Microvasculature of the mouse eye: Scanning electron microscopy of vascular corrosion casts

Purpose

For drug safety assessment, ophthalmic fundus examination is of diagnostic importance in experimental animals. Interim blood samples are usually collected from the orbital venous sinus in the mouse. This report characterizes the angioarchitecture of the mouse eye.

Methods

In 10 mice, the microvasculature of the eyes of was investigated using scanning electron micrographs of corrosion casts.

Results

The mouse eye was characterized as having a rich vasculature with many thick retinal arteries and a well-developed orbital venous sinus. The eye receives its primary blood supply from the external ophthalmic artery, which is divided into three branches: the central retinal artery, as well as the medial and lateral long posterior ciliary arteries. The central retinal artery is divided into 8-9 radiating retinal arteries. The mouse has an orbital venous sinus around the orbit rather than a well-developed orbital venous plexus in the retrobulbar space as is in the rat. The orbital venous sinus is formed by the episcleral veins, the ophthalmic vein, the superior palpebral vein, inferior palpebral vein and numerous anastomotic veins among these veins.

Conclusions

The mouse ocular vasculature is quite similar to that of rats. It is recommended that the best location for insertion of a capillary tube for collecting blood is in the lateral canthus around the eye where the sinus is larger and is most readily accessible. Functional significance of the vascular patterns of the eye is discussed.     

颈性眩晕中医证型与经颅超声脑动脉血流检测结果的相关性分析

摘要 目的：分析颈性眩晕中医证型与经颅超声脑动脉血流检测结果的相关性。方法：选取2021年5月-2023年5月收治颈性眩晕患者作为研究对象,根据不同中医证型分为痰湿中阻组、肝阳上亢组、肝肾阴虚组和气血亏虚组,每组各纳入20例;并另选取健康体检患者30例作为对照组,均给予多普勒超声检查。分析不同中医证型者与对照组者多普勒超声检查特征与脑动脉血流变化[左右椎动脉、基底动脉及大脑中动脉收缩期峰值血流速度（VS）、平均血流速度(Vm)、舒张期峰值血流速度(Vd)及搏动指数(PI)]。结果：痰湿中阻组、肝肾阴虚组和气血亏虚组左右椎动脉、基底动脉及大脑中动脉VS均低于对照组（P＜0.05）;肝阳上亢组左右椎动脉、基底动脉及大脑中动脉VS均高于对照组（P＜0.05）;不同中医证型组间VS比较,肝阳上亢组＞痰湿中阻组＞肝肾阴虚组＞气血亏虚组;痰湿中阻组左右椎动脉、基底动脉均高于对照组（P＜0.05）,大脑中动脉Vm均低于对照组（P＜0.05）;肝阳上亢组左右椎动脉、基底动脉及大脑中动脉Vm均高于对照组（P＜0.05）;肝肾阴虚组左右椎动脉、基底动脉及大脑中动脉Vm均低于对照组（P＜0.05）;气血亏虚组大脑中动脉Vm均低于对照组（P＜0.05）,左右椎动脉、基底动脉Vm和对照组无显著性差异（P>0.05）;不同中医证型组间Vm比较,肝阳上亢组＞痰湿中阻组＞气血亏虚组＞肝肾阴虚组;痰湿中阻组左右椎动脉、基底动脉Vd均低于对照组（P＜0.05）,大脑中动脉Vd均高于对照组（P＜0.05）;肝阳上亢组左右椎动脉、基底动脉及大脑中动脉Vd均低于对照组（P＜0.05）;肝肾阴虚组左右椎动脉及大脑中动脉Vd均低于对照组（P＜0.05）,基底动脉Vd和对照组无差异（P＞0.05）;气血亏虚组左右椎动脉Vd均低于对照组（P＜0.05）,基底动脉Vd和对照组无差异（P＞0.05）,大脑中动脉Vd均高于对照组（P＜0.05）;不同中医证型组间Vd比较,气血亏虚组＞痰湿中阻组＞肝肾阴虚组＞肝阳上亢组;痰湿中阻组和气血亏虚组左右椎动脉、基底动脉及大脑中动脉PI均低于对照组（P＜0.05）;肝阳上亢组和肝肾阴虚组左右椎动脉、基底动脉及大脑中动脉PI均高于对照组（P＜0.05）;不同中医证型组间PI比较,肝阳上亢组＞肝肾阴虚组＞痰湿中阻组＞气血亏虚组。结论：不同中医证型的眩晕患者会出现不同程度脑动脉血流动力学异常,且不同组间存在差异,通过经颅多普勒超声检查,可以对眩晕中医证型提供参考价值。     

