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1.3 Vascular Anatomy

17

Bernoulli’s Principle and Deductions Concerning Changes in Central Retinal Vein Diameter at the Lamina Cribrosa

BernoulliÕs principle is a statement of conservation of energy applied to hydraulic systems of steady ßow, no friction, and an incompressible ßuid. It states that the sum of thermal (Et), kinetic (Ek), and gravitational energy (Eg) of a ßuid in a closed system of pipes is a constant. That is

Et + Ek + Eg = K.

(1.1)

In the eye, there is no change in gravitational energy of the blood as it circulates, thus the formula is

 

Et

+ Ek

= K.

(1.2)

 

 

Et = PH,

(1.3)

where P = intravenous pressure, and H = volume of the blood.

 

E

k

=

(

)

MV 2 ,

(1.4)

 

1/2

where M = mass of the blood and V = velocity of the blood.

 

Dividing Eq. 1.2 by volume gives

 

 

 

 

 

 

P + ρV 2 /2 = K,

(1.5)

where r = density of the blood.

The reader should note that there is a published error in the literature on this topic. It is stated erroneously that BernoulliÕs principle is Òpressure × (kinetic energy/volume) = constant.Ó87

The energy of the blood in the prelaminar CRV equals the energy of the blood in the postlaminar CRV, thus

Pprelaminar + ρVprelaminar2 /2 = Ppostlaminar + ρVpostlaminar2 /2. (1.6)

We know from measurements that Pprelaminar > Ppostlaminar. Therefore, it follows from (1.6) that

ρVprelaminar

2 /2 < ρVpostlaminar

2 /2.

(1.7)

Canceling the common constants and taking the square root of both sides yield

 

Vprelaminar < Vpostlaminar

 

(1.8)

We also know that the prelaminar blood ßow (Q1) must equal the postlaminar blood ßow (Q2),

Qprelaminar = Qpostlaminar or

 

(1.9)

AprelaminarVprelaminar = ApostlaminarVpostlaminar .

 

(1.10)

But

 

 

 

Aprelaminar = π Dprelaminar

2 /4 and Apostlaminar = π Dpostlaminar

2 /4,

(1.11)

18 1 Anatomy and Pathologic Anatomy of Retinal Vein Occlusions

where Dprelaminar = prelaminar CRV

diameter and

Dpostlaminar = postlaminar

CRV diameter.

Substituting (1.11) into (1.10) and canceling the common constants yields

 

D2

V

= D2

V

(1.12)

prelaminar

prelaminar

postlaminar postlaminar

 

Therefore, if (1.8) is true, then it follows that Dprelaminar > Dpostlaminar, which is consonant with pathologic and Doppler ultrasonic evidence.

Higher order retinal branch veins

Major (first order) retinal branch veins

 

Hemicentral retinal vein

Terminal

Central retinal vein

venules

 

Fig. 1.17 Terminology used for retinal veins. The central retinal vein is the sole vein that drains venous blood from the retina. Hemicentral retinal veins usually join in the optic disc cup to form the central vein but join deeper within the optic nerve in 20% of persons. Major branch veins, or Þrst-order branch veins, represent the Þrst four

branches of the central retinal vein or the Þrst bifurcations of the hemicentral retinal veins. Higher-order branch retinal veins are subsequent branchings of the major branch retinal veins. Terminal venules are the smallest visible veins into which capillaries converge to drain (Redrawn from Beaumont and Kang78)

primary open-angle glaucoma with CRVO as opposed to the less reproducibly observed association with BRVO, where this mechanism would not apply.78,92

The wall of the central retinal vein consists of a layer of endothelial cells, subendothelial connective tissue, a medium consisting mostly of elastic Þbers, a few smooth muscle cells, and a thin connective tissue adventitia. It is separated from the surrounding neural tissue by Muller cell and astrocyte processes.

Small collaterals connect the central retinal vein to the choroidal venous circulation, but they are hemodynamically unimportant unless an abnormal rise in retrolaminar central venous pressure develops. Behind the lamina cribrosa, there is an intraneural portion of the central retinal vein. Over this segment, the central retinal vein is subjected to the cerebrospinal ßuid pressure as it is surrounded by the subarachnoid space that bathes the optic nerve. Once the central retinal vein leaves the optic nerve, it primarily drains into the ophthalmic vein, although there are anastomoses with the angular

vein (Fig. 1.18). Within the orbit, these veins are subjected to the orbital tissue pressure, which is normally low, but can rise in situations of thyroid orbitopathy, orbital tumors, and orbital hematomas. The angular vein drains to the facial vein and thence to the superior vena cava by larger connecting veins. Blood from both the central retinal vein and the vortex veins drains into the superior ophthalmic vein which in turn empties into the cavernous sinus and thence to the superior vena cava. Cavernous sinus thrombosis can lead to secondary CRVO.36,93

Certain normal relationships of retinal arteries and veins are observed. The normal ratio of diameter of Þrst-order retinal veins to Þrst-order retinal arteries in vivo is 1.3.10 First-order retinal arterioles have diameter 115±8 m compared to 146±16 m for Þrstorder retinal veins.10 At the site of an arteriovenous crossing, there is thinning of the ganglion cell, inner, and outer nuclear layers (p. 28).94 In the more common instance of the artery crossing over the vein, the artery is located just beneath the internal limiting membrane, and the vein dips down to the level of the external limiting membrane (Fig. 1.19).94

1.3 Vascular Anatomy

19

Fig. 1.18 Diagram of the venous drainage from the eye

Superior lateral vortex vein

Central retinal vein

Cavernous sinus

Superior medial vortex vein

Superior opthalmic vein

Fig. 1.19 Histologic section from the postmortem retina of a person with a clinically normal fundus. The retinal artery traveling across the page (blue arrow) crosses above the retinal vein pointed out of the page (green arrow). The artery and the vein share a wall (orange arrow) that is narrower at the point of crossing than the wall of the artery adjacent to the crossing. The inner

nuclear layer is lost at the location of the vein, and the outer nuclear layer (double headed yellow arrow) is thinner than at locations without the presence of the vein. The vein dips to the level of the external limiting membrane. The turquoise arrow denotes the retinal pigment epithelium. The red arrow denotes the internal limiting membrane (Reproduced from Seitz,94 [p. 26])

At points where larger branch retinal veins and arteries cross, the two vessels share a common adventitial sheath, and in some cases the media are shared, but this is lacking at smaller vessel crossings.95 At an arteriovenous crossing, the fused vessel wall can be as thin as 15 m at the point of contact which is thinner than the adjacent, nonshared arterial wall.94,96

The lumen of the vein at the point of crossing is narrowed to approximately 2/3 the diameter of the adjacent venous lumen (Fig. 1.19).94

In normal eyes, the artery lies in front of the vein in 54Ð71% of arteriovenous crossings (Fig. 1.20).50,97-100 In the arteriovenous crossings associated with BRVO, however, the artery lies in