The circulatory system of Penaeus vannamei Boone, 1931—Lacunar function and a reconsideration of the “open vs. closed system” debate

The morphology of hemolymph circulatory systems has been studied in many arthropod groups over the past decades. In most cases, however, the focus of these studies has been the vascular system, while its counterpart, the lacunar system, has often been neglected. To further understanding of the interrelationships between these two complementary subsystems, we investigated both, the hemolymph vascular system and the hemolymph lacunar system, of the decapod Penaeus vannamei using 3D‐imaging techniques (micro‐computed tomography and confocal laser scanning microscopy) in combination with 3D reconstruction. Major parts of the vascular and lacunar system are described. Our insights into their morphology are used to derive functional conclusions for a model illustrating the interrelationships between the two subsystems. The morphology of and the functional interaction between the vascular and lacunar systems are discussed in the context of the debate on “open vs. closed circulatory systems.”


| INTRODUCTION
The morphology of the hemolymph circulatory systems of arthropods, especially of decapods, has been studied in great detail in recent years (e.g., Keiler, Richter, & Wirkner, 2013McGaw & Reiber, 2002;McGaw & Stillman, 2010). However, what has actually been studied in detail is the hemolymph vascular system (i.e., the heart and the arteries), only one of the two constituent subsystems of the hemolymph circulatory system (Wirkner et al., 2017;Wirkner, Tögel, & Pass, 2013). The hemolymph lacunar system (i.e., lacunae and sinuses) has mostly been neglected in studies on arthropod circulatory morphology.
In arthropods, the heart pumps hemolymph through arteries which emanate from it. These arteries have open endings (Dumont, Anderson, & Chomyn, 1965) through which the hemolymph leaves the hemolymph vascular system (which is therefore termed an open vascular system;  and enters the hemolymph lacunar system. Through the lacunae and sinuses, the hemolymph is ultimately channeled back to the pericardial sinus which surrounds the heart. The hemolymph can then reenter the heart through ostia, that is, slit-like valves in the heart. There are no veins, that is, no afferent vessels, and the lacunar system therefore takes over venous function . The hemolymph within the vascular and lacunar system is constantly moved by systolic pumping and diastolic suction . The ostia and the arterial valves at the base of all arteries that leave the heart (Göpel & Wirkner, 2018) prevent backflow and thus ensure that the flow of hemolymph is unidirectional. The morphology of the lacunae and sinuses has mainly been studied in arthropods lacking an elaborate vascular system, for example, branchiopods (Pirow, Wollinger, & Paul, 1999;Vehstedt, 1940) and insects (Jones, 1977;Snodgrass, 1935). Hemolymph flow in these taxa has also been observed and reconstructed (Jones, 1977;Vehstedt, 1940;Wigglesworth, 1974). Accounts of lacunar morphology and hemolymph flow in Malacostraca have been published for Anaspidacea (Siewing, 1959) and Isopoda (Silén, 1954), among a few other groups. In many cases, the reason for the neglect of the lacunae and sinuses might have been methodological. In dissections, lacunae are barely recognizable as distinct entities (Mayrat, McMahon, & Tanaka, 2006) and in histological sections, lacunae appear as "free space" between the organs and tissues, or are erroneously interpreted as a consequence of shrinkage artifacts. For this reason, lacunae and sinuses in arthropods have sometimes been considered ill-defined spaces or residual recesses rather than distinct morphological entities.
The three-dimensional approach offered by modern morphological methods, however, allows the lacunar system to be documented properly and its functional importance to be highlighted.
Decapods are known to show the highest degree of complexity in vascular systems within Mandibulata (Keiler et al., 2013(Keiler et al., , 2015McGaw & Reiber, 2002;, which implies that hemolymph flow has to be accurately and precisely maintained in the various body regions. As the vascular system constitutes only half of the circulatory system, it can be assumed that a specialized and defined lacunar system is equally important for maintaining this precision of hemolymph flow. We investigated the hemolymph circulatory system of the decapod Penaeus vannamei Boone, 1931, using micro-computed tomography (μCT) and confocal laser scanning microscopy (cLSM) in order to describe the vascular and the lacunar systems in detail. We integrate the main vascular and lacunar constituents of the cephalothorax into a functional model of hemolymph flow derived from our three-dimensional morphological findings.