Microvasculature of the avian eye: studies on the eye of the duckling with microcorrosion casting, scanning electron microscopy, and stereology

The microvasculature of the eye of the duckling was studied with microcorrosion casting, scanning electron microscopy, and stereology. Most blood to the eyeball first passes through the arterial ophthalmic rete mirabile, a complex of small arteries which intermixes with a similar complex of veins (venous ophthalmic rete mirabile) at the ventrotemporal angle of the eye. The present study reveals the ultrastructural anatomy and the compact, three-dimensional arrangement of vessels in this rete, which had been shown by previous investigators to function as a countercurrent heat exchanger. Vessels from this rete include the supraorbital and infraorbital arteries, which supply the eyeball anteriorly, and the ophthalmotemporal artery, which supplies the eyeball posteriorly. The internal ophthalmic and ethmoidal arteries, branches of the cerebral carotid artery, anastomose with the ophthalmotemporal artery posteriorly. Blood is distributed to the eyeball anteriorly by two ring arteries: the iridial ring artery, which circumscribes the iris and which receives blood from the long ciliary and infraorbital arteries; and the more peripheral, ciliary ring artery, which receives blood mostly from the infraorbital and ethmoidal arteries. Within the iris is a dense, freely anastomosing bed of capillaries which extends to the edge of the pupil and then loops back beneath the ciliary body. The vasculature of the ciliary body consists of radially arranged plates of anastomosing capillaries of irregular bore which mimic the contours of that organ, but permit changes in pupil diameter. The present study demonstrates the three-dimensional anatomy of the very dense capillary net of the choriocapillaris deep to the retina and the capillary mass of the pecten, and thus supports the finding of earlier investigators that nutrients diffusing from these structures nourish the avascular retina. The pecten consists of a pleated sheet of freely anastomosing capillaries which protrudes into the vitreous body from near the optic nerve. The choriocapillaris and the pecten are supplied by branches of the ophthalmotemporal artery: the former by numerous short posterior ciliary arteries, the latter by two or three arteries which further divide into one or two smaller vessels for each of its folds. Veins of the choroid layer at the periphery of the anterior surface of the eyeball, and to some extent on its lateral walls, are revealed by the corrosion-casting technique as unusual, flattened vessels of large caliber which lie in closely spaced parallel arrays. The large surface area thus created may function in heat dissipation.(ABSTRACT TRUNCATED AT 400 WORDS)     

Behavior of fibrinogen in diabetic patients in comparison with objective vascular measurements in the ocular fundus

Objective measurements of vessels were performed in vivo in 10 patients affected with diabetes mellitus, the fibrinogen concentrations in the venous blood being determined simultaneously. Whereas the ensured correlations with fibrinogen concentration could be recognized from the diameter of arteries and veins and from the flow velocity, a linear correlation could be found to exist between the fibrinogen level and the volume flowing through a retinal artery. These findings prove that the very existence of a hyperfibrinogen anemia does not justify the assumption of the blood volume flow being decreased. In patients with diabetes mellitus the enhanced volume flowing through retinal arteries is rather connected with an increased fibrinogen level.     

Adrenergic innervation of the large arteries and veins of the semiarboreal rat snake Elaphe obsoleta

Fluorescence histochemistry was used to study the adrenergic innervation of the large arteries and veins at six points along the body of the semiarboreal rat snake Elaphe obsoleta. Apart from the vessels adjacent to the heart, there was a marked contrast in the density of adrenergic innervation of anterior and posterior systemic arteries and veins. The anterior arteries and veins have little adrenergic innervation in contrast to the extremely dense innervation of the arteries and veins posterior to the heart. The innervation pattern is consistent with known physiological adjustments to gravity and suggests a mechanism for regulating dependent blood flow via sympathetic nerves. In comparison to the posterior systemic arteries, parallel segments of pulmonary artery taken from the same body position of Elaphe contained a much sparser innervation by adrenergic nerves. The sparser innervation can be correlated with less gravitational disturbance in the pulmonary artery, which is relatively short in this and in other arboreal snakes.     

