac vessels in the cis-trans configuration (secondary circulation stage). (a) A typical cis-trans vascular pattern at a later developmental stage (4-day embryo). One must pay attention to the fact that, in (a) and (b), almost all arteries are paired with a vein. (b) A magnified view of a 4-day embryo showing the process of formation of the vein paired to each artery, in a more distal area than (a). To the sides of the arteries (stars), dangling sprouts due to capillary disconnection (see text, Sec. 4B) become discernible because they contain pools of stagnant blood (arrows).

Figure 7

Schematic description of the flow pattern in the cis-cis (left) and in the cis-trans (right) configuration. The initial arterial entry and venous exit points are indicated by $\mathrm{A}$ and $\mathrm{V}$, respectively. The formation of a venous path adjacent to the artery will lead to a flow decrease in the initial set of veins, indicated by a dotted line in the right panel, which may lead, or not, to their regression.

Figure 8

Pictorial description of the formation of veins next to the arteries. First, the capillary plexus is homogeneous (a). It is then remodeled to form an arterial pathway (b). The growing artery disconnects from the plexus, leaving dangling capillaries (c), with flow stagnation areas (indicated by stars). See also Fig. 6b, where the dangling capillaries become discernible because they contain pools of stagnant blood. The useless endothelial material is progressively excluded from the neighborhood of the artery and contributes to enlarge the capillary lumens at a short distance from the artery (d).

Figure 9

(Color online) Direct in vivo imaging of the yolk-sac of a 2-day embryo still exhibiting the cis-cis configuration: surface observed by optical microscopy (left) and topography observed by shadowgraph (right). Boxes: the same young arteriole, imaged by both techniques, is highlighted. The shadowgraph reveals a swollen region around the growing arteries (right, bright areas in the red box).

Figure 10

Yolk-sac deformability measurements by APT in scanning mode (a) and local mode (b). (a) A typical scan performed by APT in scanning mode at right angle from a growing artery in a 4-day yolk-sac. Spot size as a function of the distance from the center of the growing artery (denoted by $\mathrm{A}$ in the left image, where $\mathrm{P}$ indicates the tip of the micropipette). In this experiment, the spot is positioned such that its size increases when the local deformability increases. Thus, APT evidences two distinct areas: a stiff area including the growing artery and its immediate neighborhood, about $150\mu \text{m}$ large from the artery center, and a softer area, outside. In this example, the vein forming in between arteries is found to follow the area of largest deformability. (b) Twelve examples of pairs of local-mode APT measurements performed along the growing arteries (dotted lines) and outside the stiff area (plain lines) of a 2.5 days yolk-sac [($\mathrm{A}$) and [($\mathrm{B}$)] and of a 4-day yolk-sac [$(\mathrm{C})-(\mathrm{L})$]. In these data, the APT spot was positioned for detection of the spot displacement (which is more accurate than the spot size). Spot deflection in pixel units $\left(1\text{pixel}=4\mu \text{m}\right)$ is plotted as a function of time. The time interval between each data point is 0.1 s.

Figure 11

Schematic representation of the yolk-sac cross section in the neighborhood of a growing artery. The fluid phase (blood) is represented in gray. The capillary lumens form an interconnected network of capillary pores whereas the arterial lumen has been previously disconnected from the capillary pore space, as indicated by the dashed lines.

Figure 12

(Color online) Direct in vivo observation by transmission illumination of 2-day (a) and 4-day (b) rinsed yolk-sacs: Evidence of a specific region surrounding the arteries. (a) When a yolk-sac is rinsed and transferred to a glass slide, direct observation by transmission illumination shows that there exists a region around the largest arteries, devoid of capillaries and of erythrocytes, which appears brighter in the figure. This brighter area is not observable around the distal arterioles [e.g., arterioles extending toward the sinus vein (SV) in (a)]. Indeed, arteries develop from the yolk-sac center to its periphery and, thus, the vessels which lie in a peripheric position have developed later (younger vessels) than the vessels that lie in a proximal (central) position. As a consequence, these arterioles have not disconnected from the capillary plexus, yet. In addition, several cis-trans veins $\left(\mathrm{V}\right)$ are developing or have already developed. In the latter case, a slight bright area is observable, too (b), which is consistent with the lesser extent and later appearance of venous (compared to arterial) disconnection.

Figure 13

Brain vessels configuration during the development of the cis-trans venous pattern. (a) Left: direct in vivo detection of the cis-trans configuration formation. The favored paths created by the remodeling of the capillary tissue in the vicinity of the growing arteries appear in the midbrain of a chicken embryo by day 5. Along the existing arteries (stars), an avascular region has appeared (see below). An area of denser capillaries can be observed somewhat afar from the existing arteries, on both sides. Thus, venous paths form parallel to the arteries (arrows). Right, top: enlarged view of the rectangular area highlighted in the left panel. Bottom: gray-level profile of this enlarged view, averaged along the vertical direction (direction parallel to the main vessel): very close to the arteries, on both sides, a strong decrease in the gray level is observable (gray value $\sim 6$), demonstrating the presence of an avascular area. Further away from the central artery, bumps of gray are consistent with wider capillary lumens. The bumps maxima correspond to favored venous paths, the left one being almost formed and the right one not being recognizable as a vessel, yet. Farther away, on the left, the capillary plexus reverts to an intermediate gray level (gray value $\sim 10–12$), representative of vascularized regions of the nonremodeled capillary plexus. (b) Similar analysis performed on a 6-day brain, from a “polar” view. Left: the growing arteries are indicated by stars. The cis-cis venous pattern $\left(\mathrm{V}\right)$ is at the center of this view. Arrows are pointing to the developing cis-trans venous pattern. Right: gray-level profile, averaged along the direction parallel to the vessel of the enlarged area highlighted in the left panel: two presumptive venous paths, not being recognizable as vessels yet, are evidenced.