| Specimen preparation
Subadult specimens of P. vannamei Boone, 1931, with a total body length of 8-14 cm were obtained from a local aquaculture facility (Garnelenfarm Grevesmühlen GmbH, Grevesmühlen, Germany) and sacrificed using some drops of ethyl acetate. In total, 41 specimens have been studied. Specimens used for μCT were either fixed directly in 2-3% formaldehyde at a salinity of 15-20 PSU (n=5) or were injected with the casting resin Mercox II (Ladd Reserch, Williston, Vermont) into the heart prior to fixation (n=32). Additionally, specimens for μCT imaging were critical-point dried (Leica EM CPD300, Leica Microsystems, Wetzlar, Germany), while dissected parts of specimens were chemically dried using HMDS (Nation, 1983). Three specimens used for cLSM were fixed in 4% paraformaldehyde in 1× phosphate-buffered saline (PBS) for 12 to 48 hours.
These specimens were dissected to obtain tissue samples for cLSM imaging. Samples were stained with 1 1:600 dilution of CellMask™ Green (ThermoFisher Scientific, Waltham, Massachusetts) in 1× PBS or a 1:200 dilution of Alexa Fluor 546 conjugated Phalloidin (Thermo Fisher Scientific) in 1× PBS for 2 hours. One specimen for stereomicroscopy was perfused with 20 ml of 3% formaldehyde solution with a salinity of 15 PSU dyed with congo red before fixation with 2% formaldehyde in 1× PBS.

| Micro-computed tomography
Specimens for μCT imaging were selected after evaluation of injection quality under a stereomicroscope. Eleven injected and three noninjected specimens (as well as three dissected gills) were used for μCT imaging. Specimens were mounted onto a specimen holder. X-ray imaging was performed on a ZEISS Xradia Versa 410 X-ray microscope (ZEISS; Oberkochen, Germany) using the software Scout and Scan v.11. Acquisition properties were 30 or 40 kV, 150-200 μA, 1,601-3,201 projections, 3-10 s acquisition time per single transmission image.

| Confocal laser scanning microscopy
Stained samples were mounted in RapiClear 1.47 (SunJin Lab Co., Taiwan) in chambers made of two coverslips and iSpacers (SunJin Lab Co., Taiwan) which were sealed with clear nail polish. Imaging was performed using a Leica DMI6000 CFS microscope equipped with a Leica TCS SP5 II confocal laser scanning unit (Leica Microsystems, Wetzlar, Germany). Stained samples were imaged by excitation with the appropriate wavelength for the dye, and autofluorescence was recorded additionally at multiple wavelengths.

| Stereomicroscopy
The specimen dyed with congo red was analyzed using a ZEISS Discovery.V12 (ZEISS Microscopy, Jena, Germany).

| Image processing
All figures were arranged and labeled using the software package CorelDraw Graphics Suite X3 (Corel Corp., Ottawa, Canada).

| Terminology
All terms used to refer to morphemes of the hemolymph circulatory system in P. vannamei are based on terms and classes in the Ontology of Arthropod Circulatory Systems (OArCS, accessible via http://oarcs. speciesfilegroup.org, last accessed March 3, 2020; Wirkner et al., 2017) 3 | RESULTS

| Hemolymph vascular system
The hemolymph vascular system of P. vannamei consists of a globular heart and six emanating artery systems: the paired anterior lateral artery systems, the paired hepatic artery systems, the unpaired ventral vessel system, and the unpaired posterior aorta system (Figures 1 and 2a). Our visualization and description of the vascular system focuses on larger branches, very fine vessels are not described and may not be visualized by the methods used.

