Functional end-arterial circulation of the choroid assessed by using fat embolism and electric circuit simulation

The discrepancy in the choroidal circulation between anatomy and function has remained unsolved for several decades. Postmortem cast studies revealed extensive anastomotic channels, but angiographic studies indicated end-arterial circulation. We carried out experimental fat embolism in cats and electric circuit simulation. Perfusion defects were observed in two categories. In the scatter perfusion defects suggesting an embolism at the terminal arterioles, fluorescein dye filled the non-perfused lobule slowly from the adjacent perfused lobule. In the segmental perfusion defects suggesting occlusion of the posterior ciliary arteries, the hypofluorescent segment became perfused by spontaneous resolution of the embolism without subsequent smaller infarction. The angiographic findings could be simulated with an electric circuit. Although electric currents flowed to the disconnected lobule, the level was very low compared with that of the connected ones. The choroid appeared to be composed of multiple sectors with no anastomosis to other sectors, but to have its own anastomotic arterioles in each sector. Blood flows through the continuous choriocapillaris bed in an end-arterial nature functionally to follow a pressure gradient due to the drainage through the collector venule.

observed in the occlusion of the posterior ciliary artery (PCA) cannot be explained by their theory, as the pressure gradient in the choroidal arterioles will be reversed when the PCA is occluded, and the non-perfusion would be resolved rapidly by perfusion via the anastomosing arterioles from the adjacent sectors.
Triolein emulsion was used for an experimental fat embolism model 18,19 . Infusion of triolein emulsion into the carotid artery causes microembolism in the intraocular circulation, and has several advantages in the investigation of the microcirculation of the eye. A triolein emulsion can have various particle sizes, which result in different findings, as vessels of various sizes were occluded. This allowed the observation of both sectorial and lobular perfusion defects. Another important feature is that triolein is liquid, and thus, embolization can be readily resolved. Angiographic findings can be recorded at the moment when embolism is resolved 19 . The feline eye has a special layer, the tapetum lucidum cellulosum, between the choriocapillaris and the larger choroidal vessels 20 . This layer reflects incident light back to the photoreceptor and increases light perception in darkness. In addition, the dense pigmentation of the layer blocks fluorescence from the large choroidal vessels, which were not demonstrated even in indocyanine green angiography in our preliminary study. Thus, we decided to use fluorescein angiography (FA) to obtain higher-contrast images. The use of FA in feline eyes has the advantage of assessing the choriocapillaris circulation without interfering with background fluorescence.
Meanwhile, blood circulation may be demonstrated schematically using an electric circuit, with the electric current corresponding to flow, voltage to pressure, and electric resistance to vascular resistance 21 . This model would be helpful in simplifying a complicated vascular network and provide explanation for the circulation changes observed in experiments as well as in pathologic conditions. We investigated the choriocapillary circulation using FA in an experimental fat embolism model, and the angiographic findings were interpreted by using an electric circuit model simulating the choriocapillary bed.

Results
Choroidal circulation in the fat embolism model. Various degrees of perfusion defects were demonstrated in the retina and choroid. The difference in degrees was due to the various sizes of triolein emulsion droplets 18 . Stop-and-go movements of intravascular lipid drops were observed in the retinal vessels, and the perfusion defects were resolved in most areas in the late phase.
The perfusion defects of the choroid were observed in two categories ( Fig. 1): (1) perfusion defects scattered among small choroidal patch fillings in 8 cats and (2) segmental perfusion and defects assumed to correspond to territories supplied by the PCAs in 4 cats.
In the former, the small choroidal patches were filled with fluorescein dye at multiple locations in a centrifugal pattern from the center of each location, representing lobular perfusion of the choriocapillaris. All the centers of the lobules could not be marked in areas having broad and prolonged non-perfusion. The distance between two adjacent feeding arterioles, measured based on the points where hyperfluorescence began to show in each lobule, was approximately 200 to 400 μm. The scattered perfusion defects suggested a fat embolism at the terminal arterioles supplying the lobules. Some defects were resolved as the dye began to fill the choriocapillaris centrifugally from the lobular center, conversely some of the perfused lobules became non-perfused due to delayed embolism ( Fig. 2a-d, Supplemental Video). As reported previously, various findings were noted related to various particle size of triolein emulsion. Irregular initial filling of the lobule was observed, probably because of triolein emulsion in the choriocapillaris. Filling of fluorescein was slow and sometimes creeping. Reperfusion of several lobules in a group was also noted. Notably, dye filling from the perfused lobule to the adjacent non-perfused lobule was clearly observed, indicating that the choriocapillaris is not an end-arterial system anatomically. However, the filling rate was so slow that a non-perfused lobule surrounded by perfused lobules was barely filled after approximately 10 seconds.