Gender differences in myogenic regulation along the vascular tree of the gerbil cochlea

Regulation of cochlear blood flow is critical for hearing due to its exquisite sensitivity to ischemia and oxidative stress. Many forms of hearing loss such as sensorineural hearing loss and presbyacusis may involve or be aggravated by blood flow disorders. Animal experiments and clinical outcomes further suggest that there is a gender preference in hearing loss, with males being more susceptible. Autoregulation of cochlear blood flow has been demonstrated in some animal models in vivo, suggesting that similar to the brain, blood vessels supplying the cochlea have the ability to control flow within normal limits, despite variations in systemic blood pressure. Here, we investigated myogenic regulation in the cochlear blood supply of the Mongolian gerbil, a widely used animal model in hearing research. The cochlear blood supply originates at the basilar artery, followed by the anterior inferior cerebellar artery, and inside the inner ear, by the spiral modiolar artery and the radiating arterioles that supply the capillary beds of the spiral ligament and stria vascularis. Arteries from male and female gerbils were isolated and pressurized using a concentric pipette system. Diameter changes in response to increasing luminal pressures were recorded by laser scanning microscopy. Our results show that cochlear vessels from male and female gerbils exhibit myogenic regulation but with important differences. Whereas in male gerbils, both spiral modiolar arteries and radiating arterioles exhibited pressure-dependent tone, in females, only radiating arterioles had this property. Male spiral modiolar arteries responded more to L-NNA than female spiral modiolar arteries, suggesting that NO-dependent mechanisms play a bigger role in the myogenic regulation of male than female gerbil cochlear vessels.     

A mathematical model of the flow in the circle of Willis

A mathematical model of the flow in the circle of Willis has been designed and the effects of (a) the large anatomical variation of the communicating arteries and (b) physiological changes of the resistances of the vertebral arteries have been studied. The influence of the posterior perforating arteries on the flow in the posterior communicating arteries has been investigated as well, with special attention being paid to the possible occurrence of a 'dead point'. In the model, the influence of diameters of the communicating arteries on the flow in the afferent vessels and the segments of the circle turns out to be considerable, especially in the range of the anatomical variation of the diameters. Within this range flow reductions due to an increased resistance of the vertebral artery will be compensated for by the system. Assuming that the values and ratios of the peripheral resistances are within the physiological range, a dead point is not to be expected in the flow in the posterior communicating arteries.     

Cerebral perfusion changes in patients with internal carotid artery stenoses after surgical revascularization

Changes of cerebral perfusion and the condition of collateral blood supply in patients with internal carotid artery stenoses may have a prognostic value for effective blood flow restoration after revascularization of the internal carotid arteries (ICAs). To determine the patterns of cerebral perfusion changes in patients with ICA stenoses before and after surgical treatment, a clinical CT perfusion study of 41 patients with moderate to severe ICA stenoses was performed. Perfusion CT (PCT) had been conducted in 17 patients with moderate ICA stenoses (50–69%) and in 24 patients with severe ICA stenoses (70–99%) 3 times: before intervention (balloon angioplasty with stenting or carotid endarterectomy), on the 3rd to 7th day, and within 1 to 3 months after surgery. Scanning was performed at the level of the basal ganglia and semioval centers. In patients without ICA stenosis (control group of 39 individuals), PCT was conducted once. We found that surgical recanalization of the ICA leads to normalization of the cerebral blood flow parameters in the perfusion area of the middle cranial artery, as evidenced by a decrease of MTT and CBV and an increase of CBF to values comparable to those in the control group. However, blood flow restoration in the anterior and posterior watershed areas, which are known to be mostly affected under chronic hypoperfusion conditions, was observed only in patients with a complete circle of Willis (CW) and moderate ICA stenosis. Therefore, severe stenosis (>70%) and the incomplete CW are the prognostic factors for inadequate blood flow restoration after revascularization in patients with ICA stenoses.     