| Heart
The globular heart is located dorsally in the posterior cephalothorax ( Figures 1 and 2a) and appears roughly pentagonal in dorsal view and roughly triangular in sagittal section (Figure 3a, b). It is made up of a rather thick, spongious outer epicard and an inner myocard ( Figure 3a). As distinctive for globular hearts, the myocard is a thick, with a peripheral layer of cardiomyocytes which run in various directions, and bundles of cardiomyocytes traversing the heart lumen ( Figure 3a, d). The heart is equipped with five pairs of ostia (Figure 3b, c). The first pair (counted from anterior to posterior) is situated anterolaterally, the second and third pairs are situated dorsally, the fourth is situated ventrolaterally, and the fifth posterolaterally. The fifth pair of ostia is distinctly larger in diameter than the other four pairs. In some specimens, one of the four dorsal ostia is rudimentary. Which of the four, however, appears to be subject to intraspecific variation Along their course, the anterior lateral arteries give rise to a number of arteries, of which only the larger ones will be described in more F I G U R E 1 Penaeus vannamei, schematic representation of the main parts of the hemolymph vascular system (red) and hemolymph lacunar system (blue). Right thoracopodal arteries and right posterior lateral arteries are indicated by dashed lines. Only three gills and their respective branchio-pericardial sinuses are shown in order to prevent the drawing from being cluttered. agl1: first-order afferent gill lacuna; ala: anterior lateral artery; ana: antennal artery; aua: antennular artery; bps: branchio-pericardial sinus; bstga: branchiostegal artery; da: descending artery; egl1: first-order efferent gill lacuna; h: heart; ha: hepatic artery; mp3: third maxillipedal artery; oa: optic artery; ost: ostium; p3: third pereiopodal artery; pa: posterior aorta; pcs: pericardial sinus; pla3: third osterior lateral artery; pnl: perineural lacuna; rar: rostral arch; tll: trough-like lacuna; upa: uropodal artery; vll: ventrolateral lacuna; vv: ventral vessel [Color figure can be viewed at wileyonlinelibrary.com] detail. Shortly after originating from the heart, each of the anterior lateral artery gives rise to an artery extending in a ventromedian direction. One of the two contralateral arteries is larger and more ramified and continues anteroventrally to supply the stomach from its posterior side, and the midgut (Figure 2b). The other median branch, however, is finer and runs ventrally to supply the midgut and the anterior portion of the midgut gland. Which anterior lateral artery gives rise to the larger artery supplying the stomach, however, is subject to intraspecific variability. A little more distally, each anterior lateral artery gives rise to the branchiostegal artery (Figures 1 and 2b; bstga) which first runs ventrolaterally and then bends posteriorly to run into the branchiostegite. The branchiostegal artery gives rise to several arteries along its course before actually running posteriorly in the direction of the branchiostegite. Before it bends in a posterior direction, one branchiostegal artery gives rise to an artery which runs ventromedially and supplies the foregut (Figure 2b; left bstga). More anteriorly, the antennal artery branches off from the anterior lateral artery in an anteroventral direction (Figure 2b; ana). The proximal part of the antennal artery gives rise to several smaller arteries which supply the extrinsic musculature of the second antenna. A little more distally, the antennal artery bifurcates into the two arteries which run into the endopodite and the scaphocerite, respectively. Anterior to the junction of the antennal artery, the anterior lateral arteries bend slightly anteromedially giving rise to the rostral arch (Figure 2b; rar), an anastomosis between the two contralateral anterior lateral arteries which runs dorsally to the cerebral region, and at its crest gives rise to the rostral artery. After this junction, the anterior lateral arteries curve anteroventrally around the brain and give rise to numerous F I G U R E 2 Penaeus vannamei, hemolymph vascular system reconstructed from micro-computed tomography data. (a) Lateral view (montage; cephalothorax, and pleon were scanned separately); (b) dorsal view of the anterior lateral artery systems; (c) posterodorsal view of the posterior aorta system in the posterior part of the pleon; arrowhead indicates the bifurcation of the posterior aorta; (d) dorsal view of the ventral vessel system. ala: anterior lateral artery; ana: antennal artery; aua: antennular artery; bstga: branchiostegal artery; da: descending artery; h: heart; ha: hepatic artery; md: mandibular artery; mp1: first maxillipedal artery; mp2: second maxillipedal artery; mp3: third maxillipedal artery; mx1: first maxillar artery; mx2: second maxillar artery; oa: optic artery; p1: first pereiopodal artery; p2: second pereiopodal artery; p3: third pereiopodal artery; p4: fourth pereiopodal artery; p5: fifth pereiopodal artery; pa: posterior aorta; pla1: first posterior lateral artery; pla2: second posterior lateral artery; pla3: third posterior lateral artery; pla4: fourth posterior lateral artery; pla5: fifth posterior lateral artery; rar: rostral arch; upa: uropodal artery; vv: ventral vessel. The PDF version contains interactive 3D content. Open in Adobe Reader and click on the figure to activate [Color figure can be viewed at wileyonlinelibrary.com] fine brain arteries. Ventrolaterally, the antennular artery (Figure 2b; aua) emanates from each anterior lateral artery and soon bends in a directly anterior direction. The last major branch to emanate from each anterior lateral artery is the optic artery ( Figure 2b; oa), which runs into the respective eyestalk. Anteriormost, the final tributaries of the anterior lateral arteries anastomose in the anterior cerebral region.