In the latter, the perfused and non-perfused segments were demonstrated as discrete hyperfluorescent and hypofluorescent areas, respectively ( Fig. 2e-h). The boundaries remained almost unchanged, with minimal spread of fluorescence for 12 seconds in average (range; 9-15 s). Then, the hypofluorescent segment was perfused, indicating spontaneous resolution of the triolein embolism, and the segments became indiscernible (Fig. 2h). Subsequent non-perfusion of the smaller segments or flow of the released triolein was not observed.
Interpretation using electric circuit simulation. In the normal circuit model, the direction of the electric currents was centrifugal from the anodes toward the periphery of the hexagon and centripetal around the cathodes to follow the voltage gradient ( Fig. 3a-c). The electric current from adjacent hexagons converged in the boundaries and flowed along the boundaries to the cathodes. No current crossing the boundaries of the hexagon was observed. When the resistance of the hexagon boundary was set at 16 Ω, representing the collector venule with the same diameter as the capillary, the direct currents were dominant from the anode to the cathodes in the hexagon. As the resistance of the hexagon boundary decreased from 16 to 1 Ω, the average current of a hexagon increased, and electric currents were distributed more evenly in the hexagon.
When a single anode was removed in the single feeding arteriole embolism model, electric currents were rearranged. As the voltage gradient from the hexagon center was reversed, electric currents flowed to the disconnected hexagon from the adjacent hexagon, crossing the boundary (Fig. 3d). However, the influx to the disconnected hexagon decreased dramatically to 27.3-2.5% of the anode-connected hexagon depending on the resistance of the boundary. Circuits with lower boundary resistance had lower currents to the disconnected hexagon when disconnected (Fig. 4).
In the model of ciliary artery occlusion, the electric currents in the disconnected hexagons were even lower than in the solitary disconnection condition (Fig. 3e). The electric influx in the first-order hexagons in the disconnected sector reduced to 18.6-1.8% of the connected hexagon, whereas that of the second-order hexagons had electric influx reduced to 2.8-0.04% (Fig. 4).

Discussion
Our study revealed that the choriocapillary lobule was perfused via capillary anastomosis from the adjacent lobule in vivo, which has never been observed in previous studies. The method different from that used in previous studies enabled to find the novel results in the present study.
Many angiography studies in animals demonstrated that the choroid has an end-arterial system, and the use of FA in rhesus monkey showed a mosaic pattern of choriocapillary perfusion 22 . A study using continuous laser-targeted angiography also demonstrated that the fluorescence did not spread outside of the choroidal  The normal choroid shows that electric currents follow the voltage gradient and do not cross the boundary of the hexagon. As the resistance of the boundary becomes lower, the blood flows become more evenly distributed in the hexagon. (d) When one anode is disconnected from the hexagon, the voltage gradient is reversed. Electric currents flow from the adjacent hexagons and cross the boundary to the disconnected hexagon, but at very low level. (e) Reduction of electric current is more severe in sectorial disconnection. Diameter ratio indicates ratio of the collector venule at the lobular boundary and the choriocapillaris. Electric resistance is inversely proportional to the fourth power of the radius (r 4 ) by Poiseuille's equation. . Changes in electric current influx into a hexagon due to change in boundary resistance. When the resistance of the boundary is lower, more currents flow normally, but to a lesser degree in the disconnected hexagons. lobule 15 . The above experiments were performed in eyes with normal circulation. Our electric circuit model simulating normal circulation also revealed that electric currents flow as a unit of hexagon with no currents crossing the boundary, as the voltage gradient was formed in each lobule from the central anode to the boundary and the cathodes. The currents were higher near the cathode and anode, and showed inhomogeneity consistent to findings in previous theoretical models 23,24 . If this model is applied to the choriocapillaris in the interpretation of in vivo observations, blood flows from the feeding arteriole to the collector venule and then to the draining venules in each lobule and will not flow to the adjacent lobules.
Although angiographic findings of triolein embolism in cat eyes were diverse due to various lipid size of triolein emulsion and complexity of the choroidal vasculature, we identified the following noteworthy observations. When triolein emulsion embolized a feeding arteriole to a lobule, the flow of fluorescent dye was observed from the adjacent lobules to the embolized lobule. The hyperfluorescent lines seen in Fig. 2b and c were different from the mosaic pattern observed in the experiment using bolus injection of fluorescein dye 22 , and did not indicate the borders of the choroidal lobules. In our experiment, fluorescein dye was not injected as a bolus, and the hyperfluorescent lines suggest stasis of the flow due to triolein emulsion. Between the perfused lobules, the bright lines were not demonstrated, as fluorescein dye was drained through the draining venule. However, once fluorescein dye flowed into the non-perfused lobule, it would not be easily washed out. Although the choriocapillaris has fenestration and triolein may increase leakage by opening the blood-retinal barrier, the spread of the fluorescein dye to the center of the embolized lobule appeared to be much faster than the diffusion. In addition, diffusion follows the concentration gradient, and spread of fluorescein by diffusion should have the frontier of less fluorescence then the source. Accordingly, the pattern of spreading fluorescence in Fig. 2b-d indicates that filling of the choriocapillaris perfused the embolized lobule.