Figure 14

Direct inspection of the capillary lattice of a 2-day embryo showing the variation in vascular density from the proximal to distal direction. Averaging over a few lines shows a regular increase of the gray level corresponding to a gradient of vascular density from the yolk-sac center to its edge. This is consistent with narrow capillary lumens at the yolk-sac center (high pressure) and larger lumens at its edge (low pressure).

Figure 15

(Color online) Left: schematic representation of the flow in a plexus which grows from the proximal to distal direction, before the apparition of large veins, for prescribed arterial entry $\left(\mathrm{A}\right)$ end venous exit $\left(\mathrm{V}\right)$ points. The vessels’ lumens are represented in gray and the interstitial tissue in white. The enlarged capillaries in the vicinity of the growing artery are represented in green. Arrows indicate the preferential flow path, which tends initially to explore the distal region because the capillary density is greater there. Red arrows correspond to arterial flow, blue arrows to venous flow. Right: electrical analogy for the distribution of the resistances of the preferential flow path. The upper-left “Cis-cis” panel shows the initial situation where no artery is formed yet. The cis-cis configuration provides the lowest hemodynamic resistance and thus the preferential path for blood flow. The middle panel shows the situation at start of arterial growth, with the cis-cis configuration still providing the preferential path for flow. The lower-left panel “Cis-trans” shows the situation after some time of growth with the cis-trans configuration providing the preferential path for flow. The (small) resistivity per unit length in the distal area and the (large) resistivity per unit length in the proximal area are denoted by $r$ and $R$, respectively. The total resistance of the proximal path (path parallel to the artery), the total resistance of the distal path (path from the arterial end to the organ distal limit), and the resistance of the growing artery are denoted by $R_{\text{prox}}$, $R_{\text{dist}}$, and $R_a$, respectively. As the artery grows, it disconnects from the capillaries. The neighboring capillaries reshape and enlarge, so that a favored path of capillaries, with their resistance divided by a factor of order 16, appears along the growing artery $\left(R_{\text{prox}}/16\right)$.

Figure 16

(Color) Numerical simulations of the wall shear-stress spatial distribution in a model configuration representing a bidimensional growing organ at different steps, for prescribed arterial entry $\left(\mathrm{A}\right)$ and venous exit $\left(\mathrm{V}\right)$ points. Panel 1: geometry and notation: an artery (length $L_a$ and radius $40\mu \text{m}$) and a vein (length $L_v$, radius $40\mu \text{m}$) in a rectangular heterogeneous capillary plexus (length $L$, width $l=7.3\text{mm}$). The radius distribution of the vessels is represented by the color scale and varies linearly from $2.5\mu \text{m}$ proximally to $5\mu \text{m}$ distally. The vessels with a larger radius (including the artery and vein) appear in red. The stars indicate the end points of the artery and vein. Note that, in this case, the radius of the capillaries along the disconnected artery and vein has been increased twofold in order to account for capillary remodeling. Panels 2–6: distribution of wall shear stress: The distribution of wall shear stress (in Pa) is represented by the logarithmic color scale (note that the scale is different for the different values of $L$ in the different panels). Panel 2: $L=1.2\text{mm}$ and $L_a=L_v=0.24\text{mm}$. Panels 3 (accounting for capillary remodeling along the disconnected arteries and veins) and 4 (reference case without capillary remodeling): $L=3.6\text{mm}$, $L_a=1.8\text{mm}$, and $L_v=0.24\text{mm}$. Panels 5 (accounting for capillary remodeling along the disconnected arteries and veins) and 6 (reference case without capillary remodeling): $L=13.5\text{mm}$, $L_a=9\text{mm}$, and $L_v=4.5\text{mm}$; Panels 5a and 6a: enlarged views of highlighted areas of panels 5 and 6. Panels 2–4: for $L<l$, the wall shear stress exhibits a cis-cis configuration, with a high level of shear in the distal area (between arrows), favoring a proximal to distal growth of the artery and vein. At this stage, the capillary remodeling along the disconnected arteries and veins has a negligible influence (no significant differences between panel 3 and 4). Panels 5 and 6: For $L>l$, the wall shear stress exhibits a cis-trans configuration, with a higher level of shear in the capillaries neighboring the artery compared to the shear level in the distal area (bottom of the panel). At this stage, the capillary remodeling has an important local effect, increasing the order of magnitude of the wall shear stress in the remodeled capillaries (along the artery) by one to two orders of magnitude (area between arrows in the enlarged view displayed on panels 5a and 6a).