| Hepatic artery systems
The paired hepatic arteries originate from the anteroventral portion of the heart extending anteroventrally at a 45 angle to the longitudinal axis ( Figure 2a). The hepatic arteries are found between the diverticles of the midgut gland and soon bifurcate into an anterior and a posterior branch each. These branches give rise to numerous smaller arteries which continue between the diverticles of the midgut gland to supply every region of this organ. Anteriorly, some smaller branches of the hepatic artery system come close to branches of the anterior lateral artery systems, though anastomoses between the two artery systems do not occur.

| Ventral vessel system
The descending artery emanates at the posteroventral apex pereiopodal arteries, as well as the third and second maxillipedal arteries, which share a common stem (Figure 2d; mp3, mp2). Anterior to the second maxillipedal arteries, the ventral vessel bifurcates into branches from which the first maxillipedal arteries and the arteries running into the two maxillae emanate (Figure 2d; mp1, mx2, mx1). Close to the bifurcation of the ventral vessel, from one of the two branches, an unpaired artery originates which runs anteriorly and bifurcates into the two mandibular arteries (Figure 2d; md). In the two specimens in which this unpaired branch could be seen best, it originated from the right branch, though close to the bifurcation. Furthermore, the ventral vessel gives rise to several fine arteries dorsally which supply the ventral nerve cord.

Branchio-pericardial sinuses
The branchio-pericardial sinuses (Figure 4a; bps) connect the efferent gill lacunae with the pericardial sinus. However, there are not 18 inlets into the pericardial sinus on each side, rather the sinuses merge before opening into the pericardial sinus. The branchio-pericardial sinuses are located laterally and enclosed by a sinus septum and the lateral integument. The sinuses are elliptical in horizontal section. On each side, three major systems of branchio-pericardial sinuses open into the pericardial sinus, with the second efferent to the largest group of gills (9 of 18 gills; three proximal sinuses efferent to 3 gills each). The anteriormost of the three major sinus systems extends posterodorsally, while the posteriormost extends anterodorsally ( Figure 4a). The transition from the branchio-pericardial sinuses to the pericardial sinus is smooth as the sinus septa merge with the pericardial septum.

Trough-like lacuna
The trough-like lacuna (Figures 1 and 4b; tll) is located in the posterior cephalothorax directly underneath the midgut gland. Ventrally, it is bordered by the extensive ventral musculature of the cephalothorax.
In cross section, this lacuna resembles a compressed "u." It runs along the longitudinal axis, that is, it has a trough-like shape in 3D view. It is connected dorsally to the numerous small lacunae between the diverticula of the midgut gland. Ventrally, the trough-like lacuna connects to the smaller lacunae which interlace the ventral thoracic musculature. The trough-like lacuna is connected ventrally to the perineural lacuna (Figure 4b; pnl) along the median line via straight, ventrally oriented lacunae which occur predominantly in its anterior portion.

Perineural lacuna and ventrolateral lacunae
The perineural lacuna (Figures 1 and 4b (Figures 1 and 4b; vll). The ventrolateral lacunae are superficially segmental in their arrangement but cannot actually be assigned to a specific segment as they are so difficult to differentiate. Six "clusters" of afferent gill lacunae which emanate from the ventrolateral lacunae could be distinguished (more or less).   (Keiler et al., 2013), crayfish (Scholz et al., 2018), and caridean shrimps (Pillai, 1965), and actually most arthropods in general (Göpel & Wirkner, 2018;, exhibit an anterior aorta, P. vannamei is lacking such an artery. Young (1959) described a fine unpaired anterior artery for Penaeus setiferus which he concluded might be a vestige of the anterior aorta (an idea taken up and generalized for Dendrobranchiata by McLaughlin, 1980), but Mayrat (1958) explicitly noted the lack of an anterior aorta for Penaeus kerathurus. It is unambiguous in P. vannamei that the only arteries emanating from the anterior apex of the heart are the anterior lateral arteries. There is, however, a proximal side branch of one anterior lateral artery which runs dorsomedially and gives rise to a fine longitudinal artery which in turn follows the course one would expect from a rudimentary anterior aorta. Because of its relative vicinity to the heart, this artery might be confused with an anterior aorta. The anterior lateral arteries take on the functions of the anterior aorta and supply the eyes and the brain, for example, via a remarkably complex set of ramifications (Figure 2a,   b). As in other decapods (Keiler et al., 2015), the hepatic arteries and their branches only supply the midgut gland, so although they exhibit complex ramifications, they are restricted to a rather narrow region.