This could also be simulated using the electric circuit model by removing an anode connection from a single hexagon. As the voltage gradient from the lobular center was reversed, electric currents were formed from the adjacent hexagons. However, the currents decreased to a very low level compared with an anode-connected hexagon. Especially around the anode, the electric current dropped to about 1% level of the perfused (Fig. 3d). When changing the boundary resistance, circuits with lower resistance had higher currents in the connected hexagon and lower currents in the disconnected hexagon. Applying the simulation results to the choriocapillaris circulation indicates that a more efficient drainage via the choroidal venule results in more reduction of blood flow to the lobule when embolized. The profound reduction in blood flow seems sufficient in causing focal ischemic changes in the choroid, such as Elschinig's spot and acute posterior multifocal placoid pigment epitheliopathy, despite a potentially redundant flow.
Both angiographic studies in triolein embolism and electric circuit simulation demonstrated results corresponding to the occlusion of a PCV or its branches. However, a discrepancy remained because anastomosis among the choroidal arterioles was depicted in postmortem studies 25,26 . Autonomic regulation in vivo 12 or development of quick collaterals 11 has been suggested as an explanation for the discrepancy. The most interesting finding of the present study was the spontaneous resolution of the short PCA occlusion, as subsequent embolization of smaller vessels was not observed. These results cannot be explained by autonomic nerve regulation or collateral formation. If a sector of the choroid has no established anastomosis among the arterioles, a drop of triolein released from a large artery will flow down to smaller arterioles or capillaries, which should be embolized and show up as a perfusion defect in angiography. Even if a drop is broken into small droplets which flow without embolism, they should be observed as a flow of fragmented fluorescence 18 . However, such a flow of triolein was not observed either.
Based on the above observations, we suggest a new model for the choroidal vascular pattern (Fig. 5). The choroid is composed of multiple sectors with no anastomosis to other sectors, but each sector has its own anastomotic arterioles. Itotagawa et al. reported an example in the second figure of the literature 6 . The postmortem cast demonstrated that two anastomosing vessels had the common trunk. The choriocapillaris has a continuous vascular bed, but the blood flows in an end-arterial nature because of drainage to the collector venule at the periphery of each lobule. In this vascular pattern, occlusion of a terminal arteriole and a PCA results in a lobular (Fig. 5a) and sectorial infarction (Fig. 5b), respectively. By contrast, when a small choroidal arteriole is occluded by triolein emboli released from the distributing PCA, choroidal perfusion will be restored via anastomosis (Fig. 5c). For an example, experimental occlusion of medial PCA or lateral PCA resulted in a perfusion defect of the area supplied by the PCA 27 . These findings can be explained as the segments supplied by the PCA do not have anastomosis with each other, but may have anastomosis within each segment. Our model proposes that the choroidal circulation is functionally end-arterial not only in physiologic conditions but also in pathologic conditions, and may explain the results from the present and previous studies 15, 25-27 without disparity.
One of the limitations of our study was that the large choroidal vasculature was not visualized directly using angiography or postmortem cast study. Occlusion of the large vessels may have affected the perfusion of the choriocapillaris. In addition, the arteriolar structures in the suggested model were based on the interpretations of the studies for the choriocapillaris. Our model should be verified in future studies, as understanding the choroidal circulation is essential in the investigation of its role in both physiologic and pathologic conditions.
In summary, our results suggest that the findings of the postmortem study directly correspond with the angiographic findings and that the discrepancy was a misunderstanding. The choroid is composed of multiple sectors, each having anastomotic arterioles within the sector. Blood flows through the continuous choriocapillaris bed in an end-arterial nature functionally to follow a pressure gradient, as efficient drainage through the collecter venules prevents flow from crossing the boundary among the choroidal lobules. These structures of the choroid substantiate its vulnerability to ischemic damages in spite of existing anastomosis.
Scientific RepoRts | 7: 2490 | DOI:10.1038/s41598-017-02695-z Methods Fat embolism model. FA was acquired in the previous experiment of fat embolism using a triolein emulsion to assess the blood-ocular barrier breakdown 19 . The study design was approved by Institutional Animal Care and Use Committee (IACUC) at Pusan National University Hospital (2012-038), and the procedures were performed in adherence to the Institutional Guidelines.