Poland syndrome associated with an aberrant subclavian artery and vascular abnormalities of the retina in a child exposed to misoprostol during pregnancy

BACKGROUND: Poland syndrome has been attributed to a process of vascular disruption, and exposure to misoprostol at 6-8 weeks of gestation has been shown to produce defects attributed to vascular disruption. Herein we report the first case of a patient with Poland syndrome associated with an aberrant subclavian artery and vascular abnormalities of the retina, whose mother used misoprostol during pregnancy. CASE: A White boy of 1 year and 7 months of age, whose mother used misoprostol during the second month of pregnancy, presented with bilateral epicanthal folds, aplasia of the sternocostal head of the pectoralis major muscle with a hypoplastic nipple on the right side, and asymmetry between the upper limbs. The results of an angiotomographic study showed the presence of an aberrant right subclavian artery. Ultrasonographic evaluation showed turbulence and a high peak in the diastolic velocity in both carotid arteries, suggesting stenosis. Ophthalmologic assessment disclosed an intense bilateral tortuosity of the retinal blood vessels, with arterialnarrowing and rarefaction of the retinal pigment epithelium. CONCLUSIONS: This case suggests that the mechanism of vascular disruption of misoprostol could be related to the aberrant subclavian artery and the observed Poland syndrome. His retinal findings are different from those in cases described thus far in the literature, and this pattern of anomaly has never been associated with a gestational exposure to misoprostol. The possibility of a relationship of the aberrant right subclavian artery and the pattern of blood flow verified in the carotid arteries with the eye fundus abnormalities could be causally related or simply coincidental.     

Hemodynamic analysis of Hyrtl anastomosis in human placenta

The Hyrtl anastomosis is a common connection between the umbilical arteries near the cord insertion in most human placentas. It has been speculated that it equalizes the blood pressure between the territories supplied by the umbilical arteries. However, its functional role in the regulation and distribution of fetal blood flow to the placenta has not yet been explored. A computational model has been developed for quantitative analysis of hemodynamic characteristic of the Hyrtl anastomosis in cases of discordant blood flow in the umbilical arteries. Simulations were performed for cases of either increased placental resistance at the downstream end or reduced arterial blood flow due to some pathologies upstream of one of the arteries. The results indicate that when placental territories of one artery impose increased resistance to fetal blood flow, the Hyrtl anastomosis redistributes the blood flow into the second artery to reduce the large pressure gradients that are developed in the affected artery. When one of the arteries conducts a smaller blood flow into the placenta and a relatively smaller pressure gradient is developed, the Hyrtl anastomosis rebuilds the pressure gradients in the affected artery and redistributes blood flow from the unaffected artery to the affected one to improve placental perfusion. In conclusion, the Hyrtl anastomosis plays the role of either a safety valve or a pressure stabilizer between the umbilical arteries at the placental insertion.     

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase transient non-Newtonian three-dimensional (3-D) computational fluid dynamics (CFD) simulation has been performed for pulsatile hemodynamics in an idealized curved section of a human coronary artery. We present the first prediction, to the authors' knowledge, of particulate buildup on the inside curvature using the multiphase theory of dense suspension hemodynamics. In this study, the particulates are red blood cells (RBCs). The location of RBC buildup on the inside curvature correlates with lower wall shear stress (WSS) relative to the outside curvature. These predictions provide insight into how blood-borne particulates interact with artery walls and hence, have relevance for understanding atherogenesis since clinical observations show that atherosclerotic plaques generally form on the inside curvatures of arteries. The buildup of RBCs on the inside curvature is driven by the secondary flow and higher residence times. The higher viscosity in the central portion of the curved vessel tends to block their flow, causing them to migrate preferentially through the boundary layer. The reason for this is the nearly neutrally buoyant nature of the dense two-phase hemodynamic flow. The two-phase non-Newtonian viscosity model predicts greater shear thinning than the single-phase non-Newtonian model. Consequently, the secondary flow induced in the curvature is weaker. The waveforms for computed hemodynamic parameters, such as hematocrit, WSS, and viscosity, follow the prescribed inlet velocity waveforms. The lower oscillatory WSS produced on the inside curvature has implications for understanding thickening of the intimal layer.     