| Branchiostegites
The descending artery shows some intraspecific variability in whether it passes the gut on the right side or the left, a phenomenon that has also been observed in marbled crayfish (Scholz et al., 2018;Vogt, Wirkner, & Richter, 2009), among other species. In general, the morphology of the vascular system of P. vannamei bears a strong resemblance to that of P. kerathurus (Mayrat, 1958), including features such as the rostral arch (Figure 2b, rar).
The heart of P. vannamei is equipped with five pairs of ostia, which are identical in position to the five pairs in P. kerathurus (Mayrat, 1958). Five pairs of ostia have also been found in the caridid shrimp Caridina laevis (Pillai, 1965) and thus might well represent the plesiomorphic condition within Decapoda. Young (1959) described only three pairs of ostia for P. setiferus, as have been found in other decapods (e.g., Keiler et al., 2015;Scholz et al., 2018). Although a difference of this nature between two species of dendrobranchiate shrimp is possible, it is also imaginable that the anterior and the ventrolateral pairs of ostia (pairs one and four in P. vannamei) might have been overlooked in P. setiferus. These two pairs of ostia are rather small and are located in regions of the heart that are difficult to examine by dissection. Another distinctive feature of the heart in P. vannamei is the intraspecific variability of the dorsal ostia. In most specimens, one of the four dorsally situated ostia (Pairs 2 and 3) is only rudimentarily developed, sometimes to the extent that it is not recognizable as an ostium from the outside at all. Which of the four this applies to appears to follow no obvious rule. However, because in the μCT volume the missing ostium can be identified as vestigial and is thus not lacking entirely (Figure 3b, d), it is possible that some unspecified and yet undescribed developmental processes might be the reason for the reduction of one of the four dorsal ostia.

| Branchiostegite
The branchiostegites of P. vannamei are amply supplied with hemolymph, mirroring the situation in P. setiferus as described by Young (1959). The carapaces of various malacostracans are ascribed osmoregulatory (Cieluch, Charmantier, Grousset, Charmantier-Daures, & Anger, 2005;Lignot, Charmantier-Daures, & Charmantier, 1999) and respiratory functions and are also supplied with hemolymph through an elaborate system of lacunae (Farrelly & Greenaway, 1993, 2005. While respiratory regions of the carapace in Lophogastrida, Mysida, and Brachyura are supplied via afferent lacunae (Gruner, 1993), the branchiostegites of P. vannamei are supplied simultaneously via afferent lacunae and afferent arteries. The afferent arteries are the branchiostegal artery, which enters the branchiostegite approximately halfway along its length, and a smaller artery which enters the branchiostegite at its posterior margin ( Figure 6a). Both arteries ramify, with their side branches ultimately ending openly to let hemolymph into the lacunae. Separate afferent lacunar supply to the branchiostegite is provided by the major branchiostegal lacuna, which enters the branchiostegite close to the branchiostegal artery and then ramifies radially into an elaborate system of small lacunae. Closer to the margins of the branchiostegite, the lacunae merge and then join the branchiostegal-pericardial lacuna, the only efferent lacuna of the branchiostegite, which channels hemolymph into the pericardial sinus. In his description of hemolymph supply in P. setiferus, Young (1959) termed all the hemolymph channels "vessels," without distinguishing between vascular and lacunar elements. Nevertheless, our results clearly show that both afferent vessels and afferent lacunae are present in P. vannamei. Young (1959) distinguished two types of channels in the branchiostegite: the radially ramifying channels and a set of channels running parallel to the margin of the branchiostegite (figure 77 in Young, 1959). However, as described above, the only lacuna running parallel to the margin of the branchiostegite is the branchiostegal-pericardial lacuna. What Young (1959) might have mistaken for hemolymph channels are the concentric loops described above (Figure 6a, arrowhead) which cLSM image data clearly show not to be any kind of hemolymph channel (Figure 6d, e).