In brief, 12 adult cats weighing 2.5-3.7 kg were anesthetized with intramuscularly administered ketamine HCl (2.5 mg/kg; Korea United Pharm, Seoul, South Korea) and xylazine (0.125 mg/kg; Bayer Korea, Seoul, South Korea) and ventilated with room air. Their body temperature was monitored with a rectal probe (MGA-III219; Shibaura Electronics, Tokyo, Japan) and maintained at 35-36 °C. The right femoral artery was isolated under anesthesia. A 3.0-F microcatheter (MicroFerret-18 infusion catheter; William Cook Europe, Bjaeverskov, Denmark) was passed through an 18-gauge catheter inserted into the femoral artery. The tip of the microcatheter was positioned in the internal carotid artery under digital subtraction angiography. The triolein emulsion was prepared by mixing neutral triglyceride triolein (1,2,3-tri[cis-9-octadecenoyl] glycerol; Sigma, St. Louis, MO, USA) and normal saline with vigorous to-and-fro movements. The emulsified triolein (2.2%, 10 mL) was infused into the internal carotid artery at a rate of 4 mL/min. Fluorescein dye (0.3 mg/kg) was injected through the femoral vein immediately after the infusion of the triolein emulsion. Video FA was recorded in the ipsilateral eye at variable frame rate up to 16 Hz for approximately 30 seconds after the injection of fluorescein using a scanning laser ophthalmoscope (HRA2; Heidelberg Engineering, Heidelberg, Germany). FA photographs were obtained in both eyes at a rate of one frame per 2-3 seconds for 1 minute and then every 5 minutes for up to 30 minutes.
The locations of the terminal arterioles were marked based on the perfusion pattern observed in video FA. A terminal arteriole was identified to be located at where centrifugal filling and wash-out of fluorescein dye began. In some of non-perfused lobules, the center of the lobule was presumed based on the filling pattern of the surrounding lobules. Each location was overlapped in FA images, and was marked as a red dot in the perfused lobule and as a red circle in the non-perfused.
Electric circuit model. The choriocapillaris was simulated as a schematic electric circuit using the custom software to interpret the angiographic findings. Blood flow was modeled as electric current (I), intravascular pressure as voltage (V), and vascular resistance as electric resistance(R) 21 .
The custom software was developed with Microsoft Visual Studio 2012 and C# language with. NET Framework (Microsoft, Redmond, WA, USA). To analyze the complicated electric circuit, we used Kirchhoff 's current law, which is the basis of most modern circuit analyzer software. Kirchhoff 's current law states that the total sum of in-and out-current is always zero at every point where there is a confluence of electric currents.
For example (Fig. 6a), at point r, the sum of currents is zero. Because current (I) is equal to voltage (V)/resistance (R), the currents at node r can be written as equation (1).
In the same way, we can get more linear equations at any confluence points as many as unknown variables. These equations can be simplified for Vp = 0 and Vq = 10:  These linear equations make a matrix which composed of unknown voltage column and constants column: Once after the equation matrix is completed, Gaussian elimination method can be used to get the inverse of the equation matrix. The product of the inverse matrix and constant column vector gives the solution vector of voltages.
The structures of the choriocapillaris bed were taken from corrosion cast study literature 7,25 . A dual-layered hexagon with an internal grid composed of triangles was designed for the choriocapillaris lobule (Fig. 6). Each line of the grid has a resistance of 16 Ω, representing the capillary, and the boundary of the hexagon has a resistance of 1 to 16 Ω, representing the collector venule. The lumen of the vessels in the choriocapillaris plane measured 8-15 μm in the cats' eyes 9 . The resistance was calculated based on the estimation that the diameter of the collector venule is between 1 × and 2 × that of the capillary; flow resistance is inversely proportional to the fourth power of the radius (r 4 ) by Poiseuille's equation. An anode representing the terminal arteriole was placed at the center of the hexagon, and cathodes representing the draining venules were connected at every other corner of the hexagon. The voltage was set as 51 V at the anode and 23 V at the cathodes to correspond with the intravascular pressure of the choroidal arteriole and venule in mmHg (equivalent to 69 and 31 cm H 2 O) 28 . A total 25 or 5 × 5 hexagons were arrayed to represent the choriocapillaris bed (Fig. 6c).
The flow of each vascular channel was calculated as an electric current, and the direction and amount were demonstrated by an arrow and its thickness, respectively. The average current in each hexagon was also calculated. Changes in electric currents were analyzed when changing the resistance of the hexagon boundary representing the collector venule. In this model, removing the anode connected to the center of one hexagon can simulate the occlusion of a single feeding arteriole (Fig. 6d), and multiple removals can simulate the occlusion of a PCA (Fig. 6e). Although the electric circuit model cannot calculate the actual flow in the choriocapillaris, the relative changes can be estimated compared with normal circulation.