Circulatory effects of VIP in anesthetized man

VIP was given intravenously over 1 min at the doses 0.1 and 0.2 micrograms X kg X min-1 to twenty-one anesthetized patients undergoing abdominal surgery. Intra-arterial blood pressure was monitored and various blood flows were measured simultaneously by electromagnetic technique. Following VIP, intra-arterial blood pressure was decreased. The blood flows were increased in the gastroduodenal-, and the left gastric arteries. The flow in the hepatic artery proper was increased only following the 0.2 micrograms dose. The flow in the superior mesenteric artery varied considerably inter-individually. In branches supplying only the small intestine, it seemed to be unaffected. The flow in the splenic artery was decreased in normal-sized spleens, but unaffected in enlarged spleens. The flow in the external iliac artery initially decreased and thereafter increased. Changes in vascular resistances showed that VIP acted as a vasodilator in the splanchnic region except in the superior mesenteric vasculature, where it was ineffective. In normal spleens it was a vasoconstrictor. In the external iliac artery, an initial insignificant vasoconstriction was followed by vasodilation. It seemed that VIP acts directly on the vessels and has a specific pattern of vasoactivity of probable physiological significance.     

改良眼底激光光凝合康柏西普治疗增殖性糖尿病视网膜病变的效果及对视力水平、黄斑区血流密度的影响

摘要 目的：探究改良眼底激光光凝联合康柏西普治疗增殖性糖尿病视网膜病变（PDR）的效果及对视力水平、黄斑区血流密度的影响。方法：回顾性分析2019.06-2022.06于我院接受改良眼底激光光凝治疗的62例（124眼）PDR患者临床资料,纳入对照组,回顾性分析同期于我院接受改良眼底激光光凝联合康柏西普治疗的62例（124眼）PDR患者临床资料,纳入试验组。比较治疗前和治疗后3个月两组患者视力水平[最佳矫正视力（BCVA）、视野指数（VFI）、视野平均缺损（MD）]、视网膜中央动脉血流动力学[峰值血流速度（PSV）、平均血流速度（MV）、搏动指数（PI）、阻力指数（RI）]、黄斑区血流密度[浅层毛细血管丛（SCP）、深层毛细血管丛（DCP）]、生活质量[低视力者生存质量量表（CLVQOL）]差异,记录3个月内两组患者并发症（黄斑水肿、高眼压、视网膜出血）发生情况。结果：治疗后3个月,两组患者BCVA、PSV、MV、SCP、DCP、CLVQOL较治疗前升高,试验组高于对照组（P均<0.05）;而VFI、MD、PI、RI水平降低,试验组低于对照组（P均<0.05）;两组患者术后并发症无显著性差异（P>0.05）。结论：改良眼底激光光凝治疗联合康柏西普治疗可增强PDR患者视力功能,改善患者视网膜中央动脉血流动力学及黄斑区血流密度,提高生活质量。     

The variability of the circle of Willis: univariate and bivariate analysis

The results are presented of a statistical analysis of the variability of the circle of Willis using univariate and bivariate methods. For this purpose 100 circles of Willis were available. From each circle 19 indexes of arterial size were determined, the basilar artery was measured in two places. Half the circumference was measured. This data yielded no evidence of differences between left- and right-sided vessels in the sample. An important source of variation is the general size of all vessels considered. When the data are cleared from this general size variation, correlation coefficients reveal interesting relations between the vessels. The posterior communicating arteries are strongly related to the ipsilateral carotid artery, whereas a strong inverse relationship exists with the basilar artery and the precommunicating part of the ipsilateral posterior cerebral artery. These relationships can be understood from the expected patterns of the blood flow in these vessels. Similar relationships can be found in the anterior part of the circle of Willis and in the vertebro-basilar junction. In a different manner, based on previous haemodynamic studies, the relation between blood flow and vessel size within the circle of Willis can be demonstrated by relating the ratios of the sizes of afferent and efferent arteries to the sizes of the posterior communicating arteries, an "intuitive" model. The supposed correlations of the outcome of this "intuitive" model with the size of the communicating arteries appeared to by highly significant. It is concluded that the variations of the circle of Willis are related to the individual variations of the blood flow in this arterial network.     