| A functional model of hemolymph flow in the cephalothorax
As described above, the hemolymph lacunar system exhibits a definite morphology and major lacunae of the cephalothorax can be identified. Silén (1954) described well-defined lacunae and sinuses in Oniscoidea and derived a model of the main hemolymph currents in the posterior thorax. However, the internal organization of oniscoid isopods, especially with regard to lacunae and sinuses, apparently differs substantially from that of P. vannamei (Gruner, 1993). Thus, implications for lacunar hemolymph flow are expected to differ as well.
In bringing together our findings on the morphology of the vascular and lacunar systems in P. vannamei, we hope to achieve a better functional understanding of the relationships between these two subsystems of the circulatory system. As a first step, morphology is used to derive function (Bock & von Wahlert, 1965). In the following, we seek to integrate the vascular system and the major lacunae and Hemolymph is ejected from the heart through the hepatic arteries, which ramify between the diverticles of the midgut gland. At this point, the hemolymph leaves the arteries of the hepatic artery systems and enters the lacunar system, flowing around the midgut and the diverticles of the midgut gland through a number of fine lacunae.
Here, it is likely that nutrients are taken up into the hemolymph (while the midgut gland is supplied with oxygen) to be transported to the tar-

| Not an open circulatory system?
The arthropod circulatory system, which is traditionally considered an "open circulatory system" (Gruner, 1993), has often been derided as a "primitive," poorly designed system. The point of reference for this implicit comparison is always the vertebrate (basically mammalian and avian) "closed circulatory system," whose highest expression of F I G U R E 7 Penaeus vannamei, schematic overview of the vascular (red) and lacunar (blue) parts of the circulatory system in the posterior cephalothorax. agl1: first-order afferent gill lacuna; bps: branchio-pericardial sinus; bstg: branchiostegite; da: descending artery; egl1: firstorder efferent gill lacuna; g: gut; h: heart; ha: hepatic artery; mgg: midgut gland; mu: muscle; ost: ostium; pcs: pericardial sinus; pnl: perineural lacuna; tll: trough-like lacuna; vll: ventrolateral lacuna; vnc: ventral nerve cord; vv: ventral vessel [Color figure can be viewed at wileyonlinelibrary.com] complexity is held to be its separate systemic and pulmonary circuits (McMahon, 2012).
However, the definitions of "open" and "closed" in this context are not the same as in thermodynamics, for example, where closed systems can only exchange energy, not matter, with their environment (Khonsari & Amiri, 2012, p. 11). The definition of "closed" in terms of biological circulatory systems is that such systems are completely separated from the body cavity and bounded by an endothelial layer across which substance exchange takes place (Reiber & McGaw, 2009). Though vessels with an endothelial lining are indeed a peculiarity of vertebrates, the dense specialized arterial walls found in arthropods (e.g., Göpel & Wirkner, 2015;Lane, Harrison, & Bowerman, 1981), while not endothelial per se, are also assumed to similarly seal the arteries (Lane et al., 1981). On the other hand, even vertebrate circulatory systems are not completely "closed" as fenestrated and discontinuous endothelia in capillaries allow not only blood plasma and dissolved molecules but also (in the case of discontinuous endothelia) blood cells to pass the capillary wall (e.g., Noble, Johnson, Thomas, & Bass, 2013, pp. 126-127).
Another problem with the terms "open" and "closed" is that they have been applied to the circulatory system as a whole (see McGaw, 2005 and literature therein), hence "open circulatory system" of arthropods. However, the circulatory system as a whole, consisting of the vascular system and the lacunar system, is closed to the same degree as the circulatory system of vertebrates. As pointed out previously , it is the vascular (sub) system (and the lacunar system respectively) of arthropods which should be considered open as the hemolymph never leaves the circulatory system, it just moves between the vascular subsystem and the lacunar subsystem. To cloud the matter even further, the vascular systems of decapod crustaceans have been assigned the exceptional status "incompletely closed" due to their complexity (McGaw, 2005;Reiber & McGaw, 2009). Although it recognizes the complexity of decapod vascular systems (horseshoe crabs and pulmonate arachnid taxa should be regarded as equally complex; Huckstorf, Kosok, Seyfarth, & Wirkner, 2013;Klußmann-Fricke, Pomrehn, & Wirkner, 2014;Göpel & Wirkner, 2015), the term "incompletely closed" dilutes the conceptual pair of "open" vs. "closed". Apart from the arbitrariness of the decision regarding the degree of complexity (e.g., in terms of ramifications) above which an arthropod circulatory system can be called "incompletely closed," the abstract situation in decapods is no different from that in other arthropod taxa: the hemolymph always leaves the arteries, no matter how much they ramify, and passes into the lacunar system and then ultimately back to the heart, that is, back to the vascular system again.
To uphold the conceptual pair of "open" vs. "closed" vascular systems, a new and ubiquitously applicable definition of these concepts is called for, a definition independent of the histological properties of the arterial lining, the fuzzy parameter of separation from the body cavity or the inevitably arbitrary degree of complexity. We suggest that a vascular system should be considered closed if fluid (including cells) can complete a full heart-back-to-heart circuit within the lumen of vessels (although a fraction of the fluid might leave the lumen, for example, through discontinuous capillaries). In open vascular systems, on the other hand, the fluid inevitably leaves the vascular lumen at some point and the vessels end (Dumont et al., 1965). This definition fits the perception of the mammalian vascular system as closed despite its discontinuous capillaries, as not all the blood leaves via the fenestrated capillaries, and most of it will leave and reenter the heart within the pulmonary and systemic circuit without leaving the vascular lumen. This conceptual definition also fits taxa other than arthropods and vertebrates. Some molluscs, for example, unlike arthropods, have arteries and veins, but in pulmonate gastropods, for example, hemolymph passes through a lacunar system between the arterial and venous systems. This would match the definition of an open vascular system, while the circulatory systems of cephalopods would match the definition of a closed vascular system (Bourne, Redmond, & Jorgensen, 1990).
It is worthwhile considering the complexity of the vascular systems found in some arthropod taxa in terms of functional aspects.
The open vascular systems of arthropods have been derided as "primitive" and poorly designed in comparison to the elaborate closed vascular systems of vertebrates (Gruner, 1993;Pyle & Cronin, 1950).
However, some arthropod taxa (e.g., Xiphosura, Decapoda) possess a vascular system that, despite being open, exhibits a level of complexity in terms of ramification that is comparable to that in smaller vertebrates. This is the main argument for Reiber and McGaw (2009) to consider the decapod vascular system "incompletely closed." Apparently, the view persists that a closed vascular system, as found in vertebrates, represents the "ideal" or "best" condition which arthropods have unfortunately not been able to evolve. However, the functional importance of the vascular systems in arthropods is likely to differ from that in their vertebrate counterparts. The key functions of circulatory systems are, of course, to supply the body with nutrients and oxygen, remove waste material and carbon dioxide, provide immunocompetent cells, and distribute hormones . In arthropods, exchange between tissues and hemolymph mainly takes place in the lacunar system, which "bathes" the organs in hemolymph (the only prominent exception being the perineural vascular sheath in Xiphosura and apulmonate arachnid taxa; Göpel & Wirkner, 2015, Klußmann-Fricke & Wirkner, 2018. The overarching functional purpose of the vascular system is to circulate and replace hemolymph which has already interacted with organs and tissues. This is a different function than that fulfilled by the vascular system in vertebrates, and it is entirely possible that a closed vascular system in arthropods would not be the "desirable" condition at all. The vascular system provides various hemolymph inlets into the interstitial lacunae and permits constant hemolymph flow to all parts of the body. If the vascular system in P. vannamei were to consist only of a heart and one short anterior aorta (e.g., as in copepods), there would most likely be no significant hemolymph flow in the pleon or the appendages and homeostasis could not be upheld. Such simple vascular systems are thus only found in minute arthropods, independent of their phylogenetic position (Göpel & Wirkner, 2018;. Larger arthropods have evolved a remarkable disparity of vascular systems, with those in horseshoe crabs, pulmonate arachnids, and decapod crustaceans-the three taxa boasting the largest arthropod organisms-doubtlessly exhibiting the highest complexity (Göpel & Wirkner, 2015;Klußmann-Fricke et al., 2014;McGaw & Reiber, 2015). This high degree of ramification is likely to ensure steady circulation even in remote body regions. Organs with high nutrient and oxygen consumption are equipped with extensive vasculature to permit faster exchange of hemolymph in the adjacent lacunae to keep nutrient and oxygen concentration as high as possible (Wilkens, 1999). Furthermore, many arthropod taxa have centralized respiratory organs such as gills or book lungs which demand an elaborate vascular system to evenly distribute oxygenated hemolymph (Wirkner et al., 2013 and literature therein).

Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon request.