Blood flow velocity--a constantly acting factor in dilatation of the large arteries

Acute experiments on cats have demonstrated the presence of renal artery sensitivity to the bloodstream velocity; the artery is enlarged with the blood flow increase and is narrowed with its decrease. The dilatation of the artery caused by the double increase of the blood flow (from 20 to 40 ml/min) is 23 +/- 8%. It has been established experimentally that carotid, femoral and renal arteries of cats respond to minor changes (of the order of 1 ml/min) in the volumetric velocity of the bloodstream by changing their diameters. Therefore, the arteries continuously follow the bloodstream velocity changes by changing their diameters. It may thus be concluded that the bloodstream itself is the artery dilatation factor.     

Functional Organization of the Teleost Gill

The circulation of the gills has been studied in the perch, trout and eel combining the conventional histological methods and casting techniques. The existence of two blood pathways in each gill arch was confirmed. 1 — An arterio-arterial pathway assuming the respiratory function. It includes the afferent branchial artery and in each primary lamella the afferent primary artery, the secondary lamellae capillaries and the primary and branchial efferent arteries. 2 — An arterio-venous pathway arising from both the branchial artery, in the gill arch, and the primary arteries in each primary lamella. This pathway includes the central venous sinus of the primary lamella, several small veins and is finally connected with the branchial veins. 3 — The lack of connections between afferent primary arteries and cvs in the trout and the perch makes impossible a direct blood flow from the afferent to the efferent artery (shunt). In the eel connections between cvs and both afferent and efferent arteries do not mean that a shunt is operating according to the pressure gradient.     

Increased Arterial Diameters in the Posterior Cerebral Circulation in Men with Fabry Disease

A high load of white matter lesions and enlarged basilar arteries have been shown in selected patients with Fabry disease, a disorder associated with an increased stroke risk. We studied a large cohort of patients with Fabry disease to differentially investigate white matter lesion load and cerebral artery diameters. We retrospectively analyzed cranial magnetic resonance imaging scans of 87 consecutive Fabry patients, 20 patients with ischemic stroke, and 36 controls. We determined the white matter lesion load applying the Fazekas score on fluid-attenuated inversion recovery sequences and measured the diameters of cerebral arteries on 3D-reconstructions of the time-of-flight-MR-angiography scans. Data of different Fabry patient subgroups (males – females; normal – impaired renal function) were compared with data of patients with stroke and controls. A history of stroke or transient ischemic attacks was present in 4/30 males (13%) and 5/57 (9%) females with Fabry disease, all in the anterior circulation. Only one man with Fabry disease showed confluent cerebral white matter lesions in the Fazekas score assessment (1%). Male Fabry patients had a larger basilar artery (p<0.01) and posterior cerebral artery diameter (p<0.05) compared to male controls. This was independent of disease severity as measured by renal function and did not lead to changes in arterial blood flow properties. A basilar artery diameter of >3.2 mm distinguished between men with Fabry disease and controls (sensitivity: 87%, specificity: 86%, p<0.001), but not from stroke patients. Enlarged arterial diameters of the posterior circulation are present only in men with Fabry disease independent of disease severity.     

Mathematical models of the flow in the basilar artery

The flow in the basilar artery arises from the merging of the flows from the two vertebral arteries. This study deals with the question whether a parabolic (Poiseuille) profile will have been established before the basilar artery divides into both posterior cerebral arteries. The inlet length (that is, the downstream distance needed for the flow to become approximately equal to the limiting Poiseuille flow) and velocity profiles have been computed from two- and three-dimensional mathematical models in which flow pulsatility and vessel wall distensibility have been neglected and the complex geometry of the junction has been taken into account in a simplified form. The results show that the flow at the end of the basilar artery is far from being parabolic and that an asymmetry in the entrance flow will be carried along towards the end of the basilar artery, thus affecting flows in the circle of Willis.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.     

A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length [L(r) = 7.4r ^